Finite Group Databasebeta

← #21462116

Subgroups — #21462116

Order 7808.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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×#14519838C212yesmaximal, complemented
2#16840673C212yesmaximal, complemented
3#16840671C212yesmaximal, complemented
4#16840338C211yesmaximal, characteristic
5C2×#11758217—22no—
6#14519838—22no—
7#14519838C2214yes—
8C2×#11758222C411yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519777C411yescharacteristic
11#14519777C2211yescharacteristic
12#14519765C411yescharacteristic
13#14519765C2211yescharacteristic
14#14519761—22no—
15#14519757—22no—
16#117×C61C411yescharacteristic
17C22×C4×C61C2×C411yescharacteristic
18C2×C22⋊D61—21no—
19C22×Dic61D412yes—
20#11758222—42no—
21C2×D244C2×C411yescharacteristic
22C2×C4×D61—21no—
23C2×Dic122—42no—
24C2×Dic122C2×C411yescharacteristic
25C2×Dic122C2×C411yescharacteristic
26C2×Dic122D412yes—
27C2×Dic122C2311yescharacteristic
28#11758217—24no—
29#11758217—42no—
30C2×#92420—42no—
31C4⋊C4×C61—21no—
32C22⋊C4×C61—21no—
33C42×C61C2×C411yescharacteristic
34C42×C61C2×C411yescharacteristic
35#11758198—22no—
36#11758198—22no—
37C4⋊Dic61—22no—
38C4⋊Dic61—22no—
39C23×C61C22⋊C411yescharacteristic
40C22×D61—21no—
41C2×C4×C61—22no—
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22×C411yescharacteristic
46C22⋊D61—42no—
47C2×Dic61—22no—
48C2×Dic61—22no—
49C2×Dic61—21no—
50C2×Dic61C22⋊C412yes—
51C2×Dic61C2×D412yes—
52D244—41no—
53C4×D61—42no—
54Dic122—41no—
55Dic122—42no—
56Dic122—41no—
57Dic122—41no—
58#92420—44no—
59C22×C61—41no—
60C22×C61#9912yes—
61C22×C61C2×C22⋊C411yescharacteristic
62C2×D61—42no—
63C2×D61—41no—
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—41no—
67C4×C61—41no—
68Dic61—22no—
69Dic61—22no—
70Dic61—41no—
71#2133—611nomaximal, Sylow
72C2×C61—21no—
73C2×C61—22no—
74C2×C61C2×#9911yescharacteristic
75D61—81no—
76#536—611no—
77C2×#101—612no—
78#356—612no—
79#355—612no—
80C61#213311yescharacteristic, complemented, Sylow
81C2×#41—611no—
82C22×Q8—611no—
83C2×M16—1222no—
84C4⋊Q8—611no—
85C4⋊Q8—611no—
86#124—611no—
87#124—611no—
88#123—1222no—
89C22⋊Q8—1222no—
90#117#692311yescharacteristic
91#101—614no—
92#101—1222no—
93#41—2442no—
94C2×Q8—612no—
95C2×Q8—611no—
96C2×Q8—611no—
97C2×Q8—611no—
98C2×Q8—2442no—
99C2×D4—611no—
100C2×D4—1221no—
101C22×C4—612no—
102C22×C4—1221no—
103C22×C4C2×#692311yescharacteristic
104M16—1224no—
105M16—2442no—
106C2×C8—2442no—
107C4⋊C4—21no—
108C4⋊C4—1222no—
109C4⋊C4—1222no—
110C22⋊C4—21no—
111C22⋊C4—1222no—
112C22⋊C4—1222no—
113C42C2×#692311yescharacteristic
114C42C2×#692311yescharacteristic
115C23—1221no—
116C23C22⋊#692311yescharacteristic
117Q8—2442no—
118Q8—2441no—
119Q8—2441no—
120Q8—2441no—
121D4—2441no—
122D4—2442no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—612no—
127C2×C4—612no—
128C2×C4—1222no—
129C2×C4—1222no—
130C2×C4—1221no—
131C2×C4—2442no—
132C2×C4C22⋊#692311yescharacteristic
133C2×C4C22×#692311yescharacteristic
134C8—2444no—
135C22—41no—
136C22—2442no—
137C22—2441no—
138C22#1451983612yes—
139C22C2×C22⋊#692311yescharacteristic
140C4—21no—
141C4—21no—
142C4—41no—
143C4—41no—
144C4—1222no—
145C4—1222no—
146C4—2441no—
147C2—21no—
148C2—22no—
149C2—4881no—
150C2C2×#1451983611yescharacteristic
subgroupG/H
centerC2C2×#14519836
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC2×C61C2×#99
hypercenter#117#6923
hypocenterC61#2133
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#14519838C2semidirect
2. #16840673C2semidirect
3. #16840671C2semidirect
80. C61#2133semidirect