Finite Group Databasebeta

← #21448625

Subgroups — #21448625

Order 7808.

428 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 217 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#16839661C212yesmaximal
2#16839648C212yesmaximal
3#16839648C212yesmaximal
4#16839648C212yesmaximal
5#16839648C212yesmaximal
6#16839630C211yesmaximal, characteristic
7C4⋊C4×Dic61C212yesmaximal
8C4×C4⋊Dic61C211yesmaximal, characteristic
9C2×#125×C61C211yesmaximal, characteristic
10C2×C4⋊Dic61C2212yes—
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2212yes—
13C2×C4×Dic61C2212yes—
14C2×C4×Dic61C2211yescharacteristic
15C2×C4×Dic61C2211yescharacteristic
16C2×C4×Dic61C2212yes—
17#14519684C2212yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#125×C61C418yescomplemented
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30C2×C4⋊C4×C61C2212yes—
31C2×C42×C61C2211yescharacteristic
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C4⋊C4×C61C2×C418yes—
42C4⋊C4×C61C2×C414yes—
43C4⋊C4×C61C2×C414yes—
44C4⋊C4×C61C2×C418yes—
45C42×C61C2×C414yes—
46C4⋊Dic61—24no—
47C4⋊Dic61—24no—
48C4⋊Dic61—42no—
49C4×Dic61—24no—
50C4×Dic61—41no—
51C4×Dic61—42no—
52C4×Dic61—41no—
53C23×C61C2411yescharacteristic
54C2×C4×C61—22no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—21no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61C22×C412yes—
63C2×C4×C61C22×C412yes—
64C2×C4×C61C22×C412yes—
65C2×C4×C61C22×C414yes—
66C2×C4×C61C22×C414yes—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61#4114yes—
79C22×C61C23×C411yescharacteristic
80C22×C61C2×#4112yes—
81C22×C61H(5,𝔽2)11yescharacteristic
82C22×C612−1+411yescharacteristic
83C22×C612−1+412yes—
84C4×C61—24no—
85C4×C61—22no—
86C4×C61—22no—
87C4×C61—22no—
88C4×C61—24no—
89Dic61—24no—
90Dic61—42no—
91Dic61—42no—
92Dic61—42no—
93#2336—611nomaximal, Sylow
94C2×C61C4×#4111yescharacteristic
95C2×C61#51911yescharacteristic
96C2×C61#52011yescharacteristic
97C2×C61#53912yes—
98C2×C61#54112yes—
99C2×#125D6111yescharacteristic
100#389—612no—
101#387—612no—
102#387—612no—
103#387—612no—
104#387—612no—
105#383—611no—
106C4×C4⋊C4—612no—
107C4×C4⋊C4—611no—
108C61#233611yescharacteristic, complemented, Sylow
109#125Dic6118yescomplemented
110C2×C4⋊C4—612no—
111C2×C4⋊C4—612no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4C2×D6112yes—
114C2×C4⋊C4C2×D6111yescharacteristic
115C2×C4⋊C4C2×D6111yescharacteristic
116C2×C4⋊C4C2×D6112yes—
117C2×C42—612no—
118C2×C42—611no—
119C2×C42—611no—
120C2×C42—612no—
121C2×C42C2×D6111yescharacteristic
122#95—612no—
123#95—612no—
124#95—612no—
125#95—611no—
126#95—612no—
127#95—611no—
128#95—612no—
129#95—612no—
130#95—612no—
131C22×C4—612no—
132C22×C4—612no—
133C22×C4—612no—
134C22×C4—612no—
135C22×C4C22×D6111yescharacteristic
136C22×C4C22×D6111yescharacteristic
137C22×C4C22×D6112yes—
138C22×C4C22×D6112yes—
139C22×C4C22×D6111yescharacteristic
140C4⋊C4—1224no—
141C4⋊C4—1224no—
142C4⋊C4—2442no—
143C4⋊C4C2×Dic6118yes—
144C4⋊C4C2×Dic6114yes—
145C4⋊C4C2×Dic6114yes—
146C4⋊C4C2×Dic6118yes—
147C42—1224no—
148C42—2441no—
149C42—2441no—
150C42—2442no—
151C42C2×Dic6114yes—
152C23C23×D6111yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—614no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4C22×Dic6112yes—
174C2×C4C22×Dic6112yes—
175C2×C4C22×Dic6112yes—
176C2×C4C22×Dic6114yes—
177C2×C4C22×Dic6114yes—
178C22C23×Dic6111yescharacteristic
179C22#41×D6112yes—
180C22#1451982311yescharacteristic
181C22#1451982411yescharacteristic
182C22#1451982512yes—
183C4—24no—
184C4—22no—
185C4—22no—
186C4—22no—
187C4—24no—
188C4—1224no—
189C4—2442no—
190C4—2442no—
191C4—2442no—
192C2#41×Dic6111yescharacteristic
193C2#1684024011yescharacteristic
194C2#1684024511yescharacteristic
195C2#1684036012yes—
196C2#1684037112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC2×#125×C61C2
socleC23×C61C24
hypercenterC2×#125D61
hypocenterC61#2336
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
26. #125×C61C4semidirect
108. C61#2336semidirect
109. #125Dic61semidirect