Finite Group Databasebeta

← #21460666

Subgroups — #21460666

Order 7808.

226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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#16840733C211yesmaximal, characteristic
2C4×C22⋊#6923C211yesmaximal, characteristic
3#16839624C211yesmaximal, characteristic
4C2×#11758213—21no—
5C2×C22⋊#6923—21no—
6C2×C4×#6923C412yescomplemented
7#14519834C412yescomplemented
8C22⋊#92420—21no—
9(C2×#6923)⋊C4—21no—
10C22×C4×D61C2211yescharacteristic
11C2×#11758198—21no—
12#14519684—21no—
13#14519684C411yescharacteristic, complemented
14#95×C61C411yescharacteristic, complemented
15C23×D61D411yescharacteristic
16C22×#6923—22no—
17C22×C4×C61—21no—
18C22×C4×C61C2×C411yescharacteristic
19C22×Dic61—21no—
20C22×Dic61D411yescharacteristic
21C2×C4×D61—42no—
22C2×C4×D61C2×C411yescharacteristic
23C2×C4×D61C2×C411yescharacteristic
24C2×C4×D61D411yescharacteristic
25C2×C4×D61Q811yescharacteristic
26C22⋊#6923—22no—
27C22⋊#6923—22no—
28C2×#92420—22no—
29C4×#6923—42no—
30#11758213—42no—
31#11758198—42no—
32C23×C61C22⋊C411yescharacteristic
33C22×D61—21no—
34C22×D61—21no—
35C22×D61—22no—
36C22×D61—41no—
37C22×D61C22⋊C411yescharacteristic
38C22×D61C4⋊C411yescharacteristic
39C2×#6923—24no—
40C2×#6923—42no—
41C2×#6923—42no—
42C2×C4×C61—41no—
43C2×C4×C61—41no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61C4211yescharacteristic
47C2×C4×C61C4⋊C411yescharacteristic
48C2×Dic61—41no—
49C2×Dic61—41no—
50C2×Dic61—41no—
51C2×Dic61—41no—
52C2×Dic61C22⋊C411yescharacteristic
53C2×Dic61C4⋊C411yescharacteristic
54C4×D61—22no—
55C4×D61—22no—
56C4×D61—41no—
57C4×D61—41no—
58#92420—42no—
59C22×C61—21no—
60C22×C61—21no—
61C22×C61#9511yescharacteristic
62C22×C61#10411yescharacteristic
63C22×C61#10411yescharacteristic
64C2×D61—21no—
65C2×D61—21no—
66C2×D61—21no—
67C2×D61—21no—
68C2×D61—21no—
69C2×D61—42no—
70C2×D61—42no—
71C2×D61#9912yes—
72#6923—44no—
73C4×C61—21no—
74C4×C61—21no—
75C4×C61—81no—
76Dic61—21no—
77Dic61—21no—
78Dic61—81no—
79#1284—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—21no—
82C2×C61H(3,ℤ/4)11yescharacteristic
83C2×C61#33911yescharacteristic
84C2×C61#34211yescharacteristic
85D61—22no—
86D61—41no—
87#407—611no—
88#381—611no—
89C4×C22⋊C4—611no—
90C61#128411yescharacteristic, complemented, Sylow
91C23×C4—611no—
92C2×M16—1221no—
93C2×C22⋊C4—1221no—
94C2×C22⋊C4—1221no—
95C2×C42—612no—
96C22⋊C8—612no—
97C22⋊C8—1221no—
98#95—611no—
99#95—1221no—
100#95—1221no—
101#95#692311yescharacteristic, complemented
102C24—611no—
103C22×C4—21no—
104C22×C4—611no—
105C22×C4—611no—
106C22×C4—611no—
107C22×C4—611no—
108C22×C4—611no—
109C22×C4—1222no—
110C22×C4—1221no—
111C22×C4—2442no—
112C22×C4C2×#692311yescharacteristic
113M16—2442no—
114C2×C8—1222no—
115C22⋊C4—1222no—
116C22⋊C4—1222no—
117C22⋊C4—2442no—
118C42—2442no—
119C23—611no—
120C23—611no—
121C23—1222no—
122C23—1221no—
123C23—1221no—
124C23—2441no—
125C23C22⋊#692311yescharacteristic
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—611no—
131C2×C4—611no—
132C2×C4—1222no—
133C2×C4—1222no—
134C2×C4—1224no—
135C2×C4—2441no—
136C2×C4—2441no—
137C2×C4—2441no—
138C2×C4—2441no—
139C2×C4—2441no—
140C2×C4—2441no—
141C2×C4—2442no—
142C2×C4—2442no—
143C2×C4C4×#692311yescharacteristic
144C2×C4C4⋊#692311yescharacteristic
145C8—2442no—
146C22—21no—
147C22—21no—
148C22—612no—
149C22—1221no—
150C22—1221no—
151C22—1221no—
152C22—1221no—
153C22—1221no—
154C22—2442no—
155C22—2442no—
156C22(C2×#6923)⋊C411yescharacteristic
157C22#1451984111yescharacteristic
158C22#1451984211yescharacteristic
159C4—21no—
160C4—21no—
161C4—81no—
162C4—1221no—
163C4—1221no—
164C4—4881no—
165C4—2444no—
166C2—21no—
167C2—21no—
168C2—1222no—
169C2—2441no—
170C2#1684062911yescharacteristic
171C2#1684063211yescharacteristic
172C2#1684063911yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC2×C4×C61C42
FrattiniC22×C4C2×#6923
Fitting#95×C61C4
socleC22×C61#95
hypercenter#95#6923
hypocenterC61#1284
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
6. C2×C4×#6923C4semidirect
7. #14519834C4semidirect
13. #14519684C4semidirect
14. #95×C61C4semidirect
90. C61#1284semidirect
101. #95#6923semidirect