Finite Group Databasebeta

← #21450106

Subgroups — #21450106

Order 7808.

512 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519736C211yesmaximal, characteristic
2#16839701C212yesmaximal, complemented
3#16839692C212yesmaximal, complemented
4#16839643C214yesmaximal, complemented
5#16839635C212yesmaximal
6#16839625C212yesmaximal
7#16839625C211yesmaximal, characteristic
8C22×C4⋊C4×C61C211yesmaximal, characteristic
9#14519736—24no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2214yes—
13C2×C22⋊Dic61C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C4×Dic61C2212yes—
16#14519684C2212yes—
17#14519684C2214yes—
18#14519684C2214yes—
19#14519684C2214yes—
20#14519684C2212yes—
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—24no—
30C22×C4×C61—24no—
31C22×C4×C61—22no—
32C22×C4×C61—24no—
33C22×C4×C61D414yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×Dic61C2314yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C4⋊C4×C61—24no—
42C4⋊C4×C61—24no—
43C22⋊Dic61—24no—
44C22⋊Dic61—24no—
45C4⋊Dic61—22no—
46C4⋊Dic61—22no—
47#11758196—28no—
48C4×Dic61—24no—
49C23×C61—22no—
50C23×C61—22no—
51C23×C61C2×D412yes—
52C23×C61#4114yes—
53C23×C61C2411yescharacteristic
54C2×C4×C61—28no—
55C2×C4×C61—28no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—24no—
62C2×C4×C61—44no—
63C2×C4×C61C2×D412yes—
64C2×C4×C61C2×D412yes—
65C2×C4×C61#4114yes—
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—24no—
69C2×Dic61—24no—
70C2×Dic61—24no—
71C2×Dic61—24no—
72C2×Dic61—24no—
73C22×C61—22no—
74C22×C61—22no—
75C22×C61—28no—
76C22×C61#12314yes—
77C22×C61C22×D411yescharacteristic
78C22×C61C2×#4112yes—
79C22×C61C2×#4112yes—
80C22×C612−1+412yes—
81C4×C61—22no—
82C4×C61—22no—
83C4×C61—24no—
84C4×C61—42no—
85Dic61—42no—
86Dic61—42no—
87Dic61—44no—
88#2484—611nomaximal, Sylow
89C2×C61—24no—
90C2×C61C2×#12311yescharacteristic
91C2×C61#52511yescharacteristic
92C2×C61#53611yescharacteristic
93C2×C61#55214yes—
94C2×#117—611no—
95C22×C4⋊C4D6111yescharacteristic
96#400—612no—
97#398—612no—
98#387—614no—
99#385—612no—
100#381—611no—
101#381—612no—
102C61#248411yescharacteristic, complemented, Sylow
103C23×C4C2×D6111yescharacteristic
104C23×C4C2×D6111yescharacteristic
105C23×C4C2×D6111yescharacteristic
106#117—1224no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—611no—
109C2×C4⋊C4—611no—
110C2×C4⋊C4—614no—
111C2×C4⋊C4C2×D6112yes—
112C2×C4⋊C4C2×D6112yes—
113C2×C22⋊C4—612no—
114C2×C22⋊C4—612no—
115C2×C42—612no—
116#95—612no—
117#95—614no—
118#95—614no—
119#95—612no—
120#95—614no—
121C24C22×D6111yescharacteristic
122C22×C4—24no—
123C22×C4—22no—
124C22×C4—24no—
125C22×C4—24no—
126C22×C4—22no—
127C22×C4—614no—
128C22×C4—612no—
129C22×C4—612no—
130C22×C4C22⋊D6114yes—
131C22×C4C22×D6112yes—
132C22×C4C22×D6112yes—
133C22×C4C22×D6111yescharacteristic
134C22×C4C22×D6111yescharacteristic
135C4⋊C4—24no—
136C4⋊C4—24no—
137C4⋊C4—1228no—
138C4⋊C4—1222no—
139C4⋊C4—1222no—
140C22⋊C4—1224no—
141C22⋊C4—1224no—
142C42—1224no—
143C23—22no—
144C23—22no—
145C23#1175822414yes—
146C23C2×C22⋊D6112yes—
147C23C23×D6111yescharacteristic
148C2×C4—28no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—28no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—44no—
157C2×C4—1222no—
158C2×C4—1222no—
159C2×C4—1224no—
160C2×C4—1224no—
161C2×C4—1224no—
162C2×C4—1224no—
163C2×C4—1224no—
164C2×C4#1175822214yes—
165C2×C4C2×C22⋊D6112yes—
166C2×C4C2×C22⋊D6112yes—
167C22—22no—
168C22—22no—
169C22—28no—
170C22#1451975814yes—
171C22C22×C22⋊D6111yescharacteristic
172C22C2×#1175822412yes—
173C22C2×#1175822212yes—
174C22#1451982512yes—
175C4—22no—
176C4—22no—
177C4—24no—
178C4—42no—
179C4—2442no—
180C4—2442no—
181C4—2444no—
182C2—24no—
183C2C2×#1451975811yescharacteristic
184C2#1684027311yescharacteristic
185C2#1684033611yescharacteristic
186C2#1684044714yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C4⋊C4×C61C2
hypercenterC22×C4⋊C4D61
hypocenterC61#2484
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. #16839692C2semidirect
4. #16839643C2semidirect
102. C61#2484semidirect