Finite Group Databasebeta

← #10833350

Subgroups — #10833350

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
2C3×#3006C211yesmaximal, characteristic, complemented
3C22×#837C211yesmaximal, characteristic, complemented
4C2×#5198C211yesmaximal, characteristic, complemented
5#82700C211yesmaximal, characteristic, complemented
6#82621C211yesmaximal, characteristic, complemented
7#72098C211yesmaximal, characteristic, complemented
8#72094C211yesmaximal, characteristic, complemented
9#72088C211yesmaximal, characteristic, complemented
10#70311C211yesmaximal, characteristic, complemented
11#70306C211yesmaximal, characteristic, complemented
12#70305C211yesmaximal, characteristic, complemented
13#70297C211yesmaximal, characteristic, complemented
14#69985C211yesmaximal, characteristic, complemented
15#69965C211yesmaximal, characteristic, complemented
16#24464—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×#1009C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C2×C3×#121C2211yescharacteristic, complemented
22#5834—21no—
23#5833—21no—
24#5833C2211yescharacteristic
25#5830—21no—
26#5830C2211yescharacteristic
27#5829—21no—
28#5829—22no—
29#5827C2211yescharacteristic
30#5817—21no—
31C2×#940C2211yescharacteristic, complemented
32C2×#939—22no—
33D4×#67—21no—
34D4×#67—22no—
35C2×#932C2211yescharacteristic, complemented
36#5791—21no—
37#5791C2211yescharacteristic
38C2×#930—21no—
39C2×#930C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic, complemented
41C22×#208C2211yescharacteristic, complemented
42C3×#449—21no—
43C3×#449—21no—
44C3×#448—21no—
45C3×#447—21no—
46C3×#417C2211yescharacteristic
47C3×#417C2211yescharacteristic, complemented
48C3×#407C2211yescharacteristic, complemented
49C2×#837—24no—
50C2×#837C2211yescharacteristic
51C2×#837C2211yescharacteristic
52C2×#837C2211yescharacteristic, complemented
53C2×#837C2211yescharacteristic, complemented
54#5221C2211yescharacteristic, complemented
55#5215C2211yescharacteristic, complemented
56#5198—24no—
57C2×#825C2211yescharacteristic, complemented
58C2×#825C2211yescharacteristic, complemented
59C2×#823C2211yescharacteristic, complemented
60C2×#823C2211yescharacteristic, complemented
61#5042—21no—
62#5041—21no—
63#5039—21no—
64#5038—21no—
65#4988C2211yescharacteristic, complemented
66#4975C2211yescharacteristic, complemented
67#4966C2211yescharacteristic, complemented
68#4964C2211yescharacteristic, complemented
69#4957—22no—
70#4555C2211yescharacteristic, complemented
71#4555C2211yescharacteristic, complemented
72#4554C2211yescharacteristic, complemented
73#4554C2211yescharacteristic, complemented
74#3488—31no—
75#3055—31no—
76C2×#453—31no—
77#3006D311yescharacteristic, complemented
78C22×#104—31no—
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×D4—21no—
102C22×C3×D4D411yescharacteristic, complemented
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4—21no—
105C23×C3×C4C2311yescharacteristic
106C22×#67—22no—
107C22×#67—22no—
108C22×#67D412yes—
109C23×Dic3—21no—
110#1009—22no—
111#1009—22no—
112#1009—41no—
113#1009—41no—
114C2×#239—21no—
115C2×D3×D4—22no—
116C2×D3×D4—21no—
117C2×#235—21no—
118C2×#235C2311yescharacteristic
119C22×D12—21no—
120C22×D12C2311yescharacteristic
121C3×AGL(1,ℤ/8)—22no—
122C3×AGL(1,ℤ/8)—22no—
123C3×AGL(1,ℤ/8)—41no—
124C3×AGL(1,ℤ/8)—41no—
125C2×C3×SD16—21no—
126C2×C3×SD16—21no—
127C2×C3×D8—21no—
128C2×C3×D8—21no—
129C2×C3×M16C2311yescharacteristic
130C2×C3×M16C2311yescharacteristic
131C3×#121—21no—
132C3×#121—21no—
133C3×#121—21no—
134C3×#121—21no—
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C22⋊C4—21no—
137#953—22no—
138#953—21no—
139C2×#217—22no—
140#947—22no—
141#947—21no—
142#946—22no—
143#946—21no—
144Q8×Dic3—21no—
145#940—22no—
146#940—21no—
147#940—22no—
148#940—41no—
149#939—22no—
150#939—22no—
151#939—22no—
152#939—48no—
153#938—22no—
154#938—21no—
155#937—22no—
156#937—22no—
157#937—22no—
158D4×Dic3—21no—
159D4×Dic3—22no—
160C2×#214—21no—
161#932—22no—
162#932—41no—
163C2×#213—21no—
164#930—22no—
165#930—22no—
166#930—21no—
167#930—21no—
168#930—21no—
169#930—21no—
170#930—21no—
171#930—21no—
172#930—21no—
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)⋊C4D412yes—
184#926—21no—
185#926C2311yescharacteristic
186C2×C4⋊Dic3—21no—
187C2×C4⋊Dic3C2311yescharacteristic
188#924—21no—
189#924D411yescharacteristic, complemented
190#924D411yescharacteristic, complemented
191C2×Dic3⋊C4—22no—
192C2×C4×Dic3—22no—
193C2×C4×Dic3—21no—
194C2×C4×Dic3—41no—
195C2×C4×Dic3C2311yescharacteristic
196C2×C4×Dic3C2311yescharacteristic
197C2×#208—21no—
198C2×#208—22no—
199C2×#208—41no—
200C2×#208C2311yescharacteristic
201C2×#208C2311yescharacteristic
202C22×C3⋊C8—21no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#102—21no—
206C3×#102—21no—
207C3×C22⋊C8—21no—
208C3×C22⋊C8—21no—
209#837—22no—
210#837—22no—
211#837—22no—
212#837D414yescomplemented
213#832—21no—
214#832—21no—
215#825—22no—
216#825—41no—
217#823—22no—
218#823—41no—
219#810—21no—
220#809—21no—
221#808—21no—
222#807—21no—
223C2×H(5,𝔽2)—31no—
224C22×#41C2×D311yescharacteristic
225C2×AGL(1,ℤ/8)—31no—
226C2×AGL(1,ℤ/8)C2×D311yescharacteristic
227C2×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
228C22×M16—31no—
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—61no—
244C2×#121—62no—
245C2×#121C2×D311yescharacteristic, complemented
246#520—31no—
247C22×C42—31no—
248#469—61no—
249#468—61no—
250#466—61no—
251#465—61no—
252#453—64no—
253#449—21no—
254#449—21no—
255#448—21no—
256#447—21no—
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#417C2×D311yescharacteristic
268#417C2×D311yescharacteristic, complemented
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#339—31no—
279#339—31no—
280C24×C3—21no—
281C24×C3—21no—
282C24×C3C2×D411yescharacteristic
283C23×D3—22no—
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—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—41no—
319C2×C3×D4—42no—
320C2×C3×D4—42no—
321C2×C3×D4—44no—
322C2×C3×D4—41no—
323C2×C3×D4—41no—
324C2×C3×D4C2×D411yescharacteristic
325C2×C3×D4C2×D411yescharacteristic
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—42no—
337C22×C3×C4—42no—
338C22×C3×C4C2×D411yescharacteristic
339C22×C3×C4C2×D411yescharacteristic
340C22×C3×C4C2×D411yescharacteristic
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2411yescharacteristic
344C2×#67—22no—
345C2×#67—22no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—22no—
349C2×#67—22no—
350C2×#67—22no—
351C2×#67—21no—
352C2×#67—22no—
353C2×#67—44no—
354C2×#67—44no—
355C2×#67—44no—
356C2×#67—44no—
357C2×#67—84no—
358C22×Dic3—21no—
359C22×Dic3—24no—
360C22×Dic3—21no—
361C22×Dic3—22no—
362C22×Dic3—42no—
363C22×Dic3—42no—
364C22×Dic3C2×D412yes—
365#239—42no—
366#239—42no—
367D3×D4—44no—
368D3×D4—44no—
369D3×D4—42no—
370D3×D4—42no—
371#235—21no—
372#235—21no—
373#235—21no—
374#235—21no—
375#235—42no—
376#235—42no—
377C2×D12—22no—
378C2×D12—21no—
379C2×D12—21no—
380C2×D12—21no—
381C2×D12—21no—
382C2×D12—21no—
383C2×D12—21no—
384C2×D12—42no—
385C2×D12—42no—
386C2×D12C2×D411yescharacteristic
387C2×C4×D3—22no—
388C2×C4×D3—21no—
389C2×Dic6C2×D411yescharacteristic
390C3×SD16—42no—
391C3×SD16—42no—
392C3×D8—42no—
393C3×D8—42no—
394C3×M16—21no—
395C3×M16—21no—
396C3×M16—21no—
397C3×M16—21no—
398C2×C3×C8—21no—
399C2×C3×C8—21no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C22⋊C4—41no—
403C3×C22⋊C4—41no—
404#217—22no—
405#217—22no—
406#217—21no—
407#217—21no—
408#217—21no—
409#217—44no—
410#214—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—
420C4⋊Dic3—22no—
421C4⋊Dic3—21no—
422C4⋊Dic3—21no—
423C4⋊Dic3C2×D411yescharacteristic
424C4⋊Dic3C2×D411yescharacteristic
425Dic3⋊C4—22no—
426Dic3⋊C4—21no—
427Dic3⋊C4—21no—
428Dic3⋊C4—44no—
429C4×Dic3—22no—
430C4×Dic3—21no—
431C4×Dic3—21no—
432C4×Dic3—21no—
433C4×Dic3—21no—
434C4×Dic3—42no—
435C4×Dic3C2×D412yescomplemented
436#208—21no—
437#208—21no—
438#208—21no—
439#208—42no—
440#208C2×D412yescomplemented
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—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×#41#6711yescharacteristic, complemented
458C2×#41#6711yescharacteristic, complemented
459C2×#41C22×D311yescharacteristic
460C2×#41C22×D311yescharacteristic
461C22×Q8#6711yescharacteristic, complemented
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—32no—
465C22×D4—31no—
466C22×D4—61no—
467C22×D4—62no—
468C22×D4—62no—
469C22×D4—61no—
470C22×D4—62no—
471C22×D4#6711yescharacteristic, complemented
472C22×D4C22×D311yescharacteristic
473C23×C4—21no—
474C23×C4—61no—
475C23×C4C22×D311yescharacteristic
476AGL(1,ℤ/8)—22no—
477AGL(1,ℤ/8)—22no—
478AGL(1,ℤ/8)—41no—
479AGL(1,ℤ/8)—41no—
480AGL(1,ℤ/8)—62no—
481AGL(1,ℤ/8)—121no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×SD16—61no—
485C2×D8—21no—
486C2×D8—21no—
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—62no—
497#127—62no—
498#127—61no—
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—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—31no—
514#121—31no—
515#121—61no—
516#121—61no—
517#121—61no—
518#121—62no—
519#121—62no—
520#121—62no—
521#121—62no—
522#121—62no—
523#121—62no—
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—61no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4C22×D311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—32no—
550C2×C22⋊C4—62no—
551C2×C22⋊C4—62no—
552C2×C22⋊C4—62no—
553C2×C42—31no—
554C2×C42—31no—
555C2×C42—62no—
556C2×C42—61no—
557C2×C42—121no—
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—21no—
567#103—21no—
568#103—61no—
569#102—21no—
570#102—21no—
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—21no—
581C23×C3—22no—
582C23×C3—21no—
583C23×C3—41no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—42no—
587C23×C3—42no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—81no—
592C23×C3#12011yescharacteristic
593C23×C3#12011yescharacteristic
594C23×C3C22×D411yescharacteristic
595C22×D3—22no—
596C22×D3—21no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—44no—
600C22×D3—42no—
601C22×D3—42no—
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—41no—
620C3×D4—41no—
621C3×D4—41no—
622C3×D4—41no—
623C3×D4—82no—
624C3×D4—82no—
625C3×D4#12112yescomplemented
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—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—42no—
641C2×C3×C4—42no—
642C2×C3×C4—42no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—42no—
646C2×C3×C4—41no—
647C2×C3×C4#12011yescharacteristic
648C2×C3×C4#12011yescharacteristic
649C2×C3×C4C22×D411yescharacteristic
650C2×C3×C4C22×D411yescharacteristic
651C2×C3×C4C22×D411yescharacteristic
652C2×C3×C4C2×#4111yescharacteristic
653C2×C3×C4H(5,𝔽2)11yescharacteristic
654C2×C3×C4H(5,𝔽2)11yescharacteristic
655#67—44no—
656#67—41no—
657#67—41no—
658#67—44no—
659#67—42no—
660#67—88no—
661#67—81no—
662#67—82no—
663#67—82no—
664#67—82no—
665#67—82no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—21no—
671C2×Dic3—22no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—48no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—42no—
678C2×Dic3—82no—
679D12—21no—
680D12—21no—
681D12—44no—
682D12—41no—
683D12—41no—
684D12—41no—
685D12—41no—
686C4×D3—44no—
687C4×D3—41no—
688C4×D3—41no—
689Dic6—21no—
690Dic6—21no—
691C3×C8—41no—
692C3×C8—41no—
693C3⋊C8—22no—
694C3⋊C8—41no—
695C24—21no—
696C24—21no—
697C24—32no—
698C24—62no—
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#41D3×D412yes—
723#41#23712yes—
724C2×Q8—21no—
725C2×Q8—22no—
726C2×Q8—31no—
727C2×Q8—41no—
728C2×Q8C2×#6711yescharacteristic
729C2×Q8C2×#6711yescharacteristic
730C2×D4—21no—
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—31no—
743C2×D4—41no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—44no—
747C2×D4—41no—
748C2×D4—41no—
749C2×D4—62no—
750C2×D4—62no—
751C2×D4—61no—
752C2×D4—62no—
753C2×D4—61no—
754C2×D4—62no—
755C2×D4—62no—
756C2×D4—62no—
757C2×D4—61no—
758C2×D4—62no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—61no—
762C2×D4—61no—
763C2×D4—61no—
764C2×D4—61no—
765C2×D4—122no—
766C2×D4—122no—
767C2×D4—124no—
768C2×D4—124no—
769C2×D4—124no—
770C2×D4—124no—
771C2×D4—124no—
772C2×D4—122no—
773C2×D4—122no—
774C2×D4—124no—
775C2×D4—244no—
776C2×D4C2×#6711yescharacteristic
777C2×D4C2×#6711yescharacteristic
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—32no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—62no—
792C22×C4—61no—
793C22×C4—64no—
794C22×C4—61no—
795C22×C4—62no—
796C22×C4—61no—
797C22×C4—122no—
798C22×C4—122no—
799C22×C4D3×D411yescharacteristic
800C22×C4D3×D411yescharacteristic
801C22×C4D3×D411yescharacteristic
802C22×C4C2×#6711yescharacteristic
803C22×C4C2×#6711yescharacteristic
804C22×C4C23×D311yescharacteristic
805SD16—42no—
806SD16—42no—
807SD16—122no—
808D8—42no—
809D8—42no—
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—31no—
828C4⋊C4—31no—
829C4⋊C4—62no—
830C4⋊C4—62no—
831C4⋊C4—61no—
832C4⋊C4—61no—
833C4⋊C4—61no—
834C4⋊C4—61no—
835C4⋊C4—124no—
836C22⋊C4—41no—
837C22⋊C4—41no—
838C22⋊C4—62no—
839C22⋊C4—62no—
840C22⋊C4—62no—
841C22⋊C4—62no—
842C22⋊C4—62no—
843C22⋊C4—61no—
844C22⋊C4—61no—
845C22⋊C4—61no—
846C22⋊C4—62no—
847C22⋊C4—62no—
848C22⋊C4—61no—
849C22⋊C4—61no—
850C22⋊C4—124no—
851C22⋊C4—124no—
852C42—32no—
853C42—62no—
854C42—61no—
855C42—61no—
856C42—61no—
857C42—61no—
858C42—122no—
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—82no—
876C22×C3—82no—
877C22×C3—81no—
878C22×C3—81no—
879C22×C3—81no—
880C22×C3#45312yescomplemented
881C22×C3C2×#12011yescharacteristic
882C22×C3D4211yescharacteristic
883C22×C3#54611yescharacteristic
884C2×D3—41no—
885C2×D3—42no—
886C2×D3—42no—
887C2×D3—41no—
888C2×D3—42no—
889C2×D3—41no—
890C2×D3—82no—
891C2×D3—82no—
892C2×D3—164no—
893C3×C4—22no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—41no—
897C3×C4—81no—
898C3×C4C2×#12111yescharacteristic
899C3×C4#53411yescharacteristic
900C3×C4D4211yescharacteristic
901C3×C4#54611yescharacteristic
902Dic3—24no—
903Dic3—42no—
904Dic3—41no—
905Dic3—42no—
906Dic3—41no—
907Dic3—41no—
908C23—22no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—41no—
914C23—42no—
915C23—42no—
916C23—42no—
917C23—42no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—61no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—81no—
926C23—124no—
927C23—122no—
928C23—122no—
929C23—242no—
930C23—242no—
931C23#93711yescharacteristic
932C23#93711yescharacteristic
933C23C2×D3×D411yescharacteristic
934Q8—21no—
935Q8—21no—
936Q8—21no—
937Q8—42no—
938Q8—61no—
939Q8—61no—
940Q8#93912yescomplemented
941D4—22no—
942D4—22no—
943D4—21no—
944D4—21no—
945D4—21no—
946D4—42no—
947D4—42no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—41no—
954D4—41no—
955D4—61no—
956D4—61no—
957D4—82no—
958D4—82no—
959D4—124no—
960D4—124no—
961D4—124no—
962D4—122no—
963D4—121no—
964D4—121no—
965D4—121no—
966D4—121no—
967D4—121no—
968D4—121no—
969D4—248no—
970D4—242no—
971D4—241no—
972D4—242no—
973D4—242no—
974D4—242no—
975D4#93912yescomplemented
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—42no—
996C2×C4—41no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—62no—
1004C2×C4—61no—
1005C2×C4—124no—
1006C2×C4—128no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—122no—
1012C2×C4—242no—
1013C2×C4#93711yescharacteristic
1014C2×C4#93711yescharacteristic
1015C2×C4C2×D3×D411yescharacteristic
1016C2×C4C2×D3×D411yescharacteristic
1017C2×C4C2×#23711yescharacteristic
1018C2×C4#100411yescharacteristic
1019C2×C4#100411yescharacteristic
1020C2×C4C22×#6711yescharacteristic
1021C8—41no—
1022C8—41no—
1023C8—62no—
1024C8—121no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—22no—
1028C2×C3—42no—
1029C2×C3—41no—
1030C2×C3—81no—
1031C2×C3—161no—
1032C2×C3#241011yescharacteristic
1033C2×C3C2×#45311yescharacteristic
1034C2×C3#301811yescharacteristic
1035D3—82no—
1036D3—81no—
1037C22—21no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—42no—
1046C22—42no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—84no—
1053C22—82no—
1054C22—82no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—122no—
1059C22—121no—
1060C22—121no—
1061C22—122no—
1062C22—122no—
1063C22—121no—
1064C22—242no—
1065C22—242no—
1066C22—484no—
1067C22#519812yescomplemented
1068C22#559011yescharacteristic
1069C22#559111yescharacteristic
1070C22C2×#93711yescharacteristic
1071C4—21no—
1072C4—21no—
1073C4—22no—
1074C4—41no—
1075C4—64no—
1076C4—81no—
1077C4—122no—
1078C4—121no—
1079C4—121no—
1080C4—122no—
1081C4—121no—
1082C4#559011yescharacteristic
1083C4#559111yescharacteristic
1084C4C2×#93911yescharacteristic
1085C4#580411yescharacteristic
1086C3#2446411yescharacteristic, complemented, Sylow
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—161no—
1094C2—242no—
1095C2—241no—
1096C2#8260611yescharacteristic
1097C2C2×#519811yescharacteristic
1098C2#8400411yescharacteristic
subgroupG/H
centerC22C2×#937
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3006C2
socleC22×C3C2×#120
hypercenter#3006D3
hypocenterC3#24464
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. #87275C2semidirect
2. C3×#3006C2semidirect
3. C22×#837C2semidirect
4. C2×#5198C2semidirect
5. #82700C2semidirect
6. #82621C2semidirect
7. #72098C2semidirect
8. #72094C2semidirect
9. #72088C2semidirect
10. #70311C2semidirect
11. #70306C2semidirect
12. #70305C2semidirect
13. #70297C2semidirect
14. #69985C2semidirect
15. #69965C2semidirect
20. C2×C3×AGL(1,ℤ/8)C22semidirect
21. C2×C3×#121C22semidirect
31. C2×#940C22semidirect
35. C2×#932C22semidirect
40. C22×C4×Dic3C22semidirect
41. C22×#208C22semidirect
47. C3×#417C22semidirect
48. C3×#407C22semidirect
52. C2×#837C22semidirect
53. C2×#837C22semidirect
54. #5221C22semidirect
55. #5215C22semidirect
57. C2×#825C22semidirect
58. C2×#825C22semidirect
59. C2×#823C22semidirect
60. C2×#823C22semidirect
65. #4988C22semidirect
66. #4975C22semidirect
67. #4966C22semidirect
68. #4964C22semidirect
70. #4555C22semidirect
71. #4555C22semidirect
72. #4554C22semidirect
73. #4554C22semidirect
77. #3006D3semidirect
95. C2×C3×#41D4semidirect
96. C2×C3×#41D4semidirect
99. C22×C3×Q8D4semidirect
102. C22×C3×D4D4semidirect
173. #930D4semidirect
174. #930D4semidirect
189. #924D4semidirect
190. #924D4semidirect
212. #837D4semidirect
227. C2×AGL(1,ℤ/8)C2×D3semidirect
245. C2×#121C2×D3semidirect
268. #417C2×D3semidirect
271. #407C2×D3semidirect
435. C4×Dic3C2×D4semidirect
440. #208C2×D4semidirect
457. C2×#41#67semidirect
458. C2×#41#67semidirect
461. C22×Q8#67semidirect
471. C22×D4#67semidirect
608. C3×Q8#121semidirect
625. C3×D4#121semidirect
880. C22×C3#453semidirect
940. Q8#939semidirect
975. D4#939semidirect
1067. C22#5198semidirect
1086. C3#24464semidirect

Maximal subgroups

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

subgroupindex
#872752
C3×#30062
C22×#8372
C2×#51982
#827002
#826212
#720982
#720942
#720882
#703112
#703062
#703052
#702972
#699852
#699652
#244643