Finite Group Databasebeta

← #17899549

Subgroups — #17899549

Order 4352.

1882 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542348C211yesmaximal, characteristic
2#14537942C214yesmaximal, complemented
3#14537940C212yesmaximal, complemented
4#14537929C212yesmaximal, complemented
5#14537921C214yesmaximal, complemented
6#14537910C212yesmaximal, complemented
7#14537893C212yesmaximal, complemented
8#14537727C211yesmaximal, characteristic, complemented
9#14537714C211yesmaximal, characteristic, complemented
10#14537519C211yesmaximal, characteristic, complemented
11#14537506C212yesmaximal, complemented
12#14537476C212yesmaximal, complemented
13C2×#11762874C211yesmaximal, characteristic, complemented
14#14537441C212yesmaximal, complemented
15#14537428C211yesmaximal, characteristic, complemented
16D17×#424C212yesmaximal, complemented
17C17×#2906C211yesmaximal, characteristic, complemented
18C2×M16×D17C2212yes—
19C22×C8×D17C2212yes—
20#11763532C411yescharacteristic
21#11763524C411yescharacteristic
22#11763519C411yescharacteristic
23#11763509C412yes—
24#11763500C412yes—
25#11763499C412yes—
26#11763488C414yes—
27#11763464C411yescharacteristic
28#11763455C412yes—
29#11763366C2211yescharacteristic
30#11763343C2212yes—
31#11763337C2214yes—
32#11763316C2212yes—
33C4×#63252C2212yes—
34C2×C4×D68C2211yescharacteristic
35#117×D17C2212yes—
36#11762938C2214yescomplemented
37#11762936C2212yescomplemented
38#11762936C2212yescomplemented
39#11762936C2212yescomplemented
40#11762933C2212yescomplemented
41#11762933C2212yescomplemented
42#11762933C2212yescomplemented
43#11762886C2212yes—
44#11762885C2214yescomplemented
45#11762880C2214yescomplemented
46#11762879C2214yes—
47#11762878C2214yescomplemented
48#11762878C2214yescomplemented
49#11762878C2214yescomplemented
50#11762874C2212yes—
51#11762874C2211yescharacteristic
52#11762874C2211yescharacteristic
53#11762874C2212yes—
54#11762874C2211yescharacteristic
55#11762874C2211yescharacteristic
56#11762874C2212yes—
57C8×C22⋊D17C2214yescomplemented
58C8×C22⋊D17C2214yescomplemented
59C8×C22⋊D17C2214yescomplemented
60#11762870C2212yescomplemented
61#11762870C2212yescomplemented
62#11762869C2214yescomplemented
63#11762869C2214yescomplemented
64#11762865C2214yescomplemented
65#11762862C2212yescomplemented
66#11762862C2212yescomplemented
67#11762861C2214yescomplemented
68#11762837C2212yes—
69#11762836C2211yescharacteristic
70#11762836C2211yescharacteristic
71#11762835C2212yes—
72#11762834C2214yescomplemented
73#11762834C2214yescomplemented
74C4⋊C8×D17C2214yescomplemented
75C4⋊C8×D17C2214yescomplemented
76#11762776C2211yescharacteristic
77#11762776C2211yescharacteristic
78#11762772C2212yes—
79C2×#10587491C2212yes—
80#11762767C2212yes—
81#11762764C2212yes—
82C4×#63223C2211yescharacteristic
83C2×C4×#3622C2211yescharacteristic
84C2×C17×#131C2212yes—
85C4×#41×C17C2211yescharacteristic
86C17×#424C2212yes—
87C17×#424C2214yescomplemented
88C17×#423C2211yescharacteristic
89C17×#423C2212yescomplemented
90C2×C17×C4⋊C8C2211yescharacteristic
91C2×C17×C4⋊C8C2212yescomplemented
92C2×#41×C17C2311yescharacteristic
93C2×#63252C2×C412yes—
94C22×D68C2×C411yescharacteristic
95C22×C4×D17C2312yes—
96C17×#131—44no—
97C2×M16×C17C2312yes—
98C2×M16×C17C2314yes—
99C22×C8×C17C2312yes—
100C22×C8×C17C2314yes—
101C4×Q8×C17C2×C411yescharacteristic
102C4×Q8×C17C2×C411yescharacteristic
103C4×D4×C17C2×C411yescharacteristic
104C4×D4×C17C2×C412yes—
105C4×D4×C17C2×C412yes—
106C4×D4×C17C2×C411yescharacteristic
107C17×#117C2311yescharacteristic
108C17×#117C2312yes—
109C2×C42×C17C2311yescharacteristic
110C2×C42×C17C2312yes—
111#10587632C2×C412yes—
112#10587632C2×C412yes—
113#10587624C2×C412yes—
114#10587624C2×C412yes—
115#10587623C2×C414yes—
116#10587621C2×C414yes—
117#10587616C2×C412yes—
118#10587615C2×C414yes—
119C4×C22⋊D17C2×C414yes—
120C4×C22⋊D17C2314yes—
121C4×C22⋊D17C2314yes—
122C2×#63227C2×C412yes—
123#10587612C2×C412yes—
124#10587612C2312yes—
125C2×C4⋊Dic17C2×C411yescharacteristic
126#10587610C2×C412yes—
127#10587610C2×C412yes—
128#10587610C2×C412yes—
129C2×#63223C2311yescharacteristic
130C2×#63223C2311yescharacteristic
131C22×#3622C2311yescharacteristic
132C22×#3622C2311yescharacteristic
133M16×D17—44no—
134C2×#63218C2314yes—
135C2×C8×D17—44no—
136C2×C8×D17C2312yes—
137C2×C8×D17C2312yes—
138C2×C8×D17C2312yes—
139C2×C8×D17C2312yes—
140C2×C8×D17C2314yes—
141#10587584C2×C414yes—
142#10587582C2×C414yes—
143#10587580C2×C414yes—
144#10587578C2×C412yes—
145#10587578C2×C412yes—
146C4⋊C4×D17C2×C412yes—
147C4⋊C4×D17C2×C412yes—
148#10587575C2×C414yes—
149#10587571C2×C414yes—
150#10587570C2×C414yes—
151#10587569C2×C414yes—
152C22⋊C4×D17C2×C414yes—
153#10587565C2×C414yes—
154#10587563C2×C414yes—
155#10587562C2×C414yes—
156#10587561C2×C412yes—
157C4×D68C2×C411yescharacteristic
158C4×D68C2×C412yes—
159C4×D68C2×C412yes—
160C4×D68C2×C411yescharacteristic
161C4×D68C2311yescharacteristic
162C4×D68C2312yes—
163C4×D68C2311yescharacteristic
164#10587558C2×C414yes—
165#10587558C2314yes—
166C42×D17C2314yes—
167#10587556C2×C412yes—
168#10587556C2×C412yes—
169#10587555C2×C411yescharacteristic
170#10587555C2×C411yescharacteristic
171C4×Dic34C2×C412yes—
172C4×Dic34C2312yes—
173C4×Dic34C2312yes—
174C17×C4⋊C8C2314yes—
175C17×C4⋊C8C2314yes—
176C17×C4⋊C8C2311yescharacteristic
177C17×C4⋊C8C2311yescharacteristic
178C17×C4⋊C8C2312yes—
179C17×C4⋊C8C2312yes—
180C17×C4⋊C8C2312yes—
181C22⋊#3622C2312yes—
182C22⋊#3622C2312yes—
183C22⋊#3622C2312yes—
184C22⋊#3622C2312yes—
185#10587491C2312yes—
186#10587491C2312yes—
187#10587491C2312yes—
188#10587491C2312yes—
189#10587491C2314yes—
190#10587491C2314yes—
191#10587486C2314yes—
192#10587486C2314yes—
193#10587485C2314yes—
194#10587485C2314yes—
195#10587485C2314yes—
196#10587485C2314yes—
197C8×Dic17C2314yes—
198C8×Dic17C2314yes—
199C4⋊#3622C2312yes—
200C4⋊#3622C2312yes—
201C4⋊#3622C2312yes—
202C4⋊#3622C2312yes—
203#10587474C2312yes—
204C4×#3622C2311yescharacteristic
205C4×#3622C2311yescharacteristic
206C4×#3622C2311yescharacteristic
207C4×#3622C2311yescharacteristic
208C4×#3622C2312yes—
209C23×D17C22×C412yes—
210#41×C17—22no—
211#41×C17—22no—
212C2×Q8×C17C22×C411yescharacteristic
213C2×D4×C17C22×C412yes—
214C2×D4×C17C22×C411yescharacteristic
215C22×C4×C17C22×C411yescharacteristic
216C22×C4×C17C22×C412yes—
217C22×C4×C17C22×C411yescharacteristic
218C22×C4×C17C22×C412yes—
219C22×C4×C17C2412yes—
220C22×C4×C17C2411yescharacteristic
221C2×C22⋊D17C22×C414yes—
222C2×C22⋊D17C22×C414yes—
223C22×Dic17C22×C412yes—
224#63252—28no—
225C2×D68—24no—
226C2×D68C22×C411yescharacteristic
227C2×D68C22×C412yes—
228C2×D68C22×C411yescharacteristic
229C2×C4×D17—24no—
230C2×C4×D17—24no—
231C2×C4×D17C22×C412yes—
232C2×C4×D17C22×C412yes—
233C2×C4×D17C22×C414yes—
234C2×C4×D17C22×C414yes—
235C2×C4×D17C2412yes—
236C2×C4×D17C2412yes—
237C2×Dic34C22×C412yes—
238C2×Dic34C22×C412yes—
239M16×C17—24no—
240M16×C17—44no—
241C2×C8×C17—24no—
242C2×C8×C17—44no—
243C2×C8×C17C2412yes—
244C2×C8×C17C2414yes—
245C2×C8×C17C2412yes—
246C4⋊C4×C17C22×C412yes—
247C4⋊C4×C17C22×C411yescharacteristic
248C4⋊C4×C17C22×C411yescharacteristic
249C4⋊C4×C17C22×C412yes—
250C22⋊C4×C17C22×C412yes—
251C22⋊C4×C17C22×C412yes—
252C22⋊C4×C17C22×C412yes—
253C42×C17C22×C412yes—
254C42×C17C22×C411yescharacteristic
255C42×C17C22×C411yescharacteristic
256C42×C17C22×C412yes—
257C42×C17C2411yescharacteristic
258C42×C17C2411yescharacteristic
259C42×C17C2412yes—
260C22⋊Dic17C22×C414yes—
261C22⋊Dic17C22×C414yes—
262C22⋊Dic17C22×C414yes—
263#63227C22×C412yes—
264#63227C22×C414yes—
265#63227C22×C414yes—
266#63227C22×C414yes—
267#63227C22×C412yes—
268#63227C22×C412yes—
269#63227C22×C412yes—
270#63227C22×C414yes—
271C4⋊Dic17C22×C411yescharacteristic
272C4⋊Dic17C22×C412yes—
273C4⋊Dic17C22×C412yes—
274C4⋊Dic17C22×C412yes—
275C4⋊Dic17C22×C412yes—
276C4⋊Dic17C22×C411yescharacteristic
277C4⋊Dic17C22×C412yes—
278#63225C22×C414yes—
279#63225C22×C414yes—
280#63225C22×C414yes—
281#63225C22×C414yes—
282#63225C22×C414yes—
283#63225C22×C414yes—
284C4×Dic17C22×C414yes—
285C4×Dic17C22×C414yes—
286C4×Dic17C2414yes—
287#63223—22no—
288#63223—22no—
289C2×#3622—22no—
290C2×#3622—22no—
291C2×#3622C2411yescharacteristic
292C2×#3622C2411yescharacteristic
293C2×#3622C2411yescharacteristic
294C2×#3622C2411yescharacteristic
295C2×#3622C2412yes—
296C2×#3622C2412yes—
297#63218—44no—
298C8×D17—42no—
299C8×D17—42no—
300C8×D17—42no—
301C8×D17—42no—
302C8×D17—44no—
303#60271—171nomaximal, Sylow
304C23×C17C23×C412yes—
305C23×C17C23×C411yescharacteristic
306C22×D17—24no—
307C22×D17—24no—
308C22×D17—42no—
309C22×D17C23×C412yes—
310C22×D17C23×C412yes—
311Q8×C17—22no—
312D4×C17—24no—
313D4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—24no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—41no—
319C2×C4×C17—42no—
320C2×C4×C17C23×C411yescharacteristic
321C2×C4×C17C23×C412yes—
322C2×C4×C17C23×C411yescharacteristic
323C2×C4×C17C23×C412yes—
324C2×C4×C17C23×C412yes—
325C2×C4×C17C23×C411yescharacteristic
326C2×C4×C17C23×C411yescharacteristic
327C2×C4×C17C23×C411yescharacteristic
328C2×C4×C17H(5,𝔽2)12yes—
329C2×C4×C172−1+412yes—
330C2×C4×C17C2511yescharacteristic
331C22⋊D17—28no—
332C22⋊D17—44no—
333C2×Dic17—24no—
334C2×Dic17C23×C414yes—
335C2×Dic17C23×C414yes—
336C2×Dic17C23×C412yes—
337C2×Dic17C23×C412yes—
338D68—24no—
339D68—22no—
340D68#13114yescomplemented
341C4×D17—28no—
342C4×D17—24no—
343C4×D17—24no—
344C4×D17—22no—
345C4×D17—22no—
346C4×D17—22no—
347C4×D17—22no—
348C4×D17—44no—
349Dic34—24no—
350Dic34—42no—
351C8×C17—22no—
352C8×C17—22no—
353C8×C17—24no—
354#3622—21no—
355#3622—21no—
356#3622—22no—
357#3622—21no—
358#3622—21no—
359#3622—22no—
360#3475—171no—
361#2994—174no—
362#2994—172no—
363#2993—172no—
364#2992—174no—
365#2990—172no—
366#2988—172no—
367#2962—171no—
368#2960—171no—
369D4×M16—171no—
370#2933—172no—
371#2929—172no—
372C2×C8×D4—171no—
373#2924—172no—
374#2922—171no—
375#2906D1711yescharacteristic, complemented
376C2×#424—172no—
377C22×C17—21no—
378C22×C17—21no—
379C22×C17—22no—
380C22×C17—22no—
381C22×C17—22no—
382C22×C17#52012yes—
383C22×C17C24×C411yescharacteristic
384C2×D17—22no—
385C2×D17—22no—
386C2×D17—22no—
387C2×D17—22no—
388C2×D17—22no—
389C2×D17—48no—
390C2×D17C2×#13114yes—
391C4×C17—22no—
392C4×C17—22no—
393C4×C17—21no—
394C4×C17—21no—
395C4×C17—22no—
396C4×C17—21no—
397C4×C17#52012yes—
398C4×C17C2×#13112yes—
399C4×C17C2×H(5,𝔽2)11yescharacteristic
400C4×C17C2×2−1+411yescharacteristic
401Dic17—22no—
402Dic17—22no—
403Dic17—24no—
404Dic17—24no—
405C2×#131C2×D1712yes—
406C22×M16—172no—
407C23×C8—172no—
408#556—171no—
409#555—171no—
410#554—171no—
411#553—172no—
412#552—172no—
413#552—172no—
414#551—174no—
415#547—171no—
416#546—172no—
417#533—171no—
418#529—174no—
419#529—172no—
420#525—172no—
421C4×#41—172no—
422C4×#41C2×D1711yescharacteristic
423C2×C4×D4—171no—
424C2×#117—172no—
425#446—172no—
426#446—172no—
427#446—172no—
428#446—174no—
429C8×Q8—172no—
430C8×Q8—172no—
431C8×Q8—172no—
432#436—174no—
433#436—172no—
434#435—174no—
435#435—174no—
436#435—174no—
437#435—174no—
438#435—174no—
439C8×D4—174no—
440C8×D4—174no—
441C8×D4—174no—
442C8×D4—171no—
443C8×D4—171no—
444C8×D4—172no—
445C8×D4—171no—
446C8×D4—171no—
447C8×D4—172no—
448C8×D4—172no—
449#433—172no—
450#433—172no—
451#433—174no—
452#433—174no—
453#432—174no—
454#431—172no—
455#431—172no—
456#431—174no—
457#424—172no—
458#424—172no—
459#424—171no—
460#424—171no—
461#424—174no—
462#424—174no—
463#424C2×D1712yes—
464#424C2×D1714yescomplemented
465#423C2×D1711yescharacteristic
466#423C2×D1712yescomplemented
467C2×C4⋊C8—174no—
468C2×C4⋊C8—174no—
469C2×C4⋊C8C2×D1711yescharacteristic
470C2×C4⋊C8C2×D1712yescomplemented
471#408—171no—
472#408—171no—
473#407—172no—
474C2×C22⋊C8—172no—
475#405—172no—
476#405—172no—
477C4×M16—171no—
478C2×C4×C8—171no—
479C2×C17—22no—
480C2×C17—42no—
481C2×C17C2×#52011yescharacteristic
482C2×C17C22×#13111yescharacteristic
483C2×C17#357311yescharacteristic
484D17—24no—
485D17—42no—
486C2×#41—172no—
487C2×#41C22×D1711yescharacteristic
488C22×D4—171no—
489C23×C4—172no—
490#131—44no—
491C2×M16—171no—
492C2×M16—171no—
493C2×M16—174no—
494C2×M16—684no—
495C2×M16C22×D1712yes—
496C2×M16C22×D1714yes—
497C22×C8—171no—
498C22×C8—171no—
499C22×C8—172no—
500C22×C8—172no—
501C22×C8—172no—
502C22×C8—172no—
503C22×C8—174no—
504C22×C8—684no—
505C22×C8C22×D1712yes—
506C22×C8C22×D1714yes—
507C4⋊Q8—171no—
508C4⋊Q8—171no—
509#126—174no—
510#126—174no—
511#126—174no—
512#125—174no—
513#125—172no—
514#125—172no—
515#124—174no—
516#124—172no—
517#123—174no—
518#123—174no—
519#123—174no—
520#123—174no—
521C22⋊Q8—172no—
522C22⋊Q8—172no—
523C22⋊Q8—172no—
524C22⋊Q8—172no—
525C22⋊Q8—172no—
526C22⋊Q8—174no—
527#121—172no—
528#121—172no—
529#121—172no—
530#121—174no—
531#120—174no—
532C4×Q8—172no—
533C4×Q8—172no—
534C4×Q8—172no—
535C4×Q8C4×D1711yescharacteristic
536C4×Q8C4×D1711yescharacteristic
537C4×D4—174no—
538C4×D4—174no—
539C4×D4—174no—
540C4×D4—171no—
541C4×D4—172no—
542C4×D4—171no—
543C4×D4—172no—
544C4×D4—171no—
545C4×D4—172no—
546C4×D4—171no—
547C4×D4C4×D1712yes—
548C4×D4C4×D1711yescharacteristic
549C4×D4C4×D1712yes—
550C4×D4C4×D1711yescharacteristic
551#117—172no—
552#117—172no—
553#117—172no—
554#117—172no—
555#117—174no—
556#117—174no—
557#117—174no—
558#117C22×D1711yescharacteristic
559#117C22×D1712yes—
560C2×C4⋊C4—171no—
561C2×C4⋊C4—172no—
562C2×C4⋊C4—172no—
563C2×C22⋊C4—172no—
564C2×C22⋊C4—174no—
565C2×C42—174no—
566C2×C42C22×D1711yescharacteristic
567C2×C42C22×D1712yes—
568C4⋊C8—174no—
569C4⋊C8—174no—
570C4⋊C8—174no—
571C4⋊C8—174no—
572C4⋊C8—172no—
573C4⋊C8—172no—
574C4⋊C8—172no—
575C4⋊C8—172no—
576C4⋊C8C22×D1714yes—
577C4⋊C8C22×D1714yes—
578C4⋊C8C22×D1711yescharacteristic
579C4⋊C8C22×D1711yescharacteristic
580C4⋊C8C22×D1712yes—
581C4⋊C8C22×D1712yes—
582C4⋊C8C22×D1712yes—
583C22⋊C8—172no—
584C22⋊C8—172no—
585C22⋊C8—172no—
586C22⋊C8—172no—
587C22⋊C8—172no—
588C22⋊C8—172no—
589C22⋊C8—172no—
590C22⋊C8—172no—
591C22⋊C8—174no—
592C22⋊C8—174no—
593#97—174no—
594#97—174no—
595#97—172no—
596C4×C8—174no—
597C4×C8—174no—
598C4×C8—171no—
599C4×C8—171no—
600C4×C8—171no—
601C4×C8—171no—
602C4×C8—172no—
603C17#6027111yescharacteristic, complemented, Sylow
604C24—172no—
605#41—22no—
606#41—22no—
607#41—348no—
608C2×Q8—172no—
609C2×Q8—172no—
610C2×Q8C2×C4×D1711yescharacteristic
611C2×D4—174no—
612C2×D4—174no—
613C2×D4—171no—
614C2×D4—172no—
615C2×D4—171no—
616C2×D4—344no—
617C2×D4C2×C4×D1712yes—
618C2×D4C2×C4×D1711yescharacteristic
619C22×C4—172no—
620C22×C4—174no—
621C22×C4—172no—
622C22×C4—172no—
623C22×C4—172no—
624C22×C4—172no—
625C22×C4—174no—
626C22×C4—344no—
627C22×C4—344no—
628C22×C4C2×C4×D1711yescharacteristic
629C22×C4C2×C4×D1712yes—
630C22×C4C2×C4×D1711yescharacteristic
631C22×C4C2×C4×D1712yes—
632C22×C4C23×D1712yes—
633C22×C4C23×D1711yescharacteristic
634M16—24no—
635M16—44no—
636M16—342no—
637M16—342no—
638M16—684no—
639C2×C8—24no—
640C2×C8—44no—
641C2×C8—171no—
642C2×C8—172no—
643C2×C8—171no—
644C2×C8—171no—
645C2×C8—171no—
646C2×C8—172no—
647C2×C8—342no—
648C2×C8—342no—
649C2×C8—682no—
650C2×C8—682no—
651C2×C8—682no—
652C2×C8—682no—
653C2×C8—684no—
654C2×C8C23×D1712yes—
655C2×C8C23×D1714yes—
656C2×C8C23×D1712yes—
657C4⋊C4—171no—
658C4⋊C4—172no—
659C4⋊C4—172no—
660C4⋊C4—174no—
661C4⋊C4—174no—
662C4⋊C4—171no—
663C4⋊C4—172no—
664C4⋊C4—172no—
665C4⋊C4—174no—
666C4⋊C4—174no—
667C4⋊C4—174no—
668C4⋊C4—174no—
669C4⋊C4—172no—
670C4⋊C4C2×C4×D1711yescharacteristic
671C4⋊C4C2×C4×D1711yescharacteristic
672C4⋊C4C2×C4×D1712yes—
673C4⋊C4C2×C4×D1712yes—
674C22⋊C4—174no—
675C22⋊C4—174no—
676C22⋊C4—174no—
677C22⋊C4—172no—
678C22⋊C4—174no—
679C22⋊C4—174no—
680C22⋊C4—172no—
681C22⋊C4—172no—
682C22⋊C4—172no—
683C22⋊C4—174no—
684C22⋊C4—174no—
685C22⋊C4C2×C4×D1712yes—
686C22⋊C4C2×C4×D1712yes—
687C22⋊C4C2×C4×D1712yes—
688C42—174no—
689C42—174no—
690C42—174no—
691C42C2×C4×D1712yes—
692C42C2×C4×D1711yescharacteristic
693C42C2×C4×D1711yescharacteristic
694C42C2×C4×D1712yes—
695C42C23×D1711yescharacteristic
696C42C23×D1711yescharacteristic
697C42C23×D1712yes—
698C23—172no—
699C23—172no—
700C23—344no—
701C23—344no—
702C23—682no—
703C23C22×C4×D1712yes—
704C23C22×C4×D1711yescharacteristic
705Q8—22no—
706Q8—344no—
707Q8—682no—
708D4—24no—
709D4—22no—
710D4—174no—
711D4—344no—
712D4—348no—
713D4—342no—
714D4—684no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—172no—
722C2×C4—174no—
723C2×C4—174no—
724C2×C4—172no—
725C2×C4—348no—
726C2×C4—344no—
727C2×C4—344no—
728C2×C4—344no—
729C2×C4—342no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—684no—
734C2×C4C22×C4×D1712yes—
735C2×C4C22×C4×D1712yes—
736C2×C4C22×C4×D1711yescharacteristic
737C2×C4C22×C4×D1712yes—
738C2×C4C22×C4×D1711yescharacteristic
739C2×C4C22×C4×D1711yescharacteristic
740C2×C4C22×C4×D1711yescharacteristic
741C2×C4C22×C4×D1711yescharacteristic
742C2×C4#1058769112yes—
743C2×C4#1058769412yes—
744C2×C4C24×D1711yescharacteristic
745C8—22no—
746C8—22no—
747C8—24no—
748C8—341no—
749C8—341no—
750C8—342no—
751C8—341no—
752C8—341no—
753C8—342no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—174no—
760C22—342no—
761C22—342no—
762C22—342no—
763C22—342no—
764C22—342no—
765C22—688no—
766C22#1176329012yes—
767C22C23×C4×D1711yescharacteristic
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—21no—
773C4—22no—
774C4—344no—
775C4—344no—
776C4—342no—
777C4—342no—
778C4#1176329012yes—
779C4#131×D1712yes—
780C4C2×#1058769111yescharacteristic
781C4C2×#1058769411yescharacteristic
782C2—22no—
783C2—42no—
784C2—344no—
785C2—682no—
786C2C2×#1176329011yescharacteristic
787C2C2×#131×D1711yescharacteristic
788C2#1454349711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingC17×#2906C2
prime radical#14542348C2
cosocleC2×C4×C17C25
hypercenter#2906D17
hypocenterC17#60271
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #14537942C2semidirect
3. #14537940C2semidirect
4. #14537929C2semidirect
5. #14537921C2semidirect
6. #14537910C2semidirect
7. #14537893C2semidirect
8. #14537727C2semidirect
9. #14537714C2semidirect
10. #14537519C2semidirect
11. #14537506C2semidirect
12. #14537476C2semidirect
13. C2×#11762874C2semidirect
14. #14537441C2semidirect
15. #14537428C2semidirect
16. D17×#424C2semidirect
17. C17×#2906C2semidirect
36. #11762938C22semidirect
37. #11762936C22semidirect
38. #11762936C22semidirect
39. #11762936C22semidirect
40. #11762933C22semidirect
41. #11762933C22semidirect
42. #11762933C22semidirect
44. #11762885C22semidirect
45. #11762880C22semidirect
47. #11762878C22semidirect
48. #11762878C22semidirect
49. #11762878C22semidirect
57. C8×C22⋊D17C22semidirect
58. C8×C22⋊D17C22semidirect
59. C8×C22⋊D17C22semidirect
60. #11762870C22semidirect
61. #11762870C22semidirect
62. #11762869C22semidirect
63. #11762869C22semidirect
64. #11762865C22semidirect
65. #11762862C22semidirect
66. #11762862C22semidirect
67. #11762861C22semidirect
72. #11762834C22semidirect
73. #11762834C22semidirect
74. C4⋊C8×D17C22semidirect
75. C4⋊C8×D17C22semidirect
87. C17×#424C22semidirect
89. C17×#423C22semidirect
91. C2×C17×C4⋊C8C22semidirect
340. D68#131semidirect
375. #2906D17semidirect
464. #424C2×D17semidirect
466. #423C2×D17semidirect
470. C2×C4⋊C8C2×D17semidirect
603. C17#60271semidirect

Maximal subgroups

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

subgroupindex
#145423482
#145379422
#145379402
#145379292
#145379212
#145379102
#145378932
#145377272
#145377142
#145375192
#145375062
#145374762
C2×#117628742
#145374412
#145374282
D17×#4242
C17×#29062
#6027117