Finite Group Databasebeta

← C61×#18523 #29521956

Subgroups — C61×#18523 #29521956

Order 15616.

946 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3475C211yesmaximal, characteristic
2C61×#3170C211yesmaximal, characteristic, complemented
3C61×#3101C211yesmaximal, characteristic, complemented
4C61×#3076C211yesmaximal, characteristic, complemented
5C61×#1650C211yesmaximal, characteristic, complemented
6C61×#1647C211yesmaximal, characteristic, complemented
7C61×#1646C211yesmaximal, characteristic, complemented
8C61×#1643C211yesmaximal, characteristic, complemented
9C61×#1638C211yesmaximal, characteristic, complemented
10C61×#1635C211yesmaximal, characteristic, complemented
11C61×#1634C211yesmaximal, characteristic, complemented
12C61×#1632C211yesmaximal, characteristic, complemented
13C61×#1542C211yesmaximal, characteristic, complemented
14C61×#1476C211yesmaximal, characteristic, complemented
15C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
16C61×#556C2211yescharacteristic
17C61×#555C2211yescharacteristic
18C61×#554C2211yescharacteristic
19C61×#553—21no—
20C61×#552—21no—
21C61×#552—21no—
22C61×#551—22no—
23C61×#547C2211yescharacteristic
24C61×#546—21no—
25C61×#533C2211yescharacteristic
26C61×#533C2211yescharacteristic
27C61×#529—22no—
28C61×#529—21no—
29C61×#525—21no—
30C4×#41×C61—21no—
31C4×#41×C61C2211yescharacteristic
32C2×C4×D4×C61C2211yescharacteristic
33C2×#117×C61—21no—
34C61×#500C2211yescharacteristic, complemented
35C61×#494C2211yescharacteristic, complemented
36C61×#487C2211yescharacteristic, complemented
37C61×#487C2211yescharacteristic, complemented
38C61×#483—21no—
39C61×#479—21no—
40C61×#478—21no—
41C61×#477C2211yescharacteristic, complemented
42C61×#476C2211yescharacteristic
43C61×#476C2211yescharacteristic
44C61×#476C2211yescharacteristic, complemented
45C61×#475C2211yescharacteristic, complemented
46C61×#474C2211yescharacteristic, complemented
47C61×#467—22no—
48C61×#461C2211yescharacteristic
49C61×#461C2211yescharacteristic
50C61×#450—21no—
51C4×Q16×C61—22no—
52C4×SD16×C61—21no—
53C4×SD16×C61—21no—
54C61×#431C2211yescharacteristic
55C61×#427—21no—
56C2×C4⋊C8×C61C2211yescharacteristic
57C61×#416—21no—
58C2×C4×C8×C61C2211yescharacteristic
59C61×#333C2211yescharacteristic, complemented
60C61×#333C2211yescharacteristic, complemented
61C61×#332C2211yescharacteristic, complemented
62C61×#332C2211yescharacteristic, complemented
63C61×Q8⋊C8C2211yescharacteristic, complemented
64C61×Q8⋊C8C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C61×D4⋊C8C2211yescharacteristic
68C61×D4⋊C8C2211yescharacteristic
69C61×D4⋊C8C2211yescharacteristic, complemented
70C61×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C61—21no—
72C2×#41×C61D411yescharacteristic
73C22×D4×C61D411yescharacteristic
74C23×C4×C61—21no—
75C2×Q16×C61—22no—
76C2×SD16×C61—21no—
77C2×SD16×C61—21no—
78C22×C8×C61—21no—
79C22×C8×C61—21no—
80C4⋊Q8×C61C2311yescharacteristic
81C4⋊Q8×C61C2311yescharacteristic
82C4⋊Q8×C61C2311yescharacteristic
83C4⋊Q8×C61C2311yescharacteristic
84#126×C61—22no—
85#126×C61—22no—
86#126×C61—22no—
87#125×C61—22no—
88#125×C61—21no—
89#125×C61—21no—
90#125×C61—21no—
91#124×C61—22no—
92#124×C61—21no—
93#123×C61—22no—
94#123×C61—22no—
95#123×C61—22no—
96#123×C61—22no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—21no—
99C22⋊Q8×C61—21no—
100C22⋊Q8×C61—21no—
101C22⋊Q8×C61—21no—
102C22⋊Q8×C61—21no—
103C22⋊Q8×C61—21no—
104C22⋊Q8×C61D412yes—
105#121×C61—22no—
106#121×C61—21no—
107#121×C61—21no—
108#121×C61—21no—
109#120×C61—22no—
110C4×Q8×C61—21no—
111C4×Q8×C61—21no—
112C4×Q8×C61—21no—
113C4×Q8×C61—21no—
114C4×Q8×C61D412yes—
115C4×Q8×C61D411yescharacteristic
116C4×Q8×C61C2311yescharacteristic
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120C4×D4×C61—21no—
121C4×D4×C61—21no—
122C4×D4×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61—21no—
125C4×D4×C61D411yescharacteristic
126C4×D4×C61D411yescharacteristic
127C4×D4×C61D411yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—22no—
132#117×C61—22no—
133#117×C61—22no—
134#117×C61—21no—
135#117×C61—21no—
136#117×C61—21no—
137#117×C61—21no—
138#117×C61—21no—
139#117×C61—21no—
140#117×C61D411yescharacteristic
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61D411yescharacteristic
144C2×C22⋊C4×C61—22no—
145C2×C22⋊C4×C61—21no—
146C2×C42×C61—22no—
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#107×C61—21no—
150#107×C61—21no—
151#107×C61—22no—
152#106×C61—21no—
153#106×C61—21no—
154#106×C61—21no—
155#106×C61—21no—
156C4⋊C8×C61—21no—
157C4⋊C8×C61C2311yescharacteristic
158C4⋊C8×C61C2311yescharacteristic
159C4⋊C8×C61C2311yescharacteristic
160C4⋊C8×C61C2311yescharacteristic
161#103×C61—21no—
162#103×C61—21no—
163#103×C61—22no—
164#103×C61—21no—
165#103×C61—21no—
166#103×C61—22no—
167#102×C61—21no—
168#102×C61—21no—
169#102×C61—21no—
170#102×C61—21no—
171C22⋊C8×C61—21no—
172C4×C8×C61—21no—
173C4×C8×C61—21no—
174C4×C8×C61C2311yescharacteristic
175C4×C8×C61C2311yescharacteristic
176C24×C61—21no—
177#41×C61—22no—
178#41×C61—22no—
179#41×C61—42no—
180#41×C61—42no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61C2×D411yescharacteristic
185C2×Q8×C61C2×D412yes—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61—21no—
191C2×D4×C61—41no—
192C2×D4×C61C2×D411yescharacteristic
193C2×D4×C61C2×D411yescharacteristic
194C2×D4×C61C2×D411yescharacteristic
195C22×C4×C61—22no—
196C22×C4×C61—21no—
197C22×C4×C61—22no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—42no—
206C22×C4×C61—42no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210Q16×C61—44no—
211SD16×C61—42no—
212SD16×C61—42no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—42no—
220C2×C8×C61—42no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—41no—
238C4⋊C4×C61—41no—
239C4⋊C4×C61C2×D411yescharacteristic
240C4⋊C4×C61C2×D411yescharacteristic
241C4⋊C4×C61C2×D412yes—
242C4⋊C4×C61C2×D411yescharacteristic
243C4⋊C4×C61C2×D411yescharacteristic
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C22⋊C4×C61—21no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—41no—
259C42×C61—22no—
260C42×C61—22no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61—22no—
264C42×C61—21no—
265C42×C61—41no—
266C42×C61C2×D411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C42×C61C2×D411yescharacteristic
269C42×C61C2411yescharacteristic
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61—81no—
276C23×C61#12011yescharacteristic
277Q8×C61—21no—
278Q8×C61—21no—
279Q8×C61—42no—
280Q8×C61—42no—
281Q8×C61—41no—
282Q8×C61—41no—
283Q8×C61—41no—
284Q8×C61—41no—
285D4×C61—21no—
286D4×C61—21no—
287D4×C61—21no—
288D4×C61—21no—
289D4×C61—21no—
290D4×C61—42no—
291D4×C61—44no—
292D4×C61—42no—
293D4×C61—82no—
294D4×C61#13512yes—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—41no—
305C2×C4×C61—44no—
306C2×C4×C61—42no—
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—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—81no—
319C2×C4×C61—82no—
320C2×C4×C61#12011yescharacteristic
321C2×C4×C61#12011yescharacteristic
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61#13512yes—
324C2×C4×C61#13712yes—
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C8×C61—22no—
329C8×C61—41no—
330C8×C61—41no—
331C8×C61—41no—
332C8×C61—41no—
333C8×C61—41no—
334#18523C6111yesmaximal, characteristic, direct product factor, Sylow
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—22no—
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—84no—
347C22×C61#45212yes—
348C22×C61C2×#12011yescharacteristic
349C4×C61—21no—
350C4×C61—21no—
351C4×C61—21no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61—41no—
355C4×C61—41no—
356C4×C61—42no—
357C4×C61—41no—
358C4×C61—42no—
359C4×C61—81no—
360C4×C61—81no—
361C4×C61#45212yes—
362C4×C61C2×#13511yescharacteristic
363C4×C61C2×#13511yescharacteristic
364C4×C61C2×#13711yescharacteristic
365C4×C61#57511yescharacteristic
366#3475C2×C6111yescharacteristic
367#3170C2×C6111yescharacteristic, complemented
368#3101C2×C6111yescharacteristic, complemented
369#3076C2×C6111yescharacteristic, complemented
370#1650C2×C6111yescharacteristic, complemented
371#1647C2×C6111yescharacteristic, complemented
372#1646C2×C6111yescharacteristic, complemented
373#1643C2×C6111yescharacteristic, complemented
374#1638C2×C6111yescharacteristic, complemented
375#1635C2×C6111yescharacteristic, complemented
376#1634C2×C6111yescharacteristic, complemented
377#1632C2×C6111yescharacteristic, complemented
378#1542C2×C6111yescharacteristic, complemented
379#1476C2×C6111yescharacteristic, complemented
380C2×D4⋊C8C2×C6111yescharacteristic, complemented
381C2×C61—22no—
382C2×C61—42no—
383C2×C61—81no—
384C2×C61—81no—
385C2×C61C2×#45211yescharacteristic
386C2×C61#300211yescharacteristic
387C2×C61#301811yescharacteristic
388#556C22×C6111yescharacteristic
389#555C22×C6111yescharacteristic
390#554C22×C6111yescharacteristic
391#553—21no—
392#552—21no—
393#552—21no—
394#551—22no—
395#547C22×C6111yescharacteristic
396#546—21no—
397#533C22×C6111yescharacteristic
398#533C22×C6111yescharacteristic
399#529—22no—
400#529—21no—
401#525—21no—
402C4×#41—21no—
403C4×#41C22×C6111yescharacteristic
404C2×C4×D4C22×C6111yescharacteristic
405C2×#117—21no—
406#500C22×C6111yescharacteristic, complemented
407#494C22×C6111yescharacteristic, complemented
408#487C22×C6111yescharacteristic, complemented
409#487C22×C6111yescharacteristic, complemented
410#483—21no—
411#479—21no—
412#478—21no—
413#477C22×C6111yescharacteristic, complemented
414#476C22×C6111yescharacteristic
415#476C22×C6111yescharacteristic
416#476C22×C6111yescharacteristic, complemented
417#475C22×C6111yescharacteristic, complemented
418#474C22×C6111yescharacteristic, complemented
419#467—22no—
420#461C22×C6111yescharacteristic
421#461C22×C6111yescharacteristic
422#450—21no—
423C4×Q16—22no—
424C4×SD16—21no—
425C4×SD16—21no—
426#431C22×C6111yescharacteristic
427#427—21no—
428C2×C4⋊C8C22×C6111yescharacteristic
429#416—21no—
430C2×C4×C8C22×C6111yescharacteristic
431#333C22×C6111yescharacteristic, complemented
432#333C22×C6111yescharacteristic, complemented
433#332C22×C6111yescharacteristic, complemented
434#332C22×C6111yescharacteristic, complemented
435Q8⋊C8C22×C6111yescharacteristic, complemented
436Q8⋊C8C22×C6111yescharacteristic, complemented
437D4⋊C8C22×C6111yescharacteristic
438D4⋊C8C22×C6111yescharacteristic
439D4⋊C8C22×C6111yescharacteristic
440D4⋊C8C22×C6111yescharacteristic
441D4⋊C8C22×C6111yescharacteristic, complemented
442D4⋊C8C22×C6111yescharacteristic, complemented
443C61#1852311yescharacteristic, direct product factor, Sylow
444C2×#41—21no—
445C2×#41D4×C6111yescharacteristic
446C22×D4D4×C6111yescharacteristic
447C23×C4—21no—
448C2×Q16—22no—
449C2×SD16—21no—
450C2×SD16—21no—
451C22×C8—21no—
452C22×C8—21no—
453C4⋊Q8C23×C6111yescharacteristic
454C4⋊Q8C23×C6111yescharacteristic
455C4⋊Q8C23×C6111yescharacteristic
456C4⋊Q8C23×C6111yescharacteristic
457#126—22no—
458#126—22no—
459#126—22no—
460#125—22no—
461#125—21no—
462#125—21no—
463#125—21no—
464#124—22no—
465#124—21no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8D4×C6112yes—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#120—22no—
483C4×Q8—21no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8D4×C6111yescharacteristic
488C4×Q8D4×C6112yes—
489C4×Q8C23×C6111yescharacteristic
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4D4×C6111yescharacteristic
499C4×D4D4×C6111yescharacteristic
500C4×D4D4×C6111yescharacteristic
501C4×D4C23×C6111yescharacteristic
502C4×D4C23×C6111yescharacteristic
503C4×D4C23×C6111yescharacteristic
504#117—22no—
505#117—22no—
506#117—22no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117D4×C6111yescharacteristic
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4D4×C6111yescharacteristic
517C2×C22⋊C4—22no—
518C2×C22⋊C4—21no—
519C2×C42—22no—
520C2×C42—21no—
521C2×C42C23×C6111yescharacteristic
522#107—21no—
523#107—21no—
524#107—22no—
525#106—21no—
526#106—21no—
527#106—21no—
528#106—21no—
529C4⋊C8—21no—
530C4⋊C8C23×C6111yescharacteristic
531C4⋊C8C23×C6111yescharacteristic
532C4⋊C8C23×C6111yescharacteristic
533C4⋊C8C23×C6111yescharacteristic
534#103—21no—
535#103—21no—
536#103—22no—
537#103—21no—
538#103—21no—
539#103—22no—
540#102—21no—
541#102—21no—
542#102—21no—
543#102—21no—
544C22⋊C8—21no—
545C4×C8—21no—
546C4×C8—21no—
547C4×C8C23×C6111yescharacteristic
548C4×C8C23×C6111yescharacteristic
549C24—21no—
550#41—22no—
551#41—22no—
552#41—42no—
553#41—42no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C2×D4×C6111yescharacteristic
558C2×Q8C2×D4×C6112yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—41no—
565C2×D4C2×D4×C6111yescharacteristic
566C2×D4C2×D4×C6111yescharacteristic
567C2×D4C2×D4×C6111yescharacteristic
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4C2×D4×C6111yescharacteristic
581C22×C4C2×D4×C6111yescharacteristic
582C22×C4C2×D4×C6111yescharacteristic
583Q16—44no—
584SD16—42no—
585SD16—42no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—42no—
593C2×C8—42no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4C2×D4×C6111yescharacteristic
613C4⋊C4C2×D4×C6111yescharacteristic
614C4⋊C4C2×D4×C6112yes—
615C4⋊C4C2×D4×C6111yescharacteristic
616C4⋊C4C2×D4×C6111yescharacteristic
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—21no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—41no—
632C42—22no—
633C42—22no—
634C42—21no—
635C42—22no—
636C42—21no—
637C42—21no—
638C42—41no—
639C42C2×D4×C6111yescharacteristic
640C42C2×D4×C6111yescharacteristic
641C42C2×D4×C6111yescharacteristic
642C42C24×C6111yescharacteristic
643C23—21no—
644C23—21no—
645C23—21no—
646C23—42no—
647C23—42no—
648C23—81no—
649C23#120×C6111yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—42no—
653Q8—42no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—42no—
664D4—44no—
665D4—42no—
666D4—82no—
667D4#135×C6112yes—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—81no—
692C2×C4—82no—
693C2×C4#120×C6111yescharacteristic
694C2×C4#120×C6111yescharacteristic
695C2×C4#120×C6111yescharacteristic
696C2×C4#135×C6112yes—
697C2×C4#137×C6112yes—
698C2×C4C22×D4×C6111yescharacteristic
699C2×C4C22×D4×C6111yescharacteristic
700C2×C4C22×D4×C6111yescharacteristic
701C8—22no—
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—41no—
707C22—21no—
708C22—21no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—84no—
719C22C61×#45212yes—
720C22C2×#120×C6111yescharacteristic
721C4—21no—
722C4—21no—
723C4—21no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4C61×#45212yes—
734C4C2×#135×C6111yescharacteristic
735C4C2×#135×C6111yescharacteristic
736C4C2×#137×C6111yescharacteristic
737C4C61×#57511yescharacteristic
738C2—22no—
739C2—42no—
740C2—81no—
741C2—81no—
742C2C2×C61×#45211yescharacteristic
743C2C61×#300211yescharacteristic
744C2C61×#301811yescharacteristic
subgroupG/H
centerC2×C4×C61#120
commutator, Frattini, cosocleC42C24×C61
socleC22×C61C2×#120
prime radicalC61×#3475C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3170C2semidirect
3. C61×#3101C2semidirect
4. C61×#3076C2semidirect
5. C61×#1650C2semidirect
6. C61×#1647C2semidirect
7. C61×#1646C2semidirect
8. C61×#1643C2semidirect
9. C61×#1638C2semidirect
10. C61×#1635C2semidirect
11. C61×#1634C2semidirect
12. C61×#1632C2semidirect
13. C61×#1542C2semidirect
14. C61×#1476C2semidirect
15. C2×C61×D4⋊C8C2semidirect
34. C61×#500C22semidirect
35. C61×#494C22semidirect
36. C61×#487C22semidirect
37. C61×#487C22semidirect
41. C61×#477C22semidirect
44. C61×#476C22semidirect
45. C61×#475C22semidirect
46. C61×#474C22semidirect
59. C61×#333C22semidirect
60. C61×#333C22semidirect
61. C61×#332C22semidirect
62. C61×#332C22semidirect
63. C61×Q8⋊C8C22semidirect
64. C61×Q8⋊C8C22semidirect
69. C61×D4⋊C8C22semidirect
70. C61×D4⋊C8C22semidirect
334. #18523C61direct (N × H)
367. #3170C2×C61semidirect
368. #3101C2×C61semidirect
369. #3076C2×C61semidirect
370. #1650C2×C61semidirect
371. #1647C2×C61semidirect
372. #1646C2×C61semidirect
373. #1643C2×C61semidirect
374. #1638C2×C61semidirect
375. #1635C2×C61semidirect
376. #1634C2×C61semidirect
377. #1632C2×C61semidirect
378. #1542C2×C61semidirect
379. #1476C2×C61semidirect
380. C2×D4⋊C8C2×C61semidirect
406. #500C22×C61semidirect
407. #494C22×C61semidirect
408. #487C22×C61semidirect
409. #487C22×C61semidirect
413. #477C22×C61semidirect
416. #476C22×C61semidirect
417. #475C22×C61semidirect
418. #474C22×C61semidirect
431. #333C22×C61semidirect
432. #333C22×C61semidirect
433. #332C22×C61semidirect
434. #332C22×C61semidirect
435. Q8⋊C8C22×C61semidirect
436. Q8⋊C8C22×C61semidirect
441. D4⋊C8C22×C61semidirect
442. D4⋊C8C22×C61semidirect
443. C61#18523direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#34752
C61×#31702
C61×#31012
C61×#30762
C61×#16502
C61×#16472
C61×#16462
C61×#16432
C61×#16382
C61×#16352
C61×#16342
C61×#16322
C61×#15422
C61×#14762
C2×C61×D4⋊C82
#1852361