Finite Group Databasebeta

← C61×#25232 #29528665

Subgroups — C61×#25232 #29528665

Order 15616.

988 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#480C211yesmaximal, characteristic, complemented
2C2×C8×D4×C61C211yesmaximal, characteristic, complemented
3C61×#2486C211yesmaximal, characteristic, complemented
4C61×#2416C211yesmaximal, characteristic
5C61×#2086C211yesmaximal, characteristic, complemented
6C61×#2075C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1942C211yesmaximal, characteristic, complemented
10C61×#1934C211yesmaximal, characteristic, complemented
11C61×#1893C211yesmaximal, characteristic, complemented
12C61×#1893C211yesmaximal, characteristic, complemented
13C61×#1852C211yesmaximal, characteristic, complemented
14C61×#1808C211yesmaximal, characteristic, complemented
15C2×C61×#340C211yesmaximal, characteristic, complemented
16C23×C8×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×#123×C61—21no—
19C2×#121×C61—21no—
20C2×#121×C61C2211yescharacteristic
21C2×#121×C61C2211yescharacteristic
22C2×C4×D4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C61×#480—24no—
26C8×D4×C61—24no—
27C2×#107×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C2×#107×C61C2211yescharacteristic
30C2×#107×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C4×C8×C61C2211yescharacteristic
39C61×#398—21no—
40C61×#397—21no—
41C61×#396—21no—
42C61×#394—21no—
43C61×#390C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#389C2211yescharacteristic
46C61×#389C2211yescharacteristic
47C61×#386—21no—
48C61×#381—21no—
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61D411yescharacteristic
64C22×D4×C61C2311yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C22×C8×C61—22no—
70C22×C8×C61—22no—
71C22×C8×C61—22no—
72C22×C8×C61—22no—
73C22×C8×C61—41no—
74C22×C8×C61—41no—
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77C22×C8×C61C2311yescharacteristic
78C22×C8×C61C2311yescharacteristic
79#123×C61—44no—
80#121×C61—22no—
81#121×C61—22no—
82#121×C61—22no—
83#121×C61—41no—
84#121×C61—44no—
85C4×D4×C61—22no—
86C4×D4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—22no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—41no—
96C2×C4⋊C4×C61D411yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
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×C61D411yescharacteristic
113C2×C22⋊C4×C61D411yescharacteristic
114C2×C42×C61C2311yescharacteristic
115#107×C61—22no—
116#107×C61—22no—
117#107×C61—22no—
118#107×C61—41no—
119C4⋊C8×C61—22no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—22no—
123#102×C61—41no—
124C22⋊C8×C61—22no—
125C22⋊C8×C61D414yescomplemented
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—
134C24×C61—21no—
135C24×C61C2×D411yescharacteristic
136C24×C61C2×D411yescharacteristic
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—42no—
146C2×D4×C61—42no—
147C2×D4×C61—42no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61—81no—
151C2×D4×C61D814yes—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
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—42no—
170C22×C4×C61—42no—
171C22×C4×C61—42no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61—81no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61#4112yes—
181C22×C4×C61C2411yescharacteristic
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—44no—
192C2×C8×C61—44no—
193C2×C8×C61C2×D412yes—
194C2×C8×C61C2×D412yes—
195C2×C8×C61#4112yes—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—42no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61#4112yes—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—81no—
226C42×C61—21no—
227C42×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61#12112yes—
246C23×C61C2×D812yes—
247C23×C61C2×D812yes—
248C23×C61#13512yes—
249C23×C61C22×D411yescharacteristic
250D4×C61—28no—
251D4×C61—41no—
252D4×C61—41no—
253D4×C61—41no—
254D4×C61—41no—
255D4×C61—84no—
256D4×C61—84no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
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—84no—
297C2×C4×C61—84no—
298C2×C4×C61#12112yes—
299C2×C4×C61C2×D812yes—
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C612−1+411yescharacteristic
306C8×C61—22no—
307C8×C61—22no—
308C8×C61—22no—
309C8×C61—41no—
310#25232C6111yesmaximal, characteristic, direct product factor, Sylow
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61#46614yes—
332C22×C61C2×#12111yescharacteristic
333C22×C61#54611yescharacteristic
334C22×C61#54711yescharacteristic
335C22×C61C22×D811yescharacteristic
336C22×C61C2×#13511yescharacteristic
337C22×C61#57711yescharacteristic
338C22×C61#57811yescharacteristic
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—41no—
342C4×C61—42no—
343C4×C61—41no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61—81no—
348C4×C61—81no—
349C4×C61—81no—
350C4×C61#52911yescharacteristic
351C4×C61#53911yescharacteristic
352C4×C61#54611yescharacteristic
353C4×C61#54711yescharacteristic
354C2×#480C2×C6111yescharacteristic, complemented
355C2×C8×D4C2×C6111yescharacteristic, complemented
356#2486C2×C6111yescharacteristic, complemented
357#2416C2×C6111yescharacteristic
358#2086C2×C6111yescharacteristic, complemented
359#2075C2×C6111yescharacteristic, complemented
360#2067C2×C6111yescharacteristic, complemented
361#2033C2×C6111yescharacteristic, complemented
362#1942C2×C6111yescharacteristic, complemented
363#1934C2×C6111yescharacteristic, complemented
364#1893C2×C6111yescharacteristic, complemented
365#1893C2×C6111yescharacteristic, complemented
366#1852C2×C6111yescharacteristic, complemented
367#1808C2×C6111yescharacteristic, complemented
368C2×#340C2×C6111yescharacteristic, complemented
369C2×C61—24no—
370C2×C61—42no—
371C2×C61—161no—
372C2×C61#242511yescharacteristic
373C2×C61C2×#46611yescharacteristic
374C2×C61#306311yescharacteristic
375C2×C61#329411yescharacteristic
376C2×C61#330011yescharacteristic
377C2×C61#333411yescharacteristic
378C2×C61#333711yescharacteristic
379C23×C8C22×C6111yescharacteristic
380C23×C8C22×C6111yescharacteristic
381C2×#123—21no—
382C2×#121—21no—
383C2×#121C22×C6111yescharacteristic
384C2×#121C22×C6111yescharacteristic
385C2×C4×D4C22×C6111yescharacteristic
386C22×C4⋊C4C22×C6111yescharacteristic
387C22×C4⋊C4C22×C6111yescharacteristic
388#480—24no—
389C8×D4—24no—
390C2×#107C22×C6111yescharacteristic
391C2×#107C22×C6111yescharacteristic
392C2×#107C22×C6111yescharacteristic
393C2×#107C22×C6111yescharacteristic
394C2×C4⋊C8C22×C6111yescharacteristic
395C2×#102C22×C6111yescharacteristic
396C2×#102C22×C6111yescharacteristic
397C2×#102C22×C6111yescharacteristic
398C2×#102C22×C6111yescharacteristic
399C2×C22⋊C8C22×C6111yescharacteristic
400C2×C22⋊C8C22×C6111yescharacteristic
401C2×C4×C8C22×C6111yescharacteristic
402#398—21no—
403#397—21no—
404#396—21no—
405#394—21no—
406#390C22×C6111yescharacteristic
407#389C22×C6111yescharacteristic
408#389C22×C6111yescharacteristic
409#389C22×C6111yescharacteristic
410#386—21no—
411#381—21no—
412#380C22×C6111yescharacteristic
413#380C22×C6111yescharacteristic
414#380C22×C6111yescharacteristic
415#380C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419#340C22×C6111yescharacteristic
420#340C22×C6111yescharacteristic
421#340C22×C6111yescharacteristic
422#340C22×C6111yescharacteristic
423#340C22×C6111yescharacteristic
424C61#2523211yescharacteristic, direct product factor, Sylow
425C22×D4—21no—
426C22×D4—21no—
427C22×D4D4×C6111yescharacteristic
428C22×D4C23×C6111yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4C23×C6111yescharacteristic
432C23×C4C23×C6111yescharacteristic
433C22×C8—22no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8—41no—
439C22×C8C23×C6111yescharacteristic
440C22×C8C23×C6111yescharacteristic
441C22×C8C23×C6111yescharacteristic
442C22×C8C23×C6111yescharacteristic
443#123—44no—
444#121—22no—
445#121—22no—
446#121—22no—
447#121—41no—
448#121—44no—
449C4×D4—22no—
450C4×D4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4D4×C6111yescharacteristic
461C2×C4⋊C4C23×C6111yescharacteristic
462C2×C4⋊C4C23×C6111yescharacteristic
463C2×C4⋊C4C23×C6111yescharacteristic
464C2×C4⋊C4C23×C6111yescharacteristic
465C2×C4⋊C4C23×C6111yescharacteristic
466C2×C4⋊C4C23×C6111yescharacteristic
467C2×C4⋊C4C23×C6111yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4D4×C6111yescharacteristic
477C2×C22⋊C4D4×C6111yescharacteristic
478C2×C42C23×C6111yescharacteristic
479#107—22no—
480#107—22no—
481#107—22no—
482#107—41no—
483C4⋊C8—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—41no—
488C22⋊C8—22no—
489C22⋊C8D4×C6114yescomplemented
490C4×C8—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498C24—21no—
499C24C2×D4×C6111yescharacteristic
500C24C2×D4×C6111yescharacteristic
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—81no—
515C2×D4D8×C6114yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—81no—
539C22×C4C2×D4×C6111yescharacteristic
540C22×C4C2×D4×C6111yescharacteristic
541C22×C4C2×D4×C6111yescharacteristic
542C22×C4C2×D4×C6112yes—
543C22×C4C2×D4×C6111yescharacteristic
544C22×C4#41×C6112yes—
545C22×C4C24×C6111yescharacteristic
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—44no—
556C2×C8—44no—
557C2×C8C2×D4×C6112yes—
558C2×C8C2×D4×C6112yes—
559C2×C8#41×C6112yes—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4#41×C6112yes—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23#121×C6112yes—
610C23C2×D8×C6112yes—
611C23C2×D8×C6112yes—
612C23#135×C6112yes—
613C23C22×D4×C6111yescharacteristic
614D4—28no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
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—84no—
661C2×C4—84no—
662C2×C4#121×C6112yes—
663C2×C4C2×D8×C6112yes—
664C2×C4C22×D4×C6111yescharacteristic
665C2×C4C2×#41×C6111yescharacteristic
666C2×C4C2×#41×C6111yescharacteristic
667C2×C4C2×#41×C6111yescharacteristic
668C2×C4H(5,𝔽2)×C6111yescharacteristic
669C2×C42−1+4×C6111yescharacteristic
670C8—22no—
671C8—22no—
672C8—22no—
673C8—41no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22C61×#46614yes—
695C22C2×#121×C6111yescharacteristic
696C22C61×#54611yescharacteristic
697C22C61×#54711yescharacteristic
698C22C22×D8×C6111yescharacteristic
699C22C2×#135×C6111yescharacteristic
700C22C61×#57711yescharacteristic
701C22C61×#57811yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—41no—
706C4—41no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4C61×#52911yescharacteristic
714C4C61×#53911yescharacteristic
715C4C61×#54611yescharacteristic
716C4C61×#54711yescharacteristic
717C2—24no—
718C2—42no—
719C2—161no—
720C2C61×#242511yescharacteristic
721C2C2×C61×#46611yescharacteristic
722C2C61×#306311yescharacteristic
723C2C61×#329411yescharacteristic
724C2C61×#330011yescharacteristic
725C2C61×#333411yescharacteristic
726C2C61×#333711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#480C2semidirect
2. C2×C8×D4×C61C2semidirect
3. C61×#2486C2semidirect
5. C61×#2086C2semidirect
6. C61×#2075C2semidirect
7. C61×#2067C2semidirect
8. C61×#2033C2semidirect
9. C61×#1942C2semidirect
10. C61×#1934C2semidirect
11. C61×#1893C2semidirect
12. C61×#1893C2semidirect
13. C61×#1852C2semidirect
14. C61×#1808C2semidirect
15. C2×C61×#340C2semidirect
125. C22⋊C8×C61D4semidirect
310. #25232C61direct (N × H)
354. C2×#480C2×C61semidirect
355. C2×C8×D4C2×C61semidirect
356. #2486C2×C61semidirect
358. #2086C2×C61semidirect
359. #2075C2×C61semidirect
360. #2067C2×C61semidirect
361. #2033C2×C61semidirect
362. #1942C2×C61semidirect
363. #1934C2×C61semidirect
364. #1893C2×C61semidirect
365. #1893C2×C61semidirect
366. #1852C2×C61semidirect
367. #1808C2×C61semidirect
368. C2×#340C2×C61semidirect
424. C61#25232direct (N × H)
489. C22⋊C8D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4802
C2×C8×D4×C612
C61×#24862
C61×#24162
C61×#20862
C61×#20752
C61×#20672
C61×#20332
C61×#19422
C61×#19342
C61×#18932
C61×#18522
C61×#18082
C2×C61×#3402
#2523261