Finite Group Databasebeta

← C61×#61892 #29565325

Subgroups — C61×#61892 #29565325

Order 15616.

1770 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3502C211yesmaximal, characteristic, complemented
2C2×C61×#559C211yesmaximal, characteristic
3C61×#3400C218yesmaximal, complemented
4C61×#3375C218yesmaximal, complemented
5C61×#3215C214yesmaximal, complemented
6C61×#3208C212yesmaximal
7C61×#3110C214yesmaximal, complemented
8C61×#3104C212yesmaximal, complemented
9C61×#2983C211yesmaximal, characteristic, complemented
10C61×#559—24no—
11C61×#559C2218yes—
12Q82×C61C2214yescomplemented
13C61×#557—24no—
14C61×#557C2214yescomplemented
15C61×#544—21no—
16C61×#544—22no—
17C61×#533C2212yes—
18C61×#533C2214yes—
19C2×#127×C61C2211yescharacteristic
20C2×#124×C61—21no—
21C2×#124×C61C2212yes—
22C2×#123×C61—22no—
23C61×#519—21no—
24C2×C4×Q8×C61C2211yescharacteristic
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4×D4×C61—21no—
27C2×C4×D4×C61C2212yes—
28C61×#497C2218yescomplemented
29C61×#492C2214yes—
30C61×#489C2218yescomplemented
31C61×#486C2214yes—
32C61×#484C2214yes—
33C61×#477C2214yescomplemented
34C61×#474C2218yescomplemented
35C61×#464C22116yescomplemented
36C61×#462C2214yescomplemented
37C61×#461C2218yescomplemented
38C61×#460C2218yes—
39C61×#451C2214yes—
40C61×#450C2218yes—
41C61×#446C2218yescomplemented
42C61×#440C22116yescomplemented
43C4×Q16×C61C2218yescomplemented
44C61×#432C2214yes—
45C61×#431C2212yes—
46C22×Q8×C61D411yescharacteristic
47C22×Q8×C61C2311yescharacteristic
48C22×D4×C61—21no—
49C22×D4×C61—21no—
50C22×D4×C61C2312yes—
51C23×C4×C61—22no—
52C2×Q16×C61C2318yes—
53C2×SD16×C61C23116yes—
54C4⋊Q8×C61—24no—
55C4⋊Q8×C61—28no—
56C4⋊Q8×C61C2314yes—
57C4⋊Q8×C61C2312yes—
58C4⋊Q8×C61C2314yes—
59C4⋊Q8×C61C2312yes—
60#127×C61—22no—
61#127×C61C2314yes—
62#125×C61—24no—
63#125×C61—28no—
64#125×C61—24no—
65#125×C61—22no—
66#124×C61—28no—
67#124×C61—24no—
68#124×C61C2318yes—
69#123×C61—216no—
70C22⋊Q8×C61—24no—
71C22⋊Q8×C61—22no—
72C22⋊Q8×C61C2314yes—
73C4×Q8×C61—24no—
74C4×Q8×C61—24no—
75C4×Q8×C61—24no—
76C4×Q8×C61—22no—
77C4×Q8×C61—22no—
78C4×Q8×C61D414yes—
79C4×Q8×C61C2314yes—
80C4×Q8×C61C2318yes—
81C4×Q8×C61C2314yes—
82C4×Q8×C61C2314yes—
83C4×D4×C61—28no—
84C4×D4×C61—24no—
85C4×D4×C61C2318yes—
86#117×C61—24no—
87#117×C61—22no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61D411yescharacteristic
90C2×C4⋊C4×C61D412yes—
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C22⋊C4×C61—22no—
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61—22no—
95C2×C42×C61—21no—
96C2×C42×C61C2311yescharacteristic
97C2×C42×C61C2312yes—
98#107×C61C2318yes—
99C4⋊C8×C61C2314yes—
100C4⋊C8×C61C2318yes—
101#103×C61C2318yes—
102#103×C61C2318yes—
103#102×C61C23116yes—
104C22⋊C8×C61C2314yes—
105#97×C61C2318yes—
106C4×C8×C61C2314yes—
107C24×C61—22no—
108C2×Q8×C61—24no—
109C2×Q8×C61—21no—
110C2×Q8×C61—24no—
111C2×Q8×C61—22no—
112C2×Q8×C61—42no—
113C2×Q8×C61C2×D414yes—
114C2×Q8×C61C2412yes—
115C2×Q8×C61C2414yes—
116C2×D4×C61—22no—
117C2×D4×C61—24no—
118C2×D4×C61—24no—
119C2×D4×C61—44no—
120C2×D4×C61—44no—
121C2×D4×C61—82no—
122C2×D4×C61C2414yes—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—28no—
126C22×C4×C61—84no—
127C22×C4×C61C2×D412yes—
128C22×C4×C61C2×D412yes—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2411yescharacteristic
132Q16×C61—48no—
133SD16×C61—416no—
134C2×C8×C61C2418yes—
135C4⋊C4×C61—24no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—24no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—24no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—24no—
142C4⋊C4×C61—24no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—28no—
145C4⋊C4×C61—24no—
146C4⋊C4×C61C2×D414yes—
147C4⋊C4×C61C2×D418yes—
148C4⋊C4×C61C2414yes—
149C4⋊C4×C61C2412yes—
150C22⋊C4×C61—24no—
151C22⋊C4×C61—28no—
152C22⋊C4×C61—28no—
153C22⋊C4×C61—28no—
154C42×C61—24no—
155C42×C61—28no—
156C42×C61—24no—
157C42×C61C2×D414yes—
158C42×C61C2×D412yes—
159C42×C61C2412yes—
160C42×C61C2414yes—
161C23×C61—24no—
162C23×C61—44no—
163C23×C61—44no—
164C23×C61—44no—
165C23×C61C22×D411yescharacteristic
166Q8×C61—28no—
167Q8×C61—28no—
168Q8×C61—24no—
169Q8×C61—42no—
170Q8×C61—84no—
171Q8×C61—82no—
172D4×C61—28no—
173D4×C61—44no—
174D4×C61—48no—
175D4×C61—84no—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—24no—
179C2×C4×C61—24no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—42no—
183C2×C4×C61—41no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—88no—
187C2×C4×C61#13714yes—
188C2×C4×C61C22×D414yes—
189C2×C4×C61C22×D411yescharacteristic
190C2×C4×C61C22×D414yes—
191C2×C4×C61C22×D412yes—
192C2×C4×C61C22×D412yes—
193C2×C4×C61C2511yescharacteristic
194C8×C61—28no—
195#61892C6111yesmaximal, characteristic, direct product factor, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—44no—
199C22×C61—44no—
200C22×C61—44no—
201C22×C61—88no—
202C22×C61C2×#13712yes—
203C22×C61C23×D411yescharacteristic
204C4×C61—24no—
205C4×C61—22no—
206C4×C61—21no—
207C4×C61—24no—
208C4×C61—42no—
209C4×C61—44no—
210C4×C61—42no—
211C4×C61—44no—
212C4×C61C2×#13714yes—
213C4×C61#58512yes—
214#3502C2×C6111yescharacteristic, complemented
215C2×#559C2×C6111yescharacteristic
216#3400C2×C6118yescomplemented
217#3375C2×C6118yescomplemented
218#3215C2×C6114yescomplemented
219#3208C2×C6112yes—
220#3110C2×C6114yescomplemented
221#3104C2×C6112yescomplemented
222#2983C2×C6111yescharacteristic, complemented
223C2×C61—22no—
224C2×C61—84no—
225C2×C61#348711yescharacteristic
226C2×C61C22×#13711yescharacteristic
227C2×C61#358511yescharacteristic
228#559—24no—
229#559C22×C6118yes—
230Q82C22×C6114yescomplemented
231#557—24no—
232#557C22×C6114yescomplemented
233#544—21no—
234#544—22no—
235#533C22×C6112yes—
236#533C22×C6114yes—
237C2×#127C22×C6111yescharacteristic
238C2×#124—21no—
239C2×#124C22×C6112yes—
240C2×#123—22no—
241#519—21no—
242C2×C4×Q8C22×C6111yescharacteristic
243C2×C4×Q8C22×C6111yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4C22×C6112yes—
246#497C22×C6118yescomplemented
247#492C22×C6114yes—
248#489C22×C6118yescomplemented
249#486C22×C6114yes—
250#484C22×C6114yes—
251#477C22×C6114yescomplemented
252#474C22×C6118yescomplemented
253#464C22×C61116yescomplemented
254#462C22×C6114yescomplemented
255#461C22×C6118yescomplemented
256#460C22×C6118yes—
257#451C22×C6114yes—
258#450C22×C6118yes—
259#446C22×C6118yescomplemented
260#440C22×C61116yescomplemented
261C4×Q16C22×C6118yescomplemented
262#432C22×C6114yes—
263#431C22×C6112yes—
264C61#6189211yescharacteristic, direct product factor, Sylow
265C22×Q8D4×C6111yescharacteristic
266C22×Q8C23×C6111yescharacteristic
267C22×D4—21no—
268C22×D4—21no—
269C22×D4C23×C6112yes—
270C23×C4—22no—
271C2×Q16C23×C6118yes—
272C2×SD16C23×C61116yes—
273C4⋊Q8—24no—
274C4⋊Q8—28no—
275C4⋊Q8C23×C6114yes—
276C4⋊Q8C23×C6112yes—
277C4⋊Q8C23×C6114yes—
278C4⋊Q8C23×C6112yes—
279#127—22no—
280#127C23×C6114yes—
281#125—24no—
282#125—28no—
283#125—24no—
284#125—22no—
285#124—28no—
286#124—24no—
287#124C23×C6118yes—
288#123—216no—
289C22⋊Q8—24no—
290C22⋊Q8—22no—
291C22⋊Q8C23×C6114yes—
292C4×Q8—24no—
293C4×Q8—24no—
294C4×Q8—22no—
295C4×Q8—24no—
296C4×Q8—22no—
297C4×Q8D4×C6114yes—
298C4×Q8C23×C6114yes—
299C4×Q8C23×C6114yes—
300C4×Q8C23×C6118yes—
301C4×Q8C23×C6114yes—
302C4×D4—28no—
303C4×D4—24no—
304C4×D4C23×C6118yes—
305#117—24no—
306#117—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4D4×C6111yescharacteristic
309C2×C4⋊C4D4×C6112yes—
310C2×C4⋊C4C23×C6111yescharacteristic
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C42—21no—
315C2×C42C23×C6112yes—
316C2×C42C23×C6111yescharacteristic
317#107C23×C6118yes—
318C4⋊C8C23×C6114yes—
319C4⋊C8C23×C6118yes—
320#103C23×C6118yes—
321#103C23×C6118yes—
322#102C23×C61116yes—
323C22⋊C8C23×C6114yes—
324#97C23×C6118yes—
325C4×C8C23×C6114yes—
326C24—22no—
327C2×Q8—24no—
328C2×Q8—21no—
329C2×Q8—24no—
330C2×Q8—22no—
331C2×Q8—42no—
332C2×Q8C2×D4×C6114yes—
333C2×Q8C24×C6112yes—
334C2×Q8C24×C6114yes—
335C2×D4—22no—
336C2×D4—24no—
337C2×D4—24no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—82no—
341C2×D4C24×C6114yes—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—28no—
345C22×C4—84no—
346C22×C4C2×D4×C6112yes—
347C22×C4C2×D4×C6112yes—
348C22×C4C2×D4×C6111yescharacteristic
349C22×C4C2×D4×C6111yescharacteristic
350C22×C4C24×C6111yescharacteristic
351Q16—48no—
352SD16—416no—
353C2×C8C24×C6118yes—
354C4⋊C4—24no—
355C4⋊C4—21no—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—28no—
364C4⋊C4—24no—
365C4⋊C4C2×D4×C6114yes—
366C4⋊C4C2×D4×C6118yes—
367C4⋊C4C24×C6114yes—
368C4⋊C4C24×C6112yes—
369C22⋊C4—24no—
370C22⋊C4—28no—
371C22⋊C4—28no—
372C22⋊C4—28no—
373C42—24no—
374C42—28no—
375C42—24no—
376C42C2×D4×C6114yes—
377C42C2×D4×C6112yes—
378C42C24×C6112yes—
379C42C24×C6114yes—
380C23—24no—
381C23—44no—
382C23—44no—
383C23—44no—
384C23C22×D4×C6111yescharacteristic
385Q8—28no—
386Q8—28no—
387Q8—24no—
388Q8—42no—
389Q8—84no—
390Q8—82no—
391D4—28no—
392D4—44no—
393D4—48no—
394D4—84no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—88no—
406C2×C4#137×C6114yes—
407C2×C4C22×D4×C6114yes—
408C2×C4C22×D4×C6111yescharacteristic
409C2×C4C22×D4×C6114yes—
410C2×C4C22×D4×C6112yes—
411C2×C4C22×D4×C6112yes—
412C2×C4C25×C6111yescharacteristic
413C8—28no—
414C22—21no—
415C22—21no—
416C22—44no—
417C22—44no—
418C22—44no—
419C22—88no—
420C22C2×#137×C6112yes—
421C22C23×D4×C6111yescharacteristic
422C4—24no—
423C4—24no—
424C4—22no—
425C4—21no—
426C4—42no—
427C4—44no—
428C4—42no—
429C4—44no—
430C4C2×#137×C6114yes—
431C4C61×#58512yes—
432C2—22no—
433C2—84no—
434C2C61×#348711yescharacteristic
435C2C22×#137×C6111yescharacteristic
436C2C61×#358511yescharacteristic
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
prime radicalC2×#127×C61C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C4×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3502C2semidirect
3. C61×#3400C2semidirect
4. C61×#3375C2semidirect
5. C61×#3215C2semidirect
7. C61×#3110C2semidirect
8. C61×#3104C2semidirect
9. C61×#2983C2semidirect
12. Q82×C61C22semidirect
14. C61×#557C22semidirect
28. C61×#497C22semidirect
30. C61×#489C22semidirect
33. C61×#477C22semidirect
34. C61×#474C22semidirect
35. C61×#464C22semidirect
36. C61×#462C22semidirect
37. C61×#461C22semidirect
41. C61×#446C22semidirect
42. C61×#440C22semidirect
43. C4×Q16×C61C22semidirect
195. #61892C61direct (N × H)
214. #3502C2×C61semidirect
216. #3400C2×C61semidirect
217. #3375C2×C61semidirect
218. #3215C2×C61semidirect
220. #3110C2×C61semidirect
221. #3104C2×C61semidirect
222. #2983C2×C61semidirect
230. Q82C22×C61semidirect
232. #557C22×C61semidirect
246. #497C22×C61semidirect
248. #489C22×C61semidirect
251. #477C22×C61semidirect
252. #474C22×C61semidirect
253. #464C22×C61semidirect
254. #462C22×C61semidirect
255. #461C22×C61semidirect
259. #446C22×C61semidirect
260. #440C22×C61semidirect
261. C4×Q16C22×C61semidirect
264. C61#61892direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35022
C2×C61×#5592
C61×#34002
C61×#33752
C61×#32152
C61×#32082
C61×#31102
C61×#31042
C61×#29832
#6189261