Finite Group Databasebeta

← #21453619

Subgroups — #21453619

Order 7808.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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#16839692C212yesmaximal
2#16839683C212yesmaximal
3#16839682C211yesmaximal, characteristic
4#16839661C212yesmaximal
5#16839659C212yesmaximal
6#16839644C212yesmaximal
7#16839643C212yesmaximal
8#16839631C211yesmaximal, characteristic
9C61×#398C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2212yes—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4×Dic61C2212yes—
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C2×C4⋊C4×C61C2212yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29#95×C61C2212yes—
30#95×C61C2211yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C2×Dic122—42no—
41C2×Dic122—41no—
42C4⋊C4×C61—24no—
43C4⋊C4×C61—41no—
44C4⋊C4×C61—41no—
45C4⋊Dic61—42no—
46C4⋊Dic61—41no—
47C4⋊Dic61—42no—
48#11758196—42no—
49#11758196—42no—
50#11758196—42no—
51#11758196Q818yescomplemented
52C4×Dic61—22no—
53C4×Dic61—42no—
54C23×C61C2411yescharacteristic
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×C61#4112yes—
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×Dic61C2×Q814yes—
79C2×Dic61C2×Q814yes—
80Dic122—44no—
81C22×C61C22×Q812yes—
82C22×C61C2×#4111yescharacteristic
83C22×C61H(5,𝔽2)11yescharacteristic
84C22×C61H(5,𝔽2)12yes—
85C22×C612−1+411yescharacteristic
86C4×C61—22no—
87C4×C61—24no—
88C4×C61—42no—
89C4×C61—41no—
90C4×C61—41no—
91Dic61—24no—
92Dic61—24no—
93Dic61—42no—
94Dic61—42no—
95#2792—611nomaximal, Sylow
96C2×C61#53911yescharacteristic
97C2×C61#54412yes—
98C2×C61#55412yes—
99C2×C61Q8211yescharacteristic
100C2×C61#56011yescharacteristic
101#398—612no—
102#398D6111yescharacteristic
103#395—611no—
104#395—612no—
105#389—612no—
106#389—612no—
107#387—612no—
108#387—612no—
109#384—611no—
110C61#279211yescharacteristic, complemented, Sylow
111C22×Q8—611no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4—612no—
116C2×C4⋊C4—612no—
117C2×C4⋊C4—612no—
118C2×C4⋊C4—612no—
119C2×C4⋊C4C2×D6112yes—
120C2×C4⋊C4C2×D6111yescharacteristic
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C42—611no—
123C2×C42—612no—
124#95—611no—
125#95—612no—
126#95—612no—
127#95—612no—
128#95—612no—
129#95—612no—
130#95C2×D6112yes—
131#95C2×D6111yescharacteristic
132C2×Q8—2441no—
133C2×Q8—2442no—
134C22×C4—612no—
135C22×C4—612no—
136C22×C4—612no—
137C22×C4—612no—
138C22×C4C22×D6112yes—
139C22×C4C22×D6111yescharacteristic
140C22×C4C22×D6111yescharacteristic
141C22×C4C22×D6111yescharacteristic
142C22×C4C22×D6112yes—
143C4⋊C4—24no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—618no—
147C4⋊C4—2442no—
148C4⋊C4—2442no—
149C4⋊C4—2442no—
150C4⋊C4—2441no—
151C4⋊C4—2442no—
152C4⋊C4—2442no—
153C42—1222no—
154C42—2442no—
155C23C23×D6111yescharacteristic
156Q8—2444no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—614no—
169C2×C4—614no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4#1175822412yes—
181C2×C4Q8×D6114yes—
182C22C2×Q8×D6112yes—
183C22C2×#1175822411yescharacteristic
184C22#1451982211yescharacteristic
185C22#1451982312yes—
186C22#1451982411yescharacteristic
187C4—24no—
188C4—22no—
189C4—41no—
190C4—41no—
191C4—42no—
192C4—1224no—
193C4—1224no—
194C4—2442no—
195C4—2442no—
196C2#1684035711yescharacteristic
197C2#1684039212yes—
198C2#1684047012yes—
199C2#1684049211yescharacteristic
200C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2792
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
51. #11758196Q8semidirect
110. C61#2792semidirect