Finite Group Databasebeta

← #30620641

Subgroups — #30620641

Order 15616.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462512C211yesmaximal, characteristic, complemented
2#21462407C211yesmaximal, characteristic
3#21461915C211yesmaximal, characteristic, complemented
4#21461913C211yesmaximal, characteristic, complemented
5#21461901C211yesmaximal, characteristic, complemented
6#21461900C211yesmaximal, characteristic, complemented
7#21461788C211yesmaximal, characteristic, complemented
8#21461786C211yesmaximal, characteristic, complemented
9#21461727C211yesmaximal, characteristic, complemented
10#21461700C211yesmaximal, characteristic, complemented
11#21461660C211yesmaximal, characteristic
12#21461598C211yesmaximal, characteristic, complemented
13#21461594C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#21454333C211yesmaximal, characteristic
16C2×#14519864C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18#16840786—21no—
19#16840786—21no—
20#16840784—21no—
21#16840780—21no—
22C2×#14519848C2211yescharacteristic, complemented
23C2×#14519847C2211yescharacteristic, complemented
24#16840769C2211yescharacteristic, complemented
25#16840769C2211yescharacteristic, complemented
26C2×#14519841C2211yescharacteristic
27C2×#14519841C2211yescharacteristic
28C2×#14519841C2211yescharacteristic
29C2×#14519841C2211yescharacteristic
30#16840736C2211yescharacteristic
31#16840736C2211yescharacteristic
32#16840735—21no—
33#16840735—21no—
34#16840733C2211yescharacteristic
35#16840733C2211yescharacteristic
36#16840732—21no—
37D61⋊(C22⋊C8)C2211yescharacteristic
38C2×C22⋊#92420—21no—
39#16840727C2211yescharacteristic, complemented
40#16840727C2211yescharacteristic, complemented
41C2×#14519831C2211yescharacteristic, complemented
42C2×C8×#6923C2211yescharacteristic, complemented
43C4×C22⋊#6923C2211yescharacteristic
44#16840638C2211yescharacteristic, complemented
45#16840638C2211yescharacteristic, complemented
46#16840632C2211yescharacteristic, complemented
47#16840632C2211yescharacteristic, complemented
48#16840632C2211yescharacteristic, complemented
49#16840632C2211yescharacteristic, complemented
50(C2×#6923)⋊C8C2211yescharacteristic, complemented
51(C2×#6923)⋊C8C2211yescharacteristic, complemented
52C22×#11758224C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54#117×D61C2211yescharacteristic
55#16839772C411yescharacteristic, complemented
56#16839770C411yescharacteristic, complemented
57#16839767C411yescharacteristic, complemented
58#16839760C411yescharacteristic, complemented
59#16839760C411yescharacteristic, complemented
60#16839760C411yescharacteristic, complemented
61#16839760C411yescharacteristic, complemented
62#16839755C2211yescharacteristic
63#16839755C2211yescharacteristic
64#16839755C2211yescharacteristic
65#16839755C2211yescharacteristic
66C61×#418C411yescharacteristic, complemented
67#14519864—22no—
68#14519864—22no—
69#14519864—41no—
70#14519864—41no—
71C2×#11758213C2311yescharacteristic
72C2×#11758213C2311yescharacteristic
73C2×#11758213C2311yescharacteristic
74C2×#11758213C2311yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79C22×#92420—21no—
80C22×#92420—21no—
81C2×C22⋊#6923—21no—
82C2×C4×#6923C2311yescharacteristic
83C2×C4×#6923C2311yescharacteristic
84#14519848—41no—
85#14519847—41no—
86#14519844—21no—
87#14519844—21no—
88C4⋊#92420—21no—
89C4⋊#92420—21no—
90#14519841—22no—
91#14519841—22no—
92#14519841—41no—
93#14519841—41no—
94#14519834—21no—
95#14519834—21no—
96#14519834D411yescharacteristic
97#14519834D411yescharacteristic
98C22⋊#92420—21no—
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101C22⋊#92420—21no—
102C22⋊#92420—21no—
103C22⋊#92420—21no—
104C22⋊#92420D411yescharacteristic
105C22⋊#92420D411yescharacteristic
106#14519832—21no—
107#14519832—21no—
108#14519831—41no—
109C4×#92420—21no—
110C4×#92420—21no—
111C8×#6923—41no—
112(C2×#6923)⋊C4—21no—
113C2×#11758224—22no—
114C2×#11758224—22no—
115C2×#11758224—21no—
116C2×#11758224—21no—
117C2×#11758224—41no—
118C2×#11758224—41no—
119C2×#11758224C2×C411yescharacteristic
120C2×#11758224C2×C411yescharacteristic
121C2×#11758224C2311yescharacteristic
122C2×#11758224C2311yescharacteristic
123C22×Dic122C2×C411yescharacteristic
124C22×C22⋊D61—21no—
125C23×Dic61—21no—
126C22×C4×D61C2311yescharacteristic
127C2×#11758194C2×C411yescharacteristic
128C2×#11758189C2×C411yescharacteristic
129C2×#11758189C2×C411yescharacteristic
130M16×D61—41no—
131M16×D61—41no—
132C2×C8×D61C2311yescharacteristic
133C2×C8×D61C2311yescharacteristic
134#14519736C2×C411yescharacteristic
135#14519735C2311yescharacteristic
136#14519735C2311yescharacteristic
137#14519734—21no—
138#14519733—21no—
139C4⋊C4×D61C2×C411yescharacteristic
140C4⋊C4×D61C2×C411yescharacteristic
141C22⋊C4×D61—21no—
142C42×D61—21no—
143#14519702C2×C411yescharacteristic
144#14519702C2×C411yescharacteristic
145#14519702C2×C411yescharacteristic
146#14519702C2×C411yescharacteristic
147#14519700C2×C411yescharacteristic
148#14519700C2×C411yescharacteristic
149#14519700C2×C411yescharacteristic
150#14519700C2×C411yescharacteristic
151#14519698C2×C411yescharacteristic
152#14519698C2×C411yescharacteristic
153#14519698C2×C411yescharacteristic
154#14519698C2×C411yescharacteristic
155C22×D4×C61C2×C411yescharacteristic
156C2×M16×C61C2×C411yescharacteristic
157#117×C61C2×C411yescharacteristic
158#102×C61C2×C411yescharacteristic
159#102×C61C2×C411yescharacteristic
160#102×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic
162C24×C61—21no—
163C23×D61#4111yescharacteristic
164C22×#6923—21no—
165C22×#6923—21no—
166C2×D4×C61—22no—
167C2×D4×C61—21no—
168C2×D4×C61—41no—
169C2×D4×C61C22×C411yescharacteristic
170C2×D4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C2×C22⋊D61—21no—
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—42no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—42no—
184C22×Dic61—42no—
185C22×Dic61C2×D411yescharacteristic
186#11758224—22no—
187#11758224—21no—
188#11758224—21no—
189#11758224—21no—
190#11758224—21no—
191#11758224—21no—
192#11758224—21no—
193#11758224—22no—
194#11758224—41no—
195#11758224—41no—
196#11758224—42no—
197#11758224—42no—
198#11758224—42no—
199#11758224—42no—
200#11758224#4112yes—
201#11758224#4112yes—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61C22×C411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61#4111yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—22no—
213C2×Dic122—21no—
214C2×Dic122—41no—
215C2×Dic122C22×C411yescharacteristic
216C2×Dic122C22×C411yescharacteristic
217C22⋊#6923—42no—
218#11758217—42no—
219#11758217—42no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—42no—
225C2×#92420—42no—
226C2×#92420C2×D411yescharacteristic
227C2×#92420C2×D411yescharacteristic
228C2×#92420C2×D411yescharacteristic
229C2×#92420C2×D411yescharacteristic
230C4×#6923—21no—
231C4×#6923—21no—
232C4×#6923—21no—
233C4×#6923—21no—
234#11758213—21no—
235#11758213—21no—
236#11758213—21no—
237#11758213—21no—
238#11758213—21no—
239#11758213—21no—
240#11758213—21no—
241#11758213—21no—
242D61⋊C8—21no—
243D61⋊C8—21no—
244D61⋊C8—21no—
245D61⋊C8—21no—
246M16×C61—41no—
247C2×C8×C61C22×C411yescharacteristic
248C2×C8×C61C22×C411yescharacteristic
249C4⋊C4×C61C22×C411yescharacteristic
250C4⋊C4×C61C22×C411yescharacteristic
251C22⋊C4×C61—21no—
252C42×C61—21no—
253C22⋊Dic61—21no—
254#11758198—21no—
255#11758198—21no—
256C4⋊Dic61C22×C411yescharacteristic
257C4⋊Dic61C22×C411yescharacteristic
258#11758196—21no—
259#11758196—21no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C4×Dic61—21no—
263#11758194—41no—
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266#11758189—41no—
267#11758189—41no—
268C8×D61—21no—
269C8×D61—21no—
270C8×D61—21no—
271C8×D61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61—81no—
277C23×C61C4×D411yescharacteristic
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61C4×D411yescharacteristic
283C22×D61C2×#4111yescharacteristic
284C2×#6923—22no—
285C2×#6923—41no—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923—41no—
289C2×#6923—41no—
290D4×C61—21no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—42no—
294D4×C61#11712yes—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C22⋊D61—22no—
302C22⋊D61—22no—
303C22⋊D61—42no—
304C22⋊D61—42no—
305C22⋊D61—41no—
306C22⋊D61—41no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61C4×D411yescharacteristic
321C2×Dic61C22×D411yescharacteristic
322C4×D61—21no—
323C4×D61—21no—
324C4×D61—21no—
325C4×D61—21no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—42no—
329C4×D61—81no—
330C4×D61C2×#4111yescharacteristic
331C4×D61C2×#4111yescharacteristic
332C4×D61H(5,𝔽2)11yescharacteristic
333C4×D61H(5,𝔽2)11yescharacteristic
334Dic122—21no—
335Dic122—21no—
336Dic122—21no—
337Dic122—42no—
338Dic122#11712yes—
339#92420—21no—
340#92420—21no—
341#92420—21no—
342#92420—21no—
343#92420—41no—
344#92420—41no—
345#92420—41no—
346#92420—41no—
347C8×C61—21no—
348C8×C61—21no—
349#92418—21no—
350#92418—21no—
351#22588—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—22no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—84no—
362C22×C61C2×C4×D411yescharacteristic
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—21no—
366C2×D61—21no—
367C2×D61—21no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61#55111yescharacteristic
371C2×D61#55111yescharacteristic
372#6923—42no—
373#6923—81no—
374C4×C61—21no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61C2×#11711yescharacteristic
378C4×C61#51811yescharacteristic
379Dic61—22no—
380Dic61—21no—
381Dic61—41no—
382Dic61—41no—
383Dic61—41no—
384Dic61#54611yescharacteristic
385Dic61#54611yescharacteristic
386#2924—611no—
387#2896—611no—
388#2880—611no—
389#1938—611no—
390#1937—611no—
391#1929—611no—
392#1929—611no—
393#1866—611no—
394#1866—611no—
395#1826—611no—
396#1811—611no—
397#1789—611no—
398#1765—611no—
399#1764—611no—
400#1753—611no—
401C2×C61—41no—
402C2×C61—42no—
403C2×C61—81no—
404C2×C61#234211yescharacteristic
405C2×C61#295511yescharacteristic
406C2×C61#295611yescharacteristic
407D61—21no—
408D61—21no—
409D61—41no—
410C22×#41—611no—
411C2×#131—611no—
412C2×#131—611no—
413C22×M16—611no—
414C2×#117—611no—
415#433—1221no—
416#433—1221no—
417#432—1221no—
418#431—1221no—
419C2×#108—611no—
420C2×#108—611no—
421#424—611no—
422#424—611no—
423C2×#104—611no—
424C2×#104—611no—
425C2×#104—611no—
426C2×#104—611no—
427#419—611no—
428#419—611no—
429#418—611no—
430#418#692311yescharacteristic, complemented
431#417—611no—
432#417—611no—
433#417—611no—
434#417—611no—
435#416—611no—
436#416—611no—
437#416—611no—
438#416—611no—
439#408—611no—
440#408—611no—
441#408—1221no—
442#408—1221no—
443#407—611no—
444#407—611no—
445#407—1221no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—1221no—
448#405—611no—
449#405—611no—
450C2×#97—611no—
451C2×C4×C8—611no—
452C4×C22⋊C4—611no—
453#341—611no—
454#341—611no—
455#339—611no—
456#339—611no—
457#339—611no—
458#339—611no—
459#336—611no—
460#336—611no—
461C61#2258811yescharacteristic, complemented, Sylow
462C2×#41—611no—
463C2×#41—611no—
464C2×#41—611no—
465C2×#41—611no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1222no—
469C2×#41—1222no—
470C2×#41—2441no—
471C2×#41—2441no—
472C22×Q8—611no—
473C22×D4—1221no—
474C22×D4C2×#692311yescharacteristic
475C23×C4—611no—
476C23×C4—1221no—
477#131—1222no—
478#131—1222no—
479#131—2441no—
480#131—2441no—
481C2×M16—611no—
482C2×M16—611no—
483C2×M16—611no—
484C2×M16—611no—
485C2×M16—611no—
486C2×M16—611no—
487C2×M16—611no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—2441no—
491C2×M16—2441no—
492C2×M16C2×#692311yescharacteristic
493C22×C8—611no—
494C22×C8—611no—
495C22×C8—611no—
496C22×C8—611no—
497C22×C8—1221no—
498C22×C8—1221no—
499#117—611no—
500#117—611no—
501#117—611no—
502#117—1221no—
503#117—1221no—
504#117C2×#692311yescharacteristic
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C42—611no—
510C2×C42—611no—
511C2×C42—1221no—
512#108—2441no—
513#108—2441no—
514C4⋊C8—1221no—
515C4⋊C8—1221no—
516C4⋊C8—1221no—
517C4⋊C8—1221no—
518#104—1222no—
519#104—1222no—
520#104—2441no—
521#104—2441no—
522#103—611no—
523#103—611no—
524#103—611no—
525#103—611no—
526#103—611no—
527#103—611no—
528#103—611no—
529#103—611no—
530#102—611no—
531#102—611no—
532#102—611no—
533#102—611no—
534#102C2×#692311yescharacteristic
535#102C2×#692311yescharacteristic
536#102C2×#692311yescharacteristic
537#102C2×#692311yescharacteristic
538C22⋊C8—611no—
539C22⋊C8—611no—
540C22⋊C8—611no—
541C22⋊C8—611no—
542C22⋊C8—1221no—
543C22⋊C8—1221no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8—1221no—
547C22⋊C8—1221no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550#97—1221no—
551#97—1221no—
552#97—2441no—
553C4×C8—1221no—
554C4×C8—1221no—
555C4×C8—2441no—
556#95—1221no—
557C24—21no—
558C24—611no—
559#41—612no—
560#41—612no—
561#41—1221no—
562#41—1221no—
563#41—1221no—
564#41—1221no—
565#41—1221no—
566#41—1221no—
567#41—1222no—
568#41—1222no—
569#41—2442no—
570#41—2442no—
571#41—2441no—
572#41—2441no—
573#41—2442no—
574#41—2442no—
575C2×Q8—611no—
576C2×Q8—611no—
577C2×Q8—1222no—
578C2×Q8—1221no—
579C2×Q8—2441no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—41no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—2442no—
588C2×D4—2442no—
589C2×D4C22×#692311yescharacteristic
590C2×D4C22×#692311yescharacteristic
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4C22×#692311yescharacteristic
612M16—41no—
613M16—1221no—
614M16—1221no—
615M16—1221no—
616M16—1221no—
617M16—1221no—
618M16—1221no—
619M16—1221no—
620M16—1221no—
621M16—2441no—
622M16—2441no—
623M16—2441no—
624M16—2442no—
625M16—2442no—
626C2×C8—611no—
627C2×C8—611no—
628C2×C8—611no—
629C2×C8—611no—
630C2×C8—611no—
631C2×C8—611no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—2442no—
645C2×C8—2442no—
646C2×C8C22×#692311yescharacteristic
647C2×C8C22×#692311yescharacteristic
648C4⋊C4—611no—
649C4⋊C4—611no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4C22×#692311yescharacteristic
653C4⋊C4C22×#692311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—2442no—
659C42—21no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C23—21no—
668C23—21no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—611no—
673C23—611no—
674C23—1221no—
675C23—1221no—
676C23—2441no—
677C23—2441no—
678C23D4×#692311yescharacteristic
679Q8—612no—
680Q8—1221no—
681Q8—1221no—
682Q8—1221no—
683Q8—2442no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—42no—
688D4—1222no—
689D4—1222no—
690D4—2442no—
691D4—2442no—
692D4—2441no—
693D4—2441no—
694D4#1451985612yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—611no—
700C2×C4—611no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1222no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—4881no—
721C2×C4—2442no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4D4×#692311yescharacteristic
733C2×C4C23×#692311yescharacteristic
734C8—21no—
735C8—21no—
736C8—1221no—
737C8—1221no—
738C8—1221no—
739C8—1221no—
740C8—1221no—
741C8—1221no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C8—2441no—
746C22—21no—
747C22—22no—
748C22—21no—
749C22—21no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—84no—
756C22—611no—
757C22—611no—
758C22—1221no—
759C22—1221no—
760C22—1221no—
761C22—1221no—
762C22—1221no—
763C22—4881no—
764C22—4881no—
765C22C2×D4×#692311yescharacteristic
766C4—21no—
767C4—41no—
768C4—41no—
769C4—611no—
770C4—611no—
771C4—1221no—
772C4—1222no—
773C4—4881no—
774C4—2442no—
775C4—2441no—
776C4—2441no—
777C4—2441no—
778C4C2×#1451985611yescharacteristic
779C4#1684082911yescharacteristic
780C2—41no—
781C2—42no—
782C2—81no—
783C2—1221no—
784C2—1221no—
785C2—2441no—
786C2#2146232511yescharacteristic
787C2#2146259111yescharacteristic
788C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#418C4
socleC22×C61C2×C4×D4
prime radicalC22×#11758224C22
cosocleC2×C4×D61C24
hypercenter#418#6923
hypocenterC61#22588
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #21462512C2semidirect
3. #21461915C2semidirect
4. #21461913C2semidirect
5. #21461901C2semidirect
6. #21461900C2semidirect
7. #21461788C2semidirect
8. #21461786C2semidirect
9. #21461727C2semidirect
10. #21461700C2semidirect
12. #21461598C2semidirect
13. #21461594C2semidirect
14. #21461559C2semidirect
22. C2×#14519848C22semidirect
23. C2×#14519847C22semidirect
24. #16840769C22semidirect
25. #16840769C22semidirect
39. #16840727C22semidirect
40. #16840727C22semidirect
41. C2×#14519831C22semidirect
42. C2×C8×#6923C22semidirect
44. #16840638C22semidirect
45. #16840638C22semidirect
46. #16840632C22semidirect
47. #16840632C22semidirect
48. #16840632C22semidirect
49. #16840632C22semidirect
50. (C2×#6923)⋊C8C22semidirect
51. (C2×#6923)⋊C8C22semidirect
55. #16839772C4semidirect
56. #16839770C4semidirect
57. #16839767C4semidirect
58. #16839760C4semidirect
59. #16839760C4semidirect
60. #16839760C4semidirect
61. #16839760C4semidirect
66. C61×#418C4semidirect
430. #418#6923semidirect
461. C61#22588semidirect

Maximal subgroups

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

subgroupindex
#214625122
#214624072
#214619152
#214619132
#214619012
#214619002
#214617882
#214617862
#214617272
#214617002
#214616602
#214615982
#214615942
#214615592
#214543332
#2258861