Finite Group Databasebeta

← #10833353

Subgroups — #10833353

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#86041C211yesmaximal, characteristic, complemented
2#82924C211yesmaximal, characteristic, complemented
3#82081C211yesmaximal, characteristic, complemented
4C22×#805C211yesmaximal, characteristic, complemented
5C2×#4822C211yesmaximal, characteristic, complemented
6#78639C211yesmaximal, characteristic, complemented
7C3×#1896C211yesmaximal, characteristic, complemented
8#70392C211yesmaximal, characteristic, complemented
9#70384C211yesmaximal, characteristic, complemented
10#70361C211yesmaximal, characteristic, complemented
11#69985C211yesmaximal, characteristic, complemented
12#68776C211yesmaximal, characteristic, complemented
13#68771C211yesmaximal, characteristic, complemented
14#68761C211yesmaximal, characteristic, complemented
15#68733C211yesmaximal, characteristic, complemented
16#24464—31nomaximal, Sylow
17C2×#1009C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C3×#525C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic, complemented
21#5833C2211yescharacteristic
22C2×#949C2211yescharacteristic, complemented
23C2×#930—22no—
24C2×#930C2211yescharacteristic
25C2×#930C2211yescharacteristic, complemented
26C22×#208C2211yescharacteristic, complemented
27C2×#908C2211yescharacteristic
28C2×#908C2211yescharacteristic, complemented
29#5654—22no—
30#5629—21no—
31#5627—21no—
32#5607—21no—
33D3×#121—21no—
34#5590—22no—
35#5553—21no—
36#5552—21no—
37#5550—21no—
38D4×D12—21no—
39#5525C2211yescharacteristic
40#5523C2211yescharacteristic
41C2×#874C2211yescharacteristic, complemented
42C2×C3×#104C2211yescharacteristic, complemented
43C2×C3×#104C2211yescharacteristic, complemented
44C3×#407C2211yescharacteristic, complemented
45#5232C2211yescharacteristic, complemented
46#5133C2211yescharacteristic
47#5133C2211yescharacteristic, complemented
48C2×#823C2211yescharacteristic, complemented
49C2×#823C2211yescharacteristic, complemented
50#5049—21no—
51#5048—21no—
52#5039—21no—
53#5038—21no—
54#5001C2211yescharacteristic, complemented
55#4995C2211yescharacteristic, complemented
56#4939—22no—
57#4939C2211yescharacteristic, complemented
58#4939C2211yescharacteristic, complemented
59#4935C2211yescharacteristic, complemented
60C2×#805—24no—
61C2×#805C2211yescharacteristic
62C2×#805C2211yescharacteristic
63C2×#805C2211yescharacteristic, complemented
64C2×#805C2211yescharacteristic, complemented
65#4822—24no—
66#4738—21no—
67#4734—21no—
68#4734—21no—
69#4732—21no—
70C3×#339C2211yescharacteristic, complemented
71C3×#339C2211yescharacteristic, complemented
72#4554C2211yescharacteristic, complemented
73#4554C2211yescharacteristic, complemented
74#3488—31no—
75#3055—31no—
76C2×#453—31no—
77#3006—31no—
78C22×#104—31no—
79#2856—31no—
80#2039—31no—
81#2037—31no—
82#2006—31no—
83#2002—31no—
84#1900—31no—
85#1896D311yescharacteristic, complemented
86#1883—31no—
87#1859—31no—
88#1792—31no—
89C2×C3×#41C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C22×#67—21no—
93C22×#67—21no—
94C22×#67D412yes—
95#1009—22no—
96#1009—22no—
97#1009—41no—
98#1009—41no—
99C2×#239—21no—
100C2×D3×D4—22no—
101C2×D3×D4—21no—
102C2×D3×D4—22no—
103C2×#235—21no—
104C2×#235—21no—
105C2×#235—22no—
106C2×#235—22no—
107C2×#235—21no—
108C2×#235—41no—
109C2×#235—41no—
110C2×#235D411yescharacteristic, complemented
111C2×#235D411yescharacteristic, complemented
112C2×#235C2311yescharacteristic
113C2×#235C2311yescharacteristic
114C22×D12—21no—
115C22×D12—22no—
116C22×D12D411yescharacteristic, complemented
117C22×D12C2311yescharacteristic
118C22×D12C2311yescharacteristic
119C22×C4×D3—21no—
120C22×Dic6D411yescharacteristic, complemented
121C2×C3×M16C2311yescharacteristic
122C2×C3×M16C2311yescharacteristic
123C3×#123—21no—
124C3×C22⋊Q8D411yescharacteristic, complemented
125C3×C22⋊Q8D411yescharacteristic, complemented
126C3×#121D411yescharacteristic, complemented
127C3×#121D411yescharacteristic, complemented
128C3×#120—21no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×#117C2311yescharacteristic
132C2×C3×C42—22no—
133C2×C3×C42—21no—
134C2×C3×C42—41no—
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137#949—22no—
138#949—41no—
139#946—21no—
140C2×#215—21no—
141#940—22no—
142#939—22no—
143#939—22no—
144#938—21no—
145#937—22no—
146C2×#213—21no—
147#930—21no—
148#930—21no—
149#930—21no—
150#930—21no—
151#930—21no—
152#930—21no—
153#930—21no—
154#930—21no—
155#930—21no—
156#930—48no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—21no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4D412yes—
161C2×C4⋊Dic3—22no—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164#924—21no—
165C2×#208—21no—
166C2×#208—22no—
167C2×#208—41no—
168C2×#208C2311yescharacteristic
169C2×#208C2311yescharacteristic
170C22×C3⋊C8—21no—
171#908—22no—
172#908—22no—
173#908—41no—
174#908—41no—
175C2×D24—21no—
176C2×D24—21no—
177C2×#204—21no—
178C2×#204—21no—
179#896—22no—
180#895—22no—
181#895—21no—
182#895—21no—
183#894—22no—
184#893—22no—
185#892—21no—
186D3×C4⋊C4—21no—
187#885—22no—
188#884—22no—
189#884—22no—
190#884—22no—
191#882—22no—
192#882—22no—
193#882—22no—
194#67⋊C4—22no—
195#67⋊C4—22no—
196D3×C22⋊C4—22no—
197#875—21no—
198#874—21no—
199#874—22no—
200#874—41no—
201C4×D12—21no—
202C4×Dic6—21no—
203C3×#104—22no—
204C3×#104—41no—
205C3×C22⋊C8—21no—
206C3×C22⋊C8—21no—
207#835—21no—
208#832—21no—
209#823—22no—
210#823—41no—
211#821—21no—
212#821—21no—
213#816—21no—
214#816—21no—
215#809—21no—
216#809—21no—
217#808—21no—
218#807—21no—
219#805—22no—
220#805—22no—
221#805—22no—
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—62no—
232#546—61no—
233D42—61no—
234D42—62no—
235#537—31no—
236#537—61no—
237#535—31no—
238#535—61no—
239C2×#127—31no—
240#525—61no—
241#525C2×D311yescharacteristic
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—31no—
259C2×#104—31no—
260C2×#104—31no—
261C2×#104—31no—
262C2×#104—64no—
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#407C2×D311yescharacteristic, complemented
272#390—31no—
273#390—31no—
274#390—62no—
275#384—31no—
276#343—31no—
277#343—31no—
278#339C2×D311yescharacteristic, complemented
279#339C2×D311yescharacteristic, complemented
280C24×C3C2×D411yescharacteristic
281C23×D3—21no—
282C23×D3—22no—
283C23×D3—21no—
284C23×D3C2×D412yes—
285C3×#41—21no—
286C3×#41—21no—
287C3×#41—21no—
288C3×#41—21no—
289C2×C3×Q8C2×D411yescharacteristic
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4C2×D411yescharacteristic
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—24no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—42no—
303C22×C3×C4—42no—
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2411yescharacteristic
310C2×#67—21no—
311C2×#67—22no—
312C2×#67—22no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—22no—
317C2×#67—22no—
318C2×#67—42no—
319C2×#67—42no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—41no—
323C2×#67—41no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3C2×D412yes—
327#239—42no—
328#239—42no—
329D3×D4—42no—
330D3×D4—42no—
331D3×D4—44no—
332D3×D4—44no—
333D3×D4—84no—
334#235—21no—
335#235—21no—
336#235—21no—
337#235—21no—
338#235—21no—
339#235—21no—
340#235—22no—
341#235—22no—
342#235—41no—
343#235—41no—
344#235—42no—
345#235—42no—
346#235—42no—
347#235—42no—
348#235—42no—
349#235—42no—
350#235C2×D412yes—
351#235#4112yes—
352C2×D12—22no—
353C2×D12—22no—
354C2×D12—21no—
355C2×D12—21no—
356C2×D12—21no—
357C2×D12—21no—
358C2×D12—21no—
359C2×D12—21no—
360C2×D12—21no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12—21no—
365C2×D12—21no—
366C2×D12—21no—
367C2×D12—22no—
368C2×D12—22no—
369C2×D12—41no—
370C2×D12—42no—
371C2×D12—42no—
372C2×D12—44no—
373C2×D12—44no—
374C2×D12—44no—
375C2×D12C2×D411yescharacteristic
376C2×D12C2×D411yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—22no—
379C2×C4×D3—21no—
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—22no—
383C2×C4×D3—42no—
384C2×C4×D3—42no—
385C2×Dic6—22no—
386C2×Dic6—21no—
387C2×Dic6—41no—
388C2×Dic6C2×D411yescharacteristic
389C2×Dic6C2×D411yescharacteristic
390C3×M16—21no—
391C3×M16—21no—
392C3×M16—21no—
393C3×M16—21no—
394C2×C3×C8—21no—
395C2×C3×C8—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4C2×D411yescharacteristic
399C3×C4⋊C4C2×D411yescharacteristic
400C3×C22⋊C4—21no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C42—21no—
406C3×C42—21no—
407C3×C42—21no—
408C3×C42—21no—
409C3×C42—42no—
410C3×C42C2×D412yescomplemented
411#217—22no—
412#215—42no—
413#213—42no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—44no—
421(C2×D3)⋊C4—44no—
422(C2×D3)⋊C4—41no—
423(C2×D3)⋊C4—41no—
424C4⋊Dic3—21no—
425C4⋊Dic3—21no—
426C4⋊Dic3—21no—
427C4⋊Dic3—21no—
428C4⋊Dic3—44no—
429Dic3⋊C4—22no—
430Dic3⋊C4—22no—
431C4×Dic3—22no—
432#208—21no—
433#208—21no—
434#208—21no—
435#208—42no—
436#208C2×D412yescomplemented
437C2×C3⋊C8—21no—
438C2×C3⋊C8—21no—
439C2×C3⋊C8—42no—
440D24—42no—
441D24—42no—
442#204—42no—
443#204—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—61no—
453C2×#41—62no—
454C2×#41—62no—
455C2×#41—61no—
456C2×#41—61no—
457C2×#41—61no—
458C2×#41—121no—
459C2×#41—121no—
460C2×#41C22×D311yescharacteristic
461C22×Q8—31no—
462C22×D4—32no—
463C22×D4—31no—
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×D4—61no—
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—61no—
491C2×M16—62no—
492C2×M16—121no—
493C2×M16C22×D311yescharacteristic
494C2×M16C22×D311yescharacteristic
495C22×C8—61no—
496#127—61no—
497#127—62no—
498#127—62no—
499#127—121no—
500#124—61no—
501#124—62no—
502#123—21no—
503#123—62no—
504C22⋊Q8—62no—
505C22⋊Q8—61no—
506C22⋊Q8—61no—
507C22⋊Q8D1211yescharacteristic, complemented
508C22⋊Q8D1211yescharacteristic, complemented
509#121—62no—
510#121—62no—
511#121—62no—
512#121—62no—
513#121—61no—
514#121—62no—
515#121—62no—
516#121—61no—
517#121—61no—
518#121—61no—
519#121—61no—
520#121—61no—
521#121—61no—
522#121—61no—
523#121—61no—
524#121—61no—
525#121—61no—
526#121—61no—
527#121—128no—
528#121D1211yescharacteristic, complemented
529#121D1211yescharacteristic, complemented
530#120—21no—
531#120—62no—
532#120—62no—
533#120—62no—
534#120—62no—
535C4×Q8—61no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—61no—
539C4×D4—62no—
540C4×D4—62no—
541C4×D4—62no—
542#117—61no—
543#117C22×D311yescharacteristic
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—34no—
562#104—41no—
563#104—62no—
564#104—62no—
565#104—62no—
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—21no—
577C22⋊C8—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—22no—
581C23×C3—21no—
582C23×C3—41no—
583C23×C3#12011yescharacteristic
584C23×C3#12011yescharacteristic
585C23×C3C22×D411yescharacteristic
586C22×D3—21no—
587C22×D3—22no—
588C22×D3—21no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—42no—
592C22×D3—44no—
593C22×D3—42no—
594C22×D3—42no—
595C22×D3—42no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—81no—
602C22×D3—82no—
603C22×D3—82no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×D4—21no—
607C3×D4—21no—
608C3×D4—41no—
609C3×D4—41no—
610C3×D4—42no—
611C3×D4—81no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—22no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—48no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4#12011yescharacteristic
635C2×C3×C4#12011yescharacteristic
636C2×C3×C4C22×D411yescharacteristic
637C2×C3×C4C22×D411yescharacteristic
638C2×C3×C4C22×D411yescharacteristic
639C2×C3×C4C2×#4111yescharacteristic
640C2×C3×C4H(5,𝔽2)11yescharacteristic
641C2×C3×C4H(5,𝔽2)11yescharacteristic
642#67—22no—
643#67—22no—
644#67—42no—
645#67—44no—
646#67—42no—
647#67—41no—
648#67—41no—
649#67—44no—
650#67—82no—
651#67—82no—
652#67—82no—
653#67—82no—
654C2×Dic3—21no—
655C2×Dic3—22no—
656C2×Dic3—21no—
657C2×Dic3—42no—
658C2×Dic3—42no—
659C2×Dic3—42no—
660C2×Dic3—41no—
661D12—21no—
662D12—21no—
663D12—21no—
664D12—42no—
665D12—44no—
666D12—41no—
667D12—41no—
668D12—41no—
669D12—41no—
670D12—41no—
671D12—41no—
672D12—41no—
673D12—41no—
674D12—88no—
675D12—82no—
676D12—82no—
677D12#12112yescomplemented
678C4×D3—22no—
679C4×D3—22no—
680C4×D3—42no—
681C4×D3—44no—
682C4×D3—42no—
683C4×D3—41no—
684C4×D3—41no—
685C4×D3—82no—
686Dic6—21no—
687Dic6—21no—
688Dic6—21no—
689Dic6—42no—
690Dic6#12112yescomplemented
691C3×C8—41no—
692C3×C8—41no—
693C3⋊C8—22no—
694C3⋊C8—41no—
695C24—32no—
696C24—62no—
697C24—61no—
698C24—61no—
699C24D3×D411yescharacteristic
700#41—21no—
701#41—21no—
702#41—21no—
703#41—21no—
704#41—32no—
705#41—32no—
706#41—62no—
707#41—62no—
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—62no—
727C2×Q8—61no—
728C2×Q8—121no—
729C2×Q8C2×D1211yescharacteristic
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—31no—
734C2×D4—31no—
735C2×D4—62no—
736C2×D4—62no—
737C2×D4—62no—
738C2×D4—62no—
739C2×D4—61no—
740C2×D4—62no—
741C2×D4—62no—
742C2×D4—61no—
743C2×D4—61no—
744C2×D4—61no—
745C2×D4—62no—
746C2×D4—62no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
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—121no—
761C2×D4—124no—
762C2×D4—124no—
763C2×D4—124no—
764C2×D4—122no—
765C2×D4—122no—
766C2×D4—122no—
767C2×D4—122no—
768C2×D4—124no—
769C2×D4—124no—
770C2×D4—122no—
771C2×D4—122no—
772C2×D4—124no—
773C2×D4—124no—
774C2×D4—121no—
775C2×D4—121no—
776C2×D4—244no—
777C2×D4C2×D1211yescharacteristic
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—32no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—62no—
790C22×C4—62no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—122no—
798C22×C4—122no—
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—21no—
815M16—32no—
816M16—61no—
817M16—61no—
818M16—61no—
819M16—122no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—61no—
823C2×C8—61no—
824C2×C8—122no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—62no—
828C4⋊C4—62no—
829C4⋊C4—61no—
830C4⋊C4—61no—
831C4⋊C4—61no—
832C4⋊C4—61no—
833C4⋊C4—124no—
834C4⋊C4C2×D1211yescharacteristic
835C4⋊C4C2×D1211yescharacteristic
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—62no—
842C22⋊C4—62no—
843C22⋊C4—62no—
844C22⋊C4—62no—
845C22⋊C4—62no—
846C22⋊C4—62no—
847C22⋊C4—62no—
848C22⋊C4—124no—
849C22⋊C4—124no—
850C22⋊C4—121no—
851C22⋊C4—121no—
852C42—21no—
853C42—21no—
854C42—21no—
855C42—21no—
856C42—42no—
857C42—62no—
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—41no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3#45312yescomplemented
872C22×C3C2×#12011yescharacteristic
873C22×C3D4211yescharacteristic
874C22×C3#54611yescharacteristic
875C2×D3—22no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—42no—
880C2×D3—41no—
881C2×D3—42no—
882C2×D3—41no—
883C2×D3—42no—
884C2×D3—84no—
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—21no—
895C3×C4—21no—
896C3×C4—42no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4C2×#12111yescharacteristic
901C3×C4#53411yescharacteristic
902C3×C4D4211yescharacteristic
903C3×C4#54611yescharacteristic
904Dic3—22no—
905Dic3—41no—
906Dic3—42no—
907Dic3—81no—
908C23—21no—
909C23—22no—
910C23—21no—
911C23—21no—
912C23—41no—
913C23—61no—
914C23—62no—
915C23—61no—
916C23—62no—
917C23—62no—
918C23—122no—
919C23—122no—
920C23—122no—
921C23—122no—
922C23—122no—
923C23—124no—
924C23—122no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—241no—
929C23—242no—
930C23—242no—
931C23#88211yescharacteristic
932C23#88211yescharacteristic
933C23C2×D3×D411yescharacteristic
934Q8—21no—
935Q8—21no—
936Q8—32no—
937Q8—61no—
938Q8—61no—
939Q8—61no—
940Q8—122no—
941D4—21no—
942D4—21no—
943D4—32no—
944D4—41no—
945D4—42no—
946D4—41no—
947D4—62no—
948D4—62no—
949D4—61no—
950D4—61no—
951D4—61no—
952D4—81no—
953D4—122no—
954D4—124no—
955D4—122no—
956D4—124no—
957D4—122no—
958D4—121no—
959D4—124no—
960D4—121no—
961D4—121no—
962D4—121no—
963D4—121no—
964D4—121no—
965D4—121no—
966D4—121no—
967D4—121no—
968D4—121no—
969D4—248no—
970D4—242no—
971D4—242no—
972D4—242no—
973D4—242no—
974D4—242no—
975D4—242no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
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—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—48no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—61no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—61no—
1003C2×C4—122no—
1004C2×C4—122no—
1005C2×C4—124no—
1006C2×C4—122no—
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×D3×D411yescharacteristic
1017C2×C4C2×D3×D411yescharacteristic
1018C2×C4#100411yescharacteristic
1019C2×C4D3×#4111yescharacteristic
1020C2×C4#100911yescharacteristic
1021C8—41no—
1022C8—41no—
1023C8—62no—
1024C8—121no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—22no—
1028C2×C3—41no—
1029C2×C3—81no—
1030C2×C3#241011yescharacteristic
1031C2×C3C2×#45311yescharacteristic
1032C2×C3#301811yescharacteristic
1033D3—42no—
1034D3—81no—
1035D3—82no—
1036D3—161no—
1037C22—21no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—42no—
1045C22—42no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—62no—
1050C22—121no—
1051C22—121no—
1052C22—121no—
1053C22—122no—
1054C22—122no—
1055C22—121no—
1056C22—121no—
1057C22—122no—
1058C22—244no—
1059C22—242no—
1060C22—242no—
1061C22—242no—
1062C22—242no—
1063C22—241no—
1064C22—241no—
1065C22—241no—
1066C22—484no—
1067C22#482212yescomplemented
1068C22C2×#88211yescharacteristic
1069C22#559011yescharacteristic
1070C22#565411yescharacteristic
1071C4—24no—
1072C4—21no—
1073C4—21no—
1074C4—42no—
1075C4—41no—
1076C4—41no—
1077C4—41no—
1078C4—62no—
1079C4—121no—
1080C4—122no—
1081C4—241no—
1082C4D4×D1211yescharacteristic
1083C4#555411yescharacteristic
1084C4D3×#12111yescharacteristic
1085C4#560511yescharacteristic
1086C3#2446411yescharacteristic, complemented, Sylow
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—81no—
1092C2—122no—
1093C2—241no—
1094C2—242no—
1095C2—481no—
1096C2#7488811yescharacteristic
1097C2C2×#482211yescharacteristic
1098C2#7898611yescharacteristic
subgroupG/H
centerC22C2×#882
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1896C2
socleC22×C3C2×#120
hypercenter#1896D3
hypocenterC3#24464
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
1. #86041C2semidirect
2. #82924C2semidirect
3. #82081C2semidirect
4. C22×#805C2semidirect
5. C2×#4822C2semidirect
6. #78639C2semidirect
7. C3×#1896C2semidirect
8. #70392C2semidirect
9. #70384C2semidirect
10. #70361C2semidirect
11. #69985C2semidirect
12. #68776C2semidirect
13. #68771C2semidirect
14. #68761C2semidirect
15. #68733C2semidirect
20. C22×C3×C42C22semidirect
22. C2×#949C22semidirect
25. C2×#930C22semidirect
26. C22×#208C22semidirect
28. C2×#908C22semidirect
41. C2×#874C22semidirect
42. C2×C3×#104C22semidirect
43. C2×C3×#104C22semidirect
44. C3×#407C22semidirect
45. #5232C22semidirect
47. #5133C22semidirect
48. C2×#823C22semidirect
49. C2×#823C22semidirect
54. #5001C22semidirect
55. #4995C22semidirect
57. #4939C22semidirect
58. #4939C22semidirect
59. #4935C22semidirect
63. C2×#805C22semidirect
64. C2×#805C22semidirect
70. C3×#339C22semidirect
71. C3×#339C22semidirect
72. #4554C22semidirect
73. #4554C22semidirect
85. #1896D3semidirect
110. C2×#235D4semidirect
111. C2×#235D4semidirect
116. C22×D12D4semidirect
120. C22×Dic6D4semidirect
124. C3×C22⋊Q8D4semidirect
125. C3×C22⋊Q8D4semidirect
126. C3×#121D4semidirect
127. C3×#121D4semidirect
222. #805D4semidirect
247. C22×C42C2×D3semidirect
263. C2×#104C2×D3semidirect
264. C2×#104C2×D3semidirect
271. #407C2×D3semidirect
278. #339C2×D3semidirect
279. #339C2×D3semidirect
410. C3×C42C2×D4semidirect
436. #208C2×D4semidirect
507. C22⋊Q8D12semidirect
508. C22⋊Q8D12semidirect
528. #121D12semidirect
529. #121D12semidirect
677. D12#121semidirect
690. Dic6#121semidirect
858. C42D3×D4semidirect
871. C22×C3#453semidirect
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
#860412
#829242
#820812
C22×#8052
C2×#48222
#786392
C3×#18962
#703922
#703842
#703612
#699852
#687762
#687712
#687612
#687332
#244643