Finite Group Databasebeta

← C61×#18230 #29521663

Subgroups — C61×#18230 #29521663

Order 15616.

1140 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3538C211yesmaximal, characteristic, complemented
2C61×#3007C211yesmaximal, characteristic, complemented
3C61×#3002C211yesmaximal, characteristic
4C61×#2616C211yesmaximal, characteristic, complemented
5C61×#1605C212yesmaximal, complemented
6C61×#1603C212yesmaximal, complemented
7C61×#1599C212yesmaximal, complemented
8C61×#1597C212yesmaximal, complemented
9C61×#1520C211yesmaximal, characteristic, complemented
10C61×#1513C211yesmaximal, characteristic, complemented
11C61×#1472C211yesmaximal, characteristic, complemented
12C22×#41×C61C2211yescharacteristic
13C2×#137×C61—21no—
14C2×#135×C61—21no—
15C61×#563—22no—
16C61×#552—21no—
17C61×#552—21no—
18C61×#551—22no—
19D4×Q8×C61—21no—
20D4×Q8×C61—21no—
21C61×#544—21no—
22C61×#544C2212yes—
23C61×#541—21no—
24C61×#539—21no—
25C61×#539C2212yes—
26C61×#536—21no—
27C61×#525C2211yescharacteristic
28C2×C22⋊Q8×C61—21no—
29C2×C22⋊Q8×C61C2211yescharacteristic
30C2×C22⋊Q8×C61C2211yescharacteristic
31C61×#452—21no—
32C61×#452—22no—
33C61×#451C2212yes—
34C61×#451C2211yescharacteristic
35C61×#450C2212yes—
36C61×#450C2211yescharacteristic
37C61×#449—21no—
38C61×#448C2211yescharacteristic
39C61×#447C2211yescharacteristic
40C61×#417—21no—
41C61×#416—21no—
42C61×#407C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C61×#395C2212yes—
45C61×#394—22no—
46C61×#394C2212yes—
47C61×#380—21no—
48C61×#380C2211yescharacteristic
49C61×#328C2212yes—
50C61×#328C2212yes—
51C61×#328C2212yes—
52C61×#327C2212yes—
53C61×#324C2212yes—
54C61×#324C2212yes—
55C2×#41×C61—21no—
56C2×#41×C61—21no—
57C2×#41×C61—21no—
58C2×#41×C61—21no—
59C2×#41×C61—44no—
60C2×#41×C61D411yescharacteristic
61C22×Q8×C61—21no—
62C22×Q8×C61D411yescharacteristic
63C22×Q8×C61D411yescharacteristic
64C22×Q8×C61C2311yescharacteristic
65C22×D4×C61—21no—
66C22×D4×C61C2311yescharacteristic
67C23×C4×C61—21no—
68C23×C4×C61C2311yescharacteristic
69#137×C61—44no—
70#135×C61—44no—
71C2×Q16×C61—21no—
72C2×Q16×C61—22no—
73C2×SD16×C61—21no—
74C2×SD16×C61—22no—
75C2×SD16×C61—21no—
76C2×D8×C61—21no—
77C2×M16×C61—21no—
78C22×C8×C61—21no—
79C4⋊Q8×C61—21no—
80C4⋊Q8×C61—22no—
81C4⋊Q8×C61—22no—
82C4⋊Q8×C61—22no—
83#126×C61—22no—
84#126×C61—22no—
85#126×C61—22no—
86#126×C61—22no—
87#125×C61—21no—
88#125×C61—22no—
89#125×C61—22no—
90#125×C61—22no—
91#125×C61—22no—
92#124×C61—22no—
93#123×C61—22no—
94#123×C61—22no—
95#123×C61—22no—
96#123×C61—22no—
97#123×C61—21no—
98C22⋊Q8×C61—21no—
99C22⋊Q8×C61—21no—
100C22⋊Q8×C61—22no—
101C22⋊Q8×C61—22no—
102C22⋊Q8×C61—22no—
103C22⋊Q8×C61—21no—
104C22⋊Q8×C61—21no—
105C22⋊Q8×C61—21no—
106C22⋊Q8×C61—22no—
107C22⋊Q8×C61—21no—
108C22⋊Q8×C61—21no—
109C22⋊Q8×C61—21no—
110C22⋊Q8×C61—44no—
111C22⋊Q8×C61D411yescharacteristic
112C22⋊Q8×C61D412yes—
113C22⋊Q8×C61C2312yes—
114C22⋊Q8×C61C2311yescharacteristic
115#121×C61D411yescharacteristic
116#121×C61C2311yescharacteristic
117#120×C61—21no—
118C4×Q8×C61—21no—
119C4×Q8×C61—21no—
120C4×D4×C61—22no—
121C4×D4×C61—22no—
122C4×D4×C61—21no—
123C4×D4×C61—21no—
124#117×C61—21no—
125#117×C61—22no—
126#117×C61—22no—
127#117×C61D411yescharacteristic
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61C2312yes—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61D412yes—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—22no—
142#102×C61—21no—
143#102×C61—21no—
144#102×C61—22no—
145C22⋊C8×C61—21no—
146C22⋊C8×C61—21no—
147C22⋊C8×C61C2312yes—
148C22⋊C8×C61C2311yescharacteristic
149C22⋊C8×C61C2311yescharacteristic
150#95×C61—22no—
151#95×C61C2312yes—
152C24×C61—21no—
153C24×C61C2×D411yescharacteristic
154#41×C61—24no—
155#41×C61—24no—
156#41×C61—42no—
157#41×C61—42no—
158#41×C61—42no—
159#41×C61—42no—
160#41×C61—42no—
161#41×C61—42no—
162#41×C61—42no—
163C2×Q8×C61—22no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—42no—
170C2×Q8×C61—42no—
171C2×Q8×C61—42no—
172C2×Q8×C61—82no—
173C2×Q8×C61C2×D412yes—
174C2×Q8×C61C2×D411yescharacteristic
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—41no—
184C2×D4×C61—41no—
185C2×D4×C61C2×D411yescharacteristic
186C22×C4×C61—24no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—22no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—22no—
193C22×C4×C61—42no—
194C22×C4×C61—42no—
195C22×C4×C61—41no—
196C22×C4×C61—41no—
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D412yes—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2411yescharacteristic
205Q16×C61—42no—
206Q16×C61—44no—
207SD16×C61—42no—
208SD16×C61—44no—
209SD16×C61—42no—
210D8×C61—42no—
211M16×C61—42no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—22no—
215C2×C8×C61—42no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—22no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—42no—
234C4⋊C4×C61—44no—
235C4⋊C4×C61C2×D412yes—
236C4⋊C4×C61C2×D411yescharacteristic
237C4⋊C4×C61C2×D411yescharacteristic
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—44no—
251C22⋊C4×C61—82no—
252C22⋊C4×C61—81no—
253C42×C61—22no—
254C42×C61—22no—
255C42×C61—22no—
256C42×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—22no—
260C23×C61—21no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61#12011yescharacteristic
270C23×C61#12011yescharacteristic
271C23×C61C22×D411yescharacteristic
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61—42no—
277Q8×C61—41no—
278Q8×C61—42no—
279Q8×C61—42no—
280Q8×C61—81no—
281Q8×C61—82no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—42no—
288D4×C61—44no—
289D4×C61—44no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—81no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—44no—
310C2×C4×C61—42no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—44no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—81no—
320C2×C4×C61—82no—
321C2×C4×C61#12011yescharacteristic
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C8×C61—41no—
326C8×C61—41no—
327C8×C61—42no—
328#18230C6111yesmaximal, characteristic, direct product factor, Sylow
329C22×C61—21no—
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—42no—
342C22×C61—41no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61C2×#12011yescharacteristic
350C22×C61#57711yescharacteristic
351C22×C61#57811yescharacteristic
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—42no—
356C4×C61—41no—
357C4×C61—42no—
358C4×C61—41no—
359C4×C61—42no—
360C4×C61—41no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61—82no—
364C4×C61B(4,𝔽2)12yes—
365#3538C2×C6111yescharacteristic, complemented
366#3007C2×C6111yescharacteristic, complemented
367#3002C2×C6111yescharacteristic
368#2616C2×C6111yescharacteristic, complemented
369#1605C2×C6112yescomplemented
370#1603C2×C6112yescomplemented
371#1599C2×C6112yescomplemented
372#1597C2×C6112yescomplemented
373#1520C2×C6111yescharacteristic, complemented
374#1513C2×C6111yescharacteristic, complemented
375#1472C2×C6111yescharacteristic, complemented
376C2×C61—21no—
377C2×C61—21no—
378C2×C61—41no—
379C2×C61—41no—
380C2×C61—81no—
381C2×C61—82no—
382C2×C61#301311yescharacteristic
383C2×C61#302011yescharacteristic
384C2×C61C2×B(4,𝔽2)11yescharacteristic
385C22×#41C22×C6111yescharacteristic
386C2×#137—21no—
387C2×#135—21no—
388#563—22no—
389#552—21no—
390#552—21no—
391#551—22no—
392D4×Q8—21no—
393D4×Q8—21no—
394#544—21no—
395#544C22×C6112yes—
396#541—21no—
397#539—21no—
398#539C22×C6112yes—
399#536—21no—
400#525C22×C6111yescharacteristic
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8C22×C6111yescharacteristic
403C2×C22⋊Q8C22×C6111yescharacteristic
404#452—21no—
405#452—22no—
406#451C22×C6112yes—
407#451C22×C6111yescharacteristic
408#450C22×C6112yes—
409#450C22×C6111yescharacteristic
410#449—21no—
411#448C22×C6111yescharacteristic
412#447C22×C6111yescharacteristic
413#417—21no—
414#416—21no—
415#407C22×C6111yescharacteristic
416C2×C22⋊C8C22×C6111yescharacteristic
417#395C22×C6112yes—
418#394—22no—
419#394C22×C6112yes—
420#380—21no—
421#380C22×C6111yescharacteristic
422#328C22×C6112yes—
423#328C22×C6112yes—
424#328C22×C6112yes—
425#327C22×C6112yes—
426#324C22×C6112yes—
427#324C22×C6112yes—
428C61#1823011yescharacteristic, direct product factor, Sylow
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—44no—
434C2×#41D4×C6111yescharacteristic
435C22×Q8—21no—
436C22×Q8D4×C6111yescharacteristic
437C22×Q8D4×C6111yescharacteristic
438C22×Q8C23×C6111yescharacteristic
439C22×D4—21no—
440C22×D4C23×C6111yescharacteristic
441C23×C4—21no—
442C23×C4C23×C6111yescharacteristic
443#137—44no—
444#135—44no—
445C2×Q16—21no—
446C2×Q16—22no—
447C2×SD16—21no—
448C2×SD16—22no—
449C2×SD16—21no—
450C2×D8—21no—
451C2×M16—21no—
452C22×C8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—22no—
455C4⋊Q8—22no—
456C4⋊Q8—22no—
457#126—22no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#125—22no—
464#125—22no—
465#125—22no—
466#124—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—21no—
471#123—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8—44no—
485C22⋊Q8D4×C6112yes—
486C22⋊Q8D4×C6111yescharacteristic
487C22⋊Q8C23×C6112yes—
488C22⋊Q8C23×C6111yescharacteristic
489#121D4×C6111yescharacteristic
490#121C23×C6111yescharacteristic
491#120—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—22no—
498#117—21no—
499#117—22no—
500#117—22no—
501#117D4×C6111yescharacteristic
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4D4×C6111yescharacteristic
506C2×C4⋊C4D4×C6111yescharacteristic
507C2×C4⋊C4C23×C6112yes—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4D4×C6112yes—
513#103—21no—
514#103—21no—
515#103—22no—
516#102—21no—
517#102—21no—
518#102—22no—
519C22⋊C8—21no—
520C22⋊C8—21no—
521C22⋊C8C23×C6112yes—
522C22⋊C8C23×C6111yescharacteristic
523C22⋊C8C23×C6111yescharacteristic
524#95—22no—
525#95C23×C6112yes—
526C24—21no—
527C24C2×D4×C6111yescharacteristic
528#41—24no—
529#41—24no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—42no—
535#41—42no—
536#41—42no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—42no—
546C2×Q8—82no—
547C2×Q8C2×D4×C6112yes—
548C2×Q8C2×D4×C6111yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4C2×D4×C6111yescharacteristic
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4C2×D4×C6112yes—
572C22×C4C2×D4×C6111yescharacteristic
573C22×C4C2×D4×C6111yescharacteristic
574C22×C4C2×D4×C6111yescharacteristic
575C22×C4C2×D4×C6112yes—
576C22×C4C2×D4×C6111yescharacteristic
577C22×C4C2×D4×C6111yescharacteristic
578C22×C4C24×C6111yescharacteristic
579Q16—42no—
580Q16—44no—
581SD16—42no—
582SD16—44no—
583SD16—42no—
584D8—42no—
585M16—42no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—22no—
589C2×C8—42no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C6112yes—
610C4⋊C4C2×D4×C6111yescharacteristic
611C4⋊C4C2×D4×C6111yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—44no—
625C22⋊C4—82no—
626C22⋊C4—81no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—21no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23#120×C6111yescharacteristic
644C23#120×C6111yescharacteristic
645C23C22×D4×C6111yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—42no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—42no—
653Q8—42no—
654Q8—81no—
655Q8—82no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—42no—
662D4—44no—
663D4—44no—
664D4—41no—
665D4—41no—
666D4—81no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—81no—
694C2×C4—82no—
695C2×C4#120×C6111yescharacteristic
696C2×C4#120×C6111yescharacteristic
697C2×C4C22×D4×C6111yescharacteristic
698C2×C4C22×D4×C6111yescharacteristic
699C8—41no—
700C8—41no—
701C8—42no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—42no—
711C22—42no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22C2×#120×C6111yescharacteristic
723C22C61×#57711yescharacteristic
724C22C61×#57811yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—82no—
737C4C61×B(4,𝔽2)12yes—
738C2—21no—
739C2—21no—
740C2—41no—
741C2—41no—
742C2—82no—
743C2—81no—
744C2C61×#301311yescharacteristic
745C2C61×#302011yescharacteristic
746C2C2×C61×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3002C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3538C2semidirect
2. C61×#3007C2semidirect
4. C61×#2616C2semidirect
5. C61×#1605C2semidirect
6. C61×#1603C2semidirect
7. C61×#1599C2semidirect
8. C61×#1597C2semidirect
9. C61×#1520C2semidirect
10. C61×#1513C2semidirect
11. C61×#1472C2semidirect
328. #18230C61direct (N × H)
365. #3538C2×C61semidirect
366. #3007C2×C61semidirect
368. #2616C2×C61semidirect
369. #1605C2×C61semidirect
370. #1603C2×C61semidirect
371. #1599C2×C61semidirect
372. #1597C2×C61semidirect
373. #1520C2×C61semidirect
374. #1513C2×C61semidirect
375. #1472C2×C61semidirect
428. C61#18230direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35382
C61×#30072
C61×#30022
C61×#26162
C61×#16052
C61×#16032
C61×#15992
C61×#15972
C61×#15202
C61×#15132
C61×#14722
#1823061