Finite Group Databasebeta

← C61×#24563 #29527996

Subgroups — C61×#24563 #29527996

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#485C211yesmaximal, characteristic, complemented
2C2×C61×#408C211yesmaximal, characteristic
3C61×#2616C211yesmaximal, characteristic
4C61×#2311C211yesmaximal, characteristic
5C61×#2077C211yesmaximal, characteristic, complemented
6C61×#2075C211yesmaximal, characteristic, complemented
7C61×#2036C211yesmaximal, characteristic, complemented
8C61×#2036C211yesmaximal, characteristic, complemented
9C61×#1894C211yesmaximal, characteristic, complemented
10C61×#1892C211yesmaximal, characteristic, complemented
11C61×#1872C211yesmaximal, characteristic, complemented
12C61×#1852C211yesmaximal, characteristic, complemented
13C61×#1825C211yesmaximal, characteristic, complemented
14C61×#1809C211yesmaximal, characteristic, complemented
15C61×#1808C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C23×C8×C61C2211yescharacteristic
19C2×C22⋊Q8×C61C2211yescharacteristic
20C2×C22⋊Q8×C61C2211yescharacteristic
21C2×C22⋊Q8×C61C2211yescharacteristic
22C2×#117×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C61×#485—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#107×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C61×#408—24no—
34C2×C22⋊C8×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C61×#395—21no—
39C61×#394—21no—
40C61×#394—21no—
41C61×#394—21no—
42C61×#391—21no—
43C61×#390—21no—
44C61×#386—21no—
45C61×#386—21no—
46C61×#380C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#380C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C2×#41×C61—22no—
62C2×#41×C61—22no—
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—41no—
66C2×#41×C61—41no—
67C22×Q8×C61D411yescharacteristic
68C22×Q8×C61C2311yescharacteristic
69C22×D4×C61D411yescharacteristic
70C22×D4×C61D411yescharacteristic
71C22×D4×C61D411yescharacteristic
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C23×C4×C61C2311yescharacteristic
76C2×M16×C61—22no—
77C2×M16×C61—22no—
78C2×M16×C61—41no—
79C22×C8×C61—22no—
80C22×C8×C61—22no—
81C22×C8×C61—41no—
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84C22×C8×C61C2311yescharacteristic
85C22×C8×C61C2311yescharacteristic
86C22⋊Q8×C61—22no—
87C22⋊Q8×C61—22no—
88C22⋊Q8×C61—22no—
89C22⋊Q8×C61—22no—
90C22⋊Q8×C61—41no—
91C22⋊Q8×C61—41no—
92#117×C61—22no—
93#117×C61—22no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—41no—
99C2×C4⋊C4×C61—41no—
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C42×C61—21no—
119#107×C61—22no—
120#107×C61—41no—
121#107×C61—41no—
122#106×C61—22no—
123#103×C61—22no—
124#103×C61—22no—
125#103×C61—41no—
126#103×C61—41no—
127C22⋊C8×C61—22no—
128C22⋊C8×C61—22no—
129C22⋊C8×C61—22no—
130C22⋊C8×C61D414yes—
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138C24×C61C2×D411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141#41×C61—44no—
142#41×C61—44no—
143#41×C61—44no—
144#41×C61—44no—
145C2×Q8×C61—22no—
146C2×Q8×C61—22no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—41no—
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—22no—
160C2×D4×C61—41no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
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—42no—
186C22×C4×C61—81no—
187C22×C4×C61—81no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D412yes—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61#4112yes—
193C22×C4×C61#4112yes—
194C22×C4×C61#4112yes—
195C22×C4×C61C2411yescharacteristic
196M16×C61—44no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—44no—
208C2×C8×C61C2×D412yes—
209C2×C8×C61C2×D412yes—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
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×C61—42no—
226C4⋊C4×C61—42no—
227C4⋊C4×C61—42no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—42no—
232C22⋊C4×C61—81no—
233C22⋊C4×C61—81no—
234C22⋊C4×C61—81no—
235C22⋊C4×C61—81no—
236C22⋊C4×C61—81no—
237C22⋊C4×C61—81no—
238C22⋊C4×C61—81no—
239C42×C61—42no—
240C23×C61—21no—
241C23×C61—21no—
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—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61#12112yes—
260C23×C61#12312yes—
261C23×C61C22×D411yescharacteristic
262Q8×C61—44no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61—41no—
266Q8×C61—41no—
267D4×C61—44no—
268D4×C61—44no—
269D4×C61—44no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
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—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
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—84no—
314C2×C4×C61#12112yes—
315C2×C4×C61#12312yes—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C8×C61—22no—
323C8×C61—22no—
324C8×C61—41no—
325C8×C61—41no—
326#24563C6111yesmaximal, characteristic, direct product factor, Sylow
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
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×C61C2×#12111yescharacteristic
349C22×C61C2×#12311yescharacteristic
350C22×C61#53411yescharacteristic
351C22×C61#57611yescharacteristic
352C22×C61#57711yescharacteristic
353C22×C61#57811yescharacteristic
354C22×C61#57811yescharacteristic
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—41no—
358C4×C61—81no—
359C4×C61—81no—
360C4×C61—81no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61—81no—
366C4×C61#54611yescharacteristic
367C4×C61#54611yescharacteristic
368C4×C61#55111yescharacteristic
369C4×C61#55111yescharacteristic
370C2×#485C2×C6111yescharacteristic, complemented
371C2×#408C2×C6111yescharacteristic
372#2616C2×C6111yescharacteristic
373#2311C2×C6111yescharacteristic
374#2077C2×C6111yescharacteristic, complemented
375#2075C2×C6111yescharacteristic, complemented
376#2036C2×C6111yescharacteristic, complemented
377#2036C2×C6111yescharacteristic, complemented
378#1894C2×C6111yescharacteristic, complemented
379#1892C2×C6111yescharacteristic, complemented
380#1872C2×C6111yescharacteristic, complemented
381#1852C2×C6111yescharacteristic, complemented
382#1825C2×C6111yescharacteristic, complemented
383#1809C2×C6111yescharacteristic, complemented
384#1808C2×C6111yescharacteristic, complemented
385C2×C61—42no—
386C2×C61—42no—
387C2×C61—81no—
388C2×C61#241211yescharacteristic
389C2×C61#306111yescharacteristic
390C2×C61#306311yescharacteristic
391C2×C61#309711yescharacteristic
392C2×C61#309811yescharacteristic
393C2×C61#319811yescharacteristic
394C2×C61#320211yescharacteristic
395C22×#41C22×C6111yescharacteristic
396C22×M16C22×C6111yescharacteristic
397C23×C8C22×C6111yescharacteristic
398C2×C22⋊Q8C22×C6111yescharacteristic
399C2×C22⋊Q8C22×C6111yescharacteristic
400C2×C22⋊Q8C22×C6111yescharacteristic
401C2×#117C22×C6111yescharacteristic
402C22×C4⋊C4C22×C6111yescharacteristic
403#485—24no—
404C2×#107C22×C6111yescharacteristic
405C2×#107C22×C6111yescharacteristic
406C2×#107C22×C6111yescharacteristic
407C2×#106C22×C6111yescharacteristic
408C2×#103C22×C6111yescharacteristic
409C2×#103C22×C6111yescharacteristic
410C2×#103C22×C6111yescharacteristic
411C2×#103C22×C6111yescharacteristic
412#408—24no—
413C2×C22⋊C8C22×C6111yescharacteristic
414C2×C22⋊C8C22×C6111yescharacteristic
415C2×C22⋊C8C22×C6111yescharacteristic
416C2×C22⋊C8C22×C6111yescharacteristic
417#395—21no—
418#394—21no—
419#394—21no—
420#394—21no—
421#391—21no—
422#390—21no—
423#386—21no—
424#386—21no—
425#380C22×C6111yescharacteristic
426#380C22×C6111yescharacteristic
427#380C22×C6111yescharacteristic
428#380C22×C6111yescharacteristic
429#380C22×C6111yescharacteristic
430#380C22×C6111yescharacteristic
431#380C22×C6111yescharacteristic
432#340C22×C6111yescharacteristic
433#340C22×C6111yescharacteristic
434#340C22×C6111yescharacteristic
435#340C22×C6111yescharacteristic
436#340C22×C6111yescharacteristic
437#340C22×C6111yescharacteristic
438#340C22×C6111yescharacteristic
439#340C22×C6111yescharacteristic
440C61#2456311yescharacteristic, direct product factor, Sylow
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—41no—
446C2×#41—41no—
447C22×Q8D4×C6111yescharacteristic
448C22×Q8C23×C6111yescharacteristic
449C22×D4D4×C6111yescharacteristic
450C22×D4D4×C6111yescharacteristic
451C22×D4D4×C6111yescharacteristic
452C23×C4—21no—
453C23×C4C23×C6111yescharacteristic
454C23×C4C23×C6111yescharacteristic
455C23×C4C23×C6111yescharacteristic
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—41no—
459C22×C8—22no—
460C22×C8—22no—
461C22×C8—41no—
462C22×C8C23×C6111yescharacteristic
463C22×C8C23×C6111yescharacteristic
464C22×C8C23×C6111yescharacteristic
465C22×C8C23×C6111yescharacteristic
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—41no—
471C22⋊Q8—41no—
472#117—22no—
473#117—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4C23×C6111yescharacteristic
481C2×C4⋊C4C23×C6111yescharacteristic
482C2×C4⋊C4C23×C6111yescharacteristic
483C2×C4⋊C4C23×C6111yescharacteristic
484C2×C4⋊C4C23×C6111yescharacteristic
485C2×C4⋊C4C23×C6111yescharacteristic
486C2×C4⋊C4C23×C6111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C42—21no—
499#107—22no—
500#107—41no—
501#107—41no—
502#106—22no—
503#103—22no—
504#103—22no—
505#103—41no—
506#103—41no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8D4×C6114yes—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518C24C2×D4×C6111yescharacteristic
519C24C2×D4×C6111yescharacteristic
520C24C2×D4×C6111yescharacteristic
521#41—44no—
522#41—44no—
523#41—44no—
524#41—44no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—41no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4C2×D4×C6111yescharacteristic
569C22×C4C2×D4×C6111yescharacteristic
570C22×C4C2×D4×C6112yes—
571C22×C4C2×D4×C6111yescharacteristic
572C22×C4#41×C6112yes—
573C22×C4#41×C6112yes—
574C22×C4#41×C6112yes—
575C22×C4C24×C6111yescharacteristic
576M16—44no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8C2×D4×C6112yes—
589C2×C8C2×D4×C6112yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C22⋊C4—81no—
619C42—42no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23#121×C6112yes—
640C23#123×C6112yes—
641C23C22×D4×C6111yescharacteristic
642Q8—44no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647D4—44no—
648D4—44no—
649D4—44no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—84no—
694C2×C4#121×C6112yes—
695C2×C4#123×C6112yes—
696C2×C4C22×D4×C6111yescharacteristic
697C2×C4C2×#41×C6111yescharacteristic
698C2×C4C2×#41×C6111yescharacteristic
699C2×C4C2×#41×C6111yescharacteristic
700C2×C4H(5,𝔽2)×C6111yescharacteristic
701C2×C4H(5,𝔽2)×C6111yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×#121×C6111yescharacteristic
728C22C2×#123×C6111yescharacteristic
729C22C61×#53411yescharacteristic
730C22C61×#57611yescharacteristic
731C22C61×#57711yescharacteristic
732C22C61×#57811yescharacteristic
733C22C61×#57811yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C61×#54611yescharacteristic
746C4C61×#54611yescharacteristic
747C4C61×#55111yescharacteristic
748C4C61×#55111yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2C61×#241211yescharacteristic
753C2C61×#306111yescharacteristic
754C2C61×#306311yescharacteristic
755C2C61×#309711yescharacteristic
756C2C61×#309811yescharacteristic
757C2C61×#319811yescharacteristic
758C2C61×#320211yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC22×#41×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#485C2semidirect
5. C61×#2077C2semidirect
6. C61×#2075C2semidirect
7. C61×#2036C2semidirect
8. C61×#2036C2semidirect
9. C61×#1894C2semidirect
10. C61×#1892C2semidirect
11. C61×#1872C2semidirect
12. C61×#1852C2semidirect
13. C61×#1825C2semidirect
14. C61×#1809C2semidirect
15. C61×#1808C2semidirect
326. #24563C61direct (N × H)
370. C2×#485C2×C61semidirect
374. #2077C2×C61semidirect
375. #2075C2×C61semidirect
376. #2036C2×C61semidirect
377. #2036C2×C61semidirect
378. #1894C2×C61semidirect
379. #1892C2×C61semidirect
380. #1872C2×C61semidirect
381. #1852C2×C61semidirect
382. #1825C2×C61semidirect
383. #1809C2×C61semidirect
384. #1808C2×C61semidirect
440. C61#24563direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4852
C2×C61×#4082
C61×#26162
C61×#23112
C61×#20772
C61×#20752
C61×#20362
C61×#18942
C61×#18922
C61×#18722
C61×#18522
C61×#18252
C61×#18092
C61×#18082
#2456361