Finite Group Databasebeta

← #30552388

Subgroups — #30552388

Order 15616.

1690 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic, complemented
2C2×#16840377C211yesmaximal, characteristic
3#21457116C214yesmaximal, complemented
4#21457114C214yesmaximal, complemented
5#21457101C214yesmaximal, complemented
6#21457099C214yesmaximal, complemented
7#21456363C212yesmaximal, complemented
8#21456203C212yesmaximal, complemented
9#21455769C212yesmaximal, complemented
10#21455757C212yesmaximal
11#21455626C211yesmaximal, characteristic, complemented
12#21455620C211yesmaximal, characteristic, complemented
13#21455616C211yesmaximal, characteristic, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3077C211yesmaximal, characteristic, complemented
16#16840392C2212yescomplemented
17#16840392C2212yescomplemented
18#16840391—21no—
19#16840391—21no—
20#16840389C2212yescomplemented
21#16840389C2212yescomplemented
22#16840387—21no—
23#16840387—21no—
24#16840377—22no—
25#16840377—22no—
26#16840377C2214yes—
27#16840377C2214yes—
28#16840319C2211yescharacteristic
29#16840316—22no—
30#16840316—22no—
31#16840315C2212yes—
32C2×#14519776C2211yescharacteristic
33C2×#14519770—21no—
34C2×#14519764C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519760—21no—
37C2×#14519757C2211yescharacteristic
38C2×#14519756—21no—
39C2×#14519748C2211yescharacteristic
40C2×C4×Dic122C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42#117×D61C2212yes—
43#16840170C2214yescomplemented
44#16840169C2214yescomplemented
45#16840166C2214yescomplemented
46#16840159C2214yescomplemented
47#16840120C2214yescomplemented
48#16840120C2214yescomplemented
49#16840115C2214yescomplemented
50#16840115C2214yescomplemented
51#16840106C2214yescomplemented
52#16840105C2214yescomplemented
53#16840099C2214yescomplemented
54#16840094C2214yescomplemented
55#16840085C2214yes—
56#16840084C2214yes—
57#16840079C2214yes—
58#16840074C2214yes—
59#16840070C2214yescomplemented
60#16840066C2214yescomplemented
61#16840062C2214yescomplemented
62#16840058C2212yescomplemented
63#16840054C2212yescomplemented
64#16840052C2212yescomplemented
65#16840048C2212yescomplemented
66#16840044C2212yescomplemented
67#16840042C2212yescomplemented
68#16839822C2214yescomplemented
69#16839822C2214yescomplemented
70#16839805C2212yes—
71#16839804C2212yes—
72#16839802C2212yes—
73#16839786C2211yescharacteristic
74#16839772C2212yes—
75#16839770C2212yes—
76#16839767C2212yes—
77#16839725C2212yes—
78M16×Dic61C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4×D4×C61C2211yescharacteristic
81C61×#478C2214yescomplemented
82C61×#476C2212yescomplemented
83C61×#474C2212yescomplemented
84C61×#428C2212yes—
85C61×#423C2211yescharacteristic
86C61×#418C2212yes—
87C22×Dic122—21no—
88C22×Dic122C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758194C2312yes—
92#14519777C2311yescharacteristic
93#14519777C2311yescharacteristic
94#14519776—22no—
95#14519776—22no—
96#14519776—22no—
97#14519776C2314yes—
98#14519776C2312yes—
99#14519776C2312yes—
100#14519775—22no—
101#14519775—22no—
102#14519770—24no—
103#14519770—24no—
104#14519769C2312yes—
105#14519768C2312yes—
106#14519768C2312yes—
107#14519767—22no—
108#14519767—22no—
109#14519767—22no—
110#14519767—22no—
111#14519764—22no—
112#14519764C2314yes—
113#14519763—24no—
114#14519763—24no—
115#14519760—24no—
116#14519760—24no—
117#14519757—22no—
118#14519757—22no—
119#14519757—22no—
120#14519757C2314yes—
121#14519756—21no—
122#14519756—21no—
123#14519756—24no—
124#14519756—24no—
125#14519755—22no—
126#14519755—22no—
127#14519755—22no—
128#14519755—22no—
129#14519754—22no—
130#14519754—22no—
131#14519753—22no—
132#14519753—22no—
133#14519748—22no—
134#14519748C2314yes—
135C4×Dic122—21no—
136C4×Dic122—21no—
137C4×Dic122—21no—
138C4×Dic122—21no—
139C4×Dic122—22no—
140C4×Dic122—22no—
141C4×Dic122C2312yes—
142C4×Dic122C2312yes—
143#14519736C2312yes—
144#14519735C2312yes—
145#14519735C2312yes—
146#14519734—22no—
147#14519734D412yes—
148#14519734D412yes—
149#14519734C2312yes—
150#14519734C2312yes—
151#14519733—22no—
152C2×C4⋊Dic61—21no—
153C2×C4⋊Dic61C2311yescharacteristic
154C2×#11758196—21no—
155C2×#11758196—21no—
156C2×#11758196D411yescharacteristic
157C2×#11758196D411yescharacteristic
158C4⋊C4×D61C2312yes—
159C4⋊C4×D61C2312yes—
160C2×C22⋊Dic61—21no—
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61—21no—
163C2×#11758198—21no—
164C2×#11758198D411yescharacteristic
165C2×#11758198D411yescharacteristic
166C22⋊C4×D61—22no—
167C2×C4×Dic61—21no—
168C2×C4×Dic61C2311yescharacteristic
169C42×D61—22no—
170#14519711C2314yes—
171#14519710C2314yes—
172#14519710C2314yes—
173#14519709C2314yes—
174#14519708C2314yes—
175#14519708C2314yes—
176C4⋊#92418C2312yes—
177C4⋊#92418C2312yes—
178#14519702C2314yes—
179#14519702C2314yes—
180#14519700C2314yes—
181#14519700C2314yes—
182#14519698C2314yes—
183#14519698C2314yes—
184#14519689C2314yes—
185#14519689C2314yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C22×D4×C61C2311yescharacteristic
189C23×C4×C61—21no—
190C2×M16×C61C2312yes—
191C4⋊Q8×C61C2311yescharacteristic
192C4⋊Q8×C61C2311yescharacteristic
193#125×C61C2312yes—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—21no—
196C4×Q8×C61—21no—
197C4×Q8×C61—21no—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61C2312yes—
201C4×D4×C61C2312yes—
202#117×C61C2312yes—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#107×C61C2314yes—
207#106×C61C2314yes—
208C4⋊C8×C61C2312yes—
209C4⋊C8×C61C2312yes—
210#102×C61C2314yes—
211#102×C61C2314yes—
212C24×C61—21no—
213C23×D61C2×D411yescharacteristic
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—22no—
218C2×D4×C61—22no—
219C2×D4×C61C2412yes—
220C22×C4×C61—21no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—82no—
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—24no—
228C2×C22⋊D61—82no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2412yes—
240C2×Dic122—22no—
241C2×Dic122—22no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—24no—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—82no—
249C2×Dic122C2412yes—
250M16×C61—24no—
251C2×C8×C61C2414yes—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2412yes—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C42×C61—22no—
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2411yescharacteristic
267C42×C61C2411yescharacteristic
268C22⋊Dic61—22no—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271C22⋊Dic61—24no—
272#11758198—22no—
273#11758198—22no—
274#11758198—24no—
275#11758198C2×D412yes—
276#11758198C2×D412yes—
277#11758198C2×D412yes—
278#11758198C2×D412yes—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—24no—
283C4⋊Dic61—22no—
284C4⋊Dic61—22no—
285C4⋊Dic61C2412yes—
286C4⋊Dic61C2412yes—
287C4⋊Dic61C2412yes—
288#11758196—22no—
289#11758196—22no—
290#11758196—22no—
291#11758196—22no—
292#11758196—22no—
293#11758196—22no—
294#11758196—24no—
295#11758196—22no—
296#11758196—22no—
297#11758196—22no—
298#11758196—22no—
299#11758196C2×D412yes—
300#11758196C2×D412yes—
301#11758196C2×D412yes—
302#11758196C2×D412yes—
303C4×Dic61—22no—
304C4×Dic61—22no—
305C4×Dic61—22no—
306C4×Dic61—22no—
307C4×Dic61—22no—
308C4×Dic61C2×D412yes—
309C4×Dic61C2412yes—
310#11758194—24no—
311C2×#92418C2414yes—
312C23×C61—22no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61C22×D411yescharacteristic
317C22×D61—22no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61C22×D412yes—
321Q8×C61—81no—
322Q8×C61—81no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—42no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—42no—
332C2×C4×C61—82no—
333C2×C4×C61—82no—
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C612−1+412yes—
340C2×C4×C612−1+412yes—
341C2×C4×C61C2511yescharacteristic
342C22⋊D61—84no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61C22×D412yes—
353C2×Dic61C22×D412yes—
354C2×Dic61C22×D412yes—
355C4×D61—24no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—82no—
359C4×D61—82no—
360Dic122—22no—
361Dic122—22no—
362Dic122—42no—
363Dic122—82no—
364Dic122—82no—
365Dic122—84no—
366Dic122—81no—
367Dic122—81no—
368C8×C61—24no—
369#92418—24no—
370#60870—611nomaximal, Sylow
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—84no—
377C22×C61#53612yes—
378C22×C61C23×D411yescharacteristic
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—82no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61#53612yes—
391C4×C61C2×2−1+411yescharacteristic
392C4×C61C2×2−1+411yescharacteristic
393Dic61—22no—
394Dic61—22no—
395Dic61—22no—
396Dic61—42no—
397Dic61—42no—
398Dic61—42no—
399Dic61—42no—
400#3458—611no—
401C2×#542—611no—
402#3244—614no—
403#3244—614no—
404#3243—614no—
405#3243—614no—
406#3165—612no—
407#3140—612no—
408#3095—612no—
409#3094—612no—
410#3078—611no—
411#3078—611no—
412#3077—611no—
413#3077D6111yescharacteristic, complemented
414#2921—611no—
415C2×C61—22no—
416C2×C61—82no—
417C2×C61C2×#53611yescharacteristic
418C2×C61#358511yescharacteristic
419C2×C61#358611yescharacteristic
420D61—42no—
421#544—612no—
422#544—612no—
423#544—612no—
424#544—612no—
425#544—1221no—
426#544—1221no—
427#543—1221no—
428#543—1221no—
429#542—614no—
430#542—614no—
431#542—1222no—
432#542—1222no—
433#533—612no—
434#533—611no—
435#533—1222no—
436#533—1222no—
437#533C2×D6111yescharacteristic
438C2×C4⋊Q8—611no—
439C2×#126—1221no—
440C2×#124—611no—
441C2×#124—1221no—
442C2×#123—1221no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—1221no—
445C2×#121—611no—
446C2×C4×Q8—611no—
447C2×C4×D4C2×D6111yescharacteristic
448C2×#117—611no—
449C2×#117—612no—
450#501—614no—
451#501—614no—
452#500—614no—
453#498—614no—
454#489—614no—
455#489—614no—
456#488—614no—
457#488—614no—
458#485—614no—
459#485—614no—
460#484—614no—
461#483—614no—
462#482—614no—
463#482—614no—
464#481—614no—
465#480—614no—
466#479—614no—
467#479—614no—
468#478—614no—
469#478C2×D6114yescomplemented
470#477—612no—
471#477—612no—
472#476—612no—
473#476C2×D6112yescomplemented
474#475—612no—
475#475—612no—
476#474—612no—
477#474C2×D6112yescomplemented
478#433—614no—
479#433—614no—
480#428—612no—
481#428—612no—
482#428—612no—
483#428C2×D6112yes—
484#423—611no—
485#423C2×D6111yescharacteristic
486#419—612no—
487#419—612no—
488#418—612no—
489#418C2×D6112yes—
490#407—612no—
491C4×M16—612no—
492C61#6087011yescharacteristic, complemented, Sylow
493C22×Q8—611no—
494C22×Q8—1221no—
495C22×D4—1221no—
496C22×D4C22×D6111yescharacteristic
497C23×C4—21no—
498C23×C4—611no—
499C2×M16—612no—
500C2×M16C22×D6112yes—
501C4⋊Q8—614no—
502C4⋊Q8—612no—
503C4⋊Q8—612no—
504C4⋊Q8—611no—
505C4⋊Q8—611no—
506C4⋊Q8—1222no—
507C4⋊Q8—1222no—
508C4⋊Q8—1222no—
509C4⋊Q8—1222no—
510C4⋊Q8—1222no—
511C4⋊Q8C22×D6111yescharacteristic
512C4⋊Q8C22×D6111yescharacteristic
513#126—1224no—
514#126—1224no—
515#125—612no—
516#125—612no—
517#125—612no—
518#125—1222no—
519#125—1222no—
520#125—1222no—
521#125—1222no—
522#125C22×D6112yes—
523#124—614no—
524#124—1222no—
525#124—1224no—
526#124—1224no—
527#123—1224no—
528#123—1224no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—614no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536C22⋊Q8—1222no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541C22⋊Q8—1222no—
542C22⋊Q8—1222no—
543C22⋊Q8—1224no—
544C22⋊Q8—1224no—
545C22⋊Q8—1221no—
546C22⋊Q8—1221no—
547#121—614no—
548#121—1222no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8—612no—
552C4×Q8—612no—
553C4×Q8—1222no—
554C4×Q8—1222no—
555C4×Q8—1221no—
556C4×Q8—1221no—
557C4×Q8—1221no—
558C4×Q8—1221no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4C22×D6112yes—
562C4×D4C22×D6112yes—
563#117—612no—
564#117—612no—
565#117—612no—
566#117—612no—
567#117—612no—
568#117—612no—
569#117—612no—
570#117—1222no—
571#117—1222no—
572#117C22×D6112yes—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—612no—
577C2×C4⋊C4—612no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4C22×D6111yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—611no—
584C2×C22⋊C4—611no—
585C2×C22⋊C4—1222no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C42—611no—
591C2×C42—1222no—
592C2×C42—1221no—
593C2×C42C22×D6111yescharacteristic
594#107—614no—
595#107—614no—
596#107—614no—
597#107C22×D6114yes—
598#106—614no—
599#106—614no—
600#106—614no—
601#106C22×D6114yes—
602C4⋊C8—612no—
603C4⋊C8—612no—
604C4⋊C8C22×D6112yes—
605C4⋊C8C22×D6112yes—
606#103—614no—
607#103—614no—
608#103—614no—
609#103—614no—
610#102—614no—
611#102—614no—
612#102C22×D6114yes—
613#102C22×D6114yes—
614C22⋊C8—614no—
615C22⋊C8—614no—
616#97—614no—
617C4×C8—614no—
618C24—21no—
619C24—611no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—612no—
623C2×Q8—1222no—
624C2×Q8—1222no—
625C2×Q8—1224no—
626C2×Q8—1221no—
627C2×Q8—1221no—
628C2×Q8—1221no—
629C2×Q8—1222no—
630C2×Q8—1222no—
631C2×Q8—4882no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—1224no—
636C2×D4—4882no—
637C2×D4C23×D6112yes—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—82no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656M16—24no—
657M16—1224no—
658C2×C8—614no—
659C2×C8C23×D6114yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—612no—
666C4⋊C4—612no—
667C4⋊C4—612no—
668C4⋊C4—612no—
669C4⋊C4—612no—
670C4⋊C4—612no—
671C4⋊C4—612no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4—1222no—
677C4⋊C4—1222no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1222no—
682C4⋊C4—1221no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C4⋊C4—1222no—
686C4⋊C4—1222no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4C23×D6112yes—
690C4⋊C4C23×D6112yes—
691C4⋊C4C23×D6112yes—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—612no—
696C22⋊C4—612no—
697C22⋊C4—612no—
698C22⋊C4—612no—
699C22⋊C4—1222no—
700C22⋊C4—1222no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1222no—
706C42—22no—
707C42—612no—
708C42—612no—
709C42—1222no—
710C42—1222no—
711C42—1222no—
712C42—1222no—
713C42—1222no—
714C42D4×D6111yescharacteristic
715C42D4×D6111yescharacteristic
716C42C23×D6111yescharacteristic
717C42C23×D6111yescharacteristic
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—612no—
723C23—1222no—
724C23—2441no—
725C23—2441no—
726C23C2×D4×D6111yescharacteristic
727Q8—81no—
728Q8—81no—
729Q8—1222no—
730Q8—1222no—
731Q8—4881no—
732Q8—4881no—
733Q8—4882no—
734Q8—4882no—
735Q8—4884no—
736Q8—2442no—
737D4—22no—
738D4—22no—
739D4—42no—
740D4—4884no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—612no—
750C2×C4—612no—
751C2×C4—612no—
752C2×C4—1222no—
753C2×C4—1224no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—4882no—
761C2×C4—4882no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4C2×D4×D6111yescharacteristic
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4#1451982412yes—
772C2×C4#1451982512yes—
773C2×C4C24×D6111yescharacteristic
774C8—24no—
775C8—1224no—
776C22—21no—
777C22—21no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—4882no—
786C22#1684033512yes—
787C22C22×D4×D6111yescharacteristic
788C4—21no—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—1222no—
796C4—1222no—
797C4—1222no—
798C4—2442no—
799C4—2442no—
800C4—2442no—
801C4—2442no—
802C4#1684033512yes—
803C4C2×#1451982411yescharacteristic
804C4C2×#1451982511yescharacteristic
805C2—22no—
806C2—82no—
807C2—2442no—
808C2C2×#1684033511yescharacteristic
809C2#2146059511yescharacteristic
810C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3077C2
socleC22×C61C23×D4
prime radicalC2×#14519748C22
hypercenter#3077D61
hypocenterC61#60870
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #21459222C2semidirect
3. #21457116C2semidirect
4. #21457114C2semidirect
5. #21457101C2semidirect
6. #21457099C2semidirect
7. #21456363C2semidirect
8. #21456203C2semidirect
9. #21455769C2semidirect
11. #21455626C2semidirect
12. #21455620C2semidirect
13. #21455616C2semidirect
14. #21454456C2semidirect
15. C61×#3077C2semidirect
16. #16840392C22semidirect
17. #16840392C22semidirect
20. #16840389C22semidirect
21. #16840389C22semidirect
43. #16840170C22semidirect
44. #16840169C22semidirect
45. #16840166C22semidirect
46. #16840159C22semidirect
47. #16840120C22semidirect
48. #16840120C22semidirect
49. #16840115C22semidirect
50. #16840115C22semidirect
51. #16840106C22semidirect
52. #16840105C22semidirect
53. #16840099C22semidirect
54. #16840094C22semidirect
59. #16840070C22semidirect
60. #16840066C22semidirect
61. #16840062C22semidirect
62. #16840058C22semidirect
63. #16840054C22semidirect
64. #16840052C22semidirect
65. #16840048C22semidirect
66. #16840044C22semidirect
67. #16840042C22semidirect
68. #16839822C22semidirect
69. #16839822C22semidirect
81. C61×#478C22semidirect
82. C61×#476C22semidirect
83. C61×#474C22semidirect
413. #3077D61semidirect
469. #478C2×D61semidirect
473. #476C2×D61semidirect
477. #474C2×D61semidirect
492. C61#60870semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168403772
#214571162
#214571142
#214571012
#214570992
#214563632
#214562032
#214557692
#214557572
#214556262
#214556202
#214556162
#214544562
C61×#30772
#6087061