Finite Group Databasebeta

← #21451627

Subgroups — #21451627

Order 7808.

668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519756C211yesmaximal, characteristic, complemented
2C22×#11758198C211yesmaximal, characteristic
3#16839699C212yesmaximal, complemented
4#16839684C214yesmaximal, complemented
5#16839675C212yesmaximal, complemented
6#16839637C212yesmaximal, complemented
7#16839617C212yesmaximal
8C61×#380C211yesmaximal, characteristic, complemented
9C24×D61C2211yescharacteristic
10C22×Dic122C2211yescharacteristic, complemented
11C23×Dic61C2211yescharacteristic
12#14519756—24no—
13C2×C4⋊Dic61C2211yescharacteristic, complemented
14C2×C4⋊Dic61C2214yescomplemented
15C2×#11758196C2212yescomplemented
16C2×C22⋊Dic61C2212yes—
17C2×#11758198—24no—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2214yes—
21C2×#11758198C2214yes—
22#14519684C2214yescomplemented
23C23×C4×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2212yescomplemented
25C2×C22⋊C4×C61C2212yes—
26#95×C61C2212yescomplemented
27C24×C61C2311yescharacteristic
28C23×D61—22no—
29C23×D61—22no—
30C23×D61—42no—
31C23×D61—42no—
32C23×D61Q814yescomplemented
33C23×D61C2312yes—
34C22×C4×C61—42no—
35C22×C4×C61D414yes—
36C22×C4×C61C2314yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61—22no—
40C22×Dic61—42no—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C2×Dic122—22no—
45C2×Dic122—42no—
46C4⋊C4×C61—42no—
47C22⋊C4×C61—24no—
48C22⋊Dic61—24no—
49#11758198—24no—
50#11758198—24no—
51#11758198—44no—
52#11758198—44no—
53C4⋊Dic61—22no—
54C4⋊Dic61—44no—
55#11758196—24no—
56C23×C61—22no—
57C23×C61—22no—
58C23×C61C2×D412yes—
59C23×C61C2×Q812yes—
60C23×C61#4112yes—
61C23×C61C2411yescharacteristic
62C22×D61—28no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—24no—
66C22×D61—24no—
67C22×D61—48no—
68C22×D61—44no—
69C22×D61—44no—
70C22×D61—48no—
71C22×D61C2×Q814yes—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—24no—
75C2×C4×C61—24no—
76C2×C4×C61—24no—
77C2×C4×C61—44no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D412yes—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—24no—
84C2×Dic61—24no—
85C2×Dic61—24no—
86C2×Dic61—44no—
87Dic122—44no—
88C22×C61—22no—
89C22×C61—22no—
90C22×C61—24no—
91C22×C61—24no—
92C22×C61C22⋊Q814yes—
93C22×C61C22×D411yescharacteristic
94C22×C61C22×Q811yescharacteristic
95C22×C61C2×#4111yescharacteristic
96C22×C61H(5,𝔽2)12yes—
97C22×C61H(5,𝔽2)12yes—
98C2×D61—24no—
99C2×D61—28no—
100C2×D61—416no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—44no—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—44no—
107Dic61—42no—
108Dic61—42no—
109Dic61—42no—
110#2626—611nomaximal, Sylow
111C2×C61—24no—
112C2×C61C2×C22⋊Q811yescharacteristic
113C2×C61#53411yescharacteristic
114C2×C61#53511yescharacteristic
115C2×C61#53812yes—
116C2×C61#54312yes—
117D61—44no—
118C2×C22⋊Q8—611no—
119C22×C22⋊C4—611no—
120#399—612no—
121#396—614no—
122#393—612no—
123#385—612no—
124#380D6111yescharacteristic, complemented
125#379—612no—
126C61#262611yescharacteristic, complemented, Sylow
127C25—611no—
128C22×Q8—611no—
129C23×C4—611no—
130C23×C4C2×D6111yescharacteristic
131C22⋊Q8—1224no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—614no—
135C2×C4⋊C4C2×D6112yescomplemented
136C2×C22⋊C4—612no—
137C2×C22⋊C4—612no—
138C2×C22⋊C4—612no—
139C2×C22⋊C4—614no—
140C2×C22⋊C4—614no—
141C2×C22⋊C4—1224no—
142C2×C22⋊C4C2×D6112yes—
143#95—614no—
144#95C2×D6112yescomplemented
145C24—612no—
146C24—614no—
147C24—1222no—
148C24—1222no—
149C24—2442no—
150C24—2442no—
151C24C22×D6111yescharacteristic
152C2×Q8—1222no—
153C2×Q8—2442no—
154C22×C4—42no—
155C22×C4—612no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4—1222no—
159C22×C4—2442no—
160C22×C4D24414yes—
161C22×C4C22×D6114yes—
162C22×C4C22×D6111yescharacteristic
163C22×C4C22×D6111yescharacteristic
164C4⋊C4—42no—
165C4⋊C4—1224no—
166C4⋊C4—1222no—
167C4⋊C4—2444no—
168C22⋊C4—24no—
169C22⋊C4—1224no—
170C22⋊C4—1224no—
171C22⋊C4—1224no—
172C22⋊C4—2444no—
173C22⋊C4—2444no—
174C23—22no—
175C23—22no—
176C23—614no—
177C23—1222no—
178C23—1222no—
179C23—1224no—
180C23—1224no—
181C23—1228no—
182C23—2448no—
183C23—2444no—
184C23—2444no—
185C23—2448no—
186C23C2×D24412yes—
187C23#1175822412yes—
188C23Q8×D6112yes—
189C23C23×D6111yescharacteristic
190Q8—2444no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—44no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1224no—
201C2×C4—1224no—
202C2×C4—1224no—
203C2×C4—2444no—
204C2×C4C2×D24412yes—
205C2×C4C2×D24412yes—
206C22—22no—
207C22—22no—
208C22—24no—
209C22—24no—
210C22—1224no—
211C22—1228no—
212C22—24416no—
213C22—2442no—
214C22—2442no—
215C22—2444no—
216C22#1451975714yes—
217C22C22×D24411yescharacteristic
218C22C2×Q8×D6111yescharacteristic
219C22C2×#1175822411yescharacteristic
220C22#1451982212yes—
221C22#1451982312yes—
222C4—22no—
223C4—22no—
224C4—44no—
225C4—2442no—
226C4—2442no—
227C4—2442no—
228C2—24no—
229C2—2444no—
230C2C2×#1451975711yescharacteristic
231C2#1684032411yescharacteristic
232C2#1684033111yescharacteristic
233C2#1684034912yes—
234C2#1684038712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2626
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14519756C2semidirect
3. #16839699C2semidirect
4. #16839684C2semidirect
5. #16839675C2semidirect
6. #16839637C2semidirect
8. C61×#380C2semidirect
10. C22×Dic122C22semidirect
13. C2×C4⋊Dic61C22semidirect
14. C2×C4⋊Dic61C22semidirect
15. C2×#11758196C22semidirect
22. #14519684C22semidirect
24. C2×C4⋊C4×C61C22semidirect
26. #95×C61C22semidirect
32. C23×D61Q8semidirect
124. #380D61semidirect
126. C61#2626semidirect
135. C2×C4⋊C4C2×D61semidirect
144. #95C2×D61semidirect