Finite Group Databasebeta

← #21448976

Subgroups — #21448976

Order 7808.

576 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 213 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
1#16839665C212yesmaximal, complemented
2#16839655C212yesmaximal, complemented
3#16839648C212yesmaximal, complemented
4#16839642C212yesmaximal, complemented
5#16839642C212yesmaximal, complemented
6#16839637C212yesmaximal, complemented
7#16839625C211yesmaximal, characteristic, complemented
8#16839622C211yesmaximal, characteristic, complemented
9C2×#121×C61C211yesmaximal, characteristic
10C23×Dic61C2212yes—
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2212yes—
13C2×C22⋊Dic61C2211yescharacteristic
14C2×C22⋊Dic61C2211yescharacteristic
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C4×Dic61C2212yes—
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26C22×D4×C61C2211yescharacteristic
27C22×D4×C61C2212yes—
28C23×C4×C61C2211yescharacteristic
29#121×C61C418yescomplemented
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C22⋊C4×C61C2212yes—
32C24×C61C2312yes—
33C24×C61C2311yescharacteristic
34C2×D4×C61—42no—
35C2×D4×C61—42no—
36C2×D4×C61—42no—
37C2×D4×C61C2×C414yes—
38C2×D4×C61C2×C418yescomplemented
39C22×C4×C61—42no—
40C22×C4×C61C2×C414yescomplemented
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×Dic61—42no—
45C22×Dic61—42no—
46C22×Dic61—42no—
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C4⋊C4×C61C2×C414yescomplemented
52C22⋊C4×C61C2×C418yescomplemented
53C22⋊Dic61—42no—
54C22⋊Dic61—42no—
55C22⋊Dic61—41no—
56C22⋊Dic61—42no—
57C22⋊Dic61—42no—
58C22⋊Dic61—41no—
59C4⋊Dic61—42no—
60C4⋊Dic61—42no—
61C4×Dic61—42no—
62C23×C61—21no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—21no—
72C23×C61C22×C414yes—
73C23×C61C22×C412yes—
74C23×C61C2411yescharacteristic
75D4×C61—44no—
76D4×C61—48no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—44no—
82C2×C4×C61C22×C412yes—
83C2×C4×C61C22×C414yes—
84C2×C4×C61C22×C412yes—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—48no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—24no—
101C22×C61—24no—
102C22×C61—22no—
103C22×C61—24no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61C23×C411yescharacteristic
111C22×C61H(5,𝔽2)12yes—
112C22×C61H(5,𝔽2)12yes—
113C22×C61H(5,𝔽2)11yescharacteristic
114C22×C612−1+411yescharacteristic
115C4×C61—22no—
116C4×C61—22no—
117C4×C61—24no—
118Dic61—42no—
119Dic61—42no—
120Dic61—42no—
121Dic61—42no—
122#2377—611nomaximal, Sylow
123C2×C61—42no—
124C2×C61—44no—
125C2×C61#51811yescharacteristic
126C2×C61#51811yescharacteristic
127C2×C61#52011yescharacteristic
128C2×C61#56012yes—
129C2×C61#56212yes—
130C2×#121D6111yescharacteristic
131#390—612no—
132#388—612no—
133#387—612no—
134#386—612no—
135#386—612no—
136#385—612no—
137#381—611no—
138#380—611no—
139C61#237711yescharacteristic, complemented, Sylow
140C22×D4C2×D6111yescharacteristic
141C22×D4C2×D6112yes—
142C23×C4—612no—
143C23×C4C2×D6111yescharacteristic
144#121Dic6118yescomplemented
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4C2×D6111yescharacteristic
148C2×C22⋊C4—611no—
149C2×C22⋊C4—611no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154C2×C22⋊C4C2×D6112yes—
155C2×C42—612no—
156#95—612no—
157#95—611no—
158#95—612no—
159#95—611no—
160#95—612no—
161#95—612no—
162C24C22×D6111yescharacteristic
163C24C22×D6112yes—
164C2×D4—42no—
165C2×D4—42no—
166C2×D4—42no—
167C2×D4C2×Dic6114yes—
168C2×D4C2×Dic6118yescomplemented
169C22×C4—42no—
170C22×C4—612no—
171C22×C4—612no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4—2442no—
175C22×C4—2442no—
176C22×C4—2442no—
177C22×C4C2×Dic6114yescomplemented
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6112yes—
180C22×C4C22×D6111yescharacteristic
181C4⋊C4—2442no—
182C4⋊C4—2442no—
183C4⋊C4C2×Dic6114yescomplemented
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C22⋊C4—2442no—
187C22⋊C4—2441no—
188C22⋊C4—2442no—
189C22⋊C4—2441no—
190C22⋊C4C2×Dic6118yescomplemented
191C42—2442no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—21no—
199C23—22no—
200C23—21no—
201C23—22no—
202C23C22×Dic6114yes—
203C23C22×Dic6112yes—
204C23C23×D6111yescharacteristic
205D4—44no—
206D4—48no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—44no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—2448no—
225C2×C4C22×Dic6112yes—
226C2×C4C22×Dic6114yes—
227C2×C4C22×Dic6112yes—
228C22—22no—
229C22—22no—
230C22—24no—
231C22—24no—
232C22—22no—
233C22—24no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22C23×Dic6111yescharacteristic
241C22#1451982212yes—
242C22#1451982212yes—
243C22#1451982311yescharacteristic
244C22#1451982411yescharacteristic
245C4—22no—
246C4—22no—
247C4—24no—
248C4—2442no—
249C4—2442no—
250C4—2442no—
251C4—2442no—
252C2—42no—
253C2—44no—
254C2#1684023711yescharacteristic
255C2#1684023711yescharacteristic
256C2#1684024511yescharacteristic
257C2#1684050012yes—
258C2#1684050712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC2×#121×C61C2
socleC23×C61C24
hypercenterC2×#121D61
hypocenterC61#2377
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #16839665C2semidirect
2. #16839655C2semidirect
3. #16839648C2semidirect
4. #16839642C2semidirect
5. #16839642C2semidirect
6. #16839637C2semidirect
7. #16839625C2semidirect
8. #16839622C2semidirect
29. #121×C61C4semidirect
38. C2×D4×C61C2×C4semidirect
40. C22×C4×C61C2×C4semidirect
51. C4⋊C4×C61C2×C4semidirect
52. C22⋊C4×C61C2×C4semidirect
139. C61#2377semidirect
144. #121Dic61semidirect
168. C2×D4C2×Dic61semidirect
177. C22×C4C2×Dic61semidirect
183. C4⋊C4C2×Dic61semidirect
190. C22⋊C4C2×Dic61semidirect