Finite Group Databasebeta

← C61×#26147 #29529580

Subgroups — C61×#26147 #29529580

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#480C211yesmaximal, characteristic, complemented
2C2×C61×#428C211yesmaximal, characteristic, complemented
3C61×#2416C211yesmaximal, characteristic
4C61×#2352C211yesmaximal, characteristic, complemented
5C61×#2092C211yesmaximal, characteristic, complemented
6C61×#2085C211yesmaximal, characteristic, complemented
7C61×#2077C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#1925C211yesmaximal, characteristic, complemented
10C61×#1921C211yesmaximal, characteristic, complemented
11C61×#1895C211yesmaximal, characteristic, complemented
12C61×#1875C211yesmaximal, characteristic, complemented
13C61×#1870C211yesmaximal, characteristic, complemented
14C61×#1852C211yesmaximal, characteristic, complemented
15C61×#1852C211yesmaximal, characteristic, complemented
16C22×M16×C61C2211yescharacteristic
17C2×#121×C61—21no—
18C2×#121×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×C4×D4×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic
24C61×#480—24no—
25C61×#428—24no—
26C2×#107×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C2×#107×C61C2211yescharacteristic
30C2×#106×C61C2211yescharacteristic
31C2×#106×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C61×#396—21no—
40C61×#394—21no—
41C61×#390C2211yescharacteristic
42C61×#389C2211yescharacteristic
43C61×#388—21no—
44C61×#387—21no—
45C61×#386—21no—
46C61×#386—21no—
47C61×#382C2211yescharacteristic
48C61×#380C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C4×C4⋊C4×C61C2211yescharacteristic
52C4×C22⋊C4×C61—21no—
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61D411yescharacteristic
64C22×D4×C61C2311yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C2×M16×C61—22no—
70C2×M16×C61—22no—
71C2×M16×C61—22no—
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76#121×C61—22no—
77#121×C61—22no—
78#121×C61—22no—
79#121×C61—41no—
80#121×C61—44no—
81C4×D4×C61—22no—
82C4×D4×C61—22no—
83#117×C61—22no—
84#117×C61—41no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—41no—
91C2×C4⋊C4×C61—41no—
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×C61D411yescharacteristic
109C2×C22⋊C4×C61D411yescharacteristic
110C2×C42×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61C2311yescharacteristic
113#107×C61—22no—
114#107×C61—22no—
115#107×C61—41no—
116#107×C61D414yescomplemented
117#106×C61—22no—
118#106×C61—22no—
119#102×C61—22no—
120#102×C61—22no—
121#102×C61—22no—
122#102×C61—41no—
123C22⋊C8×C61—22no—
124C22⋊C8×C61—22no—
125C22⋊C8×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—42no—
171C22×C4×C61—42no—
172C22×C4×C61—81no—
173C22×C4×C61—81no—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61#4112yes—
179C22×C4×C61#4112yes—
180C22×C4×C61C2411yescharacteristic
181M16×C61—28no—
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×C61C2×D412yes—
193C2×C8×C61#4112yes—
194C4⋊C4×C61—22no—
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—21no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61C2×D412yes—
211C4⋊C4×C61C2×D412yes—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—81no—
221C22⋊C4×C61—81no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—42no—
225C42×C61—81no—
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—21no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61#12312yes—
246C23×C61AGL(1,ℤ/8)12yes—
247C23×C61C22×D411yescharacteristic
248D4×C61—44no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—41no—
252D4×C61—41no—
253D4×C61—84no—
254D4×C61—84no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
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—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—41no—
295C2×C4×C61—84no—
296C2×C4×C61—84no—
297C2×C4×C61#12312yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C612−1+411yescharacteristic
304C8×C61—22no—
305C8×C61—22no—
306C8×C61—41no—
307C8×C61—41no—
308#26147C6111yesmaximal, characteristic, direct product factor, Sylow
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61C2×#12311yescharacteristic
331C22×C61D4211yescharacteristic
332C22×C61#54711yescharacteristic
333C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C61#57511yescharacteristic
335C22×C61#57611yescharacteristic
336C22×C61#57811yescharacteristic
337C4×C61—22no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61—81no—
348C4×C61#52511yescharacteristic
349C4×C61#53911yescharacteristic
350C4×C61#54811yescharacteristic
351C4×C61#55311yescharacteristic
352C2×#480C2×C6111yescharacteristic, complemented
353C2×#428C2×C6111yescharacteristic, complemented
354#2416C2×C6111yescharacteristic
355#2352C2×C6111yescharacteristic, complemented
356#2092C2×C6111yescharacteristic, complemented
357#2085C2×C6111yescharacteristic, complemented
358#2077C2×C6111yescharacteristic, complemented
359#2034C2×C6111yescharacteristic, complemented
360#1925C2×C6111yescharacteristic, complemented
361#1921C2×C6111yescharacteristic, complemented
362#1895C2×C6111yescharacteristic, complemented
363#1875C2×C6111yescharacteristic, complemented
364#1870C2×C6111yescharacteristic, complemented
365#1852C2×C6111yescharacteristic, complemented
366#1852C2×C6111yescharacteristic, complemented
367C2×C61—42no—
368C2×C61—42no—
369C2×C61—161no—
370C2×C61#244311yescharacteristic
371C2×C61#309411yescharacteristic
372C2×C61#309811yescharacteristic
373C2×C61#326411yescharacteristic
374C2×C61#327711yescharacteristic
375C2×C61#334311yescharacteristic
376C2×C61#335511yescharacteristic
377C22×M16C22×C6111yescharacteristic
378C2×#121—21no—
379C2×#121C22×C6111yescharacteristic
380C2×#121C22×C6111yescharacteristic
381C2×C4×D4C22×C6111yescharacteristic
382C2×#117C22×C6111yescharacteristic
383C22×C4⋊C4C22×C6111yescharacteristic
384C22×C4⋊C4C22×C6111yescharacteristic
385#480—24no—
386#428—24no—
387C2×#107C22×C6111yescharacteristic
388C2×#107C22×C6111yescharacteristic
389C2×#107C22×C6111yescharacteristic
390C2×#107C22×C6111yescharacteristic
391C2×#106C22×C6111yescharacteristic
392C2×#106C22×C6111yescharacteristic
393C2×#102C22×C6111yescharacteristic
394C2×#102C22×C6111yescharacteristic
395C2×#102C22×C6111yescharacteristic
396C2×#102C22×C6111yescharacteristic
397C2×C22⋊C8C22×C6111yescharacteristic
398C2×C22⋊C8C22×C6111yescharacteristic
399C2×C22⋊C8C22×C6111yescharacteristic
400#396—21no—
401#394—21no—
402#390C22×C6111yescharacteristic
403#389C22×C6111yescharacteristic
404#388—21no—
405#387—21no—
406#386—21no—
407#386—21no—
408#382C22×C6111yescharacteristic
409#380C22×C6111yescharacteristic
410#380C22×C6111yescharacteristic
411#380C22×C6111yescharacteristic
412C4×C4⋊C4C22×C6111yescharacteristic
413C4×C22⋊C4—21no—
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419#340C22×C6111yescharacteristic
420#336C22×C6111yescharacteristic
421#336C22×C6111yescharacteristic
422C61#2614711yescharacteristic, direct product factor, Sylow
423C22×D4—21no—
424C22×D4—21no—
425C22×D4D4×C6111yescharacteristic
426C22×D4C23×C6111yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4C23×C6111yescharacteristic
430C23×C4C23×C6111yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—22no—
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—41no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4D4×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×C4⋊C4C23×C6111yescharacteristic
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×C42—21no—
474C2×C42C23×C6111yescharacteristic
475#107—22no—
476#107—22no—
477#107—41no—
478#107D4×C6114yescomplemented
479#106—22no—
480#106—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—41no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C24—21no—
496C24C2×D4×C6111yescharacteristic
497C24C2×D4×C6111yescharacteristic
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—41no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
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—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C2×D4×C6111yescharacteristic
537C22×C4C2×D4×C6111yescharacteristic
538C22×C4C2×D4×C6111yescharacteristic
539C22×C4C2×D4×C6111yescharacteristic
540C22×C4#41×C6112yes—
541C22×C4#41×C6112yes—
542C22×C4C24×C6111yescharacteristic
543M16—28no—
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×C8—21no—
553C2×C8—21no—
554C2×C8C2×D4×C6112yes—
555C2×C8#41×C6112yes—
556C4⋊C4—22no—
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—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4C2×D4×C6112yes—
573C4⋊C4C2×D4×C6112yes—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—42no—
587C42—81no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23#123×C6112yes—
608C23AGL(1,ℤ/8)×C6112yes—
609C23C22×D4×C6111yescharacteristic
610D4—44no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—84no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
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—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4#123×C6112yes—
660C2×C4C22×D4×C6111yescharacteristic
661C2×C4C2×#41×C6111yescharacteristic
662C2×C4C2×#41×C6111yescharacteristic
663C2×C4C2×#41×C6111yescharacteristic
664C2×C4H(5,𝔽2)×C6111yescharacteristic
665C2×C42−1+4×C6111yescharacteristic
666C8—22no—
667C8—22no—
668C8—41no—
669C8—41no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×#123×C6111yescharacteristic
692C22D42×C6111yescharacteristic
693C22C61×#54711yescharacteristic
694C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
695C22C61×#57511yescharacteristic
696C22C61×#57611yescharacteristic
697C22C61×#57811yescharacteristic
698C4—22no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—42no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4C61×#52511yescharacteristic
710C4C61×#53911yescharacteristic
711C4C61×#54811yescharacteristic
712C4C61×#55311yescharacteristic
713C2—42no—
714C2—42no—
715C2—161no—
716C2C61×#244311yescharacteristic
717C2C61×#309411yescharacteristic
718C2C61×#309811yescharacteristic
719C2C61×#326411yescharacteristic
720C2C61×#327711yescharacteristic
721C2C61×#334311yescharacteristic
722C2C61×#335511yescharacteristic
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×#480C2semidirect
2. C2×C61×#428C2semidirect
4. C61×#2352C2semidirect
5. C61×#2092C2semidirect
6. C61×#2085C2semidirect
7. C61×#2077C2semidirect
8. C61×#2034C2semidirect
9. C61×#1925C2semidirect
10. C61×#1921C2semidirect
11. C61×#1895C2semidirect
12. C61×#1875C2semidirect
13. C61×#1870C2semidirect
14. C61×#1852C2semidirect
15. C61×#1852C2semidirect
116. #107×C61D4semidirect
308. #26147C61direct (N × H)
352. C2×#480C2×C61semidirect
353. C2×#428C2×C61semidirect
355. #2352C2×C61semidirect
356. #2092C2×C61semidirect
357. #2085C2×C61semidirect
358. #2077C2×C61semidirect
359. #2034C2×C61semidirect
360. #1925C2×C61semidirect
361. #1921C2×C61semidirect
362. #1895C2×C61semidirect
363. #1875C2×C61semidirect
364. #1870C2×C61semidirect
365. #1852C2×C61semidirect
366. #1852C2×C61semidirect
422. C61#26147direct (N × H)
478. #107D4×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×#4282
C61×#24162
C61×#23522
C61×#20922
C61×#20852
C61×#20772
C61×#20342
C61×#19252
C61×#19212
C61×#18952
C61×#18752
C61×#18702
C61×#18522
#2614761