Finite Group Databasebeta

← #11884475

Subgroups — #11884475

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5676C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63932C211yesmaximal, characteristic, complemented
4#10593906C211yesmaximal, characteristic, complemented
5#10592753C211yesmaximal, characteristic, complemented
6C3×#5058C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591587C211yesmaximal, characteristic, complemented
9#10591586C211yesmaximal, characteristic, complemented
10#10591519C211yesmaximal, characteristic, complemented
11#10591498C211yesmaximal, characteristic, complemented
12#10591447C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590347C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83507—31nomaximal
17#81858—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C32×#124C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3754C2211yescharacteristic
25C4×#634C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#938C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#884—21no—
33C3×#883—21no—
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36C3×#874C2211yescharacteristic, complemented
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39#63947—24no—
40#63932—24no—
41#63914—21no—
42#63908C2211yescharacteristic
43#63908C2211yescharacteristic, complemented
44#63898—21no—
45#63885—21no—
46#63885—21no—
47C2×#3716C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C2×#932—31no—
66C2×#916—31no—
67C2×#911—31no—
68#5718—31no—
69#5676D311yescharacteristic, complemented
70#5553—31no—
71C3×#496—31no—
72#5238—31no—
73#5217—31no—
74#5174—31no—
75#5173—31no—
76#5172—31no—
77#5158—31no—
78#5157—31no—
79#5156—31no—
80#5072—31no—
81#5058D311yescharacteristic, complemented
82#5054—31no—
83#5054—31no—
84#5054—61no—
85#5049—31no—
86#5047—31no—
87#5038—31no—
88#5037—31no—
89#5018—31no—
90#5015—31no—
91#5011—31no—
92#4710—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×#239—22no—
101C3×#239—41no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12D411yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×#625—21no—
116C2×#625—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×D3×Dic3—21no—
120C2×D3×Dic3—21no—
121#3795—22no—
122#3795—22no—
123#3795—41no—
124#3795—41no—
125C32×C22⋊C4—21no—
126C32×C22⋊C4—21no—
127C32×C42C2311yescharacteristic
128#3756—22no—
129#3754—22no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C4×C3⋊Dic3—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#217—21no—
136C3×#215—22no—
137C3×#215—41no—
138C3×#213—22no—
139C3×#213—41no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×(C2×D3)⋊C4D411yescharacteristic
144C3×C4⋊Dic3D411yescharacteristic
145C3×C4⋊Dic3C2311yescharacteristic
146C3×Dic3⋊C4—21no—
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3716D414yescomplemented
152#3713—22no—
153#3713—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239C2×D311yescharacteristic
160C2×#237—31no—
161C2×#237—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C3×#127—31no—
170C3×#124—21no—
171C3×#124C2×D311yescharacteristic
172C3×#124C2×D311yescharacteristic
173C3×#123—61no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#120—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C22⋊C4—61no—
181#950—64no—
182#946C2×D311yescharacteristic
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—61no—
186C2×#215C2×D311yescharacteristic, complemented
187C2×#215C2×D311yescharacteristic, complemented
188#940—61no—
189#940—61no—
190#939—61no—
191#939—61no—
192#938—31no—
193#938—31no—
194#938C2×D311yescharacteristic
195D4×Dic3—61no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—61no—
200#932—64no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213C2×D311yescharacteristic
206C2×#213C2×D311yescharacteristic
207#930—31no—
208#930—31no—
209C2×#208—31no—
210C22×C3⋊C8—31no—
211#916—64no—
212#911—64no—
213C2×#204—31no—
214C2×ΓL(1,𝔽25)—31no—
215C2×D3×C8—31no—
216#893—61no—
217#884—21no—
218#884—61no—
219#884—61no—
220#883—21no—
221#882—21no—
222D3×C22⋊C4—21no—
223#874C2×D311yescharacteristic, complemented
224C4×D12C2×D311yescharacteristic
225C4×D12C2×D311yescharacteristic
226C4×Dic6—31no—
227C4×Dic6—31no—
228C4×Dic6—61no—
229C3×#97—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#830—31no—
240#830—31no—
241#821—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244#818—31no—
245#816—31no—
246#810—31no—
247#809—31no—
248#809—31no—
249#807—31no—
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—61no—
253#803C2×D311yescharacteristic, complemented
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273#634—21no—
274#634C2×D412yes—
275C3×#67—42no—
276C3×#67—81no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—41no—
286C3×D12—42no—
287C3×D12—42no—
288C3×D12—81no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×C4×D3—81no—
296#625—42no—
297#625—42no—
298#625—81no—
299#625—81no—
300D3×Dic3—42no—
301D3×Dic3—42no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—31no—
310#496—31no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—121no—
340C2×C3×D4C22×D311yescharacteristic
341C2×C3×D4C22×D311yescharacteristic
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358#239—22no—
359#239—41no—
360#237—62no—
361#237—62no—
362#237—121no—
363#237—121no—
364D3×D4—22no—
365D3×D4—41no—
366#235—62no—
367#235—62no—
368#235—121no—
369#235—121no—
370C2×D12—21no—
371C2×D12—21no—
372C2×D12—21no—
373C2×D12#6711yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—21no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C3×SD16—62no—
387C3×SD16—121no—
388C3×D8—62no—
389C3×D8—121no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—61no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—31no—
401C3×C22⋊C4—41no—
402C3×C22⋊C4—41no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C42—21no—
407C3×C42C22×D311yescharacteristic
408C3×C42C22×D311yescharacteristic
409#217—21no—
410#217—61no—
411#217—61no—
412#216—62no—
413#216—62no—
414#216—122no—
415#215—22no—
416#215—41no—
417#214—34no—
418#214—62no—
419#214—62no—
420#214—122no—
421#213—22no—
422#213—41no—
423#213—62no—
424#213—62no—
425#213—62no—
426#213—62no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4#6711yescharacteristic
432(C2×D3)⋊C4#6711yescharacteristic
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—61no—
436C4⋊Dic3#6711yescharacteristic
437C4⋊Dic3C22×D311yescharacteristic
438Dic3⋊C4—21no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—121no—
442C4×Dic3—61no—
443C4×Dic3—61no—
444C4×Dic3—121no—
445#208—62no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455#204—34no—
456ΓL(1,𝔽25)—62no—
457D3×C8—62no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—84no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—41no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—22no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—91no—
490C2×#41—91no—
491C22×D4—31no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—91no—
505#127—31no—
506#127—181no—
507#124D3211yescharacteristic
508#123—61no—
509C22⋊Q8—31no—
510#121—31no—
511#121—61no—
512#121—91no—
513#121—91no—
514#121—181no—
515#121—181no—
516#120—61no—
517C4×Q8—91no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4—181no—
521C2×C22⋊C4—61no—
522#107—91no—
523C4⋊C8—91no—
524#103—91no—
525#103—91no—
526#102—91no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—31no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—241no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—81no—
550C22×D3C2×#6711yescharacteristic
551C22×D3C2×#6711yescharacteristic
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—41no—
557C3×Q8—41no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—32no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—121no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—241no—
575C3×D4—241no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—41no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—122no—
590C2×C3×C4—241no—
591C2×C3×C4D3×D411yescharacteristic
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C2×#6711yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597#67—42no—
598#67—81no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—241no—
604#67—241no—
605#67—241no—
606#67—241no—
607C2×Dic3—21no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—121no—
613C2×Dic3—121no—
614C2×Dic3—122no—
615C2×Dic3—122no—
616C2×Dic3C2×#6711yescharacteristic
617C2×Dic3C2×#6711yescharacteristic
618D12—21no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—41no—
624D12—42no—
625D12—42no—
626D12—81no—
627D12D3×D412yes—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—42no—
633C4×D3—81no—
634C4×D3—122no—
635C4×D3—122no—
636Dic6—32no—
637Dic6—32no—
638Dic6—62no—
639Dic6—61no—
640Dic6—61no—
641Dic6—121no—
642C3×C8—32no—
643C3×C8—61no—
644C3⋊C8—21no—
645C3⋊C8—61no—
646C3⋊C8—61no—
647C3⋊C8—61no—
648C3⋊C8—61no—
649C3⋊C8—121no—
650C3⋊C8—121no—
651C3⋊C8D3×D412yes—
652C2×C32—81no—
653C2×C32D4211yescharacteristic
654C2×C32#57511yescharacteristic
655C2×C32#57611yescharacteristic
656C3×D3—41no—
657C3×D3—41no—
658C3×D3—42no—
659C3×D3—81no—
660C3×D3—81no—
661C24—61no—
662#41—62no—
663#41—121no—
664#41—182no—
665#41—182no—
666#41—361no—
667#41—361no—
668C2×Q8—91no—
669C2×Q8C2×D3211yescharacteristic
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—62no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—121no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4C2×D3211yescharacteristic
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—181no—
691C22×C4—181no—
692Q16—182no—
693SD16—62no—
694SD16—94no—
695SD16—121no—
696SD16—182no—
697D8—62no—
698D8—121no—
699D8—182no—
700D8—182no—
701M16—182no—
702C2×C8—31no—
703C2×C8—31no—
704C2×C8—91no—
705C2×C8—91no—
706C2×C8—182no—
707C4⋊C4—31no—
708C4⋊C4—31no—
709C4⋊C4—61no—
710C4⋊C4—91no—
711C4⋊C4—181no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—31no—
715C22⋊C4—31no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—181no—
722C42C2×D3211yescharacteristic
723C22×C3—21no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—62no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—244no—
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C22×#6711yescharacteristic
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—22no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—84no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—61no—
778C3×C4—61no—
779C3×C4—81no—
780C3×C4—121no—
781C3×C4C2×D3×D411yescharacteristic
782C3×C4C2×D3×D411yescharacteristic
783C3×C4#100411yescharacteristic
784C3×C4#100411yescharacteristic
785Dic3—21no—
786Dic3—21no—
787Dic3—41no—
788Dic3—62no—
789Dic3—62no—
790Dic3—122no—
791Dic3—121no—
792Dic3—121no—
793Dic3—241no—
794C32#326811yescharacteristic, complemented, Sylow
795C23—21no—
796C23—31no—
797C23—31no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—122no—
802C23—122no—
803C23—241no—
804Q8—21no—
805Q8—21no—
806Q8—92no—
807Q8—181no—
808D4—21no—
809D4—21no—
810D4—32no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—121no—
817D4—122no—
818D4—122no—
819D4—122no—
820D4—241no—
821D4—241no—
822D4—362no—
823D4—362no—
824D4—721no—
825D4—721no—
826C2×C4—21no—
827C2×C4—31no—
828C2×C4—31no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—122no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—241no—
838C2×C4—362no—
839C2×C4—362no—
840C2×C4D3×#6711yescharacteristic
841C2×C4D3×#6711yescharacteristic
842C2×C4C22×D3211yescharacteristic
843C8—32no—
844C8—61no—
845C8—181no—
846C8—181no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—81no—
851C2×C3—81no—
852C2×C3—121no—
853C2×C3—121no—
854C2×C3—122no—
855C2×C3—161no—
856C2×C3—241no—
857C2×C3—241no—
858C2×C3#571711yescharacteristic
859C2×C3#577311yescharacteristic
860C2×C3#577411yescharacteristic
861C2×C3D4×#6711yescharacteristic
862C2×C3#582211yescharacteristic
863C2×C3#583511yescharacteristic
864D3—41no—
865D3—41no—
866D3—42no—
867D3—81no—
868D3—81no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—61no—
878C22—62no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—244no—
888C22C2×D3×#6711yescharacteristic
889C4—21no—
890C4—21no—
891C4—41no—
892C4—61no—
893C4—61no—
894C4—121no—
895C4—182no—
896C4—361no—
897C4D32×D411yescharacteristic
898C4#6431311yescharacteristic
899C3—21no—
900C3#8185811yescharacteristic, complemented
901C3#8350711yescharacteristic, complemented
902C2—81no—
903C2—121no—
904C2—121no—
905C2—122no—
906C2—241no—
907C2—241no—
908C2#1059529311yescharacteristic
909C2#1059545411yescharacteristic
910C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5676C2semidirect
2. C2×#63947C2semidirect
3. C2×#63932C2semidirect
4. #10593906C2semidirect
5. #10592753C2semidirect
6. C3×#5058C2semidirect
7. #10591655C2semidirect
8. #10591587C2semidirect
9. #10591586C2semidirect
10. #10591519C2semidirect
11. #10591498C2semidirect
12. #10591447C2semidirect
13. #10590360C2semidirect
14. #10590347C2semidirect
15. #10590326C2semidirect
21. C2×#3795C22semidirect
23. C2×#3756C22semidirect
25. C4×#634C22semidirect
27. C2×C3×#215C22semidirect
28. C2×C3×#215C22semidirect
36. C3×#874C22semidirect
43. #63908C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#803C22semidirect
56. #63575C22semidirect
57. #63567C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. #5676D3semidirect
81. #5058D3semidirect
151. #3716D4semidirect
186. C2×#215C2×D3semidirect
187. C2×#215C2×D3semidirect
223. #874C2×D3semidirect
253. #803C2×D3semidirect
794. C32#3268semidirect
900. C3#81858semidirect
901. C3#83507semidirect

Maximal subgroups

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

subgroupindex
C3×#56762
C2×#639472
C2×#639322
#105939062
#105927532
C3×#50582
#105916552
#105915872
#105915862
#105915192
#105914982
#105914472
#105903602
#105903472
#105903262
#835073
#818583