Finite Group Databasebeta

← #11884796

Subgroups — #11884796

Order 1152.

999 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5633C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic, complemented
3Dic6×#67C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592751C211yesmaximal, characteristic, complemented
6C3×#5050C211yesmaximal, characteristic, complemented
7#10591627C211yesmaximal, characteristic, complemented
8#10591594C211yesmaximal, characteristic, complemented
9#10591578C211yesmaximal, characteristic, complemented
10#10591173C211yesmaximal, characteristic, complemented
11#10591151C211yesmaximal, characteristic, complemented
12#10590603C211yesmaximal, characteristic, complemented
13#10590561C211yesmaximal, characteristic, complemented
14#10590514C211yesmaximal, characteristic, complemented
15#10590477C211yesmaximal, characteristic, complemented
16#83546—31nomaximal
17#80209—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24#64133C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#896—21no—
31C3×#895C2211yescharacteristic
32C3×#893—21no—
33C3×#887C2211yescharacteristic
34C3×#885—21no—
35C3×#884—21no—
36Dic3×#67—21no—
37#63964—21no—
38D3×#216—24no—
39#63887—21no—
40#63866C2211yescharacteristic
41#63856C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43#63839—21no—
44C2×#3719C2211yescharacteristic
45C2×#3718C2211yescharacteristic
46C2×#3718C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48#63827—24no—
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic
53#63637C2211yescharacteristic
54#63635C2211yescharacteristic
55C3×#830C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic
63C3×#548—31no—
64C2×#951—31no—
65Q8×#67—31no—
66C22×#216—31no—
67C2×#942—31no—
68C2×D3×Q16—31no—
69#5633D311yescharacteristic
70D4×Dic6—31no—
71C3×#451—31no—
72#5239—31no—
73#5228—31no—
74#5190—31no—
75#5186—31no—
76#5185—31no—
77#5060—31no—
78#5054—31no—
79#5052—31no—
80#5052—31no—
81#5052—61no—
82#5050D311yescharacteristic, complemented
83#5041—31no—
84#5040—31no—
85#5031—31no—
86#5030—31no—
87#5011—31no—
88#4807—31no—
89#4806—31no—
90#4795—31no—
91#4789—31no—
92#4733—31no—
93#4728—31no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C3×D3×Q8—22no—
101C3×D3×Q8—41no—
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—22no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6—21no—
112C2×C3×Dic6—41no—
113C2×C3×Dic6C2311yescharacteristic
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#3757—21no—
124#3756—22no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
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)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
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#3718—22no—
151#3718D414yescomplemented
152#3716—41no—
153#3715—22no—
154#3715—22no—
155D3×C3⋊C8—22no—
156#3270—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8C2×D311yescharacteristic
162C2×#235C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6C2×D311yescharacteristic
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C3×#124—31no—
168C3×#124—61no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C2×D311yescharacteristic
173C3×#121—31no—
174C3×#121—61no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178#951—64no—
179#947C2×D311yescharacteristic
180#946—31no—
181#946—61no—
182Q8×Dic3—31no—
183#944—31no—
184#944—61no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—31no—
192C2×#216—61no—
193C2×#216—64no—
194C2×#216C2×D311yescharacteristic
195C2×#216C2×D311yescharacteristic
196#942—64no—
197C2×#215—31no—
198C2×#215—31no—
199D4×Dic3—61no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203C4×#67—61no—
204C4×#67C2×D311yescharacteristic
205#924—31no—
206#924—31no—
207#924—31no—
208#924—61no—
209#924—61no—
210C2×#208—31no—
211C2×#208—31no—
212C2×#208—61no—
213C22×C3⋊C8—31no—
214D3×Q16—64no—
215C2×Dic12—31no—
216C2×#204—31no—
217C2×D3×C8—31no—
218#896—21no—
219#895C2×D311yescharacteristic
220#893—21no—
221#888—61no—
222#887C2×D311yescharacteristic
223#885—21no—
224#884—21no—
225#878—61no—
226#878—61no—
227#869—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#810—31no—
245#810—31no—
246#810—61no—
247#810C2×D311yescharacteristic
248#810C2×D311yescharacteristic
249#808—31no—
250#808—31no—
251#808—61no—
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—
267#634—21no—
268#634—21no—
269C3×#67—22no—
270C3×#67—42no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—42no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—42no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—42no—
284C3×C4×D3—42no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—42no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
292C3×Dic6C2×D412yes—
293#627—42no—
294D3×Dic3—42no—
295C3⋊(C3⋊C8)—21no—
296C3⋊(C3⋊C8)C2×D412yes—
297C3×C3⋊C8—21no—
298C3×C3⋊C8—21no—
299C2×#137—91no—
300C22×Q16—91no—
301D4×Q8—91no—
302#548—31no—
303#497—91no—
304#470—91no—
305#465—91no—
306#464—91no—
307#462—91no—
308#452—91no—
309#451—31no—
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—31no—
320C2×C3×Q8—61no—
321C2×C3×Q8—62no—
322C2×C3×Q8—61no—
323C2×C3×Q8—62no—
324C2×C3×Q8—121no—
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×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—21no—
340C2×#67#6711yescharacteristic
341C22×Dic3—21no—
342C22×Dic3—61no—
343D3×Q8—22no—
344D3×Q8—41no—
345D3×Q8—62no—
346D3×Q8—121no—
347#235—22no—
348#235—41no—
349C2×D12—21no—
350C2×D12C22×D311yescharacteristic
351C2×C4×D3—21no—
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3C22×D311yescharacteristic
355C2×Dic6—22no—
356C2×Dic6—21no—
357C2×Dic6—21no—
358C2×Dic6—31no—
359C2×Dic6—31no—
360C2×Dic6—41no—
361C2×Dic6—61no—
362C2×Dic6—62no—
363C2×Dic6—61no—
364C2×Dic6—61no—
365C2×Dic6—121no—
366C2×Dic6C22×D311yescharacteristic
367C2×Dic6C22×D311yescharacteristic
368C2×Dic6C22×D311yescharacteristic
369C3×Q16—62no—
370C3×Q16—121no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—41no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C4⋊C4C22×D311yescharacteristic
381C3×C22⋊C4—21no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—41no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C42—31no—
390C3×C42—61no—
391#217—61no—
392#217—61no—
393#217—61no—
394#217—121no—
395#217#6711yescharacteristic
396#216—22no—
397#216—34no—
398#216—34no—
399#216—41no—
400#216—62no—
401#216—62no—
402#216—62no—
403#216—62no—
404#216—62no—
405#216—122no—
406#215—62no—
407#215—62no—
408#214—62no—
409#214—62no—
410#214—121no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4#6711yescharacteristic
416C4⋊Dic3—31no—
417C4⋊Dic3—31no—
418C4⋊Dic3—61no—
419C4⋊Dic3—61no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422Dic3⋊C4—21no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—121no—
431Dic3⋊C4#6711yescharacteristic
432C4×Dic3—21no—
433C4×Dic3—61no—
434C4×Dic3—61no—
435C4×Dic3C22×D311yescharacteristic
436#208—62no—
437#208—62no—
438#208—122no—
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—62no—
449#204—121no—
450D3×C8—62no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32C22×D411yescharacteristic
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3#13712yescomplemented
461C32×C4—21no—
462C32×C4—41no—
463C32×C4—41no—
464C32×C4C22×D411yescharacteristic
465C32×C4H(5,𝔽2)11yescharacteristic
466C3⋊Dic3—41no—
467C3⋊Dic3—41no—
468C3×Dic3—22no—
469C3×Dic3—21no—
470C3×Dic3—22no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—41no—
474C2×#41—31no—
475C22×Q8—31no—
476C22×Q8—31no—
477C22×Q8—91no—
478#137—184no—
479C2×Q16—31no—
480C2×Q16—31no—
481C2×Q16—91no—
482C2×Q16—91no—
483C2×Q16—91no—
484C2×Q16—91no—
485C2×Q16—184no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×SD16—91no—
489C2×M16—91no—
490C22×C8—91no—
491C4⋊Q8—91no—
492C4⋊Q8—181no—
493#124—31no—
494#124—61no—
495C22⋊Q8—61no—
496C22⋊Q8—91no—
497C22⋊Q8—91no—
498C22⋊Q8—181no—
499C22⋊Q8—181no—
500C22⋊Q8D3211yescharacteristic
501#121—31no—
502#121—61no—
503C4×Q8—31no—
504C4×Q8—91no—
505C4×D4—31no—
506C4×D4—61no—
507C4×D4—181no—
508#106—91no—
509C4⋊C8—91no—
510#103—31no—
511#103—31no—
512#103—91no—
513#103—91no—
514#103—91no—
515#102—91no—
516C22⋊C8—31no—
517C22⋊C8—91no—
518#97—91no—
519C23×C3—21no—
520C23×C3—31no—
521C23×C3—61no—
522C23×C3D3×D411yescharacteristic
523C23×C3C2×#6711yescharacteristic
524C22×D3—21no—
525C22×D3C2×#6711yescharacteristic
526C3×Q8—21no—
527C3×Q8—21no—
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—32no—
531C3×Q8—32no—
532C3×Q8—41no—
533C3×Q8—41no—
534C3×Q8—61no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8—122no—
539C3×Q8—122no—
540C3×D4—62no—
541C3×D4—61no—
542C3×D4—61no—
543C3×D4—122no—
544C3×D4—122no—
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—21no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—122no—
568C2×C3×C4—122no—
569C2×C3×C4—122no—
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4C2×#6711yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574#67—22no—
575#67—42no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—42no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—122no—
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—21no—
602Dic6—42no—
603Dic6—42no—
604Dic6—61no—
605Dic6—61no—
606Dic6—61no—
607Dic6—61no—
608Dic6—121no—
609Dic6—121no—
610Dic6—122no—
611Dic6—122no—
612Dic6D3×D412yes—
613Dic6D3×D412yes—
614C3×C8—61no—
615C3×C8—61no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C3⋊C8—32no—
619C3⋊C8—32no—
620C3⋊C8—62no—
621C3⋊C8—61no—
622C3⋊C8—61no—
623C3⋊C8—121no—
624C2×C32—41no—
625C2×C32D4211yescharacteristic
626C2×C32C2×#13711yescharacteristic
627C2×C32#57811yescharacteristic
628C3×D3—22no—
629C3×D3—81no—
630#41—62no—
631#41—121no—
632C2×Q8—31no—
633C2×Q8—31no—
634C2×Q8—31no—
635C2×Q8—61no—
636C2×Q8—62no—
637C2×Q8—61no—
638C2×Q8—62no—
639C2×Q8—91no—
640C2×Q8—121no—
641C2×Q8—121no—
642C2×Q8—181no—
643C2×Q8—182no—
644C2×Q8—361no—
645C2×Q8C2×D3211yescharacteristic
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—61no—
649C2×D4—61no—
650C22×C4—31no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—181no—
655C22×C4C2×D3211yescharacteristic
656Q16—62no—
657Q16—94no—
658Q16—121no—
659Q16—182no—
660Q16—182no—
661Q16—182no—
662SD16—182no—
663SD16—182no—
664SD16—361no—
665M16—182no—
666C2×C8—31no—
667C2×C8—31no—
668C2×C8—91no—
669C2×C8—91no—
670C2×C8—182no—
671C4⋊C4—21no—
672C4⋊C4—31no—
673C4⋊C4—61no—
674C4⋊C4—91no—
675C4⋊C4—181no—
676C4⋊C4—181no—
677C4⋊C4—181no—
678C4⋊C4—181no—
679C4⋊C4—181no—
680C4⋊C4C2×D3211yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—31no—
683C22⋊C4—31no—
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—181no—
688C22⋊C4—181no—
689C42—31no—
690C42—61no—
691C42—181no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—32no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3C2×D3×D411yescharacteristic
709C22×C3C22×#6711yescharacteristic
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3#95112yescomplemented
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—62no—
728C3×C4—61no—
729C3×C4—62no—
730C3×C4—81no—
731C3×C4—81no—
732C3×C4—121no—
733C3×C4C2×D3×D411yescharacteristic
734C3×C4C2×D3×D411yescharacteristic
735C3×C4#100411yescharacteristic
736C3×C4#100411yescharacteristic
737Dic3—22no—
738Dic3—21no—
739Dic3—21no—
740Dic3—21no—
741Dic3—22no—
742Dic3—41no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—241no—
748Dic3—241no—
749C32#327011yescharacteristic, complemented, Sylow
750C23—31no—
751C23—61no—
752C23D3×#6711yescharacteristic
753Q8—21no—
754Q8—21no—
755Q8—32no—
756Q8—32no—
757Q8—61no—
758Q8—61no—
759Q8—61no—
760Q8—61no—
761Q8—122no—
762Q8—122no—
763Q8—181no—
764Q8—181no—
765Q8—362no—
766D4—62no—
767D4—61no—
768D4—61no—
769D4—122no—
770D4—122no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4—122no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—362no—
789C2×C4D3×#6711yescharacteristic
790C2×C4C22×D3211yescharacteristic
791C8—61no—
792C8—61no—
793C8—92no—
794C8—181no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—41no—
799C2×C3—41no—
800C2×C3—62no—
801C2×C3—81no—
802C2×C3—241no—
803C2×C3#559011yescharacteristic
804C2×C3#576611yescharacteristic
805C2×C3D3×#13711yescharacteristic
806C2×C3D4×#6711yescharacteristic
807C2×C3C2×#95111yescharacteristic
808C2×C3#583811yescharacteristic
809D3—22no—
810D3—81no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—32no—
815C22—61no—
816C22—61no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22C2×D3×#6711yescharacteristic
821C4—21no—
822C4—41no—
823C4—41no—
824C4—61no—
825C4—61no—
826C4—62no—
827C4—62no—
828C4—61no—
829C4—121no—
830C4—361no—
831C4—361no—
832C4D32×D411yescharacteristic
833C4#6431311yescharacteristic
834C3—21no—
835C3#8020911yescharacteristic, complemented
836C3#8354611yescharacteristic, complemented
837C2—41no—
838C2—62no—
839C2—241no—
840C2#1059528711yescharacteristic
841C2#1059532711yescharacteristic
842C2D3×#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. Dic6×#67C2semidirect
4. C2×#63827C2semidirect
5. #10592751C2semidirect
6. C3×#5050C2semidirect
7. #10591627C2semidirect
8. #10591594C2semidirect
9. #10591578C2semidirect
10. #10591173C2semidirect
11. #10591151C2semidirect
12. #10590603C2semidirect
13. #10590561C2semidirect
14. #10590514C2semidirect
15. #10590477C2semidirect
82. #5050D3semidirect
151. #3718D4semidirect
460. C2×C3×D3#137semidirect
715. C2×D3#951semidirect
749. C32#3270semidirect
835. C3#80209semidirect
836. 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
Dic6×#672
C2×#638272
#105927512
C3×#50502
#105916272
#105915942
#105915782
#105911732
#105911512
#105906032
#105905612
#105905142
#105904772
#835463
#802093