Finite Group Databasebeta

← #11883959

Subgroups — #11883959

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2D12×#67C211yesmaximal, characteristic, complemented
3#10594902C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592814C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7#10591174C211yesmaximal, characteristic, complemented
8#10591162C211yesmaximal, characteristic, complemented
9#10590942C211yesmaximal, characteristic, complemented
10#10590881C211yesmaximal, characteristic, complemented
11#10590833C211yesmaximal, characteristic, complemented
12#10590823C211yesmaximal, characteristic, complemented
13#10590799C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590754C211yesmaximal, characteristic, complemented
16#83864—31nomaximal
17#79494—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3799C2211yescharacteristic, complemented
23C22×C32×C8C2211yescharacteristic, complemented
24#64139C2211yescharacteristic
25#64139C2211yescharacteristic, complemented
26C2×#3745C2211yescharacteristic, complemented
27C3×C4×#67C2211yescharacteristic
28C2×C3×#204—24no—
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×#204C2211yescharacteristic, complemented
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34#63978—21no—
35#63977—21no—
36#63952—21no—
37#63922—21no—
38#63911C2211yescharacteristic
39#63908C2211yescharacteristic
40#63907—21no—
41Dic3×D12C2211yescharacteristic
42#63888—21no—
43#63886—21no—
44#63864C2211yescharacteristic, complemented
45#63856C2211yescharacteristic, complemented
46Dic3×Dic6C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51#63794—24no—
52#63648C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63645C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64#5817—31no—
65D4×#67—31no—
66C2×#914—31no—
67C2×#908—31no—
68C22×#204D311yescharacteristic, complemented
69#5552—31no—
70D4×D12—31no—
71C3×#435—31no—
72#5227—31no—
73#5217—31no—
74#5176—31no—
75#5174—31no—
76#5172—31no—
77#5169—31no—
78#5165—31no—
79#5164—31no—
80#5163—31no—
81#5134—31no—
82#5115—31no—
83#5115—31no—
84#5115—61no—
85#5111D311yescharacteristic, complemented
86#4848—31no—
87#4844—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
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12—41no—
106C2×C3×D12C2311yescharacteristic
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
114D3×#67—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#3799—22no—
125#3799—41no—
126C2×C32×C8—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129#3752—21no—
130#3752—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C4⋊(C3⋊Dic3)C2311yescharacteristic
133#3745—22no—
134C3×#217D411yescharacteristic
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141C3×#204—22no—
142C3×#204—22no—
143C3×#204D414yescomplemented
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#3717—22no—
154#3717—41no—
155#3714—22no—
156#3714—41no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×#239—31no—
162C2×D3×D4—31no—
163C2×D3×D4—61no—
164C2×#235—31no—
165C22×D12—31no—
166C22×D12C2×D311yescharacteristic
167C22×Dic6C2×D311yescharacteristic, complemented
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—64no—
173C2×C3×M16—31no—
174C22×C3×C8—21no—
175C22×C3×C8C2×D311yescharacteristic, complemented
176C22×C3×C8C2×D311yescharacteristic, complemented
177C3×C4×D4—31no—
178#953—61no—
179#947—31no—
180#947—61no—
181#946—31no—
182#946—61no—
183Q8×Dic3—31no—
184C2×#215—31no—
185C2×#215—31no—
186#940—31no—
187#939—61no—
188#939—61no—
189#938—31no—
190#937—61no—
191D4×Dic3—31no—
192C2×#213—31no—
193C2×#213—31no—
194#930—31no—
195#930—31no—
196#930—31no—
197#930—31no—
198#930—31no—
199#930—61no—
200#930—61no—
201#930—61no—
202C4×#67—61no—
203C4×#67C2×D311yescharacteristic
204#924—31no—
205#914—64no—
206#908—64no—
207C2×D24—31no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—31no—
211C2×D24—61no—
212C2×#204—24no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204C2×D311yescharacteristic
216C2×#204C2×D311yescharacteristic
217C2×#204C2×D311yescharacteristic, complemented
218C2×#204C2×D311yescharacteristic, complemented
219C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
220#896—61no—
221#895—61no—
222#885—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×C22⋊C8—31no—
232C3×C22⋊C8—31no—
233C3×#97—31no—
234#835—31no—
235#835—31no—
236#832—31no—
237#832—31no—
238#830C2×D311yescharacteristic, complemented
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#818—31no—
250#818—61no—
251#816—31no—
252#816—31no—
253#815C2×D311yescharacteristic, complemented
254Dic3⋊C8C2×D311yescharacteristic, complemented
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—
272#638—42no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C3×#67—22no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×D12C2×D412yes—
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—81no—
302#625—42no—
303#624—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—31no—
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—91no—
322#440—91no—
323#435—31no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×Q8—31no—
330C2×C3×Q8—62no—
331C2×C3×Q8—61no—
332C2×C3×Q8—121no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—121no—
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—121no—
355C2×#67—121no—
356C2×#67—124no—
357C2×#67D1211yescharacteristic
358C22×Dic3—21no—
359C22×Dic3—61no—
360#239—62no—
361#239—121no—
362D3×D4—62no—
363D3×D4—121no—
364D3×D4—124no—
365#235—62no—
366#235—121no—
367C2×D12—22no—
368C2×D12—21no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—41no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—62no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—121no—
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—22no—
389C2×Dic6—21no—
390C2×Dic6—41no—
391C2×Dic6C22×D311yescharacteristic
392C2×Dic6C22×D311yescharacteristic
393C3×SD16—34no—
394C3×SD16—62no—
395C3×SD16—62no—
396C3×SD16—62no—
397C3×M16—62no—
398C2×C3×C8—22no—
399C2×C3×C8—22no—
400C2×C3×C8—21no—
401C2×C3×C8—21no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8—42no—
405C2×C3×C8C22×D311yescharacteristic
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C22×D311yescharacteristic
409C3×C4⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—31no—
412C3×C42—31no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217D1211yescharacteristic
417#215—62no—
418#215—121no—
419#213—62no—
420#213—121no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
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—121no—
433(C2×D3)⋊C4—121no—
434(C2×D3)⋊C4D1211yescharacteristic
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3—61no—
441C4⋊Dic3—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4D1211yescharacteristic
446C4×Dic3—61no—
447C4×Dic3—61no—
448C4×Dic3C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451D24—62no—
452D24—62no—
453D24—62no—
454D24—122no—
455D24—121no—
456#204—22no—
457#204—22no—
458#204—22no—
459#204—62no—
460#204—121no—
461#204#6714yescomplemented
462ΓL(1,𝔽25)—22no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32AGL(1,ℤ/8)12yescomplemented
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3×D3—21no—
474C2×C3×D3—22no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—84no—
483D32—84no—
484C32×C4—21no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—41no—
488C3⋊Dic3—41no—
489C3×Dic3—21no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—64no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—31no—
511C22×C8D3211yescharacteristic, complemented
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—91no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—31no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—31no—
530#103—91no—
531#103—91no—
532#102—91no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—31no—
538#97—31no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—122no—
544C23×C3—122no—
545C23×C3—241no—
546C23×C3C2×D1211yescharacteristic
547C23×C3D3×D411yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—81no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3C2×D1211yescharacteristic
566C3×Q8—32no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×Q8—122no—
571C3×D4—32no—
572C3×D4—62no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—122no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—122no—
593C2×C3×C4C2×D1211yescharacteristic
594C2×C3×C4D3×D411yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597#67—22no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—242no—
608#67—242no—
609#67—241no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—42no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—121no—
619C2×Dic3—122no—
620C2×Dic3C2×D1211yescharacteristic
621C2×Dic3C2×D1211yescharacteristic
622C2×Dic3C2×D1211yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—42no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—121no—
636D12—121no—
637D12—121no—
638D12—121no—
639D12—122no—
640D12—122no—
641D12—122no—
642D12—241no—
643D12C2×#6712yes—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—122no—
649Dic6—21no—
650Dic6—21no—
651Dic6—21no—
652Dic6—42no—
653Dic6C2×#6712yescomplemented
654C3×C8—21no—
655C3×C8—21no—
656C3×C8—22no—
657C3×C8—41no—
658C3×C8—61no—
659C3×C8—61no—
660C3×C8D3×D412yescomplemented
661C3×C8C2×#6712yescomplemented
662C3⋊C8—21no—
663C3⋊C8—21no—
664C2×C32—22no—
665C2×C32D4211yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C2×C32#57711yescharacteristic
668C3⋊D3—81no—
669C3⋊D3—81no—
670C3×D3—41no—
671C3×D3—42no—
672C3×D3—81no—
673C24—61no—
674C24—181no—
675#41—182no—
676#41—361no—
677C2×Q8—31no—
678C2×Q8—31no—
679C2×Q8—62no—
680C2×Q8—61no—
681C2×Q8—121no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—62no—
686C2×D4—61no—
687C2×D4—91no—
688C2×D4—91no—
689C2×D4—121no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—182no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—361no—
699C2×D4—364no—
700C22×C4—31no—
701C22×C4—61no—
702C22×C4—181no—
703C22×C4—181no—
704C22×C4C2×D3211yescharacteristic
705SD16—34no—
706SD16—62no—
707SD16—62no—
708SD16—62no—
709SD16—182no—
710SD16—361no—
711D8—182no—
712D8—182no—
713D8—361no—
714M16—62no—
715C2×C8—22no—
716C2×C8—31no—
717C2×C8—31no—
718C2×C8C2×D3211yescharacteristic
719C2×C8C2×D3211yescharacteristic
720C4⋊C4—31no—
721C4⋊C4—91no—
722C4⋊C4—91no—
723C4⋊C4—181no—
724C4⋊C4—181no—
725C22⋊C4—31no—
726C22⋊C4—31no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—31no—
735C42—181no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—22no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—62no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—244no—
754C22×C3#90812yescomplemented
755C22×C3#91412yescomplemented
756C22×C3C22×D1211yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—22no—
761C2×D3—21no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—84no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—244no—
787C2×D3—244no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—41no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—62no—
797C3×C4—121no—
798C3×C4C2×D3×D411yescharacteristic
799C3×C4#100411yescharacteristic
800C3×C4#100911yescharacteristic
801C3×C4C22×#6711yescharacteristic
802Dic3—21no—
803Dic3—21no—
804Dic3—22no—
805Dic3—21no—
806Dic3—41no—
807Dic3—121no—
808Dic3—121no—
809Dic3—121no—
810Dic3—121no—
811Dic3—241no—
812Dic3—241no—
813C32#326511yescharacteristic, complemented, Sylow
814C23—31no—
815C23—61no—
816C23—61no—
817C23—122no—
818C23—122no—
819C23—181no—
820C23—181no—
821C23—241no—
822C23—362no—
823C23—362no—
824C23—721no—
825C23D3×D1211yescharacteristic
826Q8—32no—
827Q8—61no—
828Q8—61no—
829Q8—61no—
830Q8—122no—
831D4—32no—
832D4—62no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—122no—
837D4—181no—
838D4—181no—
839D4—181no—
840D4—181no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—362no—
846D4—362no—
847D4—721no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—122no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—362no—
861C2×C4—362no—
862C2×C4D3×D1211yescharacteristic
863C2×C4C22×D3211yescharacteristic
864C8—21no—
865C8—61no—
866C8—61no—
867C8D3×#6712yescomplemented
868C2×C3—22no—
869C2×C3—22no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—42no—
874C2×C3—122no—
875C2×C3—121no—
876C2×C3—241no—
877C2×C3D4×D1211yescharacteristic
878C2×C3C2×#90811yescharacteristic
879C2×C3#575111yescharacteristic
880C2×C3C2×#91411yescharacteristic
881C2×C3#576211yescharacteristic
882C2×C3D4×#6711yescharacteristic
883D3—41no—
884D3—42no—
885D3—81no—
886D3—241no—
887D3—241no—
888D3—241no—
889D3—241no—
890D3—481no—
891D3—481no—
892C22—21no—
893C22—21no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—62no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—244no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—724no—
911C22#6379412yescomplemented
912C22C2×D3×D1211yescharacteristic
913C4—21no—
914C4—61no—
915C4—61no—
916C4—61no—
917C4—62no—
918C4—121no—
919C4—361no—
920C4—361no—
921C4#6430711yescharacteristic
922C4C2×D3×#6711yescharacteristic
923C3—21no—
924C3#7949411yescharacteristic, complemented
925C3#8386411yescharacteristic, complemented
926C2—22no—
927C2—121no—
928C2—122no—
929C2—241no—
930C2—721no—
931C2—721no—
932C2C2×#6379411yescharacteristic
933C2#1059467711yescharacteristic
934C2D12×#6711yescharacteristic
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×C3×#204C2semidirect
2. D12×#67C2semidirect
3. #10594902C2semidirect
4. C2×#63794C2semidirect
5. #10592814C2semidirect
6. C3×#5111C2semidirect
7. #10591174C2semidirect
8. #10591162C2semidirect
9. #10590942C2semidirect
10. #10590881C2semidirect
11. #10590833C2semidirect
12. #10590823C2semidirect
13. #10590799C2semidirect
14. #10590766C2semidirect
15. #10590754C2semidirect
19. C22×C3×Dic6C22semidirect
22. C2×#3799C22semidirect
23. C22×C32×C8C22semidirect
25. #64139C22semidirect
26. C2×#3745C22semidirect
31. C2×C3×#204C22semidirect
32. C2×C3×#204C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
44. #63864C22semidirect
45. #63856C22semidirect
46. Dic3×Dic6C22semidirect
47. C2×#3717C22semidirect
48. C2×#3717C22semidirect
50. C2×#3714C22semidirect
52. #63648C22semidirect
53. #63648C22semidirect
54. #63645C22semidirect
55. C3×#830C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
62. #63563C22semidirect
68. C22×#204D3semidirect
85. #5111D3semidirect
143. C3×#204D4semidirect
167. C22×Dic6C2×D3semidirect
175. C22×C3×C8C2×D3semidirect
176. C22×C3×C8C2×D3semidirect
217. C2×#204C2×D3semidirect
218. C2×#204C2×D3semidirect
219. C2×ΓL(1,𝔽25)C2×D3semidirect
238. #830C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
253. #815C2×D3semidirect
254. Dic3⋊C8C2×D3semidirect
297. C3×Dic6C2×D4semidirect
306. C32×C8C2×D4semidirect
461. #204#67semidirect
465. C22×C32AGL(1,ℤ/8)semidirect
511. C22×C8D32semidirect
653. Dic6C2×#67semidirect
660. C3×C8D3×D4semidirect
661. C3×C8C2×#67semidirect
754. C22×C3#908semidirect
755. C22×C3#914semidirect
813. C32#3265semidirect
867. C8D3×#67semidirect
911. C22#63794semidirect
924. C3#79494semidirect
925. C3#83864semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
D12×#672
#105949022
C2×#637942
#105928142
C3×#51112
#105911742
#105911622
#105909422
#105908812
#105908332
#105908232
#105907992
#105907662
#105907542
#838643
#794943