Finite Group Databasebeta

← D17×#2461 #17202175

Subgroups — D17×#2461 #17202175

Order 4352.

3786 conjugacy classes of subgroups.

The subgroup lattice has 1908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D17C211yesmaximal, characteristic, complemented
2C2×#123×D17C211yesmaximal, characteristic, complemented
3C2×C22⋊Q8×D17C211yesmaximal, characteristic, complemented
4C2×C4×D4×D17C211yesmaximal, characteristic, complemented
5#14532758C211yesmaximal, characteristic, complemented
6#14532757C211yesmaximal, characteristic, complemented
7#14532756C211yesmaximal, characteristic, complemented
8#14532755C211yesmaximal, characteristic, complemented
9#14532754C211yesmaximal, characteristic, complemented
10#14532753C211yesmaximal, characteristic, complemented
11#14532752C211yesmaximal, characteristic, complemented
12#14532751C211yesmaximal, characteristic, complemented
13#14532750C211yesmaximal, characteristic, complemented
14#14532749C211yesmaximal, characteristic, complemented
15#14532748C211yesmaximal, characteristic, complemented
16#14532747C211yesmaximal, characteristic, complemented
17#14532746C211yesmaximal, characteristic, complemented
18#14532745C211yesmaximal, characteristic, complemented
19#14532744C211yesmaximal, characteristic, complemented
20D17×#396C211yesmaximal, characteristic, complemented
21D17×#395C211yesmaximal, characteristic, complemented
22D17×#394C211yesmaximal, characteristic, complemented
23D17×#392C211yesmaximal, characteristic
24D17×#390C211yesmaximal, characteristic, complemented
25D17×#388C211yesmaximal, characteristic, complemented
26D17×#388C211yesmaximal, characteristic, complemented
27D17×#388C211yesmaximal, characteristic, complemented
28D17×#386C211yesmaximal, characteristic, complemented
29D17×#385C211yesmaximal, characteristic, complemented
30C4×C4⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2461C211yesmaximal, characteristic, complemented
32C22×Q8×D17C2211yescharacteristic
33C22×D4×D17C2211yescharacteristic
34C22×D4×D17C2211yescharacteristic
35C22×D4×D17C2211yescharacteristic
36C23×C4×D17C2211yescharacteristic
37C23×C4×D17C2211yescharacteristic
38C2×#10587633C2211yescharacteristic, complemented
39C2×#10587561C2211yescharacteristic, complemented
40C2×#10587622C2211yescharacteristic, complemented
41C2×#10587571C2211yescharacteristic, complemented
42C2×#10587571C2211yescharacteristic, complemented
43C2×#10587571C2211yescharacteristic, complemented
44C2×#10587571C2211yescharacteristic, complemented
45#124×D17—28no—
46C2×#10587580C2211yescharacteristic, complemented
47C2×#10587580C2211yescharacteristic, complemented
48C2×#10587572C2211yescharacteristic, complemented
49C2×#10587615C2211yescharacteristic, complemented
50C2×#10587569C2211yescharacteristic, complemented
51C2×#10587569C2211yescharacteristic, complemented
52C2×#10587621C2211yescharacteristic, complemented
53#123×D17—28no—
54C2×#10587583C2211yescharacteristic, complemented
55C2×#10587610C2211yescharacteristic, complemented
56C2×#10587582C2211yescharacteristic, complemented
57C2×#10587582C2211yescharacteristic, complemented
58C2×#10587564C2211yescharacteristic, complemented
59C2×#10587564C2211yescharacteristic, complemented
60C2×#10587632C2211yescharacteristic, complemented
61C22⋊Q8×D17—28no—
62C2×C4×D68C2211yescharacteristic, complemented
63C2×D4×Dic17C2211yescharacteristic, complemented
64C2×#10587579C2211yescharacteristic, complemented
65C2×C4×C22⋊D17C2211yescharacteristic, complemented
66C2×C4×C22⋊D17C2211yescharacteristic, complemented
67C2×#10587567C2211yescharacteristic, complemented
68C2×#10587567C2211yescharacteristic, complemented
69C4×D4×D17—28no—
70C2×C4⋊C4×D17C2211yescharacteristic
71C2×C4⋊C4×D17C2211yescharacteristic
72C2×C4⋊C4×D17C2211yescharacteristic
73C2×C4⋊C4×D17C2211yescharacteristic
74C2×C4⋊C4×D17C2211yescharacteristic
75C2×C4⋊C4×D17C2211yescharacteristic
76C2×C4⋊C4×D17C2211yescharacteristic
77C2×C22⋊C4×D17C2211yescharacteristic
78C2×C22⋊C4×D17C2211yescharacteristic
79C2×C22⋊C4×D17C2211yescharacteristic
80C2×C22⋊C4×D17C2211yescharacteristic
81C2×C22⋊C4×D17C2211yescharacteristic
82C2×C22⋊C4×D17C2211yescharacteristic
83C2×C22⋊C4×D17C2211yescharacteristic
84C2×C22⋊C4×D17C2211yescharacteristic
85C2×C22⋊C4×D17C2211yescharacteristic
86C2×C22⋊C4×D17C2211yescharacteristic
87C2×C22⋊C4×D17C2211yescharacteristic
88C2×C22⋊C4×D17C2211yescharacteristic
89C2×C22⋊C4×D17C2211yescharacteristic
90C2×C42×D17C2211yescharacteristic
91C2×C42×D17C2211yescharacteristic
92C2×C42×D17C2211yescharacteristic
93#11762733C2211yescharacteristic, complemented
94#11762732C2211yescharacteristic, complemented
95#11762732C2211yescharacteristic, complemented
96#11762732C2211yescharacteristic, complemented
97#11762731C2211yescharacteristic, complemented
98#11762731C2211yescharacteristic, complemented
99#11762731C2211yescharacteristic, complemented
100#11762730C2211yescharacteristic, complemented
101#11762730C2211yescharacteristic, complemented
102#11762730C2211yescharacteristic, complemented
103#11762729C2211yescharacteristic, complemented
104#11762729C2211yescharacteristic, complemented
105#11762729C2211yescharacteristic, complemented
106#11762728C2211yescharacteristic, complemented
107#11762727C2211yescharacteristic, complemented
108#11762726C2211yescharacteristic, complemented
109#11762725C2211yescharacteristic, complemented
110#11762725C2211yescharacteristic, complemented
111#11762724C2211yescharacteristic, complemented
112#11762724C2211yescharacteristic, complemented
113#11762723C2211yescharacteristic, complemented
114#11762719C2211yescharacteristic
115#11762718C2211yescharacteristic
116#11762718C2211yescharacteristic
117#11762718C2211yescharacteristic
118#11762717C2211yescharacteristic
119#11762717C2211yescharacteristic
120#11762717C2211yescharacteristic
121#11762712C2211yescharacteristic, complemented
122#11762711C2211yescharacteristic, complemented
123#11762710C2211yescharacteristic, complemented
124#11762709C2211yescharacteristic, complemented
125#11762709C2211yescharacteristic, complemented
126#11762709C2211yescharacteristic, complemented
127#11762709C2211yescharacteristic, complemented
128#11762703C2211yescharacteristic, complemented
129#11762703C2211yescharacteristic, complemented
130#11762703C2211yescharacteristic, complemented
131#11762702C2211yescharacteristic, complemented
132#11762702C2211yescharacteristic, complemented
133#11762702C2211yescharacteristic, complemented
134#11762701C2211yescharacteristic, complemented
135#11762701C2211yescharacteristic, complemented
136#11762701C2211yescharacteristic, complemented
137#11762700C2211yescharacteristic, complemented
138#11762700C2211yescharacteristic, complemented
139#11762700C2211yescharacteristic, complemented
140#11762699C2211yescharacteristic, complemented
141#11762699C2211yescharacteristic, complemented
142#11762699C2211yescharacteristic, complemented
143#11762698C2211yescharacteristic, complemented
144#11762698C2211yescharacteristic, complemented
145#11762698C2211yescharacteristic, complemented
146#11762697C2211yescharacteristic, complemented
147#11762697C2211yescharacteristic, complemented
148#11762697C2211yescharacteristic, complemented
149#11762689C2211yescharacteristic, complemented
150#11762688C2211yescharacteristic, complemented
151#11762687C2211yescharacteristic, complemented
152#11762687C2211yescharacteristic, complemented
153#11762686C2211yescharacteristic, complemented
154#11762685C2211yescharacteristic, complemented
155#11762685C2211yescharacteristic, complemented
156#11762684C2211yescharacteristic, complemented
157#11762683C2211yescharacteristic, complemented
158#11762683C2211yescharacteristic, complemented
159#11762682C2211yescharacteristic, complemented
160#11762681C2211yescharacteristic, complemented
161#11762680C2211yescharacteristic, complemented
162#11762680C2211yescharacteristic, complemented
163C4⋊C4×Dic17C2211yescharacteristic, complemented
164C4⋊C4×Dic17C2211yescharacteristic, complemented
165C4×#63225C2211yescharacteristic, complemented
166C4×#63225C2211yescharacteristic, complemented
167C4×C4⋊Dic17C2211yescharacteristic, complemented
168#11762660C2211yescharacteristic, complemented
169#11762660C2211yescharacteristic, complemented
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172#95×D17C2211yescharacteristic
173#95×D17C2211yescharacteristic
174#95×D17C2211yescharacteristic
175#95×D17C2211yescharacteristic
176C2×C17×#124C2211yescharacteristic, complemented
177C2×C17×#123C2211yescharacteristic, complemented
178C2×C17×C22⋊Q8C2211yescharacteristic, complemented
179C2×C4×D4×C17C2211yescharacteristic, complemented
180C17×#396C2211yescharacteristic, complemented
181C17×#395C2211yescharacteristic, complemented
182C17×#394C2211yescharacteristic, complemented
183C17×#392C2211yescharacteristic
184C17×#390C2211yescharacteristic, complemented
185C17×#388C2211yescharacteristic, complemented
186C17×#388C2211yescharacteristic, complemented
187C17×#388C2211yescharacteristic, complemented
188C17×#386C2211yescharacteristic, complemented
189C17×#385C2211yescharacteristic, complemented
190C4×C4⋊C4×C17C2211yescharacteristic, complemented
191C24×D17C2311yescharacteristic
192C24×D17C2311yescharacteristic
193C24×D17C2311yescharacteristic
194C22×Q8×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C2×Q8×D17—24no—
209C2×Q8×D17—24no—
210C2×Q8×D17—42no—
211C2×D4×D17—24no—
212C2×D4×D17—24no—
213C2×D4×D17—24no—
214C2×D4×D17—24no—
215C2×D4×D17—24no—
216C2×D4×D17—24no—
217C2×D4×D17—24no—
218C2×D4×D17—42no—
219C2×D4×D17—42no—
220C22×D68C2311yescharacteristic
221C22×D68C2311yescharacteristic
222C22×D68C2311yescharacteristic
223C22×C4×D17—24no—
224C22×C4×D17—24no—
225C22×C4×D17—24no—
226C22×C4×D17—24no—
227C22×C4×D17—42no—
228C22×C4×D17—42no—
229C22×C4×D17C2311yescharacteristic
230C22×C4×D17C2311yescharacteristic
231C22×C4×D17C2311yescharacteristic
232C22×C4×D17C2311yescharacteristic
233C22×C4×D17C2311yescharacteristic
234C22×C4×D17C2311yescharacteristic
235C22×C4×D17C2311yescharacteristic
236C22×C4×D17C2311yescharacteristic
237C22×C4×D17C2311yescharacteristic
238C22×C4×D17C2311yescharacteristic
239C22×C4×D17C2311yescharacteristic
240C22×C4×D17C2311yescharacteristic
241C22×C4×D17C2311yescharacteristic
242C22×C4×D17C2311yescharacteristic
243C22×C4×D17C2311yescharacteristic
244C22×C4×D17C2311yescharacteristic
245C22×Dic34C2311yescharacteristic
246C22×Dic34C2311yescharacteristic
247C22×Dic34C2311yescharacteristic
248C17×#124—24no—
249C17×#123—24no—
250C17×C22⋊Q8—24no—
251C4×D4×C17—24no—
252C2×C4⋊C4×C17C2311yescharacteristic
253C2×C4⋊C4×C17C2311yescharacteristic
254C2×C4⋊C4×C17C2311yescharacteristic
255C2×C4⋊C4×C17C2311yescharacteristic
256C2×C4⋊C4×C17C2311yescharacteristic
257C2×C4⋊C4×C17C2311yescharacteristic
258C2×C4⋊C4×C17C2311yescharacteristic
259C2×C22⋊C4×C17C2311yescharacteristic
260C2×C22⋊C4×C17C2311yescharacteristic
261C2×C22⋊C4×C17C2311yescharacteristic
262C2×C22⋊C4×C17C2311yescharacteristic
263C2×C22⋊C4×C17C2311yescharacteristic
264C2×C22⋊C4×C17C2311yescharacteristic
265C2×C22⋊C4×C17C2311yescharacteristic
266C2×C22⋊C4×C17C2311yescharacteristic
267C2×C22⋊C4×C17C2311yescharacteristic
268C2×C22⋊C4×C17C2311yescharacteristic
269C2×C22⋊C4×C17C2311yescharacteristic
270C2×C22⋊C4×C17C2311yescharacteristic
271C2×C22⋊C4×C17C2311yescharacteristic
272C2×C42×C17C2311yescharacteristic
273C2×C42×C17C2311yescharacteristic
274C2×C42×C17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277C2×C22⋊Dic17C2311yescharacteristic
278C2×C22⋊Dic17C2311yescharacteristic
279C2×C22⋊Dic17C2311yescharacteristic
280C2×C22⋊Dic17C2311yescharacteristic
281C2×C22⋊Dic17C2311yescharacteristic
282C2×C22⋊Dic17C2311yescharacteristic
283C2×C22⋊Dic17C2311yescharacteristic
284C2×C22⋊Dic17C2311yescharacteristic
285C2×C22⋊Dic17C2311yescharacteristic
286C2×C22⋊Dic17C2311yescharacteristic
287C2×C22⋊Dic17C2311yescharacteristic
288#10587633—24no—
289#10587632—24no—
290#10587622—24no—
291#10587621—24no—
292D4×Dic17—24no—
293#10587615—24no—
294C4×C22⋊D17—24no—
295C4×C22⋊D17—24no—
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×#63227C2311yescharacteristic
307C2×#63227C2311yescharacteristic
308C2×#63227C2311yescharacteristic
309C2×#63227C2311yescharacteristic
310C2×#63227C2311yescharacteristic
311C2×#63227C2311yescharacteristic
312C2×#63227C2311yescharacteristic
313C2×#63227C2311yescharacteristic
314C2×#63227C2311yescharacteristic
315C2×#63227C2311yescharacteristic
316C2×#63227C2311yescharacteristic
317C2×#63227C2311yescharacteristic
318C2×#63227C2311yescharacteristic
319C2×#63227C2311yescharacteristic
320C2×#63227C2311yescharacteristic
321C2×#63227C2311yescharacteristic
322C2×C4⋊Dic17C2311yescharacteristic
323C2×C4⋊Dic17C2311yescharacteristic
324C2×C4⋊Dic17C2311yescharacteristic
325C2×C4⋊Dic17C2311yescharacteristic
326C2×C4⋊Dic17C2311yescharacteristic
327C2×C4⋊Dic17C2311yescharacteristic
328C2×C4⋊Dic17C2311yescharacteristic
329#10587610—24no—
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×#63225C2311yescharacteristic
335C2×#63225C2311yescharacteristic
336C2×#63225C2311yescharacteristic
337C2×#63225C2311yescharacteristic
338C2×#63225C2311yescharacteristic
339C2×#63225C2311yescharacteristic
340C2×#63225C2311yescharacteristic
341C2×#63225C2311yescharacteristic
342C2×#63225C2311yescharacteristic
343C2×#63225C2311yescharacteristic
344C2×C4×Dic17C2311yescharacteristic
345C2×C4×Dic17C2311yescharacteristic
346C2×C4×Dic17C2311yescharacteristic
347C2×C4×Dic17C2311yescharacteristic
348C2×C4×Dic17C2311yescharacteristic
349C2×C4×Dic17C2311yescharacteristic
350C2×C4×Dic17C2311yescharacteristic
351C2×C4×Dic17C2311yescharacteristic
352C2×C4×Dic17C2311yescharacteristic
353#10587583—24no—
354#10587582—24no—
355#10587582—24no—
356#10587580—24no—
357#10587580—24no—
358#10587579—24no—
359C4⋊C4×D17—24no—
360C4⋊C4×D17—24no—
361C4⋊C4×D17—24no—
362C4⋊C4×D17—24no—
363C4⋊C4×D17—24no—
364C4⋊C4×D17—42no—
365C4⋊C4×D17D418yescomplemented
366#10587572—24no—
367#10587571—24no—
368#10587571—24no—
369#10587571—24no—
370#10587571—24no—
371#10587569—24no—
372#10587569—24no—
373#10587567—24no—
374#10587567—24no—
375C22⋊C4×D17—24no—
376C22⋊C4×D17—24no—
377C22⋊C4×D17—24no—
378C22⋊C4×D17—24no—
379C22⋊C4×D17—24no—
380C22⋊C4×D17—24no—
381C22⋊C4×D17—24no—
382C22⋊C4×D17—24no—
383C22⋊C4×D17—24no—
384C22⋊C4×D17—24no—
385C22⋊C4×D17—24no—
386C22⋊C4×D17—24no—
387C22⋊C4×D17D418yescomplemented
388#10587564—24no—
389#10587564—24no—
390#10587561—24no—
391C4×D68—24no—
392C42×D17—24no—
393C42×D17—24no—
394C42×D17—24no—
395C17×#95C2311yescharacteristic
396C17×#95C2311yescharacteristic
397C17×#95C2311yescharacteristic
398C17×#95C2311yescharacteristic
399C17×#95C2311yescharacteristic
400C17×#95C2311yescharacteristic
401#10587502C2311yescharacteristic
402#10587502C2311yescharacteristic
403#10587502C2311yescharacteristic
404#10587502C2311yescharacteristic
405#10587502C2311yescharacteristic
406#10587502C2311yescharacteristic
407#10587502C2311yescharacteristic
408#10587502C2311yescharacteristic
409#10587502C2311yescharacteristic
410#10587502C2311yescharacteristic
411#10587502C2311yescharacteristic
412#10587502C2311yescharacteristic
413#10587502C2311yescharacteristic
414#10587502C2311yescharacteristic
415#10587502C2311yescharacteristic
416#10587502C2311yescharacteristic
417#10587502C2311yescharacteristic
418#10587502C2311yescharacteristic
419C24×C17C2411yescharacteristic
420C24×C17C2411yescharacteristic
421C24×C17C2411yescharacteristic
422C23×D17—22no—
423C23×D17—22no—
424C23×D17—22no—
425C23×D17—22no—
426C23×D17—22no—
427C23×D17—22no—
428C23×D17—22no—
429C23×D17—22no—
430C23×D17—22no—
431C23×D17—22no—
432C23×D17—22no—
433C23×D17—22no—
434C23×D17—22no—
435C23×D17—22no—
436C23×D17—22no—
437C23×D17—22no—
438C23×D17—22no—
439C23×D17—22no—
440C23×D17—22no—
441C23×D17C2×D414yes—
442C23×D17#4114yes—
443C23×D17C2411yescharacteristic
444C23×D17C2411yescharacteristic
445C23×D17C2411yescharacteristic
446C23×D17C2411yescharacteristic
447C2×Q8×C17—22no—
448C2×Q8×C17—22no—
449C2×Q8×C17—41no—
450C2×D4×C17—22no—
451C2×D4×C17—22no—
452C2×D4×C17—22no—
453C2×D4×C17—22no—
454C2×D4×C17—22no—
455C2×D4×C17—22no—
456C2×D4×C17—22no—
457C2×D4×C17—41no—
458C2×D4×C17—41no—
459C22×C4×C17—22no—
460C22×C4×C17—22no—
461C22×C4×C17—22no—
462C22×C4×C17—22no—
463C22×C4×C17—41no—
464C22×C4×C17—41no—
465C22×C4×C17C2411yescharacteristic
466C22×C4×C17C2411yescharacteristic
467C22×C4×C17C2411yescharacteristic
468C22×C4×C17C2411yescharacteristic
469C22×C4×C17C2411yescharacteristic
470C22×C4×C17C2411yescharacteristic
471C22×C4×C17C2411yescharacteristic
472C22×C4×C17C2411yescharacteristic
473C22×C4×C17C2411yescharacteristic
474C22×C4×C17C2411yescharacteristic
475C22×C4×C17C2411yescharacteristic
476C22×C4×C17C2411yescharacteristic
477C2×C22⋊D17—22no—
478C2×C22⋊D17—22no—
479C2×C22⋊D17—22no—
480C2×C22⋊D17—22no—
481C2×C22⋊D17—22no—
482C2×C22⋊D17—22no—
483C2×C22⋊D17—22no—
484C2×C22⋊D17—22no—
485C2×C22⋊D17—22no—
486C2×C22⋊D17—22no—
487C2×C22⋊D17—22no—
488C2×C22⋊D17—22no—
489C2×C22⋊D17—22no—
490C2×C22⋊D17—22no—
491C2×C22⋊D17—41no—
492C2×C22⋊D17—41no—
493C2×C22⋊D17—41no—
494C2×C22⋊D17—41no—
495C22×Dic17—22no—
496C22×Dic17—22no—
497C22×Dic17—22no—
498C22×Dic17—22no—
499C22×Dic17—41no—
500C22×Dic17—41no—
501C22×Dic17C2411yescharacteristic
502C22×Dic17C2411yescharacteristic
503C22×Dic17C2411yescharacteristic
504C22×Dic17C2411yescharacteristic
505C22×Dic17C2411yescharacteristic
506C22×Dic17C2411yescharacteristic
507C22×Dic17C2411yescharacteristic
508C22×Dic17C2411yescharacteristic
509C22×Dic17C2411yescharacteristic
510C22×Dic17C2411yescharacteristic
511C22×Dic17C2411yescharacteristic
512C22×Dic17C2411yescharacteristic
513Q8×D17—416no—
514D4×D17—232no—
515D4×D17—416no—
516D4×D17—416no—
517C2×D68—22no—
518C2×D68—22no—
519C2×D68—22no—
520C2×D68—22no—
521C2×D68—22no—
522C2×D68—22no—
523C2×D68—22no—
524C2×D68—41no—
525C2×D68—41no—
526C2×C4×D17—22no—
527C2×C4×D17—22no—
528C2×C4×D17—22no—
529C2×C4×D17—22no—
530C2×C4×D17—22no—
531C2×C4×D17—22no—
532C2×C4×D17—22no—
533C2×C4×D17—22no—
534C2×C4×D17—22no—
535C2×C4×D17—22no—
536C2×C4×D17—22no—
537C2×C4×D17—22no—
538C2×C4×D17—22no—
539C2×C4×D17—22no—
540C2×C4×D17—22no—
541C2×C4×D17—22no—
542C2×C4×D17—22no—
543C2×C4×D17—22no—
544C2×C4×D17—22no—
545C2×C4×D17—22no—
546C2×C4×D17—22no—
547C2×C4×D17—22no—
548C2×C4×D17—22no—
549C2×C4×D17—22no—
550C2×C4×D17—22no—
551C2×C4×D17—22no—
552C2×C4×D17—22no—
553C2×C4×D17—22no—
554C2×C4×D17—22no—
555C2×C4×D17—22no—
556C2×C4×D17—22no—
557C2×C4×D17—22no—
558C2×C4×D17—22no—
559C2×C4×D17—22no—
560C2×C4×D17—22no—
561C2×C4×D17—22no—
562C2×C4×D17—22no—
563C2×C4×D17—416no—
564C2×C4×D17—416no—
565C2×C4×D17—41no—
566C2×C4×D17—41no—
567C2×C4×D17—41no—
568C2×C4×D17—41no—
569C2×C4×D17C2×D414yes—
570C2×C4×D17C2×D414yes—
571C2×C4×D17C2×D414yes—
572C2×C4×D17C2×D414yes—
573C2×C4×D17C2×D414yes—
574C2×C4×D17#4114yes—
575C2×C4×D17#4114yes—
576C2×Dic34—22no—
577C2×Dic34—22no—
578C2×Dic34—22no—
579C2×Dic34—22no—
580C2×Dic34—22no—
581C2×Dic34—22no—
582C2×Dic34—41no—
583C2×Dic34—41no—
584C2×Dic34—41no—
585C4⋊C4×C17—22no—
586C4⋊C4×C17—22no—
587C4⋊C4×C17—22no—
588C4⋊C4×C17—22no—
589C4⋊C4×C17—22no—
590C4⋊C4×C17—41no—
591C4⋊C4×C17C2×D414yescomplemented
592C22⋊C4×C17—22no—
593C22⋊C4×C17—22no—
594C22⋊C4×C17—22no—
595C22⋊C4×C17—22no—
596C22⋊C4×C17—22no—
597C22⋊C4×C17—22no—
598C22⋊C4×C17—22no—
599C22⋊C4×C17—22no—
600C22⋊C4×C17—22no—
601C22⋊C4×C17—22no—
602C22⋊C4×C17—22no—
603C22⋊C4×C17—22no—
604C22⋊C4×C17C2×D414yescomplemented
605C42×C17—22no—
606C42×C17—22no—
607C42×C17—22no—
608C22⋊Dic17—22no—
609C22⋊Dic17—22no—
610C22⋊Dic17—22no—
611C22⋊Dic17—22no—
612C22⋊Dic17—22no—
613C22⋊Dic17—22no—
614C22⋊Dic17—22no—
615C22⋊Dic17—22no—
616C22⋊Dic17—22no—
617C22⋊Dic17—22no—
618C22⋊Dic17—22no—
619C22⋊Dic17—22no—
620C22⋊Dic17C2×D414yescomplemented
621#63227—22no—
622#63227—22no—
623#63227—22no—
624#63227—22no—
625#63227—22no—
626#63227—22no—
627#63227—22no—
628#63227—22no—
629#63227—22no—
630#63227—22no—
631#63227—22no—
632#63227—22no—
633#63227—22no—
634#63227—22no—
635#63227—22no—
636#63227—22no—
637#63227—22no—
638#63227—22no—
639#63227—22no—
640#63227—22no—
641#63227—22no—
642#63227—22no—
643#63227—22no—
644#63227—22no—
645#63227C2×D414yescomplemented
646#63227C2×D414yescomplemented
647C4⋊Dic17—22no—
648C4⋊Dic17—22no—
649C4⋊Dic17—22no—
650C4⋊Dic17—22no—
651C4⋊Dic17—22no—
652C4⋊Dic17—41no—
653C4⋊Dic17C2×D414yescomplemented
654#63225—22no—
655#63225—22no—
656#63225—22no—
657#63225—22no—
658#63225—22no—
659#63225—22no—
660#63225—22no—
661#63225—22no—
662#63225—22no—
663#63225—22no—
664#63225—41no—
665#63225—41no—
666#63225C2×D414yescomplemented
667#63225C2×D414yescomplemented
668C4×Dic17—22no—
669C4×Dic17—22no—
670C4×Dic17—22no—
671C4×Dic17—22no—
672C4×Dic17—22no—
673C4×Dic17—22no—
674C4×Dic17—22no—
675C4×Dic17—22no—
676C4×Dic17—22no—
677C2×#2461—171nomaximal, Sylow
678C23×C17—21no—
679C23×C17—21no—
680C23×C17—21no—
681C23×C17—21no—
682C23×C17—21no—
683C23×C17—21no—
684C23×C17—21no—
685C23×C17—21no—
686C23×C17—21no—
687C23×C17—21no—
688C23×C17—21no—
689C23×C17—21no—
690C23×C17—21no—
691C23×C17—21no—
692C23×C17—21no—
693C23×C17—21no—
694C23×C17—21no—
695C23×C17—21no—
696C23×C17—21no—
697C23×C17C22×D412yes—
698C23×C17C2×#4112yes—
699C23×C17C2511yescharacteristic
700C22×D17—21no—
701C22×D17—21no—
702C22×D17—21no—
703C22×D17—21no—
704C22×D17—21no—
705C22×D17—21no—
706C22×D17—21no—
707C22×D17—21no—
708C22×D17—21no—
709C22×D17—21no—
710C22×D17—21no—
711C22×D17—21no—
712C22×D17—28no—
713C22×D17—28no—
714C22×D17—28no—
715C22×D17—28no—
716C22×D17—28no—
717C22×D17—28no—
718C22×D17—21no—
719C22×D17—21no—
720C22×D17—21no—
721C22×D17—21no—
722C22×D17—21no—
723C22×D17—21no—
724C22×D17—21no—
725C22×D17—44no—
726C22×D17—44no—
727C22×D17—44no—
728C22×D17—44no—
729C22×D17—44no—
730C22×D17—44no—
731C22×D17—44no—
732C22×D17—44no—
733C22×D17—44no—
734C22×D17—44no—
735C22×D17—44no—
736C22×D17—44no—
737C22×D17—44no—
738C22×D17—44no—
739C22×D17—44no—
740C22×D17C22×D412yes—
741C22×D17C22×D412yes—
742C22×D17C22×D412yes—
743C22×D17C2×#4112yes—
744C22×D17C2×#4112yes—
745C22×D17C2×#4112yes—
746C22×D17C2×#4112yes—
747C22×D17H(5,𝔽2)12yes—
748C22×D172−1+412yes—
749Q8×C17—44no—
750D4×C17—28no—
751D4×C17—44no—
752D4×C17—44no—
753C2×C4×C17—21no—
754C2×C4×C17—21no—
755C2×C4×C17—21no—
756C2×C4×C17—21no—
757C2×C4×C17—21no—
758C2×C4×C17—21no—
759C2×C4×C17—21no—
760C2×C4×C17—21no—
761C2×C4×C17—21no—
762C2×C4×C17—21no—
763C2×C4×C17—21no—
764C2×C4×C17—21no—
765C2×C4×C17—21no—
766C2×C4×C17—21no—
767C2×C4×C17—21no—
768C2×C4×C17—21no—
769C2×C4×C17—21no—
770C2×C4×C17—21no—
771C2×C4×C17—21no—
772C2×C4×C17—21no—
773C2×C4×C17—21no—
774C2×C4×C17—21no—
775C2×C4×C17—21no—
776C2×C4×C17—21no—
777C2×C4×C17—21no—
778C2×C4×C17—21no—
779C2×C4×C17—21no—
780C2×C4×C17—21no—
781C2×C4×C17—21no—
782C2×C4×C17—44no—
783C2×C4×C17—44no—
784C2×C4×C17C22×D412yes—
785C2×C4×C17C22×D412yes—
786C2×C4×C17C22×D412yes—
787C2×C4×C17C22×D412yes—
788C2×C4×C17C22×D412yes—
789C2×C4×C17C2×#4112yes—
790C2×C4×C17C2×#4112yes—
791C22⋊D17—28no—
792C22⋊D17—28no—
793C22⋊D17—44no—
794C22⋊D17—44no—
795C22⋊D17—44no—
796C22⋊D17—44no—
797C2×Dic17—21no—
798C2×Dic17—21no—
799C2×Dic17—21no—
800C2×Dic17—21no—
801C2×Dic17—21no—
802C2×Dic17—21no—
803C2×Dic17—21no—
804C2×Dic17—21no—
805C2×Dic17—21no—
806C2×Dic17—21no—
807C2×Dic17—21no—
808C2×Dic17—21no—
809C2×Dic17—21no—
810C2×Dic17—21no—
811C2×Dic17—21no—
812C2×Dic17—21no—
813C2×Dic17—21no—
814C2×Dic17—21no—
815C2×Dic17—21no—
816C2×Dic17—21no—
817C2×Dic17—21no—
818C2×Dic17—21no—
819C2×Dic17—21no—
820C2×Dic17—21no—
821C2×Dic17—21no—
822C2×Dic17—21no—
823C2×Dic17—21no—
824C2×Dic17—21no—
825C2×Dic17—21no—
826C2×Dic17—44no—
827C2×Dic17—44no—
828C2×Dic17C22×D412yes—
829C2×Dic17C22×D412yes—
830C2×Dic17C22×D412yes—
831C2×Dic17C22×D412yes—
832C2×Dic17C22×D412yes—
833C2×Dic17C2×#4112yes—
834C2×Dic17C2×#4112yes—
835D68—28no—
836D68—44no—
837D68—44no—
838C4×D17—28no—
839C4×D17—28no—
840C4×D17—28no—
841C4×D17—28no—
842C4×D17—28no—
843C4×D17—28no—
844C4×D17—28no—
845C4×D17—44no—
846C4×D17—44no—
847C4×D17—44no—
848C4×D17—44no—
849C4×D17—44no—
850C4×D17—44no—
851C4×D17—44no—
852C4×D17—44no—
853C4×D17—44no—
854Dic34—44no—
855Dic34—44no—
856Dic34—44no—
857C22×#124—171no—
858C22×#123—171no—
859C22×C22⋊Q8—171no—
860C22×C4×D4—171no—
861#2461—171no—
862#2461—171no—
863#2461—171no—
864#2461—171no—
865#2461—171no—
866#2461—171no—
867#2461—171no—
868#2461—171no—
869#2461—171no—
870#2461—171no—
871#2461—171no—
872#2461—171no—
873#2461—171no—
874#2461—171no—
875#2461—171no—
876#2461D1711yescharacteristic, direct product factor
877C2×#396—171no—
878C2×#395—171no—
879C2×#394—171no—
880C2×#392—171no—
881C2×#390—171no—
882C2×#388—171no—
883C2×#388—171no—
884C2×#388—171no—
885C2×#386—171no—
886C2×#385—171no—
887C2×C4×C4⋊C4—171no—
888C22×C17—22no—
889C22×C17—22no—
890C22×C17—22no—
891C22×C17—22no—
892C22×C17—22no—
893C22×C17—22no—
894C22×C17—41no—
895C22×C17—41no—
896C22×C17—41no—
897C22×C17—41no—
898C22×C17—41no—
899C22×C17—41no—
900C22×C17—41no—
901C22×C17—41no—
902C22×C17—41no—
903C22×C17—41no—
904C22×C17—41no—
905C22×C17—41no—
906C22×C17—41no—
907C22×C17—41no—
908C22×C17—41no—
909C22×C17C23×D411yescharacteristic
910C22×C17C23×D411yescharacteristic
911C22×C17C22×#4111yescharacteristic
912C22×C17C22×#4111yescharacteristic
913C22×C17C22×#4111yescharacteristic
914C22×C17C2×H(5,𝔽2)11yescharacteristic
915C22×C17C2×2−1+411yescharacteristic
916C2×D17—22no—
917C2×D17—22no—
918C2×D17—22no—
919C2×D17—22no—
920C2×D17—22no—
921C2×D17—22no—
922C2×D17—41no—
923C2×D17—41no—
924C2×D17—41no—
925C2×D17—41no—
926C2×D17—41no—
927C2×D17—41no—
928C2×D17—41no—
929C2×D17—41no—
930C2×D17—416no—
931C2×D17—416no—
932C2×D17—41no—
933C2×D17—41no—
934C2×D17—41no—
935C2×D17—41no—
936C2×D17—41no—
937C2×D17—41no—
938C2×D17—41no—
939C2×D17—88no—
940C2×D17#52514yes—
941C2×D17#53214yes—
942C2×D17#54214yes—
943C2×D17D4214yes—
944C2×D17#54714yes—
945C2×D17#54814yes—
946C2×D17#55114yes—
947C4×C17—22no—
948C4×C17—22no—
949C4×C17—22no—
950C4×C17—22no—
951C4×C17—22no—
952C4×C17—22no—
953C4×C17—22no—
954C4×C17—41no—
955C4×C17—41no—
956C4×C17—41no—
957C4×C17—41no—
958C4×C17—41no—
959Dic17—22no—
960Dic17—22no—
961Dic17—22no—
962Dic17—22no—
963Dic17—22no—
964Dic17—22no—
965Dic17—22no—
966Dic17—41no—
967Dic17—41no—
968Dic17—41no—
969Dic17—41no—
970Dic17—41no—
971C23×Q8—171no—
972C23×D4—171no—
973C23×D4—171no—
974C23×D4—171no—
975C24×C4—171no—
976C24×C4—171no—
977C2×#124—171no—
978C2×#124—171no—
979C2×#124—171no—
980C2×#124—171no—
981C2×#124—171no—
982C2×#124—171no—
983C2×#124—171no—
984C2×#124—348no—
985C2×#124C2×D1711yescharacteristic, complemented
986C2×#123—171no—
987C2×#123—171no—
988C2×#123—171no—
989C2×#123—171no—
990C2×#123—171no—
991C2×#123—171no—
992C2×#123—171no—
993C2×#123—348no—
994C2×#123C2×D1711yescharacteristic, complemented
995C2×C22⋊Q8—171no—
996C2×C22⋊Q8—171no—
997C2×C22⋊Q8—171no—
998C2×C22⋊Q8—171no—
999C2×C22⋊Q8—171no—
1000C2×C22⋊Q8—171no—
1001C2×C22⋊Q8—171no—
1002C2×C22⋊Q8—348no—
1003C2×C22⋊Q8C2×D1711yescharacteristic, complemented
1004C2×C4×D4—171no—
1005C2×C4×D4—171no—
1006C2×C4×D4—171no—
1007C2×C4×D4—171no—
1008C2×C4×D4—171no—
1009C2×C4×D4—171no—
1010C2×C4×D4—171no—
1011C2×C4×D4—348no—
1012C2×C4×D4C2×D1711yescharacteristic, complemented
1013C22×C4⋊C4—171no—
1014C22×C4⋊C4—171no—
1015C22×C4⋊C4—171no—
1016C22×C4⋊C4—171no—
1017C22×C4⋊C4—171no—
1018C22×C4⋊C4—171no—
1019C22×C4⋊C4—171no—
1020C22×C22⋊C4—171no—
1021C22×C22⋊C4—171no—
1022C22×C22⋊C4—171no—
1023C22×C22⋊C4—171no—
1024C22×C22⋊C4—171no—
1025C22×C22⋊C4—171no—
1026C22×C22⋊C4—171no—
1027C22×C22⋊C4—171no—
1028C22×C22⋊C4—171no—
1029C22×C22⋊C4—171no—
1030C22×C22⋊C4—171no—
1031C22×C22⋊C4—171no—
1032C22×C22⋊C4—171no—
1033C22×C42—171no—
1034C22×C42—171no—
1035C22×C42—171no—
1036#396—171no—
1037#396—171no—
1038#396—171no—
1039#396—171no—
1040#396—171no—
1041#396—171no—
1042#396—171no—
1043#396C2×D1711yescharacteristic, complemented
1044#395—171no—
1045#395—171no—
1046#395—171no—
1047#395—171no—
1048#395—171no—
1049#395—171no—
1050#395—171no—
1051#395C2×D1711yescharacteristic, complemented
1052#394—171no—
1053#394—171no—
1054#394—171no—
1055#394—171no—
1056#394—171no—
1057#394—171no—
1058#394—171no—
1059#394C2×D1711yescharacteristic, complemented
1060#392—171no—
1061#392—171no—
1062#392—171no—
1063#392—171no—
1064#392—171no—
1065#392—171no—
1066#392—171no—
1067#392C2×D1711yescharacteristic
1068#390—171no—
1069#390—171no—
1070#390—171no—
1071#390—171no—
1072#390—171no—
1073#390—171no—
1074#390—171no—
1075#390C2×D1711yescharacteristic, complemented
1076#388—171no—
1077#388—171no—
1078#388—171no—
1079#388—171no—
1080#388—171no—
1081#388—171no—
1082#388—171no—
1083#388—171no—
1084#388—171no—
1085#388—171no—
1086#388—171no—
1087#388—171no—
1088#388—171no—
1089#388—171no—
1090#388—171no—
1091#388—171no—
1092#388—171no—
1093#388—171no—
1094#388—171no—
1095#388—171no—
1096#388—171no—
1097#388C2×D1711yescharacteristic, complemented
1098#388C2×D1711yescharacteristic, complemented
1099#388C2×D1711yescharacteristic, complemented
1100#386—171no—
1101#386—171no—
1102#386—171no—
1103#386—171no—
1104#386—171no—
1105#386—171no—
1106#386—171no—
1107#386C2×D1711yescharacteristic, complemented
1108#385—171no—
1109#385—171no—
1110#385—171no—
1111#385—171no—
1112#385—171no—
1113#385—171no—
1114#385—171no—
1115#385C2×D1711yescharacteristic, complemented
1116C4×C4⋊C4—171no—
1117C4×C4⋊C4—171no—
1118C4×C4⋊C4—171no—
1119C4×C4⋊C4—171no—
1120C4×C4⋊C4—171no—
1121C4×C4⋊C4—171no—
1122C4×C4⋊C4—171no—
1123C4×C4⋊C4C2×D1711yescharacteristic, complemented
1124C2×#95—171no—
1125C2×#95—171no—
1126C2×#95—171no—
1127C2×#95—171no—
1128C2×#95—171no—
1129C2×#95—171no—
1130C2×C17—42no—
1131C2×C17—42no—
1132C2×C17—81no—
1133C2×C17C2×#52511yescharacteristic
1134C2×C17C2×#53211yescharacteristic
1135C2×C17C2×#54211yescharacteristic
1136C2×C17C2×D4211yescharacteristic
1137C2×C17C2×#54711yescharacteristic
1138C2×C17C2×#54811yescharacteristic
1139C2×C17C2×#55111yescharacteristic
1140D17—42no—
1141D17—42no—
1142D17—81no—
1143D17#246118yesdirect product factor
1144C25—171no—
1145C25—171no—
1146C25—171no—
1147C22×Q8—171no—
1148C22×Q8—171no—
1149C22×Q8—171no—
1150C22×Q8—344no—
1151C22×Q8—344no—
1152C22×Q8—682no—
1153C22×Q8C22×D1711yescharacteristic
1154C22×D4—171no—
1155C22×D4—171no—
1156C22×D4—171no—
1157C22×D4—171no—
1158C22×D4—171no—
1159C22×D4—171no—
1160C22×D4—171no—
1161C22×D4—171no—
1162C22×D4—171no—
1163C22×D4—344no—
1164C22×D4—344no—
1165C22×D4—344no—
1166C22×D4—344no—
1167C22×D4—344no—
1168C22×D4—344no—
1169C22×D4—344no—
1170C22×D4—682no—
1171C22×D4—682no—
1172C22×D4C22×D1711yescharacteristic
1173C22×D4C22×D1711yescharacteristic
1174C22×D4C22×D1711yescharacteristic
1175C23×C4—171no—
1176C23×C4—171no—
1177C23×C4—171no—
1178C23×C4—171no—
1179C23×C4—171no—
1180C23×C4—171no—
1181C23×C4—171no—
1182C23×C4—171no—
1183C23×C4—171no—
1184C23×C4—171no—
1185C23×C4—171no—
1186C23×C4—171no—
1187C23×C4—171no—
1188C23×C4—171no—
1189C23×C4—171no—
1190C23×C4—171no—
1191C23×C4—171no—
1192C23×C4—171no—
1193C23×C4—344no—
1194C23×C4—344no—
1195C23×C4—344no—
1196C23×C4—344no—
1197C23×C4—682no—
1198C23×C4—682no—
1199C23×C4C22×D1711yescharacteristic
1200C23×C4C22×D1711yescharacteristic
1201#124—24no—
1202#124—344no—
1203#124—344no—
1204#124—344no—
1205#124—344no—
1206#124—344no—
1207#124—344no—
1208#124—344no—
1209#123—24no—
1210#123—344no—
1211#123—344no—
1212#123—344no—
1213#123—344no—
1214#123—344no—
1215#123—344no—
1216#123—344no—
1217C22⋊Q8—24no—
1218C22⋊Q8—344no—
1219C22⋊Q8—344no—
1220C22⋊Q8—344no—
1221C22⋊Q8—344no—
1222C22⋊Q8—344no—
1223C22⋊Q8—344no—
1224C22⋊Q8—344no—
1225C4×D4—24no—
1226C4×D4—344no—
1227C4×D4—344no—
1228C4×D4—344no—
1229C4×D4—344no—
1230C4×D4—344no—
1231C4×D4—344no—
1232C4×D4—344no—
1233C2×C4⋊C4—171no—
1234C2×C4⋊C4—171no—
1235C2×C4⋊C4—171no—
1236C2×C4⋊C4—178no—
1237C2×C4⋊C4—171no—
1238C2×C4⋊C4—171no—
1239C2×C4⋊C4—171no—
1240C2×C4⋊C4—171no—
1241C2×C4⋊C4—171no—
1242C2×C4⋊C4—171no—
1243C2×C4⋊C4—171no—
1244C2×C4⋊C4—171no—
1245C2×C4⋊C4—171no—
1246C2×C4⋊C4—171no—
1247C2×C4⋊C4—171no—
1248C2×C4⋊C4—171no—
1249C2×C4⋊C4—171no—
1250C2×C4⋊C4—171no—
1251C2×C4⋊C4—171no—
1252C2×C4⋊C4—171no—
1253C2×C4⋊C4—171no—
1254C2×C4⋊C4—171no—
1255C2×C4⋊C4—344no—
1256C2×C4⋊C4—344no—
1257C2×C4⋊C4—344no—
1258C2×C4⋊C4—344no—
1259C2×C4⋊C4—344no—
1260C2×C4⋊C4—682no—
1261C2×C4⋊C4C22×D1711yescharacteristic
1262C2×C4⋊C4C22×D1711yescharacteristic
1263C2×C4⋊C4C22×D1711yescharacteristic
1264C2×C4⋊C4C22×D1711yescharacteristic
1265C2×C4⋊C4C22×D1711yescharacteristic
1266C2×C4⋊C4C22×D1711yescharacteristic
1267C2×C4⋊C4C22×D1711yescharacteristic
1268C2×C22⋊C4—171no—
1269C2×C22⋊C4—171no—
1270C2×C22⋊C4—171no—
1271C2×C22⋊C4—178no—
1272C2×C22⋊C4—171no—
1273C2×C22⋊C4—171no—
1274C2×C22⋊C4—171no—
1275C2×C22⋊C4—171no—
1276C2×C22⋊C4—171no—
1277C2×C22⋊C4—171no—
1278C2×C22⋊C4—171no—
1279C2×C22⋊C4—171no—
1280C2×C22⋊C4—171no—
1281C2×C22⋊C4—171no—
1282C2×C22⋊C4—171no—
1283C2×C22⋊C4—171no—
1284C2×C22⋊C4—171no—
1285C2×C22⋊C4—171no—
1286C2×C22⋊C4—171no—
1287C2×C22⋊C4—171no—
1288C2×C22⋊C4—171no—
1289C2×C22⋊C4—171no—
1290C2×C22⋊C4—171no—
1291C2×C22⋊C4—171no—
1292C2×C22⋊C4—171no—
1293C2×C22⋊C4—171no—
1294C2×C22⋊C4—171no—
1295C2×C22⋊C4—171no—
1296C2×C22⋊C4—171no—
1297C2×C22⋊C4—171no—
1298C2×C22⋊C4—171no—
1299C2×C22⋊C4—171no—
1300C2×C22⋊C4—171no—
1301C2×C22⋊C4—171no—
1302C2×C22⋊C4—171no—
1303C2×C22⋊C4—171no—
1304C2×C22⋊C4—171no—
1305C2×C22⋊C4—171no—
1306C2×C22⋊C4—171no—
1307C2×C22⋊C4—171no—
1308C2×C22⋊C4—344no—
1309C2×C22⋊C4—344no—
1310C2×C22⋊C4—344no—
1311C2×C22⋊C4—344no—
1312C2×C22⋊C4—344no—
1313C2×C22⋊C4—344no—
1314C2×C22⋊C4—344no—
1315C2×C22⋊C4—344no—
1316C2×C22⋊C4—344no—
1317C2×C22⋊C4—344no—
1318C2×C22⋊C4—344no—
1319C2×C22⋊C4—344no—
1320C2×C22⋊C4C22×D1711yescharacteristic
1321C2×C22⋊C4C22×D1711yescharacteristic
1322C2×C22⋊C4C22×D1711yescharacteristic
1323C2×C22⋊C4C22×D1711yescharacteristic
1324C2×C22⋊C4C22×D1711yescharacteristic
1325C2×C22⋊C4C22×D1711yescharacteristic
1326C2×C22⋊C4C22×D1711yescharacteristic
1327C2×C22⋊C4C22×D1711yescharacteristic
1328C2×C22⋊C4C22×D1711yescharacteristic
1329C2×C22⋊C4C22×D1711yescharacteristic
1330C2×C22⋊C4C22×D1711yescharacteristic
1331C2×C22⋊C4C22×D1711yescharacteristic
1332C2×C22⋊C4C22×D1711yescharacteristic
1333C2×C42—171no—
1334C2×C42—171no—
1335C2×C42—171no—
1336C2×C42—171no—
1337C2×C42—171no—
1338C2×C42—171no—
1339C2×C42—171no—
1340C2×C42—171no—
1341C2×C42—171no—
1342C2×C42—344no—
1343C2×C42—344no—
1344C2×C42—344no—
1345C2×C42C22×D1711yescharacteristic
1346C2×C42C22×D1711yescharacteristic
1347C2×C42C22×D1711yescharacteristic
1348#95—171no—
1349#95—171no—
1350#95—171no—
1351#95—171no—
1352#95—171no—
1353#95—171no—
1354#95—171no—
1355#95—171no—
1356#95—171no—
1357#95—171no—
1358#95—171no—
1359#95—171no—
1360#95—171no—
1361#95—171no—
1362#95—171no—
1363#95—171no—
1364#95—171no—
1365#95—171no—
1366#95C22×D1711yescharacteristic
1367#95C22×D1711yescharacteristic
1368#95C22×D1711yescharacteristic
1369#95C22×D1711yescharacteristic
1370#95C22×D1711yescharacteristic
1371#95C22×D1711yescharacteristic
1372C17C2×#246111yescharacteristic, complemented, Sylow
1373C24—171no—
1374C24—174no—
1375C24—174no—
1376C24—171no—
1377C24—171no—
1378C24—171no—
1379C24—342no—
1380C24—342no—
1381C24—342no—
1382C24—342no—
1383C24—342no—
1384C24—342no—
1385C24—342no—
1386C24—342no—
1387C24—342no—
1388C24—342no—
1389C24—342no—
1390C24—342no—
1391C24—342no—
1392C24—342no—
1393C24—342no—
1394C24—342no—
1395C24—342no—
1396C24—342no—
1397C24—342no—
1398C24C23×D1711yescharacteristic
1399C24C23×D1711yescharacteristic
1400C24C23×D1711yescharacteristic
1401C2×Q8—22no—
1402C2×Q8—22no—
1403C2×Q8—41no—
1404C2×Q8—342no—
1405C2×Q8—342no—
1406C2×Q8—342no—
1407C2×Q8—342no—
1408C2×Q8—342no—
1409C2×Q8—342no—
1410C2×Q8—681no—
1411C2×Q8—681no—
1412C2×Q8—681no—
1413C2×Q8—6816no—
1414C2×D4—22no—
1415C2×D4—22no—
1416C2×D4—22no—
1417C2×D4—22no—
1418C2×D4—22no—
1419C2×D4—22no—
1420C2×D4—22no—
1421C2×D4—41no—
1422C2×D4—41no—
1423C2×D4—342no—
1424C2×D4—342no—
1425C2×D4—342no—
1426C2×D4—342no—
1427C2×D4—342no—
1428C2×D4—342no—
1429C2×D4—342no—
1430C2×D4—342no—
1431C2×D4—342no—
1432C2×D4—342no—
1433C2×D4—3432no—
1434C2×D4—342no—
1435C2×D4—342no—
1436C2×D4—342no—
1437C2×D4—342no—
1438C2×D4—342no—
1439C2×D4—342no—
1440C2×D4—342no—
1441C2×D4—342no—
1442C2×D4—342no—
1443C2×D4—342no—
1444C2×D4—342no—
1445C2×D4—681no—
1446C2×D4—681no—
1447C2×D4—6816no—
1448C2×D4—6816no—
1449C2×D4—681no—
1450C2×D4—681no—
1451C2×D4—681no—
1452C2×D4—681no—
1453C22×C4—22no—
1454C22×C4—22no—
1455C22×C4—22no—
1456C22×C4—22no—
1457C22×C4—41no—
1458C22×C4—41no—
1459C22×C4—171no—
1460C22×C4—171no—
1461C22×C4—171no—
1462C22×C4—171no—
1463C22×C4—171no—
1464C22×C4—171no—
1465C22×C4—171no—
1466C22×C4—174no—
1467C22×C4—174no—
1468C22×C4—174no—
1469C22×C4—174no—
1470C22×C4—174no—
1471C22×C4—174no—
1472C22×C4—174no—
1473C22×C4—171no—
1474C22×C4—171no—
1475C22×C4—171no—
1476C22×C4—171no—
1477C22×C4—171no—
1478C22×C4—342no—
1479C22×C4—342no—
1480C22×C4—342no—
1481C22×C4—342no—
1482C22×C4—342no—
1483C22×C4—342no—
1484C22×C4—342no—
1485C22×C4—342no—
1486C22×C4—342no—
1487C22×C4—342no—
1488C22×C4—342no—
1489C22×C4—342no—
1490C22×C4—342no—
1491C22×C4—342no—
1492C22×C4—342no—
1493C22×C4—342no—
1494C22×C4—342no—
1495C22×C4—342no—
1496C22×C4—342no—
1497C22×C4—342no—
1498C22×C4—342no—
1499C22×C4—342no—
1500C22×C4—342no—
1501C22×C4—342no—
1502C22×C4—342no—
1503C22×C4—342no—
1504C22×C4—342no—
1505C22×C4—342no—
1506C22×C4—342no—
1507C22×C4—342no—
1508C22×C4—342no—
1509C22×C4—342no—
1510C22×C4—342no—
1511C22×C4—342no—
1512C22×C4—342no—
1513C22×C4—342no—
1514C22×C4—342no—
1515C22×C4—342no—
1516C22×C4—342no—
1517C22×C4—342no—
1518C22×C4—342no—
1519C22×C4—681no—
1520C22×C4—681no—
1521C22×C4—681no—
1522C22×C4—681no—
1523C22×C4—6816no—
1524C22×C4—6816no—
1525C22×C4—681no—
1526C22×C4—681no—
1527C22×C4C23×D1711yescharacteristic
1528C22×C4C23×D1711yescharacteristic
1529C22×C4C23×D1711yescharacteristic
1530C22×C4C23×D1711yescharacteristic
1531C22×C4C23×D1711yescharacteristic
1532C22×C4C23×D1711yescharacteristic
1533C22×C4C23×D1711yescharacteristic
1534C22×C4C23×D1711yescharacteristic
1535C22×C4C23×D1711yescharacteristic
1536C22×C4C23×D1711yescharacteristic
1537C22×C4C23×D1711yescharacteristic
1538C22×C4C23×D1711yescharacteristic
1539C4⋊C4—22no—
1540C4⋊C4—22no—
1541C4⋊C4—22no—
1542C4⋊C4—22no—
1543C4⋊C4—22no—
1544C4⋊C4—41no—
1545C4⋊C4—174no—
1546C4⋊C4—174no—
1547C4⋊C4—174no—
1548C4⋊C4—342no—
1549C4⋊C4—342no—
1550C4⋊C4—342no—
1551C4⋊C4—342no—
1552C4⋊C4—342no—
1553C4⋊C4—342no—
1554C4⋊C4—342no—
1555C4⋊C4—342no—
1556C4⋊C4—342no—
1557C4⋊C4—342no—
1558C4⋊C4—342no—
1559C4⋊C4—342no—
1560C4⋊C4—342no—
1561C4⋊C4—342no—
1562C4⋊C4—342no—
1563C4⋊C4—681no—
1564C4⋊C4—681no—
1565C4⋊C4—681no—
1566C4⋊C4D4×D1714yescomplemented
1567C22⋊C4—22no—
1568C22⋊C4—22no—
1569C22⋊C4—22no—
1570C22⋊C4—22no—
1571C22⋊C4—22no—
1572C22⋊C4—22no—
1573C22⋊C4—22no—
1574C22⋊C4—22no—
1575C22⋊C4—22no—
1576C22⋊C4—22no—
1577C22⋊C4—22no—
1578C22⋊C4—22no—
1579C22⋊C4—174no—
1580C22⋊C4—174no—
1581C22⋊C4—174no—
1582C22⋊C4—342no—
1583C22⋊C4—342no—
1584C22⋊C4—342no—
1585C22⋊C4—342no—
1586C22⋊C4—342no—
1587C22⋊C4—342no—
1588C22⋊C4—342no—
1589C22⋊C4—342no—
1590C22⋊C4—342no—
1591C22⋊C4—342no—
1592C22⋊C4—342no—
1593C22⋊C4—342no—
1594C22⋊C4—342no—
1595C22⋊C4—342no—
1596C22⋊C4—342no—
1597C22⋊C4—342no—
1598C22⋊C4—342no—
1599C22⋊C4—342no—
1600C22⋊C4—342no—
1601C22⋊C4—342no—
1602C22⋊C4—342no—
1603C22⋊C4—342no—
1604C22⋊C4—342no—
1605C22⋊C4—342no—
1606C22⋊C4—342no—
1607C22⋊C4—342no—
1608C22⋊C4—342no—
1609C22⋊C4—342no—
1610C22⋊C4—342no—
1611C22⋊C4—342no—
1612C22⋊C4—342no—
1613C22⋊C4—342no—
1614C22⋊C4—342no—
1615C22⋊C4—342no—
1616C22⋊C4—342no—
1617C22⋊C4—342no—
1618C22⋊C4D4×D1714yescomplemented
1619C42—22no—
1620C42—22no—
1621C42—22no—
1622C42—342no—
1623C42—342no—
1624C42—342no—
1625C42—342no—
1626C42—342no—
1627C42—342no—
1628C42—342no—
1629C42—342no—
1630C42—342no—
1631C23—21no—
1632C23—21no—
1633C23—21no—
1634C23—21no—
1635C23—21no—
1636C23—21no—
1637C23—21no—
1638C23—21no—
1639C23—21no—
1640C23—21no—
1641C23—21no—
1642C23—21no—
1643C23—21no—
1644C23—21no—
1645C23—21no—
1646C23—21no—
1647C23—21no—
1648C23—21no—
1649C23—21no—
1650C23—172no—
1651C23—172no—
1652C23—172no—
1653C23—172no—
1654C23—172no—
1655C23—172no—
1656C23—172no—
1657C23—172no—
1658C23—172no—
1659C23—348no—
1660C23—348no—
1661C23—348no—
1662C23—348no—
1663C23—348no—
1664C23—348no—
1665C23—341no—
1666C23—341no—
1667C23—341no—
1668C23—341no—
1669C23—341no—
1670C23—341no—
1671C23—341no—
1672C23—341no—
1673C23—341no—
1674C23—341no—
1675C23—341no—
1676C23—341no—
1677C23—341no—
1678C23—341no—
1679C23—341no—
1680C23—341no—
1681C23—341no—
1682C23—341no—
1683C23—341no—
1684C23—684no—
1685C23—684no—
1686C23—684no—
1687C23—684no—
1688C23—684no—
1689C23—684no—
1690C23—684no—
1691C23—684no—
1692C23—684no—
1693C23—684no—
1694C23—684no—
1695C23—684no—
1696C23—684no—
1697C23—684no—
1698C23—684no—
1699C23C2×D4×D1712yes—
1700C23#41×D1712yes—
1701C23C24×D1711yescharacteristic
1702Q8—44no—
1703Q8—684no—
1704Q8—684no—
1705Q8—684no—
1706D4—28no—
1707D4—44no—
1708D4—44no—
1709D4—348no—
1710D4—348no—
1711D4—348no—
1712D4—684no—
1713D4—684no—
1714D4—684no—
1715D4—684no—
1716D4—684no—
1717D4—684no—
1718C2×C4—21no—
1719C2×C4—21no—
1720C2×C4—21no—
1721C2×C4—21no—
1722C2×C4—21no—
1723C2×C4—21no—
1724C2×C4—21no—
1725C2×C4—21no—
1726C2×C4—21no—
1727C2×C4—21no—
1728C2×C4—21no—
1729C2×C4—21no—
1730C2×C4—21no—
1731C2×C4—21no—
1732C2×C4—21no—
1733C2×C4—21no—
1734C2×C4—21no—
1735C2×C4—21no—
1736C2×C4—21no—
1737C2×C4—21no—
1738C2×C4—21no—
1739C2×C4—21no—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—44no—
1748C2×C4—44no—
1749C2×C4—172no—
1750C2×C4—172no—
1751C2×C4—172no—
1752C2×C4—172no—
1753C2×C4—172no—
1754C2×C4—172no—
1755C2×C4—172no—
1756C2×C4—348no—
1757C2×C4—348no—
1758C2×C4—348no—
1759C2×C4—348no—
1760C2×C4—348no—
1761C2×C4—348no—
1762C2×C4—348no—
1763C2×C4—341no—
1764C2×C4—341no—
1765C2×C4—341no—
1766C2×C4—341no—
1767C2×C4—341no—
1768C2×C4—341no—
1769C2×C4—341no—
1770C2×C4—341no—
1771C2×C4—341no—
1772C2×C4—341no—
1773C2×C4—341no—
1774C2×C4—341no—
1775C2×C4—341no—
1776C2×C4—341no—
1777C2×C4—341no—
1778C2×C4—341no—
1779C2×C4—341no—
1780C2×C4—341no—
1781C2×C4—341no—
1782C2×C4—341no—
1783C2×C4—341no—
1784C2×C4—341no—
1785C2×C4—341no—
1786C2×C4—341no—
1787C2×C4—341no—
1788C2×C4—341no—
1789C2×C4—341no—
1790C2×C4—341no—
1791C2×C4—341no—
1792C2×C4—684no—
1793C2×C4—684no—
1794C2×C4—684no—
1795C2×C4—684no—
1796C2×C4—684no—
1797C2×C4—684no—
1798C2×C4—684no—
1799C2×C4—684no—
1800C2×C4—684no—
1801C2×C4—684no—
1802C2×C4—684no—
1803C2×C4C2×D4×D1712yes—
1804C2×C4C2×D4×D1712yes—
1805C2×C4C2×D4×D1712yes—
1806C2×C4C2×D4×D1712yes—
1807C2×C4C2×D4×D1712yes—
1808C2×C4#41×D1712yes—
1809C2×C4#41×D1712yes—
1810C22—22no—
1811C22—22no—
1812C22—22no—
1813C22—22no—
1814C22—22no—
1815C22—22no—
1816C22—41no—
1817C22—41no—
1818C22—41no—
1819C22—41no—
1820C22—41no—
1821C22—41no—
1822C22—41no—
1823C22—41no—
1824C22—41no—
1825C22—41no—
1826C22—41no—
1827C22—41no—
1828C22—41no—
1829C22—41no—
1830C22—41no—
1831C22—174no—
1832C22—174no—
1833C22—174no—
1834C22—174no—
1835C22—174no—
1836C22—174no—
1837C22—174no—
1838C22—342no—
1839C22—342no—
1840C22—342no—
1841C22—342no—
1842C22—342no—
1843C22—342no—
1844C22—6816no—
1845C22—6816no—
1846C22—681no—
1847C22—681no—
1848C22—681no—
1849C22—681no—
1850C22—681no—
1851C22—681no—
1852C22—681no—
1853C22—681no—
1854C22—681no—
1855C22—681no—
1856C22—681no—
1857C22—681no—
1858C22—681no—
1859C22—681no—
1860C22—681no—
1861C22—1368no—
1862C22C22×D4×D1711yescharacteristic
1863C22C22×D4×D1711yescharacteristic
1864C22C2×#41×D1711yescharacteristic
1865C22C2×#41×D1711yescharacteristic
1866C22C2×#41×D1711yescharacteristic
1867C22H(5,𝔽2)×D1711yescharacteristic
1868C222−1+4×D1711yescharacteristic
1869C4—22no—
1870C4—22no—
1871C4—22no—
1872C4—22no—
1873C4—22no—
1874C4—22no—
1875C4—22no—
1876C4—41no—
1877C4—41no—
1878C4—41no—
1879C4—41no—
1880C4—41no—
1881C4—342no—
1882C4—342no—
1883C4—342no—
1884C4—342no—
1885C4—342no—
1886C4—342no—
1887C4—342no—
1888C4—681no—
1889C4—681no—
1890C4—681no—
1891C4—681no—
1892C4—681no—
1893C2—42no—
1894C2—42no—
1895C2—81no—
1896C2—178no—
1897C2—682no—
1898C2—682no—
1899C2—1361no—
1900C2D17×#52511yescharacteristic
1901C2D17×#53211yescharacteristic
1902C2D17×#54211yescharacteristic
1903C2D42×D1711yescharacteristic
1904C2D17×#54711yescharacteristic
1905C2D17×#54811yescharacteristic
1906C2D17×#55111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2461C2
prime radicalD17×#392C2
hypercenter#2461D17
hypocenterC17C2×#2461
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2461

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#124×D17C2semidirect
2. C2×#123×D17C2semidirect
3. C2×C22⋊Q8×D17C2semidirect
4. C2×C4×D4×D17C2semidirect
5. #14532758C2semidirect
6. #14532757C2semidirect
7. #14532756C2semidirect
8. #14532755C2semidirect
9. #14532754C2semidirect
10. #14532753C2semidirect
11. #14532752C2semidirect
12. #14532751C2semidirect
13. #14532750C2semidirect
14. #14532749C2semidirect
15. #14532748C2semidirect
16. #14532747C2semidirect
17. #14532746C2semidirect
18. #14532745C2semidirect
19. #14532744C2semidirect
20. D17×#396C2semidirect
21. D17×#395C2semidirect
22. D17×#394C2semidirect
24. D17×#390C2semidirect
25. D17×#388C2semidirect
26. D17×#388C2semidirect
27. D17×#388C2semidirect
28. D17×#386C2semidirect
29. D17×#385C2semidirect
30. C4×C4⋊C4×D17C2semidirect
31. C17×#2461C2semidirect
38. C2×#10587633C22semidirect
39. C2×#10587561C22semidirect
40. C2×#10587622C22semidirect
41. C2×#10587571C22semidirect
42. C2×#10587571C22semidirect
43. C2×#10587571C22semidirect
44. C2×#10587571C22semidirect
46. C2×#10587580C22semidirect
47. C2×#10587580C22semidirect
48. C2×#10587572C22semidirect
49. C2×#10587615C22semidirect
50. C2×#10587569C22semidirect
51. C2×#10587569C22semidirect
52. C2×#10587621C22semidirect
54. C2×#10587583C22semidirect
55. C2×#10587610C22semidirect
56. C2×#10587582C22semidirect
57. C2×#10587582C22semidirect
58. C2×#10587564C22semidirect
59. C2×#10587564C22semidirect
60. C2×#10587632C22semidirect
62. C2×C4×D68C22semidirect
63. C2×D4×Dic17C22semidirect
64. C2×#10587579C22semidirect
65. C2×C4×C22⋊D17C22semidirect
66. C2×C4×C22⋊D17C22semidirect
67. C2×#10587567C22semidirect
68. C2×#10587567C22semidirect
93. #11762733C22semidirect
94. #11762732C22semidirect
95. #11762732C22semidirect
96. #11762732C22semidirect
97. #11762731C22semidirect
98. #11762731C22semidirect
99. #11762731C22semidirect
100. #11762730C22semidirect
101. #11762730C22semidirect
102. #11762730C22semidirect
103. #11762729C22semidirect
104. #11762729C22semidirect
105. #11762729C22semidirect
106. #11762728C22semidirect
107. #11762727C22semidirect
108. #11762726C22semidirect
109. #11762725C22semidirect
110. #11762725C22semidirect
111. #11762724C22semidirect
112. #11762724C22semidirect
113. #11762723C22semidirect
121. #11762712C22semidirect
122. #11762711C22semidirect
123. #11762710C22semidirect
124. #11762709C22semidirect
125. #11762709C22semidirect
126. #11762709C22semidirect
127. #11762709C22semidirect
128. #11762703C22semidirect
129. #11762703C22semidirect
130. #11762703C22semidirect
131. #11762702C22semidirect
132. #11762702C22semidirect
133. #11762702C22semidirect
134. #11762701C22semidirect
135. #11762701C22semidirect
136. #11762701C22semidirect
137. #11762700C22semidirect
138. #11762700C22semidirect
139. #11762700C22semidirect
140. #11762699C22semidirect
141. #11762699C22semidirect
142. #11762699C22semidirect
143. #11762698C22semidirect
144. #11762698C22semidirect
145. #11762698C22semidirect
146. #11762697C22semidirect
147. #11762697C22semidirect
148. #11762697C22semidirect
149. #11762689C22semidirect
150. #11762688C22semidirect
151. #11762687C22semidirect
152. #11762687C22semidirect
153. #11762686C22semidirect
154. #11762685C22semidirect
155. #11762685C22semidirect
156. #11762684C22semidirect
157. #11762683C22semidirect
158. #11762683C22semidirect
159. #11762682C22semidirect
160. #11762681C22semidirect
161. #11762680C22semidirect
162. #11762680C22semidirect
163. C4⋊C4×Dic17C22semidirect
164. C4⋊C4×Dic17C22semidirect
165. C4×#63225C22semidirect
166. C4×#63225C22semidirect
167. C4×C4⋊Dic17C22semidirect
168. #11762660C22semidirect
169. #11762660C22semidirect
176. C2×C17×#124C22semidirect
177. C2×C17×#123C22semidirect
178. C2×C17×C22⋊Q8C22semidirect
179. C2×C4×D4×C17C22semidirect
180. C17×#396C22semidirect
181. C17×#395C22semidirect
182. C17×#394C22semidirect
184. C17×#390C22semidirect
185. C17×#388C22semidirect
186. C17×#388C22semidirect
187. C17×#388C22semidirect
188. C17×#386C22semidirect
189. C17×#385C22semidirect
190. C4×C4⋊C4×C17C22semidirect
365. C4⋊C4×D17D4semidirect
387. C22⋊C4×D17D4semidirect
591. C4⋊C4×C17C2×D4semidirect
604. C22⋊C4×C17C2×D4semidirect
620. C22⋊Dic17C2×D4semidirect
645. #63227C2×D4semidirect
646. #63227C2×D4semidirect
653. C4⋊Dic17C2×D4semidirect
666. #63225C2×D4semidirect
667. #63225C2×D4semidirect
876. #2461D17direct (N × H)
985. C2×#124C2×D17semidirect
994. C2×#123C2×D17semidirect
1003. C2×C22⋊Q8C2×D17semidirect
1012. C2×C4×D4C2×D17semidirect
1043. #396C2×D17semidirect
1051. #395C2×D17semidirect
1059. #394C2×D17semidirect
1075. #390C2×D17semidirect
1097. #388C2×D17semidirect
1098. #388C2×D17semidirect
1099. #388C2×D17semidirect
1107. #386C2×D17semidirect
1115. #385C2×D17semidirect
1123. C4×C4⋊C4C2×D17semidirect
1143. D17#2461direct (N × H)
1372. C17C2×#2461semidirect
1566. C4⋊C4D4×D17semidirect
1618. C22⋊C4D4×D17semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#124×D172
C2×#123×D172
C2×C22⋊Q8×D172
C2×C4×D4×D172
#145327582
#145327572
#145327562
#145327552
#145327542
#145327532
#145327522
#145327512
#145327502
#145327492
#145327482
#145327472
#145327462
#145327452
#145327442
D17×#3962
D17×#3952
D17×#3942
D17×#3922
D17×#3902
D17×#3882
D17×#3862
D17×#3852
C4×C4⋊C4×D172
C17×#24612
C2×#246117