Finite Group Databasebeta

← #11884641

Subgroups — #11884641

Order 1152.

1016 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5631C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3#10594902C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592748C211yesmaximal, characteristic, complemented
6C3×#5050C211yesmaximal, characteristic, complemented
7#10591608C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591574C211yesmaximal, characteristic, complemented
10#10591163C211yesmaximal, characteristic, complemented
11#10591151C211yesmaximal, characteristic, complemented
12#10590616C211yesmaximal, characteristic, complemented
13#10590534C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#83528—31nomaximal
17#80205—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24#64139C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#894—21no—
32C3×#893C2211yescharacteristic
33C3×D3×C4⋊C4—21no—
34C3×#884—21no—
35C3×#883—21no—
36#63978—21no—
37#63952—21no—
38#63949—24no—
39#63907—21no—
40#63888—21no—
41#63864C2211yescharacteristic
42#63856C2211yescharacteristic
43Dic3×Dic6C2211yescharacteristic
44C2×#3718C2211yescharacteristic
45C2×#3718C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47#63827—24no—
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic
53#63636C2211yescharacteristic
54#63634C2211yescharacteristic
55C3×#830C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic
63C3×#547—31no—
64C2×#951—31no—
65C2×#950—31no—
66#5817—31no—
67C2×#942—31no—
68C2×#919—31no—
69#5631D311yescharacteristic, complemented
70#5552—31no—
71C3×#451—31no—
72#5239—31no—
73#5238—31no—
74#5190—31no—
75#5187—31no—
76#5182—31no—
77#5090—31no—
78#5086—31no—
79#5051—31no—
80#5050D311yescharacteristic, complemented
81#5049—31no—
82#5049—31no—
83#5049—61no—
84#5047—31no—
85#5018—31no—
86#5016—31no—
87#5011—31no—
88#4819—31no—
89#4817—31no—
90#4813—31no—
91#4808—31no—
92#4734—31no—
93#4728—31no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239—41no—
103C3×#235—22no—
104C3×#235—41no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6—22no—
112C2×C3×Dic6—21no—
113C2×C3×Dic6—41no—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#624—21no—
119#3799—22no—
120#3799—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3755—22no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3748—22no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×#216—41no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3718—22no—
150#3718—22no—
151#3717—41no—
152#3715—22no—
153#3715D414yescomplemented
154#3714—22no—
155D3×C3⋊C8—22no—
156#3269—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C2×#239—31no—
161C2×#239C2×D311yescharacteristic
162C2×#235—31no—
163C2×#235C2×D311yescharacteristic
164C22×Dic6C2×D311yescharacteristic
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C3×C4⋊Q8—31no—
168C3×#123—61no—
169C3×#123—61no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8C2×D311yescharacteristic
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×#121—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C2×C3×C4⋊C4—61no—
178#951—64no—
179#950—64no—
180#947—31no—
181#947—61no—
182#946—31no—
183#946—61no—
184Q8×Dic3—31no—
185#944C2×D311yescharacteristic
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216C2×D311yescharacteristic
191C2×#216C2×D311yescharacteristic
192#942—64no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—31no—
197C2×#215—31no—
198C2×#215—61no—
199#939—61no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#213—31no—
203#930—31no—
204#930—31no—
205#930—61no—
206#930—61no—
207C4×#67—61no—
208C4×#67C2×D311yescharacteristic
209#924—31no—
210C2×#208—31no—
211C2×#208—31no—
212C2×#208—61no—
213C22×C3⋊C8—31no—
214#919—64no—
215C2×D24—31no—
216C2×#204—31no—
217C2×D3×C8—31no—
218#897C2×D311yescharacteristic
219#896—61no—
220#894—21no—
221#893C2×D311yescharacteristic
222D3×C4⋊C4—21no—
223#885—61no—
224#884—21no—
225#883—21no—
226#67⋊C4—61no—
227#875—31no—
228C4×Dic6—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#830—31no—
238#830C2×D311yescharacteristic
239#821—31no—
240(C2×D3)⋊C8—31no—
241#816—31no—
242#815—31no—
243Dic3⋊C8—31no—
244#810C2×D311yescharacteristic
245#810C2×D311yescharacteristic
246#809—31no—
247#809—31no—
248#809—61no—
249#807—31no—
250#807—31no—
251#807—61no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266#638—42no—
267C2×C3⋊Dic3—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C3×#67—41no—
271C3×#67—42no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—42no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—42no—
281C3×D12C2×D412yes—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—42no—
285C3×C4×D3—42no—
286C3×C4×D3—42no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—42no—
293C3×Dic6C2×D412yes—
294#626—42no—
295#624—42no—
296C3⋊(C3⋊C8)—21no—
297C3⋊(C3⋊C8)C2×D412yes—
298C3×C3⋊C8—21no—
299C3×C3⋊C8—21no—
300C2×#137—91no—
301C2×#135—91no—
302#548—91no—
303#547—31no—
304#497—91no—
305#468—91no—
306#467—91no—
307#463—91no—
308#462—91no—
309#452—91no—
310#452—91no—
311#451—31no—
312#449—91no—
313#440—91no—
314#435—91no—
315C3×#41—62no—
316C3×#41—62no—
317C3×#41—121no—
318C3×#41—121no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—62no—
324C2×C3×Q8—61no—
325C2×C3×Q8—121no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C22×C3×C4—21no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C2×#67—21no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—121no—
345C2×#67#6711yescharacteristic
346C22×Dic3—21no—
347#239—22no—
348#239—41no—
349#239—62no—
350#239—121no—
351#235—22no—
352#235—41no—
353#235—62no—
354#235—121no—
355C2×D12—21no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3C22×D311yescharacteristic
367C2×Dic6—22no—
368C2×Dic6—21no—
369C2×Dic6—41no—
370C2×Dic6C22×D311yescharacteristic
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C3×Q16—62no—
374C3×Q16—121no—
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—41no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—31no—
395#217—61no—
396#217#6711yescharacteristic
397#216—22no—
398#216—41no—
399#216—62no—
400#216—62no—
401#216—62no—
402#216—62no—
403#215—34no—
404#215—62no—
405#215—62no—
406#215—62no—
407#215—122no—
408#215—121no—
409#214—34no—
410#214—62no—
411#213—62no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4#6711yescharacteristic
423C4⋊Dic3—21no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428Dic3⋊C4—21no—
429Dic3⋊C4—21no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4#6711yescharacteristic
434C4×Dic3—61no—
435C4×Dic3—61no—
436C4×Dic3C22×D311yescharacteristic
437#208—62no—
438#208—62no—
439#208—122no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449D24—62no—
450#204—121no—
451D3×C8—62no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C32×C4—21no—
466C32×C4—41no—
467C32×C4—41no—
468C32×C4C22×D411yescharacteristic
469C32×C4H(5,𝔽2)11yescharacteristic
470C3⋊Dic3—41no—
471C3×Dic3—21no—
472C3×Dic3—22no—
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C2×#41—31no—
478C2×#41—31no—
479C2×#41—91no—
480C22×Q8—31no—
481#137—184no—
482#135—184no—
483C2×Q16—31no—
484C2×Q16—31no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×SD16—91no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×D8—91no—
492C2×M16—91no—
493C22×C8—91no—
494C4⋊Q8—31no—
495#124—91no—
496#124—181no—
497#123—61no—
498#123—61no—
499C22⋊Q8—31no—
500C22⋊Q8—91no—
501C22⋊Q8—181no—
502C22⋊Q8D3211yescharacteristic
503#121—61no—
504#121—91no—
505#121—181no—
506C4×Q8—91no—
507C4×D4—31no—
508C4×D4—31no—
509C4×D4—181no—
510C2×C4⋊C4—61no—
511#107—91no—
512C4⋊C8—91no—
513#103—31no—
514#103—31no—
515#103—91no—
516#103—91no—
517#102—91no—
518#102—91no—
519C22⋊C8—31no—
520C22⋊C8—91no—
521#97—91no—
522C23×C3—21no—
523C23×C3—31no—
524C23×C3—61no—
525C23×C3D3×D411yescharacteristic
526C23×C3C2×#6711yescharacteristic
527C22×D3—21no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—121no—
531C22×D3C2×#6711yescharacteristic
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—32no—
537C3×Q8—41no—
538C3×Q8—41no—
539C3×Q8—61no—
540C3×Q8—61no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—122no—
545C3×D4—32no—
546C3×D4—61no—
547C3×D4—122no—
548C3×D4—121no—
549C3×D4—122no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4—122no—
574C2×C3×C4—122no—
575C2×C3×C4—122no—
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4C2×#6711yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—41no—
581#67—42no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—242no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—42no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3C2×#6711yescharacteristic
594C2×Dic3C2×#6711yescharacteristic
595C2×Dic3C2×#6711yescharacteristic
596D12—21no—
597D12—42no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—121no—
603D12—121no—
604D12—122no—
605D12D3×D412yes—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—42no—
609C4×D3—42no—
610C4×D3—42no—
611C4×D3—122no—
612C4×D3—122no—
613Dic6—21no—
614Dic6—21no—
615Dic6—21no—
616Dic6—21no—
617Dic6—21no—
618Dic6—42no—
619Dic6D3×D412yes—
620C3×C8—61no—
621C3×C8—61no—
622C3⋊C8—21no—
623C3⋊C8—21no—
624C3⋊C8—32no—
625C3⋊C8—32no—
626C3⋊C8—62no—
627C3⋊C8—61no—
628C3⋊C8—61no—
629C3⋊C8—121no—
630C2×C32—41no—
631C2×C32D4211yescharacteristic
632C2×C32#57511yescharacteristic
633C2×C32#57811yescharacteristic
634C3⋊D3—81no—
635C3×D3—41no—
636C3×D3—42no—
637#41—62no—
638#41—62no—
639#41—121no—
640#41—121no—
641#41—182no—
642#41—361no—
643C2×Q8—31no—
644C2×Q8—31no—
645C2×Q8—31no—
646C2×Q8—62no—
647C2×Q8—61no—
648C2×Q8—121no—
649C2×Q8C2×D3211yescharacteristic
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—91no—
655C2×D4—181no—
656C2×D4—181no—
657C22×C4—31no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—181no—
663C22×C4C2×D3211yescharacteristic
664Q16—62no—
665Q16—121no—
666Q16—182no—
667Q16—182no—
668SD16—94no—
669SD16—182no—
670SD16—182no—
671SD16—361no—
672D8—182no—
673M16—182no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8—91no—
677C2×C8—91no—
678C2×C8—182no—
679C4⋊C4—21no—
680C4⋊C4—31no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—91no—
685C4⋊C4—181no—
686C4⋊C4—181no—
687C4⋊C4C2×D3211yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—31no—
690C22⋊C4—31no—
691C22⋊C4—61no—
692C22⋊C4—61no—
693C22⋊C4—181no—
694C22⋊C4—181no—
695C22⋊C4—181no—
696C22⋊C4—181no—
697C42—31no—
698C42—181no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—62no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C22×#6711yescharacteristic
717C2×D3—21no—
718C2×D3—22no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—241no—
730C2×D3—241no—
731C2×D3—241no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—62no—
744C3×C4—61no—
745C3×C4—81no—
746C3×C4—81no—
747C3×C4—121no—
748C3×C4—121no—
749C3×C4C2×D3×D411yescharacteristic
750C3×C4C2×D3×D411yescharacteristic
751C3×C4#100411yescharacteristic
752C3×C4#100411yescharacteristic
753Dic3—21no—
754Dic3—21no—
755Dic3—21no—
756Dic3—22no—
757Dic3—41no—
758Dic3—41no—
759Dic3—121no—
760Dic3—121no—
761Dic3—241no—
762C32#326911yescharacteristic, complemented, Sylow
763C23—31no—
764C23—61no—
765C23—181no—
766C23D3×#6711yescharacteristic
767Q8—21no—
768Q8—21no—
769Q8—32no—
770Q8—61no—
771Q8—61no—
772Q8—61no—
773Q8—61no—
774Q8—61no—
775Q8—122no—
776D4—32no—
777D4—61no—
778D4—122no—
779D4—121no—
780D4—122no—
781D4—181no—
782D4—181no—
783D4—362no—
784D4—362no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—122no—
800C2×C4—122no—
801C2×C4—181no—
802C2×C4—362no—
803C2×C4D3×#6711yescharacteristic
804C2×C4C22×D3211yescharacteristic
805C8—61no—
806C8—61no—
807C8—92no—
808C8—181no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—41no—
813C2×C3—41no—
814C2×C3—81no—
815C2×C3—121no—
816C2×C3—122no—
817C2×C3#559011yescharacteristic
818C2×C3#576611yescharacteristic
819C2×C3#577711yescharacteristic
820C2×C3D4×#6711yescharacteristic
821C2×C3#582211yescharacteristic
822C2×C3#583811yescharacteristic
823D3—41no—
824D3—42no—
825D3—241no—
826D3—241no—
827D3—481no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—61no—
832C22—61no—
833C22—62no—
834C22—61no—
835C22—121no—
836C22—121no—
837C22—361no—
838C22—361no—
839C22—361no—
840C22C2×D3×#6711yescharacteristic
841C4—21no—
842C4—41no—
843C4—41no—
844C4—61no—
845C4—61no—
846C4—62no—
847C4—61no—
848C4—121no—
849C4—121no—
850C4—361no—
851C4D32×D411yescharacteristic
852C4#6431311yescharacteristic
853C3—21no—
854C3#8020511yescharacteristic, complemented
855C3#8352811yescharacteristic, complemented
856C2—41no—
857C2—121no—
858C2—122no—
859C2—721no—
860C2#1059528711yescharacteristic
861C2#1059532711yescharacteristic
862C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3269
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5631C2semidirect
2. C2×#63949C2semidirect
3. #10594902C2semidirect
4. C2×#63827C2semidirect
5. #10592748C2semidirect
6. C3×#5050C2semidirect
7. #10591608C2semidirect
8. #10591597C2semidirect
9. #10591574C2semidirect
10. #10591163C2semidirect
11. #10591151C2semidirect
12. #10590616C2semidirect
13. #10590534C2semidirect
14. #10590518C2semidirect
15. #10590478C2semidirect
69. #5631D3semidirect
80. #5050D3semidirect
153. #3715D4semidirect
762. C32#3269semidirect
854. C3#80205semidirect
855. C3#83528semidirect

Maximal subgroups

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

subgroupindex
C3×#56312
C2×#639492
#105949022
C2×#638272
#105927482
C3×#50502
#105916082
#105915972
#105915742
#105911632
#105911512
#105906162
#105905342
#105905182
#105904782
#835283
#802053