Finite Group Databasebeta

← #17240492

Subgroups — #17240492

Order 4352.

2570 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763320C211yesmaximal, characteristic, complemented
2#14536819C211yesmaximal, characteristic, complemented
3#14536812C211yesmaximal, characteristic, complemented
4#14536811C211yesmaximal, characteristic, complemented
5#14536806C211yesmaximal, characteristic, complemented
6#14536797C212yesmaximal, complemented
7#14536795C212yesmaximal, complemented
8#14536786C212yesmaximal, complemented
9#14536784C212yesmaximal, complemented
10#14536779C214yesmaximal, complemented
11#14532043C212yesmaximal, complemented
12#14532041C212yesmaximal, complemented
13#14532026C214yesmaximal, complemented
14#14531999C212yesmaximal, complemented
15#14531997C212yesmaximal, complemented
16#14531167C211yesmaximal, characteristic, complemented
17C2×C17×#525C211yesmaximal, characteristic, complemented
18C22×#63252C2211yescharacteristic
19#11763320—28no—
20C2×#10587615C2212yes—
21C2×#10587610C2211yescharacteristic
22C2×#10587610C2211yescharacteristic
23C2×#10587616C2211yescharacteristic
24C2×#10587616C2211yescharacteristic
25C2×#10587639C2212yes—
26C2×C4×C22⋊D17C2212yes—
27C2×C4×C22⋊D17C2212yes—
28C2×C4×C22⋊D17C2214yescomplemented
29C2×#10587612C2211yescharacteristic
30C2×#10587612C2212yes—
31#11762748C2212yescomplemented
32#11762747C2212yescomplemented
33#11762745C2212yescomplemented
34#11762744C2212yescomplemented
35#11762742C2214yescomplemented
36#11762740C2212yescomplemented
37#11762739C2212yescomplemented
38#11762737C2214yes—
39#11762737C2214yes—
40#11762737C2214yes—
41#11762735C2212yescomplemented
42#11762734C2212yescomplemented
43#11762732C2214yescomplemented
44#11762731C2214yescomplemented
45#11762729C2212yescomplemented
46#11762728C2212yescomplemented
47#11762726C2212yescomplemented
48#11762725C2214yescomplemented
49#11762724C2214yes—
50#11762724C2214yes—
51#11762724C2214yes—
52#11762723C2214yes—
53#11762723C2214yes—
54#11762723C2214yes—
55#11762723C2212yescomplemented
56#11762721C2212yescomplemented
57#11762720C2212yescomplemented
58#11762718C2212yescomplemented
59#11762717C2214yes—
60#11762717C2214yes—
61#11762717C2214yes—
62#11762717C2212yescomplemented
63#11762672C2211yescharacteristic
64#11762672C2211yescharacteristic
65#11762669C2212yes—
66#11762669C2212yes—
67#11762665C2212yes—
68C4×#63225C2214yescomplemented
69C4×#63227C2214yescomplemented
70C4×C22⋊Dic17C2212yes—
71C4×C22⋊Dic17C2212yes—
72C4×C22⋊Dic17C2214yescomplemented
73C22×#41×C17C2211yescharacteristic
74C24×C4×C17C2211yescharacteristic
75C17×#525—28no—
76C2×C17×#123C2212yes—
77C2×C17×C22⋊Q8C2211yescharacteristic
78C2×C17×C22⋊Q8C2211yescharacteristic
79C2×C17×#121C2211yescharacteristic
80C2×C17×#121C2211yescharacteristic
81C2×C17×#120C2212yes—
82C2×C4×D4×C17C2212yes—
83C2×C4×D4×C17C2212yes—
84C2×C17×#117C2211yescharacteristic
85C25×C17C2311yescharacteristic
86C2×#41×C17—24no—
87C2×#41×C17—44no—
88C22×Q8×C17C2311yescharacteristic
89C22×D4×C17C2312yes—
90C22×D4×C17C2312yes—
91C22×D4×C17C2312yes—
92C22×D4×C17C2311yescharacteristic
93C23×C4×C17—44no—
94C23×C4×C17D418yescomplemented
95C23×C4×C17C2312yes—
96C23×C4×C17C2311yescharacteristic
97C23×C4×C17C2311yescharacteristic
98C23×C4×C17C2311yescharacteristic
99C23×C4×C17C2311yescharacteristic
100C23×C4×C17C2311yescharacteristic
101C23×C4×C17C2311yescharacteristic
102C22×C22⋊D17C2312yes—
103C22×C22⋊D17C2312yes—
104C22×C22⋊D17C2312yes—
105C22×C22⋊D17C2314yes—
106C2×#63252—24no—
107C2×#63252—44no—
108C22×D68C2311yescharacteristic
109C22×C4×D17C2312yes—
110C22×Dic34C2311yescharacteristic
111C17×#123—28no—
112C17×C22⋊Q8—24no—
113C17×C22⋊Q8—24no—
114C17×#121—24no—
115C17×#121—24no—
116C17×#120—28no—
117C4×D4×C17—28no—
118C4×D4×C17—28no—
119C17×#117—24no—
120C2×C4⋊C4×C17C2311yescharacteristic
121C2×C4⋊C4×C17C2311yescharacteristic
122C2×C4⋊C4×C17C2312yes—
123C2×C4⋊C4×C17C2312yes—
124C2×C22⋊C4×C17C2312yes—
125C2×C22⋊C4×C17C2312yes—
126C2×C22⋊C4×C17C2312yes—
127C2×C22⋊C4×C17C2312yes—
128C2×C22⋊C4×C17C2312yes—
129C2×C42×C17C2312yes—
130#10587639—28no—
131C2×C22⋊Dic17C2312yes—
132C2×C22⋊Dic17C2312yes—
133C2×C22⋊Dic17C2312yes—
134C2×C22⋊Dic17C2312yes—
135C2×C22⋊Dic17C2314yes—
136C2×C22⋊Dic17C2314yes—
137C2×C22⋊Dic17C2314yes—
138C2×C22⋊Dic17C2314yes—
139C2×C22⋊Dic17C2314yes—
140C2×C22⋊Dic17C2312yes—
141#10587616—24no—
142#10587616—24no—
143#10587615—28no—
144C4×C22⋊D17—28no—
145C4×C22⋊D17—28no—
146C4×C22⋊D17—48no—
147C2×#63227C2312yes—
148C2×#63227C2312yes—
149C2×#63227C2314yes—
150C2×#63227C2314yes—
151C2×#63227C2314yes—
152#10587612—24no—
153#10587612—44no—
154C2×C4⋊Dic17C2311yescharacteristic
155C2×C4⋊Dic17C2311yescharacteristic
156C2×C4⋊Dic17C2314yes—
157#10587610—24no—
158#10587610—24no—
159C2×#63225C2312yes—
160C2×#63225C2312yes—
161C2×#63225C2314yes—
162C2×#63225C2314yes—
163C2×#63225C2314yes—
164C2×C4×Dic17C2312yes—
165C2×C4×Dic17C2314yes—
166#10587502C2314yes—
167#10587502C2314yes—
168#10587502C2314yes—
169#10587502C2312yes—
170#10587502C2312yes—
171#10587502C2314yes—
172#10587502C2312yes—
173#10587502C2314yes—
174#10587502C2312yes—
175#10587502C2314yes—
176C24×C17—42no—
177C24×C17—42no—
178C24×C17—42no—
179C24×C17C2×D414yes—
180C24×C17C2412yes—
181C24×C17C2411yescharacteristic
182C24×C17C2411yescharacteristic
183C24×C17C2411yescharacteristic
184C23×D17C2412yes—
185#41×C17—416no—
186C2×Q8×C17—22no—
187C2×Q8×C17—42no—
188C2×D4×C17—24no—
189C2×D4×C17—24no—
190C2×D4×C17—24no—
191C2×D4×C17—22no—
192C2×D4×C17—42no—
193C2×D4×C17—44no—
194C2×D4×C17—42no—
195C2×D4×C17—42no—
196C2×D4×C17—44no—
197C22×C4×C17—24no—
198C22×C4×C17—24no—
199C22×C4×C17—24no—
200C22×C4×C17—24no—
201C22×C4×C17—28no—
202C22×C4×C17—416no—
203C22×C4×C17—42no—
204C22×C4×C17—42no—
205C22×C4×C17—42no—
206C22×C4×C17C2×D414yes—
207C22×C4×C17C2×D414yes—
208C22×C4×C17C2×D414yes—
209C22×C4×C17C2×D414yes—
210C22×C4×C17C2×D414yes—
211C22×C4×C17C2×D414yes—
212C22×C4×C17C2412yes—
213C22×C4×C17C2412yes—
214C22×C4×C17C2412yes—
215C22×C4×C17C2411yescharacteristic
216C22×C4×C17C2411yescharacteristic
217C22×C4×C17C2411yescharacteristic
218C22×C4×C17C2411yescharacteristic
219C2×C22⋊D17—24no—
220C2×C22⋊D17—24no—
221C2×C22⋊D17—24no—
222C2×C22⋊D17—44no—
223C2×C22⋊D17—42no—
224C2×C22⋊D17—44no—
225C2×C22⋊D17—44no—
226C2×C22⋊D17—44no—
227C2×C22⋊D17—42no—
228C2×C22⋊D17—44no—
229C22×Dic17C2412yes—
230C22×Dic17C2414yes—
231C22×Dic17C2412yes—
232C22×Dic17C2412yes—
233C22×Dic17C2414yes—
234#63252—416no—
235C2×D68—22no—
236C2×D68—42no—
237C2×C4×D17—24no—
238C2×C4×D17—28no—
239C2×Dic34—22no—
240C2×Dic34—42no—
241C4⋊C4×C17—24no—
242C4⋊C4×C17—24no—
243C4⋊C4×C17—22no—
244C4⋊C4×C17—22no—
245C22⋊C4×C17—24no—
246C22⋊C4×C17—24no—
247C22⋊C4×C17—24no—
248C22⋊C4×C17—24no—
249C22⋊C4×C17—24no—
250C42×C17—24no—
251C22⋊Dic17—24no—
252C22⋊Dic17—24no—
253C22⋊Dic17—24no—
254C22⋊Dic17—42no—
255C22⋊Dic17—42no—
256C22⋊Dic17—44no—
257C22⋊Dic17—44no—
258C22⋊Dic17—44no—
259C22⋊Dic17—44no—
260C22⋊Dic17—44no—
261#63227—24no—
262#63227—24no—
263#63227—44no—
264#63227—44no—
265#63227—44no—
266C4⋊Dic17—22no—
267C4⋊Dic17—22no—
268C4⋊Dic17—44no—
269#63225—24no—
270#63225—24no—
271#63225—44no—
272#63225—44no—
273#63225—44no—
274C4×Dic17—24no—
275C4×Dic17—28no—
276#36652—171nomaximal, Sylow
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—22no—
287C23×C17—24no—
288C23×C17—22no—
289C23×C17—24no—
290C23×C17—22no—
291C23×C17—44no—
292C23×C17—44no—
293C23×C17—44no—
294C23×C17—416no—
295C23×C17C22×D412yes—
296C23×C17C22×D412yes—
297C23×C17C22×D412yes—
298C23×C17C2511yescharacteristic
299C22×D17—22no—
300C22×D17—24no—
301C22×D17—22no—
302C22×D17—24no—
303C22×D17—22no—
304Q8×C17—44no—
305D4×C17—44no—
306D4×C17—48no—
307D4×C17—48no—
308D4×C17—48no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—28no—
313C2×C4×C17—28no—
314C2×C4×C17—28no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—24no—
319C2×C4×C17—22no—
320C2×C4×C17—24no—
321C2×C4×C17—22no—
322C2×C4×C17—44no—
323C2×C4×C17—44no—
324C2×C4×C17—44no—
325C2×C4×C17—48no—
326C2×C4×C17C22×D412yes—
327C2×C4×C17C22×D412yes—
328C2×C4×C17C22×D412yes—
329C2×C4×C17C22×D412yes—
330C2×C4×C17H(5,𝔽2)14yes—
331C22⋊D17—48no—
332C22⋊D17—48no—
333C22⋊D17—48no—
334C22⋊D17—416no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17—22no—
338C2×Dic17—24no—
339C2×Dic17—24no—
340C2×Dic17—24no—
341C2×Dic17—22no—
342C2×Dic17—24no—
343C2×Dic17—24no—
344C2×Dic17—24no—
345C2×Dic17—24no—
346C2×Dic17—24no—
347C2×Dic17—22no—
348D68—44no—
349C4×D17—48no—
350Dic34—44no—
351C2×#525—171no—
352C2×#525D1711yescharacteristic, complemented
353#2817—171no—
354#2816—171no—
355#2816—171no—
356#2815—171no—
357#2814—172no—
358#2814—172no—
359#2813—172no—
360#2813—172no—
361#2812—174no—
362#2395—172no—
363#2395—172no—
364#2392—174no—
365#2388—172no—
366#2388—172no—
367#2280—171no—
368C22×C17—22no—
369C22×C17—22no—
370C22×C17—22no—
371C22×C17—22no—
372C22×C17—22no—
373C22×C17—22no—
374C22×C17—22no—
375C22×C17—22no—
376C22×C17—22no—
377C22×C17—416no—
378C22×C17—44no—
379C22×C17—44no—
380C22×C17—44no—
381C22×C17—42no—
382C22×C17—42no—
383C22×C17—42no—
384C22×C17—44no—
385C22×C17—44no—
386C22×C17C23×D411yescharacteristic
387C22×C17C2×H(5,𝔽2)12yes—
388C22×C17#58512yes—
389C22×C17#58512yes—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—42no—
393C2×D17—44no—
394C2×D17—44no—
395C4×C17—22no—
396C4×C17—22no—
397C4×C17—22no—
398C4×C17—42no—
399C4×C17—42no—
400C4×C17—42no—
401C4×C17#53414yes—
402Dic17—42no—
403Dic17—42no—
404Dic17—42no—
405Dic17—44no—
406Dic17—44no—
407C22×#41—171no—
408C22×#41C2×D1711yescharacteristic
409C24×C4C2×D1711yescharacteristic
410#525—28no—
411#525—348no—
412C2×#123—172no—
413C2×#123C2×D1712yes—
414C2×C22⋊Q8—171no—
415C2×C22⋊Q8—171no—
416C2×C22⋊Q8C2×D1711yescharacteristic
417C2×C22⋊Q8C2×D1711yescharacteristic
418C2×#121—171no—
419C2×#121—171no—
420C2×#121C2×D1711yescharacteristic
421C2×#121C2×D1711yescharacteristic
422C2×#120—172no—
423C2×#120C2×D1712yes—
424C2×C4×D4—172no—
425C2×C4×D4—172no—
426C2×C4×D4—174no—
427C2×C4×D4C2×D1712yes—
428C2×C4×D4C2×D1712yes—
429C2×#117—171no—
430C2×#117—172no—
431C2×#117C2×D1711yescharacteristic
432#400—172no—
433#400—172no—
434#399—172no—
435#399—172no—
436#398—172no—
437#398—172no—
438#398—174no—
439#397—172no—
440#397—174no—
441#397—172no—
442#397—174no—
443#397—174no—
444#396—174no—
445#396—174no—
446#395—172no—
447#395—172no—
448#394—174no—
449#394—172no—
450#394—174no—
451#394—174no—
452#394—172no—
453#394—174no—
454#394—174no—
455#394—174no—
456#394—174no—
457#393—172no—
458#393—172no—
459#392—174no—
460#392—174no—
461#392—174no—
462#392—172no—
463#392—172no—
464#381—171no—
465#381—171no—
466#380—172no—
467#380—172no—
468#379—172no—
469C4×C4⋊C4—174no—
470C4×C22⋊C4—174no—
471C4×C22⋊C4—172no—
472C4×C22⋊C4—172no—
473C4×C22⋊C4—174no—
474C2×C17—42no—
475C2×C17—42no—
476C2×C17—42no—
477C2×C17—82no—
478C2×C17C2×#53411yescharacteristic
479C2×C17#344911yescharacteristic
480C2×C17#344911yescharacteristic
481C2×C17#352914yes—
482D17—82no—
483C25C22×D1711yescharacteristic
484C2×#41—24no—
485C2×#41—44no—
486C2×#41—344no—
487C2×#41—684no—
488C22×Q8—171no—
489C22×Q8C22×D1711yescharacteristic
490C22×D4—172no—
491C22×D4—172no—
492C22×D4—172no—
493C22×D4—174no—
494C22×D4—171no—
495C22×D4C22×D1712yes—
496C22×D4C22×D1712yes—
497C22×D4C22×D1712yes—
498C22×D4C22×D1711yescharacteristic
499C23×C4—44no—
500C23×C4—172no—
501C23×C4C22⋊D1718yescomplemented
502C23×C4C22×D1712yes—
503C23×C4C22×D1711yescharacteristic
504C23×C4C22×D1711yescharacteristic
505C23×C4C22×D1711yescharacteristic
506C23×C4C22×D1711yescharacteristic
507C23×C4C22×D1711yescharacteristic
508C23×C4C22×D1711yescharacteristic
509#123—28no—
510#123—348no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—344no—
514C22⋊Q8—344no—
515#121—24no—
516#121—24no—
517#121—344no—
518#121—344no—
519#120—28no—
520#120—348no—
521C4×D4—28no—
522C4×D4—28no—
523C4×D4—348no—
524C4×D4—348no—
525C4×D4—688no—
526#117—24no—
527#117—344no—
528#117—684no—
529C2×C4⋊C4—171no—
530C2×C4⋊C4—171no—
531C2×C4⋊C4—172no—
532C2×C4⋊C4—172no—
533C2×C4⋊C4—174no—
534C2×C4⋊C4—174no—
535C2×C4⋊C4—174no—
536C2×C4⋊C4—174no—
537C2×C4⋊C4C22×D1711yescharacteristic
538C2×C4⋊C4C22×D1711yescharacteristic
539C2×C4⋊C4C22×D1712yes—
540C2×C4⋊C4C22×D1712yes—
541C2×C22⋊C4—172no—
542C2×C22⋊C4—172no—
543C2×C22⋊C4—172no—
544C2×C22⋊C4—172no—
545C2×C22⋊C4—172no—
546C2×C22⋊C4—172no—
547C2×C22⋊C4—172no—
548C2×C22⋊C4—174no—
549C2×C22⋊C4—174no—
550C2×C22⋊C4—174no—
551C2×C22⋊C4—174no—
552C2×C22⋊C4—174no—
553C2×C22⋊C4—174no—
554C2×C22⋊C4—174no—
555C2×C22⋊C4—174no—
556C2×C22⋊C4C22×D1712yes—
557C2×C22⋊C4C22×D1712yes—
558C2×C22⋊C4C22×D1712yes—
559C2×C22⋊C4C22×D1712yes—
560C2×C22⋊C4C22×D1712yes—
561C2×C42—172no—
562C2×C42—174no—
563C2×C42C22×D1712yes—
564#95—172no—
565#95—172no—
566#95—172no—
567#95—172no—
568#95—174no—
569#95—174no—
570#95—174no—
571#95—174no—
572#95—174no—
573#95—174no—
574C17#3665211yescharacteristic, complemented, Sylow
575C24—42no—
576C24—42no—
577C24—42no—
578C24—172no—
579C24C2×C22⋊D1714yes—
580C24C23×D1712yes—
581C24C23×D1711yescharacteristic
582C24C23×D1711yescharacteristic
583C24C23×D1711yescharacteristic
584#41—416no—
585#41—6816no—
586C2×Q8—22no—
587C2×Q8—42no—
588C2×Q8—342no—
589C2×Q8—682no—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—22no—
594C2×D4—42no—
595C2×D4—44no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—44no—
599C2×D4—344no—
600C2×D4—344no—
601C2×D4—344no—
602C2×D4—342no—
603C2×D4—682no—
604C2×D4—684no—
605C2×D4—682no—
606C2×D4—684no—
607C2×D4—684no—
608C2×D4—684no—
609C2×D4—682no—
610C2×D4—684no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—28no—
615C22×C4—24no—
616C22×C4—416no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—174no—
621C22×C4—174no—
622C22×C4—172no—
623C22×C4—172no—
624C22×C4—172no—
625C22×C4—348no—
626C22×C4—344no—
627C22×C4C2×C22⋊D1714yes—
628C22×C4C2×C22⋊D1714yes—
629C22×C4C2×C22⋊D1714yes—
630C22×C4C2×C22⋊D1714yes—
631C22×C4C2×C22⋊D1714yes—
632C22×C4C2×C22⋊D1714yes—
633C22×C4C23×D1712yes—
634C22×C4C23×D1712yes—
635C22×C4C23×D1712yes—
636C22×C4C23×D1711yescharacteristic
637C22×C4C23×D1711yescharacteristic
638C22×C4C23×D1711yescharacteristic
639C22×C4C23×D1711yescharacteristic
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—342no—
645C4⋊C4—342no—
646C4⋊C4—344no—
647C4⋊C4—344no—
648C4⋊C4—684no—
649C4⋊C4—684no—
650C4⋊C4—684no—
651C4⋊C4—684no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—344no—
658C22⋊C4—344no—
659C22⋊C4—344no—
660C22⋊C4—344no—
661C22⋊C4—344no—
662C22⋊C4—684no—
663C22⋊C4—684no—
664C22⋊C4—684no—
665C22⋊C4—684no—
666C22⋊C4—684no—
667C22⋊C4—684no—
668C22⋊C4—684no—
669C22⋊C4—682no—
670C22⋊C4—682no—
671C22⋊C4—684no—
672C42—24no—
673C42—348no—
674C42—344no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—416no—
693C23—342no—
694C23—344no—
695C23—342no—
696C23—344no—
697C23—342no—
698C23C22×C22⋊D1712yes—
699C23C22×C22⋊D1712yes—
700C23C22×C22⋊D1712yes—
701C23C24×D1711yescharacteristic
702Q8—44no—
703Q8—684no—
704D4—44no—
705D4—48no—
706D4—48no—
707D4—48no—
708D4—684no—
709D4—688no—
710D4—688no—
711D4—688no—
712D4—6816no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—48no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—344no—
734C2×C4—344no—
735C2×C4—344no—
736C2×C4—344no—
737C2×C4—344no—
738C2×C4—342no—
739C2×C4—344no—
740C2×C4—344no—
741C2×C4—344no—
742C2×C4—342no—
743C2×C4—688no—
744C2×C4#1058769114yes—
745C2×C4C22×C22⋊D1712yes—
746C2×C4C22×C22⋊D1712yes—
747C2×C4C22×C22⋊D1712yes—
748C2×C4C22×C22⋊D1712yes—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—416no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—682no—
768C22—682no—
769C22—682no—
770C22—684no—
771C22—684no—
772C22C23×C22⋊D1711yescharacteristic
773C22C2×#1058769112yes—
774C22#1176364512yes—
775C22#1176364512yes—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—682no—
783C4—682no—
784C4—682no—
785C4—684no—
786C4—684no—
787C4#1176336814yes—
788C2—42no—
789C2—42no—
790C2—42no—
791C2—82no—
792C2—1362no—
793C2C2×#1176336811yescharacteristic
794C2#1454211311yescharacteristic
795C2#1454211311yescharacteristic
796C2#1454292214yes—
subgroupG/H
centerC22×C4C23×D17
commutator, socle, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#525C2
hypercenterC2×#525D17
hypocenterC17#36652
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#11763320C2semidirect
2. #14536819C2semidirect
3. #14536812C2semidirect
4. #14536811C2semidirect
5. #14536806C2semidirect
6. #14536797C2semidirect
7. #14536795C2semidirect
8. #14536786C2semidirect
9. #14536784C2semidirect
10. #14536779C2semidirect
11. #14532043C2semidirect
12. #14532041C2semidirect
13. #14532026C2semidirect
14. #14531999C2semidirect
15. #14531997C2semidirect
16. #14531167C2semidirect
17. C2×C17×#525C2semidirect
28. C2×C4×C22⋊D17C22semidirect
31. #11762748C22semidirect
32. #11762747C22semidirect
33. #11762745C22semidirect
34. #11762744C22semidirect
35. #11762742C22semidirect
36. #11762740C22semidirect
37. #11762739C22semidirect
41. #11762735C22semidirect
42. #11762734C22semidirect
43. #11762732C22semidirect
44. #11762731C22semidirect
45. #11762729C22semidirect
46. #11762728C22semidirect
47. #11762726C22semidirect
48. #11762725C22semidirect
55. #11762723C22semidirect
56. #11762721C22semidirect
57. #11762720C22semidirect
58. #11762718C22semidirect
62. #11762717C22semidirect
68. C4×#63225C22semidirect
69. C4×#63227C22semidirect
72. C4×C22⋊Dic17C22semidirect
94. C23×C4×C17D4semidirect
352. C2×#525D17semidirect
501. C23×C4C22⋊D17semidirect
574. C17#36652semidirect

Maximal subgroups

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

subgroupindex
C2×#117633202
#145368192
#145368122
#145368112
#145368062
#145367972
#145367952
#145367862
#145367842
#145367792
#145320432
#145320412
#145320262
#145319992
#145319972
#145311672
C2×C17×#5252
#3665217