Finite Group Databasebeta

← #21462122

Subgroups — #21462122

Order 7808.

230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 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#16840749C212yesmaximal
2#16840673C212yesmaximal, complemented
3#16840672C212yesmaximal, complemented
4#16840332C211yesmaximal, characteristic
5C2×#11758217—22no—
6#14519838C2214yes—
7#14519837—22no—
8C2×#11758224C2211yescharacteristic
9C2×Q8×D61C411yescharacteristic
10#14519777C2211yescharacteristic
11#14519775C2211yescharacteristic
12#14519764C411yescharacteristic
13#14519759—22no—
14#14519754—22no—
15#14519734C411yescharacteristic
16#124×C61C411yescharacteristic
17C2×Q8×C61C2×C411yescharacteristic
18C2×D4×C61C2×C411yescharacteristic
19C2×C22⋊D61D412yes—
20C22×Dic61D412yes—
21Q8×D61—42no—
22#11758224—42no—
23C2×C4×D61—21no—
24C2×C4×D61C2×C411yescharacteristic
25C2×Dic122—21no—
26C2×Dic122C2×C411yescharacteristic
27C2×Dic122C2311yescharacteristic
28#11758217—24no—
29#11758217—42no—
30C2×#92420—42no—
31C22⋊C4×C61—22no—
32C42×C61C2×C411yescharacteristic
33C22⋊Dic61—22no—
34#11758198—21no—
35C4⋊Dic61—22no—
36#11758196—21no—
37#11758196—22no—
38C4×Dic61C2×C411yescharacteristic
39C23×C61C22⋊C412yes—
40C22×D61C22⋊C411yescharacteristic
41Q8×C61—41no—
42D4×C61—41no—
43C2×C4×C61—21no—
44C2×C4×C61—21no—
45C2×C4×C61C22×C411yescharacteristic
46C22⋊D61—42no—
47C2×Dic61—22no—
48C2×Dic61—22no—
49C2×Dic61—21no—
50C2×Dic61—21no—
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61C2×D412yes—
53C4×D61—22no—
54C4×D61—42no—
55Dic122—41no—
56Dic122—42no—
57Dic122—41no—
58#92420—44no—
59C22×C61—22no—
60C22×C61—42no—
61C22×C61C2×C22⋊C411yescharacteristic
62C2×D61—21no—
63C2×D61—41no—
64C4×C61—21no—
65C4×C61—41no—
66C4×C61—41no—
67Dic61—22no—
68Dic61—41no—
69Dic61—41no—
70Dic61#9912yes—
71#2135—611nomaximal, Sylow
72C2×C61—21no—
73C2×C61—42no—
74C2×C61C2×#9911yescharacteristic
75D61—41no—
76#536—611no—
77#413—612no—
78#356—612no—
79#356—612no—
80C61#213511yescharacteristic, complemented, Sylow
81C2×#41—611no—
82C22×Q8—611no—
83C2×M16—1222no—
84C4⋊Q8—611no—
85C4⋊Q8—611no—
86#124—611no—
87#124#692311yescharacteristic
88#123—1222no—
89C22⋊Q8—1222no—
90#117—611no—
91#101—614no—
92#100—1222no—
93#41—2442no—
94C2×Q8—611no—
95C2×Q8—611no—
96C2×Q8—1221no—
97C2×Q8—2442no—
98C2×Q8C2×#692311yescharacteristic
99C2×D4—612no—
100C2×D4C2×#692311yescharacteristic
101C22×C4—612no—
102C22×C4—611no—
103C22×C4—1221no—
104M16—1224no—
105M16—2442no—
106C2×C8—2442no—
107C4⋊C4—1221no—
108C4⋊C4—1222no—
109C4⋊C4—1222no—
110C22⋊C4—22no—
111C22⋊C4—1221no—
112C22⋊C4—1222no—
113C42—611no—
114C42C2×#692311yescharacteristic
115C23—611no—
116C23C22⋊#692312yes—
117Q8—41no—
118Q8—2441no—
119Q8—2441no—
120Q8—2442no—
121D4—41no—
122D4—2442no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—611no—
126C2×C4—612no—
127C2×C4—1222no—
128C2×C4—1222no—
129C2×C4—1222no—
130C2×C4—1221no—
131C2×C4—1221no—
132C2×C4—2442no—
133C2×C4C22×#692311yescharacteristic
134C8—2444no—
135C22—22no—
136C22—42no—
137C22—1221no—
138C22—2441no—
139C22C2×C22⋊#692311yescharacteristic
140C4—21no—
141C4—41no—
142C4—41no—
143C4—612no—
144C4—1222no—
145C4—2441no—
146C4—2441no—
147C2—21no—
148C2—42no—
149C2—2441no—
150C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC2×C61C2×#99
hypercenter#124#6923
hypocenterC61#2135
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #16840673C2semidirect
3. #16840672C2semidirect
80. C61#2135semidirect