Finite Group Databasebeta

← #21451632

Subgroups — #21451632

Order 7808.

508 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 165 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
2#16839701C212yesmaximal, complemented
3#16839695C214yesmaximal, complemented
4#16839682C212yesmaximal, complemented
5#16839635C212yesmaximal
6#16839625C212yesmaximal
7#16839622C211yesmaximal, characteristic
8C22×C4⋊C4×C61C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10#14519756—24no—
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2214yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17#14519684C2214yes—
18#14519684C2212yes—
19#14519684C2214yes—
20#14519684C2214yes—
21C23×C4×C61C2211yescharacteristic
22C23×C4×C61C2211yescharacteristic
23C23×C4×C61C2211yescharacteristic
24C2×C4⋊C4×C61—24no—
25C2×C4⋊C4×C61C2212yes—
26C2×C4⋊C4×C61C2212yes—
27C24×C61C2311yescharacteristic
28C22×C4×C61—22no—
29C22×C4×C61—22no—
30C22×C4×C61—22no—
31C22×C4×C61—42no—
32C22×C4×C61—42no—
33C22×C4×C61D414yes—
34C22×C4×C61Q814yescomplemented
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2314yes—
42C2×Dic122—22no—
43C2×Dic122—42no—
44C4⋊C4×C61—24no—
45C4⋊C4×C61—24no—
46C22⋊Dic61—24no—
47C22⋊Dic61—24no—
48C4⋊Dic61—22no—
49C4⋊Dic61—42no—
50#11758196—24no—
51#11758196—44no—
52C23×C61—22no—
53C23×C61—22no—
54C23×C61C2×D412yes—
55C23×C61C2×Q812yes—
56C23×C61#4112yes—
57C23×C61C2411yescharacteristic
58C2×C4×C61—28no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—24no—
65C2×C4×C61—44no—
66C2×C4×C61—44no—
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×Q814yes—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—24no—
73C2×Dic61—24no—
74C2×Dic61—24no—
75C2×Dic61—24no—
76C2×Dic61—24no—
77Dic122—44no—
78C22×C61—22no—
79C22×C61—22no—
80C22×C61—24no—
81C22×C61—24no—
82C22×C61C22⋊Q814yes—
83C22×C61C22×D411yescharacteristic
84C22×C61C22×Q811yescharacteristic
85C22×C61C2×#4111yescharacteristic
86C22×C61H(5,𝔽2)12yes—
87C22×C612−1+412yes—
88C4×C61—24no—
89C4×C61—22no—
90C4×C61—22no—
91C4×C61—42no—
92Dic61—42no—
93Dic61—42no—
94Dic61—44no—
95#2627—611nomaximal, Sylow
96C2×C61—24no—
97C2×C61C2×C22⋊Q811yescharacteristic
98C2×C61#53411yescharacteristic
99C2×C61#53611yescharacteristic
100C2×C61#53912yes—
101C2×C61#54412yes—
102C2×C22⋊Q8—611no—
103C22×C4⋊C4D6111yescharacteristic
104#400—612no—
105#398—614no—
106#395—612no—
107#385—612no—
108#381—612no—
109#380—611no—
110C61#262711yescharacteristic, complemented, Sylow
111C22×Q8—611no—
112C23×C4C2×D6111yescharacteristic
113C23×C4C2×D6111yescharacteristic
114C23×C4C2×D6111yescharacteristic
115C22⋊Q8—1224no—
116C2×C4⋊C4—24no—
117C2×C4⋊C4—612no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—612no—
120C2×C4⋊C4—614no—
121C2×C4⋊C4C2×D6112yes—
122C2×C4⋊C4C2×D6112yes—
123C2×C22⋊C4—612no—
124C2×C22⋊C4—612no—
125#95—612no—
126#95—614no—
127#95—614no—
128#95—614no—
129C24C22×D6111yescharacteristic
130C2×Q8—1222no—
131C2×Q8—2442no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—42no—
136C22×C4—42no—
137C22×C4—612no—
138C22×C4—614no—
139C22×C4—612no—
140C22×C4Dic12214yescomplemented
141C22×C4C22⋊D6114yes—
142C22×C4C22×D6112yes—
143C22×C4C22×D6112yes—
144C22×C4C22×D6111yescharacteristic
145C22×C4C22×D6111yescharacteristic
146C4⋊C4—24no—
147C4⋊C4—24no—
148C4⋊C4—1224no—
149C4⋊C4—1222no—
150C4⋊C4—2444no—
151C4⋊C4—2442no—
152C22⋊C4—1224no—
153C22⋊C4—1224no—
154C23—22no—
155C23—22no—
156C23C2×Dic12212yes—
157C23#1175822212yes—
158C23C2×C22⋊D6112yes—
159C23C23×D6111yescharacteristic
160Q8—2444no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—28no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—44no—
169C2×C4—44no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1224no—
173C2×C4—1224no—
174C2×C4—1224no—
175C2×C4—1224no—
176C2×C4—1224no—
177C2×C4C2×Dic12214yes—
178C2×C4C2×C22⋊D6112yes—
179C2×C4C2×C22⋊D6112yes—
180C22—22no—
181C22—22no—
182C22—24no—
183C22—24no—
184C22#1451975614yes—
185C22C22×C22⋊D6111yescharacteristic
186C22C22×Dic12211yescharacteristic
187C22C2×#1175822211yescharacteristic
188C22#1451982212yes—
189C22#1451982512yes—
190C4—24no—
191C4—22no—
192C4—22no—
193C4—42no—
194C4—2442no—
195C4—2442no—
196C4—2444no—
197C2—24no—
198C2C2×#1451975611yescharacteristic
199C2#1684032111yescharacteristic
200C2#1684033611yescharacteristic
201C2#1684035912yes—
202C2#1684039312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C4⋊C4×C61C2
hypercenterC22×C4⋊C4D61
hypocenterC61#2627
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #16839701C2semidirect
3. #16839695C2semidirect
4. #16839682C2semidirect
34. C22×C4×C61Q8semidirect
110. C61#2627semidirect
140. C22×C4Dic122semidirect