Finite Group Databasebeta

← #11884794

Subgroups — #11884794

Order 1152.

1018 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5633C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic, complemented
3#10594915C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5#10592749C211yesmaximal, characteristic, complemented
6C3×#5052C211yesmaximal, characteristic, complemented
7#10591627C211yesmaximal, characteristic, complemented
8#10591595C211yesmaximal, characteristic, complemented
9#10591577C211yesmaximal, characteristic, complemented
10#10591170C211yesmaximal, characteristic, complemented
11#10591147C211yesmaximal, characteristic, complemented
12#10590603C211yesmaximal, characteristic, complemented
13#10590578C211yesmaximal, characteristic, complemented
14#10590561C211yesmaximal, characteristic, complemented
15#10590480C211yesmaximal, characteristic, complemented
16#83546—31nomaximal
17#80926—31nomaximal
18C22×#634C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C3×#947C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×C4×#67C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#896—21no—
31C3×#895C2211yescharacteristic
32C3×#893—21no—
33C3×#887C2211yescharacteristic
34C3×#885—21no—
35C3×#884—21no—
36#63982—21no—
37#67⋊Dic3—21no—
38D3×#216—24no—
39#63896—21no—
40#63866C2211yescharacteristic
41#63857C2211yescharacteristic
42#63844C2211yescharacteristic
43#63840—21no—
44C2×#3719C2211yescharacteristic
45C2×#3719C2211yescharacteristic
46C2×#3718C2211yescharacteristic
47#63831—24no—
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63657C2211yescharacteristic
53#63637C2211yescharacteristic
54#63637C2211yescharacteristic
55C3×#835C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#808C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic
63C3×#548—31no—
64C2×#951—31no—
65C22×#216—31no—
66C2×D3×Q16—31no—
67C2×#909—31no—
68#5633D311yescharacteristic
69#5632—31no—
70D4×Dic6—31no—
71C3×#470—31no—
72#5239—31no—
73#5228—31no—
74#5190—31no—
75#5127—31no—
76#5060—31no—
77#5054—31no—
78#5052D311yescharacteristic, complemented
79#5050—31no—
80#5050—31no—
81#5050—61no—
82#5047—31no—
83#5041—31no—
84#5040—31no—
85#5031—31no—
86#5030—31no—
87#5011—31no—
88#4864—31no—
89#4853—31no—
90#4809—31no—
91#4806—31no—
92#4798—31no—
93#4795—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×#67D411yescharacteristic
104C3×D3×Q8—22no—
105C3×D3×Q8—41no—
106C3×#235—22no—
107C3×#235—41no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#627—21no—
117C2×D3×Dic3—21no—
118D3×Dic6—22no—
119D3×Dic6—41no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123#3756—22no—
124#3756—41no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217—21no—
128C3×#217D411yescharacteristic
129C3×#216—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C3×#208—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3719—22no—
150#3719D414yescomplemented
151#3718—22no—
152#3716—22no—
153#3716—22no—
154#3715—41no—
155D3×C3⋊C8—22no—
156#3270—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8C2×D311yescharacteristic
161C2×#235C2×D311yescharacteristic
162C22×Dic6—31no—
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—61no—
166C2×C3×Q16—31no—
167C2×C3×M16—31no—
168C3×#124—31no—
169C3×#124—61no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—61no—
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×C22⋊Q8C2×D311yescharacteristic
175C3×#121—31no—
176C3×#121—61no—
177C3×C4×Q8—31no—
178C3×C4×D4—31no—
179C3×C4×D4—61no—
180#951—64no—
181#947C2×D311yescharacteristic
182#944—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—61no—
192C2×#216—61no—
193C2×#216—64no—
194C2×#216C2×D311yescharacteristic
195C2×#215—31no—
196D4×Dic3—61no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C4×#67C2×D311yescharacteristic
201#924—31no—
202#924C2×D311yescharacteristic
203C2×#208C2×D311yescharacteristic
204C22×C3⋊C8—31no—
205D3×Q16—64no—
206#909—64no—
207C2×Dic12—31no—
208C2×Dic12—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×D3×C8—31no—
212#897—31no—
213#896—21no—
214#896—61no—
215#895C2×D311yescharacteristic
216#893—21no—
217#888—61no—
218#888—61no—
219#887—31no—
220#887C2×D311yescharacteristic
221#885—21no—
222#884—21no—
223#67⋊C4—61no—
224#878—61no—
225#878—61no—
226#878—61no—
227#869—31no—
228C4×Dic6—31no—
229C3×#106—31no—
230C3×#103—31no—
231C3×#103—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#810C2×D311yescharacteristic
250#809—31no—
251#808C2×D311yescharacteristic
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C32×Q8—21no—
258C32×Q8—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—42no—
268#634—21no—
269#634—21no—
270#634—21no—
271#634—42no—
272#634C2×D412yes—
273C3×#67—22no—
274C3×#67—42no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292C3×Dic6C2×D412yes—
293#627—42no—
294D3×Dic3—42no—
295C3⋊(C3⋊C8)—21no—
296C3⋊(C3⋊C8)—21no—
297C3×C3⋊C8—21no—
298C3×C3⋊C8C2×D412yes—
299C2×#137—91no—
300C22×Q16—91no—
301D4×Q8—91no—
302#548—31no—
303#497—91no—
304#470—31no—
305#465—91no—
306#464—91no—
307#462—91no—
308#452—91no—
309#451—91no—
310#451—91no—
311#448—91no—
312#441—91no—
313#435—91no—
314C3×#41—62no—
315C3×#41—121no—
316C2×C3×Q8—21no—
317C2×C3×Q8—31no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C2×C3×Q8—62no—
321C2×C3×Q8—121no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67—21no—
335C2×#67#6711yescharacteristic
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—121no—
340D3×Q8—22no—
341D3×Q8—41no—
342D3×Q8—62no—
343D3×Q8—121no—
344#235—22no—
345#235—41no—
346C2×D12—21no—
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—61no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—21no—
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—31no—
356C2×Dic6—31no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6—62no—
360C2×Dic6—62no—
361C2×Dic6—62no—
362C2×Dic6—61no—
363C2×Dic6—61no—
364C2×Dic6—61no—
365C2×Dic6—61no—
366C2×Dic6—122no—
367C2×Dic6—121no—
368C2×Dic6—121no—
369C2×Dic6—121no—
370C2×Dic6—121no—
371C2×Dic6—122no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×Q16—62no—
375C3×M16—62no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—41no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—41no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C42—31no—
398C3×C42—61no—
399#217—21no—
400#217—61no—
401#217#6711yescharacteristic
402#216—22no—
403#216—34no—
404#216—62no—
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—121no—
414#214—62no—
415#214—62no—
416#214—121no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4#6711yescharacteristic
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—21no—
427Dic3⋊C4—21no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4#6711yescharacteristic
434C4×Dic3—21no—
435C4×Dic3—61no—
436C4×Dic3—61no—
437C4×Dic3C22×D311yescharacteristic
438#208—22no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—62no—
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D311yescharacteristic
448Dic12—34no—
449Dic12—62no—
450#204—62no—
451#204—62no—
452D3×C8—62no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32C22×D411yescharacteristic
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3#13712yescomplemented
463C32×C4—21no—
464C32×C4—41no—
465C32×C4—41no—
466C32×C4C22×D411yescharacteristic
467C32×C4H(5,𝔽2)11yescharacteristic
468C3⋊Dic3—22no—
469C3⋊Dic3—41no—
470C3×Dic3—21no—
471C3×Dic3—22no—
472C3×Dic3—21no—
473C3×Dic3—21no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C2×#41—31no—
477C22×Q8—31no—
478C22×Q8—91no—
479C22×Q8—91no—
480#137—184no—
481C2×Q16—31no—
482C2×Q16—91no—
483C2×Q16—91no—
484C2×Q16—91no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×Q16—184no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×M16—31no—
492C22×C8—91no—
493C4⋊Q8—91no—
494C4⋊Q8—181no—
495#124—31no—
496#124—61no—
497C22⋊Q8—31no—
498C22⋊Q8—61no—
499C22⋊Q8—91no—
500C22⋊Q8—181no—
501C22⋊Q8—181no—
502C22⋊Q8D3211yescharacteristic
503#121—31no—
504#121—61no—
505C4×Q8—31no—
506C4×Q8—91no—
507C4×D4—31no—
508C4×D4—61no—
509C4×D4—181no—
510#106—31no—
511C4⋊C8—91no—
512#103—31no—
513#103—31no—
514#103—91no—
515#103—91no—
516#103—91no—
517#102—91no—
518C22⋊C8—91no—
519C22⋊C8—91no—
520#97—91no—
521C23×C3—21no—
522C23×C3—31no—
523C23×C3—61no—
524C23×C3D3×D411yescharacteristic
525C23×C3C2×#6711yescharacteristic
526C22×D3—21no—
527C22×D3C2×#6711yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—32no—
533C3×Q8—41no—
534C3×Q8—41no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8—122no—
539C3×D4—62no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—122no—
543C3×D4—122no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—122no—
567C2×C3×C4—122no—
568C2×C3×C4D3×D411yescharacteristic
569C2×C3×C4C2×#6711yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—22no—
573#67—42no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—122no—
584C2×Dic3—122no—
585C2×Dic3—122no—
586C2×Dic3—124no—
587C2×Dic3C2×#6711yescharacteristic
588C2×Dic3C2×#6711yescharacteristic
589C2×Dic3C2×#6711yescharacteristic
590D12—21no—
591D12—21no—
592D12—42no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—42no—
596C4×D3—42no—
597C4×D3—122no—
598Dic6—21no—
599Dic6—21no—
600Dic6—21no—
601Dic6—32no—
602Dic6—32no—
603Dic6—42no—
604Dic6—62no—
605Dic6—61no—
606Dic6—61no—
607Dic6—62no—
608Dic6—61no—
609Dic6—61no—
610Dic6—61no—
611Dic6—61no—
612Dic6—121no—
613Dic6—121no—
614Dic6—122no—
615Dic6—122no—
616Dic6—122no—
617Dic6—122no—
618Dic6—124no—
619Dic6D3×D412yes—
620C3×C8—32no—
621C3×C8—61no—
622C3⋊C8—21no—
623C3⋊C8—61no—
624C3⋊C8—61no—
625C3⋊C8—61no—
626C3⋊C8—61no—
627C3⋊C8—121no—
628C3⋊C8—121no—
629C3⋊C8D3×D412yes—
630C2×C32—41no—
631C2×C32D4211yescharacteristic
632C2×C32C2×#13711yescharacteristic
633C2×C32#57811yescharacteristic
634C3×D3—22no—
635C3×D3—81no—
636#41—62no—
637#41—121no—
638C2×Q8—31no—
639C2×Q8—31no—
640C2×Q8—61no—
641C2×Q8—62no—
642C2×Q8—91no—
643C2×Q8—91no—
644C2×Q8—121no—
645C2×Q8—182no—
646C2×Q8—181no—
647C2×Q8—182no—
648C2×Q8—181no—
649C2×Q8—361no—
650C2×Q8—361no—
651C2×Q8C2×D3211yescharacteristic
652C2×D4—31no—
653C2×D4—31no—
654C2×D4—61no—
655C2×D4—61no—
656C22×C4—31no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—181no—
660C22×C4—181no—
661C22×C4C2×D3211yescharacteristic
662Q16—62no—
663Q16—94no—
664Q16—182no—
665Q16—182no—
666Q16—182no—
667Q16—361no—
668SD16—182no—
669SD16—182no—
670SD16—361no—
671M16—62no—
672C2×C8—31no—
673C2×C8—31no—
674C2×C8—91no—
675C2×C8—91no—
676C2×C8—182no—
677C4⋊C4—21no—
678C4⋊C4—31no—
679C4⋊C4—31no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—181no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C4⋊C4—181no—
686C4⋊C4C2×D3211yescharacteristic
687C22⋊C4—21no—
688C22⋊C4—31no—
689C22⋊C4—31no—
690C22⋊C4—61no—
691C22⋊C4—61no—
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—181no—
695C42—31no—
696C42—61no—
697C42—181no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—32no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3C2×D3×D411yescharacteristic
715C22×C3C22×#6711yescharacteristic
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3#95112yescomplemented
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—61no—
732C3×C4—61no—
733C3×C4—61no—
734C3×C4—62no—
735C3×C4—81no—
736C3×C4—81no—
737C3×C4—121no—
738C3×C4—121no—
739C3×C4C2×D3×D411yescharacteristic
740C3×C4C2×D3×D411yescharacteristic
741C3×C4#100411yescharacteristic
742C3×C4#100911yescharacteristic
743Dic3—22no—
744Dic3—21no—
745Dic3—21no—
746Dic3—21no—
747Dic3—41no—
748Dic3—41no—
749Dic3—62no—
750Dic3—62no—
751Dic3—122no—
752Dic3—122no—
753Dic3—121no—
754Dic3—121no—
755C32#327011yescharacteristic, complemented, Sylow
756C23—31no—
757C23—61no—
758C23D3×#6711yescharacteristic
759Q8—21no—
760Q8—21no—
761Q8—32no—
762Q8—61no—
763Q8—61no—
764Q8—61no—
765Q8—92no—
766Q8—122no—
767Q8—181no—
768Q8—181no—
769Q8—181no—
770Q8—362no—
771Q8—362no—
772D4—62no—
773D4—61no—
774D4—61no—
775D4—122no—
776D4—122no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—122no—
790C2×C4—122no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—362no—
794C2×C4—362no—
795C2×C4D3×#6711yescharacteristic
796C2×C4C22×D3211yescharacteristic
797C8—32no—
798C8—61no—
799C8—181no—
800C8—181no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—42no—
805C2×C3—41no—
806C2×C3—41no—
807C2×C3—62no—
808C2×C3—241no—
809C2×C3#560911yescharacteristic
810C2×C3D3×#13711yescharacteristic
811C2×C3#577911yescharacteristic
812C2×C3D4×#6711yescharacteristic
813C2×C3C2×#95111yescharacteristic
814C2×C3#583811yescharacteristic
815D3—22no—
816D3—81no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—61no—
822C22—61no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22C2×D3×#6711yescharacteristic
827C4—21no—
828C4—41no—
829C4—41no—
830C4—61no—
831C4—61no—
832C4—61no—
833C4—62no—
834C4—121no—
835C4—121no—
836C4—182no—
837C4—361no—
838C4D32×D411yescharacteristic
839C4#6431411yescharacteristic
840C3—21no—
841C3#8092611yescharacteristic, complemented
842C3#8354611yescharacteristic, complemented
843C2—41no—
844C2—62no—
845C2—241no—
846C2#1059529111yescharacteristic
847C2#1059532811yescharacteristic
848C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC3×#5633C2
hypercenterC22⋊Q8D32
hypocenterC32#3270
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
2. C2×D3×#216C2semidirect
3. #10594915C2semidirect
4. C2×#63831C2semidirect
5. #10592749C2semidirect
6. C3×#5052C2semidirect
7. #10591627C2semidirect
8. #10591595C2semidirect
9. #10591577C2semidirect
10. #10591170C2semidirect
11. #10591147C2semidirect
12. #10590603C2semidirect
13. #10590578C2semidirect
14. #10590561C2semidirect
15. #10590480C2semidirect
78. #5052D3semidirect
150. #3719D4semidirect
462. C2×C3×D3#137semidirect
721. C2×D3#951semidirect
755. C32#3270semidirect
841. C3#80926semidirect
842. C3#83546semidirect

Maximal subgroups

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

subgroupindex
C3×#56332
C2×D3×#2162
#105949152
C2×#638312
#105927492
C3×#50522
#105916272
#105915952
#105915772
#105911702
#105911472
#105906032
#105905782
#105905612
#105904802
#835463
#809263