Finite Group Databasebeta

← C61×#18727 #29522160

Subgroups — C61×#18727 #29522160

Order 15616.

996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3548C211yesmaximal, characteristic, complemented
2C61×#3205C212yesmaximal, complemented
3C61×#3138C211yesmaximal, characteristic, complemented
4C61×#1625C218yesmaximal, complemented
5C61×#1544C211yesmaximal, characteristic, complemented
6C61×#1484C212yesmaximal, complemented
7C61×#562—22no—
8C61×#554—22no—
9C61×#550—22no—
10C61×#547C2214yescomplemented
11C61×#540—22no—
12C61×#537—24no—
13C61×#533C2211yescharacteristic
14C61×#532C2212yes—
15C2×#127×C61C2211yescharacteristic
16C61×#493—22no—
17C61×#490—22no—
18C61×#486—22no—
19C61×#486C2214yes—
20C61×#459C2218yes—
21C61×#447—24no—
22C61×#431C2212yes—
23C61×#418—22no—
24C4×M16×C61C2211yescharacteristic
25C61×#332C2214yescomplemented
26C61×D4⋊C8C2218yescomplemented
27C2×#41×C61—24no—
28C2×#41×C61—22no—
29C22×D4×C61—21no—
30C22×D4×C61—22no—
31C2×D8×C61—28no—
32C2×M16×C61—21no—
33C4⋊Q8×C61D412yes—
34C4⋊Q8×C61C2312yes—
35#127×C61—22no—
36#127×C61—22no—
37#127×C61—21no—
38#127×C61D412yes—
39#127×C61C2312yes—
40#125×C61—22no—
41#125×C61D412yes—
42#124×C61—22no—
43#123×C61—28no—
44C22⋊Q8×C61—28no—
45C22⋊Q8×C61—22no—
46C22⋊Q8×C61—24no—
47#121×C61—28no—
48#121×C61—28no—
49#121×C61—24no—
50#121×C61—22no—
51#121×C61D414yes—
52C4×Q8×C61—22no—
53C4×D4×C61—24no—
54C4×D4×C61—22no—
55C4×D4×C61C2314yes—
56#117×C61D412yes—
57C2×C4⋊C4×C61—24no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61C2314yes—
60#102×C61—28no—
61#102×C61—28no—
62C22⋊C8×C61—22no—
63#97×C61—21no—
64C4×C8×C61—22no—
65C4×C8×C61C2312yes—
66C24×C61—41no—
67#41×C61—84no—
68#41×C61—88no—
69C2×Q8×C61—22no—
70C2×Q8×C61—22no—
71C2×D4×C61—28no—
72C2×D4×C61—24no—
73C2×D4×C61—22no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61—24no—
77C2×D4×C61—44no—
78C2×D4×C61—42no—
79C2×D4×C61—41no—
80C2×D4×C61—84no—
81C2×D4×C61C2×D414yes—
82C22×C4×C61—28no—
83C22×C4×C61—24no—
84C22×C4×C61C2×D412yes—
85C22×C4×C61C2×D411yescharacteristic
86D8×C61—88no—
87M16×C61—42no—
88C2×C8×C61—24no—
89C2×C8×C61—22no—
90C4⋊C4×C61—28no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—24no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61C2×D414yes—
95C4⋊C4×C61C2×D414yes—
96C22⋊C4×C61—28no—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—24no—
99C22⋊C4×C61—24no—
100C42×C61—22no—
101C42×C61C2×D412yes—
102C42×C61C2×D411yescharacteristic
103C42×C61C2411yescharacteristic
104C23×C61—24no—
105C23×C61—42no—
106C23×C61—82no—
107C23×C61—84no—
108C23×C61#12011yescharacteristic
109Q8×C61—44no—
110Q8×C61—82no—
111D4×C61—28no—
112D4×C61—44no—
113D4×C61—48no—
114D4×C61—44no—
115D4×C61—82no—
116D4×C61—84no—
117D4×C61—84no—
118D4×C61—88no—
119D4×C61—82no—
120C2×C4×C61—24no—
121C2×C4×C61—22no—
122C2×C4×C61—24no—
123C2×C4×C61—24no—
124C2×C4×C61—48no—
125C2×C4×C61—88no—
126C2×C4×C61#12012yes—
127C2×C4×C61#12011yescharacteristic
128C2×C4×C61C22×D411yescharacteristic
129C2×C4×C61C22×D412yes—
130C8×C61—42no—
131C8×C61—44no—
132#18727C6111yesmaximal, characteristic, direct product factor, Sylow
133C22×C61—22no—
134C22×C61—21no—
135C22×C61—44no—
136C22×C61—44no—
137C22×C61—44no—
138C22×C61—84no—
139C22×C61—82no—
140C22×C61—164no—
141C22×C61C2×#12011yescharacteristic
142C4×C61—22no—
143C4×C61—21no—
144C4×C61—44no—
145C4×C61—44no—
146C4×C61#45412yes—
147C4×C61#57614yes—
148#3548C2×C6111yescharacteristic, complemented
149#3205C2×C6112yescomplemented
150#3138C2×C6111yescharacteristic, complemented
151#1625C2×C6118yescomplemented
152#1544C2×C6111yescharacteristic, complemented
153#1484C2×C6112yescomplemented
154C2×C61—41no—
155C2×C61—84no—
156C2×C61—162no—
157C2×C61#300812yes—
158C2×C61C2×#45411yescharacteristic
159#562—22no—
160#554—22no—
161#550—22no—
162#547C22×C6114yescomplemented
163#540—22no—
164#537—24no—
165#533C22×C6111yescharacteristic
166#532C22×C6112yes—
167C2×#127C22×C6111yescharacteristic
168#493—22no—
169#490—22no—
170#486—22no—
171#486C22×C6114yes—
172#459C22×C6118yes—
173#447—24no—
174#431C22×C6112yes—
175#418—22no—
176C4×M16C22×C6111yescharacteristic
177#332C22×C6114yescomplemented
178D4⋊C8C22×C6118yescomplemented
179C61#1872711yescharacteristic, direct product factor, Sylow
180C2×#41—24no—
181C2×#41—22no—
182C22×D4—21no—
183C22×D4—22no—
184C2×D8—28no—
185C2×M16—21no—
186C4⋊Q8D4×C6112yes—
187C4⋊Q8C23×C6112yes—
188#127—22no—
189#127—22no—
190#127—21no—
191#127D4×C6112yes—
192#127C23×C6112yes—
193#125—22no—
194#125D4×C6112yes—
195#124—22no—
196#123—28no—
197C22⋊Q8—28no—
198C22⋊Q8—22no—
199C22⋊Q8—24no—
200#121—28no—
201#121—28no—
202#121—24no—
203#121—22no—
204#121D4×C6114yes—
205C4×Q8—22no—
206C4×D4—24no—
207C4×D4—22no—
208C4×D4C23×C6114yes—
209#117D4×C6112yes—
210C2×C4⋊C4—24no—
211C2×C42C23×C6111yescharacteristic
212C4⋊C8C23×C6114yes—
213#102—28no—
214#102—28no—
215C22⋊C8—22no—
216#97—21no—
217C4×C8—22no—
218C4×C8C23×C6112yes—
219C24—41no—
220#41—84no—
221#41—88no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×D4—28no—
225C2×D4—24no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—22no—
229C2×D4—24no—
230C2×D4—44no—
231C2×D4—42no—
232C2×D4—41no—
233C2×D4—84no—
234C2×D4C2×D4×C6114yes—
235C22×C4—28no—
236C22×C4—24no—
237C22×C4C2×D4×C6112yes—
238C22×C4C2×D4×C6111yescharacteristic
239D8—88no—
240M16—42no—
241C2×C8—24no—
242C2×C8—22no—
243C4⋊C4—28no—
244C4⋊C4—22no—
245C4⋊C4—24no—
246C4⋊C4—22no—
247C4⋊C4C2×D4×C6114yes—
248C4⋊C4C2×D4×C6114yes—
249C22⋊C4—28no—
250C22⋊C4—22no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C42—22no—
254C42C2×D4×C6112yes—
255C42C2×D4×C6111yescharacteristic
256C42C24×C6111yescharacteristic
257C23—24no—
258C23—42no—
259C23—82no—
260C23—84no—
261C23#120×C6111yescharacteristic
262Q8—44no—
263Q8—82no—
264D4—28no—
265D4—44no—
266D4—48no—
267D4—44no—
268D4—82no—
269D4—84no—
270D4—84no—
271D4—88no—
272D4—82no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—48no—
278C2×C4—88no—
279C2×C4#120×C6112yes—
280C2×C4#120×C6111yescharacteristic
281C2×C4C22×D4×C6111yescharacteristic
282C2×C4C22×D4×C6112yes—
283C8—42no—
284C8—44no—
285C22—22no—
286C22—21no—
287C22—44no—
288C22—44no—
289C22—44no—
290C22—84no—
291C22—82no—
292C22—164no—
293C22C2×#120×C6111yescharacteristic
294C4—22no—
295C4—21no—
296C4—44no—
297C4—44no—
298C4C61×#45412yes—
299C4C61×#57614yes—
300C2—41no—
301C2—84no—
302C2—162no—
303C2C61×#300812yes—
304C2C2×C61×#45411yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3548C2semidirect
2. C61×#3205C2semidirect
3. C61×#3138C2semidirect
4. C61×#1625C2semidirect
5. C61×#1544C2semidirect
6. C61×#1484C2semidirect
10. C61×#547C22semidirect
25. C61×#332C22semidirect
26. C61×D4⋊C8C22semidirect
132. #18727C61direct (N × H)
148. #3548C2×C61semidirect
149. #3205C2×C61semidirect
150. #3138C2×C61semidirect
151. #1625C2×C61semidirect
152. #1544C2×C61semidirect
153. #1484C2×C61semidirect
162. #547C22×C61semidirect
177. #332C22×C61semidirect
178. D4⋊C8C22×C61semidirect
179. C61#18727direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35482
C61×#32052
C61×#31382
C61×#16252
C61×#15442
C61×#14842
#1872761