Finite Group Databasebeta

← #21453620

Subgroups — #21453620

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#16839695C212yesmaximal
2#16839692C211yesmaximal, characteristic
3#16839681C212yesmaximal
4#16839659C212yesmaximal
5#16839658C212yesmaximal
6#16839647C212yesmaximal
7#16839645C212yesmaximal
8#16839631C211yesmaximal, characteristic
9C61×#395C211yesmaximal, characteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4×Dic61C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2212yes—
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31C2×Q8×C61—41no—
32C2×Q8×C61—42no—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C4⋊C4×C61—42no—
43C4⋊C4×C61—41no—
44C4⋊Dic61—41no—
45C4⋊Dic61—41no—
46C4⋊Dic61Q818yescomplemented
47#11758196—24no—
48#11758196—42no—
49#11758196—42no—
50#11758196—42no—
51#11758196—42no—
52C4×Dic61—22no—
53C4×Dic61—42no—
54C23×C61C2411yescharacteristic
55Q8×C61—44no—
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—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61C2×Q814yes—
68C2×C4×C61#4112yes—
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—22no—
79C2×Dic61C2×Q814yes—
80C2×Dic61C2×Q814yes—
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—41no—
89C4×C61—42no—
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—611no—
102#398—612no—
103#395—612no—
104#395D6111yescharacteristic
105#389—612no—
106#389—612no—
107#387—612no—
108#387—612no—
109#384—611no—
110C61#279211yescharacteristic, complemented, Sylow
111C22×Q8C2×D6111yescharacteristic
112C2×C4⋊C4—612no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—612no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4—612no—
117C2×C4⋊C4—612no—
118C2×C4⋊C4—612no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4C2×D6111yescharacteristic
121C2×C4⋊C4C2×D6112yes—
122C2×C42—611no—
123C2×C42—612no—
124#95—612no—
125#95—612no—
126#95—612no—
127#95—612no—
128#95—612no—
129#95—611no—
130#95C2×D6111yescharacteristic
131#95C2×D6112yes—
132C2×Q8—42no—
133C2×Q8—41no—
134C22×C4—612no—
135C22×C4—612no—
136C22×C4—612no—
137C22×C4—612no—
138C22×C4C22×D6112yes—
139C22×C4C22×D6111yescharacteristic
140C22×C4C22×D6111yescharacteristic
141C22×C4C22×D6112yes—
142C22×C4C22×D6111yescharacteristic
143C4⋊C4—42no—
144C4⋊C4—41no—
145C4⋊C4—618no—
146C4⋊C4—1224no—
147C4⋊C4—2442no—
148C4⋊C4—2442no—
149C4⋊C4—2442no—
150C4⋊C4—2442no—
151C4⋊C4—2441no—
152C4⋊C4—2441no—
153C42—1222no—
154C42—2442no—
155C23C23×D6111yescharacteristic
156Q8—44no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
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×C4Q8×D6114yes—
181C2×C4#1175822612yes—
182C22C2×Q8×D6112yes—
183C22C2×#1175822611yescharacteristic
184C22#1451982212yes—
185C22#1451982211yescharacteristic
186C22#1451982411yescharacteristic
187C4—22no—
188C4—24no—
189C4—41no—
190C4—42no—
191C4—41no—
192C4—1224no—
193C4—1224no—
194C4—2442no—
195C4—2442no—
196C2#1684036111yescharacteristic
197C2#1684039112yes—
198C2#1684047312yes—
199C2#1684049211yescharacteristic
200C2#1684050111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2792
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
46. C4⋊Dic61Q8semidirect
110. C61#2792semidirect