Finite Group Databasebeta

← #10833447

Subgroups — #10833447

Order 768.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87275C211yesmaximal, characteristic
2C2×C3×#421C211yesmaximal, characteristic, complemented
3#84084C211yesmaximal, characteristic, complemented
4#83776C211yesmaximal, characteristic, complemented
5#82287C211yesmaximal, characteristic, complemented
6C2×#4825C211yesmaximal, characteristic, complemented
7#72002C211yesmaximal, characteristic, complemented
8#71591C211yesmaximal, characteristic, complemented
9#70393C211yesmaximal, characteristic, complemented
10#70386C211yesmaximal, characteristic, complemented
11#70384C211yesmaximal, characteristic, complemented
12#70365C211yesmaximal, characteristic, complemented
13#70363C211yesmaximal, characteristic, complemented
14#70361C211yesmaximal, characteristic, complemented
15#70359C211yesmaximal, characteristic, complemented
16#24471—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×#1009C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic, complemented
20C2×C3×#117C2211yescharacteristic, complemented
21#5834—21no—
22#5833—21no—
23#5833C2211yescharacteristic
24#5830—21no—
25#5830C2211yescharacteristic
26#5829—21no—
27#5829—22no—
28#5827C2211yescharacteristic
29C2×#951C2211yescharacteristic
30C2×#951C2211yescharacteristic, complemented
31#5817—21no—
32D4×#67—21no—
33D4×#67—22no—
34#5791—21no—
35#5791C2211yescharacteristic
36C2×#930—21no—
37C2×#930C2211yescharacteristic
38C2×#924C2211yescharacteristic, complemented
39C2×#909C2211yescharacteristic, complemented
40C2×#875C2211yescharacteristic, complemented
41C3×#421—24no—
42C2×C3×#104C2211yescharacteristic
43C2×C3×#104C2211yescharacteristic
44C2×C3×#104C2211yescharacteristic, complemented
45C2×C3×#104C2211yescharacteristic, complemented
46#5239—21no—
47#5239—21no—
48#5232C2211yescharacteristic
49#5232C2211yescharacteristic, complemented
50#5228—21no—
51#5218—21no—
52#5207C2211yescharacteristic, complemented
53#5137—21no—
54#5134—21no—
55#5133C2211yescharacteristic, complemented
56C2×#823C2211yescharacteristic, complemented
57C2×#823C2211yescharacteristic, complemented
58#5121C2211yescharacteristic, complemented
59#5120C2211yescharacteristic, complemented
60#5116—21no—
61#5114—21no—
62#4994—22no—
63#4961—22no—
64#4939C2211yescharacteristic, complemented
65#4935C2211yescharacteristic, complemented
66#4929C2211yescharacteristic, complemented
67C2×#805C2211yescharacteristic, complemented
68C2×#805C2211yescharacteristic, complemented
69#4825—24no—
70#4554C2211yescharacteristic, complemented
71#4554C2211yescharacteristic, complemented
72#4523C2211yescharacteristic, complemented
73#4523C2211yescharacteristic, complemented
74#3488—31no—
75#3056—31no—
76C2×#455—31no—
77#3007—31no—
78C2×#421D311yescharacteristic, complemented
79#2620—31no—
80#2039—31no—
81#2037—31no—
82#2007—31no—
83#2004—31no—
84#1900—31no—
85#1897—31no—
86#1882—31no—
87#1859—31no—
88#1792—31no—
89C2×C3×#41—21no—
90C2×C3×#41—21no—
91C2×C3×#41—22no—
92C2×C3×#41—22no—
93C2×C3×#41—41no—
94C2×C3×#41—41no—
95C2×C3×#41D411yescharacteristic
96C2×C3×#41D411yescharacteristic
97C2×C3×#41C2311yescharacteristic
98C2×C3×#41C2311yescharacteristic
99C22×C3×Q8D411yescharacteristic
100C22×C3×D4—21no—
101C22×C3×D4D411yescharacteristic
102C23×C3×C4—21no—
103C23×C3×C4C2311yescharacteristic
104C22×#67—22no—
105C22×#67D412yes—
106#1009—22no—
107#1009—22no—
108#1009—41no—
109#1009—41no—
110C2×#239—21no—
111C2×D3×D4—22no—
112C2×D3×D4—21no—
113C2×#235—21no—
114C2×#235C2311yescharacteristic
115C22×D12—21no—
116C22×D12C2311yescharacteristic
117C22×Dic6C2311yescharacteristic
118C2×C3×M16—21no—
119C2×C3×M16—22no—
120C2×C3×M16—41no—
121C2×C3×M16C2311yescharacteristic
122C2×C3×M16C2311yescharacteristic
123C22×C3×C8—21no—
124C3×#117—22no—
125C3×#117—41no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130#953—22no—
131#953—21no—
132C2×#217—21no—
133#951—22no—
134#951—22no—
135#951—41no—
136#951—41no—
137#947—22no—
138#947—21no—
139#946—22no—
140#946—21no—
141Q8×Dic3—21no—
142C2×#216—21no—
143C2×#216—21no—
144#940—22no—
145#940—21no—
146#939—22no—
147#939—22no—
148#939—22no—
149#938—22no—
150#938—21no—
151#937—22no—
152#937—22no—
153#937—22no—
154D4×Dic3—21no—
155D4×Dic3—22no—
156C2×#214—21no—
157C2×#214—21no—
158#930—22no—
159#930—22no—
160#930—21no—
161#930—21no—
162#930—21no—
163#930—21no—
164#930—21no—
165#930—21no—
166#930—21no—
167#930D411yescharacteristic
168#930D411yescharacteristic
169#929—22no—
170#929—21no—
171C4×#67—22no—
172C4×#67—22no—
173C4×#67—21no—
174C4×#67—21no—
175C2×(C2×D3)⋊C4—22no—
176C2×(C2×D3)⋊C4—22no—
177C2×(C2×D3)⋊C4—22no—
178C2×(C2×D3)⋊C4D412yes—
179#926—21no—
180#926C2311yescharacteristic
181C2×C4⋊Dic3—21no—
182C2×C4⋊Dic3—22no—
183C2×C4⋊Dic3C2311yescharacteristic
184C2×C4⋊Dic3C2311yescharacteristic
185#924—21no—
186#924—21no—
187#924—21no—
188#924—21no—
189#924—21no—
190#924D411yescharacteristic
191#924D411yescharacteristic
192C2×Dic3⋊C4—21no—
193C2×#208C2311yescharacteristic
194C2×#208C2311yescharacteristic
195#909—22no—
196#909—41no—
197C2×Dic12—21no—
198C2×#204—21no—
199#875—22no—
200#875—41no—
201C3×#104—22no—
202C3×#104—22no—
203C3×#104—22no—
204C3×#104D414yescomplemented
205#835—21no—
206#835—21no—
207#832—21no—
208#832—21no—
209C3⋊#95—22no—
210#830—21no—
211#830—21no—
212#823—22no—
213#823—41no—
214#821—21no—
215#818—21no—
216#817—21no—
217#816—21no—
218#816—21no—
219#816—21no—
220#805—22no—
221#805—41no—
222C2×H(5,𝔽2)—31no—
223C22×#41C2×D311yescharacteristic
224C2×#137—31no—
225C2×#137—31no—
226C2×#137—31no—
227C22×M16C2×D311yescharacteristic, complemented
228#550—61no—
229#548—61no—
230#546—62no—
231#546—61no—
232D42—62no—
233D42—61no—
234#537—31no—
235#537—61no—
236#535—31no—
237#535—61no—
238C2×#124—31no—
239#525—31no—
240#525—61no—
241C2×C22⋊Q8—31no—
242C2×#121—31no—
243C2×#121—61no—
244#520—31no—
245C2×#117C2×D311yescharacteristic, complemented
246#470—61no—
247#468—61no—
248#467—61no—
249#465—61no—
250#455—64no—
251#452—61no—
252#452—61no—
253#451—61no—
254#450—61no—
255#428—31no—
256#421—24no—
257C2×#104—31no—
258C2×#104—31no—
259C2×#104C2×D311yescharacteristic
260C2×#104C2×D311yescharacteristic
261C2×#104C2×D311yescharacteristic, complemented
262C2×#104C2×D311yescharacteristic, complemented
263#419—31no—
264#417—31no—
265#417—31no—
266#417—31no—
267C2×#100—31no—
268C2×#100—31no—
269#407—31no—
270#396—62no—
271#394—62no—
272#391—31no—
273#390—31no—
274#384—31no—
275#343—31no—
276#343—31no—
277#339—31no—
278#339—31no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C23×D3—22no—
282C23×D3C2×D412yes—
283C3×#41—21no—
284C3×#41—21no—
285C3×#41—22no—
286C3×#41—22no—
287C3×#41—21no—
288C3×#41—21no—
289C3×#41—21no—
290C3×#41—21no—
291C3×#41—42no—
292C3×#41—42no—
293C3×#41—41no—
294C3×#41—41no—
295C3×#41—42no—
296C3×#41—42no—
297C3×#41C2×D412yes—
298C3×#41#4112yes—
299C2×C3×Q8—21no—
300C2×C3×Q8—22no—
301C2×C3×Q8—41no—
302C2×C3×Q8C2×D411yescharacteristic
303C2×C3×Q8C2×D411yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—22no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—41no—
311C2×C3×D4—42no—
312C2×C3×D4—42no—
313C2×C3×D4C2×D411yescharacteristic
314C2×C3×D4C2×D411yescharacteristic
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—42no—
327C22×C3×C4—42no—
328C22×C3×C4C2×D411yescharacteristic
329C22×C3×C4C2×D411yescharacteristic
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2411yescharacteristic
334C2×#67—22no—
335C2×#67—22no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—22no—
339C2×#67—22no—
340C2×#67—22no—
341C2×#67—21no—
342C2×#67—22no—
343C2×#67—82no—
344C2×#67—84no—
345C22×Dic3—22no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3C2×D412yes—
349#239—42no—
350#239—42no—
351D3×D4—44no—
352D3×D4—44no—
353D3×D4—42no—
354D3×D4—42no—
355#235—21no—
356#235—21no—
357#235—21no—
358#235—21no—
359#235—42no—
360#235—42no—
361C2×D12—22no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12—21no—
365C2×D12—21no—
366C2×D12—21no—
367C2×D12—21no—
368C2×D12—42no—
369C2×D12—42no—
370C2×D12C2×D411yescharacteristic
371C2×C4×D3—22no—
372C2×C4×D3—21no—
373C2×Dic6—21no—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6—21no—
377C2×Dic6—21no—
378C2×Dic6—21no—
379C2×Dic6C2×D411yescharacteristic
380C3×M16—21no—
381C3×M16—21no—
382C3×M16—21no—
383C3×M16—42no—
384C3×M16C2×D412yescomplemented
385C2×C3×C8—21no—
386C2×C3×C8—21no—
387C2×C3×C8—42no—
388C3×C4⋊C4—42no—
389C3×C22⋊C4—42no—
390C3×C42—21no—
391C3×C42—21no—
392C3×C42—21no—
393C3×C42C2×D412yescomplemented
394#217—22no—
395#217—22no—
396#217—21no—
397#217—21no—
398#217—21no—
399#217—41no—
400#217—41no—
401#216—42no—
402#216—42no—
403#214—42no—
404#214—42no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—44no—
413(C2×D3)⋊C4—82no—
414C4⋊Dic3—22no—
415C4⋊Dic3—21no—
416C4⋊Dic3—21no—
417C4⋊Dic3—21no—
418C4⋊Dic3—21no—
419C4⋊Dic3—82no—
420C4⋊Dic3C2×D411yescharacteristic
421C4⋊Dic3C2×D411yescharacteristic
422Dic3⋊C4—22no—
423Dic3⋊C4—21no—
424Dic3⋊C4—21no—
425Dic3⋊C4—41no—
426Dic3⋊C4—41no—
427C4×Dic3—22no—
428C4×Dic3—21no—
429#208—21no—
430#208—21no—
431#208—21no—
432#208—21no—
433C2×C3⋊C8—21no—
434C2×C3⋊C8—21no—
435Dic12—42no—
436#204—42no—
437H(5,𝔽2)—62no—
438H(5,𝔽2)—62no—
439H(5,𝔽2)—121no—
440H(5,𝔽2)—121no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—31no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41—61no—
449C2×#41—61no—
450C2×#41D1211yescharacteristic
451C2×#41D1211yescharacteristic
452C2×#41C22×D311yescharacteristic
453C2×#41C22×D311yescharacteristic
454C22×Q8—31no—
455C22×Q8D1211yescharacteristic
456C22×D4—21no—
457C22×D4—32no—
458C22×D4—31no—
459C22×D4—61no—
460C22×D4—62no—
461C22×D4—62no—
462C22×D4—61no—
463C22×D4D1211yescharacteristic
464C23×C4—21no—
465C23×C4C22×D311yescharacteristic
466#137—62no—
467#137—62no—
468#137—62no—
469#137—121no—
470#137—121no—
471#137—121no—
472C2×Q16—61no—
473C2×Q16—61no—
474C2×Q16—61no—
475C2×SD16—61no—
476C2×SD16—61no—
477C2×SD16—61no—
478C2×M16—21no—
479C2×M16—22no—
480C2×M16—31no—
481C2×M16—31no—
482C2×M16—41no—
483C2×M16C22×D311yescharacteristic
484C2×M16C22×D311yescharacteristic
485C22×C8—21no—
486#127—62no—
487#127—61no—
488#124—62no—
489#124—61no—
490#124—62no—
491#124—121no—
492#123—62no—
493#123—61no—
494C22⋊Q8—31no—
495C22⋊Q8—31no—
496C22⋊Q8—61no—
497C22⋊Q8—62no—
498C22⋊Q8—61no—
499C22⋊Q8—61no—
500C22⋊Q8—61no—
501C22⋊Q8—61no—
502C22⋊Q8—61no—
503#121—31no—
504#121—31no—
505#121—61no—
506#121—61no—
507#121—61no—
508#121—62no—
509#121—62no—
510#121—62no—
511#121—62no—
512#121—62no—
513#121—62no—
514#121—61no—
515#121—61no—
516#121—61no—
517#121—61no—
518#121—61no—
519#120—62no—
520#120—62no—
521#120—62no—
522#120—62no—
523#120—61no—
524C4×Q8—61no—
525C4×D4—62no—
526C4×D4—62no—
527C4×D4—62no—
528C4×D4—61no—
529C4×D4—61no—
530C4×D4—61no—
531#117—22no—
532#117—31no—
533#117—41no—
534#117—61no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—61no—
539C2×C4⋊C4—61no—
540C2×C4⋊C4—62no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—32no—
543C2×C22⋊C4—62no—
544C2×C22⋊C4—62no—
545C2×C22⋊C4—61no—
546C2×C22⋊C4—62no—
547C2×C42C22×D311yescharacteristic
548C2×C42C22×D311yescharacteristic
549#107—61no—
550#106—61no—
551#104—22no—
552#104—22no—
553#104—22no—
554#104—62no—
555#104—121no—
556#104#6714yescomplemented
557#103—61no—
558#103—61no—
559#103—61no—
560#103—61no—
561#103—61no—
562#102—61no—
563#102—61no—
564#102—61no—
565#100—62no—
566#100—121no—
567C22⋊C8—61no—
568C22⋊C8—61no—
569#95—62no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—42no—
577C23×C3—42no—
578C23×C3—81no—
579C23×C3#12011yescharacteristic
580C23×C3#12011yescharacteristic
581C23×C3C22×D411yescharacteristic
582C22×D3—22no—
583C22×D3—21no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—44no—
587C22×D3—42no—
588C22×D3—42no—
589C22×D3—82no—
590C22×D3—82no—
591C3×Q8—21no—
592C3×Q8—21no—
593C3×Q8—21no—
594C3×Q8—42no—
595C3×Q8#12112yes—
596C3×D4—22no—
597C3×D4—22no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—42no—
602C3×D4—42no—
603C3×D4—42no—
604C3×D4—41no—
605C3×D4—41no—
606C3×D4#12112yes—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—22no—
622C2×C3×C4—42no—
623C2×C3×C4—42no—
624C2×C3×C4—42no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4#12011yescharacteristic
633C2×C3×C4#12011yescharacteristic
634C2×C3×C4C22×D411yescharacteristic
635C2×C3×C4C22×D411yescharacteristic
636C2×C3×C4C22×D411yescharacteristic
637C2×C3×C4C2×#4111yescharacteristic
638C2×C3×C4H(5,𝔽2)11yescharacteristic
639C2×C3×C4H(5,𝔽2)11yescharacteristic
640#67—44no—
641#67—44no—
642#67—42no—
643#67—41no—
644#67—41no—
645#67—81no—
646#67—82no—
647#67—82no—
648#67—82no—
649#67—82no—
650C2×Dic3—21no—
651C2×Dic3—22no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—42no—
655C2×Dic3—42no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—82no—
661D12—21no—
662D12—21no—
663D12—44no—
664D12—41no—
665D12—41no—
666D12—41no—
667D12—41no—
668C4×D3—44no—
669C4×D3—41no—
670C4×D3—41no—
671Dic6—21no—
672Dic6—21no—
673Dic6—41no—
674Dic6—41no—
675Dic6—41no—
676Dic6—41no—
677C3×C8—22no—
678C3×C8—41no—
679C3⋊C8—41no—
680C3⋊C8—41no—
681C24—21no—
682C24—32no—
683C24—62no—
684C24D3×D411yescharacteristic
685#41—21no—
686#41—21no—
687#41—22no—
688#41—22no—
689#41—21no—
690#41—21no—
691#41—21no—
692#41—21no—
693#41—42no—
694#41—42no—
695#41—41no—
696#41—41no—
697#41—42no—
698#41—42no—
699#41—61no—
700#41—61no—
701#41—61no—
702#41—61no—
703#41—122no—
704#41—122no—
705#41—122no—
706#41—122no—
707#41#23512yes—
708#41C2×#6712yes—
709C2×Q8—21no—
710C2×Q8—22no—
711C2×Q8—31no—
712C2×Q8—41no—
713C2×Q8—61no—
714C2×Q8—61no—
715C2×Q8—61no—
716C2×Q8—61no—
717C2×Q8—61no—
718C2×Q8—61no—
719C2×Q8C2×D1211yescharacteristic
720C2×Q8C2×D1211yescharacteristic
721C2×D4—21no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—31no—
728C2×D4—41no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—62no—
732C2×D4—62no—
733C2×D4—61no—
734C2×D4—62no—
735C2×D4—61no—
736C2×D4—62no—
737C2×D4—62no—
738C2×D4—62no—
739C2×D4—61no—
740C2×D4—62no—
741C2×D4—61no—
742C2×D4—61no—
743C2×D4—61no—
744C2×D4—61no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—122no—
748C2×D4—122no—
749C2×D4—124no—
750C2×D4—124no—
751C2×D4—122no—
752C2×D4—122no—
753C2×D4—242no—
754C2×D4—244no—
755C2×D4C2×D1211yescharacteristic
756C2×D4C2×D1211yescharacteristic
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—32no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—62no—
772C22×C4—62no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4C2×D1211yescharacteristic
777C22×C4C2×D1211yescharacteristic
778C22×C4D3×D411yescharacteristic
779C22×C4D3×D411yescharacteristic
780C22×C4D3×D411yescharacteristic
781C22×C4C23×D311yescharacteristic
782Q16—122no—
783Q16—122no—
784Q16—122no—
785SD16—122no—
786SD16—122no—
787SD16—122no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—42no—
792M16—61no—
793M16—61no—
794M16—61no—
795M16—61no—
796M16C2×#6712yescomplemented
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—42no—
800C2×C8—61no—
801C2×C8—61no—
802C4⋊C4—31no—
803C4⋊C4—31no—
804C4⋊C4—42no—
805C4⋊C4—62no—
806C4⋊C4—62no—
807C4⋊C4—61no—
808C4⋊C4—61no—
809C4⋊C4—61no—
810C4⋊C4—61no—
811C4⋊C4—61no—
812C4⋊C4—61no—
813C4⋊C4—121no—
814C4⋊C4—121no—
815C4⋊C4—242no—
816C22⋊C4—42no—
817C22⋊C4—62no—
818C22⋊C4—62no—
819C22⋊C4—62no—
820C22⋊C4—62no—
821C22⋊C4—62no—
822C22⋊C4—61no—
823C22⋊C4—61no—
824C22⋊C4—61no—
825C22⋊C4—62no—
826C22⋊C4—62no—
827C22⋊C4—61no—
828C22⋊C4—61no—
829C22⋊C4—124no—
830C22⋊C4—121no—
831C22⋊C4—121no—
832C22⋊C4—242no—
833C42—21no—
834C42—21no—
835C42—21no—
836C42—62no—
837C42—61no—
838C42C2×#6712yescomplemented
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—22no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—81no—
854C22×C3—81no—
855C22×C3—84no—
856C22×C3C2×#12011yescharacteristic
857C22×C3D4211yescharacteristic
858C22×C3#54611yescharacteristic
859C2×D3—41no—
860C2×D3—42no—
861C2×D3—42no—
862C2×D3—41no—
863C2×D3—42no—
864C2×D3—41no—
865C2×D3—82no—
866C2×D3—82no—
867C2×D3—164no—
868C3×C4—22no—
869C3×C4—21no—
870C3×C4—21no—
871C3×C4—42no—
872C3×C4—41no—
873C3×C4—81no—
874C3×C4C2×#12111yescharacteristic
875C3×C4#53411yescharacteristic
876C3×C4D4211yescharacteristic
877C3×C4#54611yescharacteristic
878Dic3—41no—
879Dic3—42no—
880Dic3—41no—
881Dic3—41no—
882Dic3—81no—
883Dic3—81no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—41no—
889C23—41no—
890C23—42no—
891C23—42no—
892C23—61no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—81no—
897C23—124no—
898C23—122no—
899C23—122no—
900C23—242no—
901C23—242no—
902C23#88211yescharacteristic
903C23#88211yescharacteristic
904C23C2×D3×D411yescharacteristic
905Q8—21no—
906Q8—21no—
907Q8—21no—
908Q8—42no—
909Q8—61no—
910Q8—61no—
911Q8—121no—
912Q8—121no—
913Q8—121no—
914Q8—121no—
915Q8#93012yes—
916D4—22no—
917D4—22no—
918D4—21no—
919D4—21no—
920D4—21no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—41no—
925D4—41no—
926D4—61no—
927D4—61no—
928D4—124no—
929D4—124no—
930D4—124no—
931D4—122no—
932D4—121no—
933D4—121no—
934D4—121no—
935D4—121no—
936D4—121no—
937D4—121no—
938D4—242no—
939D4—241no—
940D4—242no—
941D4—242no—
942D4—242no—
943D4#93012yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—62no—
972C2×C4—61no—
973C2×C4—124no—
974C2×C4—121no—
975C2×C4—121no—
976C2×C4—122no—
977C2×C4—122no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—242no—
983C2×C4#88211yescharacteristic
984C2×C4#88211yescharacteristic
985C2×C4C22×D1211yescharacteristic
986C2×C4C2×#23511yescharacteristic
987C2×C4C2×D3×D411yescharacteristic
988C2×C4#100411yescharacteristic
989C2×C4#100411yescharacteristic
990C2×C4C22×#6711yescharacteristic
991C8—22no—
992C8—41no—
993C8—121no—
994C8—121no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—42no—
998C2×C3—41no—
999C2×C3—41no—
1000C2×C3—81no—
1001C2×C3#241011yescharacteristic
1002C2×C3#301911yescharacteristic
1003C2×C3#302211yescharacteristic
1004D3—82no—
1005D3—81no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—22no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—81no—
1021C22—81no—
1022C22—84no—
1023C22—122no—
1024C22—121no—
1025C22—122no—
1026C22—121no—
1027C22—121no—
1028C22—122no—
1029C22—242no—
1030C22—242no—
1031C22—484no—
1032C22C2×#88211yescharacteristic
1033C22#549011yescharacteristic
1034C22D4×#6711yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—22no—
1038C4—42no—
1039C4—41no—
1040C4—81no—
1041C4—122no—
1042C4—121no—
1043C4—121no—
1044C4—121no—
1045C4—241no—
1046C4—241no—
1047C4#549011yescharacteristic
1048C4#549311yescharacteristic
1049C4C2×#93011yescharacteristic
1050C4D4×#6711yescharacteristic
1051C3#2447111yescharacteristic, complemented, Sylow
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—242no—
1059C2—241no—
1060C2#7899311yescharacteristic
1061C2#7899511yescharacteristic
1062C2#8212711yescharacteristic
subgroupG/H
centerC22C2×#882
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#421C2
socleC22×C3C2×#120
prime radical#87275C2
hypercenterC2×#421D3
hypocenterC3#24471
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×C3×#421C2semidirect
3. #84084C2semidirect
4. #83776C2semidirect
5. #82287C2semidirect
6. C2×#4825C2semidirect
7. #72002C2semidirect
8. #71591C2semidirect
9. #70393C2semidirect
10. #70386C2semidirect
11. #70384C2semidirect
12. #70365C2semidirect
13. #70363C2semidirect
14. #70361C2semidirect
15. #70359C2semidirect
19. C22×C3×M16C22semidirect
20. C2×C3×#117C22semidirect
30. C2×#951C22semidirect
38. C2×#924C22semidirect
39. C2×#909C22semidirect
40. C2×#875C22semidirect
44. C2×C3×#104C22semidirect
45. C2×C3×#104C22semidirect
49. #5232C22semidirect
52. #5207C22semidirect
55. #5133C22semidirect
56. C2×#823C22semidirect
57. C2×#823C22semidirect
58. #5121C22semidirect
59. #5120C22semidirect
64. #4939C22semidirect
65. #4935C22semidirect
66. #4929C22semidirect
67. C2×#805C22semidirect
68. C2×#805C22semidirect
70. #4554C22semidirect
71. #4554C22semidirect
72. #4523C22semidirect
73. #4523C22semidirect
78. C2×#421D3semidirect
204. C3×#104D4semidirect
227. C22×M16C2×D3semidirect
245. C2×#117C2×D3semidirect
261. C2×#104C2×D3semidirect
262. C2×#104C2×D3semidirect
384. C3×M16C2×D4semidirect
393. C3×C42C2×D4semidirect
556. #104#67semidirect
796. M16C2×#67semidirect
838. C42C2×#67semidirect
1051. C3#24471semidirect

Maximal subgroups

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

subgroupindex
#872752
C2×C3×#4212
#840842
#837762
#822872
C2×#48252
#720022
#715912
#703932
#703862
#703842
#703652
#703632
#703612
#703592
#244713