Finite Group Databasebeta

← #11883960

Subgroups — #11883960

Order 1152.

1241 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic, complemented
2#10595074C211yesmaximal, characteristic, complemented
3#10594918C211yesmaximal, characteristic, complemented
4C2×#63795C211yesmaximal, characteristic, complemented
5C3×#5115C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7#10591181C211yesmaximal, characteristic, complemented
8#10591168C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590883C211yesmaximal, characteristic, complemented
12#10590879C211yesmaximal, characteristic, complemented
13#10590860C211yesmaximal, characteristic, complemented
14#10590838C211yesmaximal, characteristic, complemented
15#10590773C211yesmaximal, characteristic, complemented
16#80727—31nomaximal
17#79494—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×#634C2211yescharacteristic, complemented
20C2×#3811—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3795C2211yescharacteristic, complemented
23C22×C32×C8C2211yescharacteristic, complemented
24C2×#3744—24no—
25C2×#3744C2211yescharacteristic
26C2×#3744C2211yescharacteristic
27C2×#3744C2211yescharacteristic, complemented
28C2×#3744C2211yescharacteristic, complemented
29C3×#930C2211yescharacteristic
30C3×#930C2211yescharacteristic, complemented
31C3×C4×#67C2211yescharacteristic
32C2×C3×D24C2211yescharacteristic, complemented
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34#63981—21no—
35#63980—21no—
36#67⋊Dic3—21no—
37#63923—21no—
38#63913—21no—
39#63911C2211yescharacteristic
40#63910—21no—
41#63909C2211yescharacteristic
42#63896—21no—
43#63894C2211yescharacteristic
44#63860C2211yescharacteristic, complemented
45#63857C2211yescharacteristic, complemented
46#63844C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51#63795—24no—
52C3×#830C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#818C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63564C2211yescharacteristic, complemented
63C2×#911—31no—
64C2×#908—31no—
65C22×#204—31no—
66C22×#204—31no—
67C22×#204—61no—
68#5609—31no—
69#5598—31no—
70#5552—31no—
71D4×D12—31no—
72C3×#466—31no—
73C3×#435—31no—
74#5154—31no—
75#5134—31no—
76#5115D311yescharacteristic, complemented
77#5111D311yescharacteristic, complemented
78#5040—31no—
79#5036—31no—
80#4889—31no—
81#4886—31no—
82#4848—31no—
83#4844—31no—
84#4787—31no—
85#4781—31no—
86#4776—31no—
87#4762—31no—
88#4738—31no—
89#4734—31no—
90#4732—31no—
91#4731—31no—
92#4712—31no—
93#4710—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C22×C3⋊Dic3—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×#634—22no—
104C2×#634—21no—
105C2×#634—41no—
106C2×#634C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114#3811—44no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×#624—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124#3795—22no—
125#3795—41no—
126C2×C32×C8—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129#3744—22no—
130#3744—22no—
131#3744—22no—
132#3744D414yescomplemented
133C3×#217D411yescharacteristic
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—22no—
144C3×ΓL(1,𝔽25)—22no—
145#3724—21no—
146Dic3⋊Dic3—21no—
147#3722—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152Dic32—21no—
153#3716—22no—
154#3716—41no—
155#3714—22no—
156#3714—41no—
157#3265—91noSylow
158C2×#237—31no—
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C2×D3×D4—61no—
162C2×#235—31no—
163C22×D12—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—61no—
167C22×Dic6—31no—
168C22×Dic6—31no—
169C22×Dic6—61no—
170C2×C3×D8—31no—
171C2×C3×M16—31no—
172C22×C3×C8—21no—
173C22×C3×C8C2×D311yescharacteristic, complemented
174C22×C3×C8C2×D311yescharacteristic, complemented
175C3×#121—31no—
176C3×#121—31no—
177C3×C4×D4—31no—
178#940—31no—
179#939—61no—
180#939—61no—
181#937—61no—
182#936—31no—
183D4×Dic3—61no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#213—31no—
187C2×#213—31no—
188#930—31no—
189#930C2×D311yescharacteristic
190#930C2×D311yescharacteristic, complemented
191C4×#67C2×D311yescharacteristic
192#924—31no—
193#911—64no—
194#908—64no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24C2×D311yescharacteristic, complemented
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—61no—
209C2×#204—61no—
210C2×#204—61no—
211C2×#204—61no—
212C2×#204—64no—
213C2×#204—64no—
214C2×#204—68no—
215C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
216#897—31no—
217#896—61no—
218#895—31no—
219#895—61no—
220#893—31no—
221#887—31no—
222#885—61no—
223#885—61no—
224#884—61no—
225#882—61no—
226#882—61no—
227#882—61no—
228#67⋊C4—61no—
229#878—61no—
230#875—31no—
231#874—31no—
232C4×D12—31no—
233C4×Dic6—31no—
234C3×#107—31no—
235C3×C4⋊C8—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×C22⋊C8—31no—
239C3×C22⋊C8—31no—
240C3×#97—31no—
241#830C2×D311yescharacteristic, complemented
242#821—31no—
243#821—31no—
244#821C2×D311yescharacteristic, complemented
245#821C2×D311yescharacteristic, complemented
246(C2×D3)⋊C8C2×D311yescharacteristic, complemented
247#818C2×D311yescharacteristic, complemented
248#816—31no—
249#816—31no—
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#810—31no—
253#810—31no—
254#809—31no—
255#809—31no—
256C23×C32C2×D411yescharacteristic
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×D3—21no—
264C22×C3×D3C2×D411yescharacteristic
265C2×D32—42no—
266C2×D32—42no—
267C2×D32—81no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—42no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—42no—
279C4⋊(C3⋊D3)C2×D412yes—
280#634—21no—
281#634—21no—
282#634—21no—
283#634—42no—
284#634C2×D412yescomplemented
285C3×#67—22no—
286C3×#67—42no—
287C3×#67—42no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C2×C3×Dic3C2×D411yescharacteristic
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×C4×D3—21no—
298C3×C4×D3—21no—
299#626—42no—
300#626—42no—
301#626—42no—
302#626—81no—
303#625—42no—
304#624—42no—
305D3×Dic3—42no—
306C32×C8—21no—
307C32×C8C2×D412yescomplemented
308C3×C3⋊C8—21no—
309C3×C3⋊C8—21no—
310C2×AGL(1,ℤ/8)—91no—
311C22×SD16—91no—
312#548—91no—
313D42—91no—
314#496—91no—
315#468—91no—
316#466—31no—
317#463—91no—
318#460—91no—
319#450—91no—
320#449—91no—
321#448—91no—
322#447—91no—
323#440—91no—
324#435—31no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—61no—
329C23×D3—121no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67D1211yescharacteristic
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—121no—
352#237—62no—
353#237—121no—
354D3×D4—62no—
355D3×D4—121no—
356D3×D4—124no—
357D3×D4—124no—
358#235—62no—
359#235—121no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—62no—
369C2×D12—64no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12—122no—
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3C22×D311yescharacteristic
387C2×Dic6—31no—
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—31no—
391C2×Dic6—61no—
392C2×Dic6—61no—
393C2×Dic6—62no—
394C2×Dic6—62no—
395C2×Dic6—64no—
396C2×Dic6—61no—
397C2×Dic6—61no—
398C2×Dic6—121no—
399C2×Dic6—121no—
400C2×Dic6—121no—
401C2×Dic6—122no—
402C3×D8—62no—
403C3×M16—62no—
404C2×C3×C8—24no—
405C2×C3×C8—22no—
406C2×C3×C8—22no—
407C2×C3×C8—21no—
408C2×C3×C8—21no—
409C2×C3×C8—31no—
410C2×C3×C8—31no—
411C2×C3×C8C22×D311yescharacteristic
412C2×C3×C8C22×D311yescharacteristic
413C2×C3×C8C22×D311yescharacteristic
414C2×C3×C8C22×D311yescharacteristic
415C3×C4⋊C4—31no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—31no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C42—31no—
423#217—61no—
424#217—61no—
425#217—61no—
426#217D1211yescharacteristic
427#214—62no—
428#214—121no—
429#213—62no—
430#213—121no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4D1211yescharacteristic
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447Dic3⋊C4D1211yescharacteristic
448C4×Dic3—61no—
449C4×Dic3—61no—
450C4×Dic3C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—22no—
454D24—62no—
455D24—121no—
456#204—34no—
457#204—34no—
458#204—64no—
459#204—62no—
460#204—62no—
461#204—62no—
462#204—62no—
463#204—64no—
464#204—64no—
465#204—64no—
466#204—62no—
467#204—62no—
468#204—62no—
469#204—121no—
470ΓL(1,𝔽25)—22no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32AGL(1,ℤ/8)12yescomplemented
474C22×C32C22×D411yescharacteristic
475C2×C3⋊D3—22no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—84no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491D32—84no—
492C32×C4—21no—
493C32×C4C22×D411yescharacteristic
494C32×C4H(5,𝔽2)11yescharacteristic
495C3⋊Dic3—22no—
496C3⋊Dic3—41no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—21no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C2×#41—91no—
503C22×Q8—91no—
504C22×D4—91no—
505C22×D4—91no—
506C22×D4—181no—
507AGL(1,ℤ/8)—184no—
508C2×SD16—91no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×SD16—91no—
514C2×SD16—184no—
515C2×D8—31no—
516C2×D8—91no—
517C2×D8—91no—
518C2×M16—31no—
519C22×C8D3211yescharacteristic, complemented
520#127—91no—
521#124—91no—
522#124—181no—
523C22⋊Q8—91no—
524C22⋊Q8—181no—
525#121—31no—
526#121—31no—
527#121—91no—
528#121—181no—
529#121—181no—
530#120—181no—
531#120—181no—
532C4×Q8—91no—
533C4×D4—31no—
534C4×D4—91no—
535C4×D4—181no—
536#107—31no—
537C4⋊C8—31no—
538#103—91no—
539#103—91no—
540#102—31no—
541#102—31no—
542#102—91no—
543#102—91no—
544C22⋊C8—31no—
545C22⋊C8—31no—
546#97—31no—
547C23×C3—21no—
548C23×C3—31no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3C2×D1211yescharacteristic
552C23×C3D3×D411yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3—122no—
567C22×D3—124no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—242no—
571C22×D3—241no—
572C22×D3—241no—
573C22×D3—241no—
574C22×D3—241no—
575C22×D3—242no—
576C22×D3C2×D1211yescharacteristic
577C3×D4—62no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—122no—
583C3×D4—122no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4C2×D1211yescharacteristic
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603#67—22no—
604#67—42no—
605#67—42no—
606#67—122no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—241no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—121no—
619C2×Dic3—121no—
620C2×Dic3—122no—
621C2×Dic3—122no—
622C2×Dic3—122no—
623C2×Dic3—124no—
624C2×Dic3C2×D1211yescharacteristic
625C2×Dic3C2×D1211yescharacteristic
626C2×Dic3C2×D1211yescharacteristic
627D12—21no—
628D12—21no—
629D12—21no—
630D12—21no—
631D12—32no—
632D12—32no—
633D12—62no—
634D12—62no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—61no—
640D12—61no—
641D12—121no—
642D12—121no—
643D12—122no—
644D12—122no—
645D12—124no—
646D12—122no—
647D12—122no—
648D12—122no—
649D12—241no—
650C4×D3—21no—
651C4×D3—21no—
652C4×D3—122no—
653C4×D3—122no—
654C4×D3—122no—
655Dic6—32no—
656Dic6—32no—
657Dic6—62no—
658Dic6—61no—
659Dic6—61no—
660Dic6—62no—
661Dic6—61no—
662Dic6—61no—
663Dic6—61no—
664Dic6—61no—
665Dic6—121no—
666Dic6—121no—
667Dic6—122no—
668Dic6—122no—
669Dic6—124no—
670C3×C8—22no—
671C3×C8—21no—
672C3×C8—21no—
673C3×C8—22no—
674C3×C8—61no—
675C3×C8—61no—
676C3×C8D3×D412yescomplemented
677C3×C8D3×D412yescomplemented
678C3⋊C8—21no—
679C3⋊C8—21no—
680C2×C32—22no—
681C2×C32D4211yescharacteristic
682C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
683C2×C32#57711yescharacteristic
684C3⋊D3—42no—
685C3⋊D3—81no—
686C3×D3—41no—
687C3×D3—81no—
688C3×D3—81no—
689C24—181no—
690C24—181no—
691#41—182no—
692#41—361no—
693C2×Q8—91no—
694C2×Q8—91no—
695C2×Q8—182no—
696C2×Q8—181no—
697C2×Q8—361no—
698C2×D4—31no—
699C2×D4—31no—
700C2×D4—31no—
701C2×D4—61no—
702C2×D4—61no—
703C2×D4—91no—
704C2×D4—91no—
705C2×D4—182no—
706C2×D4—181no—
707C2×D4—181no—
708C2×D4—181no—
709C2×D4—182no—
710C2×D4—181no—
711C2×D4—181no—
712C2×D4—181no—
713C2×D4—361no—
714C2×D4—361no—
715C2×D4—364no—
716C22×C4—31no—
717C22×C4—181no—
718C22×C4—181no—
719C22×C4—181no—
720C22×C4C2×D3211yescharacteristic
721SD16—94no—
722SD16—182no—
723SD16—182no—
724SD16—182no—
725SD16—182no—
726SD16—361no—
727D8—62no—
728D8—182no—
729D8—361no—
730M16—62no—
731C2×C8—22no—
732C2×C8—31no—
733C2×C8—31no—
734C2×C8C2×D3211yescharacteristic
735C2×C8C2×D3211yescharacteristic
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—31no—
739C4⋊C4—181no—
740C4⋊C4—181no—
741C22⋊C4—31no—
742C22⋊C4—31no—
743C22⋊C4—61no—
744C22⋊C4—61no—
745C22⋊C4—181no—
746C22⋊C4—181no—
747C22⋊C4—181no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C42—31no—
751C42—181no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—22no—
760C22×C3—61no—
761C22×C3—61no—
762C22×C3—61no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3#90812yescomplemented
770C22×C3#91112yescomplemented
771C22×C3C22×D1211yescharacteristic
772C22×C3C2×D3×D411yescharacteristic
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—21no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—122no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—122no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—241no—
797C2×D3—241no—
798C2×D3—241no—
799C2×D3—241no—
800C2×D3—244no—
801C2×D3—244no—
802C2×D3—244no—
803C2×D3—244no—
804C2×D3—248no—
805C3×C4—22no—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—21no—
810C3×C4—61no—
811C3×C4—61no—
812C3×C4—61no—
813C3×C4—121no—
814C3×C4—121no—
815C3×C4C2×D3×D411yescharacteristic
816C3×C4C2×D3×D411yescharacteristic
817C3×C4#100911yescharacteristic
818C3×C4#100911yescharacteristic
819Dic3—21no—
820Dic3—21no—
821Dic3—21no—
822Dic3—41no—
823Dic3—41no—
824Dic3—62no—
825Dic3—62no—
826Dic3—122no—
827Dic3—122no—
828Dic3—121no—
829Dic3—121no—
830C32#326511yescharacteristic, complemented, Sylow
831C23—31no—
832C23—61no—
833C23—61no—
834C23—181no—
835C23—181no—
836C23—362no—
837C23—362no—
838C23—362no—
839C23—362no—
840C23—721no—
841C23—721no—
842C23D3×D1211yescharacteristic
843Q8—92no—
844Q8—181no—
845Q8—181no—
846Q8—181no—
847Q8—362no—
848D4—62no—
849D4—61no—
850D4—61no—
851D4—61no—
852D4—61no—
853D4—92no—
854D4—122no—
855D4—122no—
856D4—181no—
857D4—181no—
858D4—181no—
859D4—362no—
860D4—362no—
861D4—362no—
862D4—362no—
863D4—362no—
864D4—721no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—31no—
868C2×C4—31no—
869C2×C4—31no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—362no—
877C2×C4—362no—
878C2×C4—362no—
879C2×C4D3×D1211yescharacteristic
880C2×C4C22×D3211yescharacteristic
881C8—21no—
882C8—61no—
883C8—61no—
884C8#381112yescomplemented
885C2×C3—24no—
886C2×C3—22no—
887C2×C3—22no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—121no—
892C2×C3—241no—
893C2×C3—241no—
894C2×C3D4×D1211yescharacteristic
895C2×C3#560911yescharacteristic
896C2×C3C2×#90811yescharacteristic
897C2×C3#575111yescharacteristic
898C2×C3C2×#91111yescharacteristic
899C2×C3#577011yescharacteristic
900D3—41no—
901D3—81no—
902D3—81no—
903D3—122no—
904D3—122no—
905D3—242no—
906D3—242no—
907D3—241no—
908D3—241no—
909C22—21no—
910C22—21no—
911C22—61no—
912C22—61no—
913C22—61no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—182no—
921C22—361no—
922C22—361no—
923C22—361no—
924C22—361no—
925C22—361no—
926C22—724no—
927C22—724no—
928C22#6379512yescomplemented
929C22C2×D3×D1211yescharacteristic
930C4—21no—
931C4—61no—
932C4—61no—
933C4—61no—
934C4—121no—
935C4—121no—
936C4—182no—
937C4—361no—
938C4#6430811yescharacteristic
939C4C2×#381111yescharacteristic
940C3—21no—
941C3#7949411yescharacteristic, complemented
942C3#8072711yescharacteristic, complemented
943C2—22no—
944C2—121no—
945C2—241no—
946C2—241no—
947C2—362no—
948C2—721no—
949C2C2×#6379511yescharacteristic
950C2#1059467911yescharacteristic
951C2#1059507411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×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. C22×#3744C2semidirect
2. #10595074C2semidirect
3. #10594918C2semidirect
4. C2×#63795C2semidirect
5. C3×#5115C2semidirect
6. C3×#5111C2semidirect
7. #10591181C2semidirect
8. #10591168C2semidirect
9. #10590968C2semidirect
10. #10590946C2semidirect
11. #10590883C2semidirect
12. #10590879C2semidirect
13. #10590860C2semidirect
14. #10590838C2semidirect
15. #10590773C2semidirect
19. C22×#634C22semidirect
22. C2×#3795C22semidirect
23. C22×C32×C8C22semidirect
27. C2×#3744C22semidirect
28. C2×#3744C22semidirect
30. C3×#930C22semidirect
32. C2×C3×D24C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
44. #63860C22semidirect
45. #63857C22semidirect
46. #63844C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
50. C2×#3714C22semidirect
52. C3×#830C22semidirect
53. C3×#821C22semidirect
54. C3×#821C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#818C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
62. #63564C22semidirect
76. #5115D3semidirect
77. #5111D3semidirect
132. #3744D4semidirect
173. C22×C3×C8C2×D3semidirect
174. C22×C3×C8C2×D3semidirect
190. #930C2×D3semidirect
197. C2×D24C2×D3semidirect
215. C2×ΓL(1,𝔽25)C2×D3semidirect
241. #830C2×D3semidirect
244. #821C2×D3semidirect
245. #821C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
247. #818C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
284. #634C2×D4semidirect
307. C32×C8C2×D4semidirect
473. C22×C32AGL(1,ℤ/8)semidirect
519. C22×C8D32semidirect
676. C3×C8D3×D4semidirect
677. C3×C8D3×D4semidirect
769. C22×C3#908semidirect
770. C22×C3#911semidirect
830. C32#3265semidirect
884. C8#3811semidirect
928. C22#63795semidirect
941. C3#79494semidirect
942. C3#80727semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
#105950742
#105949182
C2×#637952
C3×#51152
C3×#51112
#105911812
#105911682
#105909682
#105909462
#105908832
#105908792
#105908602
#105908382
#105907732
#807273
#794943