Finite Group Databasebeta

← C61×#24907 #29528340

Subgroups — C61×#24907 #29528340

Order 15616.

994 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
1C2×C61×#452C211yesmaximal, characteristic
2C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
3C61×#2423C211yesmaximal, characteristic, complemented
4C61×#2339C211yesmaximal, characteristic
5C61×#2096C211yesmaximal, characteristic, complemented
6C61×#2077C211yesmaximal, characteristic, complemented
7C61×#2056C211yesmaximal, characteristic, complemented
8C61×#2035C211yesmaximal, characteristic, complemented
9C61×#1933C211yesmaximal, characteristic, complemented
10C61×#1923C211yesmaximal, characteristic, complemented
11C61×#1878C211yesmaximal, characteristic, complemented
12C61×#1877C211yesmaximal, characteristic, complemented
13C61×#1864C211yesmaximal, characteristic, complemented
14C61×#1802C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic
16C22×#41×C61C2211yescharacteristic
17C22×Q16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C2×C22⋊Q8×C61C2211yescharacteristic
20C2×C4×Q8×C61C2211yescharacteristic
21C2×C4×D4×C61C2211yescharacteristic
22C2×C4×D4×C61C2211yescharacteristic
23C61×#452—24no—
24C4×SD16×C61—24no—
25C2×#106×C61C2211yescharacteristic
26C2×#106×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×#103×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C4×C8×C61C2211yescharacteristic
39C61×#399—21no—
40C61×#398—21no—
41C61×#391C2211yescharacteristic
42C61×#391C2211yescharacteristic
43C61×#391C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#388—21no—
46C61×#387—21no—
47C61×#386—21no—
48C61×#386—21no—
49C61×#384C2211yescharacteristic
50C61×#381—21no—
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C4×C22⋊C4×C61C2211yescharacteristic
54C2×#95×C61—21no—
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
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×Q8×C61C2311yescharacteristic
69C22×D4×C61—21no—
70C22×D4×C61C2311yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61—21no—
74C23×C4×C61C2311yescharacteristic
75C2×Q16×C61—22no—
76C2×Q16×C61—22no—
77C2×Q16×C61—41no—
78C2×SD16×C61—22no—
79C2×SD16×C61—22no—
80C2×SD16×C61D414yes—
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84C22×C8×C61C2311yescharacteristic
85C22⋊Q8×C61—22no—
86C22⋊Q8×C61—41no—
87C4×Q8×C61—22no—
88C4×Q8×C61—41no—
89C4×D4×C61—22no—
90C4×D4×C61—22no—
91C4×D4×C61—41no—
92C4×D4×C61—41no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
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×C61D411yescharacteristic
109C2×C22⋊C4×C61D411yescharacteristic
110C2×C42×C61—21no—
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113#106×C61—22no—
114#106×C61—41no—
115C4⋊C8×C61—41no—
116#103×C61—22no—
117#103×C61—22no—
118#103×C61—22no—
119#103×C61—41no—
120#103×C61—41no—
121#102×C61—22no—
122#102×C61—22no—
123#102×C61—22no—
124C22⋊C8×C61—22no—
125C22⋊C8×C61—41no—
126C4×C8×C61—22no—
127#95×C61—21no—
128#95×C61—21no—
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×C61C2×D411yescharacteristic
140#41×C61—44no—
141#41×C61—44no—
142#41×C61—44no—
143#41×C61—44no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
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—21no—
154C2×Q8×C61C2×D412yes—
155C2×Q8×C61#4112yes—
156C2×D4×C61—24no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61C2×D412yes—
163C2×D4×C61#4112yes—
164C2×D4×C61#4112yes—
165C22×C4×C61—24no—
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—42no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61—81no—
186C22×C4×C61—81no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2411yescharacteristic
193Q16×C61—44no—
194SD16×C61—28no—
195C2×C8×C61—21no—
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×C61C2×D412yes—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
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×C61—42no—
220C4⋊C4×C61—81no—
221C4⋊C4×C61—81no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—42no—
227C22⋊C4×C61—81no—
228C22⋊C4×C61—81no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—21no—
233C42×C61—42no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—22no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61C22×D411yescharacteristic
249Q8×C61—22no—
250Q8×C61—22no—
251Q8×C61—22no—
252Q8×C61—22no—
253Q8×C61—41no—
254Q8×C61—41no—
255Q8×C61—41no—
256Q8×C61—41no—
257D4×C61—22no—
258D4×C61—22no—
259D4×C61—22no—
260D4×C61—48no—
261D4×C61#12314yes—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—48no—
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—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—84no—
302C2×C4×C61—84no—
303C2×C4×C61#13512yes—
304C2×C4×C61#13712yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C8×C61—22no—
312C8×C61—41no—
313C8×C61—41no—
314C8×C61—41no—
315#24907C6111yesmaximal, characteristic, direct product factor, Sylow
316C22×C61—24no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61#52511yescharacteristic
331C22×C61D4211yescharacteristic
332C22×C61#54611yescharacteristic
333C22×C61C2×#13511yescharacteristic
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—41no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61—81no—
348C4×C61—81no—
349C4×C61C2×#12311yescharacteristic
350C4×C61#53811yescharacteristic
351C4×C61#54611yescharacteristic
352C4×C61#55111yescharacteristic
353C2×#452C2×C6111yescharacteristic
354C2×C4×SD16C2×C6111yescharacteristic, complemented
355#2423C2×C6111yescharacteristic, complemented
356#2339C2×C6111yescharacteristic
357#2096C2×C6111yescharacteristic, complemented
358#2077C2×C6111yescharacteristic, complemented
359#2056C2×C6111yescharacteristic, complemented
360#2035C2×C6111yescharacteristic, complemented
361#1933C2×C6111yescharacteristic, complemented
362#1923C2×C6111yescharacteristic, complemented
363#1878C2×C6111yescharacteristic, complemented
364#1877C2×C6111yescharacteristic, complemented
365#1864C2×C6111yescharacteristic, complemented
366#1802C2×C6111yescharacteristic, complemented
367#1788C2×C6111yescharacteristic
368C2×C61—44no—
369C2×C61—81no—
370C2×C61#241811yescharacteristic
371C2×C61#310711yescharacteristic
372C2×C61#312511yescharacteristic
373C2×C61#326611yescharacteristic
374C2×C61#328411yescharacteristic
375C2×C61#329611yescharacteristic
376C2×C61#333111yescharacteristic
377C22×#41C22×C6111yescharacteristic
378C22×Q16C22×C6111yescharacteristic
379C22×SD16C22×C6111yescharacteristic
380C2×C22⋊Q8C22×C6111yescharacteristic
381C2×C4×Q8C22×C6111yescharacteristic
382C2×C4×D4C22×C6111yescharacteristic
383C2×C4×D4C22×C6111yescharacteristic
384#452—24no—
385C4×SD16—24no—
386C2×#106C22×C6111yescharacteristic
387C2×#106C22×C6111yescharacteristic
388C2×C4⋊C8C22×C6111yescharacteristic
389C2×#103C22×C6111yescharacteristic
390C2×#103C22×C6111yescharacteristic
391C2×#103C22×C6111yescharacteristic
392C2×#103C22×C6111yescharacteristic
393C2×#103C22×C6111yescharacteristic
394C2×#102C22×C6111yescharacteristic
395C2×#102C22×C6111yescharacteristic
396C2×#102C22×C6111yescharacteristic
397C2×C22⋊C8C22×C6111yescharacteristic
398C2×C22⋊C8C22×C6111yescharacteristic
399C2×C4×C8C22×C6111yescharacteristic
400#399—21no—
401#398—21no—
402#391C22×C6111yescharacteristic
403#391C22×C6111yescharacteristic
404#391C22×C6111yescharacteristic
405#389C22×C6111yescharacteristic
406#388—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#384C22×C6111yescharacteristic
411#381—21no—
412#380C22×C6111yescharacteristic
413#380C22×C6111yescharacteristic
414C4×C22⋊C4C22×C6111yescharacteristic
415C2×#95—21no—
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419#340C22×C6111yescharacteristic
420#336C22×C6111yescharacteristic
421#336C22×C6111yescharacteristic
422C61#2490711yescharacteristic, direct product factor, Sylow
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—41no—
428C2×#41—41no—
429C22×Q8C23×C6111yescharacteristic
430C22×Q8C23×C6111yescharacteristic
431C22×D4—21no—
432C22×D4C23×C6111yescharacteristic
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4C23×C6111yescharacteristic
437C2×Q16—22no—
438C2×Q16—22no—
439C2×Q16—41no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16D4×C6114yes—
443C22×C8C23×C6111yescharacteristic
444C22×C8C23×C6111yescharacteristic
445C22×C8C23×C6111yescharacteristic
446C22×C8C23×C6111yescharacteristic
447C22⋊Q8—22no—
448C22⋊Q8—41no—
449C4×Q8—22no—
450C4×Q8—41no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—41no—
454C4×D4—41no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
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⋊C4D4×C6111yescharacteristic
471C2×C22⋊C4D4×C6111yescharacteristic
472C2×C42—21no—
473C2×C42C23×C6111yescharacteristic
474C2×C42C23×C6111yescharacteristic
475#106—22no—
476#106—41no—
477C4⋊C8—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—41no—
482#103—41no—
483#102—22no—
484#102—22no—
485#102—22no—
486C22⋊C8—22no—
487C22⋊C8—41no—
488C4×C8—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C6111yescharacteristic
499#95D4×C6111yescharacteristic
500C24—21no—
501C24C2×D4×C6111yescharacteristic
502#41—44no—
503#41—44no—
504#41—44no—
505#41—44no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8C2×D4×C6112yes—
517C2×Q8#41×C6112yes—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4C2×D4×C6112yes—
525C2×D4#41×C6112yes—
526C2×D4#41×C6112yes—
527C22×C4—24no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4C2×D4×C6111yescharacteristic
550C22×C4C2×D4×C6111yescharacteristic
551C22×C4C2×D4×C6111yescharacteristic
552C22×C4C2×D4×C6111yescharacteristic
553C22×C4C2×D4×C6111yescharacteristic
554C22×C4C24×C6111yescharacteristic
555Q16—44no—
556SD16—28no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8C2×D4×C6112yes—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—81no—
583C4⋊C4—81no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—42no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C22×D4×C6111yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619D4—22no—
620D4—22no—
621D4—22no—
622D4—48no—
623D4#123×C6114yes—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—48no—
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—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4#135×C6112yes—
666C2×C4#137×C6112yes—
667C2×C4C22×D4×C6111yescharacteristic
668C2×C4C2×#41×C6111yescharacteristic
669C2×C4C2×#41×C6111yescharacteristic
670C2×C4C2×#41×C6111yescharacteristic
671C2×C4H(5,𝔽2)×C6111yescharacteristic
672C2×C4H(5,𝔽2)×C6111yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—24no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22C61×#52511yescharacteristic
692C22D42×C6111yescharacteristic
693C22C61×#54611yescharacteristic
694C22C2×#135×C6111yescharacteristic
695C22C2×#137×C6111yescharacteristic
696C22C61×#57711yescharacteristic
697C22C61×#57711yescharacteristic
698C4—22no—
699C4—22no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—42no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C2×#123×C6111yescharacteristic
711C4C61×#53811yescharacteristic
712C4C61×#54611yescharacteristic
713C4C61×#55111yescharacteristic
714C2—44no—
715C2—81no—
716C2C61×#241811yescharacteristic
717C2C61×#310711yescharacteristic
718C2C61×#312511yescharacteristic
719C2C61×#326611yescharacteristic
720C2C61×#328411yescharacteristic
721C2C61×#329611yescharacteristic
722C2C61×#333111yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC22×#41×C61C22
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
2. C2×C4×SD16×C61C2semidirect
3. C61×#2423C2semidirect
5. C61×#2096C2semidirect
6. C61×#2077C2semidirect
7. C61×#2056C2semidirect
8. C61×#2035C2semidirect
9. C61×#1933C2semidirect
10. C61×#1923C2semidirect
11. C61×#1878C2semidirect
12. C61×#1877C2semidirect
13. C61×#1864C2semidirect
14. C61×#1802C2semidirect
315. #24907C61direct (N × H)
354. C2×C4×SD16C2×C61semidirect
355. #2423C2×C61semidirect
357. #2096C2×C61semidirect
358. #2077C2×C61semidirect
359. #2056C2×C61semidirect
360. #2035C2×C61semidirect
361. #1933C2×C61semidirect
362. #1923C2×C61semidirect
363. #1878C2×C61semidirect
364. #1877C2×C61semidirect
365. #1864C2×C61semidirect
366. #1802C2×C61semidirect
422. C61#24907direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4522
C2×C4×SD16×C612
C61×#24232
C61×#23392
C61×#20962
C61×#20772
C61×#20562
C61×#20352
C61×#19332
C61×#19232
C61×#18782
C61×#18772
C61×#18642
C61×#18022
C61×#17882
#2490761