Finite Group Databasebeta

← #30552384

Subgroups — #30552384

Order 15616.

1690 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic, complemented
2C2×#16840381C211yesmaximal, characteristic
3#21457112C214yesmaximal, complemented
4#21457110C214yesmaximal, complemented
5#21457097C214yesmaximal, complemented
6#21457095C214yesmaximal, complemented
7#21456366C211yesmaximal, characteristic, complemented
8#21456365C211yesmaximal, characteristic, complemented
9#21456205C211yesmaximal, characteristic, complemented
10#21455765C212yesmaximal, complemented
11#21455757C212yesmaximal
12#21455621C212yesmaximal, complemented
13#21455613C212yesmaximal, complemented
14#21454455C211yesmaximal, characteristic, complemented
15C61×#3140C211yesmaximal, characteristic, complemented
16#16840392C2212yescomplemented
17#16840392C2212yescomplemented
18#16840391—21no—
19#16840391—21no—
20#16840389C2212yescomplemented
21#16840389C2212yescomplemented
22#16840387—21no—
23#16840387—21no—
24#16840381—22no—
25#16840381—22no—
26#16840381C2214yes—
27#16840381C2214yes—
28#16840319C2211yescharacteristic
29#16840316—22no—
30#16840316—22no—
31#16840315C2212yes—
32C2×#14519777C2211yescharacteristic
33C2×#14519770—21no—
34C2×#14519763—21no—
35C2×#14519761—21no—
36C2×#14519754—21no—
37C2×#14519753C2211yescharacteristic
38C2×#14519748C2211yescharacteristic
39C2×Q8×Dic61C2211yescharacteristic
40C2×D4×Dic61C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42#117×D61C2212yes—
43#16840172C2214yescomplemented
44#16840171C2214yescomplemented
45#16840167C2212yescomplemented
46#16840165C2212yescomplemented
47#16840160C2212yescomplemented
48#16840158C2212yescomplemented
49#16840121C2212yescomplemented
50#16840121C2212yescomplemented
51#16840116C2214yescomplemented
52#16840102C2214yescomplemented
53#16840101C2214yescomplemented
54#16840096C2214yescomplemented
55#16840091C2214yescomplemented
56#16840085C2214yes—
57#16840084C2214yes—
58#16840079C2214yes—
59#16840074C2214yes—
60#16840071C2214yescomplemented
61#16840067C2214yescomplemented
62#16840064C2214yescomplemented
63#16840060C2214yescomplemented
64#16840055C2214yescomplemented
65#16840050C2214yescomplemented
66#16840045C2214yescomplemented
67#16840040C2214yescomplemented
68#16839824C2214yescomplemented
69#16839821C2214yescomplemented
70#16839805C2212yes—
71#16839805C2212yes—
72#16839804C2212yes—
73#16839804C2212yes—
74#16839785C2212yes—
75#16839771C2212yes—
76#16839767C2212yes—
77#16839725C2212yes—
78C4×#11758194C2211yescharacteristic
79C61×#533C2211yescharacteristic
80C2×#124×C61C2211yescharacteristic
81C61×#489C2212yescomplemented
82C61×#489C2212yescomplemented
83C61×#488C2214yescomplemented
84C61×#419C2212yes—
85C61×#418C2212yes—
86C4×M16×C61C2211yescharacteristic
87C22×Dic122—21no—
88C22×C22⋊D61—21no—
89C23×Dic61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758194C2312yes—
92#14519777—21no—
93#14519777—21no—
94#14519777C2312yes—
95#14519777C2312yes—
96#14519777C2311yescharacteristic
97#14519777C2311yescharacteristic
98#14519776—22no—
99#14519776—22no—
100#14519776C2312yes—
101#14519776C2312yes—
102#14519775—22no—
103#14519775—22no—
104#14519770—24no—
105#14519770—24no—
106#14519769C2312yes—
107#14519768C2312yes—
108#14519768C2312yes—
109#14519767—22no—
110#14519767—22no—
111#14519767—22no—
112#14519767—22no—
113#14519763—24no—
114#14519763—24no—
115#14519761—24no—
116#14519761—24no—
117#14519757—22no—
118#14519757—22no—
119#14519756—21no—
120#14519756—21no—
121#14519755—22no—
122#14519755—22no—
123#14519755—22no—
124#14519755—22no—
125#14519754—22no—
126#14519754—22no—
127#14519754—24no—
128#14519754—24no—
129#14519753—22no—
130#14519753—22no—
131#14519753—22no—
132#14519753C2314yes—
133#14519748—22no—
134#14519748C2314yes—
135Q8×Dic61—22no—
136Q8×Dic61C2314yes—
137C4×Dic122—21no—
138C4×Dic122—21no—
139C4×Dic122—22no—
140C4×Dic122—22no—
141D4×Dic61—22no—
142D4×Dic61C2314yes—
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⋊Dic61—21no—
154C2×C4⋊Dic61C2311yescharacteristic
155C2×C4⋊Dic61C2311yescharacteristic
156C2×#11758196—21no—
157C2×#11758196D411yescharacteristic
158C2×#11758196D411yescharacteristic
159C4⋊C4×D61C2312yes—
160C4⋊C4×D61C2312yes—
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#14519711C2314yes—
172#14519710C2314yes—
173#14519710C2314yes—
174#14519709C2314yes—
175#14519709C2314yes—
176#14519708C2314yes—
177#14519708C2314yes—
178#14519706C2314yes—
179#14519706C2314yes—
180#14519701C2314yes—
181#14519701C2314yes—
182#14519698C2314yes—
183#14519698C2314yes—
184#14519689C2314yes—
185#14519689C2314yes—
186#14519688C2312yes—
187C4×#92418C2312yes—
188C22×Q8×C61C2311yescharacteristic
189C22×D4×C61C2311yescharacteristic
190C2×M16×C61C2312yes—
191C4⋊Q8×C61C2311yescharacteristic
192C4⋊Q8×C61C2311yescharacteristic
193#125×C61C2312yes—
194#124×C61—21no—
195#124×C61—21no—
196#124×C61C2312yes—
197#124×C61C2312yes—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61—21no—
200C4×Q8×C61—21no—
201C4×Q8×C61—21no—
202#117×C61C2312yes—
203C2×C22⋊C4×C61—21no—
204C2×C22⋊C4×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#103×C61C2314yes—
207#103×C61C2314yes—
208#102×C61C2314yes—
209#102×C61C2314yes—
210#97×C61C2312yes—
211C4×C8×C61C2312yes—
212C24×C61—21no—
213C23×D61C2×D411yescharacteristic
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—24no—
218C2×Q8×C61C2412yes—
219C2×D4×C61—21no—
220C2×D4×C61—24no—
221C2×D4×C61C2412yes—
222C22×C4×C61—21no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2411yescharacteristic
226C2×C22⋊D61—24no—
227C2×C22⋊D61—82no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—24no—
231C22×Dic61—82no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C2×C4×D61—24no—
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—22no—
245C2×Dic122—22no—
246C2×Dic122—82no—
247M16×C61—24no—
248C2×C8×C61C2414yes—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2412yes—
254C4⋊C4×C61C2412yes—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—22no—
260C42×C61—22no—
261C42×C61C2×D411yescharacteristic
262C42×C61C2×D411yescharacteristic
263C42×C61C2411yescharacteristic
264C42×C61C2411yescharacteristic
265C22⋊Dic61—22no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268#11758198—22no—
269#11758198—22no—
270#11758198—24no—
271#11758198C2×D412yes—
272#11758198C2×D412yes—
273#11758198C2×D412yes—
274#11758198C2×D412yes—
275C4⋊Dic61—22no—
276C4⋊Dic61—22no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—24no—
282C4⋊Dic61—22no—
283C4⋊Dic61—22no—
284C4⋊Dic61C2412yes—
285C4⋊Dic61C2412yes—
286C4⋊Dic61C2412yes—
287C4⋊Dic61C2412yes—
288#11758196—22no—
289#11758196—22no—
290#11758196—22no—
291#11758196—22no—
292#11758196—24no—
293#11758196—22no—
294#11758196—22no—
295#11758196—22no—
296#11758196—22no—
297#11758196C2×D412yes—
298#11758196C2×D412yes—
299#11758196C2×D412yes—
300#11758196C2×D412yes—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61—24no—
305C4×Dic61C2×D412yes—
306C4×Dic61C2412yes—
307#11758194—24no—
308C2×#92418C2414yes—
309C23×C61—22no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61C22×D411yescharacteristic
314C22×D61—22no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61C22×D412yes—
318Q8×C61—24no—
319Q8×C61—42no—
320Q8×C61—81no—
321Q8×C61—81no—
322D4×C61—24no—
323D4×C61—42no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—42no—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C612−1+414yes—
336C2×C4×C61C2511yescharacteristic
337C22⋊D61—84no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—84no—
348C2×Dic61C22×D412yes—
349C2×Dic61C22×D412yes—
350C2×Dic61C22×D412yes—
351C4×D61—24no—
352C4×D61—24no—
353C4×D61—82no—
354C4×D61—82no—
355Dic122—82no—
356Dic122—82no—
357Dic122—81no—
358Dic122—81no—
359Dic122—82no—
360Dic122—82no—
361C8×C61—24no—
362#92418—24no—
363#60870—611nomaximal, Sylow
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—84no—
370C22×C61#53612yes—
371C22×C61C23×D411yescharacteristic
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—82no—
376C4×C61—21no—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61#53612yes—
384C4×C61C2×2−1+412yes—
385Dic61—22no—
386Dic61—22no—
387Dic61—22no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392#3458—611no—
393C2×#542—611no—
394#3244—614no—
395#3244—614no—
396#3243—614no—
397#3243—614no—
398#3165—611no—
399#3165—611no—
400#3140—611no—
401#3140D6111yescharacteristic, complemented
402#3095—612no—
403#3094—612no—
404#3078—612no—
405#3077—612no—
406#2921—611no—
407C2×C61—22no—
408C2×C61—82no—
409C2×C61C2×#53611yescharacteristic
410C2×C61#358511yescharacteristic
411C2×C61#358611yescharacteristic
412D61—42no—
413#544—612no—
414#544—612no—
415#544—612no—
416#544—612no—
417#544—1221no—
418#544—1221no—
419#543—1221no—
420#543—1221no—
421#542—614no—
422#542—614no—
423#542—1222no—
424#542—1222no—
425#533—612no—
426#533—611no—
427#533—1222no—
428#533—1222no—
429#533C2×D6111yescharacteristic
430C2×C4⋊Q8—611no—
431C2×#126—1221no—
432C2×#124—1221no—
433C2×#124C2×D6111yescharacteristic
434C2×#123—1221no—
435C2×C22⋊Q8—611no—
436C2×C22⋊Q8—1221no—
437C2×#121—611no—
438C2×C4×Q8—611no—
439C2×C4×D4—611no—
440C2×#117—611no—
441C2×#117—612no—
442#501—614no—
443#501—614no—
444#500—612no—
445#500—612no—
446#498—612no—
447#498—612no—
448#489—612no—
449#489—612no—
450#489C2×D6112yescomplemented
451#489C2×D6112yescomplemented
452#488—614no—
453#488C2×D6114yescomplemented
454#485—614no—
455#485—614no—
456#484—614no—
457#483—614no—
458#482—614no—
459#482—614no—
460#481—614no—
461#480—614no—
462#479—614no—
463#479—614no—
464#478—614no—
465#478—614no—
466#477—614no—
467#476—614no—
468#475—614no—
469#474—614no—
470#433—614no—
471#433—614no—
472#428—612no—
473#428—612no—
474#428—612no—
475#428—612no—
476#423—612no—
477#419—612no—
478#419C2×D6112yes—
479#418—612no—
480#418C2×D6112yes—
481#407—612no—
482C4×M16—611no—
483C4×M16C2×D6111yescharacteristic
484C61#6087011yescharacteristic, complemented, Sylow
485C22×Q8—1221no—
486C22×Q8C22×D6111yescharacteristic
487C22×D4—1221no—
488C22×D4C22×D6111yescharacteristic
489C23×C4—611no—
490C23×C4—1221no—
491C2×M16—612no—
492C2×M16C22×D6112yes—
493C4⋊Q8—612no—
494C4⋊Q8—612no—
495C4⋊Q8—612no—
496C4⋊Q8—612no—
497C4⋊Q8—611no—
498C4⋊Q8—611no—
499C4⋊Q8—1222no—
500C4⋊Q8—1222no—
501C4⋊Q8—1222no—
502C4⋊Q8—1222no—
503C4⋊Q8—1221no—
504C4⋊Q8—1221no—
505C4⋊Q8C22×D6111yescharacteristic
506C4⋊Q8C22×D6111yescharacteristic
507#126—1224no—
508#126—1224no—
509#125—612no—
510#125—612no—
511#125—612no—
512#125—1222no—
513#125—1222no—
514#125—1222no—
515#125—1222no—
516#125C22×D6112yes—
517#124—21no—
518#124—21no—
519#124—1224no—
520#124—1224no—
521#124C22×D6112yes—
522#124C22×D6112yes—
523#123—1224no—
524#123—1224no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—614no—
528C22⋊Q8—1224no—
529C22⋊Q8—1224no—
530C22⋊Q8—1222no—
531C22⋊Q8—1222no—
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—1221no—
542C22⋊Q8—1221no—
543#121—614no—
544#121—1222no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8—614no—
548C4×Q8—1222no—
549C4×Q8—1222no—
550C4×Q8—1222no—
551C4×Q8—1221no—
552C4×Q8—1221no—
553C4×D4—614no—
554C4×D4—1222no—
555#117—612no—
556#117—612no—
557#117—612no—
558#117—612no—
559#117—612no—
560#117—612no—
561#117—612no—
562#117—1222no—
563#117—1222no—
564#117C22×D6112yes—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—612no—
570C2×C4⋊C4—612no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—611no—
578C2×C22⋊C4—1222no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C42—611no—
583C2×C42—1222no—
584C2×C42—1221no—
585C2×C42C22×D6111yescharacteristic
586#107—614no—
587#107—614no—
588#107—614no—
589#107—614no—
590#106—614no—
591#106—614no—
592#106—614no—
593#106—614no—
594C4⋊C8—614no—
595C4⋊C8—614no—
596#103—614no—
597#103—614no—
598#103C22×D6114yes—
599#103C22×D6114yes—
600#102—614no—
601#102—614no—
602#102C22×D6114yes—
603#102C22×D6114yes—
604C22⋊C8—614no—
605C22⋊C8—614no—
606#97—612no—
607#97C22×D6112yes—
608C4×C8—612no—
609C4×C8C22×D6112yes—
610C24—21no—
611C24—611no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—24no—
616C2×Q8—1222no—
617C2×Q8—1222no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1222no—
621C2×Q8—1222no—
622C2×Q8—4882no—
623C2×Q8C23×D6112yes—
624C2×D4—21no—
625C2×D4—24no—
626C2×D4—1224no—
627C2×D4—4882no—
628C2×D4C23×D6112yes—
629C22×C4—21no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1224no—
638C22×C4—1224no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—4882no—
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4C23×D6111yescharacteristic
645M16—24no—
646M16—1224no—
647C2×C8—614no—
648C2×C8C23×D6114yes—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—612no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—612no—
659C4⋊C4—612no—
660C4⋊C4—612no—
661C4⋊C4—1222no—
662C4⋊C4—1222no—
663C4⋊C4—1224no—
664C4⋊C4—1224no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1222no—
674C4⋊C4—1222no—
675C4⋊C4—1222no—
676C4⋊C4—1222no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4C23×D6112yes—
680C4⋊C4C23×D6112yes—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—612no—
687C22⋊C4—612no—
688C22⋊C4—612no—
689C22⋊C4—612no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4—1224no—
695C22⋊C4—1222no—
696C42—22no—
697C42—612no—
698C42—612no—
699C42—1222no—
700C42—1222no—
701C42—1224no—
702C42—1222no—
703C42D4×D6111yescharacteristic
704C42D4×D6111yescharacteristic
705C42C23×D6111yescharacteristic
706C42C23×D6111yescharacteristic
707C23—22no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—612no—
712C23—1222no—
713C23—2441no—
714C23—2441no—
715C23C2×D4×D6111yescharacteristic
716Q8—24no—
717Q8—42no—
718Q8—81no—
719Q8—81no—
720Q8—4881no—
721Q8—4881no—
722Q8—4882no—
723Q8—4882no—
724Q8—4882no—
725Q8—4882no—
726D4—24no—
727D4—42no—
728D4—4884no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—612no—
736C2×C4—612no—
737C2×C4—612no—
738C2×C4—1222no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—4882no—
746C2×C4—4882no—
747C2×C4—4884no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4C2×D4×D6111yescharacteristic
753C2×C4C2×D4×D6111yescharacteristic
754C2×C4C2×D4×D6111yescharacteristic
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4C2×D4×D6111yescharacteristic
757C2×C4#1451982414yes—
758C2×C4C24×D6111yescharacteristic
759C8—24no—
760C8—1224no—
761C22—21no—
762C22—21no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—4882no—
771C22#1684033212yes—
772C22C22×D4×D6111yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—1222no—
781C4—1222no—
782C4—1222no—
783C4—2442no—
784C4—2442no—
785C4—2442no—
786C4—2442no—
787C4#1684033212yes—
788C4C2×#1451982412yes—
789C2—22no—
790C2—82no—
791C2—2442no—
792C2C2×#1684033211yescharacteristic
793C2#2146059611yescharacteristic
794C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3140C2
socleC22×C61C23×D4
prime radicalC2×#14519748C22
hypercenter#3140D61
hypocenterC61#60870
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3140

Complements

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

NH ≅ G/Ntype
1. #21459222C2semidirect
3. #21457112C2semidirect
4. #21457110C2semidirect
5. #21457097C2semidirect
6. #21457095C2semidirect
7. #21456366C2semidirect
8. #21456365C2semidirect
9. #21456205C2semidirect
10. #21455765C2semidirect
12. #21455621C2semidirect
13. #21455613C2semidirect
14. #21454455C2semidirect
15. C61×#3140C2semidirect
16. #16840392C22semidirect
17. #16840392C22semidirect
20. #16840389C22semidirect
21. #16840389C22semidirect
43. #16840172C22semidirect
44. #16840171C22semidirect
45. #16840167C22semidirect
46. #16840165C22semidirect
47. #16840160C22semidirect
48. #16840158C22semidirect
49. #16840121C22semidirect
50. #16840121C22semidirect
51. #16840116C22semidirect
52. #16840102C22semidirect
53. #16840101C22semidirect
54. #16840096C22semidirect
55. #16840091C22semidirect
60. #16840071C22semidirect
61. #16840067C22semidirect
62. #16840064C22semidirect
63. #16840060C22semidirect
64. #16840055C22semidirect
65. #16840050C22semidirect
66. #16840045C22semidirect
67. #16840040C22semidirect
68. #16839824C22semidirect
69. #16839821C22semidirect
81. C61×#489C22semidirect
82. C61×#489C22semidirect
83. C61×#488C22semidirect
401. #3140D61semidirect
450. #489C2×D61semidirect
451. #489C2×D61semidirect
453. #488C2×D61semidirect
484. C61#60870semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168403812
#214571122
#214571102
#214570972
#214570952
#214563662
#214563652
#214562052
#214557652
#214557572
#214556212
#214556132
#214544552
C61×#31402
#6087061