Finite Group Databasebeta

← C61×#25554 #29528987

Subgroups — C61×#25554 #29528987

Order 15616.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#555C211yesmaximal, characteristic, complemented
2C2×C61×#482C211yesmaximal, characteristic, complemented
3C2×C61×#469C211yesmaximal, characteristic, complemented
4C61×#2416C211yesmaximal, characteristic, complemented
5C61×#2058C211yesmaximal, characteristic, complemented
6C61×#2034C211yesmaximal, characteristic, complemented
7C61×#2023C211yesmaximal, characteristic, complemented
8C61×#1999C211yesmaximal, characteristic, complemented
9C61×#1879C211yesmaximal, characteristic, complemented
10C61×#1875C211yesmaximal, characteristic, complemented
11C61×#1874C211yesmaximal, characteristic, complemented
12C61×#1870C211yesmaximal, characteristic, complemented
13C61×#1862C211yesmaximal, characteristic, complemented
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C61×#555—24no—
19C61×#555—24no—
20C2×C4⋊Q8×C61C2211yescharacteristic
21C2×#124×C61—21no—
22C2×#124×C61—21no—
23C2×#121×C61—21no—
24C2×#121×C61—21no—
25C2×#121×C61C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×C4×D4×C61C2211yescharacteristic
30C2×C4×D4×C61C2211yescharacteristic
31C2×#117×C61—21no—
32C2×#117×C61C2211yescharacteristic
33C2×#117×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C61×#482—24no—
36C61×#469—24no—
37C2×#107×C61C2211yescharacteristic
38C2×#106×C61C2211yescharacteristic
39C2×#106×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C61×#396—21no—
50C61×#394—21no—
51C61×#390C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#386—21no—
54C61×#380C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Q8×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61—21no—
68C22×D4×C61D411yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C22×D4×C61C2311yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C2×D8×C61—22no—
76C2×D8×C61—22no—
77C2×D8×C61—41no—
78C2×M16×C61—22no—
79C2×M16×C61—22no—
80C2×M16×C61—41no—
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84C22×C8×C61C2311yescharacteristic
85C4⋊Q8×C61—22no—
86C4⋊Q8×C61—22no—
87#124×C61—28no—
88#124×C61—28no—
89#121×C61—28no—
90#121×C61—22no—
91#121×C61—22no—
92#121×C61—22no—
93#121×C61—22no—
94#121×C61—22no—
95#121×C61—22no—
96#121×C61—41no—
97#121×C61—44no—
98#121×C61D414yescomplemented
99C4×D4×C61—22no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103#117×C61—28no—
104#117×C61—22no—
105#117×C61—22no—
106#117×C61—22no—
107#117×C61D414yescomplemented
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—41no—
113C2×C4⋊C4×C61D411yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C42×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61—22no—
136#106×C61—22no—
137#106×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61—41no—
144C22⋊C8×C61—22no—
145C22⋊C8×C61—22no—
146C22⋊C8×C61—41no—
147#95×C61—21no—
148#95×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C24×C61C2×D411yescharacteristic
153C2×Q8×C61—24no—
154C2×Q8×C61—81no—
155C2×Q8×C61—81no—
156C2×D4×C61—22no—
157C2×D4×C61—24no—
158C2×D4×C61—24no—
159C2×D4×C61—22no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—41no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C2×D4×C61—42no—
177C2×D4×C61—81no—
178C2×D4×C61—81no—
179C2×D4×C61—81no—
180C2×D4×C61—81no—
181C2×D4×C61—81no—
182C2×D4×C61C2×D412yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—24no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—42no—
201C22×C4×C61—42no—
202C22×C4×C61—42no—
203C22×C4×C61—42no—
204C22×C4×C61—81no—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2×D412yes—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2411yescharacteristic
212D8×C61—44no—
213M16×C61—44no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61#4112yes—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—42no—
237C4⋊C4×C61—42no—
238C4⋊C4×C61C2×D412yes—
239C4⋊C4×C61C2×D412yes—
240C4⋊C4×C61C2×D412yes—
241C4⋊C4×C61#4112yes—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—24no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—81no—
254C42×C61—24no—
255C42×C61—24no—
256C42×C61—21no—
257C42×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—22no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61#12012yes—
286C23×C61C22×D411yescharacteristic
287Q8×C61—84no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—44no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—84no—
298D4×C61—84no—
299D4×C61—84no—
300D4×C61—84no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—22no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—48no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—84no—
339C2×C4×C61#12012yes—
340C2×C4×C61AGL(1,ℤ/8)12yes—
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C612−1+411yescharacteristic
347C8×C61—22no—
348C8×C61—41no—
349C8×C61—41no—
350C8×C61—41no—
351#25554C6111yesmaximal, characteristic, direct product factor, Sylow
352C22×C61—22no—
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—42no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61C2×#12011yescharacteristic
381C22×C61#54611yescharacteristic
382C22×C61#54711yescharacteristic
383C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C61#57511yescharacteristic
385C22×C61#57611yescharacteristic
386C22×C61#57711yescharacteristic
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—41no—
390C4×C61—42no—
391C4×C61—41no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61—81no—
396C4×C61—81no—
397C4×C61#53211yescharacteristic
398C4×C61#53711yescharacteristic
399C4×C61#54611yescharacteristic
400C4×C61#54711yescharacteristic
401C2×#555C2×C6111yescharacteristic, complemented
402C2×#482C2×C6111yescharacteristic, complemented
403C2×#469C2×C6111yescharacteristic, complemented
404#2416C2×C6111yescharacteristic, complemented
405#2058C2×C6111yescharacteristic, complemented
406#2034C2×C6111yescharacteristic, complemented
407#2023C2×C6111yescharacteristic, complemented
408#1999C2×C6111yescharacteristic, complemented
409#1879C2×C6111yescharacteristic, complemented
410#1875C2×C6111yescharacteristic, complemented
411#1874C2×C6111yescharacteristic, complemented
412#1870C2×C6111yescharacteristic, complemented
413#1862C2×C6111yescharacteristic, complemented
414#1854C2×C6111yescharacteristic, complemented
415#1736C2×C6111yescharacteristic, complemented
416C2×C61—42no—
417C2×C61—81no—
418C2×C61—82no—
419C2×C61—161no—
420C2×C61#243011yescharacteristic
421C2×C61#300611yescharacteristic
422C2×C61#301211yescharacteristic
423C2×C61#332111yescharacteristic
424C2×C61#332511yescharacteristic
425C2×C61#334711yescharacteristic
426C2×C61#335411yescharacteristic
427C22×D8C22×C6111yescharacteristic
428C22×M16C22×C6111yescharacteristic
429#555—24no—
430#555—24no—
431C2×C4⋊Q8C22×C6111yescharacteristic
432C2×#124—21no—
433C2×#124—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C6111yescharacteristic
437C2×#121C22×C6111yescharacteristic
438C2×#121C22×C6111yescharacteristic
439C2×#121C22×C6111yescharacteristic
440C2×C4×D4C22×C6111yescharacteristic
441C2×C4×D4C22×C6111yescharacteristic
442C2×#117—21no—
443C2×#117C22×C6111yescharacteristic
444C2×#117C22×C6111yescharacteristic
445C22×C4⋊C4C22×C6111yescharacteristic
446#482—24no—
447#469—24no—
448C2×#107C22×C6111yescharacteristic
449C2×#106C22×C6111yescharacteristic
450C2×#106C22×C6111yescharacteristic
451C2×#102C22×C6111yescharacteristic
452C2×#102C22×C6111yescharacteristic
453C2×#102C22×C6111yescharacteristic
454C2×#102C22×C6111yescharacteristic
455C2×#102C22×C6111yescharacteristic
456C2×#102C22×C6111yescharacteristic
457C2×C22⋊C8C22×C6111yescharacteristic
458C2×C22⋊C8C22×C6111yescharacteristic
459C2×C22⋊C8C22×C6111yescharacteristic
460#396—21no—
461#394—21no—
462#390C22×C6111yescharacteristic
463#389C22×C6111yescharacteristic
464#386—21no—
465#380C22×C6111yescharacteristic
466#340C22×C6111yescharacteristic
467#340C22×C6111yescharacteristic
468#340C22×C6111yescharacteristic
469#340C22×C6111yescharacteristic
470#340C22×C6111yescharacteristic
471#340C22×C6111yescharacteristic
472#336C22×C6111yescharacteristic
473#336C22×C6111yescharacteristic
474C61#2555411yescharacteristic, direct product factor, Sylow
475C22×Q8—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4D4×C6111yescharacteristic
481C22×D4C23×C6111yescharacteristic
482C22×D4C23×C6111yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C6111yescharacteristic
486C23×C4C23×C6111yescharacteristic
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C6111yescharacteristic
494C22×C8C23×C6111yescharacteristic
495C22×C8C23×C6111yescharacteristic
496C22×C8C23×C6111yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499#124—28no—
500#124—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—44no—
510#121D4×C6114yescomplemented
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—28no—
516#117—22no—
517#117—22no—
518#117—22no—
519#117D4×C6114yescomplemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4D4×C6111yescharacteristic
526C2×C4⋊C4C23×C6111yescharacteristic
527C2×C4⋊C4C23×C6111yescharacteristic
528C2×C4⋊C4C23×C6111yescharacteristic
529C2×C4⋊C4C23×C6111yescharacteristic
530C2×C4⋊C4C23×C6111yescharacteristic
531C2×C4⋊C4C23×C6111yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4D4×C6111yescharacteristic
543C2×C22⋊C4D4×C6111yescharacteristic
544C2×C42—21no—
545C2×C42—21no—
546C2×C42C23×C6111yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—41no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561C24—21no—
562C24—21no—
563C24C2×D4×C6111yescharacteristic
564C24C2×D4×C6111yescharacteristic
565C2×Q8—24no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4C2×D4×C6112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C6111yescharacteristic
618C22×C4C2×D4×C6111yescharacteristic
619C22×C4C2×D4×C6111yescharacteristic
620C22×C4C2×D4×C6112yes—
621C22×C4C2×D4×C6112yes—
622C22×C4C2×D4×C6111yescharacteristic
623C22×C4C24×C6111yescharacteristic
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8#41×C6112yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4C2×D4×C6112yes—
651C4⋊C4C2×D4×C6112yes—
652C4⋊C4C2×D4×C6112yes—
653C4⋊C4#41×C6112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C42—24no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23#120×C6112yes—
698C23C22×D4×C6111yescharacteristic
699Q8—84no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4#120×C6112yes—
752C2×C4AGL(1,ℤ/8)×C6112yes—
753C2×C4C22×D4×C6111yescharacteristic
754C2×C4C22×D4×C6111yescharacteristic
755C2×C4C2×#41×C6111yescharacteristic
756C2×C4C2×#41×C6111yescharacteristic
757C2×C4H(5,𝔽2)×C6111yescharacteristic
758C2×C42−1+4×C6111yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C6111yescharacteristic
792C22C61×#54611yescharacteristic
793C22C61×#54711yescharacteristic
794C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
795C22C61×#57511yescharacteristic
796C22C61×#57611yescharacteristic
797C22C61×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4C61×#53211yescharacteristic
809C4C61×#53711yescharacteristic
810C4C61×#54611yescharacteristic
811C4C61×#54711yescharacteristic
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2C61×#243011yescharacteristic
817C2C61×#300611yescharacteristic
818C2C61×#301211yescharacteristic
819C2C61×#332111yescharacteristic
820C2C61×#332511yescharacteristic
821C2C61×#334711yescharacteristic
822C2C61×#335411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
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×#555C2semidirect
2. C2×C61×#482C2semidirect
3. C2×C61×#469C2semidirect
4. C61×#2416C2semidirect
5. C61×#2058C2semidirect
6. C61×#2034C2semidirect
7. C61×#2023C2semidirect
8. C61×#1999C2semidirect
9. C61×#1879C2semidirect
10. C61×#1875C2semidirect
11. C61×#1874C2semidirect
12. C61×#1870C2semidirect
13. C61×#1862C2semidirect
14. C61×#1854C2semidirect
15. C61×#1736C2semidirect
98. #121×C61D4semidirect
107. #117×C61D4semidirect
351. #25554C61direct (N × H)
401. C2×#555C2×C61semidirect
402. C2×#482C2×C61semidirect
403. C2×#469C2×C61semidirect
404. #2416C2×C61semidirect
405. #2058C2×C61semidirect
406. #2034C2×C61semidirect
407. #2023C2×C61semidirect
408. #1999C2×C61semidirect
409. #1879C2×C61semidirect
410. #1875C2×C61semidirect
411. #1874C2×C61semidirect
412. #1870C2×C61semidirect
413. #1862C2×C61semidirect
414. #1854C2×C61semidirect
415. #1736C2×C61semidirect
474. C61#25554direct (N × H)
510. #121D4×C61semidirect
519. #117D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5552
C2×C61×#4822
C2×C61×#4692
C61×#24162
C61×#20582
C61×#20342
C61×#20232
C61×#19992
C61×#18792
C61×#18752
C61×#18742
C61×#18702
C61×#18622
C61×#18542
C61×#17362
#2555461