Finite Group Databasebeta

← #30615505

Subgroups — #30615505

Order 15616.

1312 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840841C211yesmaximal, characteristic
2D61⋊#430C211yesmaximal, characteristic, complemented
3#21462462C211yesmaximal, characteristic, complemented
4D61⋊#421C211yesmaximal, characteristic
5#21461781C214yesmaximal, complemented
6#21461780C214yesmaximal, complemented
7C2×#16840645C211yesmaximal, characteristic, complemented
8#21461500C211yesmaximal, characteristic, complemented
9#421×D61C211yesmaximal, characteristic
10#16840841—22no—
11#16840841—22no—
12#16840841—22no—
13#16840841C2214yes—
14C2×#14519865—21no—
15C2×#14519864—22no—
16C2×#14519864—21no—
17C22×#11758213—21no—
18C22×#11758213C2211yescharacteristic
19C2×D61⋊M16—21no—
20C2×D61⋊M16C2211yescharacteristic
21C2×D61⋊M16C2211yescharacteristic
22C2×#14519856C2211yescharacteristic
23#16840777—21no—
24#16840777—21no—
25#16840777C2212yescomplemented
26#16840777C2212yescomplemented
27D61⋊#108—22no—
28#16840769—22no—
29#16840768—22no—
30#16840767C2212yescomplemented
31#16840766C2212yescomplemented
32#16840761—21no—
33#16840760—21no—
34#16840759C2212yes—
35#16840759C2212yes—
36D61⋊#104—22no—
37#16840645C2214yescomplemented
38#16840633C2214yescomplemented
39C2×#41×D61C2211yescharacteristic
40C2×M16×D61C2211yescharacteristic
41#117×D61C2211yescharacteristic
42#16839780C411yescharacteristic, complemented
43#16839779C411yescharacteristic, complemented
44#16839778C411yescharacteristic, complemented
45#16839777C414yescomplemented
46#104×D61C2214yes—
47C61×#421C411yescharacteristic, complemented
48#14519865—24no—
49#14519865—24no—
50#14519864—28no—
51#14519864—24no—
52#14519864—24no—
53#14519864—28no—
54C2×#11758213—22no—
55C2×#11758213—24no—
56C2×#11758213—21no—
57C2×#11758213—21no—
58C2×#11758213—21no—
59C2×#11758213—21no—
60C2×#11758213—24no—
61C2×#11758213D412yes—
62C2×#11758213D411yescharacteristic
63C2×#11758213D411yescharacteristic
64C2×#11758213C2311yescharacteristic
65C2×#11758213C2311yescharacteristic
66C2×#11758213C2312yes—
67D61⋊M16—24no—
68D61⋊M16—21no—
69D61⋊M16—21no—
70D61⋊M16—24no—
71D61⋊M16—21no—
72D61⋊M16—21no—
73D61⋊M16—21no—
74D61⋊M16—21no—
75D61⋊M16D412yes—
76D61⋊M16C2312yes—
77C2×#11758217—22no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×D61⋊C8—22no—
81C2×D61⋊C8—21no—
82C2×D61⋊C8—21no—
83C22×#92420—22no—
84C22×#92420D412yes—
85#14519856—21no—
86#14519856—21no—
87#14519856—21no—
88#14519856C2312yes—
89C2×C4⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C4×#6923—21no—
92#14519848—22no—
93#14519848—22no—
94#14519847—22no—
95#14519847—22no—
96#14519844—24no—
97C4⋊#92420—24no—
98#14519842—22no—
99#14519842—22no—
100#14519841—22no—
101#14519841—22no—
102C2×#11758226D411yescharacteristic
103C2×#11758222—21no—
104C2×#11758222C2×C411yescharacteristic
105C2×#11758224—21no—
106C2×#11758224D411yescharacteristic
107#41×D61—21no—
108#41×D61—21no—
109#41×D61—21no—
110#41×D61—21no—
111#41×D61C2×C412yes—
112#41×D61D412yes—
113#41×D61Q812yes—
114#41×D61C2312yes—
115C2×Q8×D61Q811yescharacteristic
116C2×D4×D61—21no—
117C2×D4×D61Q811yescharacteristic
118C22×C4×D61—21no—
119C22×C4×D61C2311yescharacteristic
120C2×#11758194C2×C411yescharacteristic
121C2×#11758189—21no—
122M16×D61—21no—
123M16×D61—21no—
124M16×D61C2×C412yes—
125M16×D61C2312yes—
126C2×C8×D61—21no—
127#14519736C2×C411yescharacteristic
128#14519735—21no—
129#14519734C2×C412yes—
130#14519733—21no—
131C4⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C42×D61C2312yes—
134#14519705C2×C414yescomplemented
135#14519704C2×C414yescomplemented
136#14519703C2×C414yescomplemented
137C2×#41×C61C2×C411yescharacteristic
138C2×M16×C61C2×C411yescharacteristic
139#117×C61C2×C411yescharacteristic
140#104×C61C2×C414yescomplemented
141C23×D61—21no—
142C23×D61#4111yescharacteristic
143C22×#6923—41no—
144#41×C61—21no—
145#41×C61—21no—
146#41×C61C4⋊C412yes—
147#41×C61C22×C412yes—
148C2×Q8×C61C4⋊C411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61C4⋊C411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—21no—
156C22×Dic61—21no—
157C22×Dic61C2×D411yescharacteristic
158#11758226—21no—
159#11758226—21no—
160#11758226C4⋊C412yes—
161#11758226C2×D412yes—
162Q8×D61—21no—
163Q8×D61—21no—
164Q8×D61C4⋊C412yes—
165Q8×D61C2×Q812yes—
166#11758224—22no—
167#11758224—22no—
168#11758224—22no—
169#11758224—22no—
170#11758224—21no—
171#11758224—21no—
172#11758224C4⋊C412yes—
173#11758224C2×D412yes—
174D4×D61—22no—
175D4×D61—22no—
176D4×D61—22no—
177D4×D61—22no—
178D4×D61—21no—
179D4×D61—21no—
180D4×D61C4⋊C412yes—
181D4×D61C2×Q812yes—
182#11758222—21no—
183#11758222—21no—
184#11758222—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222—22no—
188#11758222C4⋊C412yes—
189#11758222C22×C412yes—
190C2×D244—21no—
191C2×D244C4⋊C411yescharacteristic
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61C22×C411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2×D411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×Q811yescharacteristic
207C2×C4×D61C2×Q811yescharacteristic
208C2×C4×D61#4111yescharacteristic
209C2×C4×D61#4111yescharacteristic
210C2×C4×D61#4111yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122C4⋊C411yescharacteristic
214C22⋊#6923—22no—
215C22⋊#6923—41no—
216#11758217—28no—
217#11758217—22no—
218#11758217—22no—
219#11758217—41no—
220#11758217—41no—
221C2×#92420—28no—
222C2×#92420—21no—
223C2×#92420—22no—
224C2×#92420—22no—
225C2×#92420—21no—
226C2×#92420—21no—
227C2×#92420—21no—
228C2×#92420C2×D414yes—
229C4⋊#6923—22no—
230C4⋊#6923—41no—
231C4×#6923—22no—
232C4×#6923—41no—
233#11758213—28no—
234#11758213—21no—
235#11758213—22no—
236#11758213—21no—
237#11758213—22no—
238#11758213—22no—
239#11758213—22no—
240#11758213—21no—
241#11758213—21no—
242#11758213—21no—
243#11758213—21no—
244#11758213C2×D412yes—
245#11758213C2×D412yes—
246D61⋊C8—28no—
247D61⋊C8—22no—
248D61⋊C8—22no—
249D61⋊C8—41no—
250D61⋊C8—41no—
251M16×C61—21no—
252M16×C61C22×C412yes—
253C2×C8×C61—21no—
254C4⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C42×C61C22×C412yes—
257C22⋊Dic61—21no—
258#11758198—22no—
259C4⋊Dic61—21no—
260#11758196—22no—
261C4×Dic61—22no—
262C4×Dic61C22×C412yes—
263#11758194—21no—
264#11758194C22×C412yes—
265C2×#92418—21no—
266#11758189—22no—
267#11758189—22no—
268C8×D61—22no—
269C8×D61—22no—
270C23×C61—21no—
271C23×C61C4×D411yescharacteristic
272C22×D61—21no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—81no—
276C22×D61—82no—
277C22×D61C4×D411yescharacteristic
278C22×D61C22⋊Q811yescharacteristic
279C22×D61C22⋊Q811yescharacteristic
280C22×D61#12311yescharacteristic
281C22×D61#12311yescharacteristic
282C22×D61C2×#4111yescharacteristic
283C2×#6923—42no—
284C2×#6923—82no—
285Q8×C61—21no—
286Q8×C61C2×C4⋊C412yes—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—21no—
290D4×C61C2×C4⋊C412yes—
291C2×C4×C61—21no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61C2×C4⋊C411yescharacteristic
296C2×C4×C61C2×C4⋊C411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C22⋊D61—22no—
302C22⋊D61—22no—
303C22⋊D61—22no—
304C22⋊D61—22no—
305C22⋊D61—22no—
306C22⋊D61—22no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61C4×D411yescharacteristic
312C2×Dic61#12011yescharacteristic
313C2×Dic61#12011yescharacteristic
314C2×Dic61C22⋊Q811yescharacteristic
315C2×Dic61C22⋊Q811yescharacteristic
316C2×Dic61C22×D411yescharacteristic
317D244—22no—
318D244—22no—
319D244—21no—
320D244C2×C4⋊C412yes—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—82no—
328C4×D61C2×C4⋊C411yescharacteristic
329C4×D61C2×C4⋊C411yescharacteristic
330C4×D61C4×D411yescharacteristic
331C4×D61C4×D411yescharacteristic
332C4×D61#12011yescharacteristic
333C4×D61#12011yescharacteristic
334C4×D61C22⋊Q811yescharacteristic
335C4×D61C22⋊Q811yescharacteristic
336C4×D61C22⋊Q811yescharacteristic
337C4×D61C22⋊Q811yescharacteristic
338C4×D61#12311yescharacteristic
339C4×D61#12311yescharacteristic
340C4×D61C22×D411yescharacteristic
341C4×D61C22×D411yescharacteristic
342C4×D61C22×Q811yescharacteristic
343C4×D61C2×#4111yescharacteristic
344Dic122—21no—
345Dic122—22no—
346Dic122—22no—
347Dic122C2×C4⋊C412yes—
348#92420—22no—
349#92420—24no—
350#92420—22no—
351#92420—41no—
352#92420—41no—
353C8×C61—22no—
354#92418—22no—
355#20867—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—41no—
358C22×C61—42no—
359C22×C61#38511yescharacteristic
360C22×C61#38511yescharacteristic
361C22×C61C2×C4×D411yescharacteristic
362C2×D61—22no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—42no—
370C2×D61—82no—
371C2×D61—82no—
372C2×D61#38511yescharacteristic
373C2×D61#38511yescharacteristic
374C2×D61C2×C22⋊Q811yescharacteristic
375C2×D61C2×#12311yescharacteristic
376#6923—82no—
377C4×C61—22no—
378C4×C61—42no—
379C4×C61#38511yescharacteristic
380C4×C61#38511yescharacteristic
381C4×C61C22×C4⋊C411yescharacteristic
382C4×C61C2×C4×D411yescharacteristic
383Dic61—22no—
384Dic61—42no—
385Dic61#38511yescharacteristic
386Dic61#38511yescharacteristic
387Dic61C2×#12011yescharacteristic
388Dic61C2×C22⋊Q811yescharacteristic
389C2×#568—611no—
390C2×#430—611no—
391#2905—611no—
392C2×#421—611no—
393C2×#421—611no—
394#1861—614no—
395#1861—614no—
396C2×#344—611no—
397#1733—611no—
398C2×C61—21no—
399C2×C61—21no—
400C2×C61—21no—
401C2×C61—42no—
402C2×C61C2×#38511yescharacteristic
403D61—21no—
404D61—21no—
405D61—21no—
406D61—21no—
407D61—42no—
408C22×#41—611no—
409#568—614no—
410#568—1222no—
411#568—1222no—
412#568—1222no—
413C2×#131—1222no—
414C2×#131—1221no—
415C2×#131—1221no—
416C22×M16—611no—
417C22×M16—611no—
418C22×M16—611no—
419C22×M16—611no—
420C22×M16—1221no—
421C22×M16—1221no—
422C2×#117—611no—
423C2×#117—611no—
424#430—612no—
425#430—612no—
426#430—1221no—
427#430—1221no—
428C2×#108—1222no—
429#424—1222no—
430#424—1222no—
431#423—612no—
432#423—612no—
433#421—611no—
434#421—611no—
435#421—611no—
436#421—614no—
437#421—612no—
438#421—612no—
439#421—1221no—
440#421—1221no—
441#421#692311yescharacteristic, complemented
442C2×#104—614no—
443C2×#104—1222no—
444#344—614no—
445#339—614no—
446C61#2086711yescharacteristic, complemented, Sylow
447C2×#41—612no—
448C2×#41—612no—
449C2×#41—612no—
450C2×#41—612no—
451C2×#41—611no—
452C2×#41—611no—
453C2×#41—611no—
454C2×#41—1221no—
455C2×#41—1221no—
456C2×#41—1221no—
457C2×#41—1221no—
458C2×#41—1221no—
459C2×#41—1221no—
460C2×#41C2×#692311yescharacteristic
461C22×Q8—611no—
462C22×D4—611no—
463C22×D4—1221no—
464C23×C4—611no—
465C23×C4—1221no—
466#131—1228no—
467#131—1224no—
468#131—1224no—
469#131—1228no—
470#131—1224no—
471#131—1224no—
472C2×M16—612no—
473C2×M16—612no—
474C2×M16—611no—
475C2×M16—611no—
476C2×M16—612no—
477C2×M16—612no—
478C2×M16—611no—
479C2×M16—612no—
480C2×M16—612no—
481C2×M16—611no—
482C2×M16—611no—
483C2×M16—1221no—
484C2×M16—1221no—
485C2×M16—1221no—
486C2×M16—1224no—
487C2×M16—1224no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—1221no—
491C2×M16—1221no—
492C2×M16—1221no—
493C2×M16—1221no—
494C2×M16—1221no—
495C2×M16—1222no—
496C2×M16—1224no—
497C2×M16—1222no—
498C2×M16—1224no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16C2×#692311yescharacteristic
505C22×C8—612no—
506C22×C8—1221no—
507C22×C8—1221no—
508C22×C8—1222no—
509C22×C8—1222no—
510C22×C8—1221no—
511#117—611no—
512#117—612no—
513#117—612no—
514#117—1221no—
515#117—1221no—
516#117—1221no—
517#117—1221no—
518#117—1221no—
519#117C2×#692311yescharacteristic
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C42—612no—
525C2×C42—1221no—
526#108—1222no—
527#108—1222no—
528#108—1222no—
529#108—1222no—
530C4⋊C8—1224no—
531C4⋊C8—1224no—
532#104—614no—
533#104—614no—
534#104—614no—
535#104—1222no—
536#104—1222no—
537#104—1222no—
538#104—1222no—
539#104C2×#692314yescomplemented
540C24—611no—
541C24—1221no—
542#41—21no—
543#41—21no—
544#41—612no—
545#41—612no—
546#41—612no—
547#41—612no—
548#41—612no—
549#41—612no—
550#41—1222no—
551#41—1222no—
552#41—1222no—
553#41—1222no—
554#41—1222no—
555#41—1222no—
556#41—1221no—
557#41—1222no—
558#41—1222no—
559#41—1221no—
560#41—1221no—
561#41—1221no—
562#41—1221no—
563#41—1221no—
564#41C4⋊#692312yes—
565#41C22×#692312yes—
566C2×Q8—612no—
567C2×Q8—612no—
568C2×Q8—611no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8C4⋊#692311yescharacteristic
573C2×D4—21no—
574C2×D4—612no—
575C2×D4—612no—
576C2×D4—611no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4C4⋊#692311yescharacteristic
588C22×C4—21no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1221no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1221no—
608C22×C4—1222no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—2441no—
612C22×C4C22×#692311yescharacteristic
613M16—21no—
614M16—612no—
615M16—612no—
616M16—612no—
617M16—1222no—
618M16—1222no—
619M16—1222no—
620M16—1222no—
621M16—1221no—
622M16—1221no—
623M16—1222no—
624M16—1222no—
625M16—1222no—
626M16—1222no—
627M16—1228no—
628M16—1228no—
629M16—1221no—
630M16—1221no—
631M16—1221no—
632M16—1221no—
633M16—1221no—
634M16—2441no—
635M16—2441no—
636M16C22×#692312yes—
637C2×C8—21no—
638C2×C8—614no—
639C2×C8—1222no—
640C2×C8—1222no—
641C2×C8—1222no—
642C2×C8—1222no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1222no—
646C2×C8—1222no—
647C2×C8—1228no—
648C2×C8—1228no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—2441no—
653C2×C8—2441no—
654C4⋊C4—21no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C4⋊C4—1221no—
658C4⋊C4—2441no—
659C22⋊C4—21no—
660C22⋊C4—1222no—
661C22⋊C4—1221no—
662C22⋊C4—1222no—
663C22⋊C4—2441no—
664C42—612no—
665C42—1222no—
666C42—1222no—
667C42—2441no—
668C42C22×#692312yes—
669C23—21no—
670C23—611no—
671C23—611no—
672C23—611no—
673C23—611no—
674C23—611no—
675C23—611no—
676C23—1222no—
677C23—1222no—
678C23—1221no—
679C23—4882no—
680C23—4881no—
681C23D4×#692311yescharacteristic
682Q8—21no—
683Q8—612no—
684Q8—1222no—
685Q8—1222no—
686Q8—1221no—
687Q8C2×C4⋊#692312yes—
688D4—22no—
689D4—22no—
690D4—21no—
691D4—612no—
692D4—1222no—
693D4—1222no—
694D4—1222no—
695D4—1222no—
696D4—1222no—
697D4—1222no—
698D4—1222no—
699D4—1222no—
700D4—1221no—
701D4C2×C4⋊#692312yes—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—611no—
709C2×C4—611no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—611no—
717C2×C4—611no—
718C2×C4—611no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1221no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—4882no—
739C2×C4—4882no—
740C2×C4—2442no—
741C2×C4C2×C4⋊#692311yescharacteristic
742C2×C4C2×C4⋊#692311yescharacteristic
743C2×C4D4×#692311yescharacteristic
744C2×C4D4×#692311yescharacteristic
745C2×C4D4×#692311yescharacteristic
746C2×C4C23×#692311yescharacteristic
747C8—22no—
748C8—1224no—
749C8—1222no—
750C8—1222no—
751C8—1222no—
752C8—2441no—
753C8—2441no—
754C22—22no—
755C22—41no—
756C22—42no—
757C22—611no—
758C22—611no—
759C22—611no—
760C22—611no—
761C22—1222no—
762C22—4882no—
763C22—4882no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22—2441no—
770C22—2442no—
771C22#1684070911yescharacteristic
772C22#1684070911yescharacteristic
773C22C2×D4×#692311yescharacteristic
774C4—22no—
775C4—42no—
776C4—611no—
777C4—611no—
778C4—611no—
779C4—611no—
780C4—1222no—
781C4—4882no—
782C4—2442no—
783C4#1684070911yescharacteristic
784C4#1684070911yescharacteristic
785C4C22×C4⋊#692311yescharacteristic
786C4C2×D4×#692311yescharacteristic
787C2—21no—
788C2—21no—
789C2—21no—
790C2—42no—
791C2—1221no—
792C2—1221no—
793C2—1221no—
794C2—1221no—
795C2—2442no—
796C2C2×#1684070911yescharacteristic
subgroupG/H
centerC2C2×#16840709
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#421C4
socleC2×C61C2×#385
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#421#6923
hypocenterC61#20867
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. D61⋊#430C2semidirect
3. #21462462C2semidirect
5. #21461781C2semidirect
6. #21461780C2semidirect
7. C2×#16840645C2semidirect
8. #21461500C2semidirect
25. #16840777C22semidirect
26. #16840777C22semidirect
30. #16840767C22semidirect
31. #16840766C22semidirect
37. #16840645C22semidirect
38. #16840633C22semidirect
42. #16839780C4semidirect
43. #16839779C4semidirect
44. #16839778C4semidirect
45. #16839777C4semidirect
47. C61×#421C4semidirect
134. #14519705C2×C4semidirect
135. #14519704C2×C4semidirect
136. #14519703C2×C4semidirect
140. #104×C61C2×C4semidirect
441. #421#6923semidirect
446. C61#20867semidirect
539. #104C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408412
D61⋊#4302
#214624622
D61⋊#4212
#214617812
#214617802
C2×#168406452
#214615002
#421×D612
#2086761