Finite Group Databasebeta

← C61×#24484 #29527917

Subgroups — C61×#24484 #29527917

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#482C211yesmaximal, characteristic, complemented
2C2×C61×#416C211yesmaximal, characteristic, complemented
3C61×#2431C211yesmaximal, characteristic
4C61×#2347C211yesmaximal, characteristic, complemented
5C61×#2066C211yesmaximal, characteristic, complemented
6C61×#2065C211yesmaximal, characteristic, complemented
7C61×#2042C211yesmaximal, characteristic, complemented
8C61×#2041C211yesmaximal, characteristic, complemented
9C61×#1983C211yesmaximal, characteristic, complemented
10C61×#1982C211yesmaximal, characteristic, complemented
11C61×#1928C211yesmaximal, characteristic, complemented
12C61×#1925C211yesmaximal, characteristic, complemented
13C61×#1893C211yesmaximal, characteristic, complemented
14C61×#1850C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×#127×C61C2211yescharacteristic
19C2×#124×C61C2211yescharacteristic
20C2×#121×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C61×#482—24no—
23C2×#107×C61C2211yescharacteristic
24C2×#106×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#416—24no—
28C2×#103×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×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
41C61×#392—21no—
42C61×#392—21no—
43C61×#391C2211yescharacteristic
44C61×#390C2211yescharacteristic
45C61×#389C2211yescharacteristic
46C61×#389C2211yescharacteristic
47C61×#388—21no—
48C61×#388—21no—
49C61×#386—21no—
50C61×#386—21no—
51C61×#383—21no—
52C61×#380C2211yescharacteristic
53C4×C4⋊C4×C61—21no—
54C4×C4⋊C4×C61C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
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×C61C2311yescharacteristic
68C22×D4×C61—21no—
69C22×D4×C61—21no—
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61C2311yescharacteristic
73C22×D4×C61C2311yescharacteristic
74C23×C4×C61—21no—
75C23×C4×C61C2311yescharacteristic
76C22×C8×C61—22no—
77C22×C8×C61—41no—
78C22×C8×C61—41no—
79C22×C8×C61C2311yescharacteristic
80C22×C8×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83#127×C61—22no—
84#127×C61—41no—
85#124×C61—22no—
86#124×C61—41no—
87#121×C61—22no—
88#121×C61—22no—
89#117×C61—22no—
90#117×C61D414yescomplemented
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
105C2×C22⋊C4×C61D411yescharacteristic
106C2×C22⋊C4×C61D411yescharacteristic
107C2×C42×C61—21no—
108C2×C42×C61—21no—
109C2×C42×C61—21no—
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112#107×C61—22no—
113#106×C61—22no—
114C4⋊C8×C61—41no—
115C4⋊C8×C61—41no—
116#103×C61—22no—
117#103×C61—22no—
118#103×C61—22no—
119#103×C61—41no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—22no—
123#102×C61—22no—
124#102×C61—22no—
125#102×C61—41no—
126#102×C61—41no—
127#102×C61—41no—
128C22⋊C8×C61—22no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61D411yescharacteristic
137#95×C61D411yescharacteristic
138C24×C61—21no—
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141#41×C61—28no—
142#41×C61—44no—
143#41×C61—44no—
144#41×C61—44no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61#4112yes—
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—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
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#4112yes—
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—42no—
187C22×C4×C61—42no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61#4112yes—
195C22×C4×C61C2411yescharacteristic
196C2×C8×C61—21no—
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—21no—
208C2×C8×C61—44no—
209C4⋊C4×C61—21no—
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—42no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61C2×D412yes—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—24no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—41no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—42no—
227C22⋊C4×C61—81no—
228C22⋊C4×C61—81no—
229C22⋊C4×C61—81no—
230C42×C61—24no—
231C42×C61—21no—
232C42×C61—21no—
233C42×C61—21no—
234C42×C61—21no—
235C42×C61—81no—
236C42×C61—81no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—22no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61#12112yes—
258C23×C61C22×D411yescharacteristic
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—41no—
262Q8×C61—41no—
263D4×C61—22no—
264D4×C61—22no—
265D4×C61—48no—
266D4×C61—41no—
267D4×C61—41no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—84no—
273D4×C61—84no—
274D4×C61—84no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—22no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—48no—
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#12112yes—
312C2×C4×C61#13512yes—
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C8×C61—41no—
320C8×C61—41no—
321C8×C61—41no—
322C8×C61—41no—
323#24484C6111yesmaximal, characteristic, direct product factor, Sylow
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61C2×#12111yescharacteristic
346C22×C61#54611yescharacteristic
347C22×C61#54611yescharacteristic
348C22×C61C2×#13511yescharacteristic
349C22×C61#57511yescharacteristic
350C22×C61#57611yescharacteristic
351C22×C61#57711yescharacteristic
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—81no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61#52511yescharacteristic
364C4×C61#53511yescharacteristic
365C4×C61#55111yescharacteristic
366C4×C61#55111yescharacteristic
367C2×#482C2×C6111yescharacteristic, complemented
368C2×#416C2×C6111yescharacteristic, complemented
369#2431C2×C6111yescharacteristic
370#2347C2×C6111yescharacteristic, complemented
371#2066C2×C6111yescharacteristic, complemented
372#2065C2×C6111yescharacteristic, complemented
373#2042C2×C6111yescharacteristic, complemented
374#2041C2×C6111yescharacteristic, complemented
375#1983C2×C6111yescharacteristic, complemented
376#1982C2×C6111yescharacteristic, complemented
377#1928C2×C6111yescharacteristic, complemented
378#1925C2×C6111yescharacteristic, complemented
379#1893C2×C6111yescharacteristic, complemented
380#1850C2×C6111yescharacteristic, complemented
381#1788C2×C6111yescharacteristic, complemented
382C2×C61—42no—
383C2×C61—82no—
384C2×C61—161no—
385C2×C61#241111yescharacteristic
386C2×C61#303511yescharacteristic
387C2×C61#304511yescharacteristic
388C2×C61#329711yescharacteristic
389C2×C61#330411yescharacteristic
390C2×C61#330911yescharacteristic
391C2×C61#331111yescharacteristic
392C22×#41C22×C6111yescharacteristic
393C23×C8C22×C6111yescharacteristic
394C2×#127C22×C6111yescharacteristic
395C2×#124C22×C6111yescharacteristic
396C2×#121C22×C6111yescharacteristic
397C2×#117C22×C6111yescharacteristic
398#482—24no—
399C2×#107C22×C6111yescharacteristic
400C2×#106C22×C6111yescharacteristic
401C2×C4⋊C8C22×C6111yescharacteristic
402C2×C4⋊C8C22×C6111yescharacteristic
403#416—24no—
404C2×#103C22×C6111yescharacteristic
405C2×#103C22×C6111yescharacteristic
406C2×#103C22×C6111yescharacteristic
407C2×#103C22×C6111yescharacteristic
408C2×#102C22×C6111yescharacteristic
409C2×#102C22×C6111yescharacteristic
410C2×#102C22×C6111yescharacteristic
411C2×#102C22×C6111yescharacteristic
412C2×#102C22×C6111yescharacteristic
413C2×#102C22×C6111yescharacteristic
414C2×#102C22×C6111yescharacteristic
415C2×#102C22×C6111yescharacteristic
416C2×C22⋊C8C22×C6111yescharacteristic
417#392—21no—
418#392—21no—
419#391C22×C6111yescharacteristic
420#390C22×C6111yescharacteristic
421#389C22×C6111yescharacteristic
422#389C22×C6111yescharacteristic
423#388—21no—
424#388—21no—
425#386—21no—
426#386—21no—
427#383—21no—
428#380C22×C6111yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4C22×C6111yescharacteristic
431C4×C4⋊C4C22×C6111yescharacteristic
432C4×C22⋊C4C22×C6111yescharacteristic
433#340C22×C6111yescharacteristic
434#340C22×C6111yescharacteristic
435#336C22×C6111yescharacteristic
436#336C22×C6111yescharacteristic
437C61#2448411yescharacteristic, direct product factor, Sylow
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—41no—
443C2×#41—41no—
444C22×Q8C23×C6111yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C6111yescharacteristic
450C22×D4C23×C6111yescharacteristic
451C23×C4—21no—
452C23×C4C23×C6111yescharacteristic
453C22×C8—22no—
454C22×C8—41no—
455C22×C8—41no—
456C22×C8C23×C6111yescharacteristic
457C22×C8C23×C6111yescharacteristic
458C22×C8C23×C6111yescharacteristic
459C22×C8C23×C6111yescharacteristic
460#127—22no—
461#127—41no—
462#124—22no—
463#124—41no—
464#121—22no—
465#121—22no—
466#117—22no—
467#117D4×C6114yescomplemented
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4C23×C6111yescharacteristic
471C2×C4⋊C4C23×C6111yescharacteristic
472C2×C4⋊C4C23×C6111yescharacteristic
473C2×C4⋊C4C23×C6111yescharacteristic
474C2×C4⋊C4C23×C6111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4D4×C6111yescharacteristic
483C2×C22⋊C4D4×C6111yescharacteristic
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42C23×C6111yescharacteristic
488C2×C42C23×C6111yescharacteristic
489#107—22no—
490#106—22no—
491C4⋊C8—41no—
492C4⋊C8—41no—
493#103—22no—
494#103—22no—
495#103—22no—
496#103—41no—
497#102—22no—
498#102—22no—
499#102—22no—
500#102—22no—
501#102—22no—
502#102—41no—
503#102—41no—
504#102—41no—
505C22⋊C8—22no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95D4×C6111yescharacteristic
514#95D4×C6111yescharacteristic
515C24—21no—
516C24—21no—
517C24C2×D4×C6111yescharacteristic
518#41—28no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#41×C6112yes—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4#41×C6112yes—
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—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4C2×D4×C6111yescharacteristic
566C22×C4C2×D4×C6111yescharacteristic
567C22×C4C2×D4×C6111yescharacteristic
568C22×C4C2×D4×C6111yescharacteristic
569C22×C4C2×D4×C6112yes—
570C22×C4C2×D4×C6111yescharacteristic
571C22×C4#41×C6112yes—
572C22×C4C24×C6111yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
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—44no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4C2×D4×C6112yes—
597C4⋊C4C2×D4×C6112yes—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—41no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C42—24no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—81no—
613C42—81no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23#121×C6112yes—
635C23C22×D4×C6111yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—41no—
639Q8—41no—
640D4—22no—
641D4—22no—
642D4—48no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—84no—
650D4—84no—
651D4—84no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—48no—
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#121×C6112yes—
689C2×C4#135×C6112yes—
690C2×C4C22×D4×C6111yescharacteristic
691C2×C4C2×#41×C6111yescharacteristic
692C2×C4C2×#41×C6111yescharacteristic
693C2×C4C2×#41×C6111yescharacteristic
694C2×C4H(5,𝔽2)×C6111yescharacteristic
695C2×C4H(5,𝔽2)×C6111yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×#121×C6111yescharacteristic
722C22C61×#54611yescharacteristic
723C22C61×#54611yescharacteristic
724C22C2×#135×C6111yescharacteristic
725C22C61×#57511yescharacteristic
726C22C61×#57611yescharacteristic
727C22C61×#57711yescharacteristic
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4C61×#52511yescharacteristic
740C4C61×#53511yescharacteristic
741C4C61×#55111yescharacteristic
742C4C61×#55111yescharacteristic
743C2—42no—
744C2—82no—
745C2—161no—
746C2C61×#241111yescharacteristic
747C2C61×#303511yescharacteristic
748C2C61×#304511yescharacteristic
749C2C61×#329711yescharacteristic
750C2C61×#330411yescharacteristic
751C2C61×#330911yescharacteristic
752C2C61×#331111yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2431C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#482C2semidirect
2. C2×C61×#416C2semidirect
4. C61×#2347C2semidirect
5. C61×#2066C2semidirect
6. C61×#2065C2semidirect
7. C61×#2042C2semidirect
8. C61×#2041C2semidirect
9. C61×#1983C2semidirect
10. C61×#1982C2semidirect
11. C61×#1928C2semidirect
12. C61×#1925C2semidirect
13. C61×#1893C2semidirect
14. C61×#1850C2semidirect
15. C61×#1788C2semidirect
90. #117×C61D4semidirect
323. #24484C61direct (N × H)
367. C2×#482C2×C61semidirect
368. C2×#416C2×C61semidirect
370. #2347C2×C61semidirect
371. #2066C2×C61semidirect
372. #2065C2×C61semidirect
373. #2042C2×C61semidirect
374. #2041C2×C61semidirect
375. #1983C2×C61semidirect
376. #1982C2×C61semidirect
377. #1928C2×C61semidirect
378. #1925C2×C61semidirect
379. #1893C2×C61semidirect
380. #1850C2×C61semidirect
381. #1788C2×C61semidirect
437. C61#24484direct (N × H)
467. #117D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4822
C2×C61×#4162
C61×#24312
C61×#23472
C61×#20662
C61×#20652
C61×#20422
C61×#20412
C61×#19832
C61×#19822
C61×#19282
C61×#19252
C61×#18932
C61×#18502
C61×#17882
#2448461