Finite Group Databasebeta

← #30620341

Subgroups — #30620341

Order 15616.

1132 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462557C212yesmaximal, complemented
2#21462013C212yesmaximal, complemented
3#21461845C212yesmaximal, complemented
4#21461844C212yesmaximal, complemented
5#21461720C211yesmaximal, characteristic, complemented
6#21461718C211yesmaximal, characteristic, complemented
7#21461683C211yesmaximal, characteristic, complemented
8C4×#14519837C211yesmaximal, characteristic, complemented
9#21461524C211yesmaximal, characteristic, complemented
10C2×#16840642C211yesmaximal, characteristic, complemented
11C2×#16840461C211yesmaximal, characteristic
12C2×D61⋊M16C2212yes—
13C22×#11758217C2212yes—
14#16840795—22no—
15#16840794—22no—
16#16840791—22no—
17#16840789—22no—
18#16840765C2212yes—
19C2×#14519837C2212yes—
20C2×#14519837C2212yes—
21#16840734C2212yes—
22#16840732C2212yes—
23C4×#11758217C2212yes—
24#16840642C2211yescharacteristic
25#16840642C2212yes—
26#16840642C2211yescharacteristic
27#16840642C2212yes—
28#16840642C2211yescharacteristic
29#16840642C2211yescharacteristic
30#16840642C2212yes—
31#16840642C2212yes—
32#16840461—22no—
33#16840461—22no—
34#16840461—22no—
35#16840461—22no—
36C2×#14519771C411yescharacteristic
37C2×#14519770C411yescharacteristic
38C2×#14519767C2211yescharacteristic
39C2×#14519762C411yescharacteristic
40C2×#14519760C411yescharacteristic
41C2×#14519751C411yescharacteristic
42C2×#14519750C2211yescharacteristic
43C2×#14519749C411yescharacteristic
44C2×#14519749C2211yescharacteristic
45C2×C4×C22⋊D61C2211yescharacteristic
46C2×#14519737C411yescharacteristic
47C2×#14519737C2211yescharacteristic
48C2×#14519734C2211yescharacteristic
49C22×#11758196C2211yescharacteristic
50C2×C4×D4×C61C411yescharacteristic
51C2×#11758213—22no—
52D61⋊M16—24no—
53D61⋊M16—42no—
54C2×#11758217—22no—
55C2×#11758217—24no—
56C2×#11758217—42no—
57C2×#11758217C2312yes—
58C2×#11758217C2312yes—
59C2×#11758217C2312yes—
60C2×#11758217C2312yes—
61C2×D61⋊C8—22no—
62C22×#92420—22no—
63#14519844—22no—
64C4⋊#92420—22no—
65#14519837—24no—
66#14519837—42no—
67#14519834—22no—
68#14519834—22no—
69C22⋊#92420—22no—
70C22⋊#92420—22no—
71#14519832—22no—
72C4×#92420—22no—
73C22×D244C2×C411yescharacteristic
74C22×C22⋊D61C2×C411yescharacteristic
75C22×C22⋊D61C2×C411yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C22×C22⋊D61C2311yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2311yescharacteristic
82#14519771—22no—
83#14519771—22no—
84#14519770—22no—
85#14519770—22no—
86#14519767—22no—
87#14519767—22no—
88#14519762—22no—
89#14519762—22no—
90#14519760—22no—
91#14519760—22no—
92#14519751—22no—
93#14519751—22no—
94#14519750—22no—
95#14519750—22no—
96#14519749—22no—
97#14519749—22no—
98#14519749—22no—
99#14519749—22no—
100C4×C22⋊D61—22no—
101C4×C22⋊D61—22no—
102#14519737—21no—
103#14519737—21no—
104#14519737—21no—
105#14519737—21no—
106#14519737D412yes—
107#14519737D412yes—
108#14519737D412yes—
109#14519737D412yes—
110#14519734—22no—
111#14519734—22no—
112C2×C4⋊Dic61C2×C411yescharacteristic
113C2×#11758196—22no—
114C2×#11758196—22no—
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2311yescharacteristic
121C2×#11758196C2311yescharacteristic
122C2×#11758196C2311yescharacteristic
123C2×C22⋊Dic61C2×C411yescharacteristic
124C2×C22⋊Dic61C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×C4×Dic61C2×C411yescharacteristic
132C2×C4×Dic61C2311yescharacteristic
133C22×D4×C61C2×C411yescharacteristic
134C23×C4×C61C2×C411yescharacteristic
135C23×C4×C61C2×C411yescharacteristic
136C4×D4×C61—21no—
137C4×D4×C61—21no—
138C4×D4×C61—21no—
139C4×D4×C61—21no—
140C2×C4⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C42×C61C2×C411yescharacteristic
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—42no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—81no—
156C22×C4×C61—81no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—21no—
168C2×C22⋊D61—21no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—81no—
172C2×C22⋊D61C22⋊C412yes—
173C2×C22⋊D61C22⋊C412yes—
174C22×Dic61—22no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—81no—
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C2×D412yes—
186C22×Dic61C2×D412yes—
187C22×Dic61C2411yescharacteristic
188C2×D244—22no—
189C2×D244—81no—
190C2×C4×D61—22no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—81no—
196C2×C4×D61C2×D412yes—
197C2×C4×D61C2×D412yes—
198#11758217—22no—
199#11758217—22no—
200#11758217—22no—
201#11758217—22no—
202#11758217—22no—
203#11758217—22no—
204#11758217—22no—
205#11758217—44no—
206#11758217#4114yes—
207C2×#92420—22no—
208C2×#92420—22no—
209C2×#92420—22no—
210C2×#92420—22no—
211C2×#92420—44no—
212#11758213—44no—
213D61⋊C8—44no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C22⋊C4×C61—21no—
217C22⋊C4×C61—21no—
218C22⋊C4×C61C22⋊C411yescharacteristic
219C22⋊C4×C61C22⋊C411yescharacteristic
220C22⋊C4×C61C22⋊C411yescharacteristic
221C22⋊C4×C61C22⋊C411yescharacteristic
222C42×C61—21no—
223C42×C61—21no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—21no—
229#11758198—21no—
230#11758198—22no—
231#11758198—22no—
232#11758198C22⋊C412yes—
233#11758198C22⋊C412yes—
234C4⋊Dic61—22no—
235#11758196—21no—
236#11758196—21no—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241#11758196—22no—
242#11758196—22no—
243#11758196C22⋊C412yes—
244#11758196C22⋊C412yes—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61C2×D412yes—
248C4×Dic61C2×D412yes—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C2×C22⋊C411yescharacteristic
259C23×C61C2×C22⋊C411yescharacteristic
260C23×C61C23×C411yescharacteristic
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61C2×C22⋊C412yes—
271D4×C61—42no—
272D4×C61—42no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—81no—
283C2×C4×C61—81no—
284C2×C4×C61—81no—
285C2×C4×C61—81no—
286C2×C4×C61C2×C22⋊C411yescharacteristic
287C2×C4×C61C2×C22⋊C411yescharacteristic
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C22⋊D61—24no—
291C22⋊D61—42no—
292C22⋊D61—42no—
293C22⋊D61—42no—
294C22⋊D61—42no—
295C22⋊D61—42no—
296C22⋊D61—82no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—81no—
311C2×Dic61—81no—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61C22×D412yes—
315C2×Dic61C2×#4112yes—
316C2×Dic61H(5,𝔽2)11yescharacteristic
317C2×Dic612−1+411yescharacteristic
318D244—82no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—81no—
324C4×D61—81no—
325#92420—24no—
326#92420—42no—
327#92420—42no—
328#92420—42no—
329#22482—611nomaximal, Sylow
330C22×C61—21no—
331C22×C61—21no—
332C22×C61—21no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61#41312yes—
345C22×C61C22×C22⋊C411yescharacteristic
346C22×C61C4×#4111yescharacteristic
347C22×C61#52011yescharacteristic
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C4×C61—21no—
359C4×C61—21no—
360C4×C61—21no—
361C4×C61—21no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—41no—
365Dic61—22no—
366Dic61—22no—
367Dic61—41no—
368Dic61—41no—
369Dic61—41no—
370Dic61#54612yes—
371Dic61#54712yes—
372C2×#553—611no—
373D4×M16—612no—
374#1998—612no—
375#1900—612no—
376#1900—612no—
377#1822—611no—
378#1821—611no—
379#1800—611no—
380C4×#100—611no—
381#1742—611no—
382C2×#343—611no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—22no—
386C2×C61—41no—
387C2×C61—81no—
388C2×C61#233911yescharacteristic
389C2×C61C2×#41311yescharacteristic
390C2×C61#288811yescharacteristic
391D61—42no—
392D61—81no—
393C22×M16—612no—
394C22×M16—612no—
395#553—1222no—
396#553—1222no—
397#553—1222no—
398#553—1222no—
399C2×#126—611no—
400C2×#126—611no—
401C2×#125—611no—
402C2×#123—611no—
403C2×#123—611no—
404C2×#121—611no—
405C2×#121—611no—
406C2×#121—611no—
407C2×#121—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411C2×C4×D4#692311yescharacteristic
412C2×#117—611no—
413C22×C4⋊C4—611no—
414#436—1222no—
415#435—1222no—
416#435—1222no—
417C8×D4—1222no—
418#423—612no—
419C2×#100—612no—
420C2×#100—612no—
421#407—612no—
422#407—612no—
423C4×M16—612no—
424#343—611no—
425#343—611no—
426#343—611no—
427#343—612no—
428#343—612no—
429#343—612no—
430#343—612no—
431#343—611no—
432C61#2248211yescharacteristic, complemented, Sylow
433C22×D4—611no—
434C22×D4—611no—
435C22×D4—611no—
436C22×D4—611no—
437C22×D4—611no—
438C22×D4C2×#692311yescharacteristic
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4C2×#692311yescharacteristic
444C23×C4C2×#692311yescharacteristic
445C2×M16—612no—
446C2×M16—612no—
447C2×M16—612no—
448C2×M16—612no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1224no—
452C2×M16—1224no—
453C2×M16—2442no—
454C2×M16—2442no—
455C22×C8—1222no—
456C22×C8—1222no—
457#126—1222no—
458#126—1222no—
459#126—1222no—
460#126—1222no—
461#125—1222no—
462#125—1222no—
463#123—1222no—
464#123—1222no—
465#123—1222no—
466#123—1222no—
467#121—1222no—
468#121—1222no—
469#121—1222no—
470#121—1222no—
471#121—1222no—
472#121—1222no—
473#121—1222no—
474#121—1222no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—612no—
480C4×D4—612no—
481C4×D4—612no—
482C4×D4—612no—
483C4×D4—1222no—
484C4×D4—1222no—
485C4×D4—1221no—
486C4×D4—1221no—
487C4×D4—1221no—
488C4×D4—1221no—
489#117—1222no—
490#117—1222no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1222no—
502C2×C4⋊C4C2×#692311yescharacteristic
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4C2×#692311yescharacteristic
512C2×C22⋊C4C2×#692311yescharacteristic
513C2×C42—611no—
514C2×C42—611no—
515C2×C42C2×#692311yescharacteristic
516C4⋊C8—1222no—
517C4⋊C8—1222no—
518#100—1224no—
519#100—2442no—
520C22⋊C8—1222no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524#97—1222no—
525C4×C8—1222no—
526C24—611no—
527C24—611no—
528C24C22×#692311yescharacteristic
529C24C22×#692311yescharacteristic
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—42no—
533C2×D4—612no—
534C2×D4—612no—
535C2×D4—1222no—
536C2×D4—1222no—
537C2×D4—1221no—
538C2×D4—1222no—
539C2×D4—1221no—
540C2×D4—1222no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—4881no—
544C2×D4—4881no—
545C2×D4—2442no—
546C2×D4—2442no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—611no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—1222no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1222no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—4881no—
574C22×C4—4881no—
575C22×C4C22×#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C22×C4C22×#692311yescharacteristic
578C22×C4C22×#692311yescharacteristic
579C22×C4C22×#692311yescharacteristic
580M16—614no—
581M16—1222no—
582M16—1222no—
583M16—1222no—
584M16—1222no—
585M16—1222no—
586M16—1222no—
587M16—1222no—
588M16—2444no—
589M16—2444no—
590C2×C8—1222no—
591C2×C8—1222no—
592C2×C8—1222no—
593C2×C8—1222no—
594C2×C8—2444no—
595C2×C8—2444no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—612no—
599C4⋊C4—612no—
600C4⋊C4—1222no—
601C4⋊C4—1222no—
602C4⋊C4—1222no—
603C4⋊C4—1222no—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—1222no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—612no—
612C22⋊C4—612no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1221no—
620C22⋊C4—1221no—
621C22⋊C4C22⋊#692311yescharacteristic
622C22⋊C4C22⋊#692311yescharacteristic
623C22⋊C4C22⋊#692311yescharacteristic
624C22⋊C4C22⋊#692311yescharacteristic
625C42—21no—
626C42—21no—
627C42—612no—
628C42—612no—
629C42—1221no—
630C42—1221no—
631C23—22no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—612no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23C2×C22⋊#692311yescharacteristic
651C23C2×C22⋊#692311yescharacteristic
652C23C23×#692311yescharacteristic
653D4—42no—
654D4—42no—
655D4—1224no—
656D4—4882no—
657D4—4882no—
658D4—2442no—
659D4—2442no—
660D4—2442no—
661D4—2442no—
662D4—2442no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—611no—
679C2×C4—611no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—4881no—
696C2×C4—4881no—
697C2×C4—4881no—
698C2×C4—4881no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4C2×C22⋊#692311yescharacteristic
704C2×C4C2×C22⋊#692311yescharacteristic
705C2×C4C2×C22⋊#692311yescharacteristic
706C2×C4C2×C22⋊#692311yescharacteristic
707C8—1224no—
708C8—2442no—
709C8—2442no—
710C8—2442no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—81no—
724C22—81no—
725C22—1222no—
726C22—1222no—
727C22—1222no—
728C22—4881no—
729C22—4881no—
730C22—4881no—
731C22—4881no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22#1684074812yes—
736C22C22×C22⋊#692311yescharacteristic
737C22#41×#692311yescharacteristic
738C22#1684083111yescharacteristic
739C4—21no—
740C4—21no—
741C4—21no—
742C4—21no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—612no—
747C4—612no—
748C4—1222no—
749C4—1222no—
750C4—2441no—
751C4—2441no—
752C4—2441no—
753C2—21no—
754C2—21no—
755C2—22no—
756C2—41no—
757C2—81no—
758C2—4881no—
759C2—2442no—
760C2#2146232211yescharacteristic
761C2C2×#1684074811yescharacteristic
762C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840461C2
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#22482
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462557C2semidirect
2. #21462013C2semidirect
3. #21461845C2semidirect
4. #21461844C2semidirect
5. #21461720C2semidirect
6. #21461718C2semidirect
7. #21461683C2semidirect
8. C4×#14519837C2semidirect
9. #21461524C2semidirect
10. C2×#16840642C2semidirect
432. C61#22482semidirect

Maximal subgroups

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

subgroupindex
#214625572
#214620132
#214618452
#214618442
#214617202
#214617182
#214616832
C4×#145198372
#214615242
C2×#168406422
C2×#168404612
#2248261