Finite Group Databasebeta

← #21460661

Subgroups — #21460661

Order 7808.

228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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
1D61⋊(C22⋊C8)C211yesmaximal, characteristic
2C4×C22⋊#6923C211yesmaximal, characteristic
3C2×#14519689C211yesmaximal, characteristic
4C2×D61⋊C8—21no—
5C2×C22⋊#6923C412yes—
6C2×C4×#6923—21no—
7#14519834—21no—
8C22⋊#92420C412yescomplemented
9(C2×#6923)⋊C4—21no—
10C22×C4×D61C2211yescharacteristic
11C22×#92418C411yescharacteristic, complemented
12#14519689—21no—
13#14519689—21no—
14C22×C8×C61C411yescharacteristic, complemented
15C23×D61C2×C411yescharacteristic
16C22×#6923—22no—
17C22×C4×C61C2×C411yescharacteristic
18C22×Dic61C2×C411yescharacteristic
19C2×C4×D61—41no—
20C2×C4×D61—41no—
21C2×C4×D61D411yescharacteristic
22C2×C4×D61D411yescharacteristic
23C2×C4×D61D411yescharacteristic
24C2×C4×D61Q811yescharacteristic
25C22⋊#6923—22no—
26C22⋊#6923C814yescomplemented
27C2×#92420—22no—
28C4×#6923—41no—
29C4×#6923—41no—
30D61⋊C8—41no—
31D61⋊C8—41no—
32C2×C8×C61—21no—
33C2×C8×C61—41no—
34C2×#92418—21no—
35C2×#92418—41no—
36C23×C61C4211yescharacteristic
37C22×D61—41no—
38C22×D61—41no—
39C22×D61C22⋊C411yescharacteristic
40C22×D61C4⋊C411yescharacteristic
41C22×D61C2×C812yes—
42C22×D61M1612yes—
43C2×#6923—24no—
44C2×#6923—42no—
45C2×#6923—42no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C4⋊C411yescharacteristic
50C2×Dic61—41no—
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61C4⋊C411yescharacteristic
53C4×D61—21no—
54C4×D61—21no—
55C4×D61—21no—
56C4×D61—21no—
57C4×D61—41no—
58C4×D61—41no—
59#92420—42no—
60C8×C61—41no—
61#92418—41no—
62C22×C61—21no—
63C22×C61—21no—
64C22×C61#9511yescharacteristic
65C22×C61C4×C811yescharacteristic
66C22×C61#9711yescharacteristic
67C2×D61—21no—
68C2×D61—21no—
69C2×D61—21no—
70C2×D61—21no—
71C2×D61—42no—
72C2×D61—42no—
73C2×D61C22⋊C812yes—
74C2×D61C4⋊C812yes—
75#6923—44no—
76C4×C61—21no—
77C4×C61#9911yescharacteristic
78C4×C61#9911yescharacteristic
79Dic61—21no—
80Dic61—21no—
81#1282—611nomaximal, Sylow
82C2×C61—21no—
83C2×C61—21no—
84C2×C61#33611yescharacteristic
85C2×C61#34211yescharacteristic
86C2×C61#34411yescharacteristic
87D61—22no—
88D61—22no—
89C2×C22⋊C8—611no—
90C2×C22⋊C8—611no—
91C4×C22⋊C4—611no—
92C61#128211yescharacteristic, complemented, Sylow
93C23×C4—611no—
94C22×C8—611no—
95C22×C8—1221no—
96C22×C8#692311yescharacteristic, complemented
97C2×C22⋊C4—612no—
98C2×C42—1221no—
99C22⋊C8—612no—
100C22⋊C8—1221no—
101C22⋊C8—1221no—
102C22⋊C8—1221no—
103#95—1221no—
104C24—611no—
105C22×C4—611no—
106C22×C4—611no—
107C22×C4—611no—
108C22×C4—611no—
109C22×C4—611no—
110C22×C4—1222no—
111C22×C4—2441no—
112C22×C4—2441no—
113C22×C4C2×#692311yescharacteristic
114C2×C8—21no—
115C2×C8—41no—
116C2×C8—1222no—
117C2×C8—1221no—
118C2×C8—2441no—
119C2×C8—2441no—
120C2×C8—2441no—
121C22⋊C4—614no—
122C22⋊C4—1222no—
123C42—2441no—
124C42—2441no—
125C23—611no—
126C23—611no—
127C23—612no—
128C23—612no—
129C23—2441no—
130C23—2441no—
131C23C4×#692311yescharacteristic
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—611no—
135C2×C4—611no—
136C2×C4—1221no—
137C2×C4—1221no—
138C2×C4—1221no—
139C2×C4—1221no—
140C2×C4—1224no—
141C2×C4—2441no—
142C2×C4—2441no—
143C2×C4—2441no—
144C2×C4—2442no—
145C2×C4—2442no—
146C2×C4C4⋊#692311yescharacteristic
147C2×C4C22⋊#692311yescharacteristic
148C8—41no—
149C8—2442no—
150C8—2441no—
151C22—21no—
152C22—21no—
153C22—612no—
154C22—612no—
155C22—1221no—
156C22—1221no—
157C22—1221no—
158C22—1221no—
159C22—2442no—
160C22—2442no—
161C22(C2×#6923)⋊C411yescharacteristic
162C22C8×#692311yescharacteristic
163C22#1451983111yescharacteristic
164C4—21no—
165C4—1221no—
166C4—1221no—
167C4—2444no—
168C4#1451983511yescharacteristic
169C4#1451983611yescharacteristic
170C2—21no—
171C2—21no—
172C2—1222no—
173C2—1222no—
174C2(C2×#6923)⋊C811yescharacteristic
175C2#1684064011yescharacteristic
176C2#1684064411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC22×C61C4×C8
FrattiniC22×C4C2×#6923
FittingC22×C8×C61C4
socleC22×C61#95
hypercenterC22×C8#6923
hypocenterC61#1282
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
8. C22⋊#92420C4semidirect
11. C22×#92418C4semidirect
14. C22×C8×C61C4semidirect
26. C22⋊#6923C8semidirect
92. C61#1282semidirect
96. C22×C8#6923semidirect