Finite Group Databasebeta

← #10833342

Subgroups — #10833342

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#87275C211yesmaximal, characteristic, complemented
2C22×C3×#104C211yesmaximal, characteristic, complemented
3#84082C211yesmaximal, characteristic, complemented
4#83772C211yesmaximal, characteristic, complemented
5#82081C211yesmaximal, characteristic, complemented
6C2×#4822C211yesmaximal, characteristic, complemented
7#72002C211yesmaximal, characteristic, complemented
8#71532C211yesmaximal, characteristic, complemented
9#70392C211yesmaximal, characteristic, complemented
10#70385C211yesmaximal, characteristic, complemented
11#70384C211yesmaximal, characteristic, complemented
12#70366C211yesmaximal, characteristic, complemented
13#70363C211yesmaximal, characteristic, complemented
14#70361C211yesmaximal, characteristic, complemented
15#70359C211yesmaximal, characteristic, complemented
16#24464—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×#1009C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic, complemented
20C22×C3×C42C2211yescharacteristic, complemented
21#5834—21no—
22#5833—21no—
23#5833C2211yescharacteristic
24#5830—21no—
25#5830C2211yescharacteristic
26#5829—21no—
27#5829—22no—
28#5827C2211yescharacteristic
29C2×#949C2211yescharacteristic
30C2×#949C2211yescharacteristic, complemented
31#5817—21no—
32D4×#67—21no—
33D4×#67—22no—
34#5791—21no—
35#5791C2211yescharacteristic
36C2×#930—21no—
37C2×#930—22no—
38C2×#930C2211yescharacteristic
39C2×#930C2211yescharacteristic, complemented
40C2×#908C2211yescharacteristic, complemented
41C2×#874C2211yescharacteristic, complemented
42C2×C3×#104—24no—
43C2×C3×#104C2211yescharacteristic
44C2×C3×#104C2211yescharacteristic
45C2×C3×#104C2211yescharacteristic, complemented
46C2×C3×#104C2211yescharacteristic, complemented
47#5238—21no—
48#5238—21no—
49#5232C2211yescharacteristic
50#5232C2211yescharacteristic, complemented
51#5227—21no—
52#5217—21no—
53#5207C2211yescharacteristic, complemented
54#5135—21no—
55#5134—21no—
56#5133C2211yescharacteristic, complemented
57#5131C2211yescharacteristic, complemented
58C2×#823C2211yescharacteristic, complemented
59C2×#823C2211yescharacteristic, complemented
60#5121C2211yescharacteristic, complemented
61#5115—21no—
62#5114—21no—
63#4939—22no—
64#4939C2211yescharacteristic, complemented
65#4939C2211yescharacteristic, complemented
66#4935C2211yescharacteristic, complemented
67C2×#805C2211yescharacteristic, complemented
68C2×#805C2211yescharacteristic, complemented
69#4822—24no—
70#4554C2211yescharacteristic, complemented
71#4554C2211yescharacteristic, complemented
72#4523C2211yescharacteristic, complemented
73#4523C2211yescharacteristic, complemented
74#3488—31no—
75#3055—31no—
76C2×#453—31no—
77#3006—31no—
78C22×#104D311yescharacteristic, complemented
79#2856—31no—
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—
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, complemented
96C2×C3×#41D411yescharacteristic, complemented
97C2×C3×#41C2311yescharacteristic
98C2×C3×#41C2311yescharacteristic
99C22×C3×Q8D411yescharacteristic, complemented
100C22×C3×D4—21no—
101C22×C3×D4D411yescharacteristic, complemented
102C23×C3×C4—21no—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C22×#67—22no—
106C22×#67—21no—
107C22×#67D412yes—
108#1009—22no—
109#1009—22no—
110#1009—41no—
111#1009—41no—
112C2×#239—21no—
113C2×D3×D4—22no—
114C2×D3×D4—21no—
115C2×#235—21no—
116C2×#235C2311yescharacteristic
117C22×D12—21no—
118C22×D12—22no—
119C22×D12C2311yescharacteristic
120C22×D12C2311yescharacteristic
121C2×C3×M16—21no—
122C2×C3×M16—22no—
123C2×C3×M16—41no—
124C2×C3×M16C2311yescharacteristic
125C2×C3×M16C2311yescharacteristic
126C22×C3×C8—21no—
127C2×C3×C42—22no—
128C2×C3×C42—21no—
129C2×C3×C42—41no—
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2311yescharacteristic
132#953—22no—
133#953—21no—
134#949—22no—
135#949—22no—
136#949—41no—
137#949—41no—
138#947—22no—
139#947—21no—
140#946—22no—
141#946—21no—
142Q8×Dic3—21no—
143C2×#215—21no—
144C2×#215—21no—
145#940—22no—
146#940—21no—
147#939—22no—
148#939—22no—
149#939—22no—
150#938—22no—
151#938—21no—
152#937—22no—
153#937—22no—
154#937—22no—
155D4×Dic3—21no—
156D4×Dic3—22no—
157C2×#213—21no—
158C2×#213—21no—
159#930—22no—
160#930—22no—
161#930—21no—
162#930—21no—
163#930—21no—
164#930—21no—
165#930—21no—
166#930—21no—
167#930—21no—
168#930—21no—
169#930—21no—
170#930—21no—
171#930—21no—
172#930—48no—
173#930D411yescharacteristic, complemented
174#930D411yescharacteristic, complemented
175#929—22no—
176#929—21no—
177C4×#67—22no—
178C4×#67—22no—
179C4×#67—21no—
180C4×#67—21no—
181C2×(C2×D3)⋊C4—22no—
182C2×(C2×D3)⋊C4—22no—
183C2×(C2×D3)⋊C4—21no—
184C2×(C2×D3)⋊C4—22no—
185C2×(C2×D3)⋊C4D412yes—
186#926—21no—
187#926C2311yescharacteristic
188C2×C4⋊Dic3—21no—
189C2×C4⋊Dic3—22no—
190C2×C4⋊Dic3C2311yescharacteristic
191C2×C4⋊Dic3C2311yescharacteristic
192#924—21no—
193#924D411yescharacteristic, complemented
194#924D411yescharacteristic, complemented
195C2×#208C2311yescharacteristic
196C2×#208C2311yescharacteristic
197#908—22no—
198#908—41no—
199C2×D24—21no—
200C2×#204—21no—
201#874—22no—
202#874—41no—
203C3×#104—22no—
204C3×#104—22no—
205C3×#104—22no—
206C3×#104D414yescomplemented
207#835—21no—
208#835—21no—
209#832—21no—
210#832—21no—
211#830—21no—
212#830—21no—
213#823—22no—
214#823—41no—
215#821—21no—
216#821—21no—
217#821—21no—
218#818—21no—
219#817—21no—
220#816—21no—
221#805—22no—
222#805—41no—
223C2×H(5,𝔽2)—31no—
224C22×#41C2×D311yescharacteristic
225C2×AGL(1,ℤ/8)—31no—
226C2×AGL(1,ℤ/8)—31no—
227C2×AGL(1,ℤ/8)—31no—
228C22×M16C2×D311yescharacteristic, complemented
229#550—61no—
230#548—61no—
231#546—62no—
232#546—61no—
233D42—62no—
234D42—61no—
235#537—31no—
236#537—61no—
237#535—31no—
238#535—61no—
239C2×#127—31no—
240#525—31no—
241#525—61no—
242C2×#121—31no—
243C2×#121—31no—
244C2×#121—61no—
245C2×#121—62no—
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—24no—
259C2×#104—31no—
260C2×#104—31no—
261C2×#104C2×D311yescharacteristic
262C2×#104C2×D311yescharacteristic
263C2×#104C2×D311yescharacteristic, complemented
264C2×#104C2×D311yescharacteristic, complemented
265#418—31no—
266#417—31no—
267#417—31no—
268#417—31no—
269C2×#100—31no—
270C2×#100—31no—
271#407—31no—
272#390—31no—
273#390—31no—
274#390—62no—
275#384—31no—
276#343—31no—
277#343—31no—
278#339—31no—
279#339—31no—
280C24×C3—21no—
281C24×C3C2×D411yescharacteristic
282C23×D3—22no—
283C23×D3—21no—
284C23×D3C2×D412yes—
285C3×#41—21no—
286C3×#41—21no—
287C3×#41—22no—
288C3×#41—22no—
289C3×#41—21no—
290C3×#41—21no—
291C3×#41—21no—
292C3×#41—21no—
293C3×#41—42no—
294C3×#41—42no—
295C3×#41—41no—
296C3×#41—41no—
297C3×#41—42no—
298C3×#41—42no—
299C3×#41C2×D412yes—
300C3×#41#4112yes—
301C2×C3×Q8—21no—
302C2×C3×Q8—22no—
303C2×C3×Q8—41no—
304C2×C3×Q8C2×D411yescharacteristic
305C2×C3×Q8C2×D411yescharacteristic
306C2×C3×D4—21no—
307C2×C3×D4—22no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—41no—
313C2×C3×D4—42no—
314C2×C3×D4—42no—
315C2×C3×D4C2×D411yescharacteristic
316C2×C3×D4C2×D411yescharacteristic
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—24no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—42no—
330C22×C3×C4—42no—
331C22×C3×C4—42no—
332C22×C3×C4—42no—
333C22×C3×C4C2×D411yescharacteristic
334C22×C3×C4C2×D411yescharacteristic
335C22×C3×C4C2×D411yescharacteristic
336C22×C3×C4C2×D411yescharacteristic
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2411yescharacteristic
339C2×#67—22no—
340C2×#67—22no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—22no—
344C2×#67—22no—
345C2×#67—22no—
346C2×#67—21no—
347C2×#67—22no—
348C2×#67—44no—
349C2×#67—44no—
350C2×#67—41no—
351C2×#67—41no—
352C2×#67—84no—
353C22×Dic3—22no—
354C22×Dic3—21no—
355C22×Dic3C2×D412yes—
356#239—42no—
357#239—42no—
358D3×D4—44no—
359D3×D4—44no—
360D3×D4—42no—
361D3×D4—42no—
362#235—21no—
363#235—21no—
364#235—21no—
365#235—21no—
366#235—42no—
367#235—42no—
368C2×D12—22no—
369C2×D12—21no—
370C2×D12—21no—
371C2×D12—21no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12—21no—
375C2×D12—21no—
376C2×D12—21no—
377C2×D12—21no—
378C2×D12—21no—
379C2×D12—21no—
380C2×D12—21no—
381C2×D12—42no—
382C2×D12—42no—
383C2×D12—44no—
384C2×D12—44no—
385C2×D12—44no—
386C2×D12C2×D411yescharacteristic
387C2×C4×D3—22no—
388C2×C4×D3—21no—
389C2×Dic6C2×D411yescharacteristic
390C3×M16—21no—
391C3×M16—21no—
392C3×M16—21no—
393C3×M16—42no—
394C3×M16C2×D412yescomplemented
395C2×C3×C8—21no—
396C2×C3×C8—21no—
397C2×C3×C8—42no—
398C3×C42—21no—
399C3×C42—21no—
400C3×C42—21no—
401C3×C42—42no—
402C3×C42C2×D412yescomplemented
403#217—22no—
404#217—22no—
405#217—21no—
406#217—21no—
407#217—21no—
408#215—42no—
409#215—42no—
410#213—42no—
411#213—42no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—44no—
420(C2×D3)⋊C4—44no—
421(C2×D3)⋊C4—41no—
422(C2×D3)⋊C4—41no—
423C4⋊Dic3—22no—
424C4⋊Dic3—21no—
425C4⋊Dic3—21no—
426C4⋊Dic3—21no—
427C4⋊Dic3—21no—
428C4⋊Dic3—44no—
429C4⋊Dic3C2×D411yescharacteristic
430C4⋊Dic3C2×D411yescharacteristic
431Dic3⋊C4—22no—
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434C4×Dic3—22no—
435C4×Dic3—21no—
436#208—21no—
437#208—21no—
438#208—21no—
439#208—21no—
440C2×C3⋊C8—21no—
441C2×C3⋊C8—21no—
442D24—42no—
443#204—42no—
444H(5,𝔽2)—62no—
445H(5,𝔽2)—62no—
446H(5,𝔽2)—121no—
447H(5,𝔽2)—121no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—31no—
453C2×#41—41no—
454C2×#41—41no—
455C2×#41—61no—
456C2×#41—61no—
457C2×#41D1211yescharacteristic, complemented
458C2×#41D1211yescharacteristic, complemented
459C2×#41C22×D311yescharacteristic
460C2×#41C22×D311yescharacteristic
461C22×Q8D1211yescharacteristic, complemented
462C22×D4—21no—
463C22×D4—32no—
464C22×D4—31no—
465C22×D4—31no—
466C22×D4—61no—
467C22×D4—62no—
468C22×D4—62no—
469C22×D4—62no—
470C22×D4—61no—
471C22×D4—61no—
472C22×D4D1211yescharacteristic, complemented
473C23×C4—21no—
474C23×C4—21no—
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—21no—
489C2×M16—22no—
490C2×M16—31no—
491C2×M16—31no—
492C2×M16—41no—
493C2×M16C22×D311yescharacteristic
494C2×M16C22×D311yescharacteristic
495C22×C8—21no—
496#127—62no—
497#127—61no—
498#127—62no—
499#127—121no—
500#124—62no—
501#124—61no—
502#123—62no—
503#123—61no—
504C22⋊Q8—31no—
505C22⋊Q8—31no—
506C22⋊Q8—61no—
507C22⋊Q8—62no—
508C22⋊Q8—61no—
509#121—31no—
510#121—31no—
511#121—61no—
512#121—61no—
513#121—61no—
514#121—62no—
515#121—62no—
516#121—62no—
517#121—62no—
518#121—62no—
519#121—62no—
520#121—61no—
521#121—61no—
522#121—61no—
523#121—61no—
524#121—61no—
525#121—61no—
526#121—61no—
527#121—61no—
528#121—61no—
529#121—128no—
530#120—62no—
531#120—62no—
532#120—62no—
533#120—62no—
534#120—61no—
535C4×Q8—61no—
536C4×D4—62no—
537C4×D4—62no—
538C4×D4—62no—
539C4×D4—61no—
540C4×D4—61no—
541C4×D4—61no—
542#117—31no—
543#117—61no—
544C2×C4⋊C4—31no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—61no—
547C2×C4⋊C4—62no—
548C2×C22⋊C4—32no—
549C2×C22⋊C4—62no—
550C2×C22⋊C4—62no—
551C2×C22⋊C4—62no—
552C2×C22⋊C4—61no—
553C2×C42—22no—
554C2×C42—21no—
555C2×C42—41no—
556C2×C42C22×D311yescharacteristic
557C2×C42C22×D311yescharacteristic
558#107—61no—
559#106—61no—
560#104—22no—
561#104—22no—
562#104—22no—
563#104—62no—
564#104—121no—
565#104#6714yescomplemented
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—21no—
581C23×C3—22no—
582C23×C3—21no—
583C23×C3—41no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—81no—
587C23×C3#12011yescharacteristic
588C23×C3#12011yescharacteristic
589C23×C3C22×D411yescharacteristic
590C22×D3—22no—
591C22×D3—21no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—44no—
595C22×D3—42no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—42no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—82no—
603C22×D3—82no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×Q8—21no—
607C3×Q8—42no—
608C3×Q8#12112yescomplemented
609C3×D4—22no—
610C3×D4—22no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—42no—
615C3×D4—42no—
616C3×D4—42no—
617C3×D4—41no—
618C3×D4—41no—
619C3×D4#12112yescomplemented
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—21no—
623C2×C3×C4—22no—
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—21no—
631C2×C3×C4—21no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—22no—
637C2×C3×C4—21no—
638C2×C3×C4—42no—
639C2×C3×C4—42no—
640C2×C3×C4—42no—
641C2×C3×C4—48no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4#12011yescharacteristic
647C2×C3×C4#12011yescharacteristic
648C2×C3×C4C22×D411yescharacteristic
649C2×C3×C4C22×D411yescharacteristic
650C2×C3×C4C22×D411yescharacteristic
651C2×C3×C4C2×#4111yescharacteristic
652C2×C3×C4H(5,𝔽2)11yescharacteristic
653C2×C3×C4H(5,𝔽2)11yescharacteristic
654#67—44no—
655#67—41no—
656#67—41no—
657#67—44no—
658#67—42no—
659#67—81no—
660#67—82no—
661#67—82no—
662#67—82no—
663#67—82no—
664#67—82no—
665#67—82no—
666C2×Dic3—21no—
667C2×Dic3—22no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—42no—
671C2×Dic3—42no—
672C2×Dic3—41no—
673C2×Dic3—82no—
674D12—21no—
675D12—21no—
676D12—44no—
677D12—41no—
678D12—41no—
679D12—41no—
680D12—41no—
681D12—41no—
682D12—41no—
683D12—41no—
684D12—41no—
685D12—88no—
686C4×D3—44no—
687C4×D3—41no—
688C4×D3—41no—
689Dic6—21no—
690Dic6—21no—
691C3×C8—22no—
692C3×C8—41no—
693C3⋊C8—41no—
694C3⋊C8—41no—
695C24—21no—
696C24—32no—
697C24—62no—
698C24—61no—
699C24D3×D411yescharacteristic
700#41—21no—
701#41—21no—
702#41—22no—
703#41—22no—
704#41—21no—
705#41—21no—
706#41—21no—
707#41—21no—
708#41—42no—
709#41—42no—
710#41—41no—
711#41—41no—
712#41—42no—
713#41—42no—
714#41—61no—
715#41—61no—
716#41—61no—
717#41—61no—
718#41—122no—
719#41—122no—
720#41—122no—
721#41—122no—
722#41#23512yes—
723#41C2×#6712yes—
724C2×Q8—21no—
725C2×Q8—22no—
726C2×Q8—31no—
727C2×Q8—41no—
728C2×Q8C2×D1211yescharacteristic
729C2×Q8C2×D1211yescharacteristic
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—31no—
737C2×D4—41no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—62no—
741C2×D4—62no—
742C2×D4—61no—
743C2×D4—62no—
744C2×D4—61no—
745C2×D4—62no—
746C2×D4—62no—
747C2×D4—62no—
748C2×D4—61no—
749C2×D4—62no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—61no—
762C2×D4—122no—
763C2×D4—122no—
764C2×D4—124no—
765C2×D4—124no—
766C2×D4—124no—
767C2×D4—124no—
768C2×D4—124no—
769C2×D4—122no—
770C2×D4—122no—
771C2×D4—124no—
772C2×D4—124no—
773C2×D4—121no—
774C2×D4—121no—
775C2×D4—244no—
776C2×D4C2×D1211yescharacteristic
777C2×D4C2×D1211yescharacteristic
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—24no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—32no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—62no—
796C22×C4—62no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4C2×D1211yescharacteristic
800C22×C4C2×D1211yescharacteristic
801C22×C4D3×D411yescharacteristic
802C22×C4D3×D411yescharacteristic
803C22×C4D3×D411yescharacteristic
804C22×C4C23×D311yescharacteristic
805SD16—122no—
806SD16—122no—
807SD16—122no—
808D8—122no—
809D8—122no—
810D8—122no—
811M16—21no—
812M16—21no—
813M16—21no—
814M16—42no—
815M16—61no—
816M16—61no—
817M16—61no—
818M16—61no—
819M16C2×#6712yescomplemented
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—42no—
823C2×C8—61no—
824C2×C8—61no—
825C4⋊C4—31no—
826C4⋊C4—31no—
827C4⋊C4—62no—
828C4⋊C4—62no—
829C4⋊C4—61no—
830C4⋊C4—61no—
831C4⋊C4—61no—
832C4⋊C4—61no—
833C4⋊C4—61no—
834C4⋊C4—61no—
835C4⋊C4—124no—
836C22⋊C4—62no—
837C22⋊C4—62no—
838C22⋊C4—62no—
839C22⋊C4—62no—
840C22⋊C4—62no—
841C22⋊C4—61no—
842C22⋊C4—61no—
843C22⋊C4—61no—
844C22⋊C4—62no—
845C22⋊C4—62no—
846C22⋊C4—61no—
847C22⋊C4—61no—
848C22⋊C4—124no—
849C22⋊C4—124no—
850C22⋊C4—121no—
851C22⋊C4—121no—
852C42—21no—
853C42—21no—
854C42—21no—
855C42—42no—
856C42—62no—
857C42—61no—
858C42C2×#6712yescomplemented
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—22no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—42no—
868C22×C3—42no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—84no—
875C22×C3#45312yescomplemented
876C22×C3C2×#12011yescharacteristic
877C22×C3D4211yescharacteristic
878C22×C3#54611yescharacteristic
879C2×D3—41no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—41no—
883C2×D3—42no—
884C2×D3—41no—
885C2×D3—82no—
886C2×D3—82no—
887C2×D3—82no—
888C2×D3—82no—
889C2×D3—81no—
890C2×D3—81no—
891C2×D3—81no—
892C2×D3—164no—
893C3×C4—24no—
894C3×C4—22no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—42no—
898C3×C4—41no—
899C3×C4C2×#12111yescharacteristic
900C3×C4#53411yescharacteristic
901C3×C4D4211yescharacteristic
902C3×C4#54611yescharacteristic
903Dic3—41no—
904Dic3—42no—
905Dic3—41no—
906Dic3—41no—
907Dic3—81no—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—22no—
912C23—21no—
913C23—41no—
914C23—42no—
915C23—42no—
916C23—61no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—81no—
921C23—124no—
922C23—122no—
923C23—122no—
924C23—122no—
925C23—122no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—242no—
930C23—242no—
931C23#88211yescharacteristic
932C23#88211yescharacteristic
933C23C2×D3×D411yescharacteristic
934Q8—21no—
935Q8—21no—
936Q8—21no—
937Q8—42no—
938Q8—61no—
939Q8—61no—
940Q8#93012yescomplemented
941D4—22no—
942D4—22no—
943D4—21no—
944D4—21no—
945D4—21no—
946D4—42no—
947D4—42no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—61no—
952D4—61no—
953D4—124no—
954D4—124no—
955D4—121no—
956D4—121no—
957D4—124no—
958D4—122no—
959D4—121no—
960D4—121no—
961D4—121no—
962D4—121no—
963D4—121no—
964D4—121no—
965D4—121no—
966D4—121no—
967D4—248no—
968D4—242no—
969D4—241no—
970D4—242no—
971D4—242no—
972D4—242no—
973D4—242no—
974D4—242no—
975D4#93012yescomplemented
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—48no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—62no—
1005C2×C4—61no—
1006C2×C4—124no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—122no—
1010C2×C4—122no—
1011C2×C4—121no—
1012C2×C4—242no—
1013C2×C4#88211yescharacteristic
1014C2×C4#88211yescharacteristic
1015C2×C4C22×D1211yescharacteristic
1016C2×C4C2×#23511yescharacteristic
1017C2×C4C2×D3×D411yescharacteristic
1018C2×C4#100411yescharacteristic
1019C2×C4#100411yescharacteristic
1020C2×C4C22×#6711yescharacteristic
1021C8—22no—
1022C8—41no—
1023C8—121no—
1024C8—121no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—22no—
1028C2×C3—42no—
1029C2×C3—41no—
1030C2×C3—81no—
1031C2×C3#241011yescharacteristic
1032C2×C3C2×#45311yescharacteristic
1033C2×C3#301811yescharacteristic
1034D3—82no—
1035D3—81no—
1036D3—161no—
1037C22—21no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—22no—
1045C22—42no—
1046C22—42no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—84no—
1053C22—122no—
1054C22—121no—
1055C22—122no—
1056C22—121no—
1057C22—121no—
1058C22—122no—
1059C22—242no—
1060C22—242no—
1061C22—242no—
1062C22—242no—
1063C22—241no—
1064C22—241no—
1065C22—241no—
1066C22—484no—
1067C22#482212yescomplemented
1068C22C2×#88211yescharacteristic
1069C22#549011yescharacteristic
1070C22D4×#6711yescharacteristic
1071C4—24no—
1072C4—21no—
1073C4—21no—
1074C4—22no—
1075C4—42no—
1076C4—41no—
1077C4—122no—
1078C4—121no—
1079C4—121no—
1080C4—121no—
1081C4—241no—
1082C4#549011yescharacteristic
1083C4#549311yescharacteristic
1084C4C2×#93011yescharacteristic
1085C4D4×#6711yescharacteristic
1086C3#2446411yescharacteristic, complemented, Sylow
1087C2—21no—
1088C2—22no—
1089C2—21no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—242no—
1094C2—241no—
1095C2—481no—
1096C2C2×#482211yescharacteristic
1097C2#7898611yescharacteristic
1098C2#8212711yescharacteristic
subgroupG/H
centerC22C2×#882
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC22×C3×#104C2
socleC22×C3C2×#120
hypercenterC22×#104D3
hypocenterC3#24464
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. #87275C2semidirect
2. C22×C3×#104C2semidirect
3. #84082C2semidirect
4. #83772C2semidirect
5. #82081C2semidirect
6. C2×#4822C2semidirect
7. #72002C2semidirect
8. #71532C2semidirect
9. #70392C2semidirect
10. #70385C2semidirect
11. #70384C2semidirect
12. #70366C2semidirect
13. #70363C2semidirect
14. #70361C2semidirect
15. #70359C2semidirect
19. C22×C3×M16C22semidirect
20. C22×C3×C42C22semidirect
30. C2×#949C22semidirect
39. C2×#930C22semidirect
40. C2×#908C22semidirect
41. C2×#874C22semidirect
45. C2×C3×#104C22semidirect
46. C2×C3×#104C22semidirect
50. #5232C22semidirect
53. #5207C22semidirect
56. #5133C22semidirect
57. #5131C22semidirect
58. C2×#823C22semidirect
59. C2×#823C22semidirect
60. #5121C22semidirect
64. #4939C22semidirect
65. #4939C22semidirect
66. #4935C22semidirect
67. C2×#805C22semidirect
68. C2×#805C22semidirect
70. #4554C22semidirect
71. #4554C22semidirect
72. #4523C22semidirect
73. #4523C22semidirect
78. C22×#104D3semidirect
95. C2×C3×#41D4semidirect
96. C2×C3×#41D4semidirect
99. C22×C3×Q8D4semidirect
101. C22×C3×D4D4semidirect
173. #930D4semidirect
174. #930D4semidirect
193. #924D4semidirect
194. #924D4semidirect
206. C3×#104D4semidirect
228. C22×M16C2×D3semidirect
247. C22×C42C2×D3semidirect
263. C2×#104C2×D3semidirect
264. C2×#104C2×D3semidirect
394. C3×M16C2×D4semidirect
402. C3×C42C2×D4semidirect
457. C2×#41D12semidirect
458. C2×#41D12semidirect
461. C22×Q8D12semidirect
472. C22×D4D12semidirect
565. #104#67semidirect
608. C3×Q8#121semidirect
619. C3×D4#121semidirect
819. M16C2×#67semidirect
858. C42C2×#67semidirect
875. C22×C3#453semidirect
940. Q8#930semidirect
975. D4#930semidirect
1067. C22#4822semidirect
1086. C3#24464semidirect

Maximal subgroups

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

subgroupindex
#872752
C22×C3×#1042
#840822
#837722
#820812
C2×#48222
#720022
#715322
#703922
#703852
#703842
#703662
#703632
#703612
#703592
#244643