Finite Group Databasebeta

← C61×#11500 #29514933

Subgroups — C61×#11500 #29514933

Order 15616.

706 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C2×C61×#381C211yesmaximal, characteristic
2C61×#1462C212yesmaximal
3C61×#1317C214yesmaximal, complemented
4C24×C4×C61C411yescharacteristic
5C22×C22⋊C4×C61C411yescharacteristic
6C22×C22⋊C4×C61C2211yescharacteristic
7C61×#407—22no—
8C61×#381—22no—
9C61×#381C412yes—
10C61×#381C2212yes—
11C2×#95×C61—22no—
12C61×#323—22no—
13C61×#323C2214yes—
14C25×C61C2×C411yescharacteristic
15C23×C4×C61—21no—
16C23×C4×C61—21no—
17C23×C4×C61—24no—
18C23×C4×C61—21no—
19C23×C4×C61—42no—
20C23×C4×C61—42no—
21C23×C4×C61C2×C412yes—
22C23×C4×C61D412yes—
23C2×M16×C61—42no—
24C2×C22⋊C4×C61—21no—
25C2×C22⋊C4×C61—42no—
26C2×C22⋊C4×C61—42no—
27C2×C22⋊C4×C61C2×C412yes—
28C2×C22⋊C4×C61C2×C411yescharacteristic
29C2×C22⋊C4×C61D412yes—
30C2×C22⋊C4×C61C2311yescharacteristic
31C22⋊C8×C61—24no—
32C22⋊C8×C61—42no—
33#95×C61—24no—
34#95×C61—24no—
35C24×C61—22no—
36C24×C61—22no—
37C24×C61—22no—
38C24×C61—44no—
39C24×C61C22⋊C411yescharacteristic
40C24×C61C22⋊C411yescharacteristic
41C24×C61C22×C411yescharacteristic
42C22×C4×C61—24no—
43C22×C4×C61—24no—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—22no—
47C22×C4×C61—22no—
48C22×C4×C61—22no—
49C22×C4×C61—416no—
50C22×C4×C61—42no—
51C22×C4×C61—42no—
52C22×C4×C61—42no—
53C22×C4×C61—42no—
54C22×C4×C61—42no—
55C22×C4×C61—42no—
56C22×C4×C61—44no—
57C22×C4×C61—42no—
58C22×C4×C61—44no—
59C22×C4×C61C22⋊C412yes—
60C22×C4×C61M1614yescomplemented
61C22×C4×C61C2×D412yes—
62M16×C61—84no—
63C2×C8×C61—44no—
64C22⋊C4×C61—41no—
65C22⋊C4×C61—42no—
66C22⋊C4×C61—41no—
67C22⋊C4×C61—42no—
68C22⋊C4×C61—42no—
69C23×C61—24no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—28no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—48no—
78C23×C61—48no—
79C23×C61—44no—
80C23×C61—42no—
81C23×C61—42no—
82C23×C61—44no—
83C23×C61#9912yes—
84C23×C61#10012yes—
85C23×C61C2×C22⋊C411yescharacteristic
86C23×C61C2×M1612yes—
87C2×C4×C61—24no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—48no—
91C2×C4×C61—48no—
92C2×C4×C61—44no—
93C2×C4×C61—44no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—44no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—44no—
100C2×C4×C61—42no—
101C2×C4×C61—82no—
102C2×C4×C61—84no—
103C8×C61—84no—
104#11500C6111yesmaximal, characteristic, direct product factor, Sylow
105C22×C61—24no—
106C22×C61—24no—
107C22×C61—22no—
108C22×C61—22no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—416no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61#35214yes—
120C22×C61#40711yescharacteristic
121C22×C61C2×#9911yescharacteristic
122C22×C61C2×#10011yescharacteristic
123C4×C61—42no—
124C4×C61—42no—
125C4×C61—44no—
126C4×C61—82no—
127C2×#381C2×C6111yescharacteristic
128#1462C2×C6112yes—
129#1317C2×C6114yescomplemented
130C2×C61—21no—
131C2×C61—24no—
132C2×C61—21no—
133C2×C61—42no—
134C2×C61—42no—
135C2×C61#146211yescharacteristic
136C2×C61C2×#35212yes—
137C24×C4C4×C6111yescharacteristic
138C22×C22⋊C4C4×C6111yescharacteristic
139C22×C22⋊C4C22×C6111yescharacteristic
140#407—22no—
141#381—22no—
142#381C4×C6112yes—
143#381C22×C6112yes—
144C2×#95—22no—
145#323—22no—
146#323C22×C6114yes—
147C61#1150011yescharacteristic, direct product factor, Sylow
148C25C2×C4×C6111yescharacteristic
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—24no—
152C23×C4—21no—
153C23×C4—42no—
154C23×C4—42no—
155C23×C4C2×C4×C6112yes—
156C23×C4D4×C6112yes—
157C2×M16—42no—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—42no—
160C2×C22⋊C4—42no—
161C2×C22⋊C4C2×C4×C6112yes—
162C2×C22⋊C4C2×C4×C6111yescharacteristic
163C2×C22⋊C4D4×C6112yes—
164C2×C22⋊C4C23×C6111yescharacteristic
165C22⋊C8—24no—
166C22⋊C8—42no—
167#95—24no—
168#95—24no—
169C24—22no—
170C24—22no—
171C24—22no—
172C24—44no—
173C24C22⋊C4×C6111yescharacteristic
174C24C22⋊C4×C6111yescharacteristic
175C24C22×C4×C6111yescharacteristic
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—416no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—44no—
191C22×C4—42no—
192C22×C4—44no—
193C22×C4C22⋊C4×C6112yes—
194C22×C4M16×C6114yescomplemented
195C22×C4C2×D4×C6112yes—
196M16—84no—
197C2×C8—44no—
198C22⋊C4—41no—
199C22⋊C4—42no—
200C22⋊C4—41no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C23—24no—
204C23—21no—
205C23—21no—
206C23—28no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—42no—
212C23—42no—
213C23—48no—
214C23—48no—
215C23—44no—
216C23—44no—
217C23#99×C6112yes—
218C23#100×C6112yes—
219C23C2×C22⋊C4×C6111yescharacteristic
220C23C2×M16×C6112yes—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—48no—
225C2×C4—48no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—84no—
237C8—84no—
238C22—24no—
239C22—24no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—416no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22C61×#35214yes—
253C22C61×#40711yescharacteristic
254C22C2×#99×C6111yescharacteristic
255C22C2×#100×C6111yescharacteristic
256C4—42no—
257C4—42no—
258C4—44no—
259C4—82no—
260C2—21no—
261C2—24no—
262C2—21no—
263C2—42no—
264C2—42no—
265C2C61×#146211yescharacteristic
266C2C2×C61×#35212yes—
subgroupG/H
center, socleC22×C61C2×#99
commutatorC24C22×C4×C61
Frattini, cosocleC2×C22⋊C4C23×C61
prime radicalC25×C61C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C24×C61 ◁ C22×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1317C2semidirect
60. C22×C4×C61M16semidirect
104. #11500C61direct (N × H)
129. #1317C2×C61semidirect
147. C61#11500direct (N × H)
194. C22×C4M16×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3812
C61×#14622
C61×#13172
#1150061