Finite Group Databasebeta

← C61×#25601 #29529034

Subgroups — C61×#25601 #29529034

Order 15616.

1216 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#529C211yesmaximal, characteristic, complemented
2C2×C61×#495C211yesmaximal, characteristic, complemented
3C2×C61×#488C211yesmaximal, characteristic, complemented
4C61×#2850C211yesmaximal, characteristic, complemented
5C61×#2001C211yesmaximal, characteristic, complemented
6C61×#2000C211yesmaximal, characteristic, complemented
7C61×#2000C211yesmaximal, characteristic, complemented
8C61×#1999C211yesmaximal, characteristic
9C61×#1991C211yesmaximal, characteristic, complemented
10C61×#1958C211yesmaximal, characteristic, complemented
11C61×#1880C211yesmaximal, characteristic, complemented
12C61×#1879C211yesmaximal, characteristic, complemented
13C61×#1878C211yesmaximal, characteristic, complemented
14C61×#1877C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C61C211yesmaximal, characteristic, complemented
16C22×Q16×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C61×#529—24no—
21C61×#529—24no—
22C2×#126×C61—21no—
23C2×#125×C61C2211yescharacteristic
24C2×#124×C61C2211yescharacteristic
25C2×#124×C61C2211yescharacteristic
26C2×#123×C61—21no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C2×C22⋊Q8×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic
31C2×C4×Q8×C61C2211yescharacteristic
32C2×C4×D4×C61—21no—
33C2×C4×D4×C61C2211yescharacteristic
34C2×#117×C61—21no—
35C22×C42×C61C2211yescharacteristic
36C61×#495—24no—
37C61×#488—24no—
38C2×#103×C61C2211yescharacteristic
39C2×#103×C61C2211yescharacteristic
40C2×#103×C61C2211yescharacteristic
41C2×#103×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C4×C8×C61C2211yescharacteristic
49C2×C4×C8×C61C2211yescharacteristic
50C61×#391C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#388—21no—
53C61×#388—21no—
54C61×#386—21no—
55C61×#386—21no—
56C61×#382C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Q8×C61C2311yescharacteristic
64C22×Q8×C61C2311yescharacteristic
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61C2311yescharacteristic
68C22×D4×C61C2311yescharacteristic
69C23×C4×C61—21no—
70C23×C4×C61D411yescharacteristic
71C23×C4×C61D411yescharacteristic
72C23×C4×C61C2311yescharacteristic
73C2×Q16×C61—22no—
74C2×Q16×C61—22no—
75C2×Q16×C61—41no—
76C2×SD16×C61—22no—
77C2×SD16×C61—22no—
78C2×SD16×C61—22no—
79C2×SD16×C61—22no—
80C2×SD16×C61—41no—
81C2×SD16×C61—41no—
82C2×D8×C61—22no—
83C2×D8×C61—22no—
84C2×D8×C61—41no—
85C22×C8×C61C2311yescharacteristic
86C22×C8×C61C2311yescharacteristic
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89#126×C61—28no—
90#125×C61—22no—
91#125×C61D414yescomplemented
92#124×C61—22no—
93#124×C61—22no—
94#124×C61—22no—
95#124×C61D414yescomplemented
96#123×C61—28no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—22no—
99C22⋊Q8×C61—41no—
100C22⋊Q8×C61—41no—
101#121×C61—22no—
102#121×C61—22no—
103#121×C61—41no—
104#121×C61—41no—
105C4×Q8×C61—22no—
106C4×Q8×C61—22no—
107C4×D4×C61—28no—
108C4×D4×C61—22no—
109C4×D4×C61—22no—
110#117×C61—28no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
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×C61—21no—
131C2×C42×C61—21no—
132C2×C42×C61—22no—
133C2×C42×C61—22no—
134C2×C42×C61D411yescharacteristic
135C2×C42×C61D411yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138#103×C61—22no—
139#103×C61—22no—
140#103×C61—41no—
141#103×C61—41no—
142#102×C61—22no—
143#102×C61—22no—
144#102×C61—41no—
145#102×C61—41no—
146C22⋊C8×C61—22no—
147C22⋊C8×C61—22no—
148C4×C8×C61—22no—
149C4×C8×C61—22no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61C2×D411yescharacteristic
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61C2×D412yes—
169C2×D4×C61—24no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61C2×D412yes—
187C22×C4×C61—24no—
188C22×C4×C61—22no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—41no—
205C22×C4×C61—41no—
206C22×C4×C61—42no—
207C22×C4×C61—42no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214Q16×C61—44no—
215SD16×C61—44no—
216SD16×C61—44no—
217D8×C61—44no—
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—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61#4112yes—
229C2×C8×C61#4112yes—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—42no—
241C4⋊C4×C61C2×D412yes—
242C4⋊C4×C61C2×D412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—24no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C42×C61—24no—
255C42×C61—22no—
256C42×C61—22no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61C2×D412yes—
260C42×C61C2×D412yes—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—22no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
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#13512yes—
282C23×C61C22×D411yescharacteristic
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—41no—
286Q8×C61—41no—
287Q8×C61—41no—
288Q8×C61—41no—
289Q8×C61—41no—
290Q8×C61—41no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—48no—
294D4×C61—41no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—41no—
298D4×C61—41no—
299D4×C61—41no—
300D4×C61—84no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—44no—
317C2×C4×C61—44no—
318C2×C4×C61—48no—
319C2×C4×C61—41no—
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#12012yes—
339C2×C4×C61#12012yes—
340C2×C4×C61#13512yes—
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C8×C61—22no—
348C8×C61—22no—
349C8×C61—41no—
350C8×C61—41no—
351#25601C6111yesmaximal, 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—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61C2×#12011yescharacteristic
374C22×C61#53211yescharacteristic
375C22×C61#53511yescharacteristic
376C22×C61C2×#13511yescharacteristic
377C22×C61C2×#13511yescharacteristic
378C22×C61#57511yescharacteristic
379C22×C61#57511yescharacteristic
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—22no—
383C4×C61—41no—
384C4×C61—42no—
385C4×C61—41no—
386C4×C61—42no—
387C4×C61—42no—
388C4×C61—81no—
389C4×C61—81no—
390C4×C61—81no—
391C4×C61#54611yescharacteristic
392C4×C61#54611yescharacteristic
393C4×C61#55011yescharacteristic
394C4×C61#55011yescharacteristic
395C2×#529C2×C6111yescharacteristic, complemented
396C2×#495C2×C6111yescharacteristic, complemented
397C2×#488C2×C6111yescharacteristic, complemented
398#2850C2×C6111yescharacteristic, complemented
399#2001C2×C6111yescharacteristic, complemented
400#2000C2×C6111yescharacteristic, complemented
401#2000C2×C6111yescharacteristic, complemented
402#1999C2×C6111yescharacteristic
403#1991C2×C6111yescharacteristic, complemented
404#1958C2×C6111yescharacteristic, complemented
405#1880C2×C6111yescharacteristic, complemented
406#1879C2×C6111yescharacteristic, complemented
407#1878C2×C6111yescharacteristic, complemented
408#1877C2×C6111yescharacteristic, complemented
409C4×C22⋊C8C2×C6111yescharacteristic, complemented
410C2×C61—42no—
411C2×C61—82no—
412C2×C61—161no—
413C2×C61#243111yescharacteristic
414C2×C61#300211yescharacteristic
415C2×C61#300211yescharacteristic
416C2×C61#316811yescharacteristic
417C2×C61#318311yescharacteristic
418C2×C61#321111yescharacteristic
419C2×C61#321211yescharacteristic
420C22×Q16C22×C6111yescharacteristic
421C22×SD16C22×C6111yescharacteristic
422C22×SD16C22×C6111yescharacteristic
423C22×D8C22×C6111yescharacteristic
424#529—24no—
425#529—24no—
426C2×#126—21no—
427C2×#125C22×C6111yescharacteristic
428C2×#124C22×C6111yescharacteristic
429C2×#124C22×C6111yescharacteristic
430C2×#123—21no—
431C2×C22⋊Q8C22×C6111yescharacteristic
432C2×C22⋊Q8C22×C6111yescharacteristic
433C2×#121C22×C6111yescharacteristic
434C2×#121C22×C6111yescharacteristic
435C2×C4×Q8C22×C6111yescharacteristic
436C2×C4×D4—21no—
437C2×C4×D4C22×C6111yescharacteristic
438C2×#117—21no—
439C22×C42C22×C6111yescharacteristic
440#495—24no—
441#488—24no—
442C2×#103C22×C6111yescharacteristic
443C2×#103C22×C6111yescharacteristic
444C2×#103C22×C6111yescharacteristic
445C2×#103C22×C6111yescharacteristic
446C2×#102C22×C6111yescharacteristic
447C2×#102C22×C6111yescharacteristic
448C2×#102C22×C6111yescharacteristic
449C2×#102C22×C6111yescharacteristic
450C2×C22⋊C8C22×C6111yescharacteristic
451C2×C22⋊C8C22×C6111yescharacteristic
452C2×C4×C8C22×C6111yescharacteristic
453C2×C4×C8C22×C6111yescharacteristic
454#391C22×C6111yescharacteristic
455#390C22×C6111yescharacteristic
456#388—21no—
457#388—21no—
458#386—21no—
459#386—21no—
460#382C22×C6111yescharacteristic
461#340C22×C6111yescharacteristic
462#340C22×C6111yescharacteristic
463#340C22×C6111yescharacteristic
464#340C22×C6111yescharacteristic
465#336C22×C6111yescharacteristic
466#336C22×C6111yescharacteristic
467C61#2560111yescharacteristic, direct product factor, Sylow
468C22×Q8C23×C6111yescharacteristic
469C22×Q8C23×C6111yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4C23×C6111yescharacteristic
473C22×D4C23×C6111yescharacteristic
474C23×C4—21no—
475C23×C4D4×C6111yescharacteristic
476C23×C4D4×C6111yescharacteristic
477C23×C4C23×C6111yescharacteristic
478C2×Q16—22no—
479C2×Q16—22no—
480C2×Q16—41no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—41no—
486C2×SD16—41no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C22×C8C23×C6111yescharacteristic
491C22×C8C23×C6111yescharacteristic
492C22×C8C23×C6111yescharacteristic
493C22×C8C23×C6111yescharacteristic
494#126—28no—
495#125—22no—
496#125D4×C6114yescomplemented
497#124—22no—
498#124—22no—
499#124—22no—
500#124D4×C6114yescomplemented
501#123—28no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—41no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×D4—28no—
513C4×D4—22no—
514C4×D4—22no—
515#117—28no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4C23×C6111yescharacteristic
522C2×C4⋊C4C23×C6111yescharacteristic
523C2×C4⋊C4C23×C6111yescharacteristic
524C2×C4⋊C4C23×C6111yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C42—21no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42D4×C6111yescharacteristic
540C2×C42D4×C6111yescharacteristic
541C2×C42C23×C6111yescharacteristic
542C2×C42C23×C6111yescharacteristic
543#103—22no—
544#103—22no—
545#103—41no—
546#103—41no—
547#102—22no—
548#102—22no—
549#102—41no—
550#102—41no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C4×C8—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C6111yescharacteristic
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8C2×D4×C6112yes—
574C2×D4—24no—
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—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4C2×D4×C6112yes—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
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—41no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4C2×D4×C6111yescharacteristic
614C22×C4C2×D4×C6111yescharacteristic
615C22×C4C2×D4×C6111yescharacteristic
616C22×C4C2×D4×C6111yescharacteristic
617C22×C4C2×D4×C6111yescharacteristic
618C22×C4C24×C6111yescharacteristic
619Q16—44no—
620SD16—44no—
621SD16—44no—
622D8—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C6112yes—
634C2×C8#41×C6112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4C2×D4×C6112yes—
647C4⋊C4C2×D4×C6112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C42—24no—
660C42—22no—
661C42—22no—
662C42—21no—
663C42—21no—
664C42C2×D4×C6112yes—
665C42C2×D4×C6112yes—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23#135×C6112yes—
687C23C22×D4×C6111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695Q8—41no—
696D4—22no—
697D4—22no—
698D4—48no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—84no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—48no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
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#120×C6112yes—
744C2×C4#120×C6112yes—
745C2×C4#135×C6112yes—
746C2×C4C22×D4×C6111yescharacteristic
747C2×C4C22×D4×C6111yescharacteristic
748C2×C4C2×#41×C6111yescharacteristic
749C2×C4C2×#41×C6111yescharacteristic
750C2×C4H(5,𝔽2)×C6111yescharacteristic
751C2×C4H(5,𝔽2)×C6111yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#120×C6111yescharacteristic
778C22C61×#53211yescharacteristic
779C22C61×#53511yescharacteristic
780C22C2×#135×C6111yescharacteristic
781C22C2×#135×C6111yescharacteristic
782C22C61×#57511yescharacteristic
783C22C61×#57511yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4C61×#54611yescharacteristic
796C4C61×#54611yescharacteristic
797C4C61×#55011yescharacteristic
798C4C61×#55011yescharacteristic
799C2—42no—
800C2—82no—
801C2—161no—
802C2C61×#243111yescharacteristic
803C2C61×#300211yescharacteristic
804C2C61×#300211yescharacteristic
805C2C61×#316811yescharacteristic
806C2C61×#318311yescharacteristic
807C2C61×#321111yescharacteristic
808C2C61×#321211yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#529C2semidirect
2. C2×C61×#495C2semidirect
3. C2×C61×#488C2semidirect
4. C61×#2850C2semidirect
5. C61×#2001C2semidirect
6. C61×#2000C2semidirect
7. C61×#2000C2semidirect
9. C61×#1991C2semidirect
10. C61×#1958C2semidirect
11. C61×#1880C2semidirect
12. C61×#1879C2semidirect
13. C61×#1878C2semidirect
14. C61×#1877C2semidirect
15. C4×C22⋊C8×C61C2semidirect
91. #125×C61D4semidirect
95. #124×C61D4semidirect
351. #25601C61direct (N × H)
395. C2×#529C2×C61semidirect
396. C2×#495C2×C61semidirect
397. C2×#488C2×C61semidirect
398. #2850C2×C61semidirect
399. #2001C2×C61semidirect
400. #2000C2×C61semidirect
401. #2000C2×C61semidirect
403. #1991C2×C61semidirect
404. #1958C2×C61semidirect
405. #1880C2×C61semidirect
406. #1879C2×C61semidirect
407. #1878C2×C61semidirect
408. #1877C2×C61semidirect
409. C4×C22⋊C8C2×C61semidirect
467. C61#25601direct (N × H)
496. #125D4×C61semidirect
500. #124D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5292
C2×C61×#4952
C2×C61×#4882
C61×#28502
C61×#20012
C61×#20002
C61×#19992
C61×#19912
C61×#19582
C61×#18802
C61×#18792
C61×#18782
C61×#18772
C4×C22⋊C8×C612
#2560161