Finite Group Databasebeta

← #30588408

Subgroups — #30588408

Order 15616.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459905C212yesmaximal, complemented
2#21459852C216yesmaximal, complemented
3#21459826C212yesmaximal, complemented
4#21459781C216yesmaximal, complemented
5#21459732C213yesmaximal, complemented
6#21459696C213yesmaximal, complemented
7#21459597C211yesmaximal, characteristic, complemented
8#21459557C216yesmaximal, complemented
9#21459489C212yesmaximal, complemented
10#21459446C212yesmaximal, complemented
11#21459430C216yesmaximal, complemented
12#21459419C212yesmaximal, complemented
13D4×#11758226C216yesmaximal, complemented
14#21459242C216yesmaximal, complemented
15#21459116C213yesmaximal, complemented
16C2×#16840313C213yesmaximal, complemented
17#21459025C212yesmaximal, complemented
18C4×#41×D61C211yesmaximal, characteristic, complemented
19C61×#3503C211yesmaximal, characteristic, complemented
20C2×#14519823C2212yes—
21C22×#11758226C2216yescomplemented
22C2×#41×D61C2211yescharacteristic
23#16840497C2216yescomplemented
24#16840497C2216yescomplemented
25#16840486C2216yescomplemented
26#16840478C2216yescomplemented
27#16840478C22112yescomplemented
28#16840473C2216yescomplemented
29#16840465C22112yescomplemented
30#16840465C22112yescomplemented
31#16840460C22112yescomplemented
32#16840439C22124yescomplemented
33#16840434C2214yescomplemented
34#16840434C2216yescomplemented
35#16840434C2212yescomplemented
36#16840434C2216yescomplemented
37#16840434C2212yescomplemented
38#16840424C2214yescomplemented
39#16840423C22112yescomplemented
40#16840415C2216yescomplemented
41#16840415C22112yescomplemented
42#16840407C22112yescomplemented
43#16840403C22112yescomplemented
44#16840403C22124yescomplemented
45#16840403C22112yescomplemented
46D4×D244C22112yescomplemented
47D4×D244C2216yescomplemented
48D4×D244C2216yescomplemented
49#16840386C22112yescomplemented
50#16840386C22112yescomplemented
51#16840368C22112yescomplemented
52#16840368C22112yescomplemented
53#16840352C22124yescomplemented
54#16840343C2216yescomplemented
55#16840331C2216yescomplemented
56#16840331C2216yescomplemented
57#16840317C2213yescomplemented
58#16840317C2211yescharacteristic, complemented
59#16840313C2216yescomplemented
60#16840313C2216yescomplemented
61#16840313C22112yescomplemented
62#16840313C2216yescomplemented
63#16840313C2216yescomplemented
64#16840313C2216yescomplemented
65#16840313C2216yescomplemented
66#16840313C2213yescomplemented
67#16840313C2216yescomplemented
68#16840313C2213yescomplemented
69#16840312C2213yescomplemented
70C2×#14519774C2213yescomplemented
71#16840299C2216yescomplemented
72#16840299C2216yescomplemented
73#16840298C2216yescomplemented
74#16840298C2216yescomplemented
75#16840297C2216yescomplemented
76#16840297C22112yescomplemented
77#16840297C2216yescomplemented
78C2×#14519766C2216yescomplemented
79#16840275C22124yescomplemented
80#16840275C2216yescomplemented
81#16840275C2216yescomplemented
82#16840274C2216yescomplemented
83C2×#14519752C2216yescomplemented
84C2×#14519752C2216yescomplemented
85#16840244C2214yescomplemented
86#16840243C2216yescomplemented
87#16840236C2216yescomplemented
88#16840234C22112yescomplemented
89#41×Dic61C2211yescharacteristic
90C4×#11758226C2211yescharacteristic, complemented
91C4×#11758226C2211yescharacteristic, complemented
92C4×#11758226C2214yescomplemented
93C4×#11758226C2216yescomplemented
94C4×#11758226C2216yescomplemented
95C4×#11758222C2213yescomplemented
96#16840230C2213yescomplemented
97#16840230C2216yescomplemented
98C4×#11758224C2213yescomplemented
99C4×#11758224C2213yescomplemented
100C4×Q8×D61C2211yescharacteristic, complemented
101C4×Q8×D61C2211yescharacteristic, complemented
102C2×#14519739C2216yescomplemented
103C2×#14519739C2216yescomplemented
104C4×D4×D61C2213yescomplemented
105C4×D4×D61C2213yescomplemented
106C4×D4×D61C22112yescomplemented
107#117×D61C2213yescomplemented
108C2×C42×D61C2213yescomplemented
109Q82×C61C2212yescomplemented
110C61×#557C2212yescomplemented
111C61×#554C2216yescomplemented
112D4×Q8×C61C2216yescomplemented
113C61×#544C2216yescomplemented
114C61×#533C2213yescomplemented
115C2×C4⋊Q8×C61C2213yescomplemented
116C61×#520C2212yes—
117C4×#41×C61C2211yescharacteristic
118#14519823—216no—
119C2×#11758226—424no—
120C2×#11758226C2311yescharacteristic
121C2×#11758226C2314yes—
122C2×#11758226C2316yes—
123C2×#11758226C2316yes—
124C2×#11758226C23112yes—
125C2×#11758226C23112yes—
126C2×#11758226C23112yes—
127C2×#11758222C2313yes—
128C2×#11758222C2316yes—
129C2×#11758224C2313yes—
130#41×D61—28no—
131C2×Q8×D61C2311yescharacteristic
132C22×D244C2316yes—
133C22×D244C2316yes—
134C22×D244C23112yes—
135C22×D244C2316yes—
136C2×D4×D61C2313yes—
137C2×D4×D61C23112yes—
138C22×C4×D61C2313yes—
139C22×C4×D61C2313yes—
140C22×C4×D61C2313yes—
141C22×C4×D61C23112yes—
142#14519777C2311yescharacteristic
143#14519774C2316yes—
144#14519774C2316yes—
145#14519774C2313yes—
146#14519774C2316yes—
147#14519774C23112yes—
148#14519772C23124yes—
149#14519772C23112yes—
150#14519772C23112yes—
151#14519768C2316yes—
152#14519768C2312yes—
153#14519766C23112yes—
154#14519766C23124yes—
155#14519766C23112yes—
156#14519766C2316yes—
157#14519766C2316yes—
158#14519766C23112yes—
159#14519765C23112yes—
160#14519765C2316yes—
161#14519762C23124yes—
162#14519762C23124yes—
163#14519762C23124yes—
164#14519762C23112yes—
165#14519762C23112yes—
166#14519761C23112yes—
167#14519757C23112yes—
168#14519757C2312yes—
169#14519757C2316yes—
170#14519753C23124yes—
171#14519753C2312yes—
172#14519753C2316yes—
173#14519752C23112yes—
174#14519752C23112yes—
175#14519752C23112yes—
176#14519752C23112yes—
177#14519752C23112yes—
178#14519752C23124yes—
179#14519752C23112yes—
180#14519752C23112yes—
181#14519752C23124yes—
182#14519752C2316yes—
183#14519752C2316yes—
184#14519752C23112yes—
185#14519752C23112yes—
186#14519752C2316yes—
187#14519752C2316yes—
188#14519751C2316yes—
189#14519751C23124yes—
190#14519751C2316yes—
191#14519747C23112yes—
192#14519747C23124yes—
193#14519747C23124yes—
194Q8×Dic61C2311yescharacteristic
195Q8×Dic61C2311yescharacteristic
196Q8×Dic61C2316yes—
197Q8×Dic61C2312yes—
198C4×Dic122C2313yes—
199C4×Dic122C2313yes—
200#14519742C2313yes—
201#14519742C2313yes—
202#14519742C2312yes—
203#14519742C2316yes—
204C4×D244C23112yes—
205C4×D244C23112yes—
206C4×D244C23112yes—
207C4×D244C23112yes—
208C4×D244C2316yes—
209C4×D244C2313yes—
210C4×D244C2313yes—
211C4×D244C2316yes—
212D4×Dic61C2313yes—
213D4×Dic61C2313yes—
214#14519739C23112yes—
215#14519739C23112yes—
216#14519739C23112yes—
217#14519739C23112yes—
218#14519739C2313yes—
219#14519739C2313yes—
220#14519739C2316yes—
221#14519739C2316yes—
222#14519739C23112yes—
223#14519739C23112yes—
224#14519739C23112yes—
225#14519739C2316yes—
226#14519739C2316yes—
227#14519739C23112yes—
228C4×C22⋊D61C2316yes—
229C4×C22⋊D61C23124yes—
230C4×C22⋊D61C2316yes—
231#14519737C23112yes—
232#14519737C2316yes—
233#14519737C2316yes—
234#14519737C23112yes—
235#14519736C2313yes—
236#14519735C2316yes—
237#14519735C2313yes—
238#14519735C23112yes—
239#14519735C2313yes—
240#14519735C23112yes—
241#14519735C2312yes—
242#14519735C23112yes—
243#14519734C2316yes—
244#14519734C23112yes—
245#14519733C2316yes—
246C4⋊C4×D61C2313yes—
247C4⋊C4×D61C23112yes—
248C4⋊C4×D61C2313yes—
249C2×#11758198C23112yes—
250C2×#11758198C23112yes—
251C22⋊C4×D61C2316yes—
252C22⋊C4×D61C23124yes—
253C2×C4×Dic61C2313yes—
254C2×C4×Dic61C2313yes—
255C2×C4×Dic61C2313yes—
256C42×D61C2311yescharacteristic
257C42×D61C2313yes—
258C42×D61C2313yes—
259C42×D61C2313yes—
260C42×D61C2313yes—
261C42×D61C2313yes—
262C42×D61C2313yes—
263C42×D61C2313yes—
264C42×D61C23112yes—
265C2×#41×C61C2311yescharacteristic
266C22×Q8×C61C2316yes—
267C4⋊Q8×C61C2313yes—
268C4⋊Q8×C61C2316yes—
269C4⋊Q8×C61C2316yes—
270C4⋊Q8×C61C2316yes—
271C4⋊Q8×C61C2311yescharacteristic
272C4⋊Q8×C61C23112yes—
273#125×C61C2316yes—
274#125×C61C23112yes—
275C22⋊Q8×C61C2316yes—
276C22⋊Q8×C61C2316yes—
277C22⋊Q8×C61C23124yes—
278C4×Q8×C61C2316yes—
279C4×Q8×C61C2316yes—
280C4×Q8×C61C2311yescharacteristic
281C4×Q8×C61C2314yes—
282C4×Q8×C61C2311yescharacteristic
283C4×D4×C61C2313yes—
284C4×D4×C61C23112yes—
285C4×D4×C61C2313yes—
286#117×C61C2316yes—
287#117×C61C2313yes—
288C2×C4⋊C4×C61C2316yes—
289C2×C4⋊C4×C61C2316yes—
290C2×C42×C61C2313yes—
291C23×D61C2413yes—
292C23×D61C24112yes—
293#41×C61#4118yescomplemented
294C2×Q8×C61—412no—
295C2×Q8×C61C2412yes—
296C2×Q8×C61C2416yes—
297C2×Q8×C61C24112yes—
298C2×Q8×C61C2411yescharacteristic
299C2×D4×C61C2413yes—
300C22×C4×C61C2413yes—
301C22×C4×C61C2413yes—
302C22×C4×C61C24112yes—
303C22×C4×C61C2413yes—
304C2×C22⋊D61C24112yes—
305C2×C22⋊D61C2416yes—
306C22×Dic61C2413yes—
307C22×Dic61C2413yes—
308C22×Dic61C2413yes—
309#11758226—24no—
310#11758226—216no—
311#11758226—224no—
312#11758226—424no—
313#11758226—424no—
314#11758226—424no—
315#11758226—412no—
316Q8×D61—24no—
317#11758224—212no—
318D4×D61—212no—
319D4×D61—248no—
320#11758222—212no—
321#11758222—224no—
322C2×D244—224no—
323C2×D244—412no—
324C2×D244—412no—
325C2×D244—424no—
326C2×D244C24112yes—
327C2×D244C2413yes—
328C2×D244C2416yes—
329C2×D244C24112yes—
330C2×D244C2416yes—
331C2×D244C2416yes—
332C2×D244C24112yes—
333C2×D244C24124yes—
334C2×D244C24112yes—
335C2×D244C24112yes—
336C2×C4×D61—212no—
337C2×C4×D61—212no—
338C2×C4×D61—424no—
339C2×C4×D61—46no—
340C2×C4×D61C2411yescharacteristic
341C2×C4×D61C2411yescharacteristic
342C2×C4×D61C24112yes—
343C2×C4×D61C2413yes—
344C2×C4×D61C2413yes—
345C2×C4×D61C2413yes—
346C2×C4×D61C2413yes—
347C2×C4×D61C2413yes—
348C2×C4×D61C2413yes—
349C2×C4×D61C2413yes—
350C2×C4×D61C24112yes—
351C2×C4×D61C24124yes—
352C2×C4×D61C2413yes—
353C2×C4×D61C2413yes—
354C2×C4×D61C24112yes—
355C2×C4×D61C2411yescharacteristic
356C2×Dic122C2413yes—
357C2×Dic122C2412yes—
358C4⋊C4×C61C2416yes—
359C4⋊C4×C61C2416yes—
360C4⋊C4×C61C24112yes—
361C4⋊C4×C61C24112yes—
362C4⋊C4×C61C2412yes—
363C4⋊C4×C61C2413yes—
364C4⋊C4×C61C2413yes—
365C4⋊C4×C61C2412yes—
366C4⋊C4×C61C24112yes—
367C4⋊C4×C61C24112yes—
368C22⋊C4×C61C24112yes—
369C22⋊C4×C61C2416yes—
370C42×C61C2411yescharacteristic
371C42×C61C2413yes—
372C42×C61C2413yes—
373C42×C61C2413yes—
374C42×C61C24112yes—
375C22⋊Dic61C2416yes—
376#11758198C24112yes—
377#11758198C24124yes—
378#11758198C2416yes—
379#11758198C2416yes—
380#11758198C24112yes—
381#11758198C24112yes—
382#11758198C24124yes—
383#11758198C2414yes—
384#11758198C24112yes—
385#11758198C24112yes—
386#11758198C24112yes—
387#11758198C24112yes—
388C4⋊Dic61C2413yes—
389C4⋊Dic61C2413yes—
390C4⋊Dic61C2412yes—
391C4⋊Dic61C2414yes—
392C4⋊Dic61C2412yes—
393C4⋊Dic61C24112yes—
394#11758196C24112yes—
395#11758196C2416yes—
396#11758196C2416yes—
397#11758196C2414yes—
398C4×Dic61C2413yes—
399C4×Dic61C2411yescharacteristic
400C4×Dic61C2411yescharacteristic
401C4×Dic61C2411yescharacteristic
402C4×Dic61C2414yes—
403C4×Dic61C2413yes—
404C4×Dic61C2413yes—
405C4×Dic61C2413yes—
406C4×Dic61C2413yes—
407C4×Dic61C2413yes—
408C4×Dic61C2413yes—
409C4×Dic61C2413yes—
410C4×Dic61C2413yes—
411C4×Dic61C24112yes—
412C23×C61C2513yes—
413C22×D61—26no—
414C22×D61—224no—
415C22×D61—26no—
416C22×D61—43no—
417C22×D61—412no—
418C22×D61—412no—
419C22×D61C25112yes—
420C22×D61C2513yes—
421C22×D61C2511yescharacteristic
422Q8×C61—212no—
423Q8×C61—24no—
424Q8×C61—412no—
425Q8×C61C2×#4114yescomplemented
426D4×C61C2×#41112yescomplemented
427C2×C4×C61—26no—
428C2×C4×C61—26no—
429C2×C4×C61—412no—
430C2×C4×C61C2×#41112yescomplemented
431C2×C4×C61C2513yes—
432C2×C4×C61C2513yes—
433C2×C4×C61C2514yes—
434C2×C4×C61C25112yes—
435C2×C4×C61C2511yescharacteristic
436C2×C4×C61C2513yes—
437C2×C4×C61C2511yescharacteristic
438C2×C4×C61C2511yescharacteristic
439C22⋊D61—224no—
440C22⋊D61—212no—
441C2×Dic61—26no—
442C2×Dic61—26no—
443C2×Dic61—43no—
444C2×Dic61C2511yescharacteristic
445C2×Dic61C2513yes—
446C2×Dic61C2511yescharacteristic
447C2×Dic61C2513yes—
448C2×Dic61C2514yes—
449C2×Dic61C2513yes—
450C2×Dic61C2511yescharacteristic
451D244—224no—
452D244—212no—
453D244—224no—
454D244—26no—
455D244—212no—
456D244—212no—
457D244—412no—
458D244—412no—
459D244—424no—
460D244—412no—
461C4×D61—26no—
462C4×D61—22no—
463C4×D61—26no—
464C4×D61—26no—
465C4×D61—26no—
466C4×D61—224no—
467C4×D61—26no—
468C4×D61—22no—
469C4×D61—26no—
470C4×D61—26no—
471C4×D61—224no—
472C4×D61—43no—
473C4×D61—43no—
474C4×D61—424no—
475C4×D61—412no—
476C4×D61H(5,𝔽2)14yescomplemented
477Dic122—24no—
478Dic122—26no—
479#62800—611nomaximal, Sylow
480C22×C61—23no—
481C22×C61—23no—
482C22×C61C22×#4116yes—
483C22×C61C2611yescharacteristic
484C2×D61—21no—
485C2×D61—21no—
486C2×D61—23no—
487C2×D61—212no—
488C2×D61—23no—
489C2×D61—212no—
490C2×D61—23no—
491C2×D61—212no—
492C2×D61—412no—
493C2×D61—824no—
494C2×D61C2×H(5,𝔽2)12yes—
495C4×C61—23no—
496C4×C61—212no—
497C4×C61—24no—
498C4×C61—23no—
499C4×C61C22×#4112yes—
500C4×C61C22×#4116yes—
501C4×C61C2×H(5,𝔽2)12yes—
502C4×C61#58512yes—
503Dic61—23no—
504Dic61—24no—
505Dic61—21no—
506Dic61—23no—
507Dic61—23no—
508Dic61—21no—
509Dic61C2×H(5,𝔽2)12yes—
510#3522—612no—
511#3519—616no—
512#3517—612no—
513#3514—616no—
514#3511—613no—
515#3508—613no—
516#3503D6111yescharacteristic, complemented
517#3498—611no—
518#3494—616no—
519#3488—612no—
520#3483—612no—
521#3481—616no—
522#3480—612no—
523D4×#41—616no—
524#3460—616no—
525#3444—613no—
526C2×#532—613no—
527C4×H(5,𝔽2)—612no—
528C2×C4×#41—611no—
529C2×C61—26no—
530C2×C61C23×#4111yescharacteristic
531C2×C61C22×H(5,𝔽2)11yescharacteristic
532C2×C61C2×#58511yescharacteristic
533D61—22no—
534D61—43no—
535D61—412no—
536C2×H(5,𝔽2)—612no—
537C22×#41—611no—
538C22×#41—616no—
539#559—616no—
540#559—616no—
541Q82C2×D6112yescomplemented
542#557C2×D6112yescomplemented
543#556—616no—
544#555—6112no—
545#555—616no—
546#554—616no—
547#554C2×D6116yescomplemented
548#553—6112no—
549#553—6112no—
550#553—6112no—
551#551—6124no—
552#550—616no—
553#550—612no—
554#550—614no—
555#550—612no—
556#550—616no—
557D4×Q8C2×D6116yescomplemented
558#548—6112no—
559#548—614no—
560#547—6112no—
561#547—616no—
562#546—6124no—
563#546—6112no—
564#546—6112no—
565#546—6112no—
566D42—6112no—
567D42—616no—
568D42—616no—
569#544C2×D6116yescomplemented
570#542—6112no—
571#542—6112no—
572#540—6112no—
573#540—6112no—
574#538—6124no—
575#537—616no—
576#535—616no—
577#535—616no—
578#533—611no—
579#533—613no—
580#533C2×D6113yescomplemented
581#532—613no—
582#532—616no—
583#532—616no—
584#532—616no—
585#532—616no—
586#532—616no—
587#532—616no—
588#532—616no—
589#532—613no—
590#532—6112no—
591#532—613no—
592C2×C4⋊Q8C2×D6113yescomplemented
593C2×#127—613no—
594#529—616no—
595#529—616no—
596#529—6112no—
597#529—616no—
598#529—616no—
599#529—616no—
600#529—616no—
601C2×#124—616no—
602#525—616no—
603#525—616no—
604#525—6124no—
605#525—616no—
606C2×#121—616no—
607C2×#121—616no—
608#520—614no—
609#520—616no—
610#520C2×D6112yes—
611#518—6112no—
612#518—616no—
613C4×#41—611no—
614C4×#41—611no—
615C4×#41—611no—
616C4×#41—614no—
617C4×#41—616no—
618C4×#41—616no—
619C4×#41—613no—
620C4×#41—613no—
621C4×#41—613no—
622C4×#41—616no—
623C4×#41—613no—
624C4×#41C2×D6111yescharacteristic
625C2×C4×Q8—611no—
626C2×C4×Q8—611no—
627C2×C4×D4—613no—
628C2×C4×D4—613no—
629C2×C4×D4—6112no—
630C2×C4×D4—616no—
631C2×C4×D4—616no—
632C2×#117—613no—
633C22×C42—613no—
634C61#6280011yescharacteristic, complemented, Sylow
635H(5,𝔽2)—12216no—
636C2×#41—611no—
637C2×#41—614no—
638C2×#41—616no—
639C2×#41—616no—
640C2×#41—6112no—
641C2×#41—6112no—
642C2×#41—6112no—
643C2×#41—613no—
644C2×#41—613no—
645C2×#41—616no—
646C2×#41—1228no—
647C2×#41—24424no—
648C2×#41C22×D6111yescharacteristic
649C22×Q8—611no—
650C22×Q8C22×D6116yes—
651C22×D4—613no—
652C22×D4—6112no—
653C22×D4—616no—
654C22×D4—616no—
655C22×D4—6112no—
656C22×D4—616no—
657C23×C4—613no—
658C23×C4—613no—
659C23×C4—6112no—
660C23×C4—613no—
661C4⋊Q8—611no—
662C4⋊Q8C22×D6113yes—
663C4⋊Q8C22×D6116yes—
664C4⋊Q8C22×D6116yes—
665C4⋊Q8C22×D6116yes—
666C4⋊Q8C22×D6111yescharacteristic
667C4⋊Q8C22×D61112yes—
668#127—613no—
669#127—616no—
670#127—616no—
671#127—616no—
672#127—6112no—
673#126—6112no—
674#126—6112no—
675#126—6124no—
676#125—612no—
677#125—616no—
678#125C22×D6116yes—
679#125C22×D61112yes—
680#124—616no—
681#124—6112no—
682#124—6112no—
683#124—6112no—
684#124—616no—
685#124—6124no—
686#124—616no—
687#124—6112no—
688#123—6112no—
689#123—6112no—
690#123—6124no—
691#123—6124no—
692#123—6124no—
693#123—6112no—
694C22⋊Q8—612no—
695C22⋊Q8—616no—
696C22⋊Q8—6124no—
697C22⋊Q8—612no—
698C22⋊Q8—616no—
699C22⋊Q8—6112no—
700C22⋊Q8C22×D6116yes—
701C22⋊Q8C22×D6116yes—
702C22⋊Q8C22×D61124yes—
703#121—616no—
704#121—616no—
705#121—6124no—
706#121—616no—
707#121—616no—
708#121—6112no—
709#121—6112no—
710#121—6112no—
711#121—6112no—
712#121—6112no—
713#121—6112no—
714#121—616no—
715#121—616no—
716#121—6124no—
717#121—6112no—
718#121—6112no—
719#121—6112no—
720#121—6124no—
721#120—6112no—
722#120—6124no—
723#120—6124no—
724C4×Q8—611no—
725C4×Q8—611no—
726C4×Q8—612no—
727C4×Q8—616no—
728C4×Q8—613no—
729C4×Q8—613no—
730C4×Q8—612no—
731C4×Q8—616no—
732C4×Q8—613no—
733C4×Q8—613no—
734C4×Q8C22×D6111yescharacteristic
735C4×Q8C22×D6111yescharacteristic
736C4×Q8C22×D6114yes—
737C4×Q8C22×D6116yes—
738C4×Q8C22×D6116yes—
739C4×D4—613no—
740C4×D4—613no—
741C4×D4—616no—
742C4×D4—616no—
743C4×D4—6124no—
744C4×D4—6112no—
745C4×D4—616no—
746C4×D4—616no—
747C4×D4—613no—
748C4×D4—613no—
749C4×D4—6112no—
750C4×D4—6112no—
751C4×D4—6112no—
752C4×D4—6112no—
753C4×D4—6112no—
754C4×D4—616no—
755C4×D4—6112no—
756C4×D4—6112no—
757C4×D4—616no—
758C4×D4—6112no—
759C4×D4—616no—
760C4×D4—616no—
761C4×D4—6112no—
762C4×D4—613no—
763C4×D4—613no—
764C4×D4—6112no—
765C4×D4—6112no—
766C4×D4—6112no—
767C4×D4—6112no—
768C4×D4—616no—
769C4×D4—616no—
770C4×D4C22×D6113yes—
771C4×D4C22×D6113yes—
772C4×D4C22×D61112yes—
773#117—613no—
774#117—613no—
775#117—613no—
776#117—612no—
777#117—6112no—
778#117—6112no—
779#117—616no—
780#117—6112no—
781#117—616no—
782#117—616no—
783#117—6112no—
784#117C22×D6113yes—
785#117C22×D6116yes—
786C2×C4⋊C4—613no—
787C2×C4⋊C4—613no—
788C2×C4⋊C4—6112no—
789C2×C4⋊C4C22×D6116yes—
790C2×C4⋊C4C22×D6116yes—
791C2×C22⋊C4—6112no—
792C2×C22⋊C4—6112no—
793C2×C22⋊C4—616no—
794C2×C22⋊C4—6124no—
795C2×C42—613no—
796C2×C42—613no—
797C2×C42—613no—
798C2×C42—613no—
799C2×C42—613no—
800C2×C42—613no—
801C2×C42—6112no—
802C2×C42—613no—
803C2×C42—613no—
804C2×C42—613no—
805C2×C42—613no—
806C2×C42—611no—
807C2×C42C22×D6113yes—
808C24—613no—
809C24—6112no—
810#41—12224no—
811#41—1224no—
812#41—12216no—
813#41—12212no—
814#41—12212no—
815#41—12224no—
816#41—24424no—
817#41—24424no—
818#41—24424no—
819#41—24412no—
820#41#1175822618yescomplemented
821C2×Q8—412no—
822C2×Q8—613no—
823C2×Q8—612no—
824C2×Q8—1224no—
825C2×Q8C23×D6112yes—
826C2×Q8C23×D6116yes—
827C2×Q8C23×D61112yes—
828C2×Q8C23×D6111yescharacteristic
829C2×D4—616no—
830C2×D4—6112no—
831C2×D4—616no—
832C2×D4—6112no—
833C2×D4—616no—
834C2×D4—613no—
835C2×D4—6112no—
836C2×D4—616no—
837C2×D4—6112no—
838C2×D4—6112no—
839C2×D4—6112no—
840C2×D4—6124no—
841C2×D4—12212no—
842C2×D4—12248no—
843C2×D4—12224no—
844C2×D4—24412no—
845C2×D4—24412no—
846C2×D4—24424no—
847C2×D4C23×D6113yes—
848C22×C4—611no—
849C22×C4—613no—
850C22×C4—613no—
851C22×C4—613no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—613no—
855C22×C4—613no—
856C22×C4—613no—
857C22×C4—613no—
858C22×C4—613no—
859C22×C4—613no—
860C22×C4—613no—
861C22×C4—6112no—
862C22×C4—6112no—
863C22×C4—613no—
864C22×C4—613no—
865C22×C4—6112no—
866C22×C4—6124no—
867C22×C4—12212no—
868C22×C4—12212no—
869C22×C4—2446no—
870C22×C4—24424no—
871C22×C4C23×D6113yes—
872C22×C4C23×D6113yes—
873C22×C4C23×D61112yes—
874C22×C4C23×D6113yes—
875C4⋊C4—613no—
876C4⋊C4—6112no—
877C4⋊C4—616no—
878C4⋊C4—616no—
879C4⋊C4—613no—
880C4⋊C4—614no—
881C4⋊C4—612no—
882C4⋊C4—614no—
883C4⋊C4—612no—
884C4⋊C4—6112no—
885C4⋊C4C23×D61112yes—
886C4⋊C4C23×D6113yes—
887C4⋊C4C23×D6113yes—
888C4⋊C4C23×D6116yes—
889C4⋊C4C23×D6116yes—
890C4⋊C4C23×D61112yes—
891C4⋊C4C23×D6112yes—
892C4⋊C4C23×D61112yes—
893C4⋊C4C23×D61112yes—
894C4⋊C4C23×D6112yes—
895C22⋊C4—616no—
896C22⋊C4—6112no—
897C22⋊C4—6112no—
898C22⋊C4—6124no—
899C22⋊C4—6112no—
900C22⋊C4—616no—
901C22⋊C4—616no—
902C22⋊C4—6124no—
903C22⋊C4—614no—
904C22⋊C4—6112no—
905C22⋊C4—6112no—
906C22⋊C4—6112no—
907C22⋊C4—6112no—
908C22⋊C4C23×D61112yes—
909C22⋊C4C23×D6116yes—
910C42—611no—
911C42—613no—
912C42—611no—
913C42—611no—
914C42—613no—
915C42—613no—
916C42—614no—
917C42—613no—
918C42—613no—
919C42—613no—
920C42—613no—
921C42—613no—
922C42—613no—
923C42—6112no—
924C42C23×D6111yescharacteristic
925C42C23×D6113yes—
926C42C23×D6113yes—
927C42C23×D6113yes—
928C42C23×D61112yes—
929C23—611no—
930C23—6112no—
931C23—613no—
932C23—1226no—
933C23—12224no—
934C23—1226no—
935C23—24412no—
936C23—24412no—
937C23—2443no—
938C23C24×D6113yes—
939Q8—212no—
940Q8—24no—
941Q8—412no—
942Q8—1226no—
943Q8—1224no—
944Q8C2×#1175822614yescomplemented
945D4—12224no—
946D4—12224no—
947D4—12212no—
948D4—12224no—
949D4—12212no—
950D4—1226no—
951D4—12212no—
952D4—12212no—
953D4—24412no—
954D4—24412no—
955D4—24424no—
956D4—24412no—
957D4C2×#11758226112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—412no—
961C2×C4—611no—
962C2×C4—614no—
963C2×C4—611no—
964C2×C4—611no—
965C2×C4—613no—
966C2×C4—613no—
967C2×C4—614no—
968C2×C4—613no—
969C2×C4—1226no—
970C2×C4—12224no—
971C2×C4—1226no—
972C2×C4—1226no—
973C2×C4—1226no—
974C2×C4—1222no—
975C2×C4—1226no—
976C2×C4—1226no—
977C2×C4—1226no—
978C2×C4—12224no—
979C2×C4—1226no—
980C2×C4—1222no—
981C2×C4—1226no—
982C2×C4—2443no—
983C2×C4—2443no—
984C2×C4—24424no—
985C2×C4—24412no—
986C2×C4—2443no—
987C2×C4C2×#11758226112yescomplemented
988C2×C4C24×D6113yes—
989C2×C4C24×D6113yes—
990C2×C4C24×D6114yes—
991C2×C4C24×D61112yes—
992C2×C4C24×D6111yescharacteristic
993C2×C4C24×D6113yes—
994C2×C4C24×D6111yescharacteristic
995C2×C4C24×D6111yescharacteristic
996C22—23no—
997C22—23no—
998C22—612no—
999C22—1221no—
1000C22—1221no—
1001C22—1223no—
1002C22—12212no—
1003C22—1223no—
1004C22—12212no—
1005C22—1223no—
1006C22—12212no—
1007C22—48824no—
1008C22—24412no—
1009C22C22×#1175822616yes—
1010C22C25×D6111yescharacteristic
1011C4—23no—
1012C4—212no—
1013C4—23no—
1014C4—24no—
1015C4—612no—
1016C4—1221no—
1017C4—1224no—
1018C4—1223no—
1019C4—1223no—
1020C4—1223no—
1021C4—1221no—
1022C4C22×#1175822616yes—
1023C4C22×#1175822612yes—
1024C4H(5,𝔽2)×D6112yes—
1025C4#1684059912yes—
1026C2—26no—
1027C2—1222no—
1028C2—24412no—
1029C2—2443no—
1030C2C23×#1175822611yescharacteristic
1031C2C2×H(5,𝔽2)×D6111yescharacteristic
1032C2C2×#1684059911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D61
commutator, socle, cosocleC22×C61C26
FittingC61×#3503C2
hypercenter#3503D61
hypocenterC61#62800
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #21459905C2semidirect
2. #21459852C2semidirect
3. #21459826C2semidirect
4. #21459781C2semidirect
5. #21459732C2semidirect
6. #21459696C2semidirect
7. #21459597C2semidirect
8. #21459557C2semidirect
9. #21459489C2semidirect
10. #21459446C2semidirect
11. #21459430C2semidirect
12. #21459419C2semidirect
13. D4×#11758226C2semidirect
14. #21459242C2semidirect
15. #21459116C2semidirect
16. C2×#16840313C2semidirect
17. #21459025C2semidirect
18. C4×#41×D61C2semidirect
19. C61×#3503C2semidirect
21. C22×#11758226C22semidirect
23. #16840497C22semidirect
24. #16840497C22semidirect
25. #16840486C22semidirect
26. #16840478C22semidirect
27. #16840478C22semidirect
28. #16840473C22semidirect
29. #16840465C22semidirect
30. #16840465C22semidirect
31. #16840460C22semidirect
32. #16840439C22semidirect
33. #16840434C22semidirect
34. #16840434C22semidirect
35. #16840434C22semidirect
36. #16840434C22semidirect
37. #16840434C22semidirect
38. #16840424C22semidirect
39. #16840423C22semidirect
40. #16840415C22semidirect
41. #16840415C22semidirect
42. #16840407C22semidirect
43. #16840403C22semidirect
44. #16840403C22semidirect
45. #16840403C22semidirect
46. D4×D244C22semidirect
47. D4×D244C22semidirect
48. D4×D244C22semidirect
49. #16840386C22semidirect
50. #16840386C22semidirect
51. #16840368C22semidirect
52. #16840368C22semidirect
53. #16840352C22semidirect
54. #16840343C22semidirect
55. #16840331C22semidirect
56. #16840331C22semidirect
57. #16840317C22semidirect
58. #16840317C22semidirect
59. #16840313C22semidirect
60. #16840313C22semidirect
61. #16840313C22semidirect
62. #16840313C22semidirect
63. #16840313C22semidirect
64. #16840313C22semidirect
65. #16840313C22semidirect
66. #16840313C22semidirect
67. #16840313C22semidirect
68. #16840313C22semidirect
69. #16840312C22semidirect
70. C2×#14519774C22semidirect
71. #16840299C22semidirect
72. #16840299C22semidirect
73. #16840298C22semidirect
74. #16840298C22semidirect
75. #16840297C22semidirect
76. #16840297C22semidirect
77. #16840297C22semidirect
78. C2×#14519766C22semidirect
79. #16840275C22semidirect
80. #16840275C22semidirect
81. #16840275C22semidirect
82. #16840274C22semidirect
83. C2×#14519752C22semidirect
84. C2×#14519752C22semidirect
85. #16840244C22semidirect
86. #16840243C22semidirect
87. #16840236C22semidirect
88. #16840234C22semidirect
90. C4×#11758226C22semidirect
91. C4×#11758226C22semidirect
92. C4×#11758226C22semidirect
93. C4×#11758226C22semidirect
94. C4×#11758226C22semidirect
95. C4×#11758222C22semidirect
96. #16840230C22semidirect
97. #16840230C22semidirect
98. C4×#11758224C22semidirect
99. C4×#11758224C22semidirect
100. C4×Q8×D61C22semidirect
101. C4×Q8×D61C22semidirect
102. C2×#14519739C22semidirect
103. C2×#14519739C22semidirect
104. C4×D4×D61C22semidirect
105. C4×D4×D61C22semidirect
106. C4×D4×D61C22semidirect
107. #117×D61C22semidirect
108. C2×C42×D61C22semidirect
109. Q82×C61C22semidirect
110. C61×#557C22semidirect
111. C61×#554C22semidirect
112. D4×Q8×C61C22semidirect
113. C61×#544C22semidirect
114. C61×#533C22semidirect
115. C2×C4⋊Q8×C61C22semidirect
293. #41×C61#41semidirect
425. Q8×C61C2×#41semidirect
426. D4×C61C2×#41semidirect
430. C2×C4×C61C2×#41semidirect
476. C4×D61H(5,𝔽2)semidirect
516. #3503D61semidirect
541. Q82C2×D61semidirect
542. #557C2×D61semidirect
547. #554C2×D61semidirect
557. D4×Q8C2×D61semidirect
569. #544C2×D61semidirect
580. #533C2×D61semidirect
592. C2×C4⋊Q8C2×D61semidirect
634. C61#62800semidirect
820. #41#11758226semidirect
944. Q8C2×#11758226semidirect
957. D4C2×#11758226semidirect
987. C2×C4C2×#11758226semidirect

Maximal subgroups

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

subgroupindex
#214599052
#214598522
#214598262
#214597812
#214597322
#214596962
#214595972
#214595572
#214594892
#214594462
#214594302
#214594192
D4×#117582262
#214592422
#214591162
C2×#168403132
#214590252
C4×#41×D612
C61×#35032
#6280061