Finite Group Databasebeta

← #30552355

Subgroups — #30552355

Order 15616.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840392C211yesmaximal, characteristic, complemented
2#21459208C211yesmaximal, characteristic
3#21457110C214yesmaximal, complemented
4#21457095C214yesmaximal, complemented
5#21457082C214yesmaximal, complemented
6#21457067C214yesmaximal, complemented
7#21456368C211yesmaximal, characteristic, complemented
8#21456365C211yesmaximal, characteristic, complemented
9#21456212C211yesmaximal, characteristic, complemented
10#21455749C212yesmaximal, complemented
11#21455740C212yesmaximal, complemented
12#21455639C212yesmaximal, complemented
13#21455630C212yesmaximal, complemented
14#21454455C211yesmaximal, characteristic, complemented
15C61×#3142C211yesmaximal, characteristic, complemented
16#16840392—22no—
17#16840392—22no—
18#16840392C2214yes—
19#16840392C2214yes—
20#16840381C2212yes—
21#16840381C2212yes—
22#16840373C2212yes—
23#16840366C2212yes—
24#16840357—21no—
25#16840357—21no—
26#16840349—21no—
27#16840349—21no—
28#16840319C2211yescharacteristic
29C2×#14519777C2211yescharacteristic
30C2×#14519776—21no—
31C2×#14519776C2211yescharacteristic
32#16840292—22no—
33#16840292—22no—
34C2×#14519768C2211yescharacteristic
35C2×#14519767—21no—
36#16840269C2212yes—
37C2×#14519757—21no—
38C2×#14519755—21no—
39#41×Dic61C2212yes—
40C2×#14519735C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840172C2212yescomplemented
44#16840172C2212yescomplemented
45#16840171C2214yescomplemented
46#16840167C2212yescomplemented
47#16840161C2214yescomplemented
48#16840160C2212yescomplemented
49#16840121C2214yescomplemented
50#16840112C2212yescomplemented
51#16840108C2212yescomplemented
52#16840102C2214yes—
53#16840101C2214yes—
54#16840096C2214yes—
55#16840091C2214yes—
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#16839824C2214yes—
69#16839821C2214yes—
70#16839804C2212yes—
71#16839804C2212yes—
72#16839802C2212yes—
73#16839802C2212yes—
74#16839785C2212yes—
75#16839763C2212yes—
76#16839763C2212yes—
77#16839725C2212yes—
78C4×#11758194C2211yescharacteristic
79C61×#532C2211yescharacteristic
80C2×#125×C61C2211yescharacteristic
81C61×#491C2212yescomplemented
82C61×#490C2212yescomplemented
83C61×#488C2214yescomplemented
84C61×#417C2212yes—
85C61×#417C2212yes—
86C4×M16×C61C2211yescharacteristic
87C22×Dic122—21no—
88C22×Dic122—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758194C2312yes—
92#14519777—21no—
93#14519777—21no—
94#14519777C2312yes—
95#14519777C2312yes—
96#14519777C2311yescharacteristic
97#14519777C2311yescharacteristic
98#14519776—24no—
99#14519776—24no—
100#14519776—22no—
101#14519776C2314yes—
102#14519772—22no—
103#14519772—22no—
104#14519770—22no—
105#14519770—22no—
106#14519769C2312yes—
107#14519768—22no—
108#14519768C2314yes—
109#14519767—24no—
110#14519767—24no—
111#14519767—22no—
112#14519767—22no—
113#14519763—22no—
114#14519763—22no—
115#14519761—22no—
116#14519761—22no—
117#14519758—22no—
118#14519758—22no—
119#14519758—22no—
120#14519757—24no—
121#14519757—24no—
122#14519756—21no—
123#14519756—21no—
124#14519755—24no—
125#14519755—24no—
126#14519754—22no—
127#14519754—22no—
128#14519753C2312yes—
129#14519753C2312yes—
130#14519749—22no—
131#14519749—22no—
132#14519748C2312yes—
133#14519748C2312yes—
134#14519745—22no—
135Q8×Dic61C2312yes—
136Q8×Dic61C2312yes—
137C4×Dic122—21no—
138C4×Dic122—21no—
139D4×Dic61—22no—
140D4×Dic61—22no—
141D4×Dic61C2312yes—
142D4×Dic61C2312yes—
143C4×C22⋊D61—22no—
144C4×C22⋊D61—22no—
145#14519736—22no—
146#14519736C2312yes—
147#14519735—22no—
148#14519735C2314yes—
149#14519734D412yes—
150#14519734D412yes—
151#14519734C2312yes—
152#14519734C2312yes—
153C2×C4⋊Dic61—21no—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61C2311yescharacteristic
156C2×C4⋊Dic61C2311yescharacteristic
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—22no—
163C4⋊C4×D61C2314yes—
164C2×#11758198—21no—
165C2×#11758198D411yescharacteristic
166C2×#11758198D411yescharacteristic
167C2×C4×Dic61—21no—
168C2×C4×Dic61—22no—
169C2×C4×Dic61C2311yescharacteristic
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—
188C2×#41×C61C2312yes—
189C2×M16×C61C2312yes—
190C4⋊Q8×C61C2311yescharacteristic
191#127×C61C2311yescharacteristic
192#125×C61—21no—
193#125×C61—21no—
194#125×C61C2312yes—
195#125×C61C2312yes—
196#124×C61C2312yes—
197#121×C61—21no—
198#121×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61—21no—
201C2×C4⋊C4×C61—21no—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206#103×C61C2314yes—
207#103×C61C2314yes—
208#102×C61C2314yes—
209#102×C61C2314yes—
210#97×C61C2312yes—
211C4×C8×C61C2312yes—
212C23×D61C2×D411yescharacteristic
213#41×C61—28no—
214C2×Q8×C61C2412yes—
215C2×D4×C61—22no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61C2412yes—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—22no—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—22no—
226C2×C22⋊D61—22no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—22no—
230C22×Dic61—22no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—82no—
237C2×C4×D61C2×D412yes—
238C2×C4×D61C2412yes—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—24no—
244C2×Dic122—82no—
245C2×Dic122—82no—
246M16×C61—24no—
247C2×C8×C61C2414yes—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—22no—
260C42×C61C2×D411yescharacteristic
261C42×C61C2×D411yescharacteristic
262C42×C61C2411yescharacteristic
263C42×C61C2411yescharacteristic
264C22⋊Dic61—22no—
265C22⋊Dic61—22no—
266C22⋊Dic61—22no—
267C22⋊Dic61—22no—
268C22⋊Dic61—22no—
269#11758198—24no—
270#11758198—22no—
271#11758198—22no—
272#11758198C2×D412yes—
273#11758198C2×D412yes—
274#11758198C2×D412yes—
275#11758198C2×D412yes—
276C4⋊Dic61—21no—
277C4⋊Dic61—22no—
278C4⋊Dic61—22no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—24no—
283C4⋊Dic61—22no—
284C4⋊Dic61—22no—
285C4⋊Dic61C2412yes—
286C4⋊Dic61C2412yes—
287C4⋊Dic61C2412yes—
288C4⋊Dic61C2412yes—
289#11758196—22no—
290#11758196—22no—
291#11758196—24no—
292#11758196—24no—
293#11758196—24no—
294#11758196—22no—
295#11758196—22no—
296#11758196C2×D412yes—
297#11758196C2×D412yes—
298#11758196C2×D412yes—
299#11758196C2×D412yes—
300C4×Dic61—22no—
301C4×Dic61—24no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61C2×D412yes—
305C4×Dic61C2412yes—
306#11758194—24no—
307C2×#92418C2414yes—
308C23×C61—22no—
309C23×C61C22×D411yescharacteristic
310C22×D61—22no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61C22×D412yes—
314Q8×C61—24no—
315D4×C61—24no—
316D4×C61—44no—
317D4×C61—81no—
318D4×C61—81no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—44no—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C612−1+414yes—
333C2×C4×C61C2511yescharacteristic
334C22⋊D61—82no—
335C22⋊D61—82no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—82no—
346C2×Dic61—82no—
347C2×Dic61C22×D412yes—
348C2×Dic61C22×D412yes—
349C2×Dic61C22×D412yes—
350C4×D61—24no—
351C4×D61—24no—
352C4×D61—84no—
353Dic122—84no—
354Dic122—81no—
355Dic122—81no—
356Dic122—82no—
357Dic122—82no—
358C8×C61—24no—
359#92418—24no—
360#60867—611nomaximal, Sylow
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61#53612yes—
367C22×C61C23×D411yescharacteristic
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—44no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—21no—
375C4×C61—21no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61#53612yes—
380C4×C61C2×2−1+412yes—
381Dic61—22no—
382Dic61—22no—
383Dic61—22no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C2×#544—611no—
389#3455—611no—
390#3244—614no—
391#3243—614no—
392#3242—614no—
393#3241—614no—
394#3166—611no—
395#3165—611no—
396#3142D6111yescharacteristic, complemented
397#3141—611no—
398#3093—612no—
399#3092—612no—
400#3080—612no—
401#3079—612no—
402#2921—611no—
403C2×C61—22no—
404C2×C61—82no—
405C2×C61C2×#53611yescharacteristic
406C2×C61#358511yescharacteristic
407C2×C61#358611yescharacteristic
408D61—42no—
409#544—614no—
410#544—614no—
411#544—1222no—
412#544—1222no—
413#542—612no—
414#542—612no—
415#541—612no—
416#540—612no—
417#539—1221no—
418#539—1221no—
419#538—1221no—
420#538—1221no—
421#533—611no—
422#532C2×D6111yescharacteristic
423C2×C4⋊Q8—611no—
424C2×C4⋊Q8—611no—
425C2×C4⋊Q8—1221no—
426#529—1222no—
427#529—1222no—
428C2×#125—611no—
429C2×#125—1221no—
430C2×#125C2×D6111yescharacteristic
431#525—612no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C4×#41—612no—
435C2×#117—611no—
436C2×#117—611no—
437C22×C4⋊C4—611no—
438#501—612no—
439#501—612no—
440#501—614no—
441#500—612no—
442#499—614no—
443#498—612no—
444#491C2×D6112yescomplemented
445#490C2×D6112yescomplemented
446#489—614no—
447#488C2×D6114yescomplemented
448#487—612no—
449#486—612no—
450#485—614no—
451#485—614no—
452#484—614no—
453#483—614no—
454#482—614no—
455#482—614no—
456#481—614no—
457#480—614no—
458#479—614no—
459#479—614no—
460#478—614no—
461#478—614no—
462#477—614no—
463#476—614no—
464#475—614no—
465#474—614no—
466#433—614no—
467#433—614no—
468#428—612no—
469#428—612no—
470#428—612no—
471#428—612no—
472#423—612no—
473#417—612no—
474#417—612no—
475#417C2×D6112yes—
476#417C2×D6112yes—
477#407—612no—
478C4×M16—611no—
479C4×M16C2×D6111yescharacteristic
480C61#6086711yescharacteristic, complemented, Sylow
481C2×#41C22×D6112yes—
482C22×Q8—1221no—
483C22×Q8—1221no—
484C23×C4—611no—
485C23×C4—1221no—
486C2×M16—612no—
487C2×M16C22×D6112yes—
488C4⋊Q8—614no—
489C4⋊Q8—612no—
490C4⋊Q8—612no—
491C4⋊Q8—611no—
492C4⋊Q8—611no—
493C4⋊Q8—1222no—
494C4⋊Q8—1224no—
495C4⋊Q8—1224no—
496C4⋊Q8—1221no—
497C4⋊Q8—1221no—
498C4⋊Q8C22×D6111yescharacteristic
499#127C22×D6111yescharacteristic
500#126—1222no—
501#126—1222no—
502#126—1222no—
503#126—1222no—
504#125—21no—
505#125—21no—
506#125—614no—
507#125—612no—
508#125—1222no—
509#125—1224no—
510#125—1224no—
511#125—1222no—
512#125—1222no—
513#125C22×D6112yes—
514#125C22×D6112yes—
515#124—1222no—
516#124—1222no—
517#124C22×D6112yes—
518#123—1222no—
519#123—1222no—
520#123—1222no—
521#123—1222no—
522#123—1222no—
523C22⋊Q8—612no—
524C22⋊Q8—612no—
525C22⋊Q8—1222no—
526C22⋊Q8—1222no—
527C22⋊Q8—1224no—
528C22⋊Q8—1224no—
529C22⋊Q8—1224no—
530C22⋊Q8—1224no—
531C22⋊Q8—1221no—
532C22⋊Q8—1221no—
533#121—21no—
534#121—21no—
535#121—612no—
536#121—612no—
537#121—1222no—
538#121—1222no—
539#120—1222no—
540C4×Q8—612no—
541C4×Q8—612no—
542C4×Q8—1221no—
543C4×Q8—1221no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—612no—
547C4×D4—612no—
548C4×D4—1222no—
549C4×D4—1222no—
550C4×D4—1222no—
551C4×D4—1222no—
552#117—612no—
553#117—612no—
554#117—612no—
555#117—612no—
556#117—612no—
557#117—614no—
558#117—1222no—
559#117—1222no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—614no—
567C2×C4⋊C4—1222no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C22⋊C4—611no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—1221no—
578C2×C42—611no—
579C2×C42—1222no—
580C2×C42—1221no—
581C2×C42C22×D6111yescharacteristic
582#107—614no—
583#107—614no—
584#107—614no—
585#107—614no—
586#106—614no—
587#106—614no—
588#106—614no—
589#106—614no—
590C4⋊C8—614no—
591C4⋊C8—614no—
592#103—614no—
593#103—614no—
594#103C22×D6114yes—
595#103C22×D6114yes—
596#102—614no—
597#102—614no—
598#102C22×D6114yes—
599#102C22×D6114yes—
600C22⋊C8—614no—
601C22⋊C8—614no—
602#97—612no—
603#97C22×D6112yes—
604C4×C8—612no—
605C4×C8C22×D6112yes—
606C24—611no—
607#41—28no—
608C2×Q8—1224no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1222no—
612C2×Q8—1222no—
613C2×Q8—4882no—
614C2×Q8—4882no—
615C2×Q8C23×D6112yes—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4C23×D6112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—1224no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1224no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—4882no—
637C22×C4D4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4C23×D6111yescharacteristic
640M16—24no—
641M16—1224no—
642C2×C8—614no—
643C2×C8C23×D6114yes—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—612no—
653C4⋊C4—612no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—612no—
659C4⋊C4—612no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4C23×D6112yes—
677C4⋊C4C23×D6112yes—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—612no—
681C22⋊C4—612no—
682C22⋊C4—612no—
683C22⋊C4—612no—
684C22⋊C4—1224no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C42—612no—
693C42—612no—
694C42—1224no—
695C42—1222no—
696C42—1222no—
697C42—1222no—
698C42D4×D6111yescharacteristic
699C42D4×D6111yescharacteristic
700C42C23×D6111yescharacteristic
701C42C23×D6111yescharacteristic
702C23—22no—
703C23—612no—
704C23—1222no—
705C23—2441no—
706C23—2441no—
707C23C2×D4×D6111yescharacteristic
708Q8—24no—
709Q8—4881no—
710Q8—4881no—
711Q8—4882no—
712Q8—4882no—
713Q8—4884no—
714D4—24no—
715D4—44no—
716D4—81no—
717D4—81no—
718D4—4882no—
719D4—4882no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—612no—
731C2×C4—1222no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—4884no—
739C2×C4—4882no—
740C2×C4—4882no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4C2×D4×D6111yescharacteristic
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4C2×D4×D6111yescharacteristic
750C2×C4#1451982414yes—
751C2×C4C24×D6111yescharacteristic
752C8—24no—
753C8—1224no—
754C22—21no—
755C22—21no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—1222no—
760C22—1222no—
761C22—1222no—
762C22—2444no—
763C22#1684033212yes—
764C22C22×D4×D6111yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—1222no—
773C4—1222no—
774C4—1222no—
775C4—2442no—
776C4—2442no—
777C4—2442no—
778C4—2442no—
779C4#1684033212yes—
780C4C2×#1451982412yes—
781C2—22no—
782C2—82no—
783C2—2442no—
784C2C2×#1684033211yescharacteristic
785C2#2146059611yescharacteristic
786C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3142C2
socleC22×C61C23×D4
prime radical#21459208C2
hypercenter#3142D61
hypocenterC61#60867
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
3. #21457110C2semidirect
4. #21457095C2semidirect
5. #21457082C2semidirect
6. #21457067C2semidirect
7. #21456368C2semidirect
8. #21456365C2semidirect
9. #21456212C2semidirect
10. #21455749C2semidirect
11. #21455740C2semidirect
12. #21455639C2semidirect
13. #21455630C2semidirect
14. #21454455C2semidirect
15. C61×#3142C2semidirect
43. #16840172C22semidirect
44. #16840172C22semidirect
45. #16840171C22semidirect
46. #16840167C22semidirect
47. #16840161C22semidirect
48. #16840160C22semidirect
49. #16840121C22semidirect
50. #16840112C22semidirect
51. #16840108C22semidirect
60. #16840071C22semidirect
61. #16840067C22semidirect
62. #16840064C22semidirect
63. #16840060C22semidirect
64. #16840055C22semidirect
65. #16840050C22semidirect
66. #16840045C22semidirect
67. #16840040C22semidirect
81. C61×#491C22semidirect
82. C61×#490C22semidirect
83. C61×#488C22semidirect
396. #3142D61semidirect
444. #491C2×D61semidirect
445. #490C2×D61semidirect
447. #488C2×D61semidirect
480. C61#60867semidirect

Maximal subgroups

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

subgroupindex
C2×#168403922
#214592082
#214571102
#214570952
#214570822
#214570672
#214563682
#214563652
#214562122
#214557492
#214557402
#214556392
#214556302
#214544552
C61×#31422
#6086761