Finite Group Databasebeta

← C61×#26246 #29529679

Subgroups — C61×#26246 #29529679

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#481C211yesmaximal, characteristic, complemented
2C2×C61×#482C211yesmaximal, characteristic, complemented
3C61×#2541C211yesmaximal, characteristic
4C61×#2352C211yesmaximal, characteristic, complemented
5C61×#2034C211yesmaximal, characteristic, complemented
6C61×#2033C211yesmaximal, characteristic, complemented
7C61×#2033C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1982C211yesmaximal, characteristic, complemented
10C61×#1961C211yesmaximal, characteristic, complemented
11C61×#1955C211yesmaximal, characteristic, complemented
12C61×#1949C211yesmaximal, characteristic, complemented
13C61×#1875C211yesmaximal, characteristic, complemented
14C61×#1874C211yesmaximal, characteristic, complemented
15C61×#1776C211yesmaximal, characteristic, complemented
16C2×#127×C61—21no—
17C2×#127×C61C2211yescharacteristic
18C2×#121×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×#121×C61C2211yescharacteristic
21C2×#121×C61C2211yescharacteristic
22C2×C4×D4×C61C2211yescharacteristic
23C2×#117×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C61×#482—24no—
26C61×#481—24no—
27C2×#107×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C2×#106×C61C2211yescharacteristic
30C2×#106×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×C22⋊C8×C61C2211yescharacteristic
41C2×C22⋊C8×C61C2211yescharacteristic
42C2×C22⋊C8×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×#97×C61C2211yescharacteristic
45C61×#392—21no—
46C61×#392—21no—
47C61×#390—21no—
48C61×#388—21no—
49C61×#387—21no—
50C61×#386—21no—
51C61×#382C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C61×#380C2211yescharacteristic
54C4×C4⋊C4×C61C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C4×C22⋊C4×C61—21no—
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61D411yescharacteristic
68C22×D4×C61C2311yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C23×C4×C61—21no—
71C23×C4×C61C2311yescharacteristic
72C23×C4×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77#127×C61—22no—
78#127×C61—22no—
79#127×C61—44no—
80#121×C61—22no—
81#121×C61—22no—
82#121×C61—22no—
83#121×C61—22no—
84#121×C61—41no—
85#121×C61—41no—
86#121×C61—41no—
87#121×C61—41no—
88C4×D4×C61—22no—
89C4×D4×C61—22no—
90#117×C61—22no—
91#117×C61—41no—
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—41no—
95C2×C4⋊C4×C61D411yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61D411yescharacteristic
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C42×C61—21no—
112C2×C42×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61C2311yescharacteristic
115#107×C61—22no—
116#107×C61—22no—
117#106×C61—22no—
118#106×C61D414yescomplemented
119C4⋊C8×C61—22no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—22no—
123#102×C61—22no—
124#102×C61—41no—
125#102×C61—41no—
126#102×C61—41no—
127#102×C61—41no—
128C22⋊C8×C61—22no—
129C22⋊C8×C61—22no—
130C22⋊C8×C61—41no—
131C22⋊C8×C61—41no—
132#97×C61—22no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—41no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—42no—
167C2×D4×C61—42no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—81no—
171C2×D4×C61—81no—
172C2×D4×C61—81no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—42no—
195C22×C4×C61—42no—
196C22×C4×C61—81no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61C2×D412yes—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—42no—
225C4⋊C4×C61C2×D412yes—
226C4⋊C4×C61C2×D412yes—
227C4⋊C4×C61#4112yes—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—42no—
232C22⋊C4×C61—42no—
233C22⋊C4×C61—42no—
234C22⋊C4×C61—42no—
235C22⋊C4×C61—42no—
236C22⋊C4×C61—81no—
237C42×C61—42no—
238C42×C61—42no—
239C42×C61—81no—
240C42×C61#4112yes—
241C42×C61#4112yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
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×C61AGL(1,ℤ/8)12yes—
270C23×C61C22×D411yescharacteristic
271D4×C61—44no—
272D4×C61—41no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—41no—
276D4×C61—41no—
277D4×C61—41no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—84no—
281D4×C61—84no—
282D4×C61—84no—
283D4×C61—84no—
284D4×C61—84no—
285D4×C61—84no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—84no—
323C2×C4×C61#12312yes—
324C2×C4×C61#12312yes—
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61C2×#4111yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C2×C4×C61H(5,𝔽2)11yescharacteristic
331C8×C61—22no—
332C8×C61—41no—
333C8×C61—41no—
334C8×C61—41no—
335#26246C6111yesmaximal, characteristic, direct product factor, Sylow
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61C2×#12311yescharacteristic
365C22×C61D4211yescharacteristic
366C22×C61#54611yescharacteristic
367C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C61#57511yescharacteristic
369C22×C61#57611yescharacteristic
370C22×C61#57711yescharacteristic
371C4×C61—22no—
372C4×C61—22no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61—81no—
379C4×C61—81no—
380C4×C61—81no—
381C4×C61#53211yescharacteristic
382C4×C61#54011yescharacteristic
383C4×C61#55011yescharacteristic
384C4×C61#55911yescharacteristic
385C2×#481C2×C6111yescharacteristic, complemented
386C2×#482C2×C6111yescharacteristic, complemented
387#2541C2×C6111yescharacteristic
388#2352C2×C6111yescharacteristic, complemented
389#2034C2×C6111yescharacteristic, complemented
390#2033C2×C6111yescharacteristic, complemented
391#2033C2×C6111yescharacteristic, complemented
392#2033C2×C6111yescharacteristic, complemented
393#1982C2×C6111yescharacteristic, complemented
394#1961C2×C6111yescharacteristic, complemented
395#1955C2×C6111yescharacteristic, complemented
396#1949C2×C6111yescharacteristic, complemented
397#1875C2×C6111yescharacteristic, complemented
398#1874C2×C6111yescharacteristic, complemented
399#1776C2×C6111yescharacteristic, complemented
400C2×C61—42no—
401C2×C61—81no—
402C2×C61—161no—
403C2×C61—161no—
404C2×C61#244511yescharacteristic
405C2×C61#309411yescharacteristic
406C2×C61#309611yescharacteristic
407C2×C61#326511yescharacteristic
408C2×C61#326811yescharacteristic
409C2×C61#331711yescharacteristic
410C2×C61#331811yescharacteristic
411C2×#127—21no—
412C2×#127C22×C6111yescharacteristic
413C2×#121C22×C6111yescharacteristic
414C2×#121C22×C6111yescharacteristic
415C2×#121C22×C6111yescharacteristic
416C2×#121C22×C6111yescharacteristic
417C2×C4×D4C22×C6111yescharacteristic
418C2×#117C22×C6111yescharacteristic
419C22×C4⋊C4C22×C6111yescharacteristic
420#482—24no—
421#481—24no—
422C2×#107C22×C6111yescharacteristic
423C2×#107C22×C6111yescharacteristic
424C2×#106C22×C6111yescharacteristic
425C2×#106C22×C6111yescharacteristic
426C2×C4⋊C8C22×C6111yescharacteristic
427C2×#102C22×C6111yescharacteristic
428C2×#102C22×C6111yescharacteristic
429C2×#102C22×C6111yescharacteristic
430C2×#102C22×C6111yescharacteristic
431C2×#102C22×C6111yescharacteristic
432C2×#102C22×C6111yescharacteristic
433C2×#102C22×C6111yescharacteristic
434C2×#102C22×C6111yescharacteristic
435C2×C22⋊C8C22×C6111yescharacteristic
436C2×C22⋊C8C22×C6111yescharacteristic
437C2×C22⋊C8C22×C6111yescharacteristic
438C2×C22⋊C8C22×C6111yescharacteristic
439C2×#97C22×C6111yescharacteristic
440#392—21no—
441#392—21no—
442#390—21no—
443#388—21no—
444#387—21no—
445#386—21no—
446#382C22×C6111yescharacteristic
447#380C22×C6111yescharacteristic
448#380C22×C6111yescharacteristic
449C4×C4⋊C4C22×C6111yescharacteristic
450C4×C4⋊C4C22×C6111yescharacteristic
451C4×C22⋊C4—21no—
452#340C22×C6111yescharacteristic
453#340C22×C6111yescharacteristic
454#340C22×C6111yescharacteristic
455#340C22×C6111yescharacteristic
456C61#2624611yescharacteristic, direct product factor, Sylow
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4D4×C6111yescharacteristic
464C22×D4C23×C6111yescharacteristic
465C22×D4C23×C6111yescharacteristic
466C23×C4—21no—
467C23×C4C23×C6111yescharacteristic
468C23×C4C23×C6111yescharacteristic
469C22×C8C23×C6111yescharacteristic
470C22×C8C23×C6111yescharacteristic
471C22×C8C23×C6111yescharacteristic
472C22×C8C23×C6111yescharacteristic
473#127—22no—
474#127—22no—
475#127—44no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—41no—
481#121—41no—
482#121—41no—
483#121—41no—
484C4×D4—22no—
485C4×D4—22no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4D4×C6111yescharacteristic
492C2×C4⋊C4C23×C6111yescharacteristic
493C2×C4⋊C4C23×C6111yescharacteristic
494C2×C4⋊C4C23×C6111yescharacteristic
495C2×C4⋊C4C23×C6111yescharacteristic
496C2×C4⋊C4C23×C6111yescharacteristic
497C2×C4⋊C4C23×C6111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C6111yescharacteristic
506C2×C22⋊C4D4×C6111yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42C23×C6111yescharacteristic
511#107—22no—
512#107—22no—
513#106—22no—
514#106D4×C6114yescomplemented
515C4⋊C8—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102—41no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528#97—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C6111yescharacteristic
538C24C2×D4×C6111yescharacteristic
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—81no—
593C22×C4C2×D4×C6111yescharacteristic
594C22×C4C2×D4×C6111yescharacteristic
595C22×C4C2×D4×C6111yescharacteristic
596C22×C4C2×D4×C6111yescharacteristic
597C22×C4C24×C6111yescharacteristic
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8C2×D4×C6112yes—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4C2×D4×C6112yes—
622C4⋊C4C2×D4×C6112yes—
623C4⋊C4#41×C6112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C42—42no—
634C42—42no—
635C42—81no—
636C42#41×C6112yes—
637C42#41×C6112yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23AGL(1,ℤ/8)×C6112yes—
666C23C22×D4×C6111yescharacteristic
667D4—44no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—84no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4#123×C6112yes—
720C2×C4#123×C6112yes—
721C2×C4C22×D4×C6111yescharacteristic
722C2×C4C2×#41×C6111yescharacteristic
723C2×C4C2×#41×C6111yescharacteristic
724C2×C4C2×#41×C6111yescharacteristic
725C2×C4H(5,𝔽2)×C6111yescharacteristic
726C2×C4H(5,𝔽2)×C6111yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#123×C6111yescharacteristic
760C22D42×C6111yescharacteristic
761C22C61×#54611yescharacteristic
762C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
763C22C61×#57511yescharacteristic
764C22C61×#57611yescharacteristic
765C22C61×#57711yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—42no—
772C4—42no—
773C4—81no—
774C4—81no—
775C4—81no—
776C4C61×#53211yescharacteristic
777C4C61×#54011yescharacteristic
778C4C61×#55011yescharacteristic
779C4C61×#55911yescharacteristic
780C2—42no—
781C2—81no—
782C2—161no—
783C2—161no—
784C2C61×#244511yescharacteristic
785C2C61×#309411yescharacteristic
786C2C61×#309611yescharacteristic
787C2C61×#326511yescharacteristic
788C2C61×#326811yescharacteristic
789C2C61×#331711yescharacteristic
790C2C61×#331811yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2541C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#481C2semidirect
2. C2×C61×#482C2semidirect
4. C61×#2352C2semidirect
5. C61×#2034C2semidirect
6. C61×#2033C2semidirect
7. C61×#2033C2semidirect
8. C61×#2033C2semidirect
9. C61×#1982C2semidirect
10. C61×#1961C2semidirect
11. C61×#1955C2semidirect
12. C61×#1949C2semidirect
13. C61×#1875C2semidirect
14. C61×#1874C2semidirect
15. C61×#1776C2semidirect
118. #106×C61D4semidirect
335. #26246C61direct (N × H)
385. C2×#481C2×C61semidirect
386. C2×#482C2×C61semidirect
388. #2352C2×C61semidirect
389. #2034C2×C61semidirect
390. #2033C2×C61semidirect
391. #2033C2×C61semidirect
392. #2033C2×C61semidirect
393. #1982C2×C61semidirect
394. #1961C2×C61semidirect
395. #1955C2×C61semidirect
396. #1949C2×C61semidirect
397. #1875C2×C61semidirect
398. #1874C2×C61semidirect
399. #1776C2×C61semidirect
456. C61#26246direct (N × H)
514. #106D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4812
C2×C61×#4822
C61×#25412
C61×#23522
C61×#20342
C61×#20332
C61×#19822
C61×#19612
C61×#19552
C61×#19492
C61×#18752
C61×#18742
C61×#17762
#2624661