Finite Group Databasebeta

← #21460909

Subgroups — #21460909

Order 7808.

158 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 38 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#16840749C211yesmaximal, characteristic
2#16840735C211yesmaximal, characteristic
3#16839743C211yesmaximal, characteristic
4C2×#11758217—21no—
5C2×#11758217C411yescharacteristic
6C22×#92420C411yescharacteristic
7#14519838—21no—
8#14519837C412yes—
9#14519834—21no—
10C22⋊#92420—21no—
11C2×#11758224C2211yescharacteristic
12M16×D61—21no—
13#14519695—21no—
14#14519694C411yescharacteristic
15#100×C61C411yescharacteristic
16C2×D4×C61C2×C411yescharacteristic
17C2×C22⋊D61C2×C411yescharacteristic
18C2×C22⋊D61Q811yescharacteristic
19C22×Dic61C2×C411yescharacteristic
20C22×Dic61D411yescharacteristic
21#11758224—41no—
22#11758224—41no—
23C2×C4×D61D411yescharacteristic
24C2×Dic122D411yescharacteristic
25#11758217—22no—
26#11758217—41no—
27#11758217—41no—
28C2×#92420—21no—
29C2×#92420—21no—
30C2×#92420—41no—
31C2×#92420—41no—
32M16×C61—21no—
33#11758194—21no—
34#11758189—41no—
35C8×D61—41no—
36C23×C61C4211yescharacteristic
37C23×C61C4⋊C411yescharacteristic
38C22×D61C4⋊C411yescharacteristic
39D4×C61—41no—
40C2×C4×C61C22⋊C411yescharacteristic
41C22⋊D61—41no—
42C22⋊D61—41no—
43C2×Dic61—21no—
44C2×Dic61—21no—
45C2×Dic61—21no—
46C2×Dic61—21no—
47C2×Dic61C22⋊C411yescharacteristic
48C2×Dic61C22⋊C411yescharacteristic
49C2×Dic61C4⋊C411yescharacteristic
50C4×D61—21no—
51C4×D61—21no—
52Dic122—41no—
53#92420—42no—
54#92420—41no—
55#92420—41no—
56C8×C61—41no—
57#92418—41no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61—41no—
61C22×C61—41no—
62C22×C61#9511yescharacteristic
63C2×D61—21no—
64C2×D61—41no—
65C4×C61—21no—
66Dic61—21no—
67Dic61—21no—
68Dic61#9911yescharacteristic
69Dic61#9911yescharacteristic
70#1392—611nomaximal, Sylow
71C2×C61—21no—
72C2×C61—41no—
73C2×C61—41no—
74C2×C61#34211yescharacteristic
75D61—41no—
76#413—611no—
77#413—611no—
78#408—611no—
79C61#139211yescharacteristic, complemented, Sylow
80C2×#41—611no—
81C2×M16—611no—
82C2×M16—1221no—
83C2×M16—1221no—
84C22×C8—611no—
85#101—1221no—
86#101—1221no—
87#100—612no—
88#100—611no—
89#100#692311yescharacteristic
90C22⋊C8—1221no—
91C22⋊C8—1221no—
92#41—2441no—
93#41—2441no—
94C2×Q8—611no—
95C2×D4—611no—
96C2×D4—611no—
97C2×D4C2×#692311yescharacteristic
98C22×C4—611no—
99C22×C4—611no—
100C22×C4—611no—
101M16—21no—
102M16—1222no—
103M16—1221no—
104M16—2441no—
105M16—2441no—
106M16—2441no—
107C2×C8—1221no—
108C2×C8—1221no—
109C2×C8—2441no—
110C2×C8—2441no—
111C2×C8—2441no—
112C23—611no—
113C23C4×#692311yescharacteristic
114C23C4⋊#692311yescharacteristic
115Q8—2441no—
116D4—41no—
117D4—2441no—
118D4—2441no—
119C2×C4—611no—
120C2×C4—611no—
121C2×C4—611no—
122C2×C4—1221no—
123C2×C4—1221no—
124C2×C4—1221no—
125C2×C4—1221no—
126C2×C4—1221no—
127C2×C4—1221no—
128C2×C4C22⋊#692311yescharacteristic
129C8—41no—
130C8—2441no—
131C8—2441no—
132C8—2441no—
133C8—2442no—
134C22—21no—
135C22—21no—
136C22—41no—
137C22—41no—
138C22—1221no—
139C22—2441no—
140C22(C2×#6923)⋊C411yescharacteristic
141C4—21no—
142C4—611no—
143C4—611no—
144C4—1221no—
145C4—1221no—
146C2—21no—
147C2—41no—
148C2—41no—
149C2—2441no—
150C2#1684063911yescharacteristic
subgroupG/H
centerC2#16840639
commutatorC23×C61C42
FrattiniC2×D4C2×#6923
Fitting#100×C61C4
socleC2×C61#342
hypercenter#100#6923
hypocenterC61#1392
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
79. C61#1392semidirect