Finite Group Databasebeta

← C61×#62863 #29566296

Subgroups — C61×#62863 #29566296

Order 15616.

7466 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3560C218yesmaximal, complemented
2C61×#3558C218yesmaximal, complemented
3C61×#3537C218yesmaximal, complemented
4C61×#3534C218yesmaximal, complemented
5C61×#3533C218yesmaximal, complemented
6C61×#3532C218yesmaximal, complemented
7C61×#3505C214yesmaximal, complemented
8C61×#3496C214yesmaximal, complemented
9C61×#3484C214yesmaximal, complemented
10C2×C61×#538C212yesmaximal, complemented
11C2×C61×#534C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C61C2214yescomplemented
13C23×D4×C61C2212yescomplemented
14C61×#563C2218yescomplemented
15C61×#562C22116yescomplemented
16C61×H(3,𝔽4)C2218yescomplemented
17C61×#560C22116yescomplemented
18C61×#560C2218yescomplemented
19C61×#560C2218yescomplemented
20C61×#559C2218yescomplemented
21C61×#553C22116yescomplemented
22C61×#553C22116yescomplemented
23C61×#553C2218yescomplemented
24C61×#552C2218yescomplemented
25C61×#551C22116yescomplemented
26C61×#551C2218yescomplemented
27C61×#551C2218yescomplemented
28C61×#548C2218yescomplemented
29C61×#547C2218yescomplemented
30C61×#547C2218yescomplemented
31C61×#546C2218yescomplemented
32C61×#546C22116yescomplemented
33C61×#546C22116yescomplemented
34C61×#546C22116yescomplemented
35C61×#546C22116yescomplemented
36C61×#546C22116yescomplemented
37D42×C61C2218yescomplemented
38D42×C61C22116yescomplemented
39D42×C61C22116yescomplemented
40D42×C61C2218yescomplemented
41D42×C61C2218yescomplemented
42C61×#542C22116yescomplemented
43C61×#540C22116yescomplemented
44C61×#539C22116yescomplemented
45C61×#539C2218yescomplemented
46C61×#538C22116yescomplemented
47C61×#538C2218yescomplemented
48C61×#538C2218yescomplemented
49C61×#538C22116yescomplemented
50C61×#538C22116yescomplemented
51C61×#538C22116yescomplemented
52C61×#538C2218yescomplemented
53C61×#537C2218yescomplemented
54C61×#535C2218yescomplemented
55C61×#535C22116yescomplemented
56C61×#534C2218yescomplemented
57C61×#534C2218yescomplemented
58C61×#534C2218yescomplemented
59C61×#534C2218yescomplemented
60C61×#534C22116yescomplemented
61C61×#534C2218yescomplemented
62C61×#532C2218yescomplemented
63C61×#529C2218yescomplemented
64C2×#126×C61C2214yescomplemented
65C2×#124×C61C2214yescomplemented
66C61×#525C2218yescomplemented
67C61×#525C2218yescomplemented
68C2×#123×C61C2214yescomplemented
69C2×#123×C61C2214yescomplemented
70C2×C22⋊Q8×C61C2212yescomplemented
71C2×#121×C61C2214yescomplemented
72C2×#121×C61C2214yescomplemented
73C2×#121×C61C2212yescomplemented
74C2×#121×C61C2218yescomplemented
75C2×#120×C61C2214yescomplemented
76C2×#120×C61C2214yescomplemented
77C2×#120×C61C2218yescomplemented
78C61×#518C2214yescomplemented
79C2×C4×D4×C61C2214yescomplemented
80C22×C22⋊C4×C61C2211yescharacteristic, complemented
81C25×C61C2311yescharacteristic
82C25×C61C2312yes—
83H(5,𝔽2)×C61—416no—
84C2×#41×C61C2318yes—
85C2×#41×C61C23116yescomplemented
86C2×#41×C61C2318yescomplemented
87C22×Q8×C61C2312yescomplemented
88C22×D4×C61—48no—
89C22×D4×C61C2314yes—
90C22×D4×C61C2314yes—
91C22×D4×C61C2314yes—
92C22×D4×C61C23116yes—
93C22×D4×C61C2318yes—
94C22×D4×C61C2314yes—
95C22×D4×C61C2314yes—
96C22×D4×C61C2314yes—
97C22×D4×C61C23116yescomplemented
98C22×D4×C61C2318yescomplemented
99C22×D4×C61C23116yescomplemented
100C22×D4×C61C2312yescomplemented
101C23×C4×C61C2312yes—
102C23×C4×C61C2312yes—
103C23×C4×C61C2314yescomplemented
104C4⋊Q8×C61C2318yescomplemented
105#127×C61C2318yes—
106#127×C61C2318yes—
107#127×C61C2318yescomplemented
108#126×C61C23116yescomplemented
109#126×C61C23116yescomplemented
110#126×C61C23116yescomplemented
111#126×C61C23116yescomplemented
112#126×C61C23116yescomplemented
113#125×C61C23116yescomplemented
114#125×C61C2318yescomplemented
115#124×C61C2318yes—
116#124×C61C2318yes—
117#124×C61C23116yescomplemented
118#124×C61C23116yescomplemented
119#124×C61C23116yescomplemented
120#124×C61C2318yescomplemented
121#124×C61C23116yescomplemented
122#123×C61C23116yes—
123#123×C61C23116yes—
124#123×C61C2318yes—
125#123×C61C2318yes—
126#123×C61C2318yes—
127#123×C61C2318yes—
128#123×C61C23116yescomplemented
129#123×C61C23116yescomplemented
130#123×C61C23116yescomplemented
131#123×C61C23116yescomplemented
132#123×C61C23116yescomplemented
133#123×C61C23116yescomplemented
134#123×C61C23116yescomplemented
135#123×C61C23116yescomplemented
136C22⋊Q8×C61C2318yes—
137C22⋊Q8×C61C23116yescomplemented
138C22⋊Q8×C61C23116yescomplemented
139C22⋊Q8×C61C2318yescomplemented
140C22⋊Q8×C61C2318yescomplemented
141C22⋊Q8×C61C23116yescomplemented
142C22⋊Q8×C61C23116yescomplemented
143#121×C61C2318yes—
144#121×C61C2318yes—
145#121×C61C2318yes—
146#121×C61C2318yes—
147#121×C61C23116yes—
148#121×C61C23116yes—
149#121×C61C23116yes—
150#121×C61C23116yes—
151#121×C61C2318yes—
152#121×C61C23116yescomplemented
153#121×C61C2318yescomplemented
154#121×C61C2318yescomplemented
155#121×C61C23116yescomplemented
156#121×C61C23116yescomplemented
157#121×C61C23116yescomplemented
158#121×C61C23116yescomplemented
159#121×C61C23116yescomplemented
160#121×C61C23116yescomplemented
161#121×C61C2318yescomplemented
162#121×C61C23116yescomplemented
163#121×C61C23116yescomplemented
164#121×C61C2318yescomplemented
165#120×C61C23116yes—
166#120×C61C2318yes—
167#120×C61C2318yes—
168#120×C61C2318yes—
169#120×C61C23116yes—
170#120×C61C23116yes—
171#120×C61C2318yes—
172#120×C61C23116yes—
173#120×C61C23116yescomplemented
174#120×C61C23116yescomplemented
175#120×C61C23116yescomplemented
176#120×C61C23116yescomplemented
177#120×C61C23116yescomplemented
178C4×Q8×C61C2318yescomplemented
179C4×D4×C61C2318yes—
180C4×D4×C61C2318yes—
181C4×D4×C61C2318yescomplemented
182C4×D4×C61C2318yescomplemented
183C4×D4×C61C23116yescomplemented
184C4×D4×C61C2318yescomplemented
185C4×D4×C61C2318yescomplemented
186C4×D4×C61C2318yescomplemented
187C4×D4×C61C23116yescomplemented
188C4×D4×C61C23116yescomplemented
189C4×D4×C61C23116yescomplemented
190C4×D4×C61C23116yescomplemented
191C4×D4×C61C23116yescomplemented
192#117×C61C2318yes—
193#117×C61C23116yescomplemented
194#117×C61C2318yescomplemented
195C2×C4⋊C4×C61C2314yes—
196C2×C4⋊C4×C61C2314yescomplemented
197C2×C4⋊C4×C61C2318yescomplemented
198C2×C4⋊C4×C61C2312yescomplemented
199C2×C4⋊C4×C61C2314yescomplemented
200C2×C4⋊C4×C61C2312yescomplemented
201C2×C22⋊C4×C61C2314yes—
202C2×C22⋊C4×C61C2314yes—
203C2×C22⋊C4×C61C2314yes—
204C2×C22⋊C4×C61C2318yes—
205C2×C22⋊C4×C61C2314yes—
206C2×C22⋊C4×C61C2314yes—
207C2×C22⋊C4×C61C2314yes—
208C2×C22⋊C4×C61C2318yes—
209C2×C22⋊C4×C61C2314yescomplemented
210C2×C22⋊C4×C61C23116yescomplemented
211C2×C22⋊C4×C61C23116yescomplemented
212C2×C22⋊C4×C61C2314yescomplemented
213C2×C42×C61C2314yescomplemented
214C24×C61—24no—
215C24×C61—44no—
216C24×C61—82no—
217C24×C61—84no—
218C24×C61C2414yes—
219C24×C61C2414yes—
220C24×C61C2412yes—
221C24×C61C2414yes—
222C24×C61C2418yes—
223C24×C61C2418yes—
224C24×C61C2411yescharacteristic
225#41×C61—416no—
226#41×C61—432no—
227#41×C61—88no—
228C2×Q8×C61—82no—
229C2×Q8×C61C2418yes—
230C2×Q8×C61C2418yes—
231C2×D4×C61—216no—
232C2×D4×C61—216no—
233C2×D4×C61—48no—
234C2×D4×C61—432no—
235C2×D4×C61—416no—
236C2×D4×C61—432no—
237C2×D4×C61—84no—
238C2×D4×C61—84no—
239C2×D4×C61—84no—
240C2×D4×C61—82no—
241C2×D4×C61—88no—
242C2×D4×C61—816no—
243C2×D4×C61C2418yes—
244C2×D4×C61C2418yes—
245C2×D4×C61C24116yes—
246C2×D4×C61C2418yes—
247C2×D4×C61C2418yes—
248C2×D4×C61C24116yes—
249C2×D4×C61C24116yes—
250C2×D4×C61C24116yes—
251C2×D4×C61C24116yes—
252C2×D4×C61C2418yes—
253C2×D4×C61C2418yes—
254C2×D4×C61C2418yes—
255C2×D4×C61C24116yes—
256C2×D4×C61C2418yes—
257C22×C4×C61—44no—
258C22×C4×C61—82no—
259C22×C4×C61—84no—
260C22×C4×C61C2414yes—
261C22×C4×C61C2414yes—
262C22×C4×C61C2414yes—
263C22×C4×C61C2414yes—
264C22×C4×C61C2414yes—
265C22×C4×C61C2412yes—
266C22×C4×C61C2412yes—
267C22×C4×C61C2414yes—
268C22×C4×C61C24116yes—
269C22×C4×C61C2418yes—
270C22×C4×C61C2418yes—
271C22×C4×C61C24116yes—
272C22×C4×C61C2418yes—
273C22×C4×C61C2418yes—
274C4⋊C4×C61C2418yes—
275C4⋊C4×C61C2418yes—
276C4⋊C4×C61C2418yes—
277C4⋊C4×C61C24116yes—
278C4⋊C4×C61C24116yes—
279C4⋊C4×C61C2418yes—
280C4⋊C4×C61C2418yes—
281C4⋊C4×C61C2418yes—
282C4⋊C4×C61C24116yes—
283C4⋊C4×C61C24116yes—
284C22⋊C4×C61C2418yes—
285C22⋊C4×C61C2414yes—
286C22⋊C4×C61C2418yes—
287C22⋊C4×C61C2414yes—
288C22⋊C4×C61C24116yes—
289C22⋊C4×C61C24116yes—
290C22⋊C4×C61C24116yes—
291C22⋊C4×C61C24116yes—
292C22⋊C4×C61C2418yes—
293C22⋊C4×C61C2418yes—
294C22⋊C4×C61C2418yes—
295C22⋊C4×C61C24116yes—
296C22⋊C4×C61C24116yes—
297C22⋊C4×C61C24116yes—
298C22⋊C4×C61C24116yes—
299C22⋊C4×C61C2418yes—
300C22⋊C4×C61C2418yes—
301C22⋊C4×C61C24116yes—
302C42×C61C2418yes—
303C42×C61C2418yes—
304C42×C61C2418yes—
305C42×C61C2418yes—
306C23×C61—24no—
307C23×C61—28no—
308C23×C61—28no—
309C23×C61—28no—
310C23×C61—42no—
311C23×C61—44no—
312C23×C61—44no—
313C23×C61—48no—
314C23×C61—44no—
315C23×C61—44no—
316C23×C61—44no—
317C23×C61—48no—
318C23×C61—416no—
319C23×C61—48no—
320C23×C61—416no—
321C23×C61—88no—
322C23×C61—816no—
323C23×C61H(5,𝔽2)14yes—
324C23×C61C2514yes—
325C23×C61C2518yes—
326C23×C61C2518yes—
327C23×C61C2511yescharacteristic
328C23×C61C2512yes—
329Q8×C61—48no—
330Q8×C61—48no—
331D4×C61—232no—
332D4×C61—216no—
333D4×C61—216no—
334D4×C61—48no—
335D4×C61—48no—
336D4×C61—48no—
337D4×C61—416no—
338D4×C61—416no—
339D4×C61—48no—
340D4×C61—416no—
341D4×C61—48no—
342D4×C61—416no—
343D4×C61—48no—
344D4×C61—416no—
345C2×C4×C61—28no—
346C2×C4×C61—28no—
347C2×C4×C61—48no—
348C2×C4×C61—44no—
349C2×C4×C61—42no—
350C2×C4×C61—44no—
351C2×C4×C61—48no—
352C2×C4×C61—44no—
353C2×C4×C61—42no—
354C2×C4×C61—48no—
355C2×C4×C61—416no—
356C2×C4×C61—48no—
357C2×C4×C61—44no—
358C2×C4×C61—416no—
359C2×C4×C61C2518yes—
360C2×C4×C61C2514yes—
361C2×C4×C61C2514yes—
362C2×C4×C61C2518yes—
363C2×C4×C61C2518yes—
364C2×C4×C61C2518yes—
365#62863C6111yesmaximal, characteristic, direct product factor, Sylow
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—28no—
370C22×C61—24no—
371C22×C61—28no—
372C22×C61—28no—
373C22×C61—216no—
374C22×C61—28no—
375C22×C61—28no—
376C22×C61—44no—
377C22×C61—48no—
378C22×C61—88no—
379C22×C61—88no—
380C22×C61—88no—
381C22×C61—816no—
382C22×C61—168no—
383C22×C61C2×H(5,𝔽2)12yes—
384C22×C61C2×H(5,𝔽2)14yes—
385C22×C61C2611yescharacteristic
386C4×C61—28no—
387C4×C61—28no—
388C4×C61—24no—
389C4×C61—28no—
390C4×C61—24no—
391C4×C61—28no—
392#3560C2×C6118yescomplemented
393#3558C2×C6118yescomplemented
394#3537C2×C6118yescomplemented
395#3534C2×C6118yescomplemented
396#3533C2×C6118yescomplemented
397#3532C2×C6118yescomplemented
398#3505C2×C6114yescomplemented
399#3496C2×C6114yescomplemented
400#3484C2×C6114yescomplemented
401C2×#538C2×C6112yescomplemented
402C2×#534C2×C6111yescharacteristic, complemented
403C2×C61—22no—
404C2×C61—24no—
405C2×C61—44no—
406C2×C61—48no—
407C2×C61—48no—
408C2×C61C22×H(5,𝔽2)11yescharacteristic
409C2×C61H(7,𝔽2)12yes—
410C2×H(5,𝔽2)C22×C6114yescomplemented
411C23×D4C22×C6112yescomplemented
412#563C22×C6118yescomplemented
413#562C22×C61116yescomplemented
414H(3,𝔽4)C22×C6118yescomplemented
415#560C22×C61116yescomplemented
416#560C22×C6118yescomplemented
417#560C22×C6118yescomplemented
418#559C22×C6118yescomplemented
419#553C22×C61116yescomplemented
420#553C22×C6118yescomplemented
421#553C22×C61116yescomplemented
422#552C22×C6118yescomplemented
423#551C22×C61116yescomplemented
424#551C22×C6118yescomplemented
425#551C22×C6118yescomplemented
426#548C22×C6118yescomplemented
427#547C22×C6118yescomplemented
428#547C22×C6118yescomplemented
429#546C22×C6118yescomplemented
430#546C22×C61116yescomplemented
431#546C22×C61116yescomplemented
432#546C22×C61116yescomplemented
433#546C22×C61116yescomplemented
434#546C22×C61116yescomplemented
435D42C22×C6118yescomplemented
436D42C22×C61116yescomplemented
437D42C22×C61116yescomplemented
438D42C22×C6118yescomplemented
439D42C22×C6118yescomplemented
440#542C22×C61116yescomplemented
441#540C22×C61116yescomplemented
442#539C22×C61116yescomplemented
443#539C22×C6118yescomplemented
444#538C22×C61116yescomplemented
445#538C22×C6118yescomplemented
446#538C22×C6118yescomplemented
447#538C22×C61116yescomplemented
448#538C22×C61116yescomplemented
449#538C22×C61116yescomplemented
450#538C22×C6118yescomplemented
451#537C22×C6118yescomplemented
452#535C22×C6118yescomplemented
453#535C22×C61116yescomplemented
454#534C22×C6118yescomplemented
455#534C22×C6118yescomplemented
456#534C22×C6118yescomplemented
457#534C22×C6118yescomplemented
458#534C22×C61116yescomplemented
459#534C22×C6118yescomplemented
460#532C22×C6118yescomplemented
461#529C22×C6118yescomplemented
462C2×#126C22×C6114yescomplemented
463C2×#124C22×C6114yescomplemented
464#525C22×C6118yescomplemented
465#525C22×C6118yescomplemented
466C2×#123C22×C6114yescomplemented
467C2×#123C22×C6114yescomplemented
468C2×C22⋊Q8C22×C6112yescomplemented
469C2×#121C22×C6114yescomplemented
470C2×#121C22×C6114yescomplemented
471C2×#121C22×C6112yescomplemented
472C2×#121C22×C6118yescomplemented
473C2×#120C22×C6114yescomplemented
474C2×#120C22×C6114yescomplemented
475C2×#120C22×C6118yescomplemented
476#518C22×C6114yescomplemented
477C2×C4×D4C22×C6114yescomplemented
478C22×C22⋊C4C22×C6111yescharacteristic, complemented
479C61#6286311yescharacteristic, direct product factor, Sylow
480C25C23×C6111yescharacteristic
481C25C23×C6112yes—
482H(5,𝔽2)—416no—
483C2×#41C23×C6118yes—
484C2×#41C23×C61116yescomplemented
485C2×#41C23×C6118yescomplemented
486C22×Q8C23×C6112yescomplemented
487C22×D4—48no—
488C22×D4C23×C6114yes—
489C22×D4C23×C6114yes—
490C22×D4C23×C6114yes—
491C22×D4C23×C6118yes—
492C22×D4C23×C61116yes—
493C22×D4C23×C6114yes—
494C22×D4C23×C6114yes—
495C22×D4C23×C6114yes—
496C22×D4C23×C61116yescomplemented
497C22×D4C23×C61116yescomplemented
498C22×D4C23×C6112yescomplemented
499C22×D4C23×C6118yescomplemented
500C23×C4C23×C6112yes—
501C23×C4C23×C6112yes—
502C23×C4C23×C6114yescomplemented
503C4⋊Q8C23×C6118yescomplemented
504#127C23×C6118yes—
505#127C23×C6118yes—
506#127C23×C6118yescomplemented
507#126C23×C61116yescomplemented
508#126C23×C61116yescomplemented
509#126C23×C61116yescomplemented
510#126C23×C61116yescomplemented
511#126C23×C61116yescomplemented
512#125C23×C6118yescomplemented
513#125C23×C61116yescomplemented
514#124C23×C6118yes—
515#124C23×C6118yes—
516#124C23×C61116yescomplemented
517#124C23×C61116yescomplemented
518#124C23×C6118yescomplemented
519#124C23×C61116yescomplemented
520#124C23×C61116yescomplemented
521#123C23×C61116yes—
522#123C23×C6118yes—
523#123C23×C6118yes—
524#123C23×C61116yes—
525#123C23×C6118yes—
526#123C23×C6118yes—
527#123C23×C61116yescomplemented
528#123C23×C61116yescomplemented
529#123C23×C61116yescomplemented
530#123C23×C61116yescomplemented
531#123C23×C61116yescomplemented
532#123C23×C61116yescomplemented
533#123C23×C61116yescomplemented
534#123C23×C61116yescomplemented
535C22⋊Q8C23×C6118yes—
536C22⋊Q8C23×C6118yescomplemented
537C22⋊Q8C23×C6118yescomplemented
538C22⋊Q8C23×C61116yescomplemented
539C22⋊Q8C23×C61116yescomplemented
540C22⋊Q8C23×C61116yescomplemented
541C22⋊Q8C23×C61116yescomplemented
542#121C23×C6118yes—
543#121C23×C6118yes—
544#121C23×C6118yes—
545#121C23×C6118yes—
546#121C23×C6118yes—
547#121C23×C61116yes—
548#121C23×C61116yes—
549#121C23×C61116yes—
550#121C23×C61116yes—
551#121C23×C6118yescomplemented
552#121C23×C61116yescomplemented
553#121C23×C61116yescomplemented
554#121C23×C61116yescomplemented
555#121C23×C6118yescomplemented
556#121C23×C61116yescomplemented
557#121C23×C6118yescomplemented
558#121C23×C6118yescomplemented
559#121C23×C61116yescomplemented
560#121C23×C61116yescomplemented
561#121C23×C61116yescomplemented
562#121C23×C61116yescomplemented
563#121C23×C61116yescomplemented
564#120C23×C61116yes—
565#120C23×C61116yes—
566#120C23×C6118yes—
567#120C23×C6118yes—
568#120C23×C61116yes—
569#120C23×C61116yes—
570#120C23×C6118yes—
571#120C23×C6118yes—
572#120C23×C61116yescomplemented
573#120C23×C61116yescomplemented
574#120C23×C61116yescomplemented
575#120C23×C61116yescomplemented
576#120C23×C61116yescomplemented
577C4×Q8C23×C6118yescomplemented
578C4×D4C23×C6118yes—
579C4×D4C23×C6118yes—
580C4×D4C23×C6118yescomplemented
581C4×D4C23×C6118yescomplemented
582C4×D4C23×C61116yescomplemented
583C4×D4C23×C61116yescomplemented
584C4×D4C23×C61116yescomplemented
585C4×D4C23×C61116yescomplemented
586C4×D4C23×C61116yescomplemented
587C4×D4C23×C6118yescomplemented
588C4×D4C23×C6118yescomplemented
589C4×D4C23×C6118yescomplemented
590C4×D4C23×C61116yescomplemented
591#117C23×C6118yes—
592#117C23×C6118yescomplemented
593#117C23×C61116yescomplemented
594C2×C4⋊C4C23×C6114yes—
595C2×C4⋊C4C23×C6114yescomplemented
596C2×C4⋊C4C23×C6114yescomplemented
597C2×C4⋊C4C23×C6112yescomplemented
598C2×C4⋊C4C23×C6118yescomplemented
599C2×C4⋊C4C23×C6112yescomplemented
600C2×C22⋊C4C23×C6114yes—
601C2×C22⋊C4C23×C6114yes—
602C2×C22⋊C4C23×C6114yes—
603C2×C22⋊C4C23×C6114yes—
604C2×C22⋊C4C23×C6118yes—
605C2×C22⋊C4C23×C6118yes—
606C2×C22⋊C4C23×C6114yes—
607C2×C22⋊C4C23×C6114yes—
608C2×C22⋊C4C23×C6114yescomplemented
609C2×C22⋊C4C23×C61116yescomplemented
610C2×C22⋊C4C23×C6114yescomplemented
611C2×C22⋊C4C23×C61116yescomplemented
612C2×C42C23×C6114yescomplemented
613C24—24no—
614C24—44no—
615C24—82no—
616C24—84no—
617C24C24×C6114yes—
618C24C24×C6114yes—
619C24C24×C6112yes—
620C24C24×C6114yes—
621C24C24×C6118yes—
622C24C24×C6118yes—
623C24C24×C6111yescharacteristic
624#41—416no—
625#41—432no—
626#41—88no—
627C2×Q8—82no—
628C2×Q8C24×C6118yes—
629C2×Q8C24×C6118yes—
630C2×D4—216no—
631C2×D4—216no—
632C2×D4—48no—
633C2×D4—432no—
634C2×D4—416no—
635C2×D4—432no—
636C2×D4—84no—
637C2×D4—84no—
638C2×D4—84no—
639C2×D4—82no—
640C2×D4—88no—
641C2×D4—816no—
642C2×D4C24×C6118yes—
643C2×D4C24×C6118yes—
644C2×D4C24×C61116yes—
645C2×D4C24×C6118yes—
646C2×D4C24×C6118yes—
647C2×D4C24×C61116yes—
648C2×D4C24×C61116yes—
649C2×D4C24×C61116yes—
650C2×D4C24×C61116yes—
651C2×D4C24×C6118yes—
652C2×D4C24×C6118yes—
653C2×D4C24×C6118yes—
654C2×D4C24×C61116yes—
655C2×D4C24×C6118yes—
656C22×C4—44no—
657C22×C4—82no—
658C22×C4—84no—
659C22×C4C24×C6114yes—
660C22×C4C24×C6114yes—
661C22×C4C24×C6114yes—
662C22×C4C24×C6114yes—
663C22×C4C24×C6114yes—
664C22×C4C24×C6112yes—
665C22×C4C24×C6112yes—
666C22×C4C24×C6114yes—
667C22×C4C24×C61116yes—
668C22×C4C24×C6118yes—
669C22×C4C24×C6118yes—
670C22×C4C24×C61116yes—
671C22×C4C24×C6118yes—
672C22×C4C24×C6118yes—
673C4⋊C4C24×C6118yes—
674C4⋊C4C24×C6118yes—
675C4⋊C4C24×C6118yes—
676C4⋊C4C24×C61116yes—
677C4⋊C4C24×C61116yes—
678C4⋊C4C24×C6118yes—
679C4⋊C4C24×C6118yes—
680C4⋊C4C24×C6118yes—
681C4⋊C4C24×C61116yes—
682C4⋊C4C24×C61116yes—
683C22⋊C4C24×C6118yes—
684C22⋊C4C24×C6114yes—
685C22⋊C4C24×C6118yes—
686C22⋊C4C24×C6114yes—
687C22⋊C4C24×C61116yes—
688C22⋊C4C24×C61116yes—
689C22⋊C4C24×C61116yes—
690C22⋊C4C24×C61116yes—
691C22⋊C4C24×C6118yes—
692C22⋊C4C24×C6118yes—
693C22⋊C4C24×C6118yes—
694C22⋊C4C24×C61116yes—
695C22⋊C4C24×C61116yes—
696C22⋊C4C24×C61116yes—
697C22⋊C4C24×C61116yes—
698C22⋊C4C24×C6118yes—
699C22⋊C4C24×C6118yes—
700C22⋊C4C24×C61116yes—
701C42C24×C6118yes—
702C42C24×C6118yes—
703C42C24×C6118yes—
704C42C24×C6118yes—
705C23—24no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—48no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—48no—
717C23—416no—
718C23—48no—
719C23—416no—
720C23—88no—
721C23—816no—
722C23H(5,𝔽2)×C6114yes—
723C23C25×C6114yes—
724C23C25×C6118yes—
725C23C25×C6118yes—
726C23C25×C6111yescharacteristic
727C23C25×C6112yes—
728Q8—48no—
729Q8—48no—
730D4—232no—
731D4—216no—
732D4—216no—
733D4—48no—
734D4—48no—
735D4—48no—
736D4—416no—
737D4—416no—
738D4—48no—
739D4—416no—
740D4—48no—
741D4—416no—
742D4—48no—
743D4—416no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—48no—
754C2×C4—416no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—416no—
758C2×C4C25×C6118yes—
759C2×C4C25×C6114yes—
760C2×C4C25×C6114yes—
761C2×C4C25×C6118yes—
762C2×C4C25×C6118yes—
763C2×C4C25×C6118yes—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—216no—
772C22—28no—
773C22—28no—
774C22—44no—
775C22—48no—
776C22—88no—
777C22—88no—
778C22—88no—
779C22—816no—
780C22—168no—
781C22C2×H(5,𝔽2)×C6112yes—
782C22C2×H(5,𝔽2)×C6114yes—
783C22C26×C6111yescharacteristic
784C4—28no—
785C4—28no—
786C4—24no—
787C4—28no—
788C4—24no—
789C4—28no—
790C2—22no—
791C2—24no—
792C2—44no—
793C2—48no—
794C2—48no—
795C2C22×H(5,𝔽2)×C6111yescharacteristic
796C2C61×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C61C26
commutator, Frattini, cosocleC22C26×C61
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3560C2semidirect
2. C61×#3558C2semidirect
3. C61×#3537C2semidirect
4. C61×#3534C2semidirect
5. C61×#3533C2semidirect
6. C61×#3532C2semidirect
7. C61×#3505C2semidirect
8. C61×#3496C2semidirect
9. C61×#3484C2semidirect
10. C2×C61×#538C2semidirect
11. C2×C61×#534C2semidirect
12. C2×H(5,𝔽2)×C61C22semidirect
13. C23×D4×C61C22semidirect
14. C61×#563C22semidirect
15. C61×#562C22semidirect
16. C61×H(3,𝔽4)C22semidirect
17. C61×#560C22semidirect
18. C61×#560C22semidirect
19. C61×#560C22semidirect
20. C61×#559C22semidirect
21. C61×#553C22semidirect
22. C61×#553C22semidirect
23. C61×#553C22semidirect
24. C61×#552C22semidirect
25. C61×#551C22semidirect
26. C61×#551C22semidirect
27. C61×#551C22semidirect
28. C61×#548C22semidirect
29. C61×#547C22semidirect
30. C61×#547C22semidirect
31. C61×#546C22semidirect
32. C61×#546C22semidirect
33. C61×#546C22semidirect
34. C61×#546C22semidirect
35. C61×#546C22semidirect
36. C61×#546C22semidirect
37. D42×C61C22semidirect
38. D42×C61C22semidirect
39. D42×C61C22semidirect
40. D42×C61C22semidirect
41. D42×C61C22semidirect
42. C61×#542C22semidirect
43. C61×#540C22semidirect
44. C61×#539C22semidirect
45. C61×#539C22semidirect
46. C61×#538C22semidirect
47. C61×#538C22semidirect
48. C61×#538C22semidirect
49. C61×#538C22semidirect
50. C61×#538C22semidirect
51. C61×#538C22semidirect
52. C61×#538C22semidirect
53. C61×#537C22semidirect
54. C61×#535C22semidirect
55. C61×#535C22semidirect
56. C61×#534C22semidirect
57. C61×#534C22semidirect
58. C61×#534C22semidirect
59. C61×#534C22semidirect
60. C61×#534C22semidirect
61. C61×#534C22semidirect
62. C61×#532C22semidirect
63. C61×#529C22semidirect
64. C2×#126×C61C22semidirect
65. C2×#124×C61C22semidirect
66. C61×#525C22semidirect
67. C61×#525C22semidirect
68. C2×#123×C61C22semidirect
69. C2×#123×C61C22semidirect
70. C2×C22⋊Q8×C61C22semidirect
71. C2×#121×C61C22semidirect
72. C2×#121×C61C22semidirect
73. C2×#121×C61C22semidirect
74. C2×#121×C61C22semidirect
75. C2×#120×C61C22semidirect
76. C2×#120×C61C22semidirect
77. C2×#120×C61C22semidirect
78. C61×#518C22semidirect
79. C2×C4×D4×C61C22semidirect
80. C22×C22⋊C4×C61C22semidirect
85. C2×#41×C61C23semidirect
86. C2×#41×C61C23semidirect
87. C22×Q8×C61C23semidirect
97. C22×D4×C61C23semidirect
98. C22×D4×C61C23semidirect
99. C22×D4×C61C23semidirect
100. C22×D4×C61C23semidirect
103. C23×C4×C61C23semidirect
104. C4⋊Q8×C61C23semidirect
107. #127×C61C23semidirect
108. #126×C61C23semidirect
109. #126×C61C23semidirect
110. #126×C61C23semidirect
111. #126×C61C23semidirect
112. #126×C61C23semidirect
113. #125×C61C23semidirect
114. #125×C61C23semidirect
117. #124×C61C23semidirect
118. #124×C61C23semidirect
119. #124×C61C23semidirect
120. #124×C61C23semidirect
121. #124×C61C23semidirect
128. #123×C61C23semidirect
129. #123×C61C23semidirect
130. #123×C61C23semidirect
131. #123×C61C23semidirect
132. #123×C61C23semidirect
133. #123×C61C23semidirect
134. #123×C61C23semidirect
135. #123×C61C23semidirect
137. C22⋊Q8×C61C23semidirect
138. C22⋊Q8×C61C23semidirect
139. C22⋊Q8×C61C23semidirect
140. C22⋊Q8×C61C23semidirect
141. C22⋊Q8×C61C23semidirect
142. C22⋊Q8×C61C23semidirect
152. #121×C61C23semidirect
153. #121×C61C23semidirect
154. #121×C61C23semidirect
155. #121×C61C23semidirect
156. #121×C61C23semidirect
157. #121×C61C23semidirect
158. #121×C61C23semidirect
159. #121×C61C23semidirect
160. #121×C61C23semidirect
161. #121×C61C23semidirect
162. #121×C61C23semidirect
163. #121×C61C23semidirect
164. #121×C61C23semidirect
173. #120×C61C23semidirect
174. #120×C61C23semidirect
175. #120×C61C23semidirect
176. #120×C61C23semidirect
177. #120×C61C23semidirect
178. C4×Q8×C61C23semidirect
181. C4×D4×C61C23semidirect
182. C4×D4×C61C23semidirect
183. C4×D4×C61C23semidirect
184. C4×D4×C61C23semidirect
185. C4×D4×C61C23semidirect
186. C4×D4×C61C23semidirect
187. C4×D4×C61C23semidirect
188. C4×D4×C61C23semidirect
189. C4×D4×C61C23semidirect
190. C4×D4×C61C23semidirect
191. C4×D4×C61C23semidirect
193. #117×C61C23semidirect
194. #117×C61C23semidirect
196. C2×C4⋊C4×C61C23semidirect
197. C2×C4⋊C4×C61C23semidirect
198. C2×C4⋊C4×C61C23semidirect
199. C2×C4⋊C4×C61C23semidirect
200. C2×C4⋊C4×C61C23semidirect
209. C2×C22⋊C4×C61C23semidirect
210. C2×C22⋊C4×C61C23semidirect
211. C2×C22⋊C4×C61C23semidirect
212. C2×C22⋊C4×C61C23semidirect
213. C2×C42×C61C23semidirect
365. #62863C61direct (N × H)
392. #3560C2×C61semidirect
393. #3558C2×C61semidirect
394. #3537C2×C61semidirect
395. #3534C2×C61semidirect
396. #3533C2×C61semidirect
397. #3532C2×C61semidirect
398. #3505C2×C61semidirect
399. #3496C2×C61semidirect
400. #3484C2×C61semidirect
401. C2×#538C2×C61semidirect
402. C2×#534C2×C61semidirect
410. C2×H(5,𝔽2)C22×C61semidirect
411. C23×D4C22×C61semidirect
412. #563C22×C61semidirect
413. #562C22×C61semidirect
414. H(3,𝔽4)C22×C61semidirect
415. #560C22×C61semidirect
416. #560C22×C61semidirect
417. #560C22×C61semidirect
418. #559C22×C61semidirect
419. #553C22×C61semidirect
420. #553C22×C61semidirect
421. #553C22×C61semidirect
422. #552C22×C61semidirect
423. #551C22×C61semidirect
424. #551C22×C61semidirect
425. #551C22×C61semidirect
426. #548C22×C61semidirect
427. #547C22×C61semidirect
428. #547C22×C61semidirect
429. #546C22×C61semidirect
430. #546C22×C61semidirect
431. #546C22×C61semidirect
432. #546C22×C61semidirect
433. #546C22×C61semidirect
434. #546C22×C61semidirect
435. D42C22×C61semidirect
436. D42C22×C61semidirect
437. D42C22×C61semidirect
438. D42C22×C61semidirect
439. D42C22×C61semidirect
440. #542C22×C61semidirect
441. #540C22×C61semidirect
442. #539C22×C61semidirect
443. #539C22×C61semidirect
444. #538C22×C61semidirect
445. #538C22×C61semidirect
446. #538C22×C61semidirect
447. #538C22×C61semidirect
448. #538C22×C61semidirect
449. #538C22×C61semidirect
450. #538C22×C61semidirect
451. #537C22×C61semidirect
452. #535C22×C61semidirect
453. #535C22×C61semidirect
454. #534C22×C61semidirect
455. #534C22×C61semidirect
456. #534C22×C61semidirect
457. #534C22×C61semidirect
458. #534C22×C61semidirect
459. #534C22×C61semidirect
460. #532C22×C61semidirect
461. #529C22×C61semidirect
462. C2×#126C22×C61semidirect
463. C2×#124C22×C61semidirect
464. #525C22×C61semidirect
465. #525C22×C61semidirect
466. C2×#123C22×C61semidirect
467. C2×#123C22×C61semidirect
468. C2×C22⋊Q8C22×C61semidirect
469. C2×#121C22×C61semidirect
470. C2×#121C22×C61semidirect
471. C2×#121C22×C61semidirect
472. C2×#121C22×C61semidirect
473. C2×#120C22×C61semidirect
474. C2×#120C22×C61semidirect
475. C2×#120C22×C61semidirect
476. #518C22×C61semidirect
477. C2×C4×D4C22×C61semidirect
478. C22×C22⋊C4C22×C61semidirect
479. C61#62863direct (N × H)
484. C2×#41C23×C61semidirect
485. C2×#41C23×C61semidirect
486. C22×Q8C23×C61semidirect
496. C22×D4C23×C61semidirect
497. C22×D4C23×C61semidirect
498. C22×D4C23×C61semidirect
499. C22×D4C23×C61semidirect
502. C23×C4C23×C61semidirect
503. C4⋊Q8C23×C61semidirect
506. #127C23×C61semidirect
507. #126C23×C61semidirect
508. #126C23×C61semidirect
509. #126C23×C61semidirect
510. #126C23×C61semidirect
511. #126C23×C61semidirect
512. #125C23×C61semidirect
513. #125C23×C61semidirect
516. #124C23×C61semidirect
517. #124C23×C61semidirect
518. #124C23×C61semidirect
519. #124C23×C61semidirect
520. #124C23×C61semidirect
527. #123C23×C61semidirect
528. #123C23×C61semidirect
529. #123C23×C61semidirect
530. #123C23×C61semidirect
531. #123C23×C61semidirect
532. #123C23×C61semidirect
533. #123C23×C61semidirect
534. #123C23×C61semidirect
536. C22⋊Q8C23×C61semidirect
537. C22⋊Q8C23×C61semidirect
538. C22⋊Q8C23×C61semidirect
539. C22⋊Q8C23×C61semidirect
540. C22⋊Q8C23×C61semidirect
541. C22⋊Q8C23×C61semidirect
551. #121C23×C61semidirect
552. #121C23×C61semidirect
553. #121C23×C61semidirect
554. #121C23×C61semidirect
555. #121C23×C61semidirect
556. #121C23×C61semidirect
557. #121C23×C61semidirect
558. #121C23×C61semidirect
559. #121C23×C61semidirect
560. #121C23×C61semidirect
561. #121C23×C61semidirect
562. #121C23×C61semidirect
563. #121C23×C61semidirect
572. #120C23×C61semidirect
573. #120C23×C61semidirect
574. #120C23×C61semidirect
575. #120C23×C61semidirect
576. #120C23×C61semidirect
577. C4×Q8C23×C61semidirect
580. C4×D4C23×C61semidirect
581. C4×D4C23×C61semidirect
582. C4×D4C23×C61semidirect
583. C4×D4C23×C61semidirect
584. C4×D4C23×C61semidirect
585. C4×D4C23×C61semidirect
586. C4×D4C23×C61semidirect
587. C4×D4C23×C61semidirect
588. C4×D4C23×C61semidirect
589. C4×D4C23×C61semidirect
590. C4×D4C23×C61semidirect
592. #117C23×C61semidirect
593. #117C23×C61semidirect
595. C2×C4⋊C4C23×C61semidirect
596. C2×C4⋊C4C23×C61semidirect
597. C2×C4⋊C4C23×C61semidirect
598. C2×C4⋊C4C23×C61semidirect
599. C2×C4⋊C4C23×C61semidirect
608. C2×C22⋊C4C23×C61semidirect
609. C2×C22⋊C4C23×C61semidirect
610. C2×C22⋊C4C23×C61semidirect
611. C2×C22⋊C4C23×C61semidirect
612. C2×C42C23×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35602
C61×#35582
C61×#35372
C61×#35342
C61×#35332
C61×#35322
C61×#35052
C61×#34962
C61×#34842
C2×C61×#5382
C2×C61×#5342
#6286361