Finite Group Databasebeta

← #17899554

Subgroups — #17899554

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#14542342C211yesmaximal, characteristic
2#14537945C212yesmaximal, complemented
3#14537937C214yesmaximal, complemented
4#14537928C212yesmaximal, complemented
5#14537924C214yesmaximal, complemented
6#14537907C212yesmaximal, complemented
7#14537891C212yesmaximal, complemented
8#14537731C211yesmaximal, characteristic, complemented
9#14537714C211yesmaximal, characteristic, complemented
10#14537509C212yesmaximal, complemented
11#14537474C212yesmaximal, complemented
12C2×D4×#3622C211yesmaximal, characteristic, complemented
13#14537444C212yesmaximal, complemented
14#14537429C211yesmaximal, characteristic, complemented
15#14537353C211yesmaximal, characteristic, complemented
16C2×#11762837C212yesmaximal, complemented
17D4×M16×C17C211yesmaximal, characteristic, complemented
18C2×#10587593C2212yes—
19C23×#3622C2212yes—
20#11763529C411yescharacteristic
21#11763524C411yescharacteristic
22#11763516C411yescharacteristic
23#11763505C412yes—
24#11763499C412yes—
25#11763494C412yes—
26#11763485C414yes—
27#11763463C411yescharacteristic
28#11763453C412yes—
29#11763366C2211yescharacteristic
30#11763341C2212yes—
31#11763339C2214yes—
32#11763320C2212yes—
33C4×#63252C2211yescharacteristic
34C4×#63254C2212yes—
35C2×#10587612C2212yes—
36#11762939C2212yescomplemented
37#11762937C2214yescomplemented
38#11762936C2212yescomplemented
39#11762936C2212yescomplemented
40C8×Dic34C2212yescomplemented
41#11762933C2212yescomplemented
42#11762933C2212yescomplemented
43#11762885C2214yescomplemented
44#11762880C2214yescomplemented
45#11762878C2214yescomplemented
46#11762877C2214yescomplemented
47#11762877C2214yescomplemented
48D4×#3622C2211yescharacteristic
49D4×#3622C2211yescharacteristic
50D4×#3622C2212yes—
51D4×#3622C2211yescharacteristic
52D4×#3622C2212yes—
53D4×#3622C2211yescharacteristic
54C8×C22⋊D17C2214yescomplemented
55#11762872C2214yescomplemented
56#11762872C2214yescomplemented
57#11762871C2212yescomplemented
58#11762871C2212yescomplemented
59#11762867C2214yescomplemented
60#11762867C2214yescomplemented
61#11762863C2214yescomplemented
62#11762860C2212yescomplemented
63#11762860C2212yescomplemented
64#11762859C2214yescomplemented
65#11762837C2212yes—
66#11762837C2212yes—
67#11762837C2211yescharacteristic
68#11762837C2212yes—
69#11762837C2211yescharacteristic
70#11762837C2214yescomplemented
71#11762837C2214yescomplemented
72#11762834C2214yescomplemented
73#11762831C2212yescomplemented
74C2×C4⋊#3622C2211yescharacteristic
75C2×#10587485C2214yescomplemented
76C2×#10587485C2214yescomplemented
77C4⋊C8×D17C2212yescomplemented
78#11762777C2211yescharacteristic
79#11762777C2211yescharacteristic
80C2×C22⋊#3622C2212yes—
81#11762767C2212yes—
82#11762767C2212yes—
83C2×C4×#3622C2211yescharacteristic
84C22×M16×C17C2212yes—
85C2×C4×D4×C17C2211yescharacteristic
86C17×#436C2212yes—
87C17×#435C2214yes—
88C8×D4×C17C2212yes—
89C17×#423C2211yescharacteristic
90C17×#407C2212yes—
91C4×M16×C17C2211yescharacteristic
92C22×D4×C17C2×C411yescharacteristic
93C23×C4×C17C2312yes—
94C2×#63254C2×C412yes—
95C2×#63252C2311yescharacteristic
96C2×M16×C17—44no—
97C2×M16×C17C2311yescharacteristic
98C2×M16×C17C2312yes—
99C2×M16×C17C2311yescharacteristic
100C2×M16×C17C2314yes—
101C22×C8×C17C2314yes—
102C4×D4×C17C2×C411yescharacteristic
103C4×D4×C17C2×C412yes—
104C4×D4×C17C2×C411yescharacteristic
105C4×D4×C17C2311yescharacteristic
106C4×D4×C17C2312yes—
107C4×D4×C17C2311yescharacteristic
108C2×C4⋊C4×C17C2×C411yescharacteristic
109C2×C22⋊C4×C17C2×C412yes—
110C2×C42×C17C2311yescharacteristic
111#10587639C2×C414yes—
112C2×C22⋊Dic17C2×C414yes—
113#10587625C2×C414yes—
114#10587624C2×C412yes—
115#10587622C2×C412yes—
116#10587621C2×C414yes—
117D4×Dic17C2×C412yes—
118#10587616C2×C412yes—
119#10587616C2×C412yes—
120#10587615C2×C414yes—
121C4×C22⋊D17C2×C412yes—
122C4×C22⋊D17C2×C412yes—
123C4×C22⋊D17C2314yes—
124C4×C22⋊D17C2314yes—
125#10587612C2×C414yes—
126#10587612C2×C412yes—
127#10587612C2×C412yes—
128#10587612C2311yescharacteristic
129#10587612C2312yes—
130#10587612C2314yes—
131C2×C4⋊Dic17C2×C412yes—
132C2×C4⋊Dic17C2×C412yes—
133#10587610C2×C412yes—
134#10587610C2×C412yes—
135#10587610C2×C412yes—
136#10587610C2×C412yes—
137C2×C4×Dic17C2314yes—
138C22×#3622—44no—
139C22×#3622C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141C22×#3622C2312yes—
142C22×#3622C2312yes—
143C22×#3622C2312yes—
144C22×#3622C2312yes—
145C22×#3622C2312yes—
146#10587593—44no—
147C2×#63218C2314yes—
148C2×C8×D17C2314yes—
149#10587584C2×C414yes—
150#10587583C2×C412yes—
151#10587578C2×C412yes—
152#10587576C2×C412yes—
153#10587575C2×C414yes—
154#10587573C2×C412yes—
155#10587572C2×C414yes—
156#10587571C2×C414yes—
157#10587569C2×C414yes—
158#10587567C2×C414yes—
159#10587565C2×C414yes—
160#10587565C2×C414yes—
161#10587564C2×C414yes—
162#10587563C2×C414yes—
163C4×D68C2×C411yescharacteristic
164C4×D68C2×C411yescharacteristic
165#10587558C2312yes—
166C42×D17C2312yes—
167#10587556C2×C412yes—
168#10587555C2×C411yescharacteristic
169#10587555C2×C411yescharacteristic
170C4×Dic34C2×C411yescharacteristic
171C4×Dic34C2×C411yescharacteristic
172C4×Dic34C2312yes—
173C4×Dic34C2312yes—
174C17×C4⋊C8C2312yes—
175C17×C4⋊C8C2312yes—
176C17×C22⋊C8C2314yes—
177C17×C22⋊C8C2314yes—
178C17×#97C2312yes—
179C4×C8×C17C2312yes—
180C22⋊#3622C2312yes—
181C22⋊#3622C2312yes—
182C22⋊#3622C2312yes—
183C22⋊#3622C2312yes—
184#10587491C2312yes—
185#10587491C2312yes—
186#10587491C2312yes—
187#10587491C2312yes—
188#10587486C2314yes—
189#10587486C2314yes—
190#10587485C2314yes—
191#10587485C2312yes—
192#10587485C2312yes—
193#10587485C2314yes—
194#10587485C2314yes—
195#10587485C2314yes—
196#10587485C2314yes—
197#10587485C2314yes—
198#10587485C2312yes—
199#10587485C2312yes—
200C8×Dic17C2314yes—
201C8×Dic17C2314yes—
202C4⋊#3622C2311yescharacteristic
203C4⋊#3622C2311yescharacteristic
204C4⋊#3622C2312yes—
205C4×#3622C2311yescharacteristic
206C4×#3622C2311yescharacteristic
207C4×#3622C2311yescharacteristic
208C4×#3622C2311yescharacteristic
209C24×C17C22×C412yes—
210C2×D4×C17—24no—
211C2×D4×C17C22×C412yes—
212C2×D4×C17C22×C411yescharacteristic
213C2×D4×C17C22×C411yescharacteristic
214C22×C4×C17—24no—
215C22×C4×C17—24no—
216C22×C4×C17C22×C412yes—
217C22×C4×C17C22×C412yes—
218C22×C4×C17C22×C412yes—
219C22×C4×C17C22×C411yescharacteristic
220C22×C4×C17C22×C411yescharacteristic
221C22×C4×C17C2412yes—
222C22×C4×C17C2412yes—
223C22×C4×C17C2411yescharacteristic
224C2×C22⋊D17C22×C412yes—
225C2×C22⋊D17C22×C414yes—
226C2×C22⋊D17C22×C414yes—
227C22×Dic17C22×C414yes—
228C22×Dic17C22×C414yes—
229#63254—28no—
230#63252—22no—
231#63252—22no—
232C2×D68C22×C411yescharacteristic
233C2×C4×D17C22×C412yes—
234C2×C4×D17C22×C412yes—
235C2×C4×D17C2412yes—
236C2×Dic34C22×C411yescharacteristic
237C2×Dic34C22×C412yes—
238C2×Dic34C22×C412yes—
239M16×C17—22no—
240M16×C17—24no—
241M16×C17—22no—
242M16×C17—44no—
243C2×C8×C17—44no—
244C2×C8×C17C2412yes—
245C2×C8×C17C2414yes—
246C2×C8×C17C2412yes—
247C4⋊C4×C17C22×C411yescharacteristic
248C4⋊C4×C17C22×C412yes—
249C4⋊C4×C17C22×C411yescharacteristic
250C22⋊C4×C17C22×C412yes—
251C22⋊C4×C17C22×C412yes—
252C22⋊C4×C17C22×C412yes—
253C22⋊C4×C17C22×C412yes—
254C42×C17C22×C411yescharacteristic
255C42×C17C22×C411yescharacteristic
256C42×C17C2411yescharacteristic
257C42×C17C2411yescharacteristic
258C22⋊Dic17C22×C414yes—
259C22⋊Dic17C22×C414yes—
260C22⋊Dic17C22×C414yes—
261C22⋊Dic17C22×C414yes—
262C22⋊Dic17C22×C414yes—
263C22⋊Dic17C22×C412yes—
264#63227C22×C412yes—
265#63227C22×C412yes—
266#63227C22×C414yes—
267#63227C22×C414yes—
268C4⋊Dic17C22×C411yescharacteristic
269C4⋊Dic17C22×C411yescharacteristic
270C4⋊Dic17C22×C412yes—
271C4⋊Dic17C22×C412yes—
272C4⋊Dic17C22×C412yes—
273C4⋊Dic17C22×C412yes—
274C4⋊Dic17C22×C414yes—
275C4⋊Dic17C22×C414yes—
276#63225C22×C412yes—
277#63225C22×C412yes—
278#63225C22×C414yes—
279#63225C22×C414yes—
280#63225C22×C414yes—
281#63225C22×C414yes—
282C4×Dic17C22×C412yes—
283C4×Dic17C22×C412yes—
284C4×Dic17C22×C414yes—
285C4×Dic17C22×C414yes—
286C4×Dic17C2414yes—
287C4×Dic17C2412yes—
288C2×#3622—24no—
289C2×#3622—22no—
290C2×#3622—22no—
291C2×#3622—42no—
292C2×#3622—42no—
293C2×#3622—42no—
294C2×#3622—42no—
295C2×#3622C2411yescharacteristic
296C2×#3622C2411yescharacteristic
297C2×#3622C2411yescharacteristic
298C2×#3622C2411yescharacteristic
299C2×#3622C2412yes—
300C2×#3622C2412yes—
301#63218—44no—
302C8×D17—44no—
303#60271—171nomaximal, Sylow
304C23×C17—24no—
305C23×C17—24no—
306C23×C17—42no—
307C23×C17C23×C412yes—
308C23×C17C23×C411yescharacteristic
309C23×C17C23×C412yes—
310C22×D17C23×C412yes—
311D4×C17—24no—
312D4×C17—22no—
313D4×C17#13114yescomplemented
314C2×C4×C17—24no—
315C2×C4×C17—24no—
316C2×C4×C17—24no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—41no—
323C2×C4×C17C23×C411yescharacteristic
324C2×C4×C17C23×C411yescharacteristic
325C2×C4×C17C23×C411yescharacteristic
326C2×C4×C17C23×C412yes—
327C2×C4×C17C23×C412yes—
328C2×C4×C17C23×C411yescharacteristic
329C2×C4×C17C23×C411yescharacteristic
330C2×C4×C17H(5,𝔽2)12yes—
331C2×C4×C172−1+412yes—
332C2×C4×C17C2511yescharacteristic
333C22⋊D17—24no—
334C22⋊D17—28no—
335C22⋊D17—44no—
336C2×Dic17—28no—
337C2×Dic17—44no—
338C2×Dic17C23×C412yes—
339C2×Dic17C23×C414yes—
340C2×Dic17C23×C414yes—
341C2×Dic17C23×C412yes—
342C2×Dic17C23×C412yes—
343D68—22no—
344C4×D17—24no—
345C4×D17—22no—
346C4×D17—22no—
347C4×D17—42no—
348Dic34—22no—
349Dic34—24no—
350Dic34—42no—
351C8×C17—22no—
352C8×C17—24no—
353C8×C17—22no—
354#3622—22no—
355#3622—22no—
356#3622—21no—
357#3622—21no—
358#3622—21no—
359#3622—21no—
360#3475—171no—
361#2994—172no—
362#2994—174no—
363#2993—172no—
364#2992—174no—
365#2990—172no—
366#2988—172no—
367#2962—171no—
368#2960—171no—
369D4×M16D1711yescharacteristic, complemented
370#2933—172no—
371#2929—172no—
372C2×C8×D4—171no—
373#2924—172no—
374#2922—171no—
375#2906—171no—
376C2×#424—172no—
377C22×C17—22no—
378C22×C17—21no—
379C22×C17—22no—
380C22×C17—21no—
381C22×C17—22no—
382C22×C17—22no—
383C22×C17—22no—
384C22×C17—48no—
385C22×C17#52012yes—
386C22×C17C2×#13114yes—
387C22×C17C24×C411yescharacteristic
388C2×D17—22no—
389C2×D17—22no—
390C2×D17—22no—
391C4×C17—22no—
392C4×C17—22no—
393C4×C17—21no—
394C4×C17—21no—
395C4×C17—21no—
396C4×C17#52012yes—
397C4×C17C2×#13112yes—
398C4×C17C2×H(5,𝔽2)11yescharacteristic
399C4×C17C2×2−1+411yescharacteristic
400Dic17—22no—
401Dic17—24no—
402Dic17—22no—
403Dic17—24no—
404Dic17—22no—
405C2×#131—172no—
406C22×M16C2×D1712yes—
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×#41—171no—
423C2×C4×D4C2×D1711yescharacteristic
424C2×#117—172no—
425#446—172no—
426#446—172no—
427#446—174no—
428#446—172no—
429C8×Q8—172no—
430C8×Q8—172no—
431C8×Q8—172no—
432#436—174no—
433#436C2×D1712yes—
434#435—174no—
435#435—174no—
436#435—174no—
437#435—174no—
438#435C2×D1714yes—
439C8×D4—174no—
440C8×D4—171no—
441C8×D4—171no—
442C8×D4—172no—
443C8×D4—171no—
444C8×D4—171no—
445C8×D4—172no—
446C8×D4—174no—
447C8×D4—174no—
448C8×D4C2×D1712yes—
449#433—174no—
450#433—174no—
451#433—172no—
452#433—172no—
453#432—174no—
454#431—174no—
455#431—172no—
456#431—172no—
457#424—171no—
458#424—172no—
459#424—172no—
460#424—172no—
461#424—174no—
462#424—174no—
463#424—171no—
464#424—174no—
465#423—172no—
466#423C2×D1711yescharacteristic
467C2×C4⋊C8—174no—
468C2×C4⋊C8—174no—
469C2×C4⋊C8—171no—
470C2×C4⋊C8—172no—
471#408—171no—
472#408—171no—
473#407C2×D1712yes—
474C2×C22⋊C8—172no—
475#405—172no—
476#405—172no—
477C4×M16C2×D1711yescharacteristic
478C2×C4×C8—171no—
479C2×C17—22no—
480C2×C17—24no—
481C2×C17—42no—
482C2×C17C2×#52011yescharacteristic
483C2×C17C22×#13111yescharacteristic
484C2×C17#357311yescharacteristic
485D17—42no—
486C2×#41—172no—
487C2×#41—171no—
488C22×D4C4×D1711yescharacteristic
489C23×C4C22×D1712yes—
490#131—684no—
491C2×M16—44no—
492C2×M16—174no—
493C2×M16C22×D1711yescharacteristic
494C2×M16C22×D1712yes—
495C2×M16C22×D1711yescharacteristic
496C2×M16C22×D1714yes—
497C22×C8—171no—
498C22×C8—172no—
499C22×C8—171no—
500C22×C8—172no—
501C22×C8—172no—
502C22×C8—172no—
503C22×C8—172no—
504C22×C8—174no—
505C22×C8—684no—
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—172no—
516#124—174no—
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—174no—
528#121—172no—
529#121—172no—
530#121—172no—
531#120—174no—
532C4×Q8—172no—
533C4×Q8—171no—
534C4×Q8—171no—
535C4×Q8—172no—
536C4×Q8—172no—
537C4×D4—172no—
538C4×D4—172no—
539C4×D4—172no—
540C4×D4—174no—
541C4×D4—174no—
542C4×D4—174no—
543C4×D4—171no—
544C4×D4—171no—
545C4×D4C4×D1711yescharacteristic
546C4×D4C4×D1712yes—
547C4×D4C4×D1711yescharacteristic
548C4×D4C22×D1711yescharacteristic
549C4×D4C22×D1712yes—
550C4×D4C22×D1711yescharacteristic
551#117—174no—
552#117—172no—
553#117—172no—
554#117—171no—
555#117—172no—
556#117—174no—
557#117—172no—
558#117—174no—
559#117—172no—
560C2×C4⋊C4—172no—
561C2×C4⋊C4—172no—
562C2×C4⋊C4C4×D1711yescharacteristic
563C2×C22⋊C4—174no—
564C2×C22⋊C4C4×D1712yes—
565C2×C42—174no—
566C2×C42—172no—
567C2×C42C22×D1711yescharacteristic
568C4⋊C8—174no—
569C4⋊C8—172no—
570C4⋊C8—172no—
571C4⋊C8—174no—
572C4⋊C8—174no—
573C4⋊C8—174no—
574C4⋊C8—174no—
575C4⋊C8—174no—
576C4⋊C8—172no—
577C4⋊C8—172no—
578C4⋊C8—171no—
579C4⋊C8—171no—
580C4⋊C8—172no—
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⋊C8C22×D1714yes—
592C22⋊C8C22×D1714yes—
593#97—174no—
594#97—174no—
595#97C22×D1712yes—
596C4×C8—174no—
597C4×C8—174no—
598C4×C8—171no—
599C4×C8—171no—
600C4×C8—171no—
601C4×C8—171no—
602C4×C8C22×D1712yes—
603C17#6027111yescharacteristic, complemented, Sylow
604C24C2×C4×D1712yes—
605#41—348no—
606#41—342no—
607#41—342no—
608C2×Q8—171no—
609C2×Q8—172no—
610C2×Q8—172no—
611C2×D4—24no—
612C2×D4—172no—
613C2×D4—174no—
614C2×D4—174no—
615C2×D4—171no—
616C2×D4C2×C4×D1712yes—
617C2×D4C2×C4×D1711yescharacteristic
618C2×D4C2×C4×D1711yescharacteristic
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—174no—
622C22×C4—174no—
623C22×C4—172no—
624C22×C4—172no—
625C22×C4—172no—
626C22×C4C2×C4×D1711yescharacteristic
627C22×C4C2×C4×D1712yes—
628C22×C4C2×C4×D1712yes—
629C22×C4C2×C4×D1712yes—
630C22×C4C2×C4×D1711yescharacteristic
631C22×C4C23×D1712yes—
632C22×C4C23×D1712yes—
633C22×C4C23×D1711yescharacteristic
634M16—22no—
635M16—24no—
636M16—22no—
637M16—44no—
638M16—684no—
639C2×C8—44no—
640C2×C8—171no—
641C2×C8—171no—
642C2×C8—172no—
643C2×C8—171no—
644C2×C8—171no—
645C2×C8—172no—
646C2×C8—342no—
647C2×C8—344no—
648C2×C8—342no—
649C2×C8—684no—
650C2×C8—682no—
651C2×C8—682no—
652C2×C8—682no—
653C2×C8—682no—
654C2×C8C23×D1712yes—
655C2×C8C23×D1714yes—
656C2×C8C23×D1712yes—
657C4⋊C4—171no—
658C4⋊C4—171no—
659C4⋊C4—172no—
660C4⋊C4—172no—
661C4⋊C4—174no—
662C4⋊C4—174no—
663C4⋊C4—172no—
664C4⋊C4—172no—
665C4⋊C4—174no—
666C4⋊C4—174no—
667C4⋊C4—172no—
668C4⋊C4—174no—
669C4⋊C4—174no—
670C4⋊C4—172no—
671C4⋊C4C2×C4×D1711yescharacteristic
672C4⋊C4C2×C4×D1711yescharacteristic
673C4⋊C4C2×C4×D1712yes—
674C22⋊C4—172no—
675C22⋊C4—174no—
676C22⋊C4—174no—
677C22⋊C4—174no—
678C22⋊C4—174no—
679C22⋊C4—174no—
680C22⋊C4—172no—
681C22⋊C4—174no—
682C22⋊C4—172no—
683C22⋊C4—174no—
684C22⋊C4C2×C4×D1712yes—
685C22⋊C4C2×C4×D1712yes—
686C22⋊C4C2×C4×D1712yes—
687C22⋊C4C2×C4×D1712yes—
688C42—174no—
689C42—174no—
690C42—172no—
691C42—172no—
692C42—174no—
693C42—172no—
694C42C2×C4×D1711yescharacteristic
695C42C2×C4×D1711yescharacteristic
696C42C23×D1711yescharacteristic
697C42C23×D1711yescharacteristic
698C23—24no—
699C23—24no—
700C23—42no—
701C23—172no—
702C23C22×C4×D1712yes—
703C23C22×C4×D1711yescharacteristic
704C23C22×C4×D1712yes—
705Q8—342no—
706Q8—344no—
707Q8—682no—
708D4—24no—
709D4—22no—
710D4—344no—
711D4—348no—
712D4—342no—
713D4—684no—
714D4#1058759314yescomplemented
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—172no—
725C2×C4—172no—
726C2×C4—174no—
727C2×C4—174no—
728C2×C4—172no—
729C2×C4—348no—
730C2×C4—344no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—682no—
734C2×C4—684no—
735C2×C4C22×C4×D1712yes—
736C2×C4C22×C4×D1711yescharacteristic
737C2×C4C22×C4×D1711yescharacteristic
738C2×C4C22×C4×D1711yescharacteristic
739C2×C4C22×C4×D1712yes—
740C2×C4C22×C4×D1711yescharacteristic
741C2×C4C22×C4×D1711yescharacteristic
742C2×C4#1058769112yes—
743C2×C4#1058769712yes—
744C2×C4C24×D1711yescharacteristic
745C8—22no—
746C8—24no—
747C8—22no—
748C8—341no—
749C8—341no—
750C8—342no—
751C8—342no—
752C8—341no—
753C8—341no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—48no—
762C22—342no—
763C22—342no—
764C22—342no—
765C22#1176328812yes—
766C22C2×#1058759314yes—
767C22C23×C4×D1711yescharacteristic
768C4—21no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—22no—
773C4—342no—
774C4—344no—
775C4—342no—
776C4—344no—
777C4—342no—
778C4#1176328812yes—
779C4C2×#1058759312yes—
780C4C2×#1058769111yescharacteristic
781C4C2×#1058769711yescharacteristic
782C2—22no—
783C2—24no—
784C2—42no—
785C2—682no—
786C2C2×#1176328811yescharacteristic
787C2C22×#1058759311yescharacteristic
788C2#1454349711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingD4×M16×C17C2
prime radical#14542342C2
cosocleC2×C4×C17C25
hypercenterD4×M16D17
hypocenterC17#60271
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #14537945C2semidirect
3. #14537937C2semidirect
4. #14537928C2semidirect
5. #14537924C2semidirect
6. #14537907C2semidirect
7. #14537891C2semidirect
8. #14537731C2semidirect
9. #14537714C2semidirect
10. #14537509C2semidirect
11. #14537474C2semidirect
12. C2×D4×#3622C2semidirect
13. #14537444C2semidirect
14. #14537429C2semidirect
15. #14537353C2semidirect
16. C2×#11762837C2semidirect
17. D4×M16×C17C2semidirect
36. #11762939C22semidirect
37. #11762937C22semidirect
38. #11762936C22semidirect
39. #11762936C22semidirect
40. C8×Dic34C22semidirect
41. #11762933C22semidirect
42. #11762933C22semidirect
43. #11762885C22semidirect
44. #11762880C22semidirect
45. #11762878C22semidirect
46. #11762877C22semidirect
47. #11762877C22semidirect
54. C8×C22⋊D17C22semidirect
55. #11762872C22semidirect
56. #11762872C22semidirect
57. #11762871C22semidirect
58. #11762871C22semidirect
59. #11762867C22semidirect
60. #11762867C22semidirect
61. #11762863C22semidirect
62. #11762860C22semidirect
63. #11762860C22semidirect
64. #11762859C22semidirect
70. #11762837C22semidirect
71. #11762837C22semidirect
72. #11762834C22semidirect
73. #11762831C22semidirect
75. C2×#10587485C22semidirect
76. C2×#10587485C22semidirect
77. C4⋊C8×D17C22semidirect
313. D4×C17#131semidirect
369. D4×M16D17semidirect
603. C17#60271semidirect
714. D4#10587593semidirect

Maximal subgroups

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

subgroupindex
#145423422
#145379452
#145379372
#145379282
#145379242
#145379072
#145378912
#145377312
#145377142
#145375092
#145374742
C2×D4×#36222
#145374442
#145374292
#145373532
C2×#117628372
D4×M16×C172
#6027117