Finite Group Databasebeta

← #11883953

Subgroups — #11883953

Order 1152.

1171 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×#67C211yesmaximal, characteristic, complemented
2#10594918C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic, complemented
4C2×#63795C211yesmaximal, characteristic, complemented
5#10592437C211yesmaximal, characteristic, complemented
6C3×#4732C211yesmaximal, characteristic, complemented
7C3×#4730C211yesmaximal, characteristic, complemented
8#10591164C211yesmaximal, characteristic, complemented
9#10590962C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590883C211yesmaximal, characteristic, complemented
12#10590879C211yesmaximal, characteristic, complemented
13#10590828C211yesmaximal, characteristic, complemented
14#10590755C211yesmaximal, characteristic, complemented
15#10590747C211yesmaximal, characteristic, complemented
16#80025—31nomaximal
17#79494—31nomaximal
18C22×#634C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3795C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24C2×#3744C2211yescharacteristic, complemented
25C2×#3744C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic, complemented
27C3×C4×#67C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29C2×C3×D24C2211yescharacteristic
30C2×C3×D24C2211yescharacteristic, complemented
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
32#63980—21no—
33#63977—21no—
34#67⋊Dic3—21no—
35#63922—21no—
36#63913—21no—
37#63911C2211yescharacteristic
38#63908C2211yescharacteristic
39#63896—21no—
40Dic3×D12C2211yescharacteristic
41#63886—21no—
42#63860C2211yescharacteristic, complemented
43#63857C2211yescharacteristic, complemented
44#63844C2211yescharacteristic, complemented
45C2×#3716—24no—
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51#63795—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#214—31no—
65C2×#911—31no—
66C2×#908—31no—
67C22×#204—31no—
68#5598—31no—
69#5552—31no—
70D4×D12—31no—
71C3×#447—31no—
72C3×#435—31no—
73#5158—31no—
74#5154—31no—
75#5153—31no—
76#5134—31no—
77#5115—31no—
78#5038—31no—
79#4848—31no—
80#4844—31no—
81#4780—31no—
82#4776—31no—
83#4762—31no—
84#4757—31no—
85#4738—31no—
86#4738—31no—
87#4738—61no—
88#4734—31no—
89#4732D311yescharacteristic, complemented
90#4731—31no—
91#4730D311yescharacteristic, complemented
92#4712—31no—
93#4710—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×#634—22no—
101C2×#634—21no—
102C2×#634—41no—
103C2×#634C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C2×C3×D12—22no—
108C2×C3×D12—21no—
109C2×C3×D12—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114D3×#67—44no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124#3795—22no—
125#3795—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3744—22no—
131#3744—41no—
132C3×#217D411yescharacteristic
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—22no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×D24—41no—
143C3×ΓL(1,𝔽25)—22no—
144#3724—21no—
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3716—22no—
153#3716—22no—
154#3716—22no—
155#3716D414yescomplemented
156#3714—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×#67—61no—
160C2×#237—31no—
161C2×D3×D4—31no—
162C2×D3×D4—61no—
163C2×#235—31no—
164C22×D12—31no—
165C22×D12C2×D311yescharacteristic
166C22×Dic6—31no—
167C22×Dic6—31no—
168C22×Dic6—61no—
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C2×C3×M16—31no—
172C22×C3×C8—31no—
173C3×#121—31no—
174C3×C4×D4—31no—
175#953—61no—
176#940—31no—
177#939—61no—
178#939—61no—
179#939—61no—
180#938—31no—
181#937—61no—
182#936—31no—
183D4×Dic3—31no—
184D4×Dic3—61no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—64no—
190C2×#213—31no—
191#930—31no—
192#930—31no—
193#930—31no—
194#930—61no—
195#930C2×D311yescharacteristic, complemented
196C4×#67C2×D311yescharacteristic
197#924—31no—
198C22×C3⋊C8C2×D311yescharacteristic, complemented
199#911—64no—
200#908—64no—
201C2×D24—31no—
202C2×D24C2×D311yescharacteristic
203C2×D24C2×D311yescharacteristic, complemented
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—61no—
213C2×#204—61no—
214C2×#204—64no—
215C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
216#897—31no—
217#896—61no—
218#895—61no—
219#887—31no—
220#885—61no—
221#885—61no—
222#882—61no—
223#882—61no—
224#67⋊C4—61no—
225#878—61no—
226#875—31no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×C4⋊C8—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×C22⋊C8—21no—
234C3×C22⋊C8—31no—
235C3×C22⋊C8C2×D311yescharacteristic, complemented
236C3×C22⋊C8C2×D311yescharacteristic, complemented
237C3×#97—31no—
238#832—31no—
239#821—31no—
240#821—31no—
241#821C2×D311yescharacteristic
242#821C2×D311yescharacteristic, complemented
243(C2×D3)⋊C8C2×D311yescharacteristic, complemented
244#818—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—31no—
249#816—61no—
250#816—61no—
251#815C2×D311yescharacteristic, complemented
252Dic3⋊C8C2×D311yescharacteristic, complemented
253#809—31no—
254#807—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—42no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278#634—21no—
279#634—21no—
280#634—21no—
281#634—42no—
282#634C2×D412yescomplemented
283C3×#67—22no—
284C3×#67—42no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—42no—
295C3×D12C2×D412yes—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298#626—42no—
299#626—42no—
300#626—81no—
301#625—42no—
302#625—42no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—31no—
322#440—91no—
323#435—31no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—121no—
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C2×#67—21no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—121no—
351C2×#67—124no—
352C2×#67D1211yescharacteristic
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—121no—
358#237—62no—
359#237—121no—
360D3×D4—62no—
361D3×D4—121no—
362D3×D4—124no—
363#235—62no—
364#235—121no—
365C2×D12—22no—
366C2×D12—21no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—41no—
370C2×D12—61no—
371C2×D12—62no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—121no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×Dic6—31no—
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—61no—
388C2×Dic6—62no—
389C2×Dic6—62no—
390C2×Dic6—61no—
391C2×Dic6—61no—
392C2×Dic6—122no—
393C2×Dic6—121no—
394C2×Dic6—121no—
395C2×Dic6—121no—
396C2×Dic6—122no—
397C3×D8—62no—
398C3×D8—121no—
399C3×M16—62no—
400C2×C3×C8—21no—
401C2×C3×C8—21no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8—62no—
405C2×C3×C8C22×D311yescharacteristic
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C22×D311yescharacteristic
409C3×C4⋊C4—31no—
410C3×C4⋊C4—31no—
411C3×C22⋊C4—31no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—61no—
414C3×C42—31no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—61no—
419#217—61no—
420#217D1211yescharacteristic
421#214—34no—
422#214—62no—
423#214—62no—
424#214—62no—
425#213—62no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—121no—
435(C2×D3)⋊C4D1211yescharacteristic
436C4⋊Dic3—31no—
437C4⋊Dic3—31no—
438C4⋊Dic3—61no—
439C4⋊Dic3—61no—
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4D1211yescharacteristic
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3C22×D311yescharacteristic
448C2×C3⋊C8—22no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451D24—22no—
452D24—41no—
453D24—62no—
454#204—34no—
455#204—62no—
456#204—62no—
457#204—62no—
458#204—62no—
459#204—62no—
460#204—122no—
461#204—121no—
462#204—121no—
463#204—122no—
464ΓL(1,𝔽25)—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32AGL(1,ℤ/8)12yescomplemented
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3×D3—21no—
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—84no—
485D32—84no—
486C32×C4—21no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—22no—
490C3⋊Dic3—41no—
491C3⋊Dic3—41no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—91no—
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—31no—
510C2×D8—31no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—31no—
514#127—91no—
515#124—91no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—31no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—91no—
527C4×D4—31no—
528C4×D4—91no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—31no—
532#103—91no—
533#103—91no—
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—31no—
539C22⋊C8D3211yescharacteristic, complemented
540#97—31no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C23×C3C2×D1211yescharacteristic
550C23×C3D3×D411yescharacteristic
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—81no—
559C22×D3—121no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3C2×D1211yescharacteristic
567C3×D4—32no—
568C3×D4—62no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—122no—
575C3×D4—122no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4C2×D1211yescharacteristic
591C2×C3×C4D3×D411yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594#67—22no—
595#67—42no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—242no—
605#67—241no—
606C2×Dic3—21no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—121no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3—124no—
621C2×Dic3C2×D1211yescharacteristic
622C2×Dic3C2×D1211yescharacteristic
623C2×Dic3C2×D1211yescharacteristic
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—21no—
629D12—42no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—121no—
635D12—121no—
636D12—122no—
637D12—122no—
638D12—241no—
639D12D3×D412yes—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—122no—
643C4×D3—122no—
644Dic6—32no—
645Dic6—32no—
646Dic6—62no—
647Dic6—61no—
648Dic6—61no—
649Dic6—62no—
650Dic6—61no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—121no—
655Dic6—121no—
656Dic6—122no—
657Dic6—122no—
658Dic6—124no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—21no—
663C3×C8—32no—
664C3×C8—41no—
665C3×C8—41no—
666C3×C8—61no—
667C3⋊C8—21no—
668C3⋊C8D3×D412yescomplemented
669C2×C32—22no—
670C2×C32D4211yescharacteristic
671C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
672C2×C32#57711yescharacteristic
673C3⋊D3—81no—
674C3×D3—41no—
675C3×D3—42no—
676C3×D3—81no—
677C3×D3—81no—
678C24—61no—
679C24—181no—
680#41—182no—
681#41—361no—
682C2×Q8—91no—
683C2×Q8—91no—
684C2×Q8—182no—
685C2×Q8—181no—
686C2×Q8—361no—
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—62no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—91no—
695C2×D4—121no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—182no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—181no—
703C2×D4—361no—
704C2×D4—364no—
705C22×C4—31no—
706C22×C4—181no—
707C22×C4—181no—
708C22×C4—181no—
709C22×C4C2×D3211yescharacteristic
710SD16—94no—
711SD16—182no—
712SD16—182no—
713SD16—182no—
714SD16—182no—
715SD16—361no—
716D8—62no—
717D8—121no—
718D8—182no—
719M16—62no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—62no—
723C2×C8C2×D3211yescharacteristic
724C2×C8C2×D3211yescharacteristic
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—91no—
728C4⋊C4—181no—
729C4⋊C4—181no—
730C22⋊C4—31no—
731C22⋊C4—31no—
732C22⋊C4—61no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—181no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—22no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—62no—
752C22×C3—61no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—244no—
762C22×C3#90812yescomplemented
763C22×C3#91112yescomplemented
764C22×C3C22×D1211yescharacteristic
765C22×C3C2×D3×D411yescharacteristic
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—21no—
769C2×D3—22no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—84no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—241no—
788C2×D3—244no—
789C2×D3—244no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—41no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—61no—
798C3×C4—121no—
799C3×C4C2×D3×D411yescharacteristic
800C3×C4C2×D3×D411yescharacteristic
801C3×C4#100411yescharacteristic
802C3×C4#100911yescharacteristic
803Dic3—21no—
804Dic3—21no—
805Dic3—21no—
806Dic3—41no—
807Dic3—62no—
808Dic3—62no—
809Dic3—122no—
810Dic3—122no—
811Dic3—121no—
812Dic3—121no—
813Dic3—121no—
814Dic3—121no—
815Dic3—241no—
816C32#326511yescharacteristic, complemented, Sylow
817C23—31no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—122no—
822C23—122no—
823C23—181no—
824C23—241no—
825C23—362no—
826C23—362no—
827C23—721no—
828C23D3×D1211yescharacteristic
829Q8—92no—
830Q8—181no—
831Q8—181no—
832Q8—181no—
833Q8—362no—
834D4—32no—
835D4—62no—
836D4—61no—
837D4—61no—
838D4—61no—
839D4—61no—
840D4—61no—
841D4—122no—
842D4—122no—
843D4—181no—
844D4—181no—
845D4—362no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—721no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—362no—
863C2×C4—362no—
864C2×C4—362no—
865C2×C4D3×D1211yescharacteristic
866C2×C4C22×D3211yescharacteristic
867C8—21no—
868C8—21no—
869C8—32no—
870C8—61no—
871C2×C3—22no—
872C2×C3—22no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—42no—
877C2×C3—122no—
878C2×C3—121no—
879C2×C3—241no—
880C2×C3—241no—
881C2×C3D4×D1211yescharacteristic
882C2×C3#559011yescharacteristic
883C2×C3C2×#90811yescharacteristic
884C2×C3#575111yescharacteristic
885C2×C3C2×#91111yescharacteristic
886C2×C3#577511yescharacteristic
887D3—41no—
888D3—42no—
889D3—81no—
890D3—81no—
891D3—241no—
892D3—241no—
893D3—481no—
894C22—21no—
895C22—21no—
896C22—61no—
897C22—61no—
898C22—61no—
899C22—62no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—244no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—724no—
913C22#6379512yescomplemented
914C22C2×D3×D1211yescharacteristic
915C4—21no—
916C4—61no—
917C4—61no—
918C4—61no—
919C4—121no—
920C4—182no—
921C4—361no—
922C4—361no—
923C4D32×D411yescharacteristic
924C4#6431411yescharacteristic
925C3—21no—
926C3#7949411yescharacteristic, complemented
927C3#8002511yescharacteristic, complemented
928C2—22no—
929C2—121no—
930C2—122no—
931C2—241no—
932C2—241no—
933C2—721no—
934C2#1059427711yescharacteristic
935C2C2×#6379511yescharacteristic
936C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. D12×#67C2semidirect
2. #10594918C2semidirect
3. C22×#3716C2semidirect
4. C2×#63795C2semidirect
5. #10592437C2semidirect
6. C3×#4732C2semidirect
7. C3×#4730C2semidirect
8. #10591164C2semidirect
9. #10590962C2semidirect
10. #10590946C2semidirect
11. #10590883C2semidirect
12. #10590879C2semidirect
13. #10590828C2semidirect
14. #10590755C2semidirect
15. #10590747C2semidirect
18. C22×#634C22semidirect
22. C2×#3795C22semidirect
24. C2×#3744C22semidirect
25. C2×#3744C22semidirect
26. C3×#930C22semidirect
28. C22×C3×C3⋊C8C22semidirect
30. C2×C3×D24C22semidirect
31. C2×C3×ΓL(1,𝔽25)C22semidirect
42. #63860C22semidirect
43. #63857C22semidirect
44. #63844C22semidirect
48. C2×#3716C22semidirect
49. C2×#3716C22semidirect
50. C2×#3714C22semidirect
52. C32×C22⋊C8C22semidirect
53. #63643C22semidirect
54. #63643C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
89. #4732D3semidirect
91. #4730D3semidirect
155. #3716D4semidirect
195. #930C2×D3semidirect
198. C22×C3⋊C8C2×D3semidirect
203. C2×D24C2×D3semidirect
215. C2×ΓL(1,𝔽25)C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
236. C3×C22⋊C8C2×D3semidirect
242. #821C2×D3semidirect
243. (C2×D3)⋊C8C2×D3semidirect
251. #815C2×D3semidirect
252. Dic3⋊C8C2×D3semidirect
282. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
467. C22×C32AGL(1,ℤ/8)semidirect
539. C22⋊C8D32semidirect
668. C3⋊C8D3×D4semidirect
762. C22×C3#908semidirect
763. C22×C3#911semidirect
816. C32#3265semidirect
913. C22#63795semidirect
926. C3#79494semidirect
927. C3#80025semidirect

Maximal subgroups

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

subgroupindex
D12×#672
#105949182
C22×#37162
C2×#637952
#105924372
C3×#47322
C3×#47302
#105911642
#105909622
#105909462
#105908832
#105908792
#105908282
#105907552
#105907472
#800253
#794943