Finite Group Databasebeta

← #10833348

Subgroups — #10833348

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
1C3×#3488C211yesmaximal, characteristic, complemented
2C2×#5241C211yesmaximal, characteristic, complemented
3#84082C211yesmaximal, characteristic, complemented
4C22×#837C211yesmaximal, characteristic, complemented
5#82924C211yesmaximal, characteristic, complemented
6#82700C211yesmaximal, characteristic, complemented
7#72140C211yesmaximal, characteristic, complemented
8#71879C211yesmaximal, characteristic, complemented
9#71876C211yesmaximal, characteristic, complemented
10#71856C211yesmaximal, characteristic, complemented
11#71852C211yesmaximal, characteristic, complemented
12#71711C211yesmaximal, characteristic, complemented
13#71683C211yesmaximal, characteristic, complemented
14#71667C211yesmaximal, characteristic, complemented
15#71664C211yesmaximal, characteristic, complemented
16#24464—31nomaximal, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C3×#550—21no—
20C3×#548—21no—
21C3×#546—21no—
22C3×#546—22no—
23C3×D42—22no—
24C3×D42—21no—
25C3×#537—21no—
26C3×#537C2211yescharacteristic
27C3×#535—21no—
28C3×#535C2211yescharacteristic
29C3×#525—21no—
30C3×#525C2211yescharacteristic
31C2×C3×#121—21no—
32C2×C3×#121C2211yescharacteristic
33C3×#520C2211yescharacteristic
34C2×#949C2211yescharacteristic
35C2×#949C2211yescharacteristic, complemented
36C2×#949C2211yescharacteristic, complemented
37C2×#940C2211yescharacteristic, complemented
38C2×#939—22no—
39C2×#930C2211yescharacteristic, complemented
40C22×C4×Dic3C2211yescharacteristic, complemented
41C22×#208C2211yescharacteristic, complemented
42#5241—24no—
43#5238—21no—
44#5238—21no—
45C2×#837—24no—
46C2×#837C2211yescharacteristic
47C2×#837C2211yescharacteristic
48C2×#837C2211yescharacteristic, complemented
49C2×#837C2211yescharacteristic, complemented
50C2×#837C2211yescharacteristic, complemented
51C2×#837C2211yescharacteristic, complemented
52#5232C2211yescharacteristic
53#5232C2211yescharacteristic, complemented
54#5232C2211yescharacteristic, complemented
55#5227—21no—
56#5221C2211yescharacteristic, complemented
57#5217—21no—
58C2×#833C2211yescharacteristic, complemented
59C2×#833C2211yescharacteristic, complemented
60#5207C2211yescharacteristic, complemented
61#5049—21no—
62#5048—21no—
63#5039—21no—
64#5038—21no—
65#5001C2211yescharacteristic, complemented
66#4995C2211yescharacteristic, complemented
67#4988C2211yescharacteristic, complemented
68#4975C2211yescharacteristic, complemented
69#4957—22no—
70#4532C2211yescharacteristic, complemented
71#4532C2211yescharacteristic, complemented
72#4530C2211yescharacteristic, complemented
73#4530C2211yescharacteristic, complemented
74#3488D311yescharacteristic, complemented
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#1896—31no—
86#1883—31no—
87#1859—31no—
88#1792—31no—
89C3×H(5,𝔽2)—22no—
90C3×H(5,𝔽2)—22no—
91C3×H(5,𝔽2)—41no—
92C3×H(5,𝔽2)—41no—
93C2×C3×#41—21no—
94C2×C3×#41—21no—
95C2×C3×#41—21no—
96C2×C3×#41—21no—
97C2×C3×#41—22no—
98C2×C3×#41—22no—
99C2×C3×#41—41no—
100C2×C3×#41—41no—
101C2×C3×#41D411yescharacteristic, complemented
102C2×C3×#41D411yescharacteristic, complemented
103C2×C3×#41C2311yescharacteristic
104C2×C3×#41C2311yescharacteristic
105C2×C3×#41C2311yescharacteristic
106C22×C3×Q8D411yescharacteristic, complemented
107C22×C3×D4—21no—
108C22×C3×D4—22no—
109C22×C3×D4—22no—
110C22×C3×D4—21no—
111C22×C3×D4—21no—
112C22×C3×D4D412yes—
113C22×C3×D4D411yescharacteristic, complemented
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C23×C3×C4C2311yescharacteristic
117C22×#67—22no—
118C22×#67—21no—
119C23×Dic3—21no—
120C22×D12C2311yescharacteristic
121C3×#127—22no—
122C3×#127—21no—
123C3×#124—22no—
124C3×#124—21no—
125C3×#123—22no—
126C3×#123—21no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—21no—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8D411yescharacteristic, complemented
131C3×C22⋊Q8D411yescharacteristic, complemented
132C3×#121—22no—
133C3×#121—22no—
134C3×#121—22no—
135C3×#121—22no—
136C3×#121—22no—
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121—21no—
141C3×#121—21no—
142C3×#121—21no—
143C3×#121—22no—
144C3×#121—21no—
145C3×#121—21no—
146C3×#121D411yescharacteristic, complemented
147C3×#121D411yescharacteristic, complemented
148C3×#120—22no—
149C3×#120—22no—
150C3×#120—22no—
151C3×#120—21no—
152C3×#120—22no—
153C3×C4×Q8—21no—
154C3×C4×D4—22no—
155C3×C4×D4—22no—
156C3×C4×D4—21no—
157C3×C4×D4—22no—
158C3×C4×D4—21no—
159C3×C4×D4—21no—
160C3×#117—21no—
161C3×#117C2311yescharacteristic
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4C2311yescharacteristic
164C2×C3×C22⋊C4—22no—
165C2×C3×C22⋊C4D412yes—
166C2×#217—22no—
167#949—22no—
168#949—22no—
169#949—22no—
170#949—41no—
171#949—41no—
172#949—41no—
173C2×#215—21no—
174C2×#215—21no—
175C2×#215—21no—
176#940—22no—
177#940—41no—
178#939—48no—
179C2×#213—21no—
180C2×#213—21no—
181C2×#213—21no—
182#930—21no—
183#930—21no—
184#930—21no—
185#930—21no—
186C2×(C2×D3)⋊C4—21no—
187C2×(C2×D3)⋊C4—22no—
188C2×C4⋊Dic3C2311yescharacteristic
189C2×Dic3⋊C4—22no—
190C2×C4×Dic3—22no—
191C2×C4×Dic3—21no—
192C2×C4×Dic3—41no—
193C2×C4×Dic3C2311yescharacteristic
194C2×C4×Dic3C2311yescharacteristic
195C2×#208—21no—
196C2×#208—22no—
197C2×#208—41no—
198C2×#208C2311yescharacteristic
199C2×#208C2311yescharacteristic
200C2×#208C2311yescharacteristic
201C2×#208C2311yescharacteristic
202C22×C3⋊C8—21no—
203#837—22no—
204#837—22no—
205#837—22no—
206#837—22no—
207#837—41no—
208#837D414yescomplemented
209#835—21no—
210#835—21no—
211#835—21no—
212#833—22no—
213#833—41no—
214#832—21no—
215#832—21no—
216#832—21no—
217#830—21no—
218#830—21no—
219#809—21no—
220#809—21no—
221#808—21no—
222#807—21no—
223C2×H(5,𝔽2)C2×D311yescharacteristic
224C22×#41C2×D311yescharacteristic
225C2×AGL(1,ℤ/8)—31no—
226C2×AGL(1,ℤ/8)—31no—
227C2×AGL(1,ℤ/8)—31no—
228C22×M16—31no—
229#550—21no—
230#548—21no—
231#546—21no—
232#546—22no—
233D42—22no—
234D42—21no—
235#537—21no—
236#537C2×D311yescharacteristic
237#535—21no—
238#535C2×D311yescharacteristic
239C2×#127—31no—
240#525—21no—
241#525C2×D311yescharacteristic
242C2×#121—21no—
243C2×#121—31no—
244C2×#121—62no—
245C2×#121C2×D311yescharacteristic
246#520C2×D311yescharacteristic
247C22×C42—31no—
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—31no—
273#390—31no—
274#390—62no—
275#384—31no—
276#343—31no—
277#343—31no—
278#339—31no—
279#339—31no—
280C24×C3—22no—
281C24×C3—21no—
282C24×C3C2×D411yescharacteristic
283C24×C3C2×D412yes—
284C23×D3—21no—
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—21no—
294C3×#41—21no—
295C3×#41—21no—
296C3×#41—21no—
297C3×#41—42no—
298C3×#41—42no—
299C3×#41—41no—
300C3×#41—41no—
301C3×#41—42no—
302C3×#41—42no—
303C3×#41—42no—
304C3×#41—42no—
305C3×#41—42no—
306C3×#41—42no—
307C3×#41C2×D412yes—
308C3×#41#4112yes—
309C2×C3×Q8—21no—
310C2×C3×Q8—22no—
311C2×C3×Q8—41no—
312C2×C3×Q8C2×D411yescharacteristic
313C2×C3×Q8C2×D411yescharacteristic
314C2×C3×Q8C2×D411yescharacteristic
315C2×C3×D4—21no—
316C2×C3×D4—22no—
317C2×C3×D4—22no—
318C2×C3×D4—22no—
319C2×C3×D4—22no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—22no—
326C2×C3×D4—22no—
327C2×C3×D4—22no—
328C2×C3×D4—21no—
329C2×C3×D4—22no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—41no—
338C2×C3×D4—42no—
339C2×C3×D4—42no—
340C2×C3×D4—42no—
341C2×C3×D4—42no—
342C2×C3×D4—44no—
343C2×C3×D4—44no—
344C2×C3×D4—42no—
345C2×C3×D4—42no—
346C2×C3×D4—44no—
347C2×C3×D4—84no—
348C2×C3×D4C2×D411yescharacteristic
349C2×C3×D4C2×D411yescharacteristic
350C2×C3×D4C2×D411yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—22no—
357C22×C3×C4—21no—
358C22×C3×C4—22no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—42no—
364C22×C3×C4—42no—
365C22×C3×C4C2×D411yescharacteristic
366C22×C3×C4C2×D411yescharacteristic
367C22×C3×C4C2×D411yescharacteristic
368C22×C3×C4C2×D411yescharacteristic
369C22×C3×C4C2×D411yescharacteristic
370C22×C3×C4C2×D412yes—
371C22×C3×C4C2411yescharacteristic
372C2×#67—44no—
373C2×#67—44no—
374C2×#67—44no—
375C2×#67—44no—
376C2×#67—41no—
377C2×#67—41no—
378C22×Dic3—21no—
379C22×Dic3—24no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—42no—
383C22×Dic3—42no—
384C2×D12—21no—
385C2×D12—21no—
386C2×D12—21no—
387C2×D12—21no—
388C2×D12—21no—
389C2×D12—21no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4C2×D411yescharacteristic
397C3×C4⋊C4C2×D411yescharacteristic
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—22no—
402C3×C22⋊C4—22no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—21no—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—22no—
409C3×C22⋊C4—21no—
410C3×C42—22no—
411C3×C42—21no—
412#217—44no—
413#215—42no—
414#215—42no—
415#215—42no—
416#213—42no—
417#213—42no—
418#213—42no—
419(C2×D3)⋊C4—44no—
420(C2×D3)⋊C4—41no—
421(C2×D3)⋊C4—41no—
422C4⋊Dic3—21no—
423C4⋊Dic3—21no—
424Dic3⋊C4—44no—
425C4×Dic3—21no—
426C4×Dic3—21no—
427C4×Dic3—21no—
428C4×Dic3—42no—
429C4×Dic3C2×D412yescomplemented
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)—22no—
445H(5,𝔽2)—22no—
446H(5,𝔽2)—41no—
447H(5,𝔽2)—41no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41#6711yescharacteristic, complemented
457C2×#41#6711yescharacteristic, complemented
458C2×#41C22×D311yescharacteristic
459C2×#41C22×D311yescharacteristic
460C2×#41C22×D311yescharacteristic
461C22×Q8#6711yescharacteristic, complemented
462C22×D4—21no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—31no—
468C22×D4—61no—
469C22×D4—62no—
470C22×D4#6712yes—
471C22×D4#6711yescharacteristic, complemented
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—21no—
498#127—62no—
499#127—121no—
500#124—22no—
501#124—21no—
502#123—22no—
503#123—21no—
504C22⋊Q8—22no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8#6711yescharacteristic, complemented
508C22⋊Q8#6711yescharacteristic, complemented
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—21no—
522#121—21no—
523#121—61no—
524#121—61no—
525#121—61no—
526#121—61no—
527#121—128no—
528#121#6711yescharacteristic, complemented
529#121#6711yescharacteristic, complemented
530#120—22no—
531#120—22no—
532#120—22no—
533#120—21no—
534#120—22no—
535C4×Q8—21no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542#117—21no—
543#117C22×D311yescharacteristic
544C2×C4⋊C4—21no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4C22×D311yescharacteristic
548C2×C22⋊C4—22no—
549C2×C22⋊C4—62no—
550C2×C22⋊C4—61no—
551C2×C22⋊C4—62no—
552C2×C22⋊C4#6712yes—
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—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—22no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—41no—
588C23×C3—42no—
589C23×C3—44no—
590C23×C3—42no—
591C23×C3—42no—
592C23×C3—42no—
593C23×C3—81no—
594C23×C3—82no—
595C23×C3—82no—
596C23×C3#12011yescharacteristic
597C23×C3#12011yescharacteristic
598C23×C3C22×D411yescharacteristic
599C22×D3—42no—
600C22×D3—42no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×Q8—21no—
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—42no—
610C3×Q8#12112yescomplemented
611C3×D4—22no—
612C3×D4—22no—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—42no—
619C3×D4—42no—
620C3×D4—44no—
621C3×D4—42no—
622C3×D4—44no—
623C3×D4—41no—
624C3×D4—41no—
625C3×D4—41no—
626C3×D4—41no—
627C3×D4—44no—
628C3×D4—42no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—41no—
632C3×D4—41no—
633C3×D4—81no—
634C3×D4—82no—
635C3×D4—82no—
636C3×D4—82no—
637C3×D4—82no—
638C3×D4#12112yescomplemented
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—22no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—22no—
652C2×C3×C4—21no—
653C2×C3×C4—22no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—42no—
658C2×C3×C4—42no—
659C2×C3×C4—42no—
660C2×C3×C4—44no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—42no—
666C2×C3×C4—82no—
667C2×C3×C4#12011yescharacteristic
668C2×C3×C4#12011yescharacteristic
669C2×C3×C4C22×D411yescharacteristic
670C2×C3×C4C22×D411yescharacteristic
671C2×C3×C4C22×D411yescharacteristic
672C2×C3×C4C2×#4111yescharacteristic
673C2×C3×C4H(5,𝔽2)11yescharacteristic
674C2×C3×C4H(5,𝔽2)11yescharacteristic
675#67—88no—
676#67—82no—
677#67—82no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—48no—
683C2×Dic3—41no—
684C2×Dic3—41no—
685C2×Dic3—42no—
686C2×Dic3—41no—
687D12—41no—
688D12—41no—
689D12—41no—
690D12—41no—
691C3⋊C8—22no—
692C3⋊C8—41no—
693C3⋊C8—41no—
694C3⋊C8—41no—
695C24—22no—
696C24—21no—
697C24—61no—
698C24C2×#6711yescharacteristic
699C24C2×#6712yes—
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—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—42no—
713#41—42no—
714#41—41no—
715#41—41no—
716#41—42no—
717#41—42no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41D3×D412yes—
723#41#23712yes—
724C2×Q8—21no—
725C2×Q8—22no—
726C2×Q8—41no—
727C2×Q8C2×#6711yescharacteristic
728C2×Q8C2×#6711yescharacteristic
729C2×Q8C2×#6711yescharacteristic
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—22no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—41no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—44no—
762C2×D4—61no—
763C2×D4—61no—
764C2×D4—61no—
765C2×D4—61no—
766C2×D4—61no—
767C2×D4—61no—
768C2×D4—84no—
769C2×D4—124no—
770C2×D4—124no—
771C2×D4—124no—
772C2×D4—124no—
773C2×D4—121no—
774C2×D4—121no—
775C2×D4C2×#6711yescharacteristic
776C2×D4C2×#6711yescharacteristic
777C2×D4C2×#6711yescharacteristic
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—61no—
793C22×C4—64no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—122no—
797C22×C4—122no—
798C22×C4C2×#6711yescharacteristic
799C22×C4C2×#6711yescharacteristic
800C22×C4C2×#6711yescharacteristic
801C22×C4C2×#6711yescharacteristic
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—22no—
826C4⋊C4—22no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—61no—
832C4⋊C4—61no—
833C4⋊C4—124no—
834C4⋊C4C2×#6711yescharacteristic
835C4⋊C4C2×#6711yescharacteristic
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—22no—
840C22⋊C4—22no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—21no—
848C22⋊C4—124no—
849C22⋊C4—124no—
850C22⋊C4—121no—
851C22⋊C4—121no—
852C42—22no—
853C42—21no—
854C42—32no—
855C42—61no—
856C42—61no—
857C42—61no—
858C42—122no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—22no—
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—42no—
874C22×C3—42no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—42no—
879C22×C3—41no—
880C22×C3—84no—
881C22×C3—82no—
882C22×C3—82no—
883C22×C3—164no—
884C22×C3#45312yescomplemented
885C22×C3C2×#12011yescharacteristic
886C22×C3D4211yescharacteristic
887C22×C3#54611yescharacteristic
888C2×D3—82no—
889C2×D3—82no—
890C2×D3—81no—
891C2×D3—81no—
892C2×D3—81no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—22no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—42no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4C2×#12111yescharacteristic
902C3×C4#53411yescharacteristic
903C3×C4D4211yescharacteristic
904C3×C4#54611yescharacteristic
905Dic3—24no—
906Dic3—42no—
907Dic3—81no—
908C23—22no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—22no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—22no—
917C23—41no—
918C23—42no—
919C23—44no—
920C23—42no—
921C23—42no—
922C23—42no—
923C23—81no—
924C23—82no—
925C23—82no—
926C23—122no—
927C23—122no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23#95311yescharacteristic
932C23#95311yescharacteristic
933C23C22×#6711yescharacteristic
934Q8—21no—
935Q8—21no—
936Q8—21no—
937Q8—21no—
938Q8—21no—
939Q8—42no—
940Q8#93912yescomplemented
941D4—22no—
942D4—22no—
943D4—21no—
944D4—21no—
945D4—21no—
946D4—21no—
947D4—21no—
948D4—42no—
949D4—42no—
950D4—44no—
951D4—42no—
952D4—44no—
953D4—44no—
954D4—42no—
955D4—41no—
956D4—41no—
957D4—41no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—82no—
964D4—81no—
965D4—82no—
966D4—82no—
967D4—82no—
968D4—121no—
969D4—121no—
970D4—121no—
971D4—121no—
972D4—248no—
973D4—242no—
974D4—242no—
975D4#93912yescomplemented
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—44no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—42no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—82no—
1008C2×C4—128no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—122no—
1012C2×C4—121no—
1013C2×C4#95311yescharacteristic
1014C2×C4#95311yescharacteristic
1015C2×C4C2×D3×D411yescharacteristic
1016C2×C4C2×#23711yescharacteristic
1017C2×C4#100411yescharacteristic
1018C2×C4#100411yescharacteristic
1019C2×C4C22×#6711yescharacteristic
1020C2×C4C22×#6711yescharacteristic
1021C8—62no—
1022C8—121no—
1023C8—121no—
1024C8—121no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—22no—
1028C2×C3—41no—
1029C2×C3—42no—
1030C2×C3—81no—
1031C2×C3—82no—
1032C2×C3—81no—
1033C2×C3#241011yescharacteristic
1034C2×C3C2×#45311yescharacteristic
1035C2×C3#301811yescharacteristic
1036D3—161no—
1037C22—21no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—22no—
1043C22—21no—
1044C22—21no—
1045C22—42no—
1046C22—42no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—42no—
1052C22—42no—
1053C22—41no—
1054C22—41no—
1055C22—41no—
1056C22—42no—
1057C22—41no—
1058C22—84no—
1059C22—82no—
1060C22—82no—
1061C22—164no—
1062C22—242no—
1063C22—242no—
1064C22—241no—
1065C22—241no—
1066C22—241no—
1067C22#524112yescomplemented
1068C22D4×#6711yescharacteristic
1069C22#580611yescharacteristic
1070C22C2×#95311yescharacteristic
1071C4—21no—
1072C4—21no—
1073C4—22no—
1074C4—41no—
1075C4—41no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—64no—
1080C4—122no—
1081C4—241no—
1082C4D4×#6711yescharacteristic
1083C4C2×#93911yescharacteristic
1084C4#580411yescharacteristic
1085C4#580611yescharacteristic
1086C3#2446411yescharacteristic, complemented, Sylow
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—481no—
1096C2#8404811yescharacteristic
1097C2C2×#524111yescharacteristic
1098C2#8412111yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3488C2
socleC22×C3C2×#120
hypercenter#3488D3
hypocenterC3#24464
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. C3×#3488C2semidirect
2. C2×#5241C2semidirect
3. #84082C2semidirect
4. C22×#837C2semidirect
5. #82924C2semidirect
6. #82700C2semidirect
7. #72140C2semidirect
8. #71879C2semidirect
9. #71876C2semidirect
10. #71856C2semidirect
11. #71852C2semidirect
12. #71711C2semidirect
13. #71683C2semidirect
14. #71667C2semidirect
15. #71664C2semidirect
35. C2×#949C22semidirect
36. C2×#949C22semidirect
37. C2×#940C22semidirect
39. C2×#930C22semidirect
40. C22×C4×Dic3C22semidirect
41. C22×#208C22semidirect
48. C2×#837C22semidirect
49. C2×#837C22semidirect
50. C2×#837C22semidirect
51. C2×#837C22semidirect
53. #5232C22semidirect
54. #5232C22semidirect
56. #5221C22semidirect
58. C2×#833C22semidirect
59. C2×#833C22semidirect
60. #5207C22semidirect
65. #5001C22semidirect
66. #4995C22semidirect
67. #4988C22semidirect
68. #4975C22semidirect
70. #4532C22semidirect
71. #4532C22semidirect
72. #4530C22semidirect
73. #4530C22semidirect
74. #3488D3semidirect
101. C2×C3×#41D4semidirect
102. C2×C3×#41D4semidirect
106. C22×C3×Q8D4semidirect
113. C22×C3×D4D4semidirect
130. C3×C22⋊Q8D4semidirect
131. C3×C22⋊Q8D4semidirect
146. C3×#121D4semidirect
147. C3×#121D4semidirect
208. #837D4semidirect
429. C4×Dic3C2×D4semidirect
438. #208C2×D4semidirect
456. C2×#41#67semidirect
457. C2×#41#67semidirect
461. C22×Q8#67semidirect
471. C22×D4#67semidirect
507. C22⋊Q8#67semidirect
508. C22⋊Q8#67semidirect
528. #121#67semidirect
529. #121#67semidirect
610. C3×Q8#121semidirect
638. C3×D4#121semidirect
884. C22×C3#453semidirect
940. Q8#939semidirect
975. D4#939semidirect
1067. C22#5241semidirect
1086. C3#24464semidirect

Maximal subgroups

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

subgroupindex
C3×#34882
C2×#52412
#840822
C22×#8372
#829242
#827002
#721402
#718792
#718762
#718562
#718522
#717112
#716832
#716672
#716642
#244643