Finite Group Databasebeta

← #11884036

Subgroups — #11884036

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×#67C211yesmaximal, characteristic, complemented
2#10594916C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5#10592433C211yesmaximal, characteristic, complemented
6C3×#4731C211yesmaximal, characteristic, complemented
7C3×#4728C211yesmaximal, characteristic, complemented
8#10591178C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590881C211yesmaximal, characteristic, complemented
11#10590879C211yesmaximal, characteristic, complemented
12#10590826C211yesmaximal, characteristic, complemented
13#10590822C211yesmaximal, characteristic, complemented
14#10590754C211yesmaximal, characteristic, complemented
15#10590747C211yesmaximal, characteristic, complemented
16#80156—31nomaximal
17#79494—31nomaximal
18C2×#3828C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24C2×#3745C2211yescharacteristic, complemented
25C2×#3744C2211yescharacteristic, complemented
26C3×C4×#67C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic, complemented
32#63977—21no—
33#63971—21no—
34#63953—21no—
35#63922—21no—
36#63911C2211yescharacteristic
37#63909C2211yescharacteristic, complemented
38#63908C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63886—21no—
41#63881—21no—
42#63865—21no—
43#63864C2211yescharacteristic, complemented
44#63844C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46#63830—24no—
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, 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#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63D4×#67—31no—
64C2×#932—31no—
65C2×D3×SD16—31no—
66C2×#908—31no—
67C22×#204—31no—
68#5633—31no—
69#5552—31no—
70D4×D12—31no—
71C3×#450—31no—
72C3×#435—31no—
73#5176—31no—
74#5170—31no—
75#5165—31no—
76#5134—31no—
77#5115—31no—
78#5049—31no—
79#4848—31no—
80#4844—31no—
81#4775—31no—
82#4773—31no—
83#4762—31no—
84#4757—31no—
85#4738—31no—
86#4734—31no—
87#4734—31no—
88#4734—61no—
89#4732—31no—
90#4731D311yescharacteristic, complemented
91#4728D311yescharacteristic, complemented
92#4712—31no—
93#4710—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99#3828—22no—
100#3828—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×#634C2311yescharacteristic
105C2×C3×#67D411yescharacteristic
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113D3×#67—44no—
114C2×#627—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3745—41no—
131#3744—22no—
132C3×#217—21no—
133C3×#217D411yescharacteristic
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C3×#208—22no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×#204—22no—
143C3×#204—41no—
144C3×D3×C8—22no—
145#3724—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3717—22no—
153#3716—22no—
154#3716D414yescomplemented
155#3714—22no—
156#3714—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×#67—61no—
160C2×D3×Q8—31no—
161C2×D3×D4—31no—
162C2×D3×D4—61no—
163C2×#235—31no—
164C2×#235—31no—
165C2×#235—61no—
166C22×D12—31no—
167C22×D12C2×D311yescharacteristic
168C22×Dic6—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×M16—31no—
172C22×C3×C8—31no—
173C3×C22⋊Q8—31no—
174C3×C4×D4—31no—
175#953—61no—
176#947—31no—
177C2×#215—31no—
178#940—31no—
179#939—61no—
180#939—61no—
181#938—31no—
182#937—61no—
183D4×Dic3—31no—
184C2×#214—31no—
185C2×#214—31no—
186#932—64no—
187C2×#213—31no—
188C2×#213—31no—
189#930—31no—
190#930—31no—
191#930—31no—
192#930—31no—
193#930—61no—
194C4×#67C2×D311yescharacteristic
195#924C2×D311yescharacteristic, complemented
196C2×#208C2×D311yescharacteristic, complemented
197D3×SD16—64no—
198#908—64no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—61no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—61no—
210C2×#204—64no—
211C2×#204C2×D311yescharacteristic
212C2×#204C2×D311yescharacteristic, complemented
213C2×D3×C8C2×D311yescharacteristic, complemented
214#896—61no—
215#896—61no—
216#895—31no—
217#895—61no—
218#893—61no—
219#887—31no—
220#885—61no—
221#885—61no—
222#884—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×#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#835—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243#821C2×D311yescharacteristic
244#821C2×D311yescharacteristic, complemented
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246#818—31no—
247#816—31no—
248#816—31no—
249#816—31no—
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—
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—
279C4×C3⋊D3—42no—
280#634—21no—
281#634C2×D412yescomplemented
282C3×#67—22no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—42no—
292C3×D12C2×D412yes—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#627—42no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—81no—
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—31no—
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×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4—121no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—61no—
340C2×#67—61no—
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—121no—
350C2×#67—121no—
351C2×#67—124no—
352C2×#67D1211yescharacteristic
353C22×Dic3—61no—
354C22×Dic3—61no—
355D3×Q8—62no—
356D3×Q8—121no—
357D3×D4—62no—
358D3×D4—121no—
359D3×D4—124no—
360#235—62no—
361#235—62no—
362#235—122no—
363#235—121no—
364#235—121no—
365#235—122no—
366C2×D12—22no—
367C2×D12—21no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—41no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—62no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—121no—
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—121no—
388C2×C4×D3C22×D311yescharacteristic
389C2×Dic6—31no—
390C2×Dic6—31no—
391C2×Dic6—61no—
392C2×Dic6—62no—
393C2×Dic6—61no—
394C2×Dic6—61no—
395C2×Dic6—121no—
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×C4⋊C4—61no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—61no—
415C3×C42—31no—
416#217—21no—
417#217—61no—
418#217—61no—
419#217D1211yescharacteristic
420#215—62no—
421#214—34no—
422#214—62no—
423#213—62no—
424#213—62no—
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—61no—
435(C2×D3)⋊C4—121no—
436(C2×D3)⋊C4D1211yescharacteristic
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4D1211yescharacteristic
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3C22×D311yescharacteristic
448#208—22no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451D24—62no—
452D24—62no—
453D24—121no—
454D24—121no—
455D24—122no—
456#204—22no—
457#204—34no—
458#204—41no—
459#204—62no—
460#204—62no—
461#204—62no—
462#204—62no—
463#204—122no—
464D3×C8—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32C22×D411yescharacteristic
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—21no—
476C2×C3×D3—21no—
477C2×C3×D3—22no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—84no—
484C2×C3×D3AGL(1,ℤ/8)12yescomplemented
485D32—84no—
486C32×C4—21no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—22no—
490C3⋊Dic3—41no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
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—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—31no—
518C22⋊Q8—181no—
519#121—91no—
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—122no—
546C23×C3—122no—
547C23×C3—241no—
548C23×C3C2×D1211yescharacteristic
549C23×C3D3×D411yescharacteristic
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—81no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—241no—
566C22×D3—241no—
567C22×D3C2×D1211yescharacteristic
568C3×Q8—61no—
569C3×Q8—61no—
570C3×D4—32no—
571C3×D4—62no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—61no—
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×C4—61no—
591C2×C3×C4C2×D1211yescharacteristic
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595#67—22no—
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—124no—
605#67—122no—
606#67—242no—
607#67—241no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3—122no—
618C2×Dic3C2×D1211yescharacteristic
619C2×Dic3C2×D1211yescharacteristic
620C2×Dic3C2×D1211yescharacteristic
621D12—21no—
622D12—21no—
623D12—21no—
624D12—42no—
625D12—62no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—121no—
635D12—121no—
636D12—121no—
637D12—122no—
638D12—122no—
639D12—122no—
640D12—241no—
641D12D3×D412yes—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—124no—
648C4×D3—122no—
649Dic6—21no—
650Dic6—21no—
651Dic6—32no—
652Dic6—32no—
653Dic6—62no—
654Dic6—61no—
655Dic6—61no—
656Dic6—121no—
657Dic6—122no—
658Dic6—122no—
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—41no—
670C2×C32D4211yescharacteristic
671C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
672C2×C32#57711yescharacteristic
673C3⋊D3—81no—
674C3⋊D3—81no—
675C3×D3—22no—
676C3×D3—42no—
677C3×D3—81no—
678C24—61no—
679C24—181no—
680#41—182no—
681#41—361no—
682C2×Q8—31no—
683C2×Q8—91no—
684C2×Q8—181no—
685C2×Q8—182no—
686C2×Q8—361no—
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—62no—
691C2×D4—61no—
692C2×D4—91no—
693C2×D4—91no—
694C2×D4—121no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—182no—
699C2×D4—181no—
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—62no—
711SD16—94no—
712SD16—121no—
713SD16—182no—
714SD16—182no—
715SD16—182no—
716D8—182no—
717D8—182no—
718D8—361no—
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—61no—
728C4⋊C4—91no—
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—21no—
747C22×C3—21no—
748C22×C3—32no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—62no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—244no—
761C22×C3C22×D1211yescharacteristic
762C22×C3C2×D3×D411yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—22no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—84no—
772C2×D3—122no—
773C2×D3—121no—
774C2×D3—121no—
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—241no—
786C2×D3—241no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—244no—
791C2×D3—244no—
792C2×D3#90812yescomplemented
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—41no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—61no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4C2×D3×D411yescharacteristic
804C3×C4C2×D3×D411yescharacteristic
805C3×C4#100411yescharacteristic
806C3×C4#100911yescharacteristic
807Dic3—21no—
808Dic3—21no—
809Dic3—21no—
810Dic3—41no—
811Dic3—41no—
812Dic3—62no—
813Dic3—62no—
814Dic3—122no—
815Dic3—121no—
816Dic3—121no—
817Dic3—241no—
818C32#326511yescharacteristic, complemented, Sylow
819C23—31no—
820C23—61no—
821C23—61no—
822C23—122no—
823C23—122no—
824C23—181no—
825C23—181no—
826C23—241no—
827C23—362no—
828C23—362no—
829C23—721no—
830C23D3×D1211yescharacteristic
831Q8—61no—
832Q8—61no—
833Q8—92no—
834Q8—181no—
835Q8—362no—
836D4—32no—
837D4—62no—
838D4—61no—
839D4—61no—
840D4—61no—
841D4—122no—
842D4—181no—
843D4—181no—
844D4—181no—
845D4—181no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—721no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—362no—
865C2×C4—362no—
866C2×C4—362no—
867C2×C4D3×D1211yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C8—21no—
870C8—21no—
871C8—32no—
872C8—61no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—62no—
879C2×C3—81no—
880C2×C3—122no—
881C2×C3—241no—
882C2×C3D4×D1211yescharacteristic
883C2×C3#559011yescharacteristic
884C2×C3C2×#90811yescharacteristic
885C2×C3#575111yescharacteristic
886C2×C3#576211yescharacteristic
887C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
888D3—22no—
889D3—42no—
890D3—81no—
891D3—242no—
892D3—241no—
893D3—241no—
894D3—241no—
895D3—241no—
896D3—481no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—32no—
901C22—61no—
902C22—61no—
903C22—62no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—244no—
910C22—361no—
911C22—361no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—361no—
916C22—724no—
917C22C2×D3×D1211yescharacteristic
918C4—21no—
919C4—61no—
920C4—61no—
921C4—61no—
922C4—121no—
923C4—121no—
924C4—182no—
925C4—361no—
926C4D32×D411yescharacteristic
927C4#6431411yescharacteristic
928C3—21no—
929C3#7949411yescharacteristic, complemented
930C3#8015611yescharacteristic, complemented
931C2—41no—
932C2—62no—
933C2—122no—
934C2—241no—
935C2—721no—
936C2—721no—
937C2#1059427711yescharacteristic
938C2#1059467711yescharacteristic
939C2D3×#90811yescharacteristic
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. #10594916C2semidirect
3. C2×#63830C2semidirect
4. C2×D3×#204C2semidirect
5. #10592433C2semidirect
6. C3×#4731C2semidirect
7. C3×#4728C2semidirect
8. #10591178C2semidirect
9. #10590947C2semidirect
10. #10590881C2semidirect
11. #10590879C2semidirect
12. #10590826C2semidirect
13. #10590822C2semidirect
14. #10590754C2semidirect
15. #10590747C2semidirect
18. C2×#3828C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3745C22semidirect
25. C2×#3744C22semidirect
27. C3×#924C22semidirect
28. C2×C3×#208C22semidirect
30. C2×C3×#204C22semidirect
31. C2×C3×D3×C8C22semidirect
37. #63909C22semidirect
43. #63864C22semidirect
44. #63844C22semidirect
45. C2×#3717C22semidirect
48. C2×#3716C22semidirect
50. C2×#3714C22semidirect
52. C32×C22⋊C8C22semidirect
53. #63648C22semidirect
54. #63643C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63566C22semidirect
62. #63564C22semidirect
90. #4731D3semidirect
91. #4728D3semidirect
154. #3716D4semidirect
195. #924C2×D3semidirect
196. C2×#208C2×D3semidirect
212. C2×#204C2×D3semidirect
213. C2×D3×C8C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
236. C3×C22⋊C8C2×D3semidirect
244. #821C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
251. #815C2×D3semidirect
252. Dic3⋊C8C2×D3semidirect
281. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
539. C22⋊C8D32semidirect
668. C3⋊C8D3×D4semidirect
792. C2×D3#908semidirect
818. C32#3265semidirect
929. C3#79494semidirect
930. C3#80156semidirect

Maximal subgroups

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

subgroupindex
D12×#672
#105949162
C2×#638302
C2×D3×#2042
#105924332
C3×#47312
C3×#47282
#105911782
#105909472
#105908812
#105908792
#105908262
#105908222
#105907542
#105907472
#801563
#794943