Finite Group Databasebeta

← C61×#24977 #29528410

Subgroups — C61×#24977 #29528410

Order 15616.

892 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2535C211yesmaximal, characteristic
2D4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
3C61×#2077C211yesmaximal, characteristic, complemented
4C61×#2076C211yesmaximal, characteristic, complemented
5C61×#2034C211yesmaximal, characteristic, complemented
6C61×#2033C211yesmaximal, characteristic, complemented
7C61×#1955C211yesmaximal, characteristic, complemented
8C61×#1949C211yesmaximal, characteristic, complemented
9C61×#1874C211yesmaximal, characteristic, complemented
10C61×#1874C211yesmaximal, characteristic, complemented
11C61×#1836C211yesmaximal, characteristic, complemented
12C61×#1824C211yesmaximal, characteristic, complemented
13C61×#1823C211yesmaximal, characteristic, complemented
14C61×#1802C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C2×#121×C61C2211yescharacteristic
17C2×#121×C61C2211yescharacteristic
18C2×C4×D4×C61—21no—
19C2×C4×D4×C61C2211yescharacteristic
20C2×C4×D4×C61C2211yescharacteristic
21C22×C4⋊C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C2×#106×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×#102×C61C2211yescharacteristic
27C2×#102×C61C2211yescharacteristic
28C2×#102×C61C2211yescharacteristic
29C2×#102×C61C2211yescharacteristic
30C2×C22⋊C8×C61C2211yescharacteristic
31C2×C22⋊C8×C61C2211yescharacteristic
32C2×C22⋊C8×C61C2211yescharacteristic
33C2×C22⋊C8×C61C2211yescharacteristic
34C2×#97×C61C2211yescharacteristic
35C61×#397—21no—
36C61×#392—21no—
37C61×#389—21no—
38C61×#386—21no—
39C61×#386—21no—
40C61×#385—21no—
41C61×#385—21no—
42C61×#384C2211yescharacteristic
43C61×#382C2211yescharacteristic
44C61×#380C2211yescharacteristic
45C61×#380C2211yescharacteristic
46C61×#380C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C4×C4⋊C4×C61C2211yescharacteristic
49C61×#340C2211yescharacteristic
50C61×#340C2211yescharacteristic
51C61×#340C2211yescharacteristic
52C61×#340C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×D4×C61D411yescharacteristic
62C22×D4×C61C2311yescharacteristic
63C23×C4×C61—21no—
64C23×C4×C61—21no—
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C22×C8×C61C2311yescharacteristic
69C22×C8×C61C2311yescharacteristic
70C22×C8×C61C2311yescharacteristic
71C22×C8×C61C2311yescharacteristic
72#121×C61—22no—
73#121×C61—22no—
74#121×C61—41no—
75#121×C61—41no—
76C4×D4×C61—22no—
77C4×D4×C61—22no—
78C4×D4×C61—22no—
79C4×D4×C61—22no—
80C4×D4×C61—44no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61—22no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—41no—
88C2×C4⋊C4×C61—41no—
89C2×C4⋊C4×C61D411yescharacteristic
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61D411yescharacteristic
105C2×C22⋊C4×C61D411yescharacteristic
106C2×C42×C61—21no—
107C2×C42×C61C2311yescharacteristic
108#107×C61—41no—
109#106×C61—41no—
110C4⋊C8×C61—22no—
111#102×C61—22no—
112#102×C61—22no—
113#102×C61—41no—
114#102×C61—41no—
115C22⋊C8×C61—41no—
116C22⋊C8×C61—41no—
117C22⋊C8×C61—41no—
118C22⋊C8×C61—41no—
119#97×C61—22no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127C24×C61—21no—
128C24×C61C2×D411yescharacteristic
129C24×C61C2×D411yescharacteristic
130C2×D4×C61—22no—
131C2×D4×C61—22no—
132C2×D4×C61—22no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—42no—
139C2×D4×C61—42no—
140C2×D4×C61—42no—
141C2×D4×C61—42no—
142C2×D4×C61—81no—
143C2×D4×C61—81no—
144C2×D4×C61#4112yes—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—42no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61—81no—
170C22×C4×C61—81no—
171C22×C4×C61—81no—
172C22×C4×C61—81no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2411yescharacteristic
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—81no—
208C4⋊C4×C61#4112yes—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—81no—
217C22⋊C4×C61—81no—
218C42×C61—42no—
219C42×C61#4112yes—
220C42×C61#4112yes—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—22no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61AGL(1,ℤ/8)12yes—
241C23×C61#13712yes—
242C23×C61C22×D411yescharacteristic
243D4×C61—28no—
244D4×C61—22no—
245D4×C61—22no—
246D4×C61—41no—
247D4×C61—41no—
248D4×C61—84no—
249D4×C61—84no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—22no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—84no—
290C2×C4×C61—84no—
291C2×C4×C61—84no—
292C2×C4×C61#12312yes—
293C2×C4×C61#12312yes—
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C8×C61—41no—
301C8×C61—41no—
302C8×C61—41no—
303C8×C61—41no—
304#24977C6111yesmaximal, characteristic, direct product factor, Sylow
305C22×C61—22no—
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61C2×#12311yescharacteristic
327C22×C61#54611yescharacteristic
328C22×C61#54611yescharacteristic
329C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C61C2×#13711yescharacteristic
331C22×C61#57611yescharacteristic
332C22×C61#57711yescharacteristic
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—41no—
336C4×C61—41no—
337C4×C61—42no—
338C4×C61—81no—
339C4×C61—81no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61#52911yescharacteristic
345C4×C61#54011yescharacteristic
346C4×C61#55311yescharacteristic
347C4×C61#55511yescharacteristic
348#2535C2×C6111yescharacteristic
349D4×C4⋊C4C2×C6111yescharacteristic, complemented
350#2077C2×C6111yescharacteristic, complemented
351#2076C2×C6111yescharacteristic, complemented
352#2034C2×C6111yescharacteristic, complemented
353#2033C2×C6111yescharacteristic, complemented
354#1955C2×C6111yescharacteristic, complemented
355#1949C2×C6111yescharacteristic, complemented
356#1874C2×C6111yescharacteristic, complemented
357#1874C2×C6111yescharacteristic, complemented
358#1836C2×C6111yescharacteristic, complemented
359#1824C2×C6111yescharacteristic, complemented
360#1823C2×C6111yescharacteristic, complemented
361#1802C2×C6111yescharacteristic, complemented
362#1762C2×C6111yescharacteristic, complemented
363C2×C61—42no—
364C2×C61—42no—
365C2×C61—82no—
366C2×C61#242011yescharacteristic
367C2×C61#309211yescharacteristic
368C2×C61#309611yescharacteristic
369C2×C61#330611yescharacteristic
370C2×C61#331411yescharacteristic
371C2×C61#331811yescharacteristic
372C2×C61#332011yescharacteristic
373C2×#121C22×C6111yescharacteristic
374C2×#121C22×C6111yescharacteristic
375C2×C4×D4—21no—
376C2×C4×D4C22×C6111yescharacteristic
377C2×C4×D4C22×C6111yescharacteristic
378C22×C4⋊C4C22×C6111yescharacteristic
379C22×C4⋊C4C22×C6111yescharacteristic
380C2×#107C22×C6111yescharacteristic
381C2×#106C22×C6111yescharacteristic
382C2×C4⋊C8C22×C6111yescharacteristic
383C2×#102C22×C6111yescharacteristic
384C2×#102C22×C6111yescharacteristic
385C2×#102C22×C6111yescharacteristic
386C2×#102C22×C6111yescharacteristic
387C2×C22⋊C8C22×C6111yescharacteristic
388C2×C22⋊C8C22×C6111yescharacteristic
389C2×C22⋊C8C22×C6111yescharacteristic
390C2×C22⋊C8C22×C6111yescharacteristic
391C2×#97C22×C6111yescharacteristic
392#397—21no—
393#392—21no—
394#389—21no—
395#386—21no—
396#386—21no—
397#385—21no—
398#385—21no—
399#384C22×C6111yescharacteristic
400#382C22×C6111yescharacteristic
401#380C22×C6111yescharacteristic
402#380C22×C6111yescharacteristic
403#380C22×C6111yescharacteristic
404#380C22×C6111yescharacteristic
405C4×C4⋊C4C22×C6111yescharacteristic
406#340C22×C6111yescharacteristic
407#340C22×C6111yescharacteristic
408#340C22×C6111yescharacteristic
409#340C22×C6111yescharacteristic
410#340C22×C6111yescharacteristic
411#340C22×C6111yescharacteristic
412#340C22×C6111yescharacteristic
413#340C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416C61#2497711yescharacteristic, direct product factor, Sylow
417C22×D4—21no—
418C22×D4—21no—
419C22×D4D4×C6111yescharacteristic
420C22×D4C23×C6111yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4C23×C6111yescharacteristic
425C23×C4C23×C6111yescharacteristic
426C22×C8C23×C6111yescharacteristic
427C22×C8C23×C6111yescharacteristic
428C22×C8C23×C6111yescharacteristic
429C22×C8C23×C6111yescharacteristic
430#121—22no—
431#121—22no—
432#121—41no—
433#121—41no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—44no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4D4×C6111yescharacteristic
448C2×C4⋊C4C23×C6111yescharacteristic
449C2×C4⋊C4C23×C6111yescharacteristic
450C2×C4⋊C4C23×C6111yescharacteristic
451C2×C4⋊C4C23×C6111yescharacteristic
452C2×C4⋊C4C23×C6111yescharacteristic
453C2×C4⋊C4C23×C6111yescharacteristic
454C2×C4⋊C4C23×C6111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C6111yescharacteristic
463C2×C22⋊C4D4×C6111yescharacteristic
464C2×C42—21no—
465C2×C42C23×C6111yescharacteristic
466#107—41no—
467#106—41no—
468C4⋊C8—22no—
469#102—22no—
470#102—22no—
471#102—41no—
472#102—41no—
473C22⋊C8—41no—
474C22⋊C8—41no—
475C22⋊C8—41no—
476C22⋊C8—41no—
477#97—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485C24—21no—
486C24C2×D4×C6111yescharacteristic
487C24C2×D4×C6111yescharacteristic
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4#41×C6112yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4C2×D4×C6111yescharacteristic
532C22×C4C2×D4×C6111yescharacteristic
533C22×C4C2×D4×C6111yescharacteristic
534C22×C4C2×D4×C6111yescharacteristic
535C22×C4C24×C6111yescharacteristic
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4#41×C6112yes—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C42—42no—
577C42#41×C6112yes—
578C42#41×C6112yes—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23AGL(1,ℤ/8)×C6112yes—
599C23#137×C6112yes—
600C23C22×D4×C6111yescharacteristic
601D4—28no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
607D4—84no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4#123×C6112yes—
651C2×C4#123×C6112yes—
652C2×C4C2×#41×C6111yescharacteristic
653C2×C4C2×#41×C6111yescharacteristic
654C2×C4C2×#41×C6111yescharacteristic
655C2×C4C2×#41×C6111yescharacteristic
656C2×C4H(5,𝔽2)×C6111yescharacteristic
657C2×C4H(5,𝔽2)×C6111yescharacteristic
658C8—41no—
659C8—41no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C2×#123×C6111yescharacteristic
684C22C61×#54611yescharacteristic
685C22C61×#54611yescharacteristic
686C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
687C22C2×#137×C6111yescharacteristic
688C22C61×#57611yescharacteristic
689C22C61×#57711yescharacteristic
690C4—22no—
691C4—22no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4C61×#52911yescharacteristic
702C4C61×#54011yescharacteristic
703C4C61×#55311yescharacteristic
704C4C61×#55511yescharacteristic
705C2—42no—
706C2—42no—
707C2—82no—
708C2C61×#242011yescharacteristic
709C2C61×#309211yescharacteristic
710C2C61×#309611yescharacteristic
711C2C61×#330611yescharacteristic
712C2C61×#331411yescharacteristic
713C2C61×#331811yescharacteristic
714C2C61×#332011yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2535C2
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
2. D4×C4⋊C4×C61C2semidirect
3. C61×#2077C2semidirect
4. C61×#2076C2semidirect
5. C61×#2034C2semidirect
6. C61×#2033C2semidirect
7. C61×#1955C2semidirect
8. C61×#1949C2semidirect
9. C61×#1874C2semidirect
10. C61×#1874C2semidirect
11. C61×#1836C2semidirect
12. C61×#1824C2semidirect
13. C61×#1823C2semidirect
14. C61×#1802C2semidirect
15. C61×#1762C2semidirect
304. #24977C61direct (N × H)
349. D4×C4⋊C4C2×C61semidirect
350. #2077C2×C61semidirect
351. #2076C2×C61semidirect
352. #2034C2×C61semidirect
353. #2033C2×C61semidirect
354. #1955C2×C61semidirect
355. #1949C2×C61semidirect
356. #1874C2×C61semidirect
357. #1874C2×C61semidirect
358. #1836C2×C61semidirect
359. #1824C2×C61semidirect
360. #1823C2×C61semidirect
361. #1802C2×C61semidirect
362. #1762C2×C61semidirect
416. C61#24977direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#25352
D4×C4⋊C4×C612
C61×#20772
C61×#20762
C61×#20342
C61×#20332
C61×#19552
C61×#19492
C61×#18742
C61×#18362
C61×#18242
C61×#18232
C61×#18022
C61×#17622
#2497761