Finite Group Databasebeta

← C61×#25916 #29529349

Subgroups — C61×#25916 #29529349

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#544C211yesmaximal, characteristic, complemented
2C2×C61×#489C211yesmaximal, characteristic, complemented
3C2×C61×#488C211yesmaximal, characteristic, complemented
4C61×#2620C211yesmaximal, characteristic
5C61×#2026C211yesmaximal, characteristic, complemented
6C61×#2025C211yesmaximal, characteristic, complemented
7C61×#2024C211yesmaximal, characteristic, complemented
8C61×#2023C211yesmaximal, characteristic, complemented
9C61×#1992C211yesmaximal, characteristic, complemented
10C61×#1990C211yesmaximal, characteristic, complemented
11C61×#1875C211yesmaximal, characteristic
12C61×#1874C211yesmaximal, characteristic
13C61×#1873C211yesmaximal, characteristic, complemented
14C61×#1872C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16C61×#544—24no—
17C61×#544—24no—
18C2×C4⋊Q8×C61—21no—
19C2×C4⋊Q8×C61C2211yescharacteristic
20C2×C4⋊Q8×C61C2211yescharacteristic
21C2×#125×C61—21no—
22C2×#125×C61C2211yescharacteristic
23C2×#125×C61C2211yescharacteristic
24C2×#124×C61C2211yescharacteristic
25C2×C22⋊Q8×C61—21no—
26C2×C22⋊Q8×C61—21no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C61×#489—24no—
33C61×#488—24no—
34C2×#103×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#103×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×C22⋊C8×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×#97×C61C2211yescharacteristic
45C2×C4×C8×C61C2211yescharacteristic
46C61×#396—21no—
47C61×#396—21no—
48C61×#394—21no—
49C61×#394—21no—
50C61×#391C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#384C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Q8×C61—21no—
64C22×Q8×C61—21no—
65C22×Q8×C61C2311yescharacteristic
66C22×D4×C61—21no—
67C22×D4×C61C2311yescharacteristic
68C23×C4×C61—21no—
69C23×C4×C61C2311yescharacteristic
70C22×C8×C61C2311yescharacteristic
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C4⋊Q8×C61—28no—
75C4⋊Q8×C61—22no—
76C4⋊Q8×C61—22no—
77C4⋊Q8×C61—22no—
78C4⋊Q8×C61D414yescomplemented
79#125×C61—28no—
80#125×C61—22no—
81#125×C61—22no—
82#125×C61—22no—
83#125×C61D414yescomplemented
84#124×C61—22no—
85#124×C61—22no—
86C22⋊Q8×C61—28no—
87C22⋊Q8×C61—28no—
88C22⋊Q8×C61—22no—
89C22⋊Q8×C61—22no—
90#121×C61—22no—
91#121×C61—22no—
92#117×C61—22no—
93#117×C61—22no—
94#117×C61—22no—
95#117×C61—22no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61—22no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61D411yescharacteristic
124C2×C22⋊C4×C61D411yescharacteristic
125C2×C42×C61—21no—
126C2×C42×C61C2311yescharacteristic
127C2×C42×C61C2311yescharacteristic
128#103×C61—22no—
129#103×C61—22no—
130#103×C61—22no—
131#103×C61—22no—
132#102×C61—22no—
133#102×C61—22no—
134#102×C61—22no—
135#102×C61—22no—
136C22⋊C8×C61—22no—
137C22⋊C8×C61—22no—
138#97×C61—22no—
139C4×C8×C61—22no—
140#95×C61—21no—
141#95×C61—21no—
142C24×C61—21no—
143C24×C61C2×D411yescharacteristic
144C2×Q8×C61—24no—
145C2×Q8×C61—24no—
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—81no—
153C2×Q8×C61—81no—
154C2×Q8×C61—81no—
155C2×Q8×C61—81no—
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—81no—
164C2×D4×C61—81no—
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—24no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—81no—
178C22×C4×C61—81no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61#4112yes—
185C22×C4×C61#4112yes—
186C22×C4×C61C2411yescharacteristic
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C4⋊C4×C61—24no—
200C4⋊C4×C61—24no—
201C4⋊C4×C61—24no—
202C4⋊C4×C61—24no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—24no—
205C4⋊C4×C61—24no—
206C4⋊C4×C61—22no—
207C4⋊C4×C61—22no—
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—42no—
217C4⋊C4×C61—81no—
218C4⋊C4×C61—81no—
219C4⋊C4×C61C2×D412yes—
220C4⋊C4×C61C2×D412yes—
221C4⋊C4×C61C2×D412yes—
222C4⋊C4×C61C2×D412yes—
223C22⋊C4×C61—24no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—42no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—81no—
231C22⋊C4×C61—81no—
232C42×C61—24no—
233C42×C61—21no—
234C42×C61—21no—
235C42×C61C2×D412yes—
236C42×C61C2×D412yes—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61#12412yes—
251C23×C61C22×D411yescharacteristic
252Q8×C61—41no—
253Q8×C61—41no—
254Q8×C61—41no—
255Q8×C61—41no—
256Q8×C61—84no—
257Q8×C61—84no—
258D4×C61—41no—
259D4×C61—41no—
260D4×C61—41no—
261D4×C61—41no—
262D4×C61—84no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
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—84no—
301C2×C4×C61#12012yes—
302C2×C4×C61#12012yes—
303C2×C4×C61#12412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C612−1+411yescharacteristic
309C2×C4×C612−1+411yescharacteristic
310C8×C61—41no—
311C8×C61—41no—
312C8×C61—41no—
313C8×C61—41no—
314#25916C6111yesmaximal, characteristic, direct product factor, Sylow
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×C61C2×#12011yescharacteristic
330C22×C61C2×#12411yescharacteristic
331C22×C61#53611yescharacteristic
332C22×C61#57611yescharacteristic
333C22×C61#57711yescharacteristic
334C22×C61#57711yescharacteristic
335C22×C61#57811yescharacteristic
336C4×C61—22no—
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—41no—
340C4×C61—42no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61—41no—
344C4×C61—42no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61—81no—
348C4×C61#54811yescharacteristic
349C4×C61#54811yescharacteristic
350C4×C61#54811yescharacteristic
351C4×C61#54811yescharacteristic
352C2×#544C2×C6111yescharacteristic, complemented
353C2×#489C2×C6111yescharacteristic, complemented
354C2×#488C2×C6111yescharacteristic, complemented
355#2620C2×C6111yescharacteristic
356#2026C2×C6111yescharacteristic, complemented
357#2025C2×C6111yescharacteristic, complemented
358#2024C2×C6111yescharacteristic, complemented
359#2023C2×C6111yescharacteristic, complemented
360#1992C2×C6111yescharacteristic, complemented
361#1990C2×C6111yescharacteristic, complemented
362#1875C2×C6111yescharacteristic
363#1874C2×C6111yescharacteristic
364#1873C2×C6111yescharacteristic, complemented
365#1872C2×C6111yescharacteristic, complemented
366#1750C2×C6111yescharacteristic, complemented
367C2×C61—42no—
368C2×C61—161no—
369C2×C61#243611yescharacteristic
370C2×C61#301211yescharacteristic
371C2×C61#301311yescharacteristic
372C2×C61#313611yescharacteristic
373C2×C61#313711yescharacteristic
374C2×C61#324311yescharacteristic
375C2×C61#324411yescharacteristic
376#544—24no—
377#544—24no—
378C2×C4⋊Q8—21no—
379C2×C4⋊Q8C22×C6111yescharacteristic
380C2×C4⋊Q8C22×C6111yescharacteristic
381C2×#125—21no—
382C2×#125C22×C6111yescharacteristic
383C2×#125C22×C6111yescharacteristic
384C2×#124C22×C6111yescharacteristic
385C2×C22⋊Q8—21no—
386C2×C22⋊Q8—21no—
387C2×C22⋊Q8C22×C6111yescharacteristic
388C2×#121C22×C6111yescharacteristic
389C2×#117C22×C6111yescharacteristic
390C2×#117C22×C6111yescharacteristic
391C22×C4⋊C4C22×C6111yescharacteristic
392#489—24no—
393#488—24no—
394C2×#103C22×C6111yescharacteristic
395C2×#103C22×C6111yescharacteristic
396C2×#103C22×C6111yescharacteristic
397C2×#103C22×C6111yescharacteristic
398C2×#102C22×C6111yescharacteristic
399C2×#102C22×C6111yescharacteristic
400C2×#102C22×C6111yescharacteristic
401C2×#102C22×C6111yescharacteristic
402C2×C22⋊C8C22×C6111yescharacteristic
403C2×C22⋊C8C22×C6111yescharacteristic
404C2×#97C22×C6111yescharacteristic
405C2×C4×C8C22×C6111yescharacteristic
406#396—21no—
407#396—21no—
408#394—21no—
409#394—21no—
410#391C22×C6111yescharacteristic
411#390C22×C6111yescharacteristic
412#384C22×C6111yescharacteristic
413#340C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419#340C22×C6111yescharacteristic
420#340C22×C6111yescharacteristic
421#336C22×C6111yescharacteristic
422#336C22×C6111yescharacteristic
423C61#2591611yescharacteristic, direct product factor, Sylow
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8C23×C6111yescharacteristic
427C22×D4—21no—
428C22×D4C23×C6111yescharacteristic
429C23×C4—21no—
430C23×C4C23×C6111yescharacteristic
431C22×C8C23×C6111yescharacteristic
432C22×C8C23×C6111yescharacteristic
433C22×C8C23×C6111yescharacteristic
434C22×C8C23×C6111yescharacteristic
435C4⋊Q8—28no—
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439C4⋊Q8D4×C6114yescomplemented
440#125—28no—
441#125—22no—
442#125—22no—
443#125—22no—
444#125D4×C6114yescomplemented
445#124—22no—
446#124—22no—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451#121—22no—
452#121—22no—
453#117—22no—
454#117—22no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4D4×C6111yescharacteristic
470C2×C4⋊C4D4×C6111yescharacteristic
471C2×C4⋊C4C23×C6111yescharacteristic
472C2×C4⋊C4C23×C6111yescharacteristic
473C2×C4⋊C4C23×C6111yescharacteristic
474C2×C4⋊C4C23×C6111yescharacteristic
475C2×C4⋊C4C23×C6111yescharacteristic
476C2×C4⋊C4C23×C6111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4D4×C6111yescharacteristic
485C2×C22⋊C4D4×C6111yescharacteristic
486C2×C42—21no—
487C2×C42C23×C6111yescharacteristic
488C2×C42C23×C6111yescharacteristic
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499#97—22no—
500C4×C8—22no—
501#95—21no—
502#95—21no—
503C24—21no—
504C24C2×D4×C6111yescharacteristic
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—81no—
514C2×Q8—81no—
515C2×Q8—81no—
516C2×Q8—81no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4C2×D4×C6111yescharacteristic
541C22×C4C2×D4×C6111yescharacteristic
542C22×C4C2×D4×C6111yescharacteristic
543C22×C4C2×D4×C6111yescharacteristic
544C22×C4C2×D4×C6111yescharacteristic
545C22×C4#41×C6112yes—
546C22×C4#41×C6112yes—
547C22×C4C24×C6111yescharacteristic
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
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—42no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4C2×D4×C6112yes—
581C4⋊C4C2×D4×C6112yes—
582C4⋊C4C2×D4×C6112yes—
583C4⋊C4C2×D4×C6112yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C42—24no—
594C42—21no—
595C42—21no—
596C42C2×D4×C6112yes—
597C42C2×D4×C6112yes—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23#124×C6112yes—
612C23C22×D4×C6111yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—84no—
618Q8—84no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
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—84no—
662C2×C4#120×C6112yes—
663C2×C4#120×C6112yes—
664C2×C4#124×C6112yes—
665C2×C4C22×D4×C6111yescharacteristic
666C2×C4C22×D4×C6111yescharacteristic
667C2×C4C2×#41×C6111yescharacteristic
668C2×C4C2×#41×C6111yescharacteristic
669C2×C42−1+4×C6111yescharacteristic
670C2×C42−1+4×C6111yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#120×C6111yescharacteristic
690C22C2×#124×C6111yescharacteristic
691C22C61×#53611yescharacteristic
692C22C61×#57611yescharacteristic
693C22C61×#57711yescharacteristic
694C22C61×#57711yescharacteristic
695C22C61×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C61×#54811yescharacteristic
709C4C61×#54811yescharacteristic
710C4C61×#54811yescharacteristic
711C4C61×#54811yescharacteristic
712C2—42no—
713C2—161no—
714C2C61×#243611yescharacteristic
715C2C61×#301211yescharacteristic
716C2C61×#301311yescharacteristic
717C2C61×#313611yescharacteristic
718C2C61×#313711yescharacteristic
719C2C61×#324311yescharacteristic
720C2C61×#324411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#544C2semidirect
2. C2×C61×#489C2semidirect
3. C2×C61×#488C2semidirect
5. C61×#2026C2semidirect
6. C61×#2025C2semidirect
7. C61×#2024C2semidirect
8. C61×#2023C2semidirect
9. C61×#1992C2semidirect
10. C61×#1990C2semidirect
13. C61×#1873C2semidirect
14. C61×#1872C2semidirect
15. C61×#1750C2semidirect
78. C4⋊Q8×C61D4semidirect
83. #125×C61D4semidirect
314. #25916C61direct (N × H)
352. C2×#544C2×C61semidirect
353. C2×#489C2×C61semidirect
354. C2×#488C2×C61semidirect
356. #2026C2×C61semidirect
357. #2025C2×C61semidirect
358. #2024C2×C61semidirect
359. #2023C2×C61semidirect
360. #1992C2×C61semidirect
361. #1990C2×C61semidirect
364. #1873C2×C61semidirect
365. #1872C2×C61semidirect
366. #1750C2×C61semidirect
423. C61#25916direct (N × H)
439. C4⋊Q8D4×C61semidirect
444. #125D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5442
C2×C61×#4892
C2×C61×#4882
C61×#26202
C61×#20262
C61×#20252
C61×#20242
C61×#20232
C61×#19922
C61×#19902
C61×#18752
C61×#18742
C61×#18732
C61×#18722
C61×#17502
#2591661