Finite Group Databasebeta

← #10833355

Subgroups — #10833355

Order 768.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85949C211yesmaximal, characteristic, complemented
2C3×#2856C211yesmaximal, characteristic, complemented
3C2×#5077C211yesmaximal, characteristic, complemented
4#82624C211yesmaximal, characteristic, complemented
5#82621C211yesmaximal, characteristic, complemented
6C22×#805C211yesmaximal, characteristic, complemented
7#71769C211yesmaximal, characteristic, complemented
8#71683C211yesmaximal, characteristic, complemented
9#71532C211yesmaximal, characteristic, complemented
10#69665C211yesmaximal, characteristic, complemented
11#69664C211yesmaximal, characteristic, complemented
12#69663C211yesmaximal, characteristic, complemented
13#69662C211yesmaximal, characteristic, complemented
14#69593C211yesmaximal, characteristic, complemented
15#69592C211yesmaximal, characteristic, complemented
16#24464—31nomaximal, Sylow
17C2×#1004C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×#127C2211yescharacteristic, complemented
20C2×C3×#121—22no—
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic, complemented
23C22×C3×C42C2211yescharacteristic, complemented
24#5805C2211yescharacteristic
25D4×#67—22no—
26C2×#932C2211yescharacteristic
27C2×#932C2211yescharacteristic, complemented
28C2×#932C2211yescharacteristic, complemented
29#5791C2211yescharacteristic
30C22×#208C2211yescharacteristic, complemented
31#5612—21no—
32#5609—21no—
33#5608—21no—
34#5607—21no—
35#5606—21no—
36D3×#121—21no—
37#5599—21no—
38#5598—21no—
39#5510C2211yescharacteristic
40#5504C2211yescharacteristic
41#5490—22no—
42C3×#390—22no—
43C3×#390C2211yescharacteristic, complemented
44C3×#390C2211yescharacteristic, complemented
45C3×#384C2211yescharacteristic, complemented
46C2×#833C2211yescharacteristic, complemented
47C2×#833C2211yescharacteristic, complemented
48#5215C2211yescharacteristic, complemented
49#5207C2211yescharacteristic, complemented
50#5077—24no—
51#5042—21no—
52#5041—21no—
53#5040—21no—
54#5039—21no—
55#5038—21no—
56#5037—21no—
57#5037—21no—
58#5036—21no—
59#4966C2211yescharacteristic
60#4966C2211yescharacteristic, complemented
61#4966C2211yescharacteristic, complemented
62#4964C2211yescharacteristic, complemented
63C2×#805—24no—
64C2×#805C2211yescharacteristic
65C2×#805C2211yescharacteristic
66C2×#805C2211yescharacteristic, complemented
67C2×#805C2211yescharacteristic, complemented
68C2×#805C2211yescharacteristic, complemented
69C2×#805C2211yescharacteristic, complemented
70#4530C2211yescharacteristic, complemented
71#4530C2211yescharacteristic, complemented
72#4523C2211yescharacteristic, complemented
73#4523C2211yescharacteristic, complemented
74#3488—31no—
75#3055—31no—
76C2×#453—31no—
77#3006—31no—
78C22×#104—31no—
79#2856D311yescharacteristic, complemented
80#2039—31no—
81#2037—31no—
82#2006—31no—
83#2002—31no—
84#1900—31no—
85#1896—31no—
86#1883—31no—
87#1859—31no—
88#1792—31no—
89C22×C3×D4—22no—
90C22×C3×D4—21no—
91C22×C3×D4D412yes—
92C22×C3×D4C2311yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4—21no—
95C23×C3×C4C2311yescharacteristic
96C22×#67—21no—
97C22×#67—22no—
98#1004—22no—
99#1004—22no—
100#1004—41no—
101#1004—41no—
102C2×#237—21no—
103C2×#237—21no—
104C2×D3×D4—22no—
105C2×D3×D4—21no—
106C2×D3×D4—21no—
107C2×#235—21no—
108C2×#235—21no—
109C2×#235—22no—
110C2×#235—22no—
111C2×#235—41no—
112C2×#235—41no—
113C2×#235D411yescharacteristic, complemented
114C2×#235D411yescharacteristic, complemented
115C2×#235C2311yescharacteristic
116C2×#235C2311yescharacteristic
117C2×#235C2311yescharacteristic
118C22×D12D411yescharacteristic, complemented
119C22×C4×D3—21no—
120C22×Dic6D411yescharacteristic, complemented
121C3×#127—22no—
122C3×#127—41no—
123C3×#121—21no—
124C3×#121—21no—
125C3×#121—21no—
126C3×#121—21no—
127C3×#121—21no—
128C3×#121—21no—
129C3×#121—21no—
130C3×#121—21no—
131C3×#121—48no—
132C2×C3×C4⋊C4—22no—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4D412yes—
139C2×C3×C42—22no—
140C2×C3×C42—21no—
141C2×C3×C42—41no—
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2311yescharacteristic
144#953—22no—
145#953—21no—
146#940—22no—
147#940—21no—
148#939—22no—
149#939—22no—
150#938—22no—
151#938—21no—
152#938—21no—
153#937—22no—
154#937—22no—
155#936—21no—
156D4×Dic3—22no—
157C2×#214—21no—
158C2×#214—21no—
159C2×#214—21no—
160#932—22no—
161#932—22no—
162#932—22no—
163#932—41no—
164#932—41no—
165#932—41no—
166C2×#213—21no—
167C2×#213—21no—
168C2×#213—21no—
169#930—22no—
170#930D411yescharacteristic, complemented
171#930D411yescharacteristic, complemented
172#929—21no—
173C4×#67—22no—
174C4×#67—21no—
175C4×#67—21no—
176#926C2311yescharacteristic
177#924D411yescharacteristic, complemented
178#924D411yescharacteristic, complemented
179C2×#208—21no—
180C2×#208—22no—
181C2×#208—41no—
182C2×#208C2311yescharacteristic
183C2×#208C2311yescharacteristic
184C2×#208C2311yescharacteristic
185C2×#208C2311yescharacteristic
186C22×C3⋊C8—21no—
187#897—21no—
188#897—21no—
189#895—21no—
190#895—21no—
191#893—21no—
192#892—21no—
193D3×C4⋊C4—21no—
194#887—21no—
195#885—22no—
196#884—22no—
197#884—22no—
198#883—22no—
199#882—22no—
200#67⋊C4—22no—
201D3×C22⋊C4—22no—
202#878—22no—
203#833—22no—
204#833—41no—
205#832—21no—
206#832—21no—
207#830—21no—
208#830—21no—
209#810—21no—
210#810—21no—
211#810—21no—
212#809—21no—
213#809—21no—
214#809—21no—
215#808—21no—
216#807—21no—
217#805—22no—
218#805—22no—
219#805—22no—
220#805—22no—
221#805—41no—
222#805D414yescomplemented
223C2×H(5,𝔽2)—31no—
224C22×#41—31no—
225C2×AGL(1,ℤ/8)—31no—
226C2×AGL(1,ℤ/8)—31no—
227C2×AGL(1,ℤ/8)—31no—
228C22×M16—31no—
229#550—61no—
230#548—61no—
231#546—61no—
232#546—62no—
233D42—61no—
234D42—62no—
235#537—31no—
236#537—61no—
237#535—31no—
238#535—61no—
239C2×#127C2×D311yescharacteristic, complemented
240#525—31no—
241#525—61no—
242C2×#121—22no—
243C2×#121—61no—
244C2×#121C2×D311yescharacteristic
245C2×#121C2×D311yescharacteristic, complemented
246#520—31no—
247C22×C42C2×D311yescharacteristic, complemented
248#469—61no—
249#468—61no—
250#466—61no—
251#465—61no—
252#453—64no—
253#449—61no—
254#449—61no—
255#448—61no—
256#447—61no—
257#428—31no—
258C2×#104—31no—
259C2×#104—31no—
260C2×#104—31no—
261C2×#104—31no—
262C2×#104—31no—
263C2×#104—31no—
264C2×#104—64no—
265#418—31no—
266#417—31no—
267#417—31no—
268#417—31no—
269C2×#100—31no—
270C2×#100—31no—
271#407—31no—
272#390—22no—
273#390C2×D311yescharacteristic, complemented
274#390C2×D311yescharacteristic, complemented
275#384C2×D311yescharacteristic, complemented
276#343—31no—
277#343—31no—
278#339—31no—
279#339—31no—
280C24×C3—21no—
281C24×C3C2×D411yescharacteristic
282C24×C3C2×D412yes—
283C23×D3—21no—
284C23×D3—22no—
285C2×C3×D4—22no—
286C2×C3×D4—22no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—44no—
302C2×C3×D4—44no—
303C2×C3×D4—44no—
304C2×C3×D4—41no—
305C2×C3×D4—41no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—24no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—42no—
315C22×C3×C4—42no—
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2411yescharacteristic
323C2×#67—21no—
324C2×#67—22no—
325C2×#67—22no—
326C2×#67—21no—
327C2×#67—21no—
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—21no—
331C2×#67—22no—
332C2×#67—22no—
333C2×#67—21no—
334C2×#67—42no—
335C2×#67—42no—
336C2×#67—44no—
337C2×#67—44no—
338C22×Dic3—22no—
339C22×Dic3—21no—
340#237—42no—
341#237—42no—
342#237—42no—
343#237—42no—
344D3×D4—42no—
345D3×D4—42no—
346D3×D4—42no—
347D3×D4—42no—
348D3×D4—84no—
349#235—21no—
350#235—21no—
351#235—21no—
352#235—21no—
353#235—21no—
354#235—21no—
355#235—21no—
356#235—21no—
357#235—21no—
358#235—21no—
359#235—22no—
360#235—22no—
361#235—41no—
362#235—41no—
363#235—42no—
364#235—42no—
365#235—42no—
366#235—42no—
367#235C2×D412yes—
368#235#4112yes—
369C2×D12—22no—
370C2×D12—21no—
371C2×D12—22no—
372C2×D12—41no—
373C2×D12C2×D411yescharacteristic
374C2×D12C2×D411yescharacteristic
375C2×D12C2×D411yescharacteristic
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3—21no—
379C2×C4×D3—21no—
380C2×C4×D3—21no—
381C2×C4×D3—22no—
382C2×C4×D3—42no—
383C2×C4×D3—42no—
384C2×Dic6—22no—
385C2×Dic6—21no—
386C2×Dic6—41no—
387C2×Dic6C2×D411yescharacteristic
388C2×Dic6C2×D411yescharacteristic
389C2×Dic6C2×D411yescharacteristic
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—44no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—44no—
398C3×C22⋊C4—44no—
399C3×C22⋊C4—41no—
400C3×C22⋊C4—41no—
401C3×C42—21no—
402C3×C42—21no—
403C3×C42—21no—
404C3×C42—42no—
405C3×C42C2×D412yescomplemented
406#217—22no—
407#217—22no—
408#217—21no—
409#217—21no—
410#217—21no—
411#214—42no—
412#214—42no—
413#214—42no—
414#213—42no—
415#213—42no—
416#213—42no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422C4⋊Dic3—22no—
423C4⋊Dic3C2×D411yescharacteristic
424C4⋊Dic3C2×D411yescharacteristic
425Dic3⋊C4—22no—
426Dic3⋊C4—21no—
427Dic3⋊C4—21no—
428C4×Dic3—22no—
429C4×Dic3—21no—
430#208—21no—
431#208—21no—
432#208—21no—
433#208—21no—
434#208—21no—
435#208—21no—
436#208—21no—
437#208—42no—
438#208C2×D412yescomplemented
439C2×C3⋊C8—21no—
440C2×C3⋊C8—21no—
441C2×C3⋊C8—21no—
442C2×C3⋊C8—21no—
443C2×C3⋊C8—42no—
444H(5,𝔽2)—62no—
445H(5,𝔽2)—62no—
446H(5,𝔽2)—121no—
447H(5,𝔽2)—121no—
448C2×#41—31no—
449C2×#41—31no—
450C2×#41—31no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—62no—
454C2×#41—62no—
455C2×#41—61no—
456C2×#41—61no—
457C2×#41—61no—
458C2×#41—61no—
459C2×#41—121no—
460C2×#41—121no—
461C22×Q8—31no—
462C22×D4—21no—
463C22×D4—22no—
464C22×D4—31no—
465C22×D4—61no—
466C22×D4—61no—
467C22×D4—62no—
468C22×D4—61no—
469C22×D4—62no—
470C22×D4#6712yes—
471C22×D4C22×D311yescharacteristic
472C22×D4C22×D311yescharacteristic
473C23×C4—21no—
474C23×C4—61no—
475C23×C4C22×D311yescharacteristic
476AGL(1,ℤ/8)—62no—
477AGL(1,ℤ/8)—62no—
478AGL(1,ℤ/8)—62no—
479AGL(1,ℤ/8)—121no—
480AGL(1,ℤ/8)—121no—
481AGL(1,ℤ/8)—121no—
482C2×SD16—61no—
483C2×SD16—61no—
484C2×SD16—61no—
485C2×D8—61no—
486C2×D8—61no—
487C2×D8—61no—
488C2×M16—31no—
489C2×M16—31no—
490C2×M16—31no—
491C2×M16—31no—
492C2×M16—61no—
493C2×M16—62no—
494C2×M16—121no—
495C22×C8—61no—
496#127—22no—
497#127—41no—
498#127—61no—
499#127—62no—
500#124—62no—
501#124—61no—
502#123—62no—
503#123—61no—
504C22⋊Q8—31no—
505C22⋊Q8—31no—
506C22⋊Q8—62no—
507C22⋊Q8—61no—
508C22⋊Q8—61no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—31no—
518#121—31no—
519#121—48no—
520#121—62no—
521#121—62no—
522#121—61no—
523#121—61no—
524#121—61no—
525#121—61no—
526#121—62no—
527#121—62no—
528#121—62no—
529#121—62no—
530#120—62no—
531#120—62no—
532#120—62no—
533#120—61no—
534#120—62no—
535C4×Q8—61no—
536C4×D4—62no—
537C4×D4—61no—
538C4×D4—62no—
539C4×D4—61no—
540C4×D4—61no—
541C4×D4—62no—
542#117—31no—
543#117—61no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—61no—
546C2×C4⋊C4C22×D311yescharacteristic
547C2×C4⋊C4C22×D311yescharacteristic
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—62no—
552C2×C22⋊C4#6712yes—
553C2×C42—22no—
554C2×C42—21no—
555C2×C42—41no—
556C2×C42C22×D311yescharacteristic
557C2×C42C22×D311yescharacteristic
558#107—61no—
559#106—61no—
560#104—34no—
561#104—62no—
562#104—62no—
563#104—62no—
564#104—62no—
565#104—121no—
566#103—61no—
567#103—61no—
568#103—61no—
569#102—61no—
570#102—61no—
571#102—61no—
572#102—61no—
573#102—61no—
574#100—62no—
575#100—121no—
576C22⋊C8—61no—
577C22⋊C8—61no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—41no—
585C23×C3—42no—
586C23×C3—42no—
587C23×C3—42no—
588C23×C3—42no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3#12011yescharacteristic
593C23×C3#12011yescharacteristic
594C23×C3C22×D411yescharacteristic
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—42no—
599C22×D3—44no—
600C22×D3—42no—
601C22×D3—81no—
602C22×D3—82no—
603C22×D3—82no—
604C3×D4—44no—
605C3×D4—41no—
606C3×D4—41no—
607C3×D4—41no—
608C3×D4—41no—
609C3×D4—41no—
610C3×D4—41no—
611C3×D4—41no—
612C3×D4—41no—
613C3×D4—88no—
614C3×D4—82no—
615C3×D4—82no—
616C3×D4—82no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—48no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—42no—
636C2×C3×C4—42no—
637C2×C3×C4—41no—
638C2×C3×C4#12011yescharacteristic
639C2×C3×C4#12011yescharacteristic
640C2×C3×C4C22×D411yescharacteristic
641C2×C3×C4C22×D411yescharacteristic
642C2×C3×C4C22×D411yescharacteristic
643C2×C3×C4C2×#4111yescharacteristic
644C2×C3×C4H(5,𝔽2)11yescharacteristic
645C2×C3×C4H(5,𝔽2)11yescharacteristic
646#67—22no—
647#67—22no—
648#67—42no—
649#67—44no—
650#67—42no—
651#67—44no—
652#67—41no—
653#67—41no—
654#67—41no—
655#67—41no—
656#67—42no—
657#67—81no—
658#67—82no—
659#67—82no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—42no—
666C2×Dic3—44no—
667D12—21no—
668D12—21no—
669D12—21no—
670D12—21no—
671D12—21no—
672D12—42no—
673D12—82no—
674D12#12112yescomplemented
675C4×D3—22no—
676C4×D3—22no—
677C4×D3—42no—
678C4×D3—42no—
679C4×D3—41no—
680C4×D3—41no—
681C4×D3—41no—
682C4×D3—41no—
683C4×D3—82no—
684Dic6—21no—
685Dic6—21no—
686Dic6—21no—
687Dic6—21no—
688Dic6—21no—
689Dic6—42no—
690Dic6#12112yescomplemented
691C3⋊C8—22no—
692C3⋊C8—41no—
693C3⋊C8—41no—
694C3⋊C8—41no—
695C24—21no—
696C24—62no—
697C24—61no—
698C24C2×#6711yescharacteristic
699C24C2×#6712yes—
700#41—32no—
701#41—32no—
702#41—62no—
703#41—62no—
704#41—61no—
705#41—61no—
706#41—61no—
707#41—61no—
708#41—61no—
709#41—61no—
710#41—61no—
711#41—61no—
712#41—61no—
713#41—61no—
714#41—122no—
715#41—122no—
716#41—121no—
717#41—121no—
718#41—122no—
719#41—122no—
720#41—122no—
721#41—122no—
722#41—122no—
723#41—122no—
724C2×Q8—31no—
725C2×Q8—31no—
726C2×Q8—31no—
727C2×Q8—62no—
728C2×Q8—61no—
729C2×Q8—121no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—31no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—62no—
755C2×D4—62no—
756C2×D4—61no—
757C2×D4—62no—
758C2×D4—62no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—61no—
762C2×D4—61no—
763C2×D4—61no—
764C2×D4—62no—
765C2×D4—62no—
766C2×D4—61no—
767C2×D4—61no—
768C2×D4—121no—
769C2×D4—122no—
770C2×D4—122no—
771C2×D4—122no—
772C2×D4—122no—
773C2×D4—122no—
774C2×D4—122no—
775C2×D4—124no—
776C2×D4—124no—
777C2×D4—244no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—24no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—62no—
789C22×C4—61no—
790C22×C4—62no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—122no—
797C22×C4—122no—
798C22×C4D3×D411yescharacteristic
799C22×C4D3×D411yescharacteristic
800C22×C4D3×D411yescharacteristic
801C22×C4D3×D411yescharacteristic
802C22×C4C2×#6711yescharacteristic
803C22×C4C2×#6712yes—
804C22×C4C23×D311yescharacteristic
805SD16—122no—
806SD16—122no—
807SD16—122no—
808D8—122no—
809D8—122no—
810D8—122no—
811M16—32no—
812M16—61no—
813M16—61no—
814M16—61no—
815M16—61no—
816M16—61no—
817M16—61no—
818M16—61no—
819M16—122no—
820C2×C8—61no—
821C2×C8—61no—
822C2×C8—61no—
823C2×C8—61no—
824C2×C8—122no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—31no—
830C4⋊C4—31no—
831C4⋊C4—44no—
832C4⋊C4—62no—
833C4⋊C4—62no—
834C4⋊C4—61no—
835C4⋊C4—61no—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—41no—
841C22⋊C4—41no—
842C22⋊C4—62no—
843C22⋊C4—62no—
844C22⋊C4—62no—
845C22⋊C4—62no—
846C22⋊C4—62no—
847C22⋊C4—61no—
848C22⋊C4—61no—
849C22⋊C4—61no—
850C22⋊C4—61no—
851C22⋊C4—61no—
852C42—21no—
853C42—21no—
854C42—21no—
855C42—42no—
856C42—62no—
857C42—61no—
858C42D3×D412yescomplemented
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—42no—
867C22×C3—42no—
868C22×C3—42no—
869C22×C3—42no—
870C22×C3—42no—
871C22×C3—82no—
872C22×C3—82no—
873C22×C3—82no—
874C22×C3—82no—
875C22×C3—81no—
876C22×C3—81no—
877C22×C3—81no—
878C22×C3#45312yescomplemented
879C22×C3C2×#12011yescharacteristic
880C22×C3D4211yescharacteristic
881C22×C3#54611yescharacteristic
882C2×D3—22no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—41no—
886C2×D3—41no—
887C2×D3—41no—
888C2×D3—41no—
889C2×D3—41no—
890C2×D3—41no—
891C2×D3—84no—
892C2×D3—164no—
893C3×C4—24no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—42no—
897C3×C4—42no—
898C3×C4—81no—
899C3×C4C2×#12111yescharacteristic
900C3×C4#53411yescharacteristic
901C3×C4D4211yescharacteristic
902C3×C4#54611yescharacteristic
903Dic3—22no—
904Dic3—41no—
905Dic3—41no—
906Dic3—41no—
907Dic3—41no—
908C23—21no—
909C23—21no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—41no—
915C23—42no—
916C23—42no—
917C23—42no—
918C23—42no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—122no—
926C23—124no—
927C23—122no—
928C23—241no—
929C23—242no—
930C23—242no—
931C23#93711yescharacteristic
932C23#93711yescharacteristic
933C23C22×#6711yescharacteristic
934Q8—32no—
935Q8—61no—
936Q8—61no—
937Q8—61no—
938Q8—61no—
939Q8—61no—
940Q8—122no—
941D4—32no—
942D4—44no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—62no—
952D4—62no—
953D4—61no—
954D4—61no—
955D4—61no—
956D4—61no—
957D4—61no—
958D4—88no—
959D4—82no—
960D4—82no—
961D4—82no—
962D4—122no—
963D4—122no—
964D4—124no—
965D4—122no—
966D4—124no—
967D4—121no—
968D4—121no—
969D4—121no—
970D4—121no—
971D4—122no—
972D4—242no—
973D4—241no—
974D4—242no—
975D4—242no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—48no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—41no—
997C2×C4—61no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—122no—
1005C2×C4—122no—
1006C2×C4—122no—
1007C2×C4—124no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—242no—
1013C2×C4#93711yescharacteristic
1014C2×C4#93711yescharacteristic
1015C2×C4C2×D3×D411yescharacteristic
1016C2×C4C2×D3×D411yescharacteristic
1017C2×C4C2×D3×D411yescharacteristic
1018C2×C4#100411yescharacteristic
1019C2×C4D3×#4111yescharacteristic
1020C2×C4#100911yescharacteristic
1021C8—62no—
1022C8—121no—
1023C8—121no—
1024C8—121no—
1025C2×C3—21no—
1026C2×C3—22no—
1027C2×C3—21no—
1028C2×C3—41no—
1029C2×C3—82no—
1030C2×C3—161no—
1031C2×C3#241011yescharacteristic
1032C2×C3C2×#45311yescharacteristic
1033C2×C3#301811yescharacteristic
1034D3—42no—
1035D3—81no—
1036D3—81no—
1037C22—21no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—62no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—121no—
1058C22—121no—
1059C22—121no—
1060C22—121no—
1061C22—121no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—244no—
1066C22—484no—
1067C22#507712yescomplemented
1068C22C2×#93711yescharacteristic
1069C22D4×#6711yescharacteristic
1070C22#582911yescharacteristic
1071C4—24no—
1072C4—21no—
1073C4—21no—
1074C4—42no—
1075C4—42no—
1076C4—62no—
1077C4—81no—
1078C4—121no—
1079C4—121no—
1080C4—121no—
1081C4—121no—
1082C4D3×#12111yescharacteristic
1083C4#560511yescharacteristic
1084C4#560911yescharacteristic
1085C4#561011yescharacteristic
1086C3#2446411yescharacteristic, complemented, Sylow
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—82no—
1092C2—122no—
1093C2—161no—
1094C2—241no—
1095C2—241no—
1096C2#8270211yescharacteristic
1097C2C2×#507711yescharacteristic
1098C2#8332211yescharacteristic
subgroupG/H
centerC22C2×#937
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2856C2
socleC22×C3C2×#120
hypercenter#2856D3
hypocenterC3#24464
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. #85949C2semidirect
2. C3×#2856C2semidirect
3. C2×#5077C2semidirect
4. #82624C2semidirect
5. #82621C2semidirect
6. C22×#805C2semidirect
7. #71769C2semidirect
8. #71683C2semidirect
9. #71532C2semidirect
10. #69665C2semidirect
11. #69664C2semidirect
12. #69663C2semidirect
13. #69662C2semidirect
14. #69593C2semidirect
15. #69592C2semidirect
19. C2×C3×#127C22semidirect
22. C2×C3×#121C22semidirect
23. C22×C3×C42C22semidirect
27. C2×#932C22semidirect
28. C2×#932C22semidirect
30. C22×#208C22semidirect
43. C3×#390C22semidirect
44. C3×#390C22semidirect
45. C3×#384C22semidirect
46. C2×#833C22semidirect
47. C2×#833C22semidirect
48. #5215C22semidirect
49. #5207C22semidirect
60. #4966C22semidirect
61. #4966C22semidirect
62. #4964C22semidirect
66. C2×#805C22semidirect
67. C2×#805C22semidirect
68. C2×#805C22semidirect
69. C2×#805C22semidirect
70. #4530C22semidirect
71. #4530C22semidirect
72. #4523C22semidirect
73. #4523C22semidirect
79. #2856D3semidirect
113. C2×#235D4semidirect
114. C2×#235D4semidirect
118. C22×D12D4semidirect
120. C22×Dic6D4semidirect
170. #930D4semidirect
171. #930D4semidirect
177. #924D4semidirect
178. #924D4semidirect
222. #805D4semidirect
239. C2×#127C2×D3semidirect
245. C2×#121C2×D3semidirect
247. C22×C42C2×D3semidirect
273. #390C2×D3semidirect
274. #390C2×D3semidirect
275. #384C2×D3semidirect
405. C3×C42C2×D4semidirect
438. #208C2×D4semidirect
674. D12#121semidirect
690. Dic6#121semidirect
858. C42D3×D4semidirect
878. C22×C3#453semidirect
1067. C22#5077semidirect
1086. C3#24464semidirect

Maximal subgroups

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

subgroupindex
#859492
C3×#28562
C2×#50772
#826242
#826212
C22×#8052
#717692
#716832
#715322
#696652
#696642
#696632
#696622
#695932
#695922
#244643