Finite Group Databasebeta

← C61×#29600 #29533033

Subgroups — C61×#29600 #29533033

Order 15616.

1540 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#525C211yesmaximal, characteristic, complemented
2C2×C61×#482C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic, complemented
4C61×#2847C211yesmaximal, characteristic, complemented
5C61×#2036C211yesmaximal, characteristic, complemented
6C61×#2035C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#2000C211yesmaximal, characteristic, complemented
10C61×#2000C211yesmaximal, characteristic, complemented
11C61×#1999C211yesmaximal, characteristic, complemented
12C61×#1999C211yesmaximal, characteristic, complemented
13C61×#1825C211yesmaximal, characteristic, complemented
14C61×#1788C211yesmaximal, characteristic, complemented
15C61×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic, complemented
19C22×D8×C61C2211yescharacteristic, complemented
20C61×#525—24no—
21C61×#525—24no—
22C2×#123×C61—21no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×C22⋊Q8×C61C2211yescharacteristic
25C2×#121×C61C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#120×C61—21no—
31C2×#120×C61—21no—
32C2×C4×D4×C61—21no—
33C2×C4×D4×C61—21no—
34C2×#117×C61C2211yescharacteristic
35C61×#482—24no—
36C61×#449—24no—
37C2×#107×C61C2211yescharacteristic, complemented
38C2×#106×C61C2211yescharacteristic, complemented
39C2×#103×C61C2211yescharacteristic, complemented
40C2×#103×C61C2211yescharacteristic, complemented
41C2×#103×C61C2211yescharacteristic, complemented
42C2×#102×C61C2211yescharacteristic, complemented
43C2×#102×C61C2211yescharacteristic, complemented
44C2×#102×C61C2211yescharacteristic, complemented
45C2×#102×C61C2211yescharacteristic, complemented
46C2×#102×C61C2211yescharacteristic, complemented
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C2×C22⋊C8×C61C2211yescharacteristic
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic
53C61×#386—21no—
54C61×#386—21no—
55C61×#386—21no—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
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×C61D414yescomplemented
70C22×Q8×C61C2311yescharacteristic
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C22×D4×C61C2311yescharacteristic
78C22×D4×C61C2311yescharacteristic
79C23×C4×C61—22no—
80C23×C4×C61—22no—
81C23×C4×C61—21no—
82C23×C4×C61—41no—
83C23×C4×C61—41no—
84C23×C4×C61—41no—
85C23×C4×C61—41no—
86C23×C4×C61D411yescharacteristic
87C23×C4×C61D411yescharacteristic
88C23×C4×C61D411yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C2×SD16×C61—22no—
93C2×SD16×C61—41no—
94C2×SD16×C61—41no—
95C2×D8×C61—22no—
96C2×D8×C61—41no—
97C2×D8×C61—41no—
98C22×C8×C61C2311yescharacteristic
99C22×C8×C61C2311yescharacteristic
100C22×C8×C61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102#123×C61—28no—
103C22⋊Q8×C61—22no—
104C22⋊Q8×C61—22no—
105C22⋊Q8×C61—22no—
106C22⋊Q8×C61—22no—
107#121×C61—22no—
108#121×C61—22no—
109#121×C61—22no—
110#121×C61—22no—
111#121×C61—22no—
112#121×C61—22no—
113#121×C61—41no—
114#121×C61—41no—
115#121×C61—41no—
116#121×C61—41no—
117#120×C61—28no—
118#120×C61—44no—
119C4×D4×C61—28no—
120C4×D4×C61—28no—
121#117×C61—22no—
122#117×C61D414yescomplemented
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
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×C22⋊C4×C61—21no—
141C2×C42×C61—21no—
142#107×C61—22no—
143#106×C61—22no—
144#103×C61—22no—
145#103×C61—41no—
146#103×C61—41no—
147#102×C61—22no—
148#102×C61—22no—
149#102×C61—22no—
150#102×C61—41no—
151#102×C61—41no—
152C22⋊C8×C61—22no—
153C22⋊C8×C61—22no—
154C22⋊C8×C61—41no—
155C22⋊C8×C61—41no—
156C22⋊C8×C61—41no—
157C22⋊C8×C61—41no—
158#95×C61—21no—
159#95×C61—21no—
160#95×C61—21no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—41no—
167C24×C61—41no—
168C24×C61—41no—
169C24×C61—41no—
170C24×C61C2×D411yescharacteristic
171C24×C61C2×D411yescharacteristic
172C24×C61C2×D411yescharacteristic
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61C2×D412yes—
183C2×D4×C61—24no—
184C2×D4×C61—24no—
185C2×D4×C61—24no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—42no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—42no—
202C2×D4×C61—42no—
203C2×D4×C61—42no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—42no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61C2×D412yes—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—22no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—24no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—41no—
240C22×C4×C61—41no—
241C22×C4×C61—41no—
242C22×C4×C61—41no—
243C22×C4×C61—41no—
244C22×C4×C61—41no—
245C22×C4×C61—44no—
246C22×C4×C61—44no—
247C22×C4×C61—44no—
248C22×C4×C61—44no—
249C22×C4×C61—42no—
250C22×C4×C61—42no—
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2×D412yes—
256C22×C4×C61C2411yescharacteristic
257SD16×C61—44no—
258D8×C61—44no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C4⋊C4×C61—24no—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61C2×D412yes—
282C4⋊C4×C61C2×D412yes—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—24no—
288C22⋊C4×C61—42no—
289C22⋊C4×C61—42no—
290C22⋊C4×C61—42no—
291C22⋊C4×C61—42no—
292C22⋊C4×C61—42no—
293C22⋊C4×C61—42no—
294C42×C61—24no—
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—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—22no—
314C23×C61—44no—
315C23×C61—44no—
316C23×C61—44no—
317C23×C61—44no—
318C23×C61—44no—
319C23×C61—44no—
320C23×C61—44no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61#12012yes—
335C23×C61#13512yes—
336C23×C61AGL(1,ℤ/8)12yes—
337C23×C61C22×D411yescharacteristic
338Q8×C61—22no—
339Q8×C61—22no—
340Q8×C61—41no—
341Q8×C61—41no—
342D4×C61—22no—
343D4×C61—22no—
344D4×C61—48no—
345D4×C61—48no—
346D4×C61—48no—
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61—41no—
353D4×C61—84no—
354D4×C61—84no—
355D4×C61—84no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—22no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—44no—
372C2×C4×C61—44no—
373C2×C4×C61—48no—
374C2×C4×C61—44no—
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—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61#12012yes—
399C2×C4×C61C22×D411yescharacteristic
400C2×C4×C61C22×D411yescharacteristic
401C2×C4×C61H(5,𝔽2)11yescharacteristic
402C2×C4×C61H(5,𝔽2)11yescharacteristic
403C2×C4×C61H(5,𝔽2)11yescharacteristic
404C2×C4×C61H(5,𝔽2)11yescharacteristic
405C8×C61—41no—
406C8×C61—41no—
407C8×C61—41no—
408C8×C61—41no—
409#29600C6111yesmaximal, characteristic, direct product factor, Sylow
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—416no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61C2×#12011yescharacteristic
447C22×C61#53411yescharacteristic
448C22×C61#53411yescharacteristic
449C22×C61C2×#13511yescharacteristic
450C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C61#57511yescharacteristic
452C22×C61#57511yescharacteristic
453C4×C61—22no—
454C4×C61—41no—
455C4×C61—41no—
456C4×C61—42no—
457C4×C61—42no—
458C4×C61—42no—
459C4×C61—81no—
460C4×C61—81no—
461C4×C61—81no—
462C4×C61#53411yescharacteristic
463C4×C61#53411yescharacteristic
464C4×C61#53511yescharacteristic
465C4×C61#53511yescharacteristic
466C2×#525C2×C6111yescharacteristic, complemented
467C2×#482C2×C6111yescharacteristic, complemented
468C2×#449C2×C6111yescharacteristic, complemented
469#2847C2×C6111yescharacteristic, complemented
470#2036C2×C6111yescharacteristic, complemented
471#2035C2×C6111yescharacteristic, complemented
472#2034C2×C6111yescharacteristic, complemented
473#2033C2×C6111yescharacteristic, complemented
474#2000C2×C6111yescharacteristic, complemented
475#2000C2×C6111yescharacteristic, complemented
476#1999C2×C6111yescharacteristic, complemented
477#1999C2×C6111yescharacteristic, complemented
478#1825C2×C6111yescharacteristic, complemented
479#1788C2×C6111yescharacteristic, complemented
480#1779C2×C6111yescharacteristic, complemented
481C2×C61—42no—
482C2×C61—42no—
483C2×C61—42no—
484C2×C61—82no—
485C2×C61—161no—
486C2×C61#261311yescharacteristic
487C2×C61#300211yescharacteristic
488C2×C61#300611yescharacteristic
489C2×C61#318811yescharacteristic
490C2×C61#319111yescharacteristic
491C2×C61#319411yescharacteristic
492C2×C61#319711yescharacteristic
493C22×#41C22×C6111yescharacteristic
494C24×C4C22×C6111yescharacteristic
495C22×SD16C22×C6111yescharacteristic, complemented
496C22×D8C22×C6111yescharacteristic, complemented
497#525—24no—
498#525—24no—
499C2×#123—21no—
500C2×C22⋊Q8C22×C6111yescharacteristic
501C2×C22⋊Q8C22×C6111yescharacteristic
502C2×#121C22×C6111yescharacteristic
503C2×#121C22×C6111yescharacteristic
504C2×#121C22×C6111yescharacteristic
505C2×#121C22×C6111yescharacteristic
506C2×#121C22×C6111yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4—21no—
510C2×C4×D4—21no—
511C2×#117C22×C6111yescharacteristic
512#482—24no—
513#449—24no—
514C2×#107C22×C6111yescharacteristic, complemented
515C2×#106C22×C6111yescharacteristic, complemented
516C2×#103C22×C6111yescharacteristic, complemented
517C2×#103C22×C6111yescharacteristic, complemented
518C2×#103C22×C6111yescharacteristic, complemented
519C2×#102C22×C6111yescharacteristic, complemented
520C2×#102C22×C6111yescharacteristic, complemented
521C2×#102C22×C6111yescharacteristic, complemented
522C2×#102C22×C6111yescharacteristic, complemented
523C2×#102C22×C6111yescharacteristic, complemented
524C2×C22⋊C8C22×C6111yescharacteristic
525C2×C22⋊C8C22×C6111yescharacteristic
526C2×C22⋊C8C22×C6111yescharacteristic
527C2×C22⋊C8C22×C6111yescharacteristic
528C2×C22⋊C8C22×C6111yescharacteristic
529C2×C22⋊C8C22×C6111yescharacteristic
530#386—21no—
531#386—21no—
532#386—21no—
533#380C22×C6111yescharacteristic
534#380C22×C6111yescharacteristic
535#380C22×C6111yescharacteristic
536#340C22×C6111yescharacteristic, complemented
537#340C22×C6111yescharacteristic, complemented
538#340C22×C6111yescharacteristic, complemented
539#340C22×C6111yescharacteristic, complemented
540C61#2960011yescharacteristic, direct product factor, Sylow
541C25D4×C6111yescharacteristic
542C2×#41—22no—
543C2×#41—41no—
544C2×#41—41no—
545C2×#41—41no—
546C2×#41—41no—
547C2×#41D4×C6114yescomplemented
548C22×Q8C23×C6111yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4C23×C6111yescharacteristic
556C22×D4C23×C6111yescharacteristic
557C23×C4—21no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4D4×C6111yescharacteristic
565C23×C4D4×C6111yescharacteristic
566C23×C4D4×C6111yescharacteristic
567C23×C4C23×C6111yescharacteristic
568C23×C4C23×C6111yescharacteristic
569C23×C4C23×C6111yescharacteristic
570C2×SD16—22no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C22×C8C23×C6111yescharacteristic
577C22×C8C23×C6111yescharacteristic
578C22×C8C23×C6111yescharacteristic
579C22×C8C23×C6111yescharacteristic
580#123—28no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#120—28no—
596#120—44no—
597C4×D4—28no—
598C4×D4—28no—
599#117—22no—
600#117D4×C6114yescomplemented
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4C23×C6111yescharacteristic
604C2×C4⋊C4C23×C6111yescharacteristic
605C2×C4⋊C4C23×C6111yescharacteristic
606C2×C4⋊C4C23×C6111yescharacteristic
607C2×C4⋊C4C23×C6111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C42—21no—
620#107—22no—
621#106—22no—
622#103—22no—
623#103—41no—
624#103—41no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630C22⋊C8—22no—
631C22⋊C8—22no—
632C22⋊C8—41no—
633C22⋊C8—41no—
634C22⋊C8—41no—
635C22⋊C8—41no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—41no—
645C24—41no—
646C24—41no—
647C24—41no—
648C24C2×D4×C6111yescharacteristic
649C24C2×D4×C6111yescharacteristic
650C24C2×D4×C6111yescharacteristic
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C6112yes—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4C2×D4×C6112yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—24no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4C2×D4×C6111yescharacteristic
730C22×C4C2×D4×C6111yescharacteristic
731C22×C4C2×D4×C6111yescharacteristic
732C22×C4C2×D4×C6112yes—
733C22×C4C2×D4×C6112yes—
734C22×C4C24×C6111yescharacteristic
735SD16—44no—
736D8—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4C2×D4×C6112yes—
760C4⋊C4C2×D4×C6112yes—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C42—24no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—22no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23#120×C6112yes—
813C23#135×C6112yes—
814C23AGL(1,ℤ/8)×C6112yes—
815C23C22×D4×C6111yescharacteristic
816Q8—22no—
817Q8—22no—
818Q8—41no—
819Q8—41no—
820D4—22no—
821D4—22no—
822D4—48no—
823D4—48no—
824D4—48no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—84no—
832D4—84no—
833D4—84no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4#120×C6112yes—
877C2×C4C22×D4×C6111yescharacteristic
878C2×C4C22×D4×C6111yescharacteristic
879C2×C4H(5,𝔽2)×C6111yescharacteristic
880C2×C4H(5,𝔽2)×C6111yescharacteristic
881C2×C4H(5,𝔽2)×C6111yescharacteristic
882C2×C4H(5,𝔽2)×C6111yescharacteristic
883C8—41no—
884C8—41no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—416no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#120×C6111yescharacteristic
924C22C61×#53411yescharacteristic
925C22C61×#53411yescharacteristic
926C22C2×#135×C6111yescharacteristic
927C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
928C22C61×#57511yescharacteristic
929C22C61×#57511yescharacteristic
930C4—22no—
931C4—41no—
932C4—41no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C61×#53411yescharacteristic
940C4C61×#53411yescharacteristic
941C4C61×#53511yescharacteristic
942C4C61×#53511yescharacteristic
943C2—42no—
944C2—42no—
945C2—42no—
946C2—82no—
947C2—161no—
948C2C61×#261311yescharacteristic
949C2C61×#300211yescharacteristic
950C2C61×#300611yescharacteristic
951C2C61×#318811yescharacteristic
952C2C61×#319111yescharacteristic
953C2C61×#319411yescharacteristic
954C2C61×#319711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
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
1. C2×C61×#525C2semidirect
2. C2×C61×#482C2semidirect
3. C2×C61×#449C2semidirect
4. C61×#2847C2semidirect
5. C61×#2036C2semidirect
6. C61×#2035C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#2000C2semidirect
10. C61×#2000C2semidirect
11. C61×#1999C2semidirect
12. C61×#1999C2semidirect
13. C61×#1825C2semidirect
14. C61×#1788C2semidirect
15. C61×#1779C2semidirect
18. C22×SD16×C61C22semidirect
19. C22×D8×C61C22semidirect
37. C2×#107×C61C22semidirect
38. C2×#106×C61C22semidirect
39. C2×#103×C61C22semidirect
40. C2×#103×C61C22semidirect
41. C2×#103×C61C22semidirect
42. C2×#102×C61C22semidirect
43. C2×#102×C61C22semidirect
44. C2×#102×C61C22semidirect
45. C2×#102×C61C22semidirect
46. C2×#102×C61C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
69. C2×#41×C61D4semidirect
122. #117×C61D4semidirect
409. #29600C61direct (N × H)
466. C2×#525C2×C61semidirect
467. C2×#482C2×C61semidirect
468. C2×#449C2×C61semidirect
469. #2847C2×C61semidirect
470. #2036C2×C61semidirect
471. #2035C2×C61semidirect
472. #2034C2×C61semidirect
473. #2033C2×C61semidirect
474. #2000C2×C61semidirect
475. #2000C2×C61semidirect
476. #1999C2×C61semidirect
477. #1999C2×C61semidirect
478. #1825C2×C61semidirect
479. #1788C2×C61semidirect
480. #1779C2×C61semidirect
495. C22×SD16C22×C61semidirect
496. C22×D8C22×C61semidirect
514. C2×#107C22×C61semidirect
515. C2×#106C22×C61semidirect
516. C2×#103C22×C61semidirect
517. C2×#103C22×C61semidirect
518. C2×#103C22×C61semidirect
519. C2×#102C22×C61semidirect
520. C2×#102C22×C61semidirect
521. C2×#102C22×C61semidirect
522. C2×#102C22×C61semidirect
523. C2×#102C22×C61semidirect
536. #340C22×C61semidirect
537. #340C22×C61semidirect
538. #340C22×C61semidirect
539. #340C22×C61semidirect
540. C61#29600direct (N × H)
547. C2×#41D4×C61semidirect
600. #117D4×C61semidirect

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×#4822
C2×C61×#4492
C61×#28472
C61×#20362
C61×#20352
C61×#20342
C61×#20332
C61×#20002
C61×#19992
C61×#18252
C61×#17882
C61×#17792
#2960061