Finite Group Databasebeta

← #30552379

Subgroups — #30552379

Order 15616.

1626 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic
2C2×#16840370C211yesmaximal, characteristic
3#21457094C214yesmaximal, complemented
4#21457092C214yesmaximal, complemented
5#21457086C214yesmaximal, complemented
6#21457084C214yesmaximal, complemented
7#21456369C212yesmaximal, complemented
8#21456197C212yesmaximal, complemented
9#21455769C212yesmaximal
10#21455765C212yesmaximal
11#21455626C211yesmaximal, characteristic, complemented
12#21455624C211yesmaximal, characteristic, complemented
13#21455620C211yesmaximal, characteristic, complemented
14#21454456C211yesmaximal, characteristic
15C61×#3078C211yesmaximal, characteristic, complemented
16#16840392C2212yes—
17#16840392C2212yes—
18#16840391—21no—
19#16840391—21no—
20#16840389C2212yes—
21#16840389C2212yes—
22#16840387—21no—
23#16840387—21no—
24#16840370—22no—
25#16840370—22no—
26#16840370C2214yes—
27#16840370C2214yes—
28#16840319C2211yescharacteristic
29#16840316—22no—
30#16840316—22no—
31#16840315C2212yes—
32C2×#14519775C2211yescharacteristic
33C2×#14519772—21no—
34C2×#14519771—21no—
35C2×#14519769—21no—
36C2×#14519768C2211yescharacteristic
37C2×#14519767—21no—
38C2×#14519757C2211yescharacteristic
39C2×#14519753C2211yescharacteristic
40C2×C4×Dic122C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42#117×D61C2212yes—
43#16840170C2214yescomplemented
44#16840169C2214yescomplemented
45#16840163C2214yescomplemented
46#16840162C2214yescomplemented
47#16840129C2214yescomplemented
48#16840129C2214yescomplemented
49#16840111C2214yescomplemented
50#16840111C2214yescomplemented
51#16840106C2214yes—
52#16840105C2214yes—
53#16840102C2214yes—
54#16840101C2214yes—
55#16840099C2214yes—
56#16840096C2214yes—
57#16840094C2214yes—
58#16840091C2214yes—
59#16840070C2214yescomplemented
60#16840069C2214yescomplemented
61#16840066C2214yescomplemented
62#16840058C2212yescomplemented
63#16840057C2212yescomplemented
64#16840054C2212yescomplemented
65#16840048C2212yescomplemented
66#16840047C2212yescomplemented
67#16840044C2212yescomplemented
68#16839822C2214yes—
69#16839822C2214yes—
70#16839805C2212yes—
71#16839804C2212yes—
72#16839802C2212yes—
73#16839786C2211yescharacteristic
74#16839772C2212yes—
75#16839771C2212yes—
76#16839770C2212yes—
77#16839725C2212yes—
78M16×Dic61C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4×Q8×C61C2211yescharacteristic
81C61×#479C2214yescomplemented
82C61×#477C2212yescomplemented
83C61×#475C2212yescomplemented
84C61×#428C2212yes—
85C61×#423C2211yescharacteristic
86C61×#419C2212yes—
87C22×Dic122C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C2×#11758194C2312yes—
90#14519777C2311yescharacteristic
91#14519777C2311yescharacteristic
92#14519776—22no—
93#14519776—22no—
94#14519776C2312yes—
95#14519776C2312yes—
96#14519775—22no—
97#14519775—22no—
98#14519775—22no—
99#14519775C2314yes—
100#14519772—24no—
101#14519772—24no—
102#14519771—24no—
103#14519771—24no—
104#14519769—24no—
105#14519769—24no—
106#14519769C2312yes—
107#14519768—22no—
108#14519768C2314yes—
109#14519768C2312yes—
110#14519768C2312yes—
111#14519767—24no—
112#14519767—24no—
113#14519767—22no—
114#14519767—22no—
115#14519767—22no—
116#14519767—22no—
117#14519757—22no—
118#14519757—22no—
119#14519757—22no—
120#14519757C2314yes—
121#14519756—21no—
122#14519756—21no—
123#14519755—22no—
124#14519755—22no—
125#14519755—22no—
126#14519755—22no—
127#14519754—22no—
128#14519754—22no—
129#14519753—22no—
130#14519753—22no—
131#14519753—22no—
132#14519753C2314yes—
133C4×Dic122—21no—
134C4×Dic122—21no—
135C4×Dic122—21no—
136C4×Dic122—21no—
137C4×Dic122—22no—
138C4×Dic122—22no—
139C4×Dic122C2312yes—
140C4×Dic122C2312yes—
141#14519736C2312yes—
142#14519735C2312yes—
143#14519735C2312yes—
144#14519734—22no—
145#14519734D412yes—
146#14519734D412yes—
147#14519734C2312yes—
148#14519734C2312yes—
149#14519733—22no—
150C2×C4⋊Dic61—21no—
151C2×C4⋊Dic61—21no—
152C2×C4⋊Dic61C2311yescharacteristic
153C2×#11758196—21no—
154C2×#11758196—21no—
155C2×#11758196—21no—
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×#11758196D411yescharacteristic
159C2×#11758196D411yescharacteristic
160C4⋊C4×D61C2312yes—
161C4⋊C4×D61C2312yes—
162C2×#11758198—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#14519701C2314yes—
181#14519701C2314yes—
182#14519700C2314yes—
183#14519700C2314yes—
184#14519689C2314yes—
185#14519689C2314yes—
186#14519687C2314yes—
187C8×Dic61C2314yes—
188C22×Q8×C61C2311yescharacteristic
189C2×M16×C61C2312yes—
190C4⋊Q8×C61C2311yescharacteristic
191C4⋊Q8×C61C2311yescharacteristic
192#125×C61C2312yes—
193C22⋊Q8×C61—21no—
194C22⋊Q8×C61—21no—
195C4×Q8×C61—21no—
196C4×Q8×C61—21no—
197C4×Q8×C61—21no—
198C4×Q8×C61—21no—
199C4×Q8×C61C2312yes—
200C4×Q8×C61C2312yes—
201#117×C61C2312yes—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C42×C61—21no—
205C2×C42×C61C2311yescharacteristic
206#107×C61C2314yes—
207#106×C61C2314yes—
208C4⋊C8×C61C2312yes—
209C4⋊C8×C61C2312yes—
210#103×C61C2314yes—
211#103×C61C2314yes—
212C23×D61C2×D411yescharacteristic
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—22no—
217C2×Q8×C61—22no—
218C2×Q8×C61C2412yes—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—22no—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2412yes—
235C2×Dic122—22no—
236C2×Dic122—22no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—22no—
241C2×Dic122—22no—
242C2×Dic122C2412yes—
243M16×C61—24no—
244C2×C8×C61C2414yes—
245C4⋊C4×C61—22no—
246C4⋊C4×C61—22no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2412yes—
253C4⋊C4×C61C2412yes—
254C4⋊C4×C61C2412yes—
255C22⋊C4×C61—22no—
256C42×C61—22no—
257C42×C61—22no—
258C42×C61—22no—
259C42×C61C2×D411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2411yescharacteristic
262C42×C61C2411yescharacteristic
263C22⋊Dic61—22no—
264#11758198—22no—
265#11758198—22no—
266#11758198—24no—
267#11758198—24no—
268#11758198C2×D412yes—
269#11758198C2×D412yes—
270#11758198C2×D412yes—
271#11758198C2×D412yes—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—24no—
276C4⋊Dic61—24no—
277C4⋊Dic61—22no—
278C4⋊Dic61—22no—
279C4⋊Dic61C2412yes—
280C4⋊Dic61C2412yes—
281C4⋊Dic61C2412yes—
282#11758196—22no—
283#11758196—22no—
284#11758196—22no—
285#11758196—22no—
286#11758196—22no—
287#11758196—22no—
288#11758196—24no—
289#11758196—24no—
290#11758196—24no—
291#11758196—24no—
292#11758196—22no—
293#11758196—22no—
294#11758196—22no—
295#11758196—22no—
296#11758196C2×D412yes—
297#11758196C2×D412yes—
298#11758196C2×D412yes—
299#11758196C2×D412yes—
300C4×Dic61—22no—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61—22no—
305C4×Dic61C2×D412yes—
306C4×Dic61C2412yes—
307#11758194—24no—
308C2×#92418C2414yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—22no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61C22×D412yes—
314Q8×C61—22no—
315Q8×C61—22no—
316Q8×C61—42no—
317Q8×C61—81no—
318Q8×C61—81no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C612−1+412yes—
333C2×C4×C612−1+412yes—
334C2×C4×C61C2511yescharacteristic
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61C22×D412yes—
345C2×Dic61C22×D412yes—
346C2×Dic61C22×D412yes—
347C4×D61—24no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—82no—
351C4×D61—82no—
352Dic122—22no—
353Dic122—22no—
354Dic122—42no—
355Dic122—82no—
356Dic122—82no—
357Dic122—81no—
358Dic122—81no—
359C8×C61—24no—
360#92418—24no—
361#60869—611nomaximal, Sylow
362C22×C61—21no—
363C22×C61—21no—
364C22×C61#53612yes—
365C22×C61C23×D411yescharacteristic
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—82no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61#53612yes—
379C4×C61C2×2−1+411yescharacteristic
380C4×C61C2×2−1+411yescharacteristic
381Dic61—22no—
382Dic61—22no—
383Dic61—22no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388#3458—611no—
389C2×#541—611no—
390#3242—614no—
391#3242—614no—
392#3242—614no—
393#3242—614no—
394#3166—612no—
395#3139—612no—
396#3095—612no—
397#3095—612no—
398#3078—611no—
399#3078—611no—
400#3078—611no—
401#3078D6111yescharacteristic, complemented
402#2921—611no—
403C2×C61—22no—
404C2×C61C2×#53611yescharacteristic
405C2×C61#358611yescharacteristic
406C2×C61#358611yescharacteristic
407D61—42no—
408#544—612no—
409#544—612no—
410#544—612no—
411#544—612no—
412#544—1221no—
413#544—1221no—
414#543—1221no—
415#543—1221no—
416#541—614no—
417#541—614no—
418#541—1222no—
419#541—1222no—
420#533—612no—
421#533—611no—
422#533—1222no—
423#533—1222no—
424#533C2×D6111yescharacteristic
425C2×C4⋊Q8—611no—
426C2×#126—1221no—
427C2×#126—1221no—
428C2×#125—611no—
429C2×#125—1221no—
430C2×#125—1221no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—611no—
433C2×C4×Q8—611no—
434C2×C4×Q8C2×D6111yescharacteristic
435C2×#117—611no—
436C2×#117—612no—
437#501—614no—
438#501—614no—
439#499—614no—
440#499—614no—
441#491—614no—
442#491—614no—
443#487—614no—
444#487—614no—
445#485—614no—
446#485—614no—
447#485—614no—
448#485—614no—
449#484—614no—
450#484—614no—
451#483—614no—
452#483—614no—
453#479—614no—
454#479—614no—
455#479—614no—
456#479C2×D6114yescomplemented
457#477—612no—
458#477—612no—
459#477—612no—
460#477C2×D6112yescomplemented
461#475—612no—
462#475—612no—
463#475—612no—
464#475C2×D6112yescomplemented
465#433—614no—
466#433—614no—
467#428—612no—
468#428—612no—
469#428—612no—
470#428C2×D6112yes—
471#423—611no—
472#423C2×D6111yescharacteristic
473#419—612no—
474#419—612no—
475#419—612no—
476#419C2×D6112yes—
477#407—612no—
478C4×M16—612no—
479C61#6086911yescharacteristic, complemented, Sylow
480C22×Q8—611no—
481C22×Q8C22×D6111yescharacteristic
482C23×C4—611no—
483C2×M16—612no—
484C2×M16C22×D6112yes—
485C4⋊Q8—612no—
486C4⋊Q8—612no—
487C4⋊Q8—614no—
488C4⋊Q8—611no—
489C4⋊Q8—611no—
490C4⋊Q8—1222no—
491C4⋊Q8—1222no—
492C4⋊Q8—1222no—
493C4⋊Q8—1222no—
494C4⋊Q8—1222no—
495C4⋊Q8C22×D6111yescharacteristic
496C4⋊Q8C22×D6111yescharacteristic
497#126—1224no—
498#126—1224no—
499#126—1224no—
500#126—1224no—
501#125—614no—
502#125—612no—
503#125—612no—
504#125—612no—
505#125—1224no—
506#125—1224no—
507#125—1222no—
508#125—1224no—
509#125—1224no—
510#125—1222no—
511#125—1222no—
512#125—1222no—
513#125—1222no—
514#125C22×D6112yes—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—614no—
518C22⋊Q8—614no—
519C22⋊Q8—1222no—
520C22⋊Q8—1222no—
521C22⋊Q8—1222no—
522C22⋊Q8—1222no—
523C22⋊Q8—1222no—
524C22⋊Q8—1222no—
525C22⋊Q8—1222no—
526C22⋊Q8—1222no—
527C22⋊Q8—1222no—
528C22⋊Q8—1222no—
529C22⋊Q8—1222no—
530C22⋊Q8—1222no—
531C22⋊Q8—1221no—
532C22⋊Q8—1221no—
533C4×Q8—21no—
534C4×Q8—21no—
535C4×Q8—21no—
536C4×Q8—21no—
537C4×Q8—612no—
538C4×Q8—612no—
539C4×Q8—1222no—
540C4×Q8—1222no—
541C4×Q8—1221no—
542C4×Q8—1221no—
543C4×Q8—1221no—
544C4×Q8—1221no—
545C4×Q8C22×D6112yes—
546C4×Q8C22×D6112yes—
547#117—612no—
548#117—612no—
549#117—612no—
550#117—612no—
551#117—612no—
552#117—612no—
553#117—612no—
554#117—1222no—
555#117—1222no—
556#117C22×D6112yes—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—612no—
562C2×C4⋊C4—612no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4C22×D6111yescharacteristic
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—1222no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C42—21no—
577C2×C42—611no—
578C2×C42—1222no—
579C2×C42—1221no—
580C2×C42C22×D6111yescharacteristic
581#107—614no—
582#107—614no—
583#107—614no—
584#107C22×D6114yes—
585#106—614no—
586#106—614no—
587#106—614no—
588#106C22×D6114yes—
589C4⋊C8—612no—
590C4⋊C8—612no—
591C4⋊C8C22×D6112yes—
592C4⋊C8C22×D6112yes—
593#103—614no—
594#103—614no—
595#103—614no—
596#103—614no—
597#103—614no—
598#103—614no—
599#103C22×D6114yes—
600#103C22×D6114yes—
601C22⋊C8—614no—
602C22⋊C8—614no—
603#97—614no—
604C4×C8—614no—
605C24—611no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—612no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1222no—
618C2×Q8—1222no—
619C2×Q8C23×D6112yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4D4×D6111yescharacteristic
634C22×C4D4×D6111yescharacteristic
635C22×C4C23×D6111yescharacteristic
636M16—24no—
637M16—1224no—
638C2×C8—614no—
639C2×C8C23×D6114yes—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—612no—
648C4⋊C4—612no—
649C4⋊C4—612no—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—612no—
653C4⋊C4—612no—
654C4⋊C4—1222no—
655C4⋊C4—1222no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1221no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4C23×D6112yes—
676C4⋊C4C23×D6112yes—
677C4⋊C4C23×D6112yes—
678C22⋊C4—22no—
679C22⋊C4—612no—
680C22⋊C4—612no—
681C22⋊C4—612no—
682C22⋊C4—612no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1222no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—612no—
692C42—612no—
693C42—1222no—
694C42—1222no—
695C42—1222no—
696C42—1222no—
697C42—1222no—
698C42D4×D6111yescharacteristic
699C42D4×D6111yescharacteristic
700C42C23×D6111yescharacteristic
701C42C23×D6111yescharacteristic
702C23—612no—
703C23—1222no—
704C23—2441no—
705C23—2441no—
706C23C2×D4×D6111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710Q8—81no—
711Q8—81no—
712Q8—1222no—
713Q8—1222no—
714Q8—4881no—
715Q8—4881no—
716Q8—4882no—
717Q8—4882no—
718Q8—2442no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—1222no—
731C2×C4—1224no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—4882no—
739C2×C4—4882no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4C2×D4×D6111yescharacteristic
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4#1451982412yes—
750C2×C4#1451982512yes—
751C2×C4C24×D6111yescharacteristic
752C8—24no—
753C8—1224no—
754C22—21no—
755C22—21no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—4882no—
760C22#1684033512yes—
761C22C22×D4×D6111yescharacteristic
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—1222no—
771C4—1222no—
772C4—1222no—
773C4—2442no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4#1684033512yes—
778C4C2×#1451982411yescharacteristic
779C4C2×#1451982511yescharacteristic
780C2—22no—
781C2—2442no—
782C2C2×#1684033511yescharacteristic
783C2#2146060211yescharacteristic
784C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3078C2
socleC22×C61C23×D4
prime radicalC23×D61C2×D4
hypercenter#3078D61
hypocenterC61#60869
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #21457094C2semidirect
4. #21457092C2semidirect
5. #21457086C2semidirect
6. #21457084C2semidirect
7. #21456369C2semidirect
8. #21456197C2semidirect
11. #21455626C2semidirect
12. #21455624C2semidirect
13. #21455620C2semidirect
15. C61×#3078C2semidirect
43. #16840170C22semidirect
44. #16840169C22semidirect
45. #16840163C22semidirect
46. #16840162C22semidirect
47. #16840129C22semidirect
48. #16840129C22semidirect
49. #16840111C22semidirect
50. #16840111C22semidirect
59. #16840070C22semidirect
60. #16840069C22semidirect
61. #16840066C22semidirect
62. #16840058C22semidirect
63. #16840057C22semidirect
64. #16840054C22semidirect
65. #16840048C22semidirect
66. #16840047C22semidirect
67. #16840044C22semidirect
81. C61×#479C22semidirect
82. C61×#477C22semidirect
83. C61×#475C22semidirect
401. #3078D61semidirect
456. #479C2×D61semidirect
460. #477C2×D61semidirect
464. #475C2×D61semidirect
479. C61#60869semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168403702
#214570942
#214570922
#214570862
#214570842
#214563692
#214561972
#214557692
#214557652
#214556262
#214556242
#214556202
#214544562
C61×#30782
#6086961