Finite Group Databasebeta

← C61×#29601 #29533034

Subgroups — C61×#29601 #29533034

Order 15616.

1462 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#525C211yesmaximal, characteristic
2C2×C61×#485C211yesmaximal, characteristic, complemented
3C2×C61×#452C211yesmaximal, characteristic, complemented
4C61×#2848C211yesmaximal, characteristic, complemented
5C61×#2036C211yesmaximal, characteristic, complemented
6C61×#2035C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#2001C211yesmaximal, characteristic, complemented
10C61×#2001C211yesmaximal, characteristic, complemented
11C61×#2000C211yesmaximal, characteristic, complemented
12C61×#2000C211yesmaximal, characteristic, complemented
13C61×#1825C211yesmaximal, characteristic, complemented
14C61×#1788C211yesmaximal, characteristic, complemented
15C61×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C22×Q16×C61C2211yescharacteristic, complemented
19C22×SD16×C61C2211yescharacteristic, complemented
20C61×#525—24no—
21C61×#525—24no—
22C2×#123×C61—21no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×C22⋊Q8×C61C2211yescharacteristic
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×C22⋊Q8×C61C2211yescharacteristic
27C2×C22⋊Q8×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#120×C61—21no—
31C2×C4×D4×C61—21no—
32C2×C4×D4×C61—21no—
33C2×#117×C61C2211yescharacteristic
34C61×#485—24no—
35C61×#452—24no—
36C2×#107×C61C2211yescharacteristic, complemented
37C2×#106×C61C2211yescharacteristic, complemented
38C2×#103×C61C2211yescharacteristic, complemented
39C2×#103×C61C2211yescharacteristic, complemented
40C2×#103×C61C2211yescharacteristic, complemented
41C2×#103×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#102×C61C2211yescharacteristic, complemented
44C2×#102×C61C2211yescharacteristic, complemented
45C2×#102×C61C2211yescharacteristic, complemented
46C2×C22⋊C8×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C2×C22⋊C8×C61C2211yescharacteristic
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C61×#385—21no—
53C61×#385—21no—
54C61×#385—21no—
55C61×#380C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#379—21no—
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C25×C61D411yescharacteristic
64C2×#41×C61—22no—
65C2×#41×C61—41no—
66C2×#41×C61—41no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C2×#41×C61D414yes—
70C22×Q8×C61C2311yescharacteristic
71C22×Q8×C61C2311yescharacteristic
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61C2311yescharacteristic
76C23×C4×C61—22no—
77C23×C4×C61—22no—
78C23×C4×C61—21no—
79C23×C4×C61—41no—
80C23×C4×C61—41no—
81C23×C4×C61—41no—
82C23×C4×C61—41no—
83C23×C4×C61D411yescharacteristic
84C23×C4×C61D411yescharacteristic
85C23×C4×C61D411yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C2×Q16×C61—22no—
90C2×Q16×C61—41no—
91C2×Q16×C61—41no—
92C2×SD16×C61—22no—
93C2×SD16×C61—41no—
94C2×SD16×C61—41no—
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97C22×C8×C61C2311yescharacteristic
98C22×C8×C61C2311yescharacteristic
99#123×C61—28no—
100C22⋊Q8×C61—22no—
101C22⋊Q8×C61—22no—
102C22⋊Q8×C61—22no—
103C22⋊Q8×C61—22no—
104C22⋊Q8×C61—22no—
105C22⋊Q8×C61—22no—
106C22⋊Q8×C61—41no—
107C22⋊Q8×C61—41no—
108C22⋊Q8×C61—41no—
109C22⋊Q8×C61—41no—
110#121×C61—22no—
111#121×C61—22no—
112#121×C61—22no—
113#121×C61—22no—
114#120×C61—28no—
115C4×D4×C61—28no—
116C4×D4×C61—28no—
117#117×C61—22no—
118#117×C61D414yes—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61—21no—
141#107×C61—22no—
142#106×C61—22no—
143#103×C61—22no—
144#103×C61—22no—
145#103×C61—22no—
146#103×C61—41no—
147#103×C61—41no—
148#102×C61—22no—
149#102×C61—41no—
150#102×C61—41no—
151C22⋊C8×C61—22no—
152C22⋊C8×C61—22no—
153C22⋊C8×C61—41no—
154C22⋊C8×C61—41no—
155C22⋊C8×C61—41no—
156C22⋊C8×C61—41no—
157#95×C61—21no—
158#95×C61—21no—
159#95×C61—21no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—21no—
164C24×C61—41no—
165C24×C61—41no—
166C24×C61—41no—
167C24×C61—41no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170C24×C61C2×D411yescharacteristic
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61C2×D412yes—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
197C2×D4×C61—42no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61C2×D412yes—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—22no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—24no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—41no—
230C22×C4×C61—41no—
231C22×C4×C61—41no—
232C22×C4×C61—41no—
233C22×C4×C61—41no—
234C22×C4×C61—41no—
235C22×C4×C61—44no—
236C22×C4×C61—44no—
237C22×C4×C61—44no—
238C22×C4×C61—44no—
239C22×C4×C61—42no—
240C22×C4×C61—42no—
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2411yescharacteristic
247Q16×C61—44no—
248SD16×C61—44no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C4⋊C4×C61—24no—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—42no—
272C4⋊C4×C61—42no—
273C4⋊C4×C61—42no—
274C4⋊C4×C61C2×D412yes—
275C4⋊C4×C61C2×D412yes—
276C22⋊C4×C61—24no—
277C22⋊C4×C61—24no—
278C22⋊C4×C61—24no—
279C22⋊C4×C61—24no—
280C22⋊C4×C61—24no—
281C22⋊C4×C61—42no—
282C22⋊C4×C61—42no—
283C22⋊C4×C61—42no—
284C22⋊C4×C61—42no—
285C22⋊C4×C61—42no—
286C22⋊C4×C61—42no—
287C42×C61—24no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—44no—
308C23×C61—44no—
309C23×C61—44no—
310C23×C61—44no—
311C23×C61—44no—
312C23×C61—44no—
313C23×C61—44no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61#12012yes—
321C23×C61#13512yes—
322C23×C61#13712yes—
323C23×C61C22×D411yescharacteristic
324Q8×C61—22no—
325Q8×C61—22no—
326Q8×C61—41no—
327Q8×C61—41no—
328Q8×C61—41no—
329Q8×C61—41no—
330Q8×C61—41no—
331Q8×C61—41no—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—48no—
335D4×C61—48no—
336D4×C61—48no—
337D4×C61—41no—
338D4×C61—41no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—44no—
355C2×C4×C61—44no—
356C2×C4×C61—48no—
357C2×C4×C61—44no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61#12012yes—
385C2×C4×C61C22×D411yescharacteristic
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61H(5,𝔽2)11yescharacteristic
388C2×C4×C61H(5,𝔽2)11yescharacteristic
389C2×C4×C61H(5,𝔽2)11yescharacteristic
390C2×C4×C61H(5,𝔽2)11yescharacteristic
391C8×C61—41no—
392C8×C61—41no—
393C8×C61—41no—
394C8×C61—41no—
395#29601C6111yesmaximal, characteristic, direct product factor, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—416no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—42no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—81no—
422C22×C61—81no—
423C22×C61—81no—
424C22×C61—81no—
425C22×C61C2×#12011yescharacteristic
426C22×C61#53411yescharacteristic
427C22×C61#53411yescharacteristic
428C22×C61C2×#13511yescharacteristic
429C22×C61C2×#13711yescharacteristic
430C22×C61#57511yescharacteristic
431C22×C61#57511yescharacteristic
432C4×C61—22no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—42no—
436C4×C61—42no—
437C4×C61—42no—
438C4×C61—81no—
439C4×C61—81no—
440C4×C61—81no—
441C4×C61—81no—
442C4×C61#53411yescharacteristic
443C4×C61#53411yescharacteristic
444C4×C61#53511yescharacteristic
445C4×C61#53511yescharacteristic
446C2×#525C2×C6111yescharacteristic
447C2×#485C2×C6111yescharacteristic, complemented
448C2×#452C2×C6111yescharacteristic, complemented
449#2848C2×C6111yescharacteristic, complemented
450#2036C2×C6111yescharacteristic, complemented
451#2035C2×C6111yescharacteristic, complemented
452#2034C2×C6111yescharacteristic, complemented
453#2033C2×C6111yescharacteristic, complemented
454#2001C2×C6111yescharacteristic, complemented
455#2001C2×C6111yescharacteristic, complemented
456#2000C2×C6111yescharacteristic, complemented
457#2000C2×C6111yescharacteristic, complemented
458#1825C2×C6111yescharacteristic, complemented
459#1788C2×C6111yescharacteristic, complemented
460#1779C2×C6111yescharacteristic, complemented
461C2×C61—42no—
462C2×C61—42no—
463C2×C61—42no—
464C2×C61—82no—
465C2×C61#261311yescharacteristic
466C2×C61#300211yescharacteristic
467C2×C61#300711yescharacteristic
468C2×C61#319011yescharacteristic
469C2×C61#319111yescharacteristic
470C2×C61#319611yescharacteristic
471C2×C61#319711yescharacteristic
472C22×#41C22×C6111yescharacteristic
473C24×C4C22×C6111yescharacteristic
474C22×Q16C22×C6111yescharacteristic, complemented
475C22×SD16C22×C6111yescharacteristic, complemented
476#525—24no—
477#525—24no—
478C2×#123—21no—
479C2×C22⋊Q8C22×C6111yescharacteristic
480C2×C22⋊Q8C22×C6111yescharacteristic
481C2×C22⋊Q8C22×C6111yescharacteristic
482C2×C22⋊Q8C22×C6111yescharacteristic
483C2×C22⋊Q8C22×C6111yescharacteristic
484C2×#121C22×C6111yescharacteristic
485C2×#121C22×C6111yescharacteristic
486C2×#120—21no—
487C2×C4×D4—21no—
488C2×C4×D4—21no—
489C2×#117C22×C6111yescharacteristic
490#485—24no—
491#452—24no—
492C2×#107C22×C6111yescharacteristic, complemented
493C2×#106C22×C6111yescharacteristic, complemented
494C2×#103C22×C6111yescharacteristic, complemented
495C2×#103C22×C6111yescharacteristic, complemented
496C2×#103C22×C6111yescharacteristic, complemented
497C2×#103C22×C6111yescharacteristic, complemented
498C2×#103C22×C6111yescharacteristic, complemented
499C2×#102C22×C6111yescharacteristic, complemented
500C2×#102C22×C6111yescharacteristic, complemented
501C2×#102C22×C6111yescharacteristic, complemented
502C2×C22⋊C8C22×C6111yescharacteristic
503C2×C22⋊C8C22×C6111yescharacteristic
504C2×C22⋊C8C22×C6111yescharacteristic
505C2×C22⋊C8C22×C6111yescharacteristic
506C2×C22⋊C8C22×C6111yescharacteristic
507C2×C22⋊C8C22×C6111yescharacteristic
508#385—21no—
509#385—21no—
510#385—21no—
511#380C22×C6111yescharacteristic
512#380C22×C6111yescharacteristic
513#380C22×C6111yescharacteristic
514#379—21no—
515#340C22×C6111yescharacteristic, complemented
516#340C22×C6111yescharacteristic, complemented
517#340C22×C6111yescharacteristic, complemented
518#340C22×C6111yescharacteristic, complemented
519C61#2960111yescharacteristic, direct product factor, Sylow
520C25D4×C6111yescharacteristic
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41D4×C6114yes—
527C22×Q8C23×C6111yescharacteristic
528C22×Q8C23×C6111yescharacteristic
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C23×C6111yescharacteristic
533C23×C4—21no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4D4×C6111yescharacteristic
541C23×C4D4×C6111yescharacteristic
542C23×C4D4×C6111yescharacteristic
543C23×C4C23×C6111yescharacteristic
544C23×C4C23×C6111yescharacteristic
545C23×C4C23×C6111yescharacteristic
546C2×Q16—22no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C22×C8C23×C6111yescharacteristic
553C22×C8C23×C6111yescharacteristic
554C22×C8C23×C6111yescharacteristic
555C22×C8C23×C6111yescharacteristic
556#123—28no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#120—28no—
572C4×D4—28no—
573C4×D4—28no—
574#117—22no—
575#117D4×C6114yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4C23×C6111yescharacteristic
582C2×C4⋊C4C23×C6111yescharacteristic
583C2×C4⋊C4C23×C6111yescharacteristic
584C2×C4⋊C4C23×C6111yescharacteristic
585C2×C4⋊C4C23×C6111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C42—21no—
598#107—22no—
599#106—22no—
600#103—22no—
601#103—22no—
602#103—22no—
603#103—41no—
604#103—41no—
605#102—22no—
606#102—41no—
607#102—41no—
608C22⋊C8—22no—
609C22⋊C8—22no—
610C22⋊C8—41no—
611C22⋊C8—41no—
612C22⋊C8—41no—
613C22⋊C8—41no—
614#95—21no—
615#95—21no—
616#95—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—41no—
622C24—41no—
623C24—41no—
624C24—41no—
625C24C2×D4×C6111yescharacteristic
626C24C2×D4×C6111yescharacteristic
627C24C2×D4×C6111yescharacteristic
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C6112yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4C2×D4×C6112yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4C2×D4×C6111yescharacteristic
699C22×C4C2×D4×C6111yescharacteristic
700C22×C4C2×D4×C6111yescharacteristic
701C22×C4C2×D4×C6112yes—
702C22×C4C2×D4×C6112yes—
703C22×C4C24×C6111yescharacteristic
704Q16—44no—
705SD16—44no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4C2×D4×C6112yes—
732C4⋊C4C2×D4×C6112yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C42—24no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C6112yes—
778C23#135×C6112yes—
779C23#137×C6112yes—
780C23C22×D4×C6111yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—44no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4#120×C6112yes—
842C2×C4C22×D4×C6111yescharacteristic
843C2×C4C22×D4×C6111yescharacteristic
844C2×C4H(5,𝔽2)×C6111yescharacteristic
845C2×C4H(5,𝔽2)×C6111yescharacteristic
846C2×C4H(5,𝔽2)×C6111yescharacteristic
847C2×C4H(5,𝔽2)×C6111yescharacteristic
848C8—41no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—416no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C6111yescharacteristic
882C22C61×#53411yescharacteristic
883C22C61×#53411yescharacteristic
884C22C2×#135×C6111yescharacteristic
885C22C2×#137×C6111yescharacteristic
886C22C61×#57511yescharacteristic
887C22C61×#57511yescharacteristic
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4C61×#53411yescharacteristic
899C4C61×#53411yescharacteristic
900C4C61×#53511yescharacteristic
901C4C61×#53511yescharacteristic
902C2—42no—
903C2—42no—
904C2—42no—
905C2—82no—
906C2C61×#261311yescharacteristic
907C2C61×#300211yescharacteristic
908C2C61×#300711yescharacteristic
909C2C61×#319011yescharacteristic
910C2C61×#319111yescharacteristic
911C2C61×#319611yescharacteristic
912C2C61×#319711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C24×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#485C2semidirect
3. C2×C61×#452C2semidirect
4. C61×#2848C2semidirect
5. C61×#2036C2semidirect
6. C61×#2035C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#2001C2semidirect
10. C61×#2001C2semidirect
11. C61×#2000C2semidirect
12. C61×#2000C2semidirect
13. C61×#1825C2semidirect
14. C61×#1788C2semidirect
15. C61×#1779C2semidirect
18. C22×Q16×C61C22semidirect
19. C22×SD16×C61C22semidirect
36. C2×#107×C61C22semidirect
37. C2×#106×C61C22semidirect
38. C2×#103×C61C22semidirect
39. C2×#103×C61C22semidirect
40. C2×#103×C61C22semidirect
41. C2×#103×C61C22semidirect
42. C2×#103×C61C22semidirect
43. C2×#102×C61C22semidirect
44. C2×#102×C61C22semidirect
45. C2×#102×C61C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
395. #29601C61direct (N × H)
447. C2×#485C2×C61semidirect
448. C2×#452C2×C61semidirect
449. #2848C2×C61semidirect
450. #2036C2×C61semidirect
451. #2035C2×C61semidirect
452. #2034C2×C61semidirect
453. #2033C2×C61semidirect
454. #2001C2×C61semidirect
455. #2001C2×C61semidirect
456. #2000C2×C61semidirect
457. #2000C2×C61semidirect
458. #1825C2×C61semidirect
459. #1788C2×C61semidirect
460. #1779C2×C61semidirect
474. C22×Q16C22×C61semidirect
475. C22×SD16C22×C61semidirect
492. C2×#107C22×C61semidirect
493. C2×#106C22×C61semidirect
494. C2×#103C22×C61semidirect
495. C2×#103C22×C61semidirect
496. C2×#103C22×C61semidirect
497. C2×#103C22×C61semidirect
498. C2×#103C22×C61semidirect
499. C2×#102C22×C61semidirect
500. C2×#102C22×C61semidirect
501. C2×#102C22×C61semidirect
515. #340C22×C61semidirect
516. #340C22×C61semidirect
517. #340C22×C61semidirect
518. #340C22×C61semidirect
519. C61#29601direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5252
C2×C61×#4852
C2×C61×#4522
C61×#28482
C61×#20362
C61×#20352
C61×#20342
C61×#20332
C61×#20012
C61×#20002
C61×#18252
C61×#17882
C61×#17792
#2960161