Finite Group Databasebeta

← C61×#25235 #29528668

Subgroups — C61×#25235 #29528668

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#482C211yesmaximal, characteristic, complemented
2C2×C8×D4×C61C211yesmaximal, characteristic, complemented
3C61×#2485C211yesmaximal, characteristic, complemented
4C61×#2414C211yesmaximal, characteristic
5C61×#2087C211yesmaximal, characteristic, complemented
6C61×#2077C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#1941C211yesmaximal, characteristic, complemented
10C61×#1934C211yesmaximal, characteristic, complemented
11C61×#1893C211yesmaximal, characteristic, complemented
12C61×#1893C211yesmaximal, characteristic, complemented
13C61×#1854C211yesmaximal, characteristic, complemented
14C61×#1808C211yesmaximal, characteristic, complemented
15C61×#1735C211yesmaximal, characteristic, complemented
16C23×C8×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×#121×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×C4×D4×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C2×#117×C61C2211yescharacteristic
23C61×#482—24no—
24C8×D4×C61—24no—
25C2×#107×C61C2211yescharacteristic
26C2×#107×C61C2211yescharacteristic
27C2×#106×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×C4×C8×C61C2211yescharacteristic
37C61×#397—21no—
38C61×#394—21no—
39C61×#394—21no—
40C61×#392—21no—
41C61×#390—21no—
42C61×#390C2211yescharacteristic
43C61×#389C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#389C2211yescharacteristic
46C61×#388—21no—
47C61×#388—21no—
48C61×#387—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×C61C2311yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—22no—
68C22×C8×C61—22no—
69C22×C8×C61—22no—
70C22×C8×C61—22no—
71C22×C8×C61—41no—
72C22×C8×C61—41no—
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77#121×C61—22no—
78#121×C61—22no—
79#121×C61—22no—
80#121×C61—41no—
81C4×D4×C61—22no—
82C4×D4×C61—22no—
83#117×C61—22no—
84#117×C61—22no—
85#117×C61—22no—
86#117×C61—41no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61D411yescharacteristic
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C4⋊C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C4⋊C4×C61C2311yescharacteristic
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
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×C61D411yescharacteristic
109C2×C22⋊C4×C61D411yescharacteristic
110C2×C42×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61C2311yescharacteristic
113#107×C61—22no—
114#107×C61—41no—
115#106×C61—22no—
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
124C4×C8×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—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—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×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D412yes—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61#4112yes—
173C22×C4×C61C2411yescharacteristic
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—44no—
184C2×C8×C61—44no—
185C2×C8×C61C2×D412yes—
186C2×C8×C61C2×D412yes—
187C2×C8×C61#4112yes—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
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—42no—
203C4⋊C4×C61—81no—
204C4⋊C4×C61—81no—
205C4⋊C4×C61#4112yes—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—81no—
215C22⋊C4×C61—81no—
216C22⋊C4×C61—81no—
217C22⋊C4×C61—81no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—42no—
221C42×C61—42no—
222C23×C61—21no—
223C23×C61—21no—
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—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61#12112yes—
242C23×C61#13512yes—
243C23×C61C22×D411yescharacteristic
244D4×C61—28no—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—41no—
248D4×C61—41no—
249D4×C61—84no—
250D4×C61—84no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
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—22no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
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#12112yes—
291C2×C4×C61#13512yes—
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×C4×C612−1+411yescharacteristic
298C8×C61—22no—
299C8×C61—22no—
300C8×C61—22no—
301C8×C61—41no—
302#25235C6111yesmaximal, characteristic, direct product factor, Sylow
303C22×C61—22no—
304C22×C61—22no—
305C22×C61—22no—
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—81no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61C2×#12111yescharacteristic
325C22×C61#54611yescharacteristic
326C22×C61#54711yescharacteristic
327C22×C61C2×#13511yescharacteristic
328C22×C61C2×#13511yescharacteristic
329C22×C61#57611yescharacteristic
330C22×C61#57711yescharacteristic
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—41no—
334C4×C61—42no—
335C4×C61—41no—
336C4×C61—81no—
337C4×C61—81no—
338C4×C61—81no—
339C4×C61—81no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61#52911yescharacteristic
343C4×C61#53911yescharacteristic
344C4×C61#54611yescharacteristic
345C4×C61#54711yescharacteristic
346C2×#482C2×C6111yescharacteristic, complemented
347C2×C8×D4C2×C6111yescharacteristic, complemented
348#2485C2×C6111yescharacteristic, complemented
349#2414C2×C6111yescharacteristic
350#2087C2×C6111yescharacteristic, complemented
351#2077C2×C6111yescharacteristic, complemented
352#2067C2×C6111yescharacteristic, complemented
353#2034C2×C6111yescharacteristic, complemented
354#1941C2×C6111yescharacteristic, complemented
355#1934C2×C6111yescharacteristic, complemented
356#1893C2×C6111yescharacteristic, complemented
357#1893C2×C6111yescharacteristic, complemented
358#1854C2×C6111yescharacteristic, complemented
359#1808C2×C6111yescharacteristic, complemented
360#1735C2×C6111yescharacteristic, complemented
361C2×C61—42no—
362C2×C61—42no—
363C2×C61—161no—
364C2×C61#242511yescharacteristic
365C2×C61#305011yescharacteristic
366C2×C61#306211yescharacteristic
367C2×C61#329611yescharacteristic
368C2×C61#330511yescharacteristic
369C2×C61#333911yescharacteristic
370C2×C61#334011yescharacteristic
371C23×C8C22×C6111yescharacteristic
372C23×C8C22×C6111yescharacteristic
373C2×#121C22×C6111yescharacteristic
374C2×#121C22×C6111yescharacteristic
375C2×C4×D4C22×C6111yescharacteristic
376C2×#117C22×C6111yescharacteristic
377C2×#117C22×C6111yescharacteristic
378#482—24no—
379C8×D4—24no—
380C2×#107C22×C6111yescharacteristic
381C2×#107C22×C6111yescharacteristic
382C2×#106C22×C6111yescharacteristic
383C2×#106C22×C6111yescharacteristic
384C2×C4⋊C8C22×C6111yescharacteristic
385C2×#102C22×C6111yescharacteristic
386C2×#102C22×C6111yescharacteristic
387C2×#102C22×C6111yescharacteristic
388C2×#102C22×C6111yescharacteristic
389C2×C22⋊C8C22×C6111yescharacteristic
390C2×C22⋊C8C22×C6111yescharacteristic
391C2×C4×C8C22×C6111yescharacteristic
392#397—21no—
393#394—21no—
394#394—21no—
395#392—21no—
396#390—21no—
397#390C22×C6111yescharacteristic
398#389C22×C6111yescharacteristic
399#389C22×C6111yescharacteristic
400#389C22×C6111yescharacteristic
401#388—21no—
402#388—21no—
403#387—21no—
404#380C22×C6111yescharacteristic
405#380C22×C6111yescharacteristic
406#380C22×C6111yescharacteristic
407#380C22×C6111yescharacteristic
408#340C22×C6111yescharacteristic
409#340C22×C6111yescharacteristic
410#340C22×C6111yescharacteristic
411#340C22×C6111yescharacteristic
412#340C22×C6111yescharacteristic
413#340C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416C61#2523511yescharacteristic, direct product factor, Sylow
417C22×D4—21no—
418C22×D4—21no—
419C22×D4D4×C6111yescharacteristic
420C22×D4C23×C6111yescharacteristic
421C23×C4C23×C6111yescharacteristic
422C23×C4C23×C6111yescharacteristic
423C22×C8—22no—
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—22no—
427C22×C8—41no—
428C22×C8—41no—
429C22×C8C23×C6111yescharacteristic
430C22×C8C23×C6111yescharacteristic
431C22×C8C23×C6111yescharacteristic
432C22×C8C23×C6111yescharacteristic
433#121—22no—
434#121—22no—
435#121—22no—
436#121—41no—
437C4×D4—22no—
438C4×D4—22no—
439#117—22no—
440#117—22no—
441#117—22no—
442#117—41no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4D4×C6111yescharacteristic
447C2×C4⋊C4C23×C6111yescharacteristic
448C2×C4⋊C4C23×C6111yescharacteristic
449C2×C4⋊C4C23×C6111yescharacteristic
450C2×C4⋊C4C23×C6111yescharacteristic
451C2×C4⋊C4C23×C6111yescharacteristic
452C2×C4⋊C4C23×C6111yescharacteristic
453C2×C4⋊C4C23×C6111yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4D4×C6111yescharacteristic
465C2×C22⋊C4D4×C6111yescharacteristic
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C6111yescharacteristic
469#107—22no—
470#107—41no—
471#106—22no—
472#106—22no—
473C4⋊C8—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—41no—
478C22⋊C8—22no—
479C22⋊C8D4×C6114yescomplemented
480C4×C8—22no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488C24—21no—
489C24C2×D4×C6111yescharacteristic
490C24C2×D4×C6111yescharacteristic
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4—81no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
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×C4C2×D4×C6111yescharacteristic
524C22×C4C2×D4×C6111yescharacteristic
525C22×C4C2×D4×C6111yescharacteristic
526C22×C4C2×D4×C6112yes—
527C22×C4C2×D4×C6111yescharacteristic
528C22×C4#41×C6112yes—
529C22×C4C24×C6111yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—44no—
540C2×C8—44no—
541C2×C8C2×D4×C6112yes—
542C2×C8C2×D4×C6112yes—
543C2×C8#41×C6112yes—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4—81no—
561C4⋊C4#41×C6112yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—42no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23#121×C6112yes—
598C23#135×C6112yes—
599C23C22×D4×C6111yescharacteristic
600D4—28no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—84no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
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#121×C6112yes—
647C2×C4#135×C6112yes—
648C2×C4C22×D4×C6111yescharacteristic
649C2×C4C2×#41×C6111yescharacteristic
650C2×C4C2×#41×C6111yescharacteristic
651C2×C4C2×#41×C6111yescharacteristic
652C2×C4H(5,𝔽2)×C6111yescharacteristic
653C2×C42−1+4×C6111yescharacteristic
654C8—22no—
655C8—22no—
656C8—22no—
657C8—41no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×#121×C6111yescharacteristic
680C22C61×#54611yescharacteristic
681C22C61×#54711yescharacteristic
682C22C2×#135×C6111yescharacteristic
683C22C2×#135×C6111yescharacteristic
684C22C61×#57611yescharacteristic
685C22C61×#57711yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C61×#52911yescharacteristic
698C4C61×#53911yescharacteristic
699C4C61×#54611yescharacteristic
700C4C61×#54711yescharacteristic
701C2—42no—
702C2—42no—
703C2—161no—
704C2C61×#242511yescharacteristic
705C2C61×#305011yescharacteristic
706C2C61×#306211yescharacteristic
707C2C61×#329611yescharacteristic
708C2C61×#330511yescharacteristic
709C2C61×#333911yescharacteristic
710C2C61×#334011yescharacteristic
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×#482C2semidirect
2. C2×C8×D4×C61C2semidirect
3. C61×#2485C2semidirect
5. C61×#2087C2semidirect
6. C61×#2077C2semidirect
7. C61×#2067C2semidirect
8. C61×#2034C2semidirect
9. C61×#1941C2semidirect
10. C61×#1934C2semidirect
11. C61×#1893C2semidirect
12. C61×#1893C2semidirect
13. C61×#1854C2semidirect
14. C61×#1808C2semidirect
15. C61×#1735C2semidirect
123. C22⋊C8×C61D4semidirect
302. #25235C61direct (N × H)
346. C2×#482C2×C61semidirect
347. C2×C8×D4C2×C61semidirect
348. #2485C2×C61semidirect
350. #2087C2×C61semidirect
351. #2077C2×C61semidirect
352. #2067C2×C61semidirect
353. #2034C2×C61semidirect
354. #1941C2×C61semidirect
355. #1934C2×C61semidirect
356. #1893C2×C61semidirect
357. #1893C2×C61semidirect
358. #1854C2×C61semidirect
359. #1808C2×C61semidirect
360. #1735C2×C61semidirect
416. C61#25235direct (N × H)
479. 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×C8×D4×C612
C61×#24852
C61×#24142
C61×#20872
C61×#20772
C61×#20672
C61×#20342
C61×#19412
C61×#19342
C61×#18932
C61×#18542
C61×#18082
C61×#17352
#2523561