Finite Group Databasebeta

← C61×#25240 #29528673

Subgroups — C61×#25240 #29528673

Order 15616.

900 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#480C211yesmaximal, characteristic, complemented
2C2×C61×#435C211yesmaximal, characteristic, complemented
3C61×#2487C211yesmaximal, characteristic, complemented
4C61×#2414C211yesmaximal, characteristic
5C61×#2086C211yesmaximal, characteristic, complemented
6C61×#2076C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#1944C211yesmaximal, characteristic, complemented
10C61×#1936C211yesmaximal, characteristic, complemented
11C61×#1895C211yesmaximal, characteristic, complemented
12C61×#1893C211yesmaximal, characteristic, complemented
13C61×#1854C211yesmaximal, characteristic, complemented
14C61×#1808C211yesmaximal, characteristic, complemented
15C61×#1736C211yesmaximal, characteristic, complemented
16C22×M16×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×#121×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×C4×D4×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C61×#480—24no—
24C61×#435—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#107×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#102×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×C22⋊C8×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2211yescharacteristic
36C2×#97×C61C2211yescharacteristic
37C61×#400—21no—
38C61×#399—21no—
39C61×#394—21no—
40C61×#392—21no—
41C61×#390—21no—
42C61×#390C2211yescharacteristic
43C61×#389C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#389C2211yescharacteristic
46C61×#388—21no—
47C61×#386—21no—
48C61×#385—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—
82C4×D4×C61—22no—
83C4×D4×C61—22no—
84#117×C61—22no—
85#117×C61—41no—
86C2×C4⋊C4×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×C61D411yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
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×C22⋊C4×C61—21no—
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×C61D411yescharacteristic
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C42×C61—21no—
112C2×C42×C61C2311yescharacteristic
113#107×C61—22no—
114#107×C61—22no—
115#107×C61—41no—
116#106×C61—22no—
117C4⋊C8×C61—22no—
118#102×C61—22no—
119#102×C61—22no—
120#102×C61—22no—
121#102×C61—41no—
122C22⋊C8×C61—22no—
123C22⋊C8×C61D414yescomplemented
124#97×C61—22no—
125#95×C61—21no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132C24×C61—21no—
133C24×C61C2×D411yescharacteristic
134C24×C61C2×D411yescharacteristic
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—41no—
144C2×D4×C61—42no—
145C2×D4×C61—42no—
146C2×D4×C61—42no—
147C2×D4×C61—81no—
148C2×D4×C61—81no—
149C2×D4×C61—81no—
150C22×C4×C61—21no—
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—42no—
168C22×C4×C61—81no—
169C22×C4×C61—81no—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D412yes—
175C22×C4×C61#4112yes—
176C22×C4×C61C2411yescharacteristic
177M16×C61—44no—
178C2×C8×C61—21no—
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—44no—
188C2×C8×C61C2×D412yes—
189C2×C8×C61C2×D412yes—
190C2×C8×C61#4112yes—
191C4⋊C4×C61—22no—
192C4⋊C4×C61—21no—
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—42no—
206C4⋊C4×C61—81no—
207C4⋊C4×C61—81no—
208C4⋊C4×C61—81no—
209C4⋊C4×C61#4112yes—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—81no—
218C22⋊C4×C61—81no—
219C22⋊C4×C61—81no—
220C22⋊C4×C61—81no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—42no—
224C23×C61—21no—
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—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61#12112yes—
244C23×C61#13712yes—
245C23×C61C22×D411yescharacteristic
246D4×C61—44no—
247D4×C61—41no—
248D4×C61—41no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—84no—
252D4×C61—84no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—22no—
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—41no—
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—84no—
294C2×C4×C61#12112yes—
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×C4×C612−1+411yescharacteristic
301C8×C61—22no—
302C8×C61—22no—
303C8×C61—22no—
304C8×C61—41no—
305#25240C6111yesmaximal, characteristic, direct product factor, Sylow
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61C2×#12111yescharacteristic
328C22×C61#54611yescharacteristic
329C22×C61#54711yescharacteristic
330C22×C61C2×#13711yescharacteristic
331C22×C61#57511yescharacteristic
332C22×C61#57611yescharacteristic
333C22×C61#57611yescharacteristic
334C4×C61—22no—
335C4×C61—41no—
336C4×C61—41no—
337C4×C61—41no—
338C4×C61—42no—
339C4×C61—81no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61#52911yescharacteristic
346C4×C61#53911yescharacteristic
347C4×C61#54611yescharacteristic
348C4×C61#54711yescharacteristic
349C2×#480C2×C6111yescharacteristic, complemented
350C2×#435C2×C6111yescharacteristic, complemented
351#2487C2×C6111yescharacteristic, complemented
352#2414C2×C6111yescharacteristic
353#2086C2×C6111yescharacteristic, complemented
354#2076C2×C6111yescharacteristic, complemented
355#2067C2×C6111yescharacteristic, complemented
356#2034C2×C6111yescharacteristic, complemented
357#1944C2×C6111yescharacteristic, complemented
358#1936C2×C6111yescharacteristic, complemented
359#1895C2×C6111yescharacteristic, complemented
360#1893C2×C6111yescharacteristic, complemented
361#1854C2×C6111yescharacteristic, complemented
362#1808C2×C6111yescharacteristic, complemented
363#1736C2×C6111yescharacteristic, complemented
364C2×C61—42no—
365C2×C61—42no—
366C2×C61—161no—
367C2×C61#242511yescharacteristic
368C2×C61#305611yescharacteristic
369C2×C61#305811yescharacteristic
370C2×C61#330911yescharacteristic
371C2×C61#331411yescharacteristic
372C2×C61#334611yescharacteristic
373C2×C61#334711yescharacteristic
374C22×M16C22×C6111yescharacteristic
375C23×C8C22×C6111yescharacteristic
376C2×#121C22×C6111yescharacteristic
377C2×#121C22×C6111yescharacteristic
378C2×C4×D4C22×C6111yescharacteristic
379C2×#117C22×C6111yescharacteristic
380C22×C4⋊C4C22×C6111yescharacteristic
381#480—24no—
382#435—24no—
383C2×#107C22×C6111yescharacteristic
384C2×#107C22×C6111yescharacteristic
385C2×#107C22×C6111yescharacteristic
386C2×#106C22×C6111yescharacteristic
387C2×C4⋊C8C22×C6111yescharacteristic
388C2×#102C22×C6111yescharacteristic
389C2×#102C22×C6111yescharacteristic
390C2×#102C22×C6111yescharacteristic
391C2×#102C22×C6111yescharacteristic
392C2×C22⋊C8C22×C6111yescharacteristic
393C2×C22⋊C8C22×C6111yescharacteristic
394C2×#97C22×C6111yescharacteristic
395#400—21no—
396#399—21no—
397#394—21no—
398#392—21no—
399#390—21no—
400#390C22×C6111yescharacteristic
401#389C22×C6111yescharacteristic
402#389C22×C6111yescharacteristic
403#389C22×C6111yescharacteristic
404#388—21no—
405#386—21no—
406#385—21no—
407#380C22×C6111yescharacteristic
408#380C22×C6111yescharacteristic
409#380C22×C6111yescharacteristic
410#380C22×C6111yescharacteristic
411#340C22×C6111yescharacteristic
412#340C22×C6111yescharacteristic
413#340C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419C61#2524011yescharacteristic, direct product factor, Sylow
420C22×D4—21no—
421C22×D4—21no—
422C22×D4D4×C6111yescharacteristic
423C22×D4C23×C6111yescharacteristic
424C23×C4—21no—
425C23×C4C23×C6111yescharacteristic
426C23×C4C23×C6111yescharacteristic
427C2×M16—22no—
428C2×M16—22no—
429C2×M16—41no—
430C22×C8—22no—
431C22×C8—22no—
432C22×C8—41no—
433C22×C8C23×C6111yescharacteristic
434C22×C8C23×C6111yescharacteristic
435C22×C8C23×C6111yescharacteristic
436C22×C8C23×C6111yescharacteristic
437#121—22no—
438#121—22no—
439#121—22no—
440#121—41no—
441C4×D4—22no—
442C4×D4—22no—
443#117—22no—
444#117—41no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4D4×C6111yescharacteristic
452C2×C4⋊C4C23×C6111yescharacteristic
453C2×C4⋊C4C23×C6111yescharacteristic
454C2×C4⋊C4C23×C6111yescharacteristic
455C2×C4⋊C4C23×C6111yescharacteristic
456C2×C4⋊C4C23×C6111yescharacteristic
457C2×C4⋊C4C23×C6111yescharacteristic
458C2×C4⋊C4C23×C6111yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
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⋊C4D4×C6111yescharacteristic
469C2×C22⋊C4D4×C6111yescharacteristic
470C2×C42—21no—
471C2×C42C23×C6111yescharacteristic
472#107—22no—
473#107—22no—
474#107—41no—
475#106—22no—
476C4⋊C8—22no—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—41no—
481C22⋊C8—22no—
482C22⋊C8D4×C6114yescomplemented
483#97—22no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491C24—21no—
492C24C2×D4×C6111yescharacteristic
493C24C2×D4×C6111yescharacteristic
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—41no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4—81no—
509C22×C4—21no—
510C22×C4—21no—
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—42no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4C2×D4×C6111yescharacteristic
530C22×C4C2×D4×C6111yescharacteristic
531C22×C4C2×D4×C6111yescharacteristic
532C22×C4C2×D4×C6111yescharacteristic
533C22×C4C2×D4×C6112yes—
534C22×C4#41×C6112yes—
535C22×C4C24×C6111yescharacteristic
536M16—44no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—44no—
547C2×C8C2×D4×C6112yes—
548C2×C8C2×D4×C6112yes—
549C2×C8#41×C6112yes—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
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—42no—
565C4⋊C4—81no—
566C4⋊C4—81no—
567C4⋊C4—81no—
568C4⋊C4#41×C6112yes—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C42—21no—
581C42—21no—
582C42—42no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23#121×C6112yes—
603C23#137×C6112yes—
604C23C22×D4×C6111yescharacteristic
605D4—44no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—84no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
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—84no—
653C2×C4#121×C6112yes—
654C2×C4C22×D4×C6111yescharacteristic
655C2×C4C2×#41×C6111yescharacteristic
656C2×C4C2×#41×C6111yescharacteristic
657C2×C4C2×#41×C6111yescharacteristic
658C2×C4H(5,𝔽2)×C6111yescharacteristic
659C2×C42−1+4×C6111yescharacteristic
660C8—22no—
661C8—22no—
662C8—22no—
663C8—41no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×#121×C6111yescharacteristic
686C22C61×#54611yescharacteristic
687C22C61×#54711yescharacteristic
688C22C2×#137×C6111yescharacteristic
689C22C61×#57511yescharacteristic
690C22C61×#57611yescharacteristic
691C22C61×#57611yescharacteristic
692C4—22no—
693C4—41no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4C61×#52911yescharacteristic
704C4C61×#53911yescharacteristic
705C4C61×#54611yescharacteristic
706C4C61×#54711yescharacteristic
707C2—42no—
708C2—42no—
709C2—161no—
710C2C61×#242511yescharacteristic
711C2C61×#305611yescharacteristic
712C2C61×#305811yescharacteristic
713C2C61×#330911yescharacteristic
714C2C61×#331411yescharacteristic
715C2C61×#334611yescharacteristic
716C2C61×#334711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2414C2
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×C61×#435C2semidirect
3. C61×#2487C2semidirect
5. C61×#2086C2semidirect
6. C61×#2076C2semidirect
7. C61×#2067C2semidirect
8. C61×#2034C2semidirect
9. C61×#1944C2semidirect
10. C61×#1936C2semidirect
11. C61×#1895C2semidirect
12. C61×#1893C2semidirect
13. C61×#1854C2semidirect
14. C61×#1808C2semidirect
15. C61×#1736C2semidirect
123. C22⋊C8×C61D4semidirect
305. #25240C61direct (N × H)
349. C2×#480C2×C61semidirect
350. C2×#435C2×C61semidirect
351. #2487C2×C61semidirect
353. #2086C2×C61semidirect
354. #2076C2×C61semidirect
355. #2067C2×C61semidirect
356. #2034C2×C61semidirect
357. #1944C2×C61semidirect
358. #1936C2×C61semidirect
359. #1895C2×C61semidirect
360. #1893C2×C61semidirect
361. #1854C2×C61semidirect
362. #1808C2×C61semidirect
363. #1736C2×C61semidirect
419. C61#25240direct (N × H)
482. 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×C61×#4352
C61×#24872
C61×#24142
C61×#20862
C61×#20762
C61×#20672
C61×#20342
C61×#19442
C61×#19362
C61×#18952
C61×#18932
C61×#18542
C61×#18082
C61×#17362
#2524061