Finite Group Databasebeta

← #30559885

Subgroups — #30559885

Order 15616.

1804 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459412C211yesmaximal, characteristic
2C2×#16840491C211yesmaximal, characteristic, complemented
3#21458666C214yesmaximal, complemented
4#21458620C212yesmaximal, complemented
5#21458592C214yesmaximal, complemented
6#21458546C212yesmaximal, complemented
7#21458513C212yesmaximal, complemented
8#21458502C212yesmaximal, complemented
9#21456217C212yesmaximal, complemented
10#21456213C211yesmaximal, characteristic, complemented
11#21455640C212yesmaximal, complemented
12#21455634C211yesmaximal, characteristic, complemented
13#21455291C211yesmaximal, characteristic, complemented
14#21455288C212yesmaximal, complemented
15M16×Dic122C211yesmaximal, characteristic, complemented
16#21454634C212yesmaximal, complemented
17C4×#137×C61C211yesmaximal, characteristic, complemented
18C2×#14519808C2212yes—
19#16840497C2211yescharacteristic
20#16840495C2212yes—
21#16840491—21no—
22#16840491—22no—
23#16840491—21no—
24#16840491C2212yes—
25#16840491C2212yes—
26#16840491C2214yes—
27#16840490C2211yescharacteristic
28#16840484C2212yes—
29#16840482C2211yescharacteristic
30#16840461—22no—
31#16840458—21no—
32#16840433C2211yescharacteristic
33#16840421—21no—
34#16840312C2211yescharacteristic
35#16840308C2212yes—
36C2×#14519777—21no—
37C2×#14519777C2211yescharacteristic
38#16840296—21no—
39#16840290—22no—
40C2×#14519768—22no—
41C2×#14519768C2212yes—
42C4×#11758222—21no—
43#16840230C2212yes—
44C2×Q8×Dic61C2212yes—
45C2×C4×Dic122—21no—
46C2×C4×Dic122C2211yescharacteristic
47#16840129C2214yes—
48#16840125C2214yes—
49#16840122C2214yes—
50#16840118C2214yes—
51#16840115C2214yes—
52#16840113C2212yes—
53#16840109C2212yes—
54#16840072C2214yes—
55#16840068C2214yes—
56#16840065C2214yes—
57#16840061C2214yes—
58#16840057C2212yes—
59#16840052C2212yes—
60#16840047C2212yes—
61#16840042C2212yes—
62#16839986C2214yes—
63#16839984C2214yes—
64#16839982C2214yes—
65#16839972C2212yes—
66#16839970C2214yes—
67#16839962C2212yes—
68#16839960C2214yes—
69#16839892C2212yes—
70#16839890C2214yes—
71C8×Dic122C2212yes—
72#16839866C2214yes—
73#16839865C2214yes—
74#16839854C2214yes—
75#16839847C2214yes—
76#16839805C2212yes—
77#16839786C2211yescharacteristic
78#16839785C2212yes—
79#16839764C2212yes—
80#16839764C2212yes—
81#16839763C2212yes—
82#16839761C2212yes—
83M16×Dic61C2212yes—
84C2×#137×C61C2211yescharacteristic
85C4×#41×C61C2211yescharacteristic
86C2×C4×Q8×C61C2211yescharacteristic
87C61×#441C2212yes—
88C61×#440C2212yes—
89C4×Q16×C61C2212yes—
90C4×SD16×C61C2212yes—
91C61×#428C2211yescharacteristic
92C61×#419C2211yescharacteristic
93C61×#417C2211yescharacteristic
94C4×M16×C61C2211yescharacteristic
95C2×#11758222—21no—
96C2×#11758222C2312yes—
97C22×Dic122—21no—
98C22×Dic122D411yescharacteristic
99#14519808—28no—
100C2×#11758202C2314yes—
101C2×#11758201C2314yes—
102C2×#11758194C2312yes—
103#14519777—22no—
104#14519777—22no—
105#14519777—24no—
106#14519777—21no—
107#14519777—21no—
108#14519777C2311yescharacteristic
109#14519777C2312yes—
110#14519777C2312yes—
111#14519775C2312yes—
112#14519774C2311yescharacteristic
113#14519773C2312yes—
114#14519772—22no—
115#14519771—22no—
116#14519770—22no—
117#14519769—21no—
118#14519768—24no—
119#14519768—24no—
120#14519768—24no—
121#14519768—24no—
122#14519768—22no—
123#14519768—22no—
124#14519768C2314yes—
125#14519768C2314yes—
126#14519767—22no—
127#14519766C2312yes—
128#14519765—21no—
129#14519765C2312yes—
130#14519764C2312yes—
131#14519763—22no—
132#14519762—22no—
133#14519760—22no—
134#14519759—22no—
135#14519756—21no—
136#14519755—22no—
137#14519751—21no—
138#14519751—21no—
139#14519751—21no—
140#14519750—22no—
141#14519749—22no—
142#14519749—22no—
143Q8×Dic61—22no—
144Q8×Dic61—22no—
145Q8×Dic61C2314yes—
146Q8×Dic61C2314yes—
147C4×Dic122—21no—
148C4×Dic122—22no—
149C4×Dic122—22no—
150C4×Dic122—24no—
151C4×Dic122D411yescharacteristic
152C4×Dic122D412yes—
153C4×Dic122D411yescharacteristic
154C4×Dic122C2311yescharacteristic
155C4×Dic122C2312yes—
156C4×Dic122C2311yescharacteristic
157#14519742C2312yes—
158#14519742C2312yes—
159C4×D244—21no—
160C4×D244—21no—
161C4×D244—21no—
162#14519739C2312yes—
163#14519739C2312yes—
164C4×C22⋊D61—22no—
165C4×C22⋊D61—22no—
166C4×C22⋊D61—22no—
167#14519737—22no—
168#14519737—22no—
169#14519736—21no—
170#14519734—22no—
171#14519734—22no—
172C2×C4⋊Dic61—21no—
173C2×C4⋊Dic61—22no—
174C2×C4⋊Dic61—22no—
175C2×C4⋊Dic61D411yescharacteristic
176C2×C4⋊Dic61C2312yes—
177C2×#11758196—22no—
178C2×#11758196D412yes—
179C2×C4×Dic61—22no—
180C2×C4×Dic61C2312yes—
181C42×D61—22no—
182#14519710C2314yes—
183#14519708C2314yes—
184C4⋊#92418C2312yes—
185C4⋊#92418C2312yes—
186#14519706C2314yes—
187#14519706C2314yes—
188#14519702C2314yes—
189#14519702C2314yes—
190#14519701C2314yes—
191#14519700C2314yes—
192#14519699C2314yes—
193#14519699C2314yes—
194#14519698C2314yes—
195#14519697C2314yes—
196#14519687C2314yes—
197C8×Dic61C2314yes—
198C2×#41×C61C2311yescharacteristic
199C22×Q8×C61C2311yescharacteristic
200#137×C61—24no—
201C2×Q16×C61C2312yes—
202C2×SD16×C61C2312yes—
203C2×M16×C61C2311yescharacteristic
204C2×M16×C61C2311yescharacteristic
205C4×Q8×C61—21no—
206C4×Q8×C61—21no—
207C4×Q8×C61C2312yes—
208C4×Q8×C61C2311yescharacteristic
209C4×Q8×C61C2311yescharacteristic
210C4×Q8×C61C2312yes—
211C4×D4×C61—21no—
212C4×D4×C61—21no—
213C4×D4×C61C2311yescharacteristic
214C4×D4×C61C2311yescharacteristic
215#117×C61—21no—
216#117×C61C2311yescharacteristic
217C2×C4⋊C4×C61—21no—
218C2×C4⋊C4×C61C2311yescharacteristic
219C2×C42×C61—21no—
220C2×C42×C61—21no—
221C2×C42×C61C2311yescharacteristic
222#107×C61C2312yes—
223#106×C61C2312yes—
224#103×C61C2312yes—
225#103×C61C2312yes—
226#103×C61C2312yes—
227#102×C61C2312yes—
228#97×C61C2312yes—
229C4×C8×C61C2312yes—
230#41×C61—22no—
231#41×C61—22no—
232C2×Q8×C61—21no—
233C2×Q8×C61—22no—
234C2×Q8×C61#4114yescomplemented
235C2×Q8×C61C2411yescharacteristic
236C2×Q8×C61C2412yes—
237C2×D4×C61—21no—
238C2×D4×C61C2411yescharacteristic
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2411yescharacteristic
247C2×C22⋊D61—22no—
248C2×C22⋊D61—22no—
249C2×C22⋊D61—22no—
250C22×Dic61—22no—
251C22×Dic61C2×D412yes—
252C22×Dic61C2×D412yes—
253#11758222—24no—
254#11758222—24no—
255#11758222—44no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244C2412yes—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—42no—
265C2×Dic122—44no—
266C2×Dic122C2×D411yescharacteristic
267C2×Dic122C2×D411yescharacteristic
268C2×Dic122C2×D412yes—
269C2×Dic122C2412yes—
270Q16×C61—24no—
271SD16×C61—24no—
272M16×C61—22no—
273M16×C61—22no—
274C2×C8×C61C2412yes—
275C2×C8×C61C2412yes—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—22no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61C2412yes—
282C4⋊C4×C61C2411yescharacteristic
283C4⋊C4×C61C2411yescharacteristic
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C42×C61—21no—
288C42×C61—21no—
289C42×C61—21no—
290C42×C61—22no—
291C42×C61—22no—
292C42×C61C2×D411yescharacteristic
293C42×C61C2×D411yescharacteristic
294C42×C61C2411yescharacteristic
295C42×C61C2411yescharacteristic
296C22⋊Dic61—22no—
297C22⋊Dic61—22no—
298#11758202—28no—
299#11758201—28no—
300#11758198—22no—
301#11758198—22no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—22no—
306C4⋊Dic61—22no—
307C4⋊Dic61—22no—
308C4⋊Dic61—22no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61—24no—
312C4⋊Dic61—24no—
313C4⋊Dic61—24no—
314C4⋊Dic61—24no—
315C4⋊Dic61C2×D411yescharacteristic
316C4⋊Dic61C2×D411yescharacteristic
317C4⋊Dic61C2×D412yes—
318C4⋊Dic61C2414yes—
319#11758196—24no—
320#11758196—24no—
321#11758196—22no—
322#11758196—22no—
323#11758196—22no—
324#11758196—22no—
325#11758196C2×D412yes—
326#11758196C2×D412yes—
327#11758196C2×D412yes—
328#11758196C2×D412yes—
329C4×Dic61—22no—
330C4×Dic61—22no—
331C4×Dic61—24no—
332C4×Dic61—24no—
333C4×Dic61C2×D412yes—
334C4×Dic61C2×D412yes—
335C4×Dic61C2412yes—
336C4×Dic61C2412yes—
337#11758194—24no—
338C2×#92418C2414yes—
339C23×C61—21no—
340C23×C61C22×D411yescharacteristic
341C22×D61—22no—
342Q8×C61—24no—
343Q8×C61—22no—
344Q8×C61—21no—
345Q8×C61—21no—
346Q8×C61C2×#4114yes—
347D4×C61—21no—
348D4×C61—21no—
349D4×C61—42no—
350C2×C4×C61—24no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—22no—
356C2×C4×C61—21no—
357C2×C4×C61—41no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
360C2×C4×C61—42no—
361C2×C4×C61—81no—
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C2×#4112yes—
368C2×C4×C612−1+412yes—
369C2×C4×C61C2511yescharacteristic
370C22⋊D61—44no—
371C22⋊D61—44no—
372C22⋊D61—82no—
373C2×Dic61—22no—
374C2×Dic61—24no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—44no—
378C2×Dic61C22×D412yes—
379C2×Dic61C22×D412yes—
380C2×Dic61C22×D412yes—
381C2×Dic61C22×D412yes—
382D244—22no—
383D244—22no—
384D244—42no—
385D244—81no—
386C4×D61—44no—
387C4×D61—44no—
388C4×D61—82no—
389Dic122—22no—
390Dic122—22no—
391Dic122—22no—
392Dic122—22no—
393Dic122—42no—
394Dic122—44no—
395Dic122—44no—
396C8×C61—22no—
397C8×C61—22no—
398#92418—24no—
399#61320—611nomaximal, Sylow
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61#54812yes—
406C22×C61C23×D411yescharacteristic
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—24no—
413C4×C61—21no—
414C4×C61—41no—
415C4×C61—42no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61#54812yes—
419C4×C61#57512yes—
420C4×C61C22×#4111yescharacteristic
421C4×C61C2×2−1+411yescharacteristic
422Dic61—22no—
423Dic61—22no—
424Dic61—22no—
425Dic61—22no—
426Dic61—42no—
427Dic61—44no—
428#3480—611no—
429C2×#557—611no—
430#3377—614no—
431#3374—612no—
432#3371—614no—
433#3368—612no—
434#3365—612no—
435#3364—612no—
436#3142—612no—
437#3141—611no—
438#3080—612no—
439#3079—611no—
440#3037—612no—
441#3037—611no—
442Q8×M16—611no—
443C4×#137—612no—
444C4×#137D6111yescharacteristic, complemented
445C2×C61—22no—
446C2×C61—81no—
447C2×C61C2×#54811yescharacteristic
448C2×C61C2×#57511yescharacteristic
449C2×C61#358611yescharacteristic
450D61—82no—
451C2×#137—612no—
452C2×#137C2×D6111yescharacteristic
453#559—611no—
454#559—612no—
455#557—612no—
456#557—612no—
457#557—614no—
458#557—611no—
459#557—1221no—
460#557—1221no—
461#557—1222no—
462#556—612no—
463#556—611no—
464#553—1221no—
465#553—1222no—
466#550—611no—
467#548—1221no—
468#532—612no—
469#532—611no—
470C2×C4⋊Q8—611no—
471C2×C4⋊Q8—1221no—
472#529—1221no—
473#529—1222no—
474C2×#125—612no—
475C2×#125—1222no—
476C4×#41—612no—
477C4×#41—1221no—
478C4×#41C2×D6111yescharacteristic
479C2×C4×Q8—611no—
480C2×C4×Q8—612no—
481C2×C4×Q8—1221no—
482C2×C4×Q8C2×D6111yescharacteristic
483#491—614no—
484#490—614no—
485#489—614no—
486#488—614no—
487#488—614no—
488#487—612no—
489#486—612no—
490#479—614no—
491#479—614no—
492#478—614no—
493#478—614no—
494#477—612no—
495#476—612no—
496#475—612no—
497#474—612no—
498#464—614no—
499#464—614no—
500#464—614no—
501#462—614no—
502#462—612no—
503#460—614no—
504#460—612no—
505#446—614no—
506#446—612no—
507C8×Q8—612no—
508#441—614no—
509#441C2×D6112yes—
510#440—614no—
511#440C2×D6112yes—
512C4×Q16—614no—
513C4×Q16C2×D6112yes—
514C4×SD16—614no—
515C4×SD16C2×D6112yes—
516#428—612no—
517#428C2×D6111yescharacteristic
518#423—612no—
519#423—611no—
520#419C2×D6111yescharacteristic
521#417—612no—
522#417—612no—
523#417—612no—
524#417—612no—
525#417C2×D6111yescharacteristic
526C4×M16—612no—
527C4×M16C2×D6111yescharacteristic
528C61#6132011yescharacteristic, complemented, Sylow
529C2×#41—612no—
530C2×#41—1221no—
531C2×#41C22×D6111yescharacteristic
532C22×Q8—611no—
533C22×Q8—1221no—
534C22×Q8C22×D6111yescharacteristic
535#137—24no—
536#137—1228no—
537C2×Q16—614no—
538C2×Q16C22×D6112yes—
539C2×SD16—614no—
540C2×SD16C22×D6112yes—
541C2×M16—612no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C4⋊Q8—612no—
545C4⋊Q8—612no—
546C4⋊Q8—612no—
547C4⋊Q8—611no—
548C4⋊Q8—1222no—
549C4⋊Q8—1222no—
550C4⋊Q8—1224no—
551C4⋊Q8—1221no—
552C4⋊Q8—1221no—
553#127—612no—
554#127—611no—
555#126—1222no—
556#126—1222no—
557#126—1222no—
558#125—614no—
559#125—614no—
560#125—1221no—
561#125—1222no—
562#125—1222no—
563#125—1224no—
564#125—1224no—
565#125—1224no—
566#125—1224no—
567#125—1222no—
568#124—612no—
569#124—612no—
570#124—612no—
571#124—1221no—
572#124—1222no—
573#123—1222no—
574#123—1222no—
575#123—1222no—
576C22⋊Q8—1222no—
577C22⋊Q8—1221no—
578#121—1222no—
579#121—1221no—
580#121—1222no—
581#121—1222no—
582#121—1221no—
583#121—1221no—
584C4×Q8—21no—
585C4×Q8—21no—
586C4×Q8—611no—
587C4×Q8—612no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—612no—
592C4×Q8—614no—
593C4×Q8—614no—
594C4×Q8—612no—
595C4×Q8—612no—
596C4×Q8—1222no—
597C4×Q8—1222no—
598C4×Q8—1224no—
599C4×Q8—1221no—
600C4×Q8—1222no—
601C4×Q8—1222no—
602C4×Q8C22×D6112yes—
603C4×Q8C22×D6112yes—
604C4×Q8C22×D6111yescharacteristic
605C4×Q8C22×D6111yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—612no—
609C4×D4—612no—
610C4×D4—1221no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1222no—
614C4×D4—1222no—
615C4×D4—1222no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4C22×D6111yescharacteristic
619C4×D4C22×D6111yescharacteristic
620#117—21no—
621#117—1222no—
622#117—1222no—
623#117—1221no—
624#117C22×D6111yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—612no—
629C2×C4⋊C4—1222no—
630C2×C4⋊C4—1222no—
631C2×C4⋊C4—1222no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4C22×D6111yescharacteristic
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—612no—
637C2×C42—1222no—
638C2×C42—1222no—
639C2×C42C22×D6111yescharacteristic
640#107—614no—
641#107C22×D6112yes—
642#106—614no—
643#106C22×D6112yes—
644C4⋊C8—614no—
645C4⋊C8—614no—
646C4⋊C8—612no—
647C4⋊C8—612no—
648#103—614no—
649#103—614no—
650#103—614no—
651#103—614no—
652#103C22×D6112yes—
653#103C22×D6112yes—
654#103C22×D6112yes—
655#102—614no—
656#102—614no—
657#102—614no—
658#102—614no—
659#102C22×D6112yes—
660#97—614no—
661#97C22×D6112yes—
662C4×C8—614no—
663C4×C8C22×D6112yes—
664#41—22no—
665#41—22no—
666#41—1224no—
667#41—1224no—
668#41—2444no—
669C2×Q8—21no—
670C2×Q8—22no—
671C2×Q8—611no—
672C2×Q8—611no—
673C2×Q8—612no—
674C2×Q8—612no—
675C2×Q8—1222no—
676C2×Q8—1222no—
677C2×Q8—2442no—
678C2×Q8—2444no—
679C2×Q8#1175822214yescomplemented
680C2×Q8C23×D6111yescharacteristic
681C2×Q8C23×D6112yes—
682C2×D4—21no—
683C2×D4—612no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4C23×D6111yescharacteristic
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—612no—
696C22×C4—612no—
697C22×C4—1222no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4D4×D6111yescharacteristic
702C22×C4D4×D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704Q16—24no—
705Q16—1228no—
706SD16—24no—
707SD16—1228no—
708M16—22no—
709M16—22no—
710M16—1224no—
711C2×C8—614no—
712C2×C8C23×D6112yes—
713C2×C8C23×D6112yes—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—612no—
720C4⋊C4—612no—
721C4⋊C4—612no—
722C4⋊C4—612no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—612no—
726C4⋊C4—614no—
727C4⋊C4—1224no—
728C4⋊C4—1224no—
729C4⋊C4—1224no—
730C4⋊C4—1224no—
731C4⋊C4—1224no—
732C4⋊C4—1224no—
733C4⋊C4—1222no—
734C4⋊C4—1222no—
735C4⋊C4—1222no—
736C4⋊C4—1222no—
737C4⋊C4—1222no—
738C4⋊C4—1222no—
739C4⋊C4—1222no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4C23×D6112yes—
743C4⋊C4C23×D6111yescharacteristic
744C4⋊C4C23×D6111yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—1222no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C22⋊C4—1222no—
752C22⋊C4—1222no—
753C22⋊C4—1222no—
754C22⋊C4—1222no—
755C22⋊C4—1222no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—22no—
760C42—22no—
761C42—612no—
762C42—612no—
763C42—612no—
764C42—612no—
765C42—1222no—
766C42—1222no—
767C42—1224no—
768C42—1224no—
769C42D4×D6111yescharacteristic
770C42D4×D6111yescharacteristic
771C42C23×D6111yescharacteristic
772C42C23×D6111yescharacteristic
773C23—21no—
774C23—1222no—
775C23C2×D4×D6111yescharacteristic
776Q8—22no—
777Q8—24no—
778Q8—21no—
779Q8—21no—
780Q8—1222no—
781Q8—1222no—
782Q8—1222no—
783Q8—1222no—
784Q8—2442no—
785Q8—2444no—
786Q8—2444no—
787Q8C2×#1175822214yes—
788D4—21no—
789D4—21no—
790D4—42no—
791D4—1222no—
792D4—1222no—
793D4—4881no—
794D4—4882no—
795D4—2444no—
796D4—2444no—
797D4—2442no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—81no—
810C2×C4—612no—
811C2×C4—612no—
812C2×C4—612no—
813C2×C4—612no—
814C2×C4—1222no—
815C2×C4—1224no—
816C2×C4—4882no—
817C2×C4—2444no—
818C2×C4—2442no—
819C2×C4—2442no—
820C2×C4—2444no—
821C2×C4—2444no—
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4C2×#1175822212yes—
828C2×C4#1451982412yes—
829C2×C4C24×D6111yescharacteristic
830C8—22no—
831C8—22no—
832C8—1224no—
833C22—21no—
834C22—21no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22#1684042112yes—
842C22C22×D4×D6111yescharacteristic
843C4—24no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—41no—
848C4—41no—
849C4—42no—
850C4—41no—
851C4—1222no—
852C4—1222no—
853C4—1222no—
854C4—1222no—
855C4—2442no—
856C4—2444no—
857C4#1684042112yes—
858C4#1684056112yes—
859C4C22×#1175822211yescharacteristic
860C4C2×#1451982411yescharacteristic
861C2—22no—
862C2—81no—
863C2—4882no—
864C2C2×#1684042111yescharacteristic
865C2C2×#1684056111yescharacteristic
866C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC4×#137×C61C2
socleC22×C61C23×D4
prime radical#21459412C2
hypercenterC4×#137D61
hypocenterC61#61320
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. C2×#16840491C2semidirect
3. #21458666C2semidirect
4. #21458620C2semidirect
5. #21458592C2semidirect
6. #21458546C2semidirect
7. #21458513C2semidirect
8. #21458502C2semidirect
9. #21456217C2semidirect
10. #21456213C2semidirect
11. #21455640C2semidirect
12. #21455634C2semidirect
13. #21455291C2semidirect
14. #21455288C2semidirect
15. M16×Dic122C2semidirect
16. #21454634C2semidirect
17. C4×#137×C61C2semidirect
234. C2×Q8×C61#41semidirect
444. C4×#137D61semidirect
528. C61#61320semidirect
679. C2×Q8#11758222semidirect

Maximal subgroups

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

subgroupindex
#214594122
C2×#168404912
#214586662
#214586202
#214585922
#214585462
#214585132
#214585022
#214562172
#214562132
#214556402
#214556342
#214552912
#214552882
M16×Dic1222
#214546342
C4×#137×C612
#6132061