Finite Group Databasebeta

← D17×#2481 #17201942

Subgroups — D17×#2481 #17201942

Order 4352.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D17C211yesmaximal, characteristic, complemented
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3#14533052C211yesmaximal, characteristic, complemented
4#14533051C211yesmaximal, characteristic, complemented
5#14533050C211yesmaximal, characteristic, complemented
6#14533049C211yesmaximal, characteristic, complemented
7#14533048C211yesmaximal, characteristic, complemented
8#14533047C211yesmaximal, characteristic, complemented
9#14533046C211yesmaximal, characteristic, complemented
10#14533045C211yesmaximal, characteristic, complemented
11#14533044C211yesmaximal, characteristic, complemented
12#14533043C211yesmaximal, characteristic, complemented
13#14533042C211yesmaximal, characteristic, complemented
14#14533041C211yesmaximal, characteristic, complemented
15#14533040C211yesmaximal, characteristic, complemented
16#14533039C211yesmaximal, characteristic, complemented
17#14533038C211yesmaximal, characteristic, complemented
18D17×#400C211yesmaximal, characteristic, complemented
19D17×#400C211yesmaximal, characteristic, complemented
20D17×#397C211yesmaximal, characteristic, complemented
21D17×#396C211yesmaximal, characteristic, complemented
22D17×#388C211yesmaximal, characteristic, complemented
23D17×#387C211yesmaximal, characteristic, complemented
24D17×#387C211yesmaximal, characteristic, complemented
25D17×#386C211yesmaximal, characteristic
26D17×#386C211yesmaximal, characteristic
27D17×#386C211yesmaximal, characteristic
28D17×#385C211yesmaximal, characteristic, complemented
29D17×#380C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2481C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C23×C4×D17C2211yescharacteristic
35C23×C4×D17C2211yescharacteristic
36C2×#10587584C2211yescharacteristic, complemented
37C2×#10587584C2211yescharacteristic, complemented
38C2×#10587584C2211yescharacteristic, complemented
39C2×#10587562C2211yescharacteristic, complemented
40C2×#10587565C2211yescharacteristic, complemented
41C2×#10587565C2211yescharacteristic, complemented
42C2×#10587565C2211yescharacteristic, complemented
43#126×D17—28no—
44C22×C4⋊Dic17C2211yescharacteristic, complemented
45C22×#63225C2211yescharacteristic, complemented
46C22×#63225C2211yescharacteristic, complemented
47C2×C4⋊C4×D17—28no—
48C2×C4⋊C4×D17C2211yescharacteristic
49C2×C4⋊C4×D17C2211yescharacteristic
50C2×C4⋊C4×D17C2211yescharacteristic
51C2×C4⋊C4×D17C2211yescharacteristic
52C2×C4⋊C4×D17C2211yescharacteristic
53C2×C4⋊C4×D17C2211yescharacteristic
54C2×C4⋊C4×D17C2211yescharacteristic
55C2×C4⋊C4×D17C2211yescharacteristic
56C2×C4⋊C4×D17C2211yescharacteristic, complemented
57C2×C4⋊C4×D17C2211yescharacteristic, complemented
58C2×C4⋊C4×D17C2211yescharacteristic, complemented
59C2×C4⋊C4×D17C2211yescharacteristic, complemented
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×C42×D17C2211yescharacteristic
70C2×C42×D17C2211yescharacteristic
71#11762751C2211yescharacteristic, complemented
72#11762751C2211yescharacteristic, complemented
73#11762751C2211yescharacteristic, complemented
74#11762751C2211yescharacteristic, complemented
75#11762750C2211yescharacteristic, complemented
76#11762750C2211yescharacteristic, complemented
77#11762750C2211yescharacteristic, complemented
78#11762750C2211yescharacteristic, complemented
79#11762749C2211yescharacteristic, complemented
80#11762749C2211yescharacteristic, complemented
81#11762748C2211yescharacteristic, complemented
82#11762748C2211yescharacteristic, complemented
83#11762747C2211yescharacteristic, complemented
84#11762747C2211yescharacteristic, complemented
85#11762738C2211yescharacteristic, complemented
86#11762738C2211yescharacteristic, complemented
87#11762737C2211yescharacteristic, complemented
88#11762737C2211yescharacteristic, complemented
89#11762736C2211yescharacteristic, complemented
90#11762735C2211yescharacteristic, complemented
91#11762734C2211yescharacteristic, complemented
92#11762733C2211yescharacteristic, complemented
93#11762732C2211yescharacteristic, complemented
94#11762732C2211yescharacteristic, complemented
95#11762732C2211yescharacteristic, complemented
96#11762731C2211yescharacteristic, complemented
97#11762731C2211yescharacteristic, complemented
98#11762731C2211yescharacteristic, complemented
99#11762703C2211yescharacteristic, complemented
100#11762702C2211yescharacteristic, complemented
101#11762701C2211yescharacteristic, complemented
102#11762700C2211yescharacteristic, complemented
103#11762699C2211yescharacteristic, complemented
104#11762698C2211yescharacteristic, complemented
105#11762697C2211yescharacteristic, complemented
106#11762696C2211yescharacteristic, complemented
107#11762696C2211yescharacteristic, complemented
108#11762695C2211yescharacteristic, complemented
109#11762695C2211yescharacteristic, complemented
110#11762694C2211yescharacteristic, complemented
111#11762694C2211yescharacteristic, complemented
112#11762693C2211yescharacteristic, complemented
113#11762693C2211yescharacteristic, complemented
114#11762692C2211yescharacteristic, complemented
115#11762692C2211yescharacteristic, complemented
116#11762691C2211yescharacteristic, complemented
117#11762691C2211yescharacteristic, complemented
118#11762690C2211yescharacteristic, complemented
119#11762690C2211yescharacteristic, complemented
120#11762689C2211yescharacteristic
121#11762689C2211yescharacteristic
122#11762689C2211yescharacteristic
123#11762688C2211yescharacteristic
124#11762688C2211yescharacteristic
125#11762688C2211yescharacteristic
126#11762687C2211yescharacteristic
127#11762687C2211yescharacteristic
128#11762687C2211yescharacteristic
129#11762687C2211yescharacteristic
130#11762687C2211yescharacteristic
131#11762687C2211yescharacteristic
132#11762686C2211yescharacteristic
133#11762686C2211yescharacteristic
134#11762686C2211yescharacteristic
135#11762685C2211yescharacteristic
136#11762685C2211yescharacteristic
137#11762685C2211yescharacteristic
138#11762685C2211yescharacteristic
139#11762685C2211yescharacteristic
140#11762685C2211yescharacteristic
141#11762684C2211yescharacteristic, complemented
142#11762683C2211yescharacteristic, complemented
143#11762683C2211yescharacteristic, complemented
144#11762682C2211yescharacteristic, complemented
145#11762681C2211yescharacteristic, complemented
146#11762680C2211yescharacteristic, complemented
147#11762680C2211yescharacteristic, complemented
148#11762669C2211yescharacteristic, complemented
149#11762668C2211yescharacteristic, complemented
150#11762668C2211yescharacteristic, complemented
151#11762667C2211yescharacteristic, complemented
152#11762667C2211yescharacteristic, complemented
153#11762666C2211yescharacteristic, complemented
154#11762666C2211yescharacteristic, complemented
155C22⋊C4×Dic17C2211yescharacteristic, complemented
156C22⋊C4×Dic17C2211yescharacteristic, complemented
157C4×#63227C2211yescharacteristic, complemented
158C4×#63227C2211yescharacteristic, complemented
159C4×C22⋊Dic17C2211yescharacteristic, complemented
160#11762656C2211yescharacteristic, complemented
161#11762656C2211yescharacteristic, complemented
162#95×D17C2211yescharacteristic
163#95×D17C2211yescharacteristic
164#95×D17C2211yescharacteristic
165#95×D17C2211yescharacteristic
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×#126C2211yescharacteristic, complemented
175C22×C4⋊C4×C17C2211yescharacteristic, complemented
176C17×#400C2211yescharacteristic, complemented
177C17×#400C2211yescharacteristic, complemented
178C17×#397C2211yescharacteristic, complemented
179C17×#396C2211yescharacteristic, complemented
180C17×#388C2211yescharacteristic, complemented
181C17×#387C2211yescharacteristic, complemented
182C17×#387C2211yescharacteristic, complemented
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#385C2211yescharacteristic, complemented
187C17×#380C2211yescharacteristic, complemented
188C4×C22⋊C4×C17C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C23×Dic17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C2×D4×D17—24no—
201C2×D4×D17—24no—
202C2×D4×D17—24no—
203C22×D68C2311yescharacteristic
204C22×C4×D17—24no—
205C22×C4×D17—24no—
206C22×C4×D17—24no—
207C22×C4×D17—24no—
208C22×C4×D17—24no—
209C22×C4×D17—24no—
210C22×C4×D17—24no—
211C22×C4×D17—42no—
212C22×C4×D17—42no—
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
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
232C17×#126—24no—
233C2×C4⋊C4×C17—24no—
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C4⋊C4×C17C2311yescharacteristic
240C2×C4⋊C4×C17C2311yescharacteristic
241C2×C4⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
252C2×C42×C17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×C4⋊Dic17—24no—
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×#63225—24no—
290C2×#63225—24no—
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313#10587584—24no—
314#10587584—24no—
315#10587584—24no—
316C4⋊C4×D17—24no—
317C4⋊C4×D17—24no—
318C4⋊C4×D17—24no—
319C4⋊C4×D17—24no—
320C4⋊C4×D17—24no—
321C4⋊C4×D17—24no—
322C4⋊C4×D17—24no—
323C4⋊C4×D17—24no—
324C4⋊C4×D17—24no—
325C4⋊C4×D17—24no—
326C4⋊C4×D17—42no—
327C4⋊C4×D17D418yescomplemented
328C22⋊C4×D17—24no—
329C22⋊C4×D17—24no—
330C22⋊C4×D17—24no—
331C22⋊C4×D17—24no—
332C22⋊C4×D17—24no—
333C22⋊C4×D17—24no—
334C22⋊C4×D17—24no—
335C22⋊C4×D17—42no—
336C22⋊C4×D17—42no—
337#10587565—24no—
338#10587565—24no—
339#10587565—24no—
340#10587562—24no—
341C42×D17—24no—
342C42×D17—42no—
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
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
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C23×D17—22no—
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—22no—
399C23×D17—22no—
400C23×D17—22no—
401C23×D17—22no—
402C23×D17—22no—
403C23×D17—22no—
404C23×D17#4114yes—
405C23×D17#4114yes—
406C23×D17#4114yes—
407C23×D17C2411yescharacteristic
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C2×D4×C17—22no—
411C2×D4×C17—22no—
412C2×D4×C17—22no—
413C22×C4×C17—22no—
414C22×C4×C17—22no—
415C22×C4×C17—22no—
416C22×C4×C17—22no—
417C22×C4×C17—22no—
418C22×C4×C17—22no—
419C22×C4×C17—22no—
420C22×C4×C17—41no—
421C22×C4×C17—41no—
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C2×C22⋊D17—22no—
436C2×C22⋊D17—22no—
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—22no—
441C22×Dic17—22no—
442C22×Dic17—22no—
443C22×Dic17—22no—
444C22×Dic17—22no—
445C22×Dic17—22no—
446C22×Dic17—22no—
447C22×Dic17—22no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463D4×D17—416no—
464C2×D68—22no—
465C2×D68—22no—
466C2×D68—22no—
467C2×C4×D17—232no—
468C2×C4×D17—22no—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—22no—
474C2×C4×D17—22no—
475C2×C4×D17—22no—
476C2×C4×D17—22no—
477C2×C4×D17—22no—
478C2×C4×D17—22no—
479C2×C4×D17—22no—
480C2×C4×D17—22no—
481C2×C4×D17—22no—
482C2×C4×D17—22no—
483C2×C4×D17—22no—
484C2×C4×D17—22no—
485C2×C4×D17—22no—
486C2×C4×D17—22no—
487C2×C4×D17—22no—
488C2×C4×D17—22no—
489C2×C4×D17—22no—
490C2×C4×D17—22no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—22no—
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—416no—
518C2×C4×D17—416no—
519C2×C4×D17—41no—
520C2×C4×D17—41no—
521C2×C4×D17—41no—
522C2×C4×D17—41no—
523C2×C4×D17C2×D414yes—
524C2×C4×D17C2×D414yes—
525C2×C4×D17C2×D414yes—
526C2×C4×D17#4114yes—
527C4⋊C4×C17—22no—
528C4⋊C4×C17—22no—
529C4⋊C4×C17—22no—
530C4⋊C4×C17—22no—
531C4⋊C4×C17—22no—
532C4⋊C4×C17—22no—
533C4⋊C4×C17—41no—
534C4⋊C4×C17C2×D414yescomplemented
535C22⋊C4×C17—22no—
536C22⋊C4×C17—22no—
537C22⋊C4×C17—22no—
538C22⋊C4×C17—22no—
539C22⋊C4×C17—22no—
540C22⋊C4×C17—22no—
541C22⋊C4×C17—22no—
542C22⋊C4×C17—41no—
543C22⋊C4×C17—41no—
544C42×C17—22no—
545C42×C17—41no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—22no—
549C22⋊Dic17—22no—
550C22⋊Dic17—22no—
551C22⋊Dic17—22no—
552C22⋊Dic17—22no—
553C22⋊Dic17—41no—
554C22⋊Dic17—41no—
555#63227—22no—
556#63227—22no—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—22no—
563#63227—22no—
564#63227—22no—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—22no—
569#63227—41no—
570#63227—41no—
571#63227—41no—
572#63227—41no—
573C4⋊Dic17—22no—
574C4⋊Dic17—22no—
575C4⋊Dic17—22no—
576C4⋊Dic17—22no—
577C4⋊Dic17—22no—
578C4⋊Dic17—22no—
579C4⋊Dic17—41no—
580C4⋊Dic17C2×D414yescomplemented
581#63225—22no—
582#63225—22no—
583#63225—22no—
584#63225—22no—
585#63225—22no—
586#63225—22no—
587#63225—22no—
588#63225—22no—
589#63225—22no—
590#63225—22no—
591#63225—22no—
592#63225—22no—
593#63225—41no—
594#63225—41no—
595#63225C2×D414yescomplemented
596#63225C2×D414yescomplemented
597C4×Dic17—22no—
598C4×Dic17—22no—
599C4×Dic17—22no—
600C4×Dic17—41no—
601C4×Dic17—41no—
602C4×Dic17—41no—
603C2×#2481—171nomaximal, Sylow
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17C2×#4112yes—
616C23×C17C2×#4112yes—
617C23×C17C2×#4112yes—
618C23×C17C2511yescharacteristic
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—28no—
624C22×D17—28no—
625C22×D17—28no—
626C22×D17—28no—
627C22×D17—28no—
628C22×D17—28no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—44no—
637C22×D17—44no—
638C22×D17—44no—
639C22×D17—44no—
640C22×D17—44no—
641C22×D17—44no—
642C22×D17—44no—
643C22×D17#126116yescomplemented
644C22×D17C22×D412yes—
645C22×D17C2×#4112yes—
646C22×D17C2×#4112yes—
647C22×D17C2×#4112yes—
648C22×D17C2×#4112yes—
649C22×D17C2×#4112yes—
650C22×D17C2×#4112yes—
651C22×D17C2×#4112yes—
652C22×D17H(5,𝔽2)12yes—
653C22×D172−1+412yes—
654D4×C17—44no—
655C2×C4×C17—28no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—44no—
692C2×C4×C17—44no—
693C2×C4×C17C22×D412yes—
694C2×C4×C17C22×D412yes—
695C2×C4×C17C22×D412yes—
696C2×C4×C17C2×#4112yes—
697C22⋊D17—44no—
698C22⋊D17—44no—
699C2×Dic17—28no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—44no—
736C2×Dic17—44no—
737C2×Dic17C22×D412yes—
738C2×Dic17C22×D412yes—
739C2×Dic17C22×D412yes—
740C2×Dic17C2×#4112yes—
741D68—44no—
742C4×D17—28no—
743C4×D17—28no—
744C4×D17—28no—
745C4×D17—28no—
746C4×D17—28no—
747C4×D17—28no—
748C4×D17—44no—
749C4×D17—44no—
750C4×D17—44no—
751C4×D17—44no—
752C4×D17—44no—
753C4×D17—44no—
754C4×D17—44no—
755C4×D17—44no—
756C4×D17—44no—
757C4×D17—44no—
758C4×D17—44no—
759C4×D17—44no—
760C4×D17—44no—
761C22×#126—171no—
762C23×C4⋊C4—171no—
763#2481—171no—
764#2481—171no—
765#2481—171no—
766#2481—171no—
767#2481—171no—
768#2481—171no—
769#2481—171no—
770#2481—171no—
771#2481—171no—
772#2481—171no—
773#2481—171no—
774#2481—171no—
775#2481—171no—
776#2481—171no—
777#2481—171no—
778#2481D1711yescharacteristic, direct product factor
779C2×#400—171no—
780C2×#400—171no—
781C2×#397—171no—
782C2×#396—171no—
783C2×#388—171no—
784C2×#387—171no—
785C2×#387—171no—
786C2×#386—171no—
787C2×#386—171no—
788C2×#386—171no—
789C2×#385—171no—
790C2×#380—171no—
791C2×C4×C22⋊C4—171no—
792C22×C17—22no—
793C22×C17—22no—
794C22×C17—22no—
795C22×C17—22no—
796C22×C17—22no—
797C22×C17—22no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17—41no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17C2×#12614yescomplemented
806C22×C17C23×D411yescharacteristic
807C22×C17C22×#4111yescharacteristic
808C22×C17C22×#4111yescharacteristic
809C22×C17C22×#4111yescharacteristic
810C22×C17C22×#4111yescharacteristic
811C22×C17C2×H(5,𝔽2)11yescharacteristic
812C22×C17C2×2−1+411yescharacteristic
813C2×D17—22no—
814C2×D17—22no—
815C2×D17—22no—
816C2×D17—22no—
817C2×D17—22no—
818C2×D17—22no—
819C2×D17—232no—
820C2×D17—41no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—88no—
828C2×D17#52514yes—
829C2×D17C2×#12614yes—
830C2×D17C2×#12614yescomplemented
831C2×D17#53914yes—
832C2×D17#54614yes—
833C2×D17#54814yes—
834C2×D17#55214yes—
835C2×D17#55314yes—
836C4×C17—22no—
837C4×C17—22no—
838C4×C17—22no—
839C4×C17—22no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843C4×C17—41no—
844C4×C17—41no—
845C4×C17—41no—
846C4×C17—41no—
847C4×C17—41no—
848C4×C17—41no—
849Dic17—22no—
850Dic17—22no—
851Dic17—22no—
852Dic17—22no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856Dic17—41no—
857Dic17—41no—
858Dic17—41no—
859Dic17—41no—
860Dic17—41no—
861Dic17—41no—
862C23×D4—171no—
863C24×C4—171no—
864C24×C4—171no—
865C24×C4—171no—
866C2×#126—171no—
867C2×#126—171no—
868C2×#126—171no—
869C2×#126—171no—
870C2×#126—171no—
871C2×#126—171no—
872C2×#126—171no—
873C2×#126—348no—
874C2×#126C2×D1711yescharacteristic, complemented
875C22×C4⋊C4—171no—
876C22×C4⋊C4—171no—
877C22×C4⋊C4—171no—
878C22×C4⋊C4—171no—
879C22×C4⋊C4—171no—
880C22×C4⋊C4—171no—
881C22×C4⋊C4—171no—
882C22×C4⋊C4—171no—
883C22×C4⋊C4—171no—
884C22×C4⋊C4—171no—
885C22×C4⋊C4—171no—
886C22×C4⋊C4—171no—
887C22×C4⋊C4—171no—
888C22×C4⋊C4—171no—
889C22×C4⋊C4—171no—
890C22×C4⋊C4—348no—
891C22×C4⋊C4C2×D1711yescharacteristic, complemented
892C22×C22⋊C4—171no—
893C22×C22⋊C4—171no—
894C22×C22⋊C4—171no—
895C22×C22⋊C4—171no—
896C22×C22⋊C4—171no—
897C22×C22⋊C4—171no—
898C22×C22⋊C4—171no—
899C22×C22⋊C4—171no—
900C22×C22⋊C4—171no—
901C22×C42—171no—
902C22×C42—171no—
903#400—171no—
904#400—171no—
905#400—171no—
906#400—171no—
907#400—171no—
908#400—171no—
909#400—171no—
910#400—171no—
911#400—171no—
912#400—171no—
913#400—171no—
914#400—171no—
915#400—171no—
916#400—171no—
917#400C2×D1711yescharacteristic, complemented
918#400C2×D1711yescharacteristic, complemented
919#397—171no—
920#397—171no—
921#397—171no—
922#397—171no—
923#397—171no—
924#397—171no—
925#397—171no—
926#397C2×D1711yescharacteristic, complemented
927#396—171no—
928#396—171no—
929#396—171no—
930#396—171no—
931#396—171no—
932#396—171no—
933#396—171no—
934#396C2×D1711yescharacteristic, complemented
935#388—171no—
936#388—171no—
937#388—171no—
938#388—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388C2×D1711yescharacteristic, complemented
943#387—171no—
944#387—171no—
945#387—171no—
946#387—171no—
947#387—171no—
948#387—171no—
949#387—171no—
950#387—171no—
951#387—171no—
952#387—171no—
953#387—171no—
954#387—171no—
955#387—171no—
956#387—171no—
957#387C2×D1711yescharacteristic, complemented
958#387C2×D1711yescharacteristic, complemented
959#386—171no—
960#386—171no—
961#386—171no—
962#386—171no—
963#386—171no—
964#386—171no—
965#386—171no—
966#386—171no—
967#386—171no—
968#386—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386C2×D1711yescharacteristic
981#386C2×D1711yescharacteristic
982#386C2×D1711yescharacteristic
983#385—171no—
984#385—171no—
985#385—171no—
986#385—171no—
987#385—171no—
988#385—171no—
989#385—171no—
990#385C2×D1711yescharacteristic, complemented
991#380—171no—
992#380—171no—
993#380—171no—
994#380—171no—
995#380—171no—
996#380—171no—
997#380—171no—
998#380C2×D1711yescharacteristic, complemented
999C4×C22⋊C4—171no—
1000C4×C22⋊C4—171no—
1001C4×C22⋊C4—171no—
1002C4×C22⋊C4—171no—
1003C4×C22⋊C4—171no—
1004C4×C22⋊C4—171no—
1005C4×C22⋊C4—171no—
1006C4×C22⋊C4C2×D1711yescharacteristic, complemented
1007C2×#95—171no—
1008C2×#95—171no—
1009C2×#95—171no—
1010C2×#95—171no—
1011C2×#95—171no—
1012C2×#95—171no—
1013C2×#95—171no—
1014C2×#95—171no—
1015C2×#95—171no—
1016C2×#95—171no—
1017C2×#95—171no—
1018C2×#95—171no—
1019C2×C17—24no—
1020C2×C17—81no—
1021C2×C17C2×#52511yescharacteristic
1022C2×C17C22×#12611yescharacteristic
1023C2×C17C2×#53911yescharacteristic
1024C2×C17C2×#54611yescharacteristic
1025C2×C17C2×#54811yescharacteristic
1026C2×C17C2×#55211yescharacteristic
1027C2×C17C2×#55311yescharacteristic
1028D17—24no—
1029D17—81no—
1030D17#248118yesdirect product factor
1031C25—171no—
1032C25—171no—
1033C22×D4—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—344no—
1037C22×D4—344no—
1038C22×D4—344no—
1039C22×D4C22×D1711yescharacteristic
1040C23×C4—171no—
1041C23×C4—171no—
1042C23×C4—171no—
1043C23×C4—171no—
1044C23×C4—171no—
1045C23×C4—171no—
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—171no—
1056C23×C4—171no—
1057C23×C4—171no—
1058C23×C4—171no—
1059C23×C4—171no—
1060C23×C4—171no—
1061C23×C4—171no—
1062C23×C4—344no—
1063C23×C4—344no—
1064C23×C4—344no—
1065C23×C4—344no—
1066C23×C4—344no—
1067C23×C4—344no—
1068C23×C4—344no—
1069C23×C4—682no—
1070C23×C4—682no—
1071C23×C4C22×D1711yescharacteristic
1072C23×C4C22×D1711yescharacteristic
1073C23×C4C22×D1711yescharacteristic
1074#126—24no—
1075#126—344no—
1076#126—344no—
1077#126—344no—
1078#126—344no—
1079#126—344no—
1080#126—344no—
1081#126—344no—
1082C2×C4⋊C4—24no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—178no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—171no—
1093C2×C4⋊C4—171no—
1094C2×C4⋊C4—171no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—171no—
1097C2×C4⋊C4—171no—
1098C2×C4⋊C4—171no—
1099C2×C4⋊C4—171no—
1100C2×C4⋊C4—171no—
1101C2×C4⋊C4—171no—
1102C2×C4⋊C4—171no—
1103C2×C4⋊C4—171no—
1104C2×C4⋊C4—171no—
1105C2×C4⋊C4—171no—
1106C2×C4⋊C4—171no—
1107C2×C4⋊C4—171no—
1108C2×C4⋊C4—344no—
1109C2×C4⋊C4—344no—
1110C2×C4⋊C4—344no—
1111C2×C4⋊C4—344no—
1112C2×C4⋊C4—344no—
1113C2×C4⋊C4—344no—
1114C2×C4⋊C4—344no—
1115C2×C4⋊C4—344no—
1116C2×C4⋊C4—344no—
1117C2×C4⋊C4—344no—
1118C2×C4⋊C4—344no—
1119C2×C4⋊C4—344no—
1120C2×C4⋊C4—344no—
1121C2×C4⋊C4—682no—
1122C2×C4⋊C4C22×D1711yescharacteristic
1123C2×C4⋊C4C22×D1711yescharacteristic
1124C2×C4⋊C4C22×D1711yescharacteristic
1125C2×C4⋊C4C22×D1711yescharacteristic
1126C2×C4⋊C4C22×D1711yescharacteristic
1127C2×C4⋊C4C22×D1711yescharacteristic
1128C2×C4⋊C4C22×D1711yescharacteristic
1129C2×C4⋊C4C22×D1711yescharacteristic
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—344no—
1158C2×C22⋊C4—344no—
1159C2×C22⋊C4—344no—
1160C2×C22⋊C4—344no—
1161C2×C22⋊C4—344no—
1162C2×C22⋊C4—344no—
1163C2×C22⋊C4—344no—
1164C2×C22⋊C4—682no—
1165C2×C22⋊C4—682no—
1166C2×C22⋊C4C22×D1711yescharacteristic
1167C2×C22⋊C4C22×D1711yescharacteristic
1168C2×C22⋊C4C22×D1711yescharacteristic
1169C2×C22⋊C4C22×D1711yescharacteristic
1170C2×C22⋊C4C22×D1711yescharacteristic
1171C2×C22⋊C4C22×D1711yescharacteristic
1172C2×C22⋊C4C22×D1711yescharacteristic
1173C2×C22⋊C4C22×D1711yescharacteristic
1174C2×C22⋊C4C22×D1711yescharacteristic
1175C2×C42—171no—
1176C2×C42—171no—
1177C2×C42—171no—
1178C2×C42—171no—
1179C2×C42—171no—
1180C2×C42—171no—
1181C2×C42—344no—
1182C2×C42—682no—
1183C2×C42C22×D1711yescharacteristic
1184C2×C42C22×D1711yescharacteristic
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95—171no—
1206#95—171no—
1207#95—171no—
1208#95—171no—
1209#95—171no—
1210#95—171no—
1211#95—171no—
1212#95—171no—
1213#95—171no—
1214#95—171no—
1215#95—171no—
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95C22×D1711yescharacteristic
1222#95C22×D1711yescharacteristic
1223#95C22×D1711yescharacteristic
1224#95C22×D1711yescharacteristic
1225#95C22×D1711yescharacteristic
1226#95C22×D1711yescharacteristic
1227#95C22×D1711yescharacteristic
1228#95C22×D1711yescharacteristic
1229#95C22×D1711yescharacteristic
1230#95C22×D1711yescharacteristic
1231#95C22×D1711yescharacteristic
1232#95C22×D1711yescharacteristic
1233C17C2×#248111yescharacteristic, complemented, Sylow
1234C24—171no—
1235C24—174no—
1236C24—174no—
1237C24—174no—
1238C24—171no—
1239C24—171no—
1240C24—342no—
1241C24—342no—
1242C24—342no—
1243C24—342no—
1244C24—342no—
1245C24—342no—
1246C24—342no—
1247C24—342no—
1248C24—342no—
1249C24—342no—
1250C24—342no—
1251C24C23×D1711yescharacteristic
1252C24C23×D1711yescharacteristic
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—342no—
1257C2×D4—342no—
1258C2×D4—342no—
1259C2×D4—342no—
1260C2×D4—342no—
1261C2×D4—342no—
1262C2×D4—342no—
1263C2×D4—342no—
1264C2×D4—342no—
1265C2×D4—6816no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—41no—
1274C22×C4—41no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—171no—
1279C22×C4—174no—
1280C22×C4—174no—
1281C22×C4—174no—
1282C22×C4—174no—
1283C22×C4—171no—
1284C22×C4—171no—
1285C22×C4—171no—
1286C22×C4—171no—
1287C22×C4—171no—
1288C22×C4—171no—
1289C22×C4—171no—
1290C22×C4—171no—
1291C22×C4—171no—
1292C22×C4—342no—
1293C22×C4—342no—
1294C22×C4—342no—
1295C22×C4—342no—
1296C22×C4—342no—
1297C22×C4—342no—
1298C22×C4—342no—
1299C22×C4—342no—
1300C22×C4—342no—
1301C22×C4—342no—
1302C22×C4—342no—
1303C22×C4—342no—
1304C22×C4—342no—
1305C22×C4—342no—
1306C22×C4—3432no—
1307C22×C4—342no—
1308C22×C4—342no—
1309C22×C4—342no—
1310C22×C4—342no—
1311C22×C4—342no—
1312C22×C4—342no—
1313C22×C4—342no—
1314C22×C4—342no—
1315C22×C4—342no—
1316C22×C4—342no—
1317C22×C4—342no—
1318C22×C4—342no—
1319C22×C4—342no—
1320C22×C4—342no—
1321C22×C4—342no—
1322C22×C4—342no—
1323C22×C4—342no—
1324C22×C4—342no—
1325C22×C4—342no—
1326C22×C4—342no—
1327C22×C4—342no—
1328C22×C4—342no—
1329C22×C4—342no—
1330C22×C4—342no—
1331C22×C4—342no—
1332C22×C4—342no—
1333C22×C4—342no—
1334C22×C4—342no—
1335C22×C4—342no—
1336C22×C4—342no—
1337C22×C4—342no—
1338C22×C4—342no—
1339C22×C4—342no—
1340C22×C4—342no—
1341C22×C4—342no—
1342C22×C4—342no—
1343C22×C4—342no—
1344C22×C4—342no—
1345C22×C4—342no—
1346C22×C4—342no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—681no—
1350C22×C4—681no—
1351C22×C4—681no—
1352C22×C4—681no—
1353C22×C4—6816no—
1354C22×C4—6816no—
1355C22×C4—681no—
1356C22×C4—681no—
1357C22×C4C23×D1711yescharacteristic
1358C22×C4C23×D1711yescharacteristic
1359C22×C4C23×D1711yescharacteristic
1360C22×C4C23×D1711yescharacteristic
1361C22×C4C23×D1711yescharacteristic
1362C22×C4C23×D1711yescharacteristic
1363C22×C4C23×D1711yescharacteristic
1364C22×C4C23×D1711yescharacteristic
1365C22×C4C23×D1711yescharacteristic
1366C22×C4C23×D1711yescharacteristic
1367C22×C4C23×D1711yescharacteristic
1368C22×C4C23×D1711yescharacteristic
1369C22×C4C23×D1711yescharacteristic
1370C4⋊C4—22no—
1371C4⋊C4—22no—
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—41no—
1377C4⋊C4—174no—
1378C4⋊C4—174no—
1379C4⋊C4—174no—
1380C4⋊C4—342no—
1381C4⋊C4—342no—
1382C4⋊C4—342no—
1383C4⋊C4—342no—
1384C4⋊C4—342no—
1385C4⋊C4—342no—
1386C4⋊C4—342no—
1387C4⋊C4—342no—
1388C4⋊C4—342no—
1389C4⋊C4—342no—
1390C4⋊C4—342no—
1391C4⋊C4—342no—
1392C4⋊C4—342no—
1393C4⋊C4—342no—
1394C4⋊C4—342no—
1395C4⋊C4—342no—
1396C4⋊C4—342no—
1397C4⋊C4—342no—
1398C4⋊C4—681no—
1399C4⋊C4—681no—
1400C4⋊C4—681no—
1401C4⋊C4D4×D1714yescomplemented
1402C22⋊C4—22no—
1403C22⋊C4—22no—
1404C22⋊C4—22no—
1405C22⋊C4—22no—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—22no—
1409C22⋊C4—41no—
1410C22⋊C4—41no—
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—681no—
1433C22⋊C4—681no—
1434C22⋊C4—681no—
1435C22⋊C4—681no—
1436C22⋊C4—681no—
1437C22⋊C4—681no—
1438C42—22no—
1439C42—41no—
1440C42—342no—
1441C42—342no—
1442C42—342no—
1443C42—681no—
1444C42—681no—
1445C42—681no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—172no—
1458C23—172no—
1459C23—172no—
1460C23—172no—
1461C23—172no—
1462C23—172no—
1463C23—172no—
1464C23—1716no—
1465C23—172no—
1466C23—172no—
1467C23—172no—
1468C23—348no—
1469C23—348no—
1470C23—348no—
1471C23—348no—
1472C23—348no—
1473C23—348no—
1474C23—341no—
1475C23—341no—
1476C23—341no—
1477C23—341no—
1478C23—341no—
1479C23—341no—
1480C23—341no—
1481C23—341no—
1482C23—341no—
1483C23—341no—
1484C23—341no—
1485C23—684no—
1486C23—684no—
1487C23—684no—
1488C23—684no—
1489C23—684no—
1490C23—684no—
1491C23—684no—
1492C23#41×D1712yes—
1493C23#41×D1712yes—
1494C23#41×D1712yes—
1495C23C24×D1711yescharacteristic
1496D4—44no—
1497D4—684no—
1498D4—684no—
1499D4—684no—
1500C2×C4—28no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—44no—
1537C2×C4—44no—
1538C2×C4—172no—
1539C2×C4—172no—
1540C2×C4—172no—
1541C2×C4—172no—
1542C2×C4—348no—
1543C2×C4—348no—
1544C2×C4—348no—
1545C2×C4—348no—
1546C2×C4—348no—
1547C2×C4—348no—
1548C2×C4—348no—
1549C2×C4—341no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—341no—
1581C2×C4—341no—
1582C2×C4—341no—
1583C2×C4—341no—
1584C2×C4—684no—
1585C2×C4—684no—
1586C2×C4—684no—
1587C2×C4—684no—
1588C2×C4—684no—
1589C2×C4—684no—
1590C2×C4—684no—
1591C2×C4—684no—
1592C2×C4—684no—
1593C2×C4—684no—
1594C2×C4—684no—
1595C2×C4—684no—
1596C2×C4—684no—
1597C2×C4—684no—
1598C2×C4—684no—
1599C2×C4C2×D4×D1712yes—
1600C2×C4C2×D4×D1712yes—
1601C2×C4C2×D4×D1712yes—
1602C2×C4#41×D1712yes—
1603C22—22no—
1604C22—22no—
1605C22—22no—
1606C22—22no—
1607C22—22no—
1608C22—22no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—174no—
1617C22—174no—
1618C22—174no—
1619C22—174no—
1620C22—174no—
1621C22—174no—
1622C22—174no—
1623C22—174no—
1624C22—3432no—
1625C22—342no—
1626C22—342no—
1627C22—342no—
1628C22—342no—
1629C22—342no—
1630C22—342no—
1631C22—681no—
1632C22—681no—
1633C22—681no—
1634C22—681no—
1635C22—681no—
1636C22—681no—
1637C22—681no—
1638C22—1368no—
1639C22#126×D1714yescomplemented
1640C22C22×D4×D1711yescharacteristic
1641C22C2×#41×D1711yescharacteristic
1642C22C2×#41×D1711yescharacteristic
1643C22C2×#41×D1711yescharacteristic
1644C22C2×#41×D1711yescharacteristic
1645C22H(5,𝔽2)×D1711yescharacteristic
1646C222−1+4×D1711yescharacteristic
1647C4—22no—
1648C4—22no—
1649C4—22no—
1650C4—22no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4—41no—
1657C4—41no—
1658C4—41no—
1659C4—41no—
1660C4—342no—
1661C4—342no—
1662C4—342no—
1663C4—342no—
1664C4—681no—
1665C4—681no—
1666C4—681no—
1667C4—681no—
1668C4—681no—
1669C4—681no—
1670C4—681no—
1671C4—681no—
1672C4—681no—
1673C2—24no—
1674C2—81no—
1675C2—178no—
1676C2—344no—
1677C2—1361no—
1678C2D17×#52511yescharacteristic
1679C2C2×#126×D1711yescharacteristic
1680C2D17×#53911yescharacteristic
1681C2D17×#54611yescharacteristic
1682C2D17×#54811yescharacteristic
1683C2D17×#55211yescharacteristic
1684C2D17×#55311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2481C2
prime radicalC22×D4×D17C22
hypercenter#2481D17
hypocenterC17C2×#2481
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2481

Complements

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

NH ≅ G/Ntype
1. C2×#126×D17C2semidirect
2. C22×C4⋊C4×D17C2semidirect
3. #14533052C2semidirect
4. #14533051C2semidirect
5. #14533050C2semidirect
6. #14533049C2semidirect
7. #14533048C2semidirect
8. #14533047C2semidirect
9. #14533046C2semidirect
10. #14533045C2semidirect
11. #14533044C2semidirect
12. #14533043C2semidirect
13. #14533042C2semidirect
14. #14533041C2semidirect
15. #14533040C2semidirect
16. #14533039C2semidirect
17. #14533038C2semidirect
18. D17×#400C2semidirect
19. D17×#400C2semidirect
20. D17×#397C2semidirect
21. D17×#396C2semidirect
22. D17×#388C2semidirect
23. D17×#387C2semidirect
24. D17×#387C2semidirect
28. D17×#385C2semidirect
29. D17×#380C2semidirect
30. C4×C22⋊C4×D17C2semidirect
31. C17×#2481C2semidirect
36. C2×#10587584C22semidirect
37. C2×#10587584C22semidirect
38. C2×#10587584C22semidirect
39. C2×#10587562C22semidirect
40. C2×#10587565C22semidirect
41. C2×#10587565C22semidirect
42. C2×#10587565C22semidirect
44. C22×C4⋊Dic17C22semidirect
45. C22×#63225C22semidirect
46. C22×#63225C22semidirect
56. C2×C4⋊C4×D17C22semidirect
57. C2×C4⋊C4×D17C22semidirect
58. C2×C4⋊C4×D17C22semidirect
59. C2×C4⋊C4×D17C22semidirect
71. #11762751C22semidirect
72. #11762751C22semidirect
73. #11762751C22semidirect
74. #11762751C22semidirect
75. #11762750C22semidirect
76. #11762750C22semidirect
77. #11762750C22semidirect
78. #11762750C22semidirect
79. #11762749C22semidirect
80. #11762749C22semidirect
81. #11762748C22semidirect
82. #11762748C22semidirect
83. #11762747C22semidirect
84. #11762747C22semidirect
85. #11762738C22semidirect
86. #11762738C22semidirect
87. #11762737C22semidirect
88. #11762737C22semidirect
89. #11762736C22semidirect
90. #11762735C22semidirect
91. #11762734C22semidirect
92. #11762733C22semidirect
93. #11762732C22semidirect
94. #11762732C22semidirect
95. #11762732C22semidirect
96. #11762731C22semidirect
97. #11762731C22semidirect
98. #11762731C22semidirect
99. #11762703C22semidirect
100. #11762702C22semidirect
101. #11762701C22semidirect
102. #11762700C22semidirect
103. #11762699C22semidirect
104. #11762698C22semidirect
105. #11762697C22semidirect
106. #11762696C22semidirect
107. #11762696C22semidirect
108. #11762695C22semidirect
109. #11762695C22semidirect
110. #11762694C22semidirect
111. #11762694C22semidirect
112. #11762693C22semidirect
113. #11762693C22semidirect
114. #11762692C22semidirect
115. #11762692C22semidirect
116. #11762691C22semidirect
117. #11762691C22semidirect
118. #11762690C22semidirect
119. #11762690C22semidirect
141. #11762684C22semidirect
142. #11762683C22semidirect
143. #11762683C22semidirect
144. #11762682C22semidirect
145. #11762681C22semidirect
146. #11762680C22semidirect
147. #11762680C22semidirect
148. #11762669C22semidirect
149. #11762668C22semidirect
150. #11762668C22semidirect
151. #11762667C22semidirect
152. #11762667C22semidirect
153. #11762666C22semidirect
154. #11762666C22semidirect
155. C22⋊C4×Dic17C22semidirect
156. C22⋊C4×Dic17C22semidirect
157. C4×#63227C22semidirect
158. C4×#63227C22semidirect
159. C4×C22⋊Dic17C22semidirect
160. #11762656C22semidirect
161. #11762656C22semidirect
174. C2×C17×#126C22semidirect
175. C22×C4⋊C4×C17C22semidirect
176. C17×#400C22semidirect
177. C17×#400C22semidirect
178. C17×#397C22semidirect
179. C17×#396C22semidirect
180. C17×#388C22semidirect
181. C17×#387C22semidirect
182. C17×#387C22semidirect
186. C17×#385C22semidirect
187. C17×#380C22semidirect
188. C4×C22⋊C4×C17C22semidirect
327. C4⋊C4×D17D4semidirect
534. C4⋊C4×C17C2×D4semidirect
580. C4⋊Dic17C2×D4semidirect
595. #63225C2×D4semidirect
596. #63225C2×D4semidirect
643. C22×D17#126semidirect
778. #2481D17direct (N × H)
805. C22×C17C2×#126semidirect
830. C2×D17C2×#126semidirect
874. C2×#126C2×D17semidirect
891. C22×C4⋊C4C2×D17semidirect
917. #400C2×D17semidirect
918. #400C2×D17semidirect
926. #397C2×D17semidirect
934. #396C2×D17semidirect
942. #388C2×D17semidirect
957. #387C2×D17semidirect
958. #387C2×D17semidirect
990. #385C2×D17semidirect
998. #380C2×D17semidirect
1006. C4×C22⋊C4C2×D17semidirect
1030. D17#2481direct (N × H)
1233. C17C2×#2481semidirect
1401. C4⋊C4D4×D17semidirect
1639. C22#126×D17semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D172
C22×C4⋊C4×D172
#145330522
#145330512
#145330502
#145330492
#145330482
#145330472
#145330462
#145330452
#145330442
#145330432
#145330422
#145330412
#145330402
#145330392
#145330382
D17×#4002
D17×#3972
D17×#3962
D17×#3882
D17×#3872
D17×#3862
D17×#3852
D17×#3802
C4×C22⋊C4×D172
C17×#24812
C2×#248117