Finite Group Databasebeta

← #21453886

Subgroups — #21453886

Order 7808.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519769C211yesmaximal, characteristic
2#16839701C212yesmaximal
3#16839700C212yesmaximal
4#16839695C214yesmaximal
5#16839693C212yesmaximal
6#16839692C212yesmaximal
7#16839628C211yesmaximal, characteristic
8C2×#125×C61C211yesmaximal, characteristic
9#14519769—24no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2214yes—
16#14519684C2214yes—
17#14519684C2212yes—
18#14519684C2214yes—
19#14519684C2212yes—
20#14519684C2214yes—
21#125×C61—24no—
22C2×C4⋊C4×C61C2212yes—
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2212yes—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C42×C61C2211yescharacteristic
27C22×C4×C61C2312yes—
28C22×C4×C61C2312yes—
29C22×C4×C61C2311yescharacteristic
30C22×C4×C61C2311yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C22×Dic61C2314yes—
33C22×Dic61C2312yes—
34C22×Dic61C2312yes—
35C4⋊C4×C61—22no—
36C4⋊C4×C61—24no—
37C4⋊C4×C61—22no—
38C4⋊C4×C61—24no—
39C42×C61D414yes—
40C4⋊Dic61—22no—
41C4⋊Dic61—22no—
42C4⋊Dic61—42no—
43#11758196—24no—
44#11758196—24no—
45#11758196—44no—
46C23×C61C2411yescharacteristic
47C2×C4×C61—21no—
48C2×C4×C61—22no—
49C2×C4×C61—22no—
50C2×C4×C61—21no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—24no—
55C2×C4×C61—22no—
56C2×C4×C61C2×D412yes—
57C2×C4×C61C2×D412yes—
58C2×C4×C61C2×D412yes—
59C2×Dic61—22no—
60C2×Dic61—22no—
61C2×Dic61—22no—
62C2×Dic61—24no—
63C2×Dic61—24no—
64C2×Dic61—22no—
65C2×Dic61—24no—
66C2×Dic61—24no—
67C22×C61C22×D411yescharacteristic
68C22×C61H(5,𝔽2)11yescharacteristic
69C22×C612−1+412yes—
70C22×C612−1+411yescharacteristic
71C22×C612−1+412yes—
72C4×C61—22no—
73C4×C61—22no—
74C4×C61—22no—
75C4×C61—42no—
76C4×C61—42no—
77Dic61—42no—
78Dic61—42no—
79Dic61—44no—
80#2822—611nomaximal, Sylow
81C2×C61#53611yescharacteristic
82C2×C61#53611yescharacteristic
83C2×C61#53711yescharacteristic
84C2×C61#56312yes—
85C2×C61#56412yes—
86C2×#125—611no—
87C2×#125D6111yescharacteristic
88#400—612no—
89#400—612no—
90#398—612no—
91#398—612no—
92#398—614no—
93#382—611no—
94C61#282211yescharacteristic, complemented, Sylow
95#125—24no—
96#125—1224no—
97C2×C4⋊C4—612no—
98C2×C4⋊C4—611no—
99C2×C4⋊C4—612no—
100C2×C4⋊C4—611no—
101C2×C4⋊C4—612no—
102C2×C4⋊C4—614no—
103C2×C4⋊C4C2×D6112yes—
104C2×C4⋊C4C2×D6111yescharacteristic
105C2×C4⋊C4C2×D6112yes—
106C2×C4⋊C4C2×D6111yescharacteristic
107C2×C42C2×D6111yescharacteristic
108#95—612no—
109#95—612no—
110#95—614no—
111#95—614no—
112#95—614no—
113C22×C4—614no—
114C22×C4—612no—
115C22×C4—612no—
116C22×C4C22×D6112yes—
117C22×C4C22×D6112yes—
118C22×C4C22×D6111yescharacteristic
119C22×C4C22×D6111yescharacteristic
120C22×C4C22×D6111yescharacteristic
121C4⋊C4—24no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—22no—
125C4⋊C4—1224no—
126C4⋊C4—1224no—
127C4⋊C4—1222no—
128C4⋊C4—1222no—
129C4⋊C4—2444no—
130C4⋊C4—2442no—
131C42C22⋊D6114yes—
132C23C23×D6111yescharacteristic
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—22no—
142C2×C4—1222no—
143C2×C4—1222no—
144C2×C4—1224no—
145C2×C4—1222no—
146C2×C4—1224no—
147C2×C4—1222no—
148C2×C4—1224no—
149C2×C4—1224no—
150C2×C4C2×C22⋊D6112yes—
151C2×C4C2×C22⋊D6112yes—
152C2×C4C2×C22⋊D6112yes—
153C22C22×C22⋊D6111yescharacteristic
154C22#1451982311yescharacteristic
155C22#1451982412yes—
156C22#1451982411yescharacteristic
157C22#1451982512yes—
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—2444no—
164C4—2442no—
165C4—2442no—
166C2#1684033311yescharacteristic
167C2#1684033611yescharacteristic
168C2#1684034011yescharacteristic
169C2#1684051612yes—
170C2C61⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#125×C61C2
hypercenterC2×#125D61
hypocenterC61#2822
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
94. C61#2822semidirect