Finite Group Databasebeta

← C61×#25243 #29528676

Subgroups — C61×#25243 #29528676

Order 15616.

920 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#482C211yesmaximal, characteristic, complemented
2C2×C61×#435C211yesmaximal, characteristic, complemented
3C61×#2485C211yesmaximal, characteristic, complemented
4C61×#2416C211yesmaximal, characteristic
5C61×#2087C211yesmaximal, characteristic, complemented
6C61×#2077C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1943C211yesmaximal, characteristic, complemented
10C61×#1936C211yesmaximal, characteristic, complemented
11C61×#1895C211yesmaximal, characteristic, complemented
12C61×#1893C211yesmaximal, characteristic, complemented
13C61×#1852C211yesmaximal, characteristic, complemented
14C61×#1808C211yesmaximal, characteristic, complemented
15C61×#1736C211yesmaximal, characteristic, complemented
16C22×M16×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×#121×C61—21no—
19C2×#121×C61C2211yescharacteristic
20C2×#121×C61C2211yescharacteristic
21C2×C4×D4×C61C2211yescharacteristic
22C2×#117×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C61×#482—24no—
25C61×#435—24no—
26C2×#107×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C2×#106×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×#97×C61C2211yescharacteristic
38C61×#397—21no—
39C61×#396—21no—
40C61×#394—21no—
41C61×#394—21no—
42C61×#390C2211yescharacteristic
43C61×#389C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#389C2211yescharacteristic
46C61×#388—21no—
47C61×#387—21no—
48C61×#386—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×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C2×M16×C61—22no—
69C2×M16×C61—22no—
70C2×M16×C61—41no—
71C22×C8×C61—22no—
72C22×C8×C61—22no—
73C22×C8×C61—41no—
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77C22×C8×C61C2311yescharacteristic
78#121×C61—22no—
79#121×C61—22no—
80#121×C61—22no—
81#121×C61—41no—
82#121×C61—44no—
83C4×D4×C61—22no—
84C4×D4×C61—22no—
85#117×C61—22no—
86#117×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—41no—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
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×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C42×C61—21no—
113C2×C42×C61C2311yescharacteristic
114#107×C61—22no—
115#107×C61—22no—
116#107×C61—41no—
117#106×C61—22no—
118C4⋊C8×C61—22no—
119#102×C61—22no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—41no—
123C22⋊C8×C61—22no—
124C22⋊C8×C61D414yescomplemented
125#97×C61—22no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133C24×C61—21no—
134C24×C61C2×D411yescharacteristic
135C24×C61C2×D411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—41no—
145C2×D4×C61—42no—
146C2×D4×C61—42no—
147C2×D4×C61—42no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61—81no—
151C22×C4×C61—21no—
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—42no—
169C22×C4×C61—42no—
170C22×C4×C61—81no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D412yes—
176C22×C4×C61#4112yes—
177C22×C4×C61C2411yescharacteristic
178M16×C61—44no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
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—44no—
189C2×C8×C61C2×D412yes—
190C2×C8×C61C2×D412yes—
191C2×C8×C61#4112yes—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
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—42no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—81no—
210C4⋊C4×C61#4112yes—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—81no—
220C22⋊C4×C61—81no—
221C22⋊C4×C61—81no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—42no—
225C23×C61—21no—
226C23×C61—21no—
227C23×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—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61#12112yes—
245C23×C61AGL(1,ℤ/8)12yes—
246C23×C61C22×D411yescharacteristic
247D4×C61—44no—
248D4×C61—41no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—41no—
252D4×C61—84no—
253D4×C61—84no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
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—84no—
295C2×C4×C61#12112yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C612−1+411yescharacteristic
302C8×C61—22no—
303C8×C61—22no—
304C8×C61—22no—
305C8×C61—41no—
306#25243C6111yesmaximal, characteristic, direct product factor, Sylow
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61C2×#12111yescharacteristic
329C22×C61#54611yescharacteristic
330C22×C61#54711yescharacteristic
331C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C61#57511yescharacteristic
333C22×C61#57611yescharacteristic
334C22×C61#57811yescharacteristic
335C4×C61—22no—
336C4×C61—41no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—42no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61#52911yescharacteristic
347C4×C61#53911yescharacteristic
348C4×C61#54611yescharacteristic
349C4×C61#54711yescharacteristic
350C2×#482C2×C6111yescharacteristic, complemented
351C2×#435C2×C6111yescharacteristic, complemented
352#2485C2×C6111yescharacteristic, complemented
353#2416C2×C6111yescharacteristic
354#2087C2×C6111yescharacteristic, complemented
355#2077C2×C6111yescharacteristic, complemented
356#2067C2×C6111yescharacteristic, complemented
357#2033C2×C6111yescharacteristic, complemented
358#1943C2×C6111yescharacteristic, complemented
359#1936C2×C6111yescharacteristic, complemented
360#1895C2×C6111yescharacteristic, complemented
361#1893C2×C6111yescharacteristic, complemented
362#1852C2×C6111yescharacteristic, complemented
363#1808C2×C6111yescharacteristic, complemented
364#1736C2×C6111yescharacteristic, complemented
365C2×C61—42no—
366C2×C61—42no—
367C2×C61—161no—
368C2×C61#242511yescharacteristic
369C2×C61#305511yescharacteristic
370C2×C61#306111yescharacteristic
371C2×C61#331311yescharacteristic
372C2×C61#331811yescharacteristic
373C2×C61#334311yescharacteristic
374C2×C61#334711yescharacteristic
375C22×M16C22×C6111yescharacteristic
376C23×C8C22×C6111yescharacteristic
377C2×#121—21no—
378C2×#121C22×C6111yescharacteristic
379C2×#121C22×C6111yescharacteristic
380C2×C4×D4C22×C6111yescharacteristic
381C2×#117C22×C6111yescharacteristic
382C22×C4⋊C4C22×C6111yescharacteristic
383#482—24no—
384#435—24no—
385C2×#107C22×C6111yescharacteristic
386C2×#107C22×C6111yescharacteristic
387C2×#107C22×C6111yescharacteristic
388C2×#106C22×C6111yescharacteristic
389C2×C4⋊C8C22×C6111yescharacteristic
390C2×#102C22×C6111yescharacteristic
391C2×#102C22×C6111yescharacteristic
392C2×#102C22×C6111yescharacteristic
393C2×#102C22×C6111yescharacteristic
394C2×C22⋊C8C22×C6111yescharacteristic
395C2×C22⋊C8C22×C6111yescharacteristic
396C2×#97C22×C6111yescharacteristic
397#397—21no—
398#396—21no—
399#394—21no—
400#394—21no—
401#390C22×C6111yescharacteristic
402#389C22×C6111yescharacteristic
403#389C22×C6111yescharacteristic
404#389C22×C6111yescharacteristic
405#388—21no—
406#387—21no—
407#386—21no—
408#380C22×C6111yescharacteristic
409#380C22×C6111yescharacteristic
410#380C22×C6111yescharacteristic
411#380C22×C6111yescharacteristic
412#340C22×C6111yescharacteristic
413#340C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419#340C22×C6111yescharacteristic
420C61#2524311yescharacteristic, direct product factor, Sylow
421C22×D4—21no—
422C22×D4—21no—
423C22×D4D4×C6111yescharacteristic
424C22×D4C23×C6111yescharacteristic
425C23×C4—21no—
426C23×C4C23×C6111yescharacteristic
427C23×C4C23×C6111yescharacteristic
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—41no—
431C22×C8—22no—
432C22×C8—22no—
433C22×C8—41no—
434C22×C8C23×C6111yescharacteristic
435C22×C8C23×C6111yescharacteristic
436C22×C8C23×C6111yescharacteristic
437C22×C8C23×C6111yescharacteristic
438#121—22no—
439#121—22no—
440#121—22no—
441#121—41no—
442#121—44no—
443C4×D4—22no—
444C4×D4—22no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4D4×C6111yescharacteristic
454C2×C4⋊C4C23×C6111yescharacteristic
455C2×C4⋊C4C23×C6111yescharacteristic
456C2×C4⋊C4C23×C6111yescharacteristic
457C2×C4⋊C4C23×C6111yescharacteristic
458C2×C4⋊C4C23×C6111yescharacteristic
459C2×C4⋊C4C23×C6111yescharacteristic
460C2×C4⋊C4C23×C6111yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
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
474#107—22no—
475#107—22no—
476#107—41no—
477#106—22no—
478C4⋊C8—22no—
479#102—22no—
480#102—22no—
481#102—22no—
482#102—41no—
483C22⋊C8—22no—
484C22⋊C8D4×C6114yescomplemented
485#97—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493C24—21no—
494C24C2×D4×C6111yescharacteristic
495C24C2×D4×C6111yescharacteristic
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—41no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—81no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
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—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4C2×D4×C6111yescharacteristic
532C22×C4C2×D4×C6111yescharacteristic
533C22×C4C2×D4×C6111yescharacteristic
534C22×C4C2×D4×C6111yescharacteristic
535C22×C4C2×D4×C6112yes—
536C22×C4#41×C6112yes—
537C22×C4C24×C6111yescharacteristic
538M16—44no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—44no—
549C2×C8C2×D4×C6112yes—
550C2×C8C2×D4×C6112yes—
551C2×C8#41×C6112yes—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—81no—
570C4⋊C4#41×C6112yes—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C42—21no—
583C42—21no—
584C42—42no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23#121×C6112yes—
605C23AGL(1,ℤ/8)×C6112yes—
606C23C22×D4×C6111yescharacteristic
607D4—44no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—84no—
613D4—84no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
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—84no—
655C2×C4#121×C6112yes—
656C2×C4C22×D4×C6111yescharacteristic
657C2×C4C2×#41×C6111yescharacteristic
658C2×C4C2×#41×C6111yescharacteristic
659C2×C4C2×#41×C6111yescharacteristic
660C2×C4H(5,𝔽2)×C6111yescharacteristic
661C2×C42−1+4×C6111yescharacteristic
662C8—22no—
663C8—22no—
664C8—22no—
665C8—41no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C2×#121×C6111yescharacteristic
688C22C61×#54611yescharacteristic
689C22C61×#54711yescharacteristic
690C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
691C22C61×#57511yescharacteristic
692C22C61×#57611yescharacteristic
693C22C61×#57811yescharacteristic
694C4—22no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4C61×#52911yescharacteristic
706C4C61×#53911yescharacteristic
707C4C61×#54611yescharacteristic
708C4C61×#54711yescharacteristic
709C2—42no—
710C2—42no—
711C2—161no—
712C2C61×#242511yescharacteristic
713C2C61×#305511yescharacteristic
714C2C61×#306111yescharacteristic
715C2C61×#331311yescharacteristic
716C2C61×#331811yescharacteristic
717C2C61×#334311yescharacteristic
718C2C61×#334711yescharacteristic
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×#482C2semidirect
2. C2×C61×#435C2semidirect
3. C61×#2485C2semidirect
5. C61×#2087C2semidirect
6. C61×#2077C2semidirect
7. C61×#2067C2semidirect
8. C61×#2033C2semidirect
9. C61×#1943C2semidirect
10. C61×#1936C2semidirect
11. C61×#1895C2semidirect
12. C61×#1893C2semidirect
13. C61×#1852C2semidirect
14. C61×#1808C2semidirect
15. C61×#1736C2semidirect
124. C22⋊C8×C61D4semidirect
306. #25243C61direct (N × H)
350. C2×#482C2×C61semidirect
351. C2×#435C2×C61semidirect
352. #2485C2×C61semidirect
354. #2087C2×C61semidirect
355. #2077C2×C61semidirect
356. #2067C2×C61semidirect
357. #2033C2×C61semidirect
358. #1943C2×C61semidirect
359. #1936C2×C61semidirect
360. #1895C2×C61semidirect
361. #1893C2×C61semidirect
362. #1852C2×C61semidirect
363. #1808C2×C61semidirect
364. #1736C2×C61semidirect
420. C61#25243direct (N × H)
484. 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×#4822
C2×C61×#4352
C61×#24852
C61×#24162
C61×#20872
C61×#20772
C61×#20672
C61×#20332
C61×#19432
C61×#19362
C61×#18952
C61×#18932
C61×#18522
C61×#18082
C61×#17362
#2524361