Finite Group Databasebeta

← C61×#26956 #29530389

Subgroups — C61×#26956 #29530389

Order 15616.

892 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×#485C211yesmaximal, characteristic, complemented
2C2×C61×#461C211yesmaximal, characteristic, complemented
3C61×#2429C211yesmaximal, characteristic, complemented
4C61×#2363C211yesmaximal, characteristic
5C61×#2087C211yesmaximal, characteristic, complemented
6C61×#2043C211yesmaximal, characteristic, complemented
7C61×#2000C211yesmaximal, characteristic
8C61×#2000C211yesmaximal, characteristic
9C61×#1973C211yesmaximal, characteristic, complemented
10C61×#1927C211yesmaximal, characteristic, complemented
11C61×#1924C211yesmaximal, characteristic, complemented
12C61×#1880C211yesmaximal, characteristic, complemented
13C61×#1873C211yesmaximal, characteristic, complemented
14C61×#1864C211yesmaximal, characteristic, complemented
15C61×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C2×C4⋊Q8×C61C2211yescharacteristic
19C2×C22⋊Q8×C61C2211yescharacteristic
20C2×C22⋊Q8×C61C2211yescharacteristic
21C2×#121×C61C2211yescharacteristic
22C2×C4×Q8×C61C2211yescharacteristic
23C2×C4×D4×C61C2211yescharacteristic
24C2×#117×C61C2211yescharacteristic
25C61×#485—24no—
26C61×#461—24no—
27C2×#107×C61C2211yescharacteristic
28C2×#106×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#103×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×C22⋊C8×C61C2211yescharacteristic
40C2×#97×C61C2211yescharacteristic
41C61×#398—21no—
42C61×#396—21no—
43C61×#391C2211yescharacteristic
44C61×#390—21no—
45C61×#390C2211yescharacteristic
46C61×#389—21no—
47C61×#389C2211yescharacteristic
48C61×#389C2211yescharacteristic
49C61×#388—21no—
50C61×#388—21no—
51C61×#386—21no—
52C4×C4⋊C4×C61C2211yescharacteristic
53C4×C22⋊C4×C61—21no—
54C4×C22⋊C4×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×Q8×C61C2311yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61C2311yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C2×SD16×C61—22no—
68C2×SD16×C61—22no—
69C2×SD16×C61—22no—
70C2×SD16×C61—22no—
71C2×SD16×C61—41no—
72C2×SD16×C61—41no—
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77C4⋊Q8×C61—22no—
78C4⋊Q8×C61—41no—
79C22⋊Q8×C61—22no—
80C22⋊Q8×C61—22no—
81C22⋊Q8×C61—41no—
82C22⋊Q8×C61—41no—
83#121×C61—22no—
84#121×C61—22no—
85C4×Q8×C61—22no—
86C4×Q8×C61—41no—
87C4×D4×C61—22no—
88C4×D4×C61—41no—
89#117×C61—22no—
90#117×C61—41no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117#107×C61—22no—
118#106×C61—22no—
119C4⋊C8×C61—22no—
120#103×C61—22no—
121#103×C61—22no—
122#103×C61—22no—
123#103×C61—22no—
124#103×C61—41no—
125#103×C61D414yescomplemented
126#102×C61—22no—
127#102×C61—41no—
128C22⋊C8×C61—22no—
129C22⋊C8×C61—41no—
130#97×C61—41no—
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61D411yescharacteristic
137#95×C61D411yescharacteristic
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61C2×D412yes—
152C2×D4×C61—24no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—81no—
159C2×D4×C61—81no—
160C2×D4×C61#4112yes—
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—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—81no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183SD16×C61—44no—
184SD16×C61—44no—
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—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61C2×D412yes—
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—42no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—81no—
211C4⋊C4×C61C2×D412yes—
212C4⋊C4×C61#4112yes—
213C4⋊C4×C61#4112yes—
214C22⋊C4×C61—24no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—41no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—81no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—42no—
228C42×C61—42no—
229C42×C61—81no—
230C23×C61—22no—
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×C61C22×D411yescharacteristic
245Q8×C61—22no—
246Q8×C61—22no—
247Q8×C61—41no—
248Q8×C61—41no—
249Q8×C61—41no—
250Q8×C61—41no—
251Q8×C61—41no—
252Q8×C61—41no—
253D4×C61—22no—
254D4×C61—22no—
255D4×C61—41no—
256D4×C61—41no—
257D4×C61—84no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
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—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
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—41no—
297C2×C4×C61—84no—
298C2×C4×C61#13712yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C8×C61—22no—
306C8×C61—41no—
307C8×C61—41no—
308C8×C61—41no—
309#26956C6111yesmaximal, characteristic, direct product factor, Sylow
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—42no—
313C22×C61—41no—
314C22×C61—42no—
315C22×C61—41no—
316C22×C61—42no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61#52511yescharacteristic
325C22×C61D4211yescharacteristic
326C22×C61#54611yescharacteristic
327C22×C61C2×#13711yescharacteristic
328C22×C61#57511yescharacteristic
329C22×C61#57711yescharacteristic
330C22×C61#57711yescharacteristic
331C4×C61—22no—
332C4×C61—41no—
333C4×C61—42no—
334C4×C61—41no—
335C4×C61—42no—
336C4×C61—42no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—42no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61#53211yescharacteristic
344C4×C61#54011yescharacteristic
345C4×C61#54611yescharacteristic
346C4×C61#55311yescharacteristic
347C2×#485C2×C6111yescharacteristic, complemented
348C2×#461C2×C6111yescharacteristic, complemented
349#2429C2×C6111yescharacteristic, complemented
350#2363C2×C6111yescharacteristic
351#2087C2×C6111yescharacteristic, complemented
352#2043C2×C6111yescharacteristic, complemented
353#2000C2×C6111yescharacteristic
354#2000C2×C6111yescharacteristic
355#1973C2×C6111yescharacteristic, complemented
356#1927C2×C6111yescharacteristic, complemented
357#1924C2×C6111yescharacteristic, complemented
358#1880C2×C6111yescharacteristic, complemented
359#1873C2×C6111yescharacteristic, complemented
360#1864C2×C6111yescharacteristic, complemented
361#1763C2×C6111yescharacteristic, complemented
362C2×C61—81no—
363C2×C61—82no—
364C2×C61#246411yescharacteristic
365C2×C61#311611yescharacteristic
366C2×C61#312311yescharacteristic
367C2×C61#326611yescharacteristic
368C2×C61#327111yescharacteristic
369C2×C61#330711yescharacteristic
370C2×C61#332911yescharacteristic
371C22×SD16C22×C6111yescharacteristic
372C22×SD16C22×C6111yescharacteristic
373C2×C4⋊Q8C22×C6111yescharacteristic
374C2×C22⋊Q8C22×C6111yescharacteristic
375C2×C22⋊Q8C22×C6111yescharacteristic
376C2×#121C22×C6111yescharacteristic
377C2×C4×Q8C22×C6111yescharacteristic
378C2×C4×D4C22×C6111yescharacteristic
379C2×#117C22×C6111yescharacteristic
380#485—24no—
381#461—24no—
382C2×#107C22×C6111yescharacteristic
383C2×#106C22×C6111yescharacteristic
384C2×C4⋊C8C22×C6111yescharacteristic
385C2×#103C22×C6111yescharacteristic
386C2×#103C22×C6111yescharacteristic
387C2×#103C22×C6111yescharacteristic
388C2×#103C22×C6111yescharacteristic
389C2×#103C22×C6111yescharacteristic
390C2×#103C22×C6111yescharacteristic
391C2×#102C22×C6111yescharacteristic
392C2×#102C22×C6111yescharacteristic
393C2×C22⋊C8C22×C6111yescharacteristic
394C2×C22⋊C8C22×C6111yescharacteristic
395C2×#97C22×C6111yescharacteristic
396#398—21no—
397#396—21no—
398#391C22×C6111yescharacteristic
399#390—21no—
400#390C22×C6111yescharacteristic
401#389—21no—
402#389C22×C6111yescharacteristic
403#389C22×C6111yescharacteristic
404#388—21no—
405#388—21no—
406#386—21no—
407C4×C4⋊C4C22×C6111yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4C22×C6111yescharacteristic
410#340C22×C6111yescharacteristic
411#340C22×C6111yescharacteristic
412#340C22×C6111yescharacteristic
413#340C22×C6111yescharacteristic
414#336C22×C6111yescharacteristic
415#336C22×C6111yescharacteristic
416C61#2695611yescharacteristic, direct product factor, Sylow
417C22×Q8C23×C6111yescharacteristic
418C22×Q8C23×C6111yescharacteristic
419C22×D4—21no—
420C22×D4C23×C6111yescharacteristic
421C23×C4—21no—
422C23×C4C23×C6111yescharacteristic
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—22no—
426C2×SD16—22no—
427C2×SD16—41no—
428C2×SD16—41no—
429C22×C8C23×C6111yescharacteristic
430C22×C8C23×C6111yescharacteristic
431C22×C8C23×C6111yescharacteristic
432C22×C8C23×C6111yescharacteristic
433C4⋊Q8—22no—
434C4⋊Q8—41no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—41no—
438C22⋊Q8—41no—
439#121—22no—
440#121—22no—
441C4×Q8—22no—
442C4×Q8—41no—
443C4×D4—22no—
444C4×D4—41no—
445#117—22no—
446#117—41no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
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⋊C4D4×C6111yescharacteristic
467C2×C22⋊C4D4×C6111yescharacteristic
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C6111yescharacteristic
472C2×C42C23×C6111yescharacteristic
473#107—22no—
474#106—22no—
475C4⋊C8—22no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103—22no—
480#103—41no—
481#103D4×C6114yescomplemented
482#102—22no—
483#102—41no—
484C22⋊C8—22no—
485C22⋊C8—41no—
486#97—41no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95D4×C6111yescharacteristic
493#95D4×C6111yescharacteristic
494C24—21no—
495C24C2×D4×C6111yescharacteristic
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8C2×D4×C6112yes—
508C2×D4—24no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—81no—
515C2×D4—81no—
516C2×D4#41×C6112yes—
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—42no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4C2×D4×C6111yescharacteristic
534C22×C4C2×D4×C6111yescharacteristic
535C22×C4C2×D4×C6111yescharacteristic
536C22×C4C2×D4×C6111yescharacteristic
537C22×C4C2×D4×C6111yescharacteristic
538C22×C4C24×C6111yescharacteristic
539SD16—44no—
540SD16—44no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8C2×D4×C6112yes—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—81no—
567C4⋊C4C2×D4×C6112yes—
568C4⋊C4#41×C6112yes—
569C4⋊C4#41×C6112yes—
570C22⋊C4—24no—
571C22⋊C4—22no—
572C22⋊C4—41no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—81no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—42no—
584C42—42no—
585C42—81no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—21no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C22×D4×C6111yescharacteristic
601Q8—22no—
602Q8—22no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609D4—22no—
610D4—22no—
611D4—41no—
612D4—41no—
613D4—84no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
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—84no—
654C2×C4#137×C6112yes—
655C2×C4C22×D4×C6111yescharacteristic
656C2×C4C2×#41×C6111yescharacteristic
657C2×C4C2×#41×C6111yescharacteristic
658C2×C4C2×#41×C6111yescharacteristic
659C2×C4H(5,𝔽2)×C6111yescharacteristic
660C2×C4H(5,𝔽2)×C6111yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—42no—
673C22—41no—
674C22—41no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C61×#52511yescharacteristic
680C22D42×C6111yescharacteristic
681C22C61×#54611yescharacteristic
682C22C2×#137×C6111yescharacteristic
683C22C61×#57511yescharacteristic
684C22C61×#57711yescharacteristic
685C22C61×#57711yescharacteristic
686C4—22no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—42no—
693C4—42no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C61×#53211yescharacteristic
699C4C61×#54011yescharacteristic
700C4C61×#54611yescharacteristic
701C4C61×#55311yescharacteristic
702C2—81no—
703C2—82no—
704C2C61×#246411yescharacteristic
705C2C61×#311611yescharacteristic
706C2C61×#312311yescharacteristic
707C2C61×#326611yescharacteristic
708C2C61×#327111yescharacteristic
709C2C61×#330711yescharacteristic
710C2C61×#332911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#485C2semidirect
2. C2×C61×#461C2semidirect
3. C61×#2429C2semidirect
5. C61×#2087C2semidirect
6. C61×#2043C2semidirect
9. C61×#1973C2semidirect
10. C61×#1927C2semidirect
11. C61×#1924C2semidirect
12. C61×#1880C2semidirect
13. C61×#1873C2semidirect
14. C61×#1864C2semidirect
15. C61×#1763C2semidirect
125. #103×C61D4semidirect
309. #26956C61direct (N × H)
347. C2×#485C2×C61semidirect
348. C2×#461C2×C61semidirect
349. #2429C2×C61semidirect
351. #2087C2×C61semidirect
352. #2043C2×C61semidirect
355. #1973C2×C61semidirect
356. #1927C2×C61semidirect
357. #1924C2×C61semidirect
358. #1880C2×C61semidirect
359. #1873C2×C61semidirect
360. #1864C2×C61semidirect
361. #1763C2×C61semidirect
416. C61#26956direct (N × H)
481. #103D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4852
C2×C61×#4612
C61×#24292
C61×#23632
C61×#20872
C61×#20432
C61×#20002
C61×#19732
C61×#19272
C61×#19242
C61×#18802
C61×#18732
C61×#18642
C61×#17632
#2695661