Finite Group Databasebeta

← #11884639

Subgroups — #11884639

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5631C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3#10594918C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5#10592749C211yesmaximal, characteristic, complemented
6C3×#5049C211yesmaximal, characteristic, complemented
7#10591605C211yesmaximal, characteristic, complemented
8#10591599C211yesmaximal, characteristic, complemented
9#10591575C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11#10591147C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590590C211yesmaximal, characteristic, complemented
14#10590579C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#83528—31nomaximal
17#80837—31nomaximal
18C22×#634C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#894—21no—
32C3×#893C2211yescharacteristic
33C3×D3×C4⋊C4—21no—
34C3×#884—21no—
35C3×#883—21no—
36#63980—21no—
37#67⋊Dic3—21no—
38#63947—24no—
39#63913—21no—
40#63896—21no—
41#63860C2211yescharacteristic
42#63857C2211yescharacteristic
43#63844C2211yescharacteristic
44C2×#3719C2211yescharacteristic
45C2×#3719C2211yescharacteristic
46#63831—24no—
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63657C2211yescharacteristic
53#63637C2211yescharacteristic
54#63637C2211yescharacteristic
55C3×#835C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#807C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic
63C3×#547—31no—
64C2×#951—31no—
65C2×#950—31no—
66C2×#916—31no—
67C2×#909—31no—
68#5631D311yescharacteristic, complemented
69#5598—31no—
70#5552—31no—
71C3×#468—31no—
72#5239—31no—
73#5238—31no—
74#5167—31no—
75#5127—31no—
76#5090—31no—
77#5086—31no—
78#5051—31no—
79#5050—31no—
80#5050—31no—
81#5050—61no—
82#5049D311yescharacteristic, complemented
83#5047—31no—
84#5037—31no—
85#5018—31no—
86#5016—31no—
87#5011—31no—
88#4889—31no—
89#4887—31no—
90#4808—31no—
91#4795—31no—
92#4787—31no—
93#4783—31no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×#634—22no—
98C2×#634—21no—
99C2×#634—41no—
100C2×#634C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C3×#239—22no—
106C3×#239—41no—
107C3×#235—22no—
108C3×#235—41no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#625—21no—
118C2×D3×Dic3—21no—
119#3795—22no—
120#3795—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3756—22no—
125#3756—41no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217D411yescharacteristic
129C3×#215—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C3×#208—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144Dic3⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3719—22no—
150#3719—22no—
151#3716—22no—
152#3716D414yescomplemented
153#3715—41no—
154#3713—22no—
155D3×C3⋊C8—22no—
156#3269—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239C2×D311yescharacteristic
160C2×#237—31no—
161C2×#235—31no—
162C2×#235C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—61no—
166C2×C3×SD16—31no—
167C2×C3×M16—31no—
168C3×C4⋊Q8—31no—
169C3×#123—61no—
170C3×#123—61no—
171C3×C22⋊Q8—21no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×C22⋊Q8C2×D311yescharacteristic
175C3×#121—31no—
176C3×#121—61no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C2×C3×C4⋊C4—61no—
180#951—64no—
181#950—64no—
182#944C2×D311yescharacteristic
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—61no—
190C2×#216—61no—
191C2×#215—31no—
192C2×#215C2×D311yescharacteristic
193#939—61no—
194#939—61no—
195#936—31no—
196D4×Dic3—61no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#213—31no—
201C2×#213—31no—
202#930C2×D311yescharacteristic
203C4×#67C2×D311yescharacteristic
204#924—31no—
205C2×#208C2×D311yescharacteristic
206C22×C3⋊C8—31no—
207#916—64no—
208#909—64no—
209C2×Dic12—31no—
210C2×Dic12—31no—
211C2×#204—31no—
212C2×#204—31no—
213C2×D3×C8—31no—
214#897—31no—
215#897C2×D311yescharacteristic
216#896—61no—
217#894—21no—
218#893C2×D311yescharacteristic
219D3×C4⋊C4—21no—
220#887—31no—
221#885—61no—
222#885—61no—
223#884—21no—
224#883—21no—
225#67⋊C4—61no—
226#878—61no—
227#875—31no—
228C4×Dic6—31no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#835C2×D311yescharacteristic
234#832—31no—
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239(C2×D3)⋊C8—31no—
240#815—31no—
241Dic3⋊C8—31no—
242#810—31no—
243#810—31no—
244#810—31no—
245#810—31no—
246#810—31no—
247#810—61no—
248#810—61no—
249#809—31no—
250#809C2×D311yescharacteristic
251#807C2×D311yescharacteristic
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
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—42no—
269#634—21no—
270#634—21no—
271#634—21no—
272#634—42no—
273#634C2×D412yes—
274C3×#67—41no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—42no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#625—42no—
295D3×Dic3—42no—
296C3⋊(C3⋊C8)—21no—
297C3⋊(C3⋊C8)—21no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8C2×D412yes—
300C2×#137—91no—
301C2×#135—91no—
302#548—91no—
303#547—31no—
304#497—91no—
305#468—31no—
306#467—91no—
307#463—91no—
308#462—91no—
309#452—91no—
310#452—91no—
311#451—91no—
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×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67#6711yescharacteristic
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344C22×Dic3—121no—
345#239—22no—
346#239—41no—
347#237—62no—
348#237—121no—
349#235—22no—
350#235—41no—
351#235—62no—
352#235—121no—
353C2×D12—21no—
354C2×D12C22×D311yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×C4×D3—21no—
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—61no—
360C2×C4×D3C22×D311yescharacteristic
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—31no—
364C2×Dic6—31no—
365C2×Dic6—61no—
366C2×Dic6—61no—
367C2×Dic6—62no—
368C2×Dic6—62no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—122no—
372C2×Dic6—121no—
373C2×Dic6—121no—
374C2×Dic6—121no—
375C2×Dic6—122no—
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×M16—62no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—41no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C42—31no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217#6711yescharacteristic
405#216—62no—
406#216—62no—
407#216—62no—
408#216—62no—
409#216—122no—
410#216—121no—
411#216—121no—
412#216—122no—
413#215—22no—
414#215—121no—
415#214—34no—
416#214—62no—
417#214—121no—
418#213—62no—
419#213—62no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4#6711yescharacteristic
427C4⋊Dic3—21no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—21no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4#6711yescharacteristic
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3C22×D311yescharacteristic
439#208—22no—
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
449Dic12—62no—
450Dic12—62no—
451#204—34no—
452#204—62no—
453D3×C8—62no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C32×C4—21no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4H(5,𝔽2)11yescharacteristic
472C3⋊Dic3—22no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—31no—
480C2×#41—31no—
481C2×#41—91no—
482C22×Q8—91no—
483#137—184no—
484#135—184no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×SD16—31no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×D8—91no—
494C2×M16—31no—
495C22×C8—91no—
496C4⋊Q8—31no—
497#124—91no—
498#124—181no—
499#123—61no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—91no—
503C22⋊Q8—181no—
504C22⋊Q8D3211yescharacteristic
505#121—31no—
506#121—61no—
507#121—181no—
508C4×Q8—91no—
509C4×D4—31no—
510C4×D4—31no—
511C4×D4—181no—
512C2×C4⋊C4—61no—
513#107—31no—
514C4⋊C8—91no—
515#103—31no—
516#103—91no—
517#103—91no—
518#103—91no—
519#102—31no—
520#102—91no—
521C22⋊C8—91no—
522C22⋊C8—91no—
523#97—91no—
524C23×C3—21no—
525C23×C3—31no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3D3×D411yescharacteristic
529C23×C3C2×#6711yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3C2×#6711yescharacteristic
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—41no—
538C3×Q8—41no—
539C3×Q8—61no—
540C3×Q8—61no—
541C3×D4—32no—
542C3×D4—61no—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—122no—
546C3×D4—121no—
547C3×D4—122no—
548C3×D4—122no—
549C2×C3×C4—21no—
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—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—122no—
571C2×C3×C4—122no—
572C2×C3×C4—122no—
573C2×C3×C4D3×D411yescharacteristic
574C2×C3×C4C2×#6711yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—41no—
578#67—42no—
579#67—42no—
580#67—122no—
581#67—122no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—124no—
594C2×Dic3C2×#6711yescharacteristic
595C2×Dic3C2×#6711yescharacteristic
596C2×Dic3C2×#6711yescharacteristic
597D12—21no—
598D12—21no—
599D12—21no—
600D12—42no—
601D12D3×D412yes—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—42no—
605C4×D3—42no—
606C4×D3—42no—
607C4×D3—122no—
608Dic6—21no—
609Dic6—21no—
610Dic6—32no—
611Dic6—32no—
612Dic6—62no—
613Dic6—61no—
614Dic6—61no—
615Dic6—62no—
616Dic6—61no—
617Dic6—61no—
618Dic6—61no—
619Dic6—61no—
620Dic6—121no—
621Dic6—121no—
622Dic6—122no—
623Dic6—122no—
624Dic6—124no—
625C3×C8—32no—
626C3×C8—61no—
627C3⋊C8—21no—
628C3⋊C8—61no—
629C3⋊C8—61no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—121no—
633C3⋊C8—121no—
634C3⋊C8D3×D412yes—
635C2×C32—41no—
636C2×C32D4211yescharacteristic
637C2×C32#57511yescharacteristic
638C2×C32#57811yescharacteristic
639C3×D3—41no—
640C3×D3—42no—
641C3×D3—81no—
642#41—62no—
643#41—62no—
644#41—121no—
645#41—121no—
646#41—182no—
647#41—361no—
648C2×Q8—31no—
649C2×Q8—91no—
650C2×Q8—91no—
651C2×Q8—182no—
652C2×Q8—181no—
653C2×Q8—361no—
654C2×Q8C2×D3211yescharacteristic
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—181no—
662C22×C4—31no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—181no—
667C22×C4—181no—
668C22×C4C2×D3211yescharacteristic
669Q16—182no—
670Q16—182no—
671Q16—182no—
672Q16—361no—
673SD16—62no—
674SD16—94no—
675SD16—182no—
676SD16—361no—
677D8—182no—
678M16—62no—
679C2×C8—31no—
680C2×C8—31no—
681C2×C8—91no—
682C2×C8—91no—
683C2×C8—182no—
684C4⋊C4—21no—
685C4⋊C4—31no—
686C4⋊C4—31no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4C2×D3211yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C42—31no—
703C42—181no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—62no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C22×#6711yescharacteristic
725C2×D3—21no—
726C2×D3—22no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—61no—
746C3×C4—81no—
747C3×C4—81no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4C2×D3×D411yescharacteristic
751C3×C4C2×D3×D411yescharacteristic
752C3×C4#100411yescharacteristic
753C3×C4#100911yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—21no—
757Dic3—41no—
758Dic3—41no—
759Dic3—62no—
760Dic3—62no—
761Dic3—122no—
762Dic3—122no—
763Dic3—121no—
764Dic3—121no—
765C32#326911yescharacteristic, complemented, Sylow
766C23—31no—
767C23—61no—
768C23—61no—
769C23D3×#6711yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—61no—
773Q8—61no—
774Q8—92no—
775Q8—181no—
776Q8—181no—
777Q8—181no—
778Q8—362no—
779D4—32no—
780D4—61no—
781D4—61no—
782D4—61no—
783D4—122no—
784D4—121no—
785D4—122no—
786D4—122no—
787D4—362no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—31no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—122no—
800C2×C4—122no—
801C2×C4—122no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—362no—
805C2×C4—362no—
806C2×C4D3×#6711yescharacteristic
807C2×C4C22×D3211yescharacteristic
808C8—32no—
809C8—61no—
810C8—181no—
811C8—181no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—42no—
816C2×C3—41no—
817C2×C3—41no—
818C2×C3—121no—
819C2×C3—122no—
820C2×C3—241no—
821C2×C3#560911yescharacteristic
822C2×C3#577311yescharacteristic
823C2×C3#577911yescharacteristic
824C2×C3D4×#6711yescharacteristic
825C2×C3#582211yescharacteristic
826C2×C3#583811yescharacteristic
827D3—41no—
828D3—42no—
829D3—81no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—62no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22C2×D3×#6711yescharacteristic
843C4—21no—
844C4—41no—
845C4—41no—
846C4—61no—
847C4—61no—
848C4—61no—
849C4—121no—
850C4—121no—
851C4—182no—
852C4—361no—
853C4D32×D411yescharacteristic
854C4#6431411yescharacteristic
855C3—21no—
856C3#8083711yescharacteristic, complemented
857C3#8352811yescharacteristic, complemented
858C2—41no—
859C2—121no—
860C2—122no—
861C2—241no—
862C2#1059529111yescharacteristic
863C2#1059532811yescharacteristic
864C2#1059546911yescharacteristic
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×#63947C2semidirect
3. #10594918C2semidirect
4. C2×#63831C2semidirect
5. #10592749C2semidirect
6. C3×#5049C2semidirect
7. #10591605C2semidirect
8. #10591599C2semidirect
9. #10591575C2semidirect
10. #10591161C2semidirect
11. #10591147C2semidirect
12. #10590614C2semidirect
13. #10590590C2semidirect
14. #10590579C2semidirect
15. #10590530C2semidirect
68. #5631D3semidirect
82. #5049D3semidirect
152. #3716D4semidirect
765. C32#3269semidirect
856. C3#80837semidirect
857. 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×#639472
#105949182
C2×#638312
#105927492
C3×#50492
#105916052
#105915992
#105915752
#105911612
#105911472
#105906142
#105905902
#105905792
#105905302
#835283
#808373