Finite Group Databasebeta

← C61×#26198 #29529631

Subgroups — C61×#26198 #29529631

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2416C211yesmaximal, characteristic
2D4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
3C61×#2099C211yesmaximal, characteristic, complemented
4C61×#2075C211yesmaximal, characteristic, complemented
5C61×#2071C211yesmaximal, characteristic, complemented
6C61×#2033C211yesmaximal, characteristic, complemented
7C61×#1925C211yesmaximal, characteristic, complemented
8C61×#1918C211yesmaximal, characteristic, complemented
9C61×#1893C211yesmaximal, characteristic, complemented
10C61×#1874C211yesmaximal, characteristic, complemented
11C61×#1874C211yesmaximal, characteristic, complemented
12C61×#1869C211yesmaximal, characteristic, complemented
13C61×#1852C211yesmaximal, characteristic, complemented
14C61×#1823C211yesmaximal, characteristic, complemented
15C2×C61×#340C211yesmaximal, characteristic, complemented
16C23×C8×C61C2211yescharacteristic
17C2×#121×C61—21no—
18C2×#121×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×C4×D4×C61—21no—
21C2×C4×D4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C2×#107×C61C2211yescharacteristic
27C2×#102×C61C2211yescharacteristic
28C2×#102×C61C2211yescharacteristic
29C2×#102×C61C2211yescharacteristic
30C2×#102×C61C2211yescharacteristic
31C2×C22⋊C8×C61C2211yescharacteristic
32C2×C22⋊C8×C61C2211yescharacteristic
33C2×C22⋊C8×C61C2211yescharacteristic
34C61×#396—21no—
35C61×#394—21no—
36C61×#390C2211yescharacteristic
37C61×#389—21no—
38C61×#389C2211yescharacteristic
39C61×#386—21no—
40C61×#385—21no—
41C61×#385—21no—
42C61×#384C2211yescharacteristic
43C61×#380C2211yescharacteristic
44C61×#380C2211yescharacteristic
45C61×#380C2211yescharacteristic
46C4×C4⋊C4×C61C2211yescharacteristic
47C61×#340C2211yescharacteristic
48C61×#340C2211yescharacteristic
49C61×#340C2211yescharacteristic
50C61×#340C2211yescharacteristic
51C61×#340C2211yescharacteristic
52C61×#340C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
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×C61—22no—
69C22×C8×C61—41no—
70C22×C8×C61—41no—
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75#121×C61—22no—
76#121×C61—22no—
77#121×C61—22no—
78#121×C61—41no—
79#121×C61—44no—
80C4×D4×C61—22no—
81C4×D4×C61—22no—
82C4×D4×C61—44no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—41no—
93C2×C4⋊C4×C61—41no—
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×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C42×C61—21no—
113C2×C42×C61C2311yescharacteristic
114#107×C61—22no—
115#107×C61—41no—
116#102×C61—22no—
117#102×C61—41no—
118#102×C61—41no—
119#102×C61—41no—
120C22⋊C8×C61—22no—
121C22⋊C8×C61—41no—
122C22⋊C8×C61—41no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127#95×C61—21no—
128C24×C61—21no—
129C24×C61C2×D411yescharacteristic
130C24×C61C2×D411yescharacteristic
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—21no—
139C2×D4×C61—42no—
140C2×D4×C61—42no—
141C2×D4×C61—42no—
142C2×D4×C61—42no—
143C2×D4×C61—42no—
144C2×D4×C61—81no—
145C2×D4×C61D814yes—
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—42no—
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×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61#4112yes—
177C22×C4×C61#4112yes—
178C22×C4×C61C2411yescharacteristic
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—
190C2×C8×C61—21no—
191C2×C8×C61—44no—
192C4⋊C4×C61—22no—
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—21no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—81no—
211C4⋊C4×C61#4112yes—
212C4⋊C4×C61#4112yes—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—81no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—42no—
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—21no—
234C23×C61—21no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61#12312yes—
243C23×C61C2×D812yes—
244C23×C61C2×D812yes—
245C23×C61#13712yes—
246C23×C61C22×D411yescharacteristic
247D4×C61—28no—
248D4×C61—41no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—41no—
252D4×C61—84no—
253D4×C61—84no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
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—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—84no—
294C2×C4×C61—84no—
295C2×C4×C61—84no—
296C2×C4×C61#12312yes—
297C2×C4×C61C2×D812yes—
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C8×C61—41no—
305C8×C61—41no—
306C8×C61—41no—
307C8×C61—41no—
308#26198C6111yesmaximal, characteristic, direct product factor, Sylow
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61#48014yes—
330C22×C61C2×#12311yescharacteristic
331C22×C61#54611yescharacteristic
332C22×C61#54611yescharacteristic
333C22×C61C22×D811yescharacteristic
334C22×C61C2×#13711yescharacteristic
335C22×C61#57711yescharacteristic
336C22×C61#57711yescharacteristic
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61—81no—
348C4×C61#52911yescharacteristic
349C4×C61#53811yescharacteristic
350C4×C61#55311yescharacteristic
351C4×C61#55311yescharacteristic
352#2416C2×C6111yescharacteristic
353D4×C4⋊C4C2×C6111yescharacteristic, complemented
354#2099C2×C6111yescharacteristic, complemented
355#2075C2×C6111yescharacteristic, complemented
356#2071C2×C6111yescharacteristic, complemented
357#2033C2×C6111yescharacteristic, complemented
358#1925C2×C6111yescharacteristic, complemented
359#1918C2×C6111yescharacteristic, complemented
360#1893C2×C6111yescharacteristic, complemented
361#1874C2×C6111yescharacteristic, complemented
362#1874C2×C6111yescharacteristic, complemented
363#1869C2×C6111yescharacteristic, complemented
364#1852C2×C6111yescharacteristic, complemented
365#1823C2×C6111yescharacteristic, complemented
366C2×#340C2×C6111yescharacteristic, complemented
367C2×C61—24no—
368C2×C61—42no—
369C2×C61—161no—
370C2×C61#244411yescharacteristic
371C2×C61C2×#48011yescharacteristic
372C2×C61#309911yescharacteristic
373C2×C61#329411yescharacteristic
374C2×C61#329411yescharacteristic
375C2×C61#331611yescharacteristic
376C2×C61#332011yescharacteristic
377C23×C8C22×C6111yescharacteristic
378C2×#121—21no—
379C2×#121C22×C6111yescharacteristic
380C2×#121C22×C6111yescharacteristic
381C2×C4×D4—21no—
382C2×C4×D4C22×C6111yescharacteristic
383C22×C4⋊C4C22×C6111yescharacteristic
384C22×C4⋊C4C22×C6111yescharacteristic
385C22×C4⋊C4C22×C6111yescharacteristic
386C2×#107C22×C6111yescharacteristic
387C2×#107C22×C6111yescharacteristic
388C2×#102C22×C6111yescharacteristic
389C2×#102C22×C6111yescharacteristic
390C2×#102C22×C6111yescharacteristic
391C2×#102C22×C6111yescharacteristic
392C2×C22⋊C8C22×C6111yescharacteristic
393C2×C22⋊C8C22×C6111yescharacteristic
394C2×C22⋊C8C22×C6111yescharacteristic
395#396—21no—
396#394—21no—
397#390C22×C6111yescharacteristic
398#389—21no—
399#389C22×C6111yescharacteristic
400#386—21no—
401#385—21no—
402#385—21no—
403#384C22×C6111yescharacteristic
404#380C22×C6111yescharacteristic
405#380C22×C6111yescharacteristic
406#380C22×C6111yescharacteristic
407C4×C4⋊C4C22×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
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#336C22×C6111yescharacteristic
419#336C22×C6111yescharacteristic
420C61#2619811yescharacteristic, direct product factor, Sylow
421C22×D4—21no—
422C22×D4—21no—
423C22×D4D4×C6111yescharacteristic
424C22×D4C23×C6111yescharacteristic
425C23×C4—21no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4C23×C6111yescharacteristic
429C23×C4C23×C6111yescharacteristic
430C22×C8—22no—
431C22×C8—41no—
432C22×C8—41no—
433C22×C8C23×C6111yescharacteristic
434C22×C8C23×C6111yescharacteristic
435C22×C8C23×C6111yescharacteristic
436C22×C8C23×C6111yescharacteristic
437#121—22no—
438#121—22no—
439#121—22no—
440#121—41no—
441#121—44no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—44no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4D4×C6111yescharacteristic
458C2×C4⋊C4C23×C6111yescharacteristic
459C2×C4⋊C4C23×C6111yescharacteristic
460C2×C4⋊C4C23×C6111yescharacteristic
461C2×C4⋊C4C23×C6111yescharacteristic
462C2×C4⋊C4C23×C6111yescharacteristic
463C2×C4⋊C4C23×C6111yescharacteristic
464C2×C4⋊C4C23×C6111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4D4×C6111yescharacteristic
473C2×C22⋊C4D4×C6111yescharacteristic
474C2×C42—21no—
475C2×C42C23×C6111yescharacteristic
476#107—22no—
477#107—41no—
478#102—22no—
479#102—41no—
480#102—41no—
481#102—41no—
482C22⋊C8—22no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490C24—21no—
491C24C2×D4×C6111yescharacteristic
492C24C2×D4×C6111yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—81no—
507C2×D4D8×C6114yes—
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—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C6111yescharacteristic
535C22×C4C2×D4×C6111yescharacteristic
536C22×C4C2×D4×C6111yescharacteristic
537C22×C4C2×D4×C6111yescharacteristic
538C22×C4#41×C6112yes—
539C22×C4#41×C6112yes—
540C22×C4C24×C6111yescharacteristic
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—44no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4#41×C6112yes—
574C4⋊C4#41×C6112yes—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—42no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23#123×C6112yes—
605C23C2×D8×C6112yes—
606C23C2×D8×C6112yes—
607C23#137×C6112yes—
608C23C22×D4×C6111yescharacteristic
609D4—28no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615D4—84no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
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—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4—84no—
658C2×C4#123×C6112yes—
659C2×C4C2×D8×C6112yes—
660C2×C4C2×#41×C6111yescharacteristic
661C2×C4C2×#41×C6111yescharacteristic
662C2×C4C2×#41×C6111yescharacteristic
663C2×C4C2×#41×C6111yescharacteristic
664C2×C4H(5,𝔽2)×C6111yescharacteristic
665C2×C4H(5,𝔽2)×C6111yescharacteristic
666C8—41no—
667C8—41no—
668C8—41no—
669C8—41no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22C61×#48014yes—
691C22C2×#123×C6111yescharacteristic
692C22C61×#54611yescharacteristic
693C22C61×#54611yescharacteristic
694C22C22×D8×C6111yescharacteristic
695C22C2×#137×C6111yescharacteristic
696C22C61×#57711yescharacteristic
697C22C61×#57711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4C61×#52911yescharacteristic
710C4C61×#53811yescharacteristic
711C4C61×#55311yescharacteristic
712C4C61×#55311yescharacteristic
713C2—24no—
714C2—42no—
715C2—161no—
716C2C61×#244411yescharacteristic
717C2C2×C61×#48011yescharacteristic
718C2C61×#309911yescharacteristic
719C2C61×#329411yescharacteristic
720C2C61×#329411yescharacteristic
721C2C61×#331611yescharacteristic
722C2C61×#332011yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2416C2
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×#2099C2semidirect
4. C61×#2075C2semidirect
5. C61×#2071C2semidirect
6. C61×#2033C2semidirect
7. C61×#1925C2semidirect
8. C61×#1918C2semidirect
9. C61×#1893C2semidirect
10. C61×#1874C2semidirect
11. C61×#1874C2semidirect
12. C61×#1869C2semidirect
13. C61×#1852C2semidirect
14. C61×#1823C2semidirect
15. C2×C61×#340C2semidirect
308. #26198C61direct (N × H)
353. D4×C4⋊C4C2×C61semidirect
354. #2099C2×C61semidirect
355. #2075C2×C61semidirect
356. #2071C2×C61semidirect
357. #2033C2×C61semidirect
358. #1925C2×C61semidirect
359. #1918C2×C61semidirect
360. #1893C2×C61semidirect
361. #1874C2×C61semidirect
362. #1874C2×C61semidirect
363. #1869C2×C61semidirect
364. #1852C2×C61semidirect
365. #1823C2×C61semidirect
366. C2×#340C2×C61semidirect
420. C61#26198direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#24162
D4×C4⋊C4×C612
C61×#20992
C61×#20752
C61×#20712
C61×#20332
C61×#19252
C61×#19182
C61×#18932
C61×#18742
C61×#18692
C61×#18522
C61×#18232
C2×C61×#3402
#2619861