Finite Group Databasebeta

← C61×#26953 #29530386

Subgroups — C61×#26953 #29530386

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#485C211yesmaximal, characteristic, complemented
2C2×C61×#464C211yesmaximal, characteristic, complemented
3C61×#2426C211yesmaximal, characteristic
4C61×#2362C211yesmaximal, characteristic, complemented
5C61×#2087C211yesmaximal, characteristic, complemented
6C61×#2042C211yesmaximal, characteristic, complemented
7C61×#2001C211yesmaximal, characteristic, complemented
8C61×#2000C211yesmaximal, characteristic
9C61×#1973C211yesmaximal, characteristic, complemented
10C61×#1926C211yesmaximal, characteristic, complemented
11C61×#1924C211yesmaximal, characteristic, complemented
12C61×#1878C211yesmaximal, characteristic, complemented
13C61×#1875C211yesmaximal, characteristic
14C61×#1865C211yesmaximal, characteristic, complemented
15C61×#1763C211yesmaximal, characteristic, complemented
16C22×Q16×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C2×#124×C61C2211yescharacteristic
19C2×C22⋊Q8×C61C2211yescharacteristic
20C2×C22⋊Q8×C61C2211yescharacteristic
21C2×#121×C61C2211yescharacteristic
22C2×C4×Q8×C61C2211yescharacteristic
23C2×C4×Q8×C61C2211yescharacteristic
24C2×#117×C61C2211yescharacteristic
25C61×#485—24no—
26C61×#464—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×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×C22⋊C8×C61C2211yescharacteristic
40C2×#97×C61C2211yescharacteristic
41C61×#396—21no—
42C61×#394—21no—
43C61×#391C2211yescharacteristic
44C61×#390—21no—
45C61×#390C2211yescharacteristic
46C61×#389C2211yescharacteristic
47C61×#389C2211yescharacteristic
48C61×#388—21no—
49C61×#388—21no—
50C61×#388—21no—
51C61×#387—21no—
52C4×C4⋊C4×C61—21no—
53C4×C4⋊C4×C61C2211yescharacteristic
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×C61C2311yescharacteristic
66C2×Q16×C61—22no—
67C2×Q16×C61—22no—
68C2×Q16×C61—41no—
69C2×SD16×C61—22no—
70C2×SD16×C61—22no—
71C2×SD16×C61—41no—
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76#124×C61—22no—
77#124×C61—41no—
78C22⋊Q8×C61—22no—
79C22⋊Q8×C61—22no—
80C22⋊Q8×C61—22no—
81C22⋊Q8×C61—41no—
82#121×C61—22no—
83#121×C61—41no—
84C4×Q8×C61—22no—
85C4×Q8×C61—22no—
86C4×Q8×C61—41no—
87C4×Q8×C61—41no—
88#117×C61—22no—
89#117×C61—41no—
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—21no—
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×C61D411yescharacteristic
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C42×C61—21no—
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—41no—
124#103×C61D414yescomplemented
125#102×C61—22no—
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×C61C2×D412yes—
151C2×Q8×C61#4112yes—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—81no—
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×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180Q16×C61—44no—
181SD16×C61—44no—
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—21no—
192C2×C8×C61—21no—
193C2×C8×C61C2×D412yes—
194C4⋊C4×C61—24no—
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—42no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61—81no—
207C4⋊C4×C61C2×D412yes—
208C4⋊C4×C61#4112yes—
209C4⋊C4×C61#4112yes—
210C22⋊C4×C61—24no—
211C22⋊C4×C61—41no—
212C22⋊C4×C61—41no—
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—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—42no—
225C42×C61—42no—
226C42×C61—42no—
227C42×C61—42no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61C22×D411yescharacteristic
243Q8×C61—22no—
244Q8×C61—22no—
245Q8×C61—22no—
246Q8×C61—22no—
247Q8×C61—41no—
248Q8×C61—41no—
249Q8×C61—41no—
250Q8×C61—41no—
251D4×C61—41no—
252D4×C61—41no—
253D4×C61—41no—
254D4×C61—41no—
255D4×C61—84no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
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×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C61H(5,𝔽2)11yescharacteristic
302C8×C61—22no—
303C8×C61—41no—
304C8×C61—41no—
305C8×C61—41no—
306#26953C6111yesmaximal, characteristic, direct product factor, Sylow
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—81no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61—81no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61—81no—
321C22×C61#52511yescharacteristic
322C22×C61D4211yescharacteristic
323C22×C61#54611yescharacteristic
324C22×C61#57511yescharacteristic
325C22×C61#57511yescharacteristic
326C22×C61#57711yescharacteristic
327C22×C61#57811yescharacteristic
328C4×C61—42no—
329C4×C61—41no—
330C4×C61—42no—
331C4×C61—42no—
332C4×C61—41no—
333C4×C61—42no—
334C4×C61—41no—
335C4×C61—41no—
336C4×C61—41no—
337C4×C61—42no—
338C4×C61—81no—
339C4×C61—81no—
340C4×C61#53211yescharacteristic
341C4×C61#54011yescharacteristic
342C4×C61#54611yescharacteristic
343C4×C61#55311yescharacteristic
344C2×#485C2×C6111yescharacteristic, complemented
345C2×#464C2×C6111yescharacteristic, complemented
346#2426C2×C6111yescharacteristic
347#2362C2×C6111yescharacteristic, complemented
348#2087C2×C6111yescharacteristic, complemented
349#2042C2×C6111yescharacteristic, complemented
350#2001C2×C6111yescharacteristic, complemented
351#2000C2×C6111yescharacteristic
352#1973C2×C6111yescharacteristic, complemented
353#1926C2×C6111yescharacteristic, complemented
354#1924C2×C6111yescharacteristic, complemented
355#1878C2×C6111yescharacteristic, complemented
356#1875C2×C6111yescharacteristic
357#1865C2×C6111yescharacteristic, complemented
358#1763C2×C6111yescharacteristic, complemented
359C2×C61—81no—
360C2×C61—161no—
361C2×C61#246411yescharacteristic
362C2×C61#311111yescharacteristic
363C2×C61#312111yescharacteristic
364C2×C61#326911yescharacteristic
365C2×C61#327111yescharacteristic
366C2×C61#331311yescharacteristic
367C2×C61#332311yescharacteristic
368C22×Q16C22×C6111yescharacteristic
369C22×SD16C22×C6111yescharacteristic
370C2×#124C22×C6111yescharacteristic
371C2×C22⋊Q8C22×C6111yescharacteristic
372C2×C22⋊Q8C22×C6111yescharacteristic
373C2×#121C22×C6111yescharacteristic
374C2×C4×Q8C22×C6111yescharacteristic
375C2×C4×Q8C22×C6111yescharacteristic
376C2×#117C22×C6111yescharacteristic
377#485—24no—
378#464—24no—
379C2×#107C22×C6111yescharacteristic
380C2×#106C22×C6111yescharacteristic
381C2×C4⋊C8C22×C6111yescharacteristic
382C2×#103C22×C6111yescharacteristic
383C2×#103C22×C6111yescharacteristic
384C2×#103C22×C6111yescharacteristic
385C2×#103C22×C6111yescharacteristic
386C2×#103C22×C6111yescharacteristic
387C2×#102C22×C6111yescharacteristic
388C2×#102C22×C6111yescharacteristic
389C2×#102C22×C6111yescharacteristic
390C2×C22⋊C8C22×C6111yescharacteristic
391C2×C22⋊C8C22×C6111yescharacteristic
392C2×#97C22×C6111yescharacteristic
393#396—21no—
394#394—21no—
395#391C22×C6111yescharacteristic
396#390—21no—
397#390C22×C6111yescharacteristic
398#389C22×C6111yescharacteristic
399#389C22×C6111yescharacteristic
400#388—21no—
401#388—21no—
402#388—21no—
403#387—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4C22×C6111yescharacteristic
406C4×C22⋊C4C22×C6111yescharacteristic
407#340C22×C6111yescharacteristic
408#340C22×C6111yescharacteristic
409#340C22×C6111yescharacteristic
410#340C22×C6111yescharacteristic
411#336C22×C6111yescharacteristic
412#336C22×C6111yescharacteristic
413C61#2695311yescharacteristic, direct product factor, Sylow
414C22×Q8C23×C6111yescharacteristic
415C22×Q8C23×C6111yescharacteristic
416C22×D4—21no—
417C22×D4C23×C6111yescharacteristic
418C23×C4C23×C6111yescharacteristic
419C2×Q16—22no—
420C2×Q16—22no—
421C2×Q16—41no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—41no—
425C22×C8C23×C6111yescharacteristic
426C22×C8C23×C6111yescharacteristic
427C22×C8C23×C6111yescharacteristic
428C22×C8C23×C6111yescharacteristic
429#124—22no—
430#124—41no—
431C22⋊Q8—22no—
432C22⋊Q8—22no—
433C22⋊Q8—22no—
434C22⋊Q8—41no—
435#121—22no—
436#121—41no—
437C4×Q8—22no—
438C4×Q8—22no—
439C4×Q8—41no—
440C4×Q8—41no—
441#117—22no—
442#117—41no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
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⋊C4D4×C6111yescharacteristic
463C2×C22⋊C4D4×C6111yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C6111yescharacteristic
469C2×C42C23×C6111yescharacteristic
470#107—22no—
471#106—22no—
472C4⋊C8—22no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—41no—
477#103D4×C6114yescomplemented
478#102—22no—
479#102—22no—
480#102—41no—
481C22⋊C8—22no—
482C22⋊C8—41no—
483#97—41no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95D4×C6111yescharacteristic
490#95D4×C6111yescharacteristic
491C24—21no—
492C24C2×D4×C6111yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×D4×C6112yes—
504C2×Q8#41×C6112yes—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—81no—
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×C4C2×D4×C6111yescharacteristic
528C22×C4C2×D4×C6111yescharacteristic
529C22×C4C2×D4×C6111yescharacteristic
530C22×C4C2×D4×C6111yescharacteristic
531C22×C4C2×D4×C6111yescharacteristic
532C22×C4C24×C6111yescharacteristic
533Q16—44no—
534SD16—44no—
535C2×C8—21no—
536C2×C8—21no—
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×C8C2×D4×C6112yes—
547C4⋊C4—24no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4C2×D4×C6112yes—
561C4⋊C4#41×C6112yes—
562C4⋊C4#41×C6112yes—
563C22⋊C4—24no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—42no—
578C42—42no—
579C42—42no—
580C42—42no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C22×D4×C6111yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—22no—
599Q8—22no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
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×C4C22×D4×C6111yescharacteristic
650C2×C4C2×#41×C6111yescharacteristic
651C2×C4C2×#41×C6111yescharacteristic
652C2×C4C2×#41×C6111yescharacteristic
653C2×C4H(5,𝔽2)×C6111yescharacteristic
654C2×C4H(5,𝔽2)×C6111yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C61×#52511yescharacteristic
674C22D42×C6111yescharacteristic
675C22C61×#54611yescharacteristic
676C22C61×#57511yescharacteristic
677C22C61×#57511yescharacteristic
678C22C61×#57711yescharacteristic
679C22C61×#57811yescharacteristic
680C4—41no—
681C4—41no—
682C4—42no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—42no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—81no—
691C4—81no—
692C4C61×#53211yescharacteristic
693C4C61×#54011yescharacteristic
694C4C61×#54611yescharacteristic
695C4C61×#55311yescharacteristic
696C2—81no—
697C2—161no—
698C2C61×#246411yescharacteristic
699C2C61×#311111yescharacteristic
700C2C61×#312111yescharacteristic
701C2C61×#326911yescharacteristic
702C2C61×#327111yescharacteristic
703C2C61×#331311yescharacteristic
704C2C61×#332311yescharacteristic
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×#464C2semidirect
4. C61×#2362C2semidirect
5. C61×#2087C2semidirect
6. C61×#2042C2semidirect
7. C61×#2001C2semidirect
9. C61×#1973C2semidirect
10. C61×#1926C2semidirect
11. C61×#1924C2semidirect
12. C61×#1878C2semidirect
14. C61×#1865C2semidirect
15. C61×#1763C2semidirect
124. #103×C61D4semidirect
306. #26953C61direct (N × H)
344. C2×#485C2×C61semidirect
345. C2×#464C2×C61semidirect
347. #2362C2×C61semidirect
348. #2087C2×C61semidirect
349. #2042C2×C61semidirect
350. #2001C2×C61semidirect
352. #1973C2×C61semidirect
353. #1926C2×C61semidirect
354. #1924C2×C61semidirect
355. #1878C2×C61semidirect
357. #1865C2×C61semidirect
358. #1763C2×C61semidirect
413. C61#26953direct (N × H)
477. #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×#4642
C61×#24262
C61×#23622
C61×#20872
C61×#20422
C61×#20012
C61×#20002
C61×#19732
C61×#19262
C61×#19242
C61×#18782
C61×#18752
C61×#18652
C61×#17632
#2695361