Finite Group Databasebeta

← #21453703

Subgroups — #21453703

Order 7808.

376 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 137 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#16839704C212yesmaximal
2#16839701C211yesmaximal, characteristic
3#16839696C212yesmaximal
4#16839682C211yesmaximal, characteristic
5#16839669C212yesmaximal
6#16839666C212yesmaximal
7#16839649C212yesmaximal
8#16839646C212yesmaximal
9C61×#391C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×C4×Dic61C2212yes—
17#14519684C2211yescharacteristic
18#14519684C2212yes—
19#14519684C2211yescharacteristic
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29#95×C61C2212yes—
30#95×C61C2212yes—
31C2×Q8×C61—41no—
32C2×Q8×C61—41no—
33C2×Q8×C61Q814yescomplemented
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C2×Dic122—24no—
44C2×Dic122—41no—
45C4⋊C4×C61—41no—
46C42×C61—41no—
47C4⋊Dic61—41no—
48C4⋊Dic61—42no—
49#11758196—24no—
50#11758196—24no—
51#11758196—42no—
52C4×Dic61—42no—
53C23×C61C2411yescharacteristic
54Q8×C61—44no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—22no—
66C2×C4×C61C2×Q814yes—
67C2×C4×C61C2×Q812yes—
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—24no—
78C2×Dic61#4114yes—
79Dic122—44no—
80C22×C61C22×Q811yescharacteristic
81C22×C61C2×#4112yes—
82C22×C61H(5,𝔽2)11yescharacteristic
83C22×C61H(5,𝔽2)11yescharacteristic
84C22×C612−1+412yes—
85C4×C61—24no—
86C4×C61—22no—
87C4×C61—42no—
88C4×C61—41no—
89C4×C61—41no—
90Dic61—24no—
91Dic61—42no—
92Dic61—42no—
93Dic61—42no—
94#2799—611nomaximal, Sylow
95C2×C61#54212yes—
96C2×C61#54311yescharacteristic
97C2×C61#55111yescharacteristic
98C2×C61#55712yes—
99C2×C61#56311yescharacteristic
100#400—611no—
101#400—612no—
102#398—612no—
103#395—611no—
104#391—612no—
105#391—612no—
106#391D6111yescharacteristic
107#387—612no—
108#387—612no—
109C61#279911yescharacteristic, complemented, Sylow
110C22×Q8—611no—
111C22×Q8C2×D6111yescharacteristic
112C2×C4⋊C4—612no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4—612no—
116C2×C4⋊C4—612no—
117C2×C4⋊C4C2×D6111yescharacteristic
118C2×C42—612no—
119C2×C42C2×D6111yescharacteristic
120#95—612no—
121#95—612no—
122#95—612no—
123#95—612no—
124#95—612no—
125#95—612no—
126#95—612no—
127#95—611no—
128#95—611no—
129#95C2×D6112yes—
130#95C2×D6112yes—
131C2×Q8—41no—
132C2×Q8—41no—
133C2×Q8—1224no—
134C2×Q8—2441no—
135C2×Q8Dic12214yescomplemented
136C22×C4—612no—
137C22×C4—612no—
138C22×C4—612no—
139C22×C4—612no—
140C22×C4C22×D6111yescharacteristic
141C22×C4C22×D6112yes—
142C22×C4C22×D6111yescharacteristic
143C22×C4C22×D6111yescharacteristic
144C22×C4C22×D6112yes—
145C4⋊C4—41no—
146C4⋊C4—1224no—
147C4⋊C4—1224no—
148C4⋊C4—2442no—
149C4⋊C4—2442no—
150C4⋊C4—2441no—
151C42—41no—
152C42—2442no—
153C23C23×D6111yescharacteristic
154Q8—44no—
155Q8—2444no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—614no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1224no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4C2×Dic12212yes—
179C2×C4C2×Dic12214yes—
180C22C22×Dic12211yescharacteristic
181C22#41×D6112yes—
182C22#1451982211yescharacteristic
183C22#1451982211yescharacteristic
184C22#1451982512yes—
185C4—22no—
186C4—24no—
187C4—42no—
188C4—41no—
189C4—41no—
190C4—1224no—
191C4—2442no—
192C4—2442no—
193C4—2442no—
194C2#1684038212yes—
195C2#1684038811yescharacteristic
196C2#1684044211yescharacteristic
197C2#1684048812yes—
198C2#1684051111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2799
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
33. C2×Q8×C61Q8semidirect
109. C61#2799semidirect
135. C2×Q8Dic122semidirect