Finite Group Databasebeta

← D17×#2602 #17205709

Subgroups — D17×#2602 #17205709

Order 4352.

3330 conjugacy classes of subgroups.

The subgroup lattice has 1822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×D17C211yesmaximal, characteristic, complemented
2C2×C4×D4×D17C211yesmaximal, characteristic, complemented
3#14534403C211yesmaximal, characteristic, complemented
4#14534402C211yesmaximal, characteristic, complemented
5#14534401C211yesmaximal, characteristic, complemented
6#14534400C211yesmaximal, characteristic, complemented
7#14534399C211yesmaximal, characteristic, complemented
8#14534398C211yesmaximal, characteristic, complemented
9#14534397C211yesmaximal, characteristic, complemented
10#14534396C211yesmaximal, characteristic, complemented
11#14534395C211yesmaximal, characteristic, complemented
12#14534394C211yesmaximal, characteristic, complemented
13#14534393C211yesmaximal, characteristic, complemented
14#14534392C211yesmaximal, characteristic, complemented
15#14534391C211yesmaximal, characteristic, complemented
16#14534390C211yesmaximal, characteristic, complemented
17#14534389C211yesmaximal, characteristic, complemented
18D17×#397C211yesmaximal, characteristic, complemented
19D17×#394C211yesmaximal, characteristic, complemented
20D17×#394C211yesmaximal, characteristic, complemented
21D17×#392C211yesmaximal, characteristic
22D17×#390C211yesmaximal, characteristic, complemented
23D17×#389C211yesmaximal, characteristic, complemented
24D17×#388C211yesmaximal, characteristic, complemented
25D17×#388C211yesmaximal, characteristic, complemented
26D17×#388C211yesmaximal, characteristic, complemented
27D17×#387C211yesmaximal, characteristic, complemented
28D17×#386C211yesmaximal, characteristic, complemented
29D17×#385C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2602C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C22×D4×D17C2211yescharacteristic
34C22×D4×D17C2211yescharacteristic
35C23×C4×D17C2211yescharacteristic
36C23×C4×D17C2211yescharacteristic
37C2×#10587580C2211yescharacteristic, complemented
38C2×#10587580C2211yescharacteristic, complemented
39C2×#10587572C2211yescharacteristic, complemented
40C2×#10587615C2211yescharacteristic, complemented
41C2×#10587569C2211yescharacteristic, complemented
42C2×#10587569C2211yescharacteristic, complemented
43C2×#10587621C2211yescharacteristic, complemented
44#123×D17—28no—
45C2×C4×D68C2211yescharacteristic, complemented
46C2×D4×Dic17C2211yescharacteristic, complemented
47C2×#10587579C2211yescharacteristic, complemented
48C2×C4×C22⋊D17C2211yescharacteristic, complemented
49C2×C4×C22⋊D17C2211yescharacteristic, complemented
50C2×#10587567C2211yescharacteristic, complemented
51C2×#10587567C2211yescharacteristic, complemented
52C4×D4×D17—28no—
53C2×C4⋊C4×D17C2211yescharacteristic
54C2×C4⋊C4×D17C2211yescharacteristic
55C2×C4⋊C4×D17C2211yescharacteristic
56C2×C4⋊C4×D17C2211yescharacteristic
57C2×C4⋊C4×D17C2211yescharacteristic
58C2×C4⋊C4×D17C2211yescharacteristic
59C2×C22⋊C4×D17C2211yescharacteristic
60C2×C22⋊C4×D17C2211yescharacteristic
61C2×C22⋊C4×D17C2211yescharacteristic
62C2×C22⋊C4×D17C2211yescharacteristic
63C2×C22⋊C4×D17C2211yescharacteristic
64C2×C22⋊C4×D17C2211yescharacteristic
65C2×C22⋊C4×D17C2211yescharacteristic
66C2×C22⋊C4×D17C2211yescharacteristic
67C2×C22⋊C4×D17C2211yescharacteristic
68C2×C22⋊C4×D17C2211yescharacteristic
69C2×C22⋊C4×D17C2211yescharacteristic
70C2×C22⋊C4×D17C2211yescharacteristic
71C2×C22⋊C4×D17C2211yescharacteristic
72C2×C42×D17C2211yescharacteristic
73C2×C42×D17C2211yescharacteristic
74C2×C42×D17C2211yescharacteristic
75#11762738C2211yescharacteristic, complemented
76#11762738C2211yescharacteristic, complemented
77#11762737C2211yescharacteristic, complemented
78#11762737C2211yescharacteristic, complemented
79#11762736C2211yescharacteristic, complemented
80#11762735C2211yescharacteristic, complemented
81#11762734C2211yescharacteristic, complemented
82#11762727C2211yescharacteristic, complemented
83#11762727C2211yescharacteristic, complemented
84#11762726C2211yescharacteristic, complemented
85#11762726C2211yescharacteristic, complemented
86#11762725C2211yescharacteristic, complemented
87#11762725C2211yescharacteristic, complemented
88#11762725C2211yescharacteristic, complemented
89#11762725C2211yescharacteristic, complemented
90#11762724C2211yescharacteristic, complemented
91#11762724C2211yescharacteristic, complemented
92#11762724C2211yescharacteristic, complemented
93#11762724C2211yescharacteristic, complemented
94#11762723C2211yescharacteristic, complemented
95#11762723C2211yescharacteristic, complemented
96#11762719C2211yescharacteristic
97#11762718C2211yescharacteristic
98#11762718C2211yescharacteristic
99#11762718C2211yescharacteristic
100#11762717C2211yescharacteristic
101#11762717C2211yescharacteristic
102#11762717C2211yescharacteristic
103#11762712C2211yescharacteristic, complemented
104#11762711C2211yescharacteristic, complemented
105#11762710C2211yescharacteristic, complemented
106#11762709C2211yescharacteristic, complemented
107#11762709C2211yescharacteristic, complemented
108#11762709C2211yescharacteristic, complemented
109#11762709C2211yescharacteristic, complemented
110#11762708C2211yescharacteristic, complemented
111#11762707C2211yescharacteristic, complemented
112#11762706C2211yescharacteristic, complemented
113#11762706C2211yescharacteristic, complemented
114#11762705C2211yescharacteristic, complemented
115#11762704C2211yescharacteristic, complemented
116#11762704C2211yescharacteristic, complemented
117#11762703C2211yescharacteristic, complemented
118#11762703C2211yescharacteristic, complemented
119#11762703C2211yescharacteristic, complemented
120#11762702C2211yescharacteristic, complemented
121#11762702C2211yescharacteristic, complemented
122#11762702C2211yescharacteristic, complemented
123#11762701C2211yescharacteristic, complemented
124#11762701C2211yescharacteristic, complemented
125#11762701C2211yescharacteristic, complemented
126#11762700C2211yescharacteristic, complemented
127#11762700C2211yescharacteristic, complemented
128#11762700C2211yescharacteristic, complemented
129#11762699C2211yescharacteristic, complemented
130#11762699C2211yescharacteristic, complemented
131#11762699C2211yescharacteristic, complemented
132#11762698C2211yescharacteristic, complemented
133#11762698C2211yescharacteristic, complemented
134#11762698C2211yescharacteristic, complemented
135#11762697C2211yescharacteristic, complemented
136#11762697C2211yescharacteristic, complemented
137#11762697C2211yescharacteristic, complemented
138#11762696C2211yescharacteristic, complemented
139#11762695C2211yescharacteristic, complemented
140#11762694C2211yescharacteristic, complemented
141#11762693C2211yescharacteristic, complemented
142#11762692C2211yescharacteristic, complemented
143#11762691C2211yescharacteristic, complemented
144#11762690C2211yescharacteristic, complemented
145#11762689C2211yescharacteristic, complemented
146#11762688C2211yescharacteristic, complemented
147#11762687C2211yescharacteristic, complemented
148#11762687C2211yescharacteristic, complemented
149#11762686C2211yescharacteristic, complemented
150#11762685C2211yescharacteristic, complemented
151#11762685C2211yescharacteristic, complemented
152#11762684C2211yescharacteristic, complemented
153#11762683C2211yescharacteristic, complemented
154#11762683C2211yescharacteristic, complemented
155#11762682C2211yescharacteristic, complemented
156#11762681C2211yescharacteristic, complemented
157#11762680C2211yescharacteristic, complemented
158#11762680C2211yescharacteristic, complemented
159C22⋊C4×Dic17C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C4×#63227C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×C22⋊Dic17C2211yescharacteristic, complemented
164#11762656C2211yescharacteristic, complemented
165#11762656C2211yescharacteristic, complemented
166#95×D17C2211yescharacteristic
167#95×D17C2211yescharacteristic
168#95×D17C2211yescharacteristic
169#95×D17C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172#95×D17C2211yescharacteristic
173#95×D17C2211yescharacteristic
174C2×C17×#123C2211yescharacteristic, complemented
175C2×C4×D4×C17C2211yescharacteristic, complemented
176C17×#397C2211yescharacteristic, complemented
177C17×#394C2211yescharacteristic, complemented
178C17×#394C2211yescharacteristic, complemented
179C17×#392C2211yescharacteristic
180C17×#390C2211yescharacteristic, complemented
181C17×#389C2211yescharacteristic, complemented
182C17×#388C2211yescharacteristic, complemented
183C17×#388C2211yescharacteristic, complemented
184C17×#388C2211yescharacteristic, complemented
185C17×#387C2211yescharacteristic, complemented
186C17×#386C2211yescharacteristic, complemented
187C17×#385C2211yescharacteristic, complemented
188C4×C22⋊C4×C17C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C24×D17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C2×D4×D17—24no—
206C2×D4×D17—24no—
207C2×D4×D17—24no—
208C2×D4×D17—24no—
209C2×D4×D17—24no—
210C2×D4×D17—24no—
211C2×D4×D17—42no—
212C2×D4×D17—42no—
213C2×D4×D17—42no—
214C22×D68C2311yescharacteristic
215C22×D68C2311yescharacteristic
216C22×D68C2311yescharacteristic
217C22×C4×D17—24no—
218C22×C4×D17—42no—
219C22×C4×D17—42no—
220C22×C4×D17—42no—
221C22×C4×D17—42no—
222C22×C4×D17D418yescomplemented
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
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
239C17×#123—24no—
240C4×D4×C17—24no—
241C2×C4⋊C4×C17C2311yescharacteristic
242C2×C4⋊C4×C17C2311yescharacteristic
243C2×C4⋊C4×C17C2311yescharacteristic
244C2×C4⋊C4×C17C2311yescharacteristic
245C2×C4⋊C4×C17C2311yescharacteristic
246C2×C4⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C22⋊C4×C17C2311yescharacteristic
252C2×C22⋊C4×C17C2311yescharacteristic
253C2×C22⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17C2311yescharacteristic
255C2×C22⋊C4×C17C2311yescharacteristic
256C2×C22⋊C4×C17C2311yescharacteristic
257C2×C22⋊C4×C17C2311yescharacteristic
258C2×C22⋊C4×C17C2311yescharacteristic
259C2×C22⋊C4×C17C2311yescharacteristic
260C2×C42×C17C2311yescharacteristic
261C2×C42×C17C2311yescharacteristic
262C2×C42×C17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276#10587621—24no—
277D4×Dic17—24no—
278#10587615—24no—
279C4×C22⋊D17—24no—
280C4×C22⋊D17—24no—
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×#63227C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×C4⋊Dic17C2311yescharacteristic
310C2×C4⋊Dic17C2311yescharacteristic
311C2×C4⋊Dic17C2311yescharacteristic
312C2×C4⋊Dic17C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334#10587580—24no—
335#10587580—24no—
336#10587579—24no—
337C4⋊C4×D17—24no—
338C4⋊C4×D17—24no—
339C4⋊C4×D17—24no—
340C4⋊C4×D17—24no—
341C4⋊C4×D17—24no—
342C4⋊C4×D17—42no—
343#10587572—24no—
344#10587569—24no—
345#10587569—24no—
346#10587567—24no—
347#10587567—24no—
348C22⋊C4×D17—24no—
349C22⋊C4×D17—24no—
350C22⋊C4×D17—24no—
351C22⋊C4×D17—24no—
352C22⋊C4×D17—24no—
353C22⋊C4×D17—24no—
354C22⋊C4×D17—24no—
355C22⋊C4×D17—24no—
356C22⋊C4×D17—24no—
357C22⋊C4×D17—24no—
358C22⋊C4×D17—24no—
359C22⋊C4×D17—42no—
360C22⋊C4×D17—42no—
361C4×D68—24no—
362C42×D17—24no—
363C42×D17—42no—
364C42×D17—42no—
365C17×#95C2311yescharacteristic
366C17×#95C2311yescharacteristic
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
369C17×#95C2311yescharacteristic
370C17×#95C2311yescharacteristic
371C17×#95C2311yescharacteristic
372C17×#95C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391#10587502C2311yescharacteristic
392#10587502C2311yescharacteristic
393#10587502C2311yescharacteristic
394#10587502C2311yescharacteristic
395#10587502C2311yescharacteristic
396#10587502C2311yescharacteristic
397C24×C17C2411yescharacteristic
398C24×C17C2411yescharacteristic
399C24×C17C2411yescharacteristic
400C23×D17—22no—
401C23×D17—22no—
402C23×D17—22no—
403C23×D17—22no—
404C23×D17—22no—
405C23×D17—22no—
406C23×D17—22no—
407C23×D17—22no—
408C23×D17—22no—
409C23×D17—22no—
410C23×D17—22no—
411C23×D17—22no—
412C23×D17—22no—
413C23×D17—22no—
414C23×D17—22no—
415C23×D17—22no—
416C23×D17—22no—
417C23×D17—22no—
418C23×D17—22no—
419C23×D17C2×D414yes—
420C23×D17#4114yes—
421C23×D17C2411yescharacteristic
422C23×D17C2411yescharacteristic
423C23×D17C2411yescharacteristic
424C23×D17C2411yescharacteristic
425C2×D4×C17—22no—
426C2×D4×C17—22no—
427C2×D4×C17—22no—
428C2×D4×C17—22no—
429C2×D4×C17—22no—
430C2×D4×C17—22no—
431C2×D4×C17—41no—
432C2×D4×C17—41no—
433C2×D4×C17—41no—
434C22×C4×C17—22no—
435C22×C4×C17—41no—
436C22×C4×C17—41no—
437C22×C4×C17—41no—
438C22×C4×C17—41no—
439C22×C4×C17C2×D414yescomplemented
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C22×C4×C17C2411yescharacteristic
444C22×C4×C17C2411yescharacteristic
445C22×C4×C17C2411yescharacteristic
446C22×C4×C17C2411yescharacteristic
447C22×C4×C17C2411yescharacteristic
448C22×C4×C17C2411yescharacteristic
449C22×C4×C17C2411yescharacteristic
450C22×C4×C17C2411yescharacteristic
451C22×C4×C17C2411yescharacteristic
452C2×C22⋊D17—22no—
453C2×C22⋊D17—22no—
454C2×C22⋊D17—22no—
455C2×C22⋊D17—22no—
456C2×C22⋊D17—22no—
457C2×C22⋊D17—22no—
458C2×C22⋊D17—22no—
459C2×C22⋊D17—22no—
460C2×C22⋊D17—22no—
461C2×C22⋊D17—22no—
462C2×C22⋊D17—22no—
463C2×C22⋊D17—22no—
464C2×C22⋊D17—41no—
465C2×C22⋊D17—41no—
466C2×C22⋊D17—41no—
467C2×C22⋊D17—41no—
468C2×C22⋊D17—41no—
469C2×C22⋊D17—41no—
470C22×Dic17—22no—
471C22×Dic17—41no—
472C22×Dic17—41no—
473C22×Dic17—41no—
474C22×Dic17—41no—
475C22×Dic17C2×D414yescomplemented
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488D4×D17—232no—
489D4×D17—416no—
490D4×D17—416no—
491C2×D68—22no—
492C2×D68—22no—
493C2×D68—22no—
494C2×D68—22no—
495C2×D68—22no—
496C2×D68—22no—
497C2×D68—41no—
498C2×D68—41no—
499C2×D68—41no—
500C2×C4×D17—22no—
501C2×C4×D17—22no—
502C2×C4×D17—22no—
503C2×C4×D17—22no—
504C2×C4×D17—22no—
505C2×C4×D17—22no—
506C2×C4×D17—22no—
507C2×C4×D17—22no—
508C2×C4×D17—22no—
509C2×C4×D17—22no—
510C2×C4×D17—22no—
511C2×C4×D17—22no—
512C2×C4×D17—22no—
513C2×C4×D17—22no—
514C2×C4×D17—22no—
515C2×C4×D17—22no—
516C2×C4×D17—22no—
517C2×C4×D17—22no—
518C2×C4×D17—22no—
519C2×C4×D17—22no—
520C2×C4×D17—22no—
521C2×C4×D17—22no—
522C2×C4×D17—22no—
523C2×C4×D17—22no—
524C2×C4×D17—22no—
525C2×C4×D17—22no—
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—416no—
534C2×C4×D17—416no—
535C2×C4×D17—41no—
536C2×C4×D17—41no—
537C2×C4×D17—41no—
538C2×C4×D17—41no—
539C2×C4×D17—41no—
540C2×C4×D17—41no—
541C2×C4×D17—41no—
542C2×C4×D17—41no—
543C2×C4×D17C2×D414yes—
544C2×C4×D17C2×D414yes—
545C2×C4×D17C2×D414yescomplemented
546C2×C4×D17C2×D414yescomplemented
547C2×C4×D17#4114yes—
548C2×C4×D17#4114yes—
549C2×C4×D17#4114yes—
550C4⋊C4×C17—22no—
551C4⋊C4×C17—22no—
552C4⋊C4×C17—22no—
553C4⋊C4×C17—22no—
554C4⋊C4×C17—22no—
555C4⋊C4×C17—41no—
556C22⋊C4×C17—22no—
557C22⋊C4×C17—22no—
558C22⋊C4×C17—22no—
559C22⋊C4×C17—22no—
560C22⋊C4×C17—22no—
561C22⋊C4×C17—22no—
562C22⋊C4×C17—22no—
563C22⋊C4×C17—22no—
564C22⋊C4×C17—22no—
565C22⋊C4×C17—22no—
566C22⋊C4×C17—22no—
567C22⋊C4×C17—41no—
568C22⋊C4×C17—41no—
569C42×C17—22no—
570C42×C17—41no—
571C42×C17—41no—
572C22⋊Dic17—22no—
573C22⋊Dic17—22no—
574C22⋊Dic17—22no—
575C22⋊Dic17—22no—
576C22⋊Dic17—22no—
577C22⋊Dic17—22no—
578C22⋊Dic17—22no—
579C22⋊Dic17—22no—
580C22⋊Dic17—22no—
581C22⋊Dic17—22no—
582C22⋊Dic17—22no—
583C22⋊Dic17—41no—
584C22⋊Dic17—41no—
585#63227—22no—
586#63227—22no—
587#63227—22no—
588#63227—22no—
589#63227—22no—
590#63227—22no—
591#63227—22no—
592#63227—22no—
593#63227—22no—
594#63227—22no—
595#63227—22no—
596#63227—22no—
597#63227—22no—
598#63227—22no—
599#63227—22no—
600#63227—22no—
601#63227—22no—
602#63227—22no—
603#63227—22no—
604#63227—22no—
605#63227—22no—
606#63227—22no—
607#63227—41no—
608#63227—41no—
609#63227—41no—
610#63227—41no—
611C4⋊Dic17—22no—
612C4⋊Dic17—22no—
613C4⋊Dic17—22no—
614C4⋊Dic17—22no—
615C4⋊Dic17—22no—
616C4⋊Dic17—41no—
617#63225—22no—
618#63225—22no—
619#63225—22no—
620#63225—22no—
621#63225—22no—
622#63225—22no—
623#63225—22no—
624#63225—22no—
625#63225—22no—
626#63225—22no—
627#63225—41no—
628#63225—41no—
629C4×Dic17—22no—
630C4×Dic17—22no—
631C4×Dic17—22no—
632C4×Dic17—41no—
633C4×Dic17—41no—
634C4×Dic17—41no—
635C4×Dic17—41no—
636C4×Dic17—41no—
637C4×Dic17—41no—
638C2×#2602—171nomaximal, Sylow
639C23×C17—21no—
640C23×C17—21no—
641C23×C17—21no—
642C23×C17—21no—
643C23×C17—21no—
644C23×C17—21no—
645C23×C17—21no—
646C23×C17—21no—
647C23×C17—21no—
648C23×C17—21no—
649C23×C17—21no—
650C23×C17—21no—
651C23×C17—21no—
652C23×C17—21no—
653C23×C17—21no—
654C23×C17—21no—
655C23×C17—21no—
656C23×C17—21no—
657C23×C17—21no—
658C23×C17C22×D412yes—
659C23×C17C2×#4112yes—
660C23×C17C2511yescharacteristic
661C22×D17—21no—
662C22×D17—21no—
663C22×D17—21no—
664C22×D17—21no—
665C22×D17—21no—
666C22×D17—21no—
667C22×D17—21no—
668C22×D17—21no—
669C22×D17—21no—
670C22×D17—21no—
671C22×D17—21no—
672C22×D17—21no—
673C22×D17—28no—
674C22×D17—28no—
675C22×D17—28no—
676C22×D17—28no—
677C22×D17—28no—
678C22×D17—28no—
679C22×D17—21no—
680C22×D17—21no—
681C22×D17—21no—
682C22×D17—21no—
683C22×D17—21no—
684C22×D17—21no—
685C22×D17—21no—
686C22×D17—44no—
687C22×D17—44no—
688C22×D17—44no—
689C22×D17—44no—
690C22×D17—44no—
691C22×D17—44no—
692C22×D17—44no—
693C22×D17—44no—
694C22×D17—44no—
695C22×D17—44no—
696C22×D17—44no—
697C22×D17—44no—
698C22×D17—44no—
699C22×D17—44no—
700C22×D17—44no—
701C22×D17C22×D412yes—
702C22×D17C22×D412yes—
703C22×D17C2×#4112yes—
704C22×D17C2×#4112yes—
705C22×D17C2×#4112yes—
706C22×D17C2×#4112yes—
707C22×D17C2×#4112yes—
708C22×D17H(5,𝔽2)12yes—
709C22×D17H(5,𝔽2)12yes—
710D4×C17—28no—
711D4×C17—44no—
712D4×C17—44no—
713C2×C4×C17—21no—
714C2×C4×C17—21no—
715C2×C4×C17—21no—
716C2×C4×C17—21no—
717C2×C4×C17—21no—
718C2×C4×C17—21no—
719C2×C4×C17—21no—
720C2×C4×C17—21no—
721C2×C4×C17—21no—
722C2×C4×C17—21no—
723C2×C4×C17—21no—
724C2×C4×C17—21no—
725C2×C4×C17—21no—
726C2×C4×C17—21no—
727C2×C4×C17—21no—
728C2×C4×C17—21no—
729C2×C4×C17—21no—
730C2×C4×C17—21no—
731C2×C4×C17—21no—
732C2×C4×C17—21no—
733C2×C4×C17—21no—
734C2×C4×C17—21no—
735C2×C4×C17—21no—
736C2×C4×C17—21no—
737C2×C4×C17—21no—
738C2×C4×C17—21no—
739C2×C4×C17—21no—
740C2×C4×C17—21no—
741C2×C4×C17—21no—
742C2×C4×C17—21no—
743C2×C4×C17—21no—
744C2×C4×C17—44no—
745C2×C4×C17—44no—
746C2×C4×C17C22×D412yes—
747C2×C4×C17C22×D412yes—
748C2×C4×C17C2×#4112yes—
749C2×C4×C17C2×#4112yes—
750C2×C4×C17C2×#4112yes—
751C22⋊D17—28no—
752C22⋊D17—28no—
753C22⋊D17—44no—
754C22⋊D17—44no—
755C22⋊D17—44no—
756C22⋊D17—44no—
757C2×Dic17—21no—
758C2×Dic17—21no—
759C2×Dic17—21no—
760C2×Dic17—21no—
761C2×Dic17—21no—
762C2×Dic17—21no—
763C2×Dic17—21no—
764C2×Dic17—21no—
765C2×Dic17—21no—
766C2×Dic17—21no—
767C2×Dic17—21no—
768C2×Dic17—21no—
769C2×Dic17—21no—
770C2×Dic17—21no—
771C2×Dic17—21no—
772C2×Dic17—21no—
773C2×Dic17—21no—
774C2×Dic17—21no—
775C2×Dic17—21no—
776C2×Dic17—21no—
777C2×Dic17—21no—
778C2×Dic17—21no—
779C2×Dic17—21no—
780C2×Dic17—21no—
781C2×Dic17—21no—
782C2×Dic17—21no—
783C2×Dic17—21no—
784C2×Dic17—21no—
785C2×Dic17—21no—
786C2×Dic17—21no—
787C2×Dic17—21no—
788C2×Dic17—44no—
789C2×Dic17—44no—
790C2×Dic17C22×D412yes—
791C2×Dic17C22×D412yes—
792C2×Dic17C2×#4112yes—
793C2×Dic17C2×#4112yes—
794C2×Dic17C2×#4112yes—
795D68—28no—
796D68—44no—
797D68—44no—
798C4×D17—28no—
799C4×D17—28no—
800C4×D17—28no—
801C4×D17—28no—
802C4×D17—28no—
803C4×D17—44no—
804C4×D17—44no—
805C4×D17—44no—
806C4×D17—44no—
807C4×D17—44no—
808C4×D17—44no—
809C4×D17—44no—
810C4×D17—44no—
811C4×D17—44no—
812C4×D17—44no—
813C4×D17—44no—
814C22×#123—171no—
815C22×C4×D4—171no—
816#2602—171no—
817#2602—171no—
818#2602—171no—
819#2602—171no—
820#2602—171no—
821#2602—171no—
822#2602—171no—
823#2602—171no—
824#2602—171no—
825#2602—171no—
826#2602—171no—
827#2602—171no—
828#2602—171no—
829#2602—171no—
830#2602—171no—
831#2602D1711yescharacteristic, direct product factor
832C2×#397—171no—
833C2×#394—171no—
834C2×#394—171no—
835C2×#392—171no—
836C2×#390—171no—
837C2×#389—171no—
838C2×#388—171no—
839C2×#388—171no—
840C2×#388—171no—
841C2×#387—171no—
842C2×#386—171no—
843C2×#385—171no—
844C2×C4×C22⋊C4—171no—
845C22×C17—22no—
846C22×C17—22no—
847C22×C17—22no—
848C22×C17—22no—
849C22×C17—22no—
850C22×C17—22no—
851C22×C17—41no—
852C22×C17—41no—
853C22×C17—41no—
854C22×C17—41no—
855C22×C17—41no—
856C22×C17—41no—
857C22×C17—41no—
858C22×C17—41no—
859C22×C17—41no—
860C22×C17—41no—
861C22×C17—41no—
862C22×C17—41no—
863C22×C17—41no—
864C22×C17—41no—
865C22×C17—41no—
866C22×C17C23×D411yescharacteristic
867C22×C17C22×#4111yescharacteristic
868C22×C17C22×#4111yescharacteristic
869C22×C17C22×#4111yescharacteristic
870C22×C17C22×#4111yescharacteristic
871C22×C17C2×H(5,𝔽2)11yescharacteristic
872C22×C17C2×H(5,𝔽2)11yescharacteristic
873C2×D17—22no—
874C2×D17—22no—
875C2×D17—22no—
876C2×D17—22no—
877C2×D17—22no—
878C2×D17—22no—
879C2×D17—41no—
880C2×D17—41no—
881C2×D17—41no—
882C2×D17—41no—
883C2×D17—41no—
884C2×D17—41no—
885C2×D17—41no—
886C2×D17—41no—
887C2×D17—416no—
888C2×D17—416no—
889C2×D17—41no—
890C2×D17—41no—
891C2×D17—41no—
892C2×D17—41no—
893C2×D17—41no—
894C2×D17—41no—
895C2×D17—41no—
896C2×D17—88no—
897C2×D17#52514yes—
898C2×D17#53214yes—
899C2×D17#53414yes—
900C2×D17#55114yes—
901C2×D17#55314yes—
902C2×D17#55314yes—
903C2×D17#55914yes—
904C4×C17—22no—
905C4×C17—22no—
906C4×C17—22no—
907C4×C17—22no—
908C4×C17—22no—
909C4×C17—41no—
910C4×C17—41no—
911C4×C17—41no—
912C4×C17—41no—
913C4×C17—41no—
914C4×C17—41no—
915C4×C17—41no—
916Dic17—22no—
917Dic17—22no—
918Dic17—22no—
919Dic17—22no—
920Dic17—22no—
921Dic17—41no—
922Dic17—41no—
923Dic17—41no—
924Dic17—41no—
925Dic17—41no—
926Dic17—41no—
927Dic17—41no—
928C23×D4—171no—
929C23×D4—171no—
930C23×D4—171no—
931C24×C4—171no—
932C24×C4—171no—
933C2×#123—171no—
934C2×#123—171no—
935C2×#123—171no—
936C2×#123—171no—
937C2×#123—171no—
938C2×#123—171no—
939C2×#123—171no—
940C2×#123—348no—
941C2×#123C2×D1711yescharacteristic, complemented
942C2×C4×D4—171no—
943C2×C4×D4—171no—
944C2×C4×D4—171no—
945C2×C4×D4—171no—
946C2×C4×D4—171no—
947C2×C4×D4—171no—
948C2×C4×D4—171no—
949C2×C4×D4—348no—
950C2×C4×D4C2×D1711yescharacteristic, complemented
951C22×C4⋊C4—171no—
952C22×C4⋊C4—171no—
953C22×C4⋊C4—171no—
954C22×C4⋊C4—171no—
955C22×C4⋊C4—171no—
956C22×C4⋊C4—171no—
957C22×C22⋊C4—171no—
958C22×C22⋊C4—171no—
959C22×C22⋊C4—171no—
960C22×C22⋊C4—171no—
961C22×C22⋊C4—171no—
962C22×C22⋊C4—171no—
963C22×C22⋊C4—171no—
964C22×C22⋊C4—171no—
965C22×C22⋊C4—171no—
966C22×C22⋊C4—171no—
967C22×C22⋊C4—171no—
968C22×C22⋊C4—171no—
969C22×C22⋊C4—171no—
970C22×C42—171no—
971C22×C42—171no—
972C22×C42—171no—
973#397—171no—
974#397—171no—
975#397—171no—
976#397—171no—
977#397—171no—
978#397—171no—
979#397—171no—
980#397C2×D1711yescharacteristic, complemented
981#394—171no—
982#394—171no—
983#394—171no—
984#394—171no—
985#394—171no—
986#394—171no—
987#394—171no—
988#394—171no—
989#394—171no—
990#394—171no—
991#394—171no—
992#394—171no—
993#394—171no—
994#394—171no—
995#394C2×D1711yescharacteristic, complemented
996#394C2×D1711yescharacteristic, complemented
997#392—171no—
998#392—171no—
999#392—171no—
1000#392—171no—
1001#392—171no—
1002#392—171no—
1003#392—171no—
1004#392C2×D1711yescharacteristic
1005#390—171no—
1006#390—171no—
1007#390—171no—
1008#390—171no—
1009#390—171no—
1010#390—171no—
1011#390—171no—
1012#390C2×D1711yescharacteristic, complemented
1013#389—171no—
1014#389—171no—
1015#389—171no—
1016#389—171no—
1017#389—171no—
1018#389—171no—
1019#389—171no—
1020#389C2×D1711yescharacteristic, complemented
1021#388—171no—
1022#388—171no—
1023#388—171no—
1024#388—171no—
1025#388—171no—
1026#388—171no—
1027#388—171no—
1028#388—171no—
1029#388—171no—
1030#388—171no—
1031#388—171no—
1032#388—171no—
1033#388—171no—
1034#388—171no—
1035#388—171no—
1036#388—171no—
1037#388—171no—
1038#388—171no—
1039#388—171no—
1040#388—171no—
1041#388—171no—
1042#388C2×D1711yescharacteristic, complemented
1043#388C2×D1711yescharacteristic, complemented
1044#388C2×D1711yescharacteristic, complemented
1045#387—171no—
1046#387—171no—
1047#387—171no—
1048#387—171no—
1049#387—171no—
1050#387—171no—
1051#387—171no—
1052#387C2×D1711yescharacteristic, complemented
1053#386—171no—
1054#386—171no—
1055#386—171no—
1056#386—171no—
1057#386—171no—
1058#386—171no—
1059#386—171no—
1060#386C2×D1711yescharacteristic, complemented
1061#385—171no—
1062#385—171no—
1063#385—171no—
1064#385—171no—
1065#385—171no—
1066#385—171no—
1067#385—171no—
1068#385C2×D1711yescharacteristic, complemented
1069C4×C22⋊C4—171no—
1070C4×C22⋊C4—171no—
1071C4×C22⋊C4—171no—
1072C4×C22⋊C4—171no—
1073C4×C22⋊C4—171no—
1074C4×C22⋊C4—171no—
1075C4×C22⋊C4—171no—
1076C4×C22⋊C4C2×D1711yescharacteristic, complemented
1077C2×#95—171no—
1078C2×#95—171no—
1079C2×#95—171no—
1080C2×#95—171no—
1081C2×#95—171no—
1082C2×#95—171no—
1083C2×#95—171no—
1084C2×#95—171no—
1085C2×C17—42no—
1086C2×C17—42no—
1087C2×C17—81no—
1088C2×C17C2×#52511yescharacteristic
1089C2×C17C2×#53211yescharacteristic
1090C2×C17C2×#53411yescharacteristic
1091C2×C17C2×#55111yescharacteristic
1092C2×C17C2×#55311yescharacteristic
1093C2×C17C2×#55311yescharacteristic
1094C2×C17C2×#55911yescharacteristic
1095D17—42no—
1096D17—42no—
1097D17—81no—
1098D17#260218yesdirect product factor
1099C25—171no—
1100C25—171no—
1101C25—171no—
1102C22×D4—171no—
1103C22×D4—171no—
1104C22×D4—171no—
1105C22×D4—171no—
1106C22×D4—171no—
1107C22×D4—171no—
1108C22×D4—171no—
1109C22×D4—171no—
1110C22×D4—171no—
1111C22×D4—344no—
1112C22×D4—344no—
1113C22×D4—344no—
1114C22×D4—344no—
1115C22×D4—344no—
1116C22×D4—344no—
1117C22×D4—682no—
1118C22×D4—682no—
1119C22×D4—682no—
1120C22×D4C22×D1711yescharacteristic
1121C22×D4C22×D1711yescharacteristic
1122C22×D4C22×D1711yescharacteristic
1123C23×C4—171no—
1124C23×C4—171no—
1125C23×C4—171no—
1126C23×C4—171no—
1127C23×C4—171no—
1128C23×C4—171no—
1129C23×C4—178no—
1130C23×C4—171no—
1131C23×C4—171no—
1132C23×C4—171no—
1133C23×C4—171no—
1134C23×C4—171no—
1135C23×C4—171no—
1136C23×C4—171no—
1137C23×C4—171no—
1138C23×C4—171no—
1139C23×C4—171no—
1140C23×C4—171no—
1141C23×C4—171no—
1142C23×C4—344no—
1143C23×C4—682no—
1144C23×C4—682no—
1145C23×C4—682no—
1146C23×C4—682no—
1147C23×C4C22×D1711yescharacteristic
1148C23×C4C22×D1711yescharacteristic
1149#123—24no—
1150#123—344no—
1151#123—344no—
1152#123—344no—
1153#123—344no—
1154#123—344no—
1155#123—344no—
1156#123—344no—
1157C4×D4—24no—
1158C4×D4—344no—
1159C4×D4—344no—
1160C4×D4—344no—
1161C4×D4—344no—
1162C4×D4—344no—
1163C4×D4—344no—
1164C4×D4—344no—
1165C2×C4⋊C4—171no—
1166C2×C4⋊C4—171no—
1167C2×C4⋊C4—171no—
1168C2×C4⋊C4—171no—
1169C2×C4⋊C4—171no—
1170C2×C4⋊C4—171no—
1171C2×C4⋊C4—171no—
1172C2×C4⋊C4—171no—
1173C2×C4⋊C4—171no—
1174C2×C4⋊C4—171no—
1175C2×C4⋊C4—171no—
1176C2×C4⋊C4—171no—
1177C2×C4⋊C4—171no—
1178C2×C4⋊C4—171no—
1179C2×C4⋊C4—171no—
1180C2×C4⋊C4—171no—
1181C2×C4⋊C4—171no—
1182C2×C4⋊C4—171no—
1183C2×C4⋊C4—344no—
1184C2×C4⋊C4—344no—
1185C2×C4⋊C4—344no—
1186C2×C4⋊C4—344no—
1187C2×C4⋊C4—344no—
1188C2×C4⋊C4—682no—
1189C2×C4⋊C4C22×D1711yescharacteristic
1190C2×C4⋊C4C22×D1711yescharacteristic
1191C2×C4⋊C4C22×D1711yescharacteristic
1192C2×C4⋊C4C22×D1711yescharacteristic
1193C2×C4⋊C4C22×D1711yescharacteristic
1194C2×C4⋊C4C22×D1711yescharacteristic
1195C2×C22⋊C4—171no—
1196C2×C22⋊C4—171no—
1197C2×C22⋊C4—171no—
1198C2×C22⋊C4—171no—
1199C2×C22⋊C4—171no—
1200C2×C22⋊C4—171no—
1201C2×C22⋊C4—171no—
1202C2×C22⋊C4—171no—
1203C2×C22⋊C4—171no—
1204C2×C22⋊C4—171no—
1205C2×C22⋊C4—171no—
1206C2×C22⋊C4—171no—
1207C2×C22⋊C4—171no—
1208C2×C22⋊C4—171no—
1209C2×C22⋊C4—171no—
1210C2×C22⋊C4—171no—
1211C2×C22⋊C4—171no—
1212C2×C22⋊C4—171no—
1213C2×C22⋊C4—171no—
1214C2×C22⋊C4—171no—
1215C2×C22⋊C4—171no—
1216C2×C22⋊C4—171no—
1217C2×C22⋊C4—171no—
1218C2×C22⋊C4—171no—
1219C2×C22⋊C4—171no—
1220C2×C22⋊C4—171no—
1221C2×C22⋊C4—171no—
1222C2×C22⋊C4—171no—
1223C2×C22⋊C4—171no—
1224C2×C22⋊C4—171no—
1225C2×C22⋊C4—171no—
1226C2×C22⋊C4—171no—
1227C2×C22⋊C4—171no—
1228C2×C22⋊C4—171no—
1229C2×C22⋊C4—171no—
1230C2×C22⋊C4—171no—
1231C2×C22⋊C4—171no—
1232C2×C22⋊C4—171no—
1233C2×C22⋊C4—171no—
1234C2×C22⋊C4—344no—
1235C2×C22⋊C4—344no—
1236C2×C22⋊C4—344no—
1237C2×C22⋊C4—344no—
1238C2×C22⋊C4—344no—
1239C2×C22⋊C4—344no—
1240C2×C22⋊C4—344no—
1241C2×C22⋊C4—344no—
1242C2×C22⋊C4—344no—
1243C2×C22⋊C4—344no—
1244C2×C22⋊C4—344no—
1245C2×C22⋊C4—682no—
1246C2×C22⋊C4—682no—
1247C2×C22⋊C4C22×D1711yescharacteristic
1248C2×C22⋊C4C22×D1711yescharacteristic
1249C2×C22⋊C4C22×D1711yescharacteristic
1250C2×C22⋊C4C22×D1711yescharacteristic
1251C2×C22⋊C4C22×D1711yescharacteristic
1252C2×C22⋊C4C22×D1711yescharacteristic
1253C2×C22⋊C4C22×D1711yescharacteristic
1254C2×C22⋊C4C22×D1711yescharacteristic
1255C2×C22⋊C4C22×D1711yescharacteristic
1256C2×C22⋊C4C22×D1711yescharacteristic
1257C2×C22⋊C4C22×D1711yescharacteristic
1258C2×C22⋊C4C22×D1711yescharacteristic
1259C2×C22⋊C4C22×D1711yescharacteristic
1260C2×C42—171no—
1261C2×C42—171no—
1262C2×C42—171no—
1263C2×C42—171no—
1264C2×C42—171no—
1265C2×C42—171no—
1266C2×C42—171no—
1267C2×C42—171no—
1268C2×C42—171no—
1269C2×C42—344no—
1270C2×C42—682no—
1271C2×C42—682no—
1272C2×C42C22×D1711yescharacteristic
1273C2×C42C22×D1711yescharacteristic
1274C2×C42C22×D1711yescharacteristic
1275#95—171no—
1276#95—171no—
1277#95—171no—
1278#95—171no—
1279#95—171no—
1280#95—171no—
1281#95—171no—
1282#95—171no—
1283#95—171no—
1284#95—171no—
1285#95—171no—
1286#95—171no—
1287#95—171no—
1288#95—171no—
1289#95—171no—
1290#95—171no—
1291#95—171no—
1292#95—171no—
1293#95—171no—
1294#95—171no—
1295#95—171no—
1296#95—171no—
1297#95—171no—
1298#95—171no—
1299#95C22×D1711yescharacteristic
1300#95C22×D1711yescharacteristic
1301#95C22×D1711yescharacteristic
1302#95C22×D1711yescharacteristic
1303#95C22×D1711yescharacteristic
1304#95C22×D1711yescharacteristic
1305#95C22×D1711yescharacteristic
1306#95C22×D1711yescharacteristic
1307C17C2×#260211yescharacteristic, complemented, Sylow
1308C24—171no—
1309C24—174no—
1310C24—174no—
1311C24—171no—
1312C24—171no—
1313C24—171no—
1314C24—342no—
1315C24—342no—
1316C24—342no—
1317C24—342no—
1318C24—342no—
1319C24—342no—
1320C24—342no—
1321C24—342no—
1322C24—342no—
1323C24—342no—
1324C24—342no—
1325C24—342no—
1326C24—342no—
1327C24—342no—
1328C24—342no—
1329C24—342no—
1330C24—342no—
1331C24—342no—
1332C24—342no—
1333C24C23×D1711yescharacteristic
1334C24C23×D1711yescharacteristic
1335C24C23×D1711yescharacteristic
1336C2×D4—22no—
1337C2×D4—22no—
1338C2×D4—22no—
1339C2×D4—22no—
1340C2×D4—22no—
1341C2×D4—22no—
1342C2×D4—41no—
1343C2×D4—41no—
1344C2×D4—41no—
1345C2×D4—342no—
1346C2×D4—342no—
1347C2×D4—342no—
1348C2×D4—342no—
1349C2×D4—342no—
1350C2×D4—342no—
1351C2×D4—342no—
1352C2×D4—342no—
1353C2×D4—3432no—
1354C2×D4—342no—
1355C2×D4—342no—
1356C2×D4—342no—
1357C2×D4—342no—
1358C2×D4—342no—
1359C2×D4—342no—
1360C2×D4—342no—
1361C2×D4—342no—
1362C2×D4—342no—
1363C2×D4—342no—
1364C2×D4—681no—
1365C2×D4—681no—
1366C2×D4—681no—
1367C2×D4—6816no—
1368C2×D4—681no—
1369C2×D4—681no—
1370C2×D4—681no—
1371C2×D4—681no—
1372C2×D4—681no—
1373C2×D4—681no—
1374C2×D4—6816no—
1375C22×C4—22no—
1376C22×C4—41no—
1377C22×C4—41no—
1378C22×C4—41no—
1379C22×C4—41no—
1380C22×C4—171no—
1381C22×C4—171no—
1382C22×C4—171no—
1383C22×C4—171no—
1384C22×C4—171no—
1385C22×C4—174no—
1386C22×C4—174no—
1387C22×C4—174no—
1388C22×C4—174no—
1389C22×C4—174no—
1390C22×C4—174no—
1391C22×C4—174no—
1392C22×C4—174no—
1393C22×C4—171no—
1394C22×C4—171no—
1395C22×C4—171no—
1396C22×C4—171no—
1397C22×C4—171no—
1398C22×C4—171no—
1399C22×C4—171no—
1400C22×C4—342no—
1401C22×C4—342no—
1402C22×C4—342no—
1403C22×C4—342no—
1404C22×C4—342no—
1405C22×C4—342no—
1406C22×C4—342no—
1407C22×C4—342no—
1408C22×C4—342no—
1409C22×C4—342no—
1410C22×C4—342no—
1411C22×C4—342no—
1412C22×C4—342no—
1413C22×C4—342no—
1414C22×C4—342no—
1415C22×C4—342no—
1416C22×C4—342no—
1417C22×C4—342no—
1418C22×C4—342no—
1419C22×C4—342no—
1420C22×C4—342no—
1421C22×C4—342no—
1422C22×C4—342no—
1423C22×C4—342no—
1424C22×C4—342no—
1425C22×C4—342no—
1426C22×C4—342no—
1427C22×C4—342no—
1428C22×C4—342no—
1429C22×C4—342no—
1430C22×C4—342no—
1431C22×C4—342no—
1432C22×C4—342no—
1433C22×C4—342no—
1434C22×C4—681no—
1435C22×C4—681no—
1436C22×C4—681no—
1437C22×C4—681no—
1438C22×C4—681no—
1439C22×C4—681no—
1440C22×C4—681no—
1441C22×C4—681no—
1442C22×C4—6816no—
1443C22×C4—6816no—
1444C22×C4—681no—
1445C22×C4—681no—
1446C22×C4—681no—
1447C22×C4—681no—
1448C22×C4D4×D1714yescomplemented
1449C22×C4C23×D1711yescharacteristic
1450C22×C4C23×D1711yescharacteristic
1451C22×C4C23×D1711yescharacteristic
1452C22×C4C23×D1711yescharacteristic
1453C22×C4C23×D1711yescharacteristic
1454C22×C4C23×D1711yescharacteristic
1455C22×C4C23×D1711yescharacteristic
1456C22×C4C23×D1711yescharacteristic
1457C22×C4C23×D1711yescharacteristic
1458C22×C4C23×D1711yescharacteristic
1459C22×C4C23×D1711yescharacteristic
1460C22×C4C23×D1711yescharacteristic
1461C4⋊C4—22no—
1462C4⋊C4—22no—
1463C4⋊C4—22no—
1464C4⋊C4—22no—
1465C4⋊C4—22no—
1466C4⋊C4—41no—
1467C4⋊C4—342no—
1468C4⋊C4—342no—
1469C4⋊C4—342no—
1470C4⋊C4—342no—
1471C4⋊C4—342no—
1472C4⋊C4—342no—
1473C4⋊C4—342no—
1474C4⋊C4—342no—
1475C4⋊C4—342no—
1476C4⋊C4—342no—
1477C4⋊C4—342no—
1478C4⋊C4—342no—
1479C4⋊C4—342no—
1480C4⋊C4—342no—
1481C4⋊C4—342no—
1482C4⋊C4—681no—
1483C4⋊C4—681no—
1484C4⋊C4—681no—
1485C22⋊C4—22no—
1486C22⋊C4—22no—
1487C22⋊C4—22no—
1488C22⋊C4—22no—
1489C22⋊C4—22no—
1490C22⋊C4—22no—
1491C22⋊C4—22no—
1492C22⋊C4—22no—
1493C22⋊C4—22no—
1494C22⋊C4—22no—
1495C22⋊C4—22no—
1496C22⋊C4—41no—
1497C22⋊C4—41no—
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—342no—
1520C22⋊C4—342no—
1521C22⋊C4—342no—
1522C22⋊C4—342no—
1523C22⋊C4—342no—
1524C22⋊C4—342no—
1525C22⋊C4—342no—
1526C22⋊C4—342no—
1527C22⋊C4—342no—
1528C22⋊C4—342no—
1529C22⋊C4—342no—
1530C22⋊C4—342no—
1531C22⋊C4—681no—
1532C22⋊C4—681no—
1533C22⋊C4—681no—
1534C22⋊C4—681no—
1535C22⋊C4—681no—
1536C22⋊C4—681no—
1537C42—22no—
1538C42—41no—
1539C42—41no—
1540C42—342no—
1541C42—342no—
1542C42—342no—
1543C42—681no—
1544C42—681no—
1545C42—681no—
1546C42—681no—
1547C42—681no—
1548C42—681no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—21no—
1558C23—21no—
1559C23—21no—
1560C23—21no—
1561C23—21no—
1562C23—21no—
1563C23—21no—
1564C23—21no—
1565C23—21no—
1566C23—21no—
1567C23—21no—
1568C23—172no—
1569C23—172no—
1570C23—172no—
1571C23—172no—
1572C23—172no—
1573C23—172no—
1574C23—172no—
1575C23—172no—
1576C23—172no—
1577C23—348no—
1578C23—348no—
1579C23—348no—
1580C23—348no—
1581C23—348no—
1582C23—348no—
1583C23—341no—
1584C23—341no—
1585C23—341no—
1586C23—341no—
1587C23—341no—
1588C23—341no—
1589C23—341no—
1590C23—341no—
1591C23—341no—
1592C23—341no—
1593C23—341no—
1594C23—341no—
1595C23—341no—
1596C23—341no—
1597C23—341no—
1598C23—341no—
1599C23—341no—
1600C23—341no—
1601C23—341no—
1602C23—684no—
1603C23—684no—
1604C23—684no—
1605C23—684no—
1606C23—684no—
1607C23—684no—
1608C23—684no—
1609C23—684no—
1610C23—684no—
1611C23—684no—
1612C23—684no—
1613C23—684no—
1614C23—684no—
1615C23—684no—
1616C23—684no—
1617C23C2×D4×D1712yes—
1618C23#41×D1712yes—
1619C23C24×D1711yescharacteristic
1620D4—28no—
1621D4—44no—
1622D4—44no—
1623D4—348no—
1624D4—348no—
1625D4—348no—
1626D4—684no—
1627D4—684no—
1628D4—684no—
1629D4—684no—
1630D4—684no—
1631D4—684no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—44no—
1664C2×C4—44no—
1665C2×C4—172no—
1666C2×C4—172no—
1667C2×C4—172no—
1668C2×C4—172no—
1669C2×C4—172no—
1670C2×C4—348no—
1671C2×C4—348no—
1672C2×C4—348no—
1673C2×C4—348no—
1674C2×C4—348no—
1675C2×C4—341no—
1676C2×C4—341no—
1677C2×C4—341no—
1678C2×C4—341no—
1679C2×C4—341no—
1680C2×C4—341no—
1681C2×C4—341no—
1682C2×C4—341no—
1683C2×C4—341no—
1684C2×C4—341no—
1685C2×C4—341no—
1686C2×C4—341no—
1687C2×C4—341no—
1688C2×C4—341no—
1689C2×C4—341no—
1690C2×C4—341no—
1691C2×C4—341no—
1692C2×C4—341no—
1693C2×C4—341no—
1694C2×C4—341no—
1695C2×C4—341no—
1696C2×C4—341no—
1697C2×C4—341no—
1698C2×C4—341no—
1699C2×C4—341no—
1700C2×C4—341no—
1701C2×C4—341no—
1702C2×C4—341no—
1703C2×C4—341no—
1704C2×C4—341no—
1705C2×C4—341no—
1706C2×C4—684no—
1707C2×C4—684no—
1708C2×C4—684no—
1709C2×C4—684no—
1710C2×C4—684no—
1711C2×C4—684no—
1712C2×C4—684no—
1713C2×C4—684no—
1714C2×C4—684no—
1715C2×C4—684no—
1716C2×C4—684no—
1717C2×C4—684no—
1718C2×C4—684no—
1719C2×C4C2×D4×D1712yes—
1720C2×C4C2×D4×D1712yes—
1721C2×C4#41×D1712yes—
1722C2×C4#41×D1712yes—
1723C2×C4#41×D1712yes—
1724C22—22no—
1725C22—22no—
1726C22—22no—
1727C22—22no—
1728C22—22no—
1729C22—22no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—41no—
1736C22—41no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—41no—
1741C22—41no—
1742C22—41no—
1743C22—41no—
1744C22—41no—
1745C22—174no—
1746C22—174no—
1747C22—174no—
1748C22—174no—
1749C22—174no—
1750C22—174no—
1751C22—174no—
1752C22—342no—
1753C22—342no—
1754C22—342no—
1755C22—342no—
1756C22—342no—
1757C22—342no—
1758C22—6816no—
1759C22—6816no—
1760C22—681no—
1761C22—681no—
1762C22—681no—
1763C22—681no—
1764C22—681no—
1765C22—681no—
1766C22—681no—
1767C22—681no—
1768C22—681no—
1769C22—681no—
1770C22—681no—
1771C22—681no—
1772C22—681no—
1773C22—681no—
1774C22—681no—
1775C22—1368no—
1776C22C22×D4×D1711yescharacteristic
1777C22C2×#41×D1711yescharacteristic
1778C22C2×#41×D1711yescharacteristic
1779C22C2×#41×D1711yescharacteristic
1780C22C2×#41×D1711yescharacteristic
1781C22H(5,𝔽2)×D1711yescharacteristic
1782C22H(5,𝔽2)×D1711yescharacteristic
1783C4—22no—
1784C4—22no—
1785C4—22no—
1786C4—22no—
1787C4—22no—
1788C4—41no—
1789C4—41no—
1790C4—41no—
1791C4—41no—
1792C4—41no—
1793C4—41no—
1794C4—41no—
1795C4—342no—
1796C4—342no—
1797C4—342no—
1798C4—342no—
1799C4—342no—
1800C4—681no—
1801C4—681no—
1802C4—681no—
1803C4—681no—
1804C4—681no—
1805C4—681no—
1806C4—681no—
1807C2—42no—
1808C2—42no—
1809C2—81no—
1810C2—178no—
1811C2—682no—
1812C2—682no—
1813C2—1361no—
1814C2D17×#52511yescharacteristic
1815C2D17×#53211yescharacteristic
1816C2D17×#53411yescharacteristic
1817C2D17×#55111yescharacteristic
1818C2D17×#55311yescharacteristic
1819C2D17×#55311yescharacteristic
1820C2D17×#55911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2602C2
prime radicalD17×#392C2
hypercenter#2602D17
hypocenterC17C2×#2602
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2602

Complements

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

NH ≅ G/Ntype
1. C2×#123×D17C2semidirect
2. C2×C4×D4×D17C2semidirect
3. #14534403C2semidirect
4. #14534402C2semidirect
5. #14534401C2semidirect
6. #14534400C2semidirect
7. #14534399C2semidirect
8. #14534398C2semidirect
9. #14534397C2semidirect
10. #14534396C2semidirect
11. #14534395C2semidirect
12. #14534394C2semidirect
13. #14534393C2semidirect
14. #14534392C2semidirect
15. #14534391C2semidirect
16. #14534390C2semidirect
17. #14534389C2semidirect
18. D17×#397C2semidirect
19. D17×#394C2semidirect
20. D17×#394C2semidirect
22. D17×#390C2semidirect
23. D17×#389C2semidirect
24. D17×#388C2semidirect
25. D17×#388C2semidirect
26. D17×#388C2semidirect
27. D17×#387C2semidirect
28. D17×#386C2semidirect
29. D17×#385C2semidirect
30. C4×C22⋊C4×D17C2semidirect
31. C17×#2602C2semidirect
37. C2×#10587580C22semidirect
38. C2×#10587580C22semidirect
39. C2×#10587572C22semidirect
40. C2×#10587615C22semidirect
41. C2×#10587569C22semidirect
42. C2×#10587569C22semidirect
43. C2×#10587621C22semidirect
45. C2×C4×D68C22semidirect
46. C2×D4×Dic17C22semidirect
47. C2×#10587579C22semidirect
48. C2×C4×C22⋊D17C22semidirect
49. C2×C4×C22⋊D17C22semidirect
50. C2×#10587567C22semidirect
51. C2×#10587567C22semidirect
75. #11762738C22semidirect
76. #11762738C22semidirect
77. #11762737C22semidirect
78. #11762737C22semidirect
79. #11762736C22semidirect
80. #11762735C22semidirect
81. #11762734C22semidirect
82. #11762727C22semidirect
83. #11762727C22semidirect
84. #11762726C22semidirect
85. #11762726C22semidirect
86. #11762725C22semidirect
87. #11762725C22semidirect
88. #11762725C22semidirect
89. #11762725C22semidirect
90. #11762724C22semidirect
91. #11762724C22semidirect
92. #11762724C22semidirect
93. #11762724C22semidirect
94. #11762723C22semidirect
95. #11762723C22semidirect
103. #11762712C22semidirect
104. #11762711C22semidirect
105. #11762710C22semidirect
106. #11762709C22semidirect
107. #11762709C22semidirect
108. #11762709C22semidirect
109. #11762709C22semidirect
110. #11762708C22semidirect
111. #11762707C22semidirect
112. #11762706C22semidirect
113. #11762706C22semidirect
114. #11762705C22semidirect
115. #11762704C22semidirect
116. #11762704C22semidirect
117. #11762703C22semidirect
118. #11762703C22semidirect
119. #11762703C22semidirect
120. #11762702C22semidirect
121. #11762702C22semidirect
122. #11762702C22semidirect
123. #11762701C22semidirect
124. #11762701C22semidirect
125. #11762701C22semidirect
126. #11762700C22semidirect
127. #11762700C22semidirect
128. #11762700C22semidirect
129. #11762699C22semidirect
130. #11762699C22semidirect
131. #11762699C22semidirect
132. #11762698C22semidirect
133. #11762698C22semidirect
134. #11762698C22semidirect
135. #11762697C22semidirect
136. #11762697C22semidirect
137. #11762697C22semidirect
138. #11762696C22semidirect
139. #11762695C22semidirect
140. #11762694C22semidirect
141. #11762693C22semidirect
142. #11762692C22semidirect
143. #11762691C22semidirect
144. #11762690C22semidirect
145. #11762689C22semidirect
146. #11762688C22semidirect
147. #11762687C22semidirect
148. #11762687C22semidirect
149. #11762686C22semidirect
150. #11762685C22semidirect
151. #11762685C22semidirect
152. #11762684C22semidirect
153. #11762683C22semidirect
154. #11762683C22semidirect
155. #11762682C22semidirect
156. #11762681C22semidirect
157. #11762680C22semidirect
158. #11762680C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C4×#63227C22semidirect
162. C4×#63227C22semidirect
163. C4×C22⋊Dic17C22semidirect
164. #11762656C22semidirect
165. #11762656C22semidirect
174. C2×C17×#123C22semidirect
175. C2×C4×D4×C17C22semidirect
176. C17×#397C22semidirect
177. C17×#394C22semidirect
178. C17×#394C22semidirect
180. C17×#390C22semidirect
181. C17×#389C22semidirect
182. C17×#388C22semidirect
183. C17×#388C22semidirect
184. C17×#388C22semidirect
185. C17×#387C22semidirect
186. C17×#386C22semidirect
187. C17×#385C22semidirect
188. C4×C22⋊C4×C17C22semidirect
222. C22×C4×D17D4semidirect
439. C22×C4×C17C2×D4semidirect
475. C22×Dic17C2×D4semidirect
545. C2×C4×D17C2×D4semidirect
546. C2×C4×D17C2×D4semidirect
831. #2602D17direct (N × H)
941. C2×#123C2×D17semidirect
950. C2×C4×D4C2×D17semidirect
980. #397C2×D17semidirect
995. #394C2×D17semidirect
996. #394C2×D17semidirect
1012. #390C2×D17semidirect
1020. #389C2×D17semidirect
1042. #388C2×D17semidirect
1043. #388C2×D17semidirect
1044. #388C2×D17semidirect
1052. #387C2×D17semidirect
1060. #386C2×D17semidirect
1068. #385C2×D17semidirect
1076. C4×C22⋊C4C2×D17semidirect
1098. D17#2602direct (N × H)
1307. C17C2×#2602semidirect
1448. C22×C4D4×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#123×D172
C2×C4×D4×D172
#145344032
#145344022
#145344012
#145344002
#145343992
#145343982
#145343972
#145343962
#145343952
#145343942
#145343932
#145343922
#145343912
#145343902
#145343892
D17×#3972
D17×#3942
D17×#3922
D17×#3902
D17×#3892
D17×#3882
D17×#3872
D17×#3862
D17×#3852
C4×C22⋊C4×D172
C17×#26022
C2×#260217