Finite Group Databasebeta

← C61×#34973 #29538406

Subgroups — C61×#34973 #29538406

Order 15616.

1716 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2524C214yesmaximal, complemented
2C61×#2519C214yesmaximal
3C61×#2469C214yesmaximal
4C61×#2462C214yesmaximal, complemented
5C61×#2402C211yesmaximal, characteristic, complemented
6C61×#2399C211yesmaximal, characteristic, complemented
7C61×#2396C212yesmaximal
8C4×#125×C61C214yesmaximal, complemented
9C4×#126×C61C214yesmaximal
10C61×#2298C211yesmaximal, characteristic
11C42×Q8×C61C212yesmaximal, complemented
12C2×#126×C61C2214yes—
13C2×#125×C61C2214yes—
14C2×C4×Q8×C61C2212yes—
15C2×C4×Q8×C61C2214yes—
16C2×#117×C61C2211yescharacteristic
17C61×#400C2212yes—
18C61×#400C2214yes—
19C61×#399C2212yes—
20C61×#398C2214yes—
21C61×#398C2214yes—
22C61×#398C2214yes—
23C61×#396C2214yes—
24C61×#395C2212yes—
25C61×#395C2214yes—
26C61×#393C2212yes—
27C61×#389C2214yes—
28C61×#389C2214yes—
29C61×#388C2214yes—
30C61×#388C2214yes—
31C61×#388C2214yes—
32C61×#388C2214yes—
33C61×#387C2214yes—
34C61×#387C2214yes—
35C61×#387C2214yes—
36C61×#387C2214yes—
37C61×#387C2214yes—
38C61×#387C2214yes—
39C61×#387C2214yes—
40C61×#387C2214yes—
41C61×#383C2214yes—
42C61×#382C2214yes—
43C4×C4⋊C4×C61C2214yes—
44C4×C4⋊C4×C61C2214yes—
45C4×C4⋊C4×C61C2214yes—
46C4×C4⋊C4×C61C2214yes—
47C4×C4⋊C4×C61C2212yes—
48C4×C4⋊C4×C61C2212yes—
49C4×C4⋊C4×C61C2214yes—
50C4×C4⋊C4×C61C2214yes—
51C4×C4⋊C4×C61C2214yes—
52C4×C22⋊C4×C61C2212yes—
53C4×C22⋊C4×C61C2214yes—
54C61×#376C2211yescharacteristic
55C43×C61C2211yescharacteristic
56C43×C61C2214yes—
57C22×Q8×C61C2312yes—
58C23×C4×C61C2311yescharacteristic
59#126×C61—216no—
60#125×C61—216no—
61C4×Q8×C61—216no—
62C4×Q8×C61—28no—
63#117×C61—24no—
64C2×C4⋊C4×C61C2314yes—
65C2×C4⋊C4×C61C2314yes—
66C2×C4⋊C4×C61C2314yes—
67C2×C4⋊C4×C61C2312yes—
68C2×C4⋊C4×C61C2314yes—
69C2×C4⋊C4×C61C2314yes—
70C2×C4⋊C4×C61C2314yes—
71C2×C4⋊C4×C61C2314yes—
72C2×C4⋊C4×C61C2314yes—
73C2×C4⋊C4×C61C2314yes—
74C2×C4⋊C4×C61C2314yes—
75C2×C4⋊C4×C61C2312yes—
76C2×C4⋊C4×C61C2314yes—
77C2×C22⋊C4×C61C2314yes—
78C2×C22⋊C4×C61C2314yes—
79C2×C22⋊C4×C61C2314yes—
80C2×C22⋊C4×C61C2312yes—
81C2×C42×C61C2314yes—
82C2×C42×C61C2314yes—
83C2×C42×C61C2314yes—
84C2×C42×C61C2314yes—
85C2×C42×C61C2314yes—
86C2×C42×C61C2312yes—
87C2×C42×C61C2314yes—
88C2×C42×C61C2314yes—
89C2×C42×C61C2312yes—
90C2×C42×C61C2311yescharacteristic
91C2×C42×C61C2311yescharacteristic
92#95×C61C2314yes—
93#95×C61C2314yes—
94#95×C61C2314yes—
95#95×C61C2314yes—
96#95×C61C2314yes—
97#95×C61C2314yes—
98#95×C61C2312yes—
99#95×C61C2312yes—
100#95×C61C2314yes—
101#95×C61C2314yes—
102#95×C61C2314yes—
103#95×C61C2314yes—
104#95×C61C2314yes—
105#95×C61C2314yes—
106#95×C61C2314yes—
107C24×C61C2411yescharacteristic
108C2×Q8×C61—28no—
109C2×Q8×C61—24no—
110C22×C4×C61—22no—
111C22×C4×C61—24no—
112C22×C4×C61C2411yescharacteristic
113C22×C4×C61C2414yes—
114C22×C4×C61C2414yes—
115C22×C4×C61C2414yes—
116C22×C4×C61C2412yes—
117C22×C4×C61C2414yes—
118C22×C4×C61C2414yes—
119C22×C4×C61C2414yes—
120C22×C4×C61C2412yes—
121C22×C4×C61C2411yescharacteristic
122C4⋊C4×C61—24no—
123C4⋊C4×C61—28no—
124C4⋊C4×C61—28no—
125C4⋊C4×C61—28no—
126C4⋊C4×C61—24no—
127C4⋊C4×C61—28no—
128C4⋊C4×C61—28no—
129C4⋊C4×C61—28no—
130C4⋊C4×C61—28no—
131C4⋊C4×C61—28no—
132C4⋊C4×C61—28no—
133C4⋊C4×C61—28no—
134C4⋊C4×C61#41116yes—
135C22⋊C4×C61—24no—
136C22⋊C4×C61—28no—
137C22⋊C4×C61—28no—
138C22⋊C4×C61—28no—
139C42×C61—22no—
140C42×C61—28no—
141C42×C61—28no—
142C42×C61—28no—
143C42×C61—28no—
144C42×C61—28no—
145C42×C61—28no—
146C42×C61—24no—
147C42×C61—28no—
148C42×C61—24no—
149C42×C61#4114yes—
150C23×C61—24no—
151C23×C61—21no—
152C23×C61—22no—
153C23×C61C2511yescharacteristic
154Q8×C61—216no—
155C2×C4×C61—24no—
156C2×C4×C61—24no—
157C2×C4×C61—24no—
158C2×C4×C61—24no—
159C2×C4×C61—24no—
160C2×C4×C61—24no—
161C2×C4×C61—24no—
162C2×C4×C61—22no—
163C2×C4×C61—24no—
164C2×C4×C61—24no—
165C2×C4×C61—24no—
166C2×C4×C61—24no—
167C2×C4×C61—24no—
168C2×C4×C61—24no—
169C2×C4×C61—24no—
170C2×C4×C61—24no—
171C2×C4×C61—21no—
172C2×C4×C61—24no—
173C2×C4×C61—24no—
174C2×C4×C61—22no—
175C2×C4×C61—44no—
176C2×C4×C61C2×#4118yes—
177C2×C4×C61C2×#4118yes—
178C2×C4×C61C2×#4118yes—
179C2×C4×C61C2×#4114yes—
180C2×C4×C61C2×#4112yes—
181C2×C4×C612−1+414yes—
182#34973C6111yesmaximal, characteristic, direct product factor, Sylow
183C22×C61—42no—
184C22×C61—41no—
185C22×C61—44no—
186C22×C61C22×#4111yescharacteristic
187C22×C61C22×#4114yes—
188C22×C61C2×2−1+412yes—
189C4×C61—28no—
190C4×C61—24no—
191C4×C61—28no—
192C4×C61—28no—
193C4×C61—44no—
194C4×C61—42no—
195C4×C61—41no—
196C4×C61—44no—
197C4×C61—44no—
198C4×C61#54114yes—
199#2524C2×C6114yescomplemented
200#2519C2×C6114yes—
201#2469C2×C6114yes—
202#2462C2×C6114yescomplemented
203#2402C2×C6111yescharacteristic, complemented
204#2399C2×C6111yescharacteristic, complemented
205#2396C2×C6112yes—
206C4×#125C2×C6114yescomplemented
207C4×#126C2×C6114yes—
208#2298C2×C6111yescharacteristic
209C42×Q8C2×C6112yescomplemented
210C2×C61—81no—
211C2×C61#344412yes—
212C2×C61C2×#54111yescharacteristic
213C2×C61#348214yes—
214C2×#126C22×C6114yes—
215C2×#125C22×C6114yes—
216C2×C4×Q8C22×C6112yes—
217C2×C4×Q8C22×C6114yes—
218C2×#117C22×C6111yescharacteristic
219#400C22×C6112yes—
220#400C22×C6114yes—
221#399C22×C6112yes—
222#398C22×C6114yes—
223#398C22×C6114yes—
224#398C22×C6114yes—
225#396C22×C6114yes—
226#395C22×C6112yes—
227#395C22×C6114yes—
228#393C22×C6112yes—
229#389C22×C6114yes—
230#389C22×C6114yes—
231#388C22×C6114yes—
232#388C22×C6114yes—
233#388C22×C6114yes—
234#388C22×C6114yes—
235#387C22×C6114yes—
236#387C22×C6114yes—
237#387C22×C6114yes—
238#387C22×C6114yes—
239#387C22×C6114yes—
240#387C22×C6114yes—
241#387C22×C6114yes—
242#387C22×C6114yes—
243#383C22×C6114yes—
244#382C22×C6114yes—
245C4×C4⋊C4C22×C6114yes—
246C4×C4⋊C4C22×C6114yes—
247C4×C4⋊C4C22×C6114yes—
248C4×C4⋊C4C22×C6114yes—
249C4×C4⋊C4C22×C6112yes—
250C4×C4⋊C4C22×C6112yes—
251C4×C4⋊C4C22×C6114yes—
252C4×C4⋊C4C22×C6114yes—
253C4×C4⋊C4C22×C6114yes—
254C4×C22⋊C4C22×C6114yes—
255C4×C22⋊C4C22×C6112yes—
256#376C22×C6111yescharacteristic
257C43C22×C6114yes—
258C43C22×C6111yescharacteristic
259C61#3497311yescharacteristic, direct product factor, Sylow
260C22×Q8C23×C6112yes—
261C23×C4C23×C6111yescharacteristic
262#126—216no—
263#125—216no—
264C4×Q8—216no—
265C4×Q8—28no—
266#117—24no—
267C2×C4⋊C4C23×C6112yes—
268C2×C4⋊C4C23×C6114yes—
269C2×C4⋊C4C23×C6114yes—
270C2×C4⋊C4C23×C6114yes—
271C2×C4⋊C4C23×C6112yes—
272C2×C4⋊C4C23×C6114yes—
273C2×C4⋊C4C23×C6114yes—
274C2×C4⋊C4C23×C6114yes—
275C2×C4⋊C4C23×C6114yes—
276C2×C4⋊C4C23×C6114yes—
277C2×C4⋊C4C23×C6114yes—
278C2×C4⋊C4C23×C6114yes—
279C2×C4⋊C4C23×C6114yes—
280C2×C22⋊C4C23×C6112yes—
281C2×C22⋊C4C23×C6114yes—
282C2×C22⋊C4C23×C6114yes—
283C2×C22⋊C4C23×C6114yes—
284C2×C42C23×C6111yescharacteristic
285C2×C42C23×C6114yes—
286C2×C42C23×C6114yes—
287C2×C42C23×C6114yes—
288C2×C42C23×C6114yes—
289C2×C42C23×C6114yes—
290C2×C42C23×C6114yes—
291C2×C42C23×C6112yes—
292C2×C42C23×C6114yes—
293C2×C42C23×C6112yes—
294C2×C42C23×C6111yescharacteristic
295#95C23×C6114yes—
296#95C23×C6114yes—
297#95C23×C6114yes—
298#95C23×C6114yes—
299#95C23×C6114yes—
300#95C23×C6114yes—
301#95C23×C6112yes—
302#95C23×C6112yes—
303#95C23×C6114yes—
304#95C23×C6114yes—
305#95C23×C6114yes—
306#95C23×C6114yes—
307#95C23×C6114yes—
308#95C23×C6114yes—
309#95C23×C6114yes—
310C24C24×C6111yescharacteristic
311C2×Q8—28no—
312C2×Q8—24no—
313C22×C4—22no—
314C22×C4—24no—
315C22×C4C24×C6111yescharacteristic
316C22×C4C24×C6114yes—
317C22×C4C24×C6114yes—
318C22×C4C24×C6114yes—
319C22×C4C24×C6112yes—
320C22×C4C24×C6114yes—
321C22×C4C24×C6114yes—
322C22×C4C24×C6114yes—
323C22×C4C24×C6112yes—
324C22×C4C24×C6111yescharacteristic
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—28no—
328C4⋊C4—28no—
329C4⋊C4—24no—
330C4⋊C4—28no—
331C4⋊C4—28no—
332C4⋊C4—28no—
333C4⋊C4—28no—
334C4⋊C4—28no—
335C4⋊C4—28no—
336C4⋊C4—28no—
337C4⋊C4#41×C61116yes—
338C22⋊C4—24no—
339C22⋊C4—28no—
340C22⋊C4—28no—
341C22⋊C4—28no—
342C42—22no—
343C42—28no—
344C42—28no—
345C42—28no—
346C42—28no—
347C42—28no—
348C42—28no—
349C42—24no—
350C42—28no—
351C42—24no—
352C42#41×C6114yes—
353C23—24no—
354C23—21no—
355C23—22no—
356C23C25×C6111yescharacteristic
357Q8—216no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—21no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—44no—
379C2×C4C2×#41×C6118yes—
380C2×C4C2×#41×C6118yes—
381C2×C4C2×#41×C6118yes—
382C2×C4C2×#41×C6114yes—
383C2×C4C2×#41×C6112yes—
384C2×C42−1+4×C6114yes—
385C22—42no—
386C22—41no—
387C22—44no—
388C22C22×#41×C6111yescharacteristic
389C22C22×#41×C6114yes—
390C22C2×2−1+4×C6112yes—
391C4—28no—
392C4—24no—
393C4—28no—
394C4—28no—
395C4—44no—
396C4—42no—
397C4—41no—
398C4—44no—
399C4—44no—
400C4C61×#54114yes—
401C2—81no—
402C2C61×#344412yes—
403C2C2×C61×#54111yescharacteristic
404C2C61×#348214yes—
subgroupG/H
centerC22×C4×C61C24
commutator, Frattini, cosocleC23C25×C61
socleC23×C61C25
prime radicalC24×C61C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#2524C2semidirect
4. C61×#2462C2semidirect
5. C61×#2402C2semidirect
6. C61×#2399C2semidirect
8. C4×#125×C61C2semidirect
11. C42×Q8×C61C2semidirect
182. #34973C61direct (N × H)
199. #2524C2×C61semidirect
202. #2462C2×C61semidirect
203. #2402C2×C61semidirect
204. #2399C2×C61semidirect
206. C4×#125C2×C61semidirect
209. C42×Q8C2×C61semidirect
259. C61#34973direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#25242
C61×#25192
C61×#24692
C61×#24622
C61×#24022
C61×#23992
C61×#23962
C4×#125×C612
C4×#126×C612
C61×#22982
C42×Q8×C612
#3497361