Finite Group Databasebeta

← #11883954

Subgroups — #11883954

Order 1152.

1191 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595074C211yesmaximal, characteristic, complemented
2#10594902C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592431C211yesmaximal, characteristic, complemented
6C3×#4738C211yesmaximal, characteristic, complemented
7C3×#4730C211yesmaximal, characteristic, complemented
8#10591164C211yesmaximal, characteristic, complemented
9#10590967C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590881C211yesmaximal, characteristic, complemented
12#10590850C211yesmaximal, characteristic, complemented
13#10590799C211yesmaximal, characteristic, complemented
14#10590795C211yesmaximal, characteristic, complemented
15#10590770C211yesmaximal, characteristic, complemented
16#80060—31nomaximal
17#79494—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×#3811—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3799C2211yescharacteristic, complemented
23#64139C2211yescharacteristic, complemented
24C2×#3745C2211yescharacteristic
25C2×#3745C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic
27C3×C4×#67C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic, complemented
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
32#63981—21no—
33#63978—21no—
34#63952—21no—
35#63923—21no—
36#63911C2211yescharacteristic
37#63910—21no—
38#63909C2211yescharacteristic
39#63907—21no—
40#63894C2211yescharacteristic
41#63888—21no—
42#63864C2211yescharacteristic, complemented
43#63856C2211yescharacteristic, complemented
44Dic3×Dic6C2211yescharacteristic, complemented
45C2×#3717—24no—
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51#63794—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63648C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#5817—31no—
64C22×#215—31no—
65C2×#914—31no—
66C2×#908—31no—
67C22×#204—31no—
68#5609—31no—
69#5552—31no—
70D4×D12—31no—
71C3×#448—31no—
72C3×#435—31no—
73#5176—31no—
74#5169—31no—
75#5163—31no—
76#5134—31no—
77#5115—31no—
78#5038—31no—
79#4848—31no—
80#4844—31no—
81#4819—31no—
82#4817—31no—
83#4812—31no—
84#4810—31no—
85#4738D311yescharacteristic, complemented
86#4734—31no—
87#4732—31no—
88#4732—31no—
89#4732—61no—
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—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C22×C3×Dic3—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—22no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6—41no—
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114#3811—44no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#624—21no—
121C2×#624—21no—
122D3×D12—22no—
123D3×D12—41no—
124#3799—22no—
125#3799—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3745—22no—
131#3745—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×#204—22no—
142C3×#204—41no—
143C3×ΓL(1,𝔽25)—22no—
144#3724—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3717—22no—
153#3717—22no—
154#3717—22no—
155#3717D414yescomplemented
156#3714—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×D3×D4—31no—
161C2×D3×D4—61no—
162C2×D3×D4—61no—
163C2×#235—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—61no—
168C22×Dic6C2×D311yescharacteristic, complemented
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×M16—31no—
172C22×C3×C8—31no—
173C3×#121—31no—
174C3×C4×D4—31no—
175#947—31no—
176#947—61no—
177#946—31no—
178#946—61no—
179Q8×Dic3—31no—
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—64no—
185#940—31no—
186#939—61no—
187#937—61no—
188C2×#213—31no—
189#930—31no—
190#930—31no—
191#930—31no—
192#930—61no—
193#930—61no—
194#930C2×D311yescharacteristic
195C4×#67—61no—
196C4×#67C2×D311yescharacteristic
197#924—31no—
198C22×C3⋊C8C2×D311yescharacteristic, complemented
199#914—64no—
200#908—64no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—31no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24—61no—
207C2×D24—61no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—64no—
213C2×#204C2×D311yescharacteristic, complemented
214C2×#204C2×D311yescharacteristic, complemented
215C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
216#896—61no—
217#895—31no—
218#895—61no—
219#893—31no—
220#885—61no—
221#884—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225#67⋊C4—61no—
226#875—31no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×C4⋊C8—31no—
231C3×#103—31no—
232C3×#103—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#821—31no—
242#821—31no—
243#821—31no—
244#821—31no—
245#821—61no—
246#821—61no—
247(C2×D3)⋊C8C2×D311yescharacteristic, complemented
248#818—31no—
249#816C2×D311yescharacteristic, complemented
250#816C2×D311yescharacteristic, complemented
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—42no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—81no—
262C22×C3×D3—21no—
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—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—42no—
279C4⋊(C3⋊D3)C2×D412yes—
280C3×#67—22no—
281C3×#67—42no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yescomplemented
298#626—42no—
299#626—42no—
300#626—42no—
301#626—42no—
302#626—81no—
303#624—42no—
304#624—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—31no—
321#447—91no—
322#440—91no—
323#435—31no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—121no—
329C2×C3×Q8—31no—
330C2×C3×Q8—31no—
331C2×C3×Q8—62no—
332C2×C3×Q8—61no—
333C2×C3×Q8—121no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—61no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—21no—
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×#67D1211yescharacteristic
352C22×Dic3—21no—
353#239—62no—
354#239—121no—
355D3×D4—62no—
356D3×D4—121no—
357D3×D4—124no—
358D3×D4—124no—
359#235—62no—
360#235—121no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—122no—
381C2×D12—121no—
382C2×D12—121no—
383C2×D12—121no—
384C2×D12—121no—
385C2×D12—122no—
386C2×D12C22×D311yescharacteristic
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3C22×D311yescharacteristic
392C2×Dic6—22no—
393C2×Dic6—21no—
394C2×Dic6—41no—
395C2×Dic6C22×D311yescharacteristic
396C2×Dic6C22×D311yescharacteristic
397C3×SD16—62no—
398C3×SD16—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#217D1211yescharacteristic
417#215—34no—
418#215—62no—
419#215—62no—
420#215—62no—
421#213—62no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
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—62no—
452D24—62no—
453D24—62no—
454D24—122no—
455D24—121no—
456D24—121no—
457D24—122no—
458#204—22no—
459#204—34no—
460#204—41no—
461#204—62no—
462#204—62no—
463#204—62no—
464ΓL(1,𝔽25)—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32AGL(1,ℤ/8)12yescomplemented
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—22no—
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—41no—
478C2×C3⋊D3—84no—
479C2×C3×D3—21no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485D32—84no—
486C32×C4—21no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—31no—
498C22×D4—91no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—91no—
510C2×D8—91no—
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—31no—
533#103—31no—
534#102—91no—
535#102—91no—
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×C3C2×D1211yescharacteristic
545C23×C3D3×D411yescharacteristic
546C22×D3—21no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—121no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—124no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—242no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3—241no—
569C22×D3—241no—
570C22×D3—242no—
571C22×D3C2×D1211yescharacteristic
572C3×Q8—32no—
573C3×Q8—61no—
574C3×Q8—61no—
575C3×Q8—61no—
576C3×Q8—122no—
577C3×D4—62no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—122no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—122no—
598C2×C3×C4C2×D1211yescharacteristic
599C2×C3×C4D3×D411yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—22no—
603#67—42no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—242no—
611#67—241no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—42no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—121no—
619C2×Dic3C2×D1211yescharacteristic
620C2×Dic3C2×D1211yescharacteristic
621C2×Dic3C2×D1211yescharacteristic
622D12—21no—
623D12—21no—
624D12—32no—
625D12—32no—
626D12—62no—
627D12—62no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—121no—
639D12—121no—
640D12—121no—
641D12—121no—
642D12—122no—
643D12—122no—
644D12—124no—
645D12—122no—
646D12—122no—
647D12—122no—
648D12—122no—
649D12—241no—
650C4×D3—21no—
651C4×D3—21no—
652C4×D3—122no—
653C4×D3—122no—
654C4×D3—122no—
655C4×D3—122no—
656Dic6—21no—
657Dic6—21no—
658Dic6—21no—
659Dic6—42no—
660Dic6D3×D412yescomplemented
661C3×C8—21no—
662C3×C8—21no—
663C3×C8—21no—
664C3×C8—21no—
665C3×C8—32no—
666C3×C8—41no—
667C3×C8—41no—
668C3×C8—61no—
669C3⋊C8—21no—
670C3⋊C8D3×D412yescomplemented
671C2×C32—22no—
672C2×C32D4211yescharacteristic
673C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
674C2×C32#57711yescharacteristic
675C3⋊D3—42no—
676C3⋊D3—81no—
677C3⋊D3—81no—
678C3×D3—41no—
679C3×D3—81no—
680C24—181no—
681C24—181no—
682#41—182no—
683#41—361no—
684C2×Q8—31no—
685C2×Q8—31no—
686C2×Q8—62no—
687C2×Q8—61no—
688C2×Q8—121no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—61no—
692C2×D4—91no—
693C2×D4—91no—
694C2×D4—91no—
695C2×D4—182no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—182no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—181no—
703C2×D4—181no—
704C2×D4—361no—
705C2×D4—361no—
706C2×D4—364no—
707C22×C4—31no—
708C22×C4—61no—
709C22×C4—181no—
710C22×C4—181no—
711C22×C4C2×D3211yescharacteristic
712SD16—62no—
713SD16—94no—
714SD16—121no—
715SD16—182no—
716SD16—182no—
717SD16—182no—
718D8—182no—
719D8—182no—
720D8—361no—
721M16—62no—
722C2×C8—31no—
723C2×C8—31no—
724C2×C8—62no—
725C2×C8C2×D3211yescharacteristic
726C2×C8C2×D3211yescharacteristic
727C4⋊C4—31no—
728C4⋊C4—31no—
729C4⋊C4—91no—
730C4⋊C4—181no—
731C4⋊C4—181no—
732C22⋊C4—31no—
733C22⋊C4—31no—
734C22⋊C4—61no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C22⋊C4—181no—
741C42—31no—
742C42—181no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—22no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3#90812yescomplemented
758C22×C3#91412yescomplemented
759C22×C3C22×D1211yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—62no—
768C2×D3—62no—
769C2×D3—122no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—122no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—241no—
791C2×D3—241no—
792C2×D3—241no—
793C2×D3—241no—
794C2×D3—244no—
795C2×D3—244no—
796C2×D3—244no—
797C2×D3—244no—
798C2×D3—248no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—41no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—62no—
807C3×C4—61no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4C2×D3×D411yescharacteristic
811C3×C4C2×D3×D411yescharacteristic
812C3×C4#100411yescharacteristic
813C3×C4#100911yescharacteristic
814Dic3—21no—
815Dic3—21no—
816Dic3—21no—
817Dic3—22no—
818Dic3—41no—
819Dic3—41no—
820Dic3—121no—
821Dic3—121no—
822Dic3—241no—
823C32#326511yescharacteristic, complemented, Sylow
824C23—31no—
825C23—61no—
826C23—181no—
827C23—181no—
828C23—181no—
829C23—362no—
830C23—362no—
831C23—362no—
832C23—362no—
833C23—721no—
834C23—721no—
835C23D3×D1211yescharacteristic
836Q8—32no—
837Q8—61no—
838Q8—61no—
839Q8—61no—
840Q8—122no—
841D4—62no—
842D4—61no—
843D4—61no—
844D4—92no—
845D4—122no—
846D4—181no—
847D4—181no—
848D4—181no—
849D4—181no—
850D4—181no—
851D4—362no—
852D4—362no—
853D4—362no—
854D4—362no—
855D4—362no—
856D4—362no—
857D4—721no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—31no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—122no—
869C2×C4—181no—
870C2×C4—362no—
871C2×C4—362no—
872C2×C4D3×D1211yescharacteristic
873C2×C4C22×D3211yescharacteristic
874C8—21no—
875C8—21no—
876C8—32no—
877C8—61no—
878C2×C3—22no—
879C2×C3—22no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—42no—
884C2×C3—121no—
885C2×C3—241no—
886C2×C3D4×D1211yescharacteristic
887C2×C3#559011yescharacteristic
888C2×C3C2×#90811yescharacteristic
889C2×C3#575111yescharacteristic
890C2×C3C2×#91411yescharacteristic
891C2×C3#577811yescharacteristic
892D3—41no—
893D3—81no—
894D3—122no—
895D3—122no—
896D3—242no—
897D3—242no—
898D3—241no—
899D3—241no—
900D3—241no—
901D3—241no—
902D3—481no—
903C22—21no—
904C22—21no—
905C22—61no—
906C22—61no—
907C22—61no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—182no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—361no—
916C22—361no—
917C22—361no—
918C22—361no—
919C22—361no—
920C22—724no—
921C22—724no—
922C22#6379412yescomplemented
923C22C2×D3×D1211yescharacteristic
924C4—21no—
925C4—61no—
926C4—61no—
927C4—61no—
928C4—62no—
929C4—121no—
930C4—121no—
931C4—361no—
932C4D32×D411yescharacteristic
933C4#6431411yescharacteristic
934C3—21no—
935C3#7949411yescharacteristic, complemented
936C3#8006011yescharacteristic, complemented
937C2—22no—
938C2—121no—
939C2—241no—
940C2—362no—
941C2—721no—
942C2—721no—
943C2#1059427711yescharacteristic
944C2C2×#6379411yescharacteristic
945C2#1059471511yescharacteristic
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. #10595074C2semidirect
2. #10594902C2semidirect
3. C22×#3717C2semidirect
4. C2×#63794C2semidirect
5. #10592431C2semidirect
6. C3×#4738C2semidirect
7. C3×#4730C2semidirect
8. #10591164C2semidirect
9. #10590967C2semidirect
10. #10590942C2semidirect
11. #10590881C2semidirect
12. #10590850C2semidirect
13. #10590799C2semidirect
14. #10590795C2semidirect
15. #10590770C2semidirect
19. C22×C3×Dic6C22semidirect
22. C2×#3799C22semidirect
23. #64139C22semidirect
25. C2×#3745C22semidirect
28. C22×C3×C3⋊C8C22semidirect
29. C2×C3×#204C22semidirect
30. C2×C3×#204C22semidirect
31. C2×C3×ΓL(1,𝔽25)C22semidirect
42. #63864C22semidirect
43. #63856C22semidirect
44. Dic3×Dic6C22semidirect
48. C2×#3717C22semidirect
49. C2×#3717C22semidirect
50. C2×#3714C22semidirect
52. C32×C22⋊C8C22semidirect
54. #63648C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#816C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
85. #4738D3semidirect
91. #4730D3semidirect
155. #3717D4semidirect
168. C22×Dic6C2×D3semidirect
198. C22×C3⋊C8C2×D3semidirect
213. C2×#204C2×D3semidirect
214. C2×#204C2×D3semidirect
215. C2×ΓL(1,𝔽25)C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
236. C3×C22⋊C8C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
249. #816C2×D3semidirect
250. #816C2×D3semidirect
251. #815C2×D3semidirect
252. Dic3⋊C8C2×D3semidirect
297. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
467. C22×C32AGL(1,ℤ/8)semidirect
539. C22⋊C8D32semidirect
660. Dic6D3×D4semidirect
670. C3⋊C8D3×D4semidirect
757. C22×C3#908semidirect
758. C22×C3#914semidirect
823. C32#3265semidirect
922. C22#63794semidirect
935. C3#79494semidirect
936. C3#80060semidirect

Maximal subgroups

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

subgroupindex
#105950742
#105949022
C22×#37172
C2×#637942
#105924312
C3×#47382
C3×#47302
#105911642
#105909672
#105909422
#105908812
#105908502
#105907992
#105907952
#105907702
#800603
#794943