Finite Group Databasebeta

← #21461146

Subgroups — #21461146

Order 7808.

312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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#16840779C211yesmaximal, characteristic, complemented
2#16840765C211yesmaximal, characteristic, complemented
3#16840610C214yesmaximal, complemented
4C2×#14519739C211yesmaximal, characteristic
5C2×#11758217—21no—
6#14519844—21no—
7#14519844—21no—
8C4⋊#92420C2212yescomplemented
9C22⋊#92420—21no—
10C4×#92420C2212yescomplemented
11C22×D244C411yescharacteristic
12C22×C4×D61—21no—
13#14519739—21no—
14#14519739—21no—
15#14519739C412yes—
16#14519739C2212yes—
17C2×#11758198—21no—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4⋊C4×C61C411yescharacteristic
20C23×D61—21no—
21C22×C4×C61—21no—
22C22×C4×C61C2×C411yescharacteristic
23C22×Dic61D411yescharacteristic
24C22×Dic61D411yescharacteristic
25C2×D244—21no—
26C2×D244—24no—
27C2×D244C2×C412yes—
28C2×C4×D61—22no—
29C2×C4×D61—22no—
30C2×C4×D61—42no—
31C2×C4×D61—42no—
32#11758217—42no—
33C2×#92420—22no—
34C2×#92420—22no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C412yes—
37#11758198—22no—
38#11758198—22no—
39C4×Dic61C2×C411yescharacteristic
40C4×Dic61D411yescharacteristic
41C4×Dic61D411yescharacteristic
42C4×Dic61C2311yescharacteristic
43C23×C61C22⋊C411yescharacteristic
44C22×D61—24no—
45C22×D61—22no—
46C22×D61—42no—
47C22×D61—42no—
48C2×C4×C61—22no—
49C2×C4×C61—22no—
50C2×C4×C61—42no—
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22×C411yescharacteristic
53C2×Dic61—41no—
54C2×Dic61C22⋊C411yescharacteristic
55C2×Dic61C22⋊C411yescharacteristic
56C2×Dic61D812yes—
57C2×Dic61SD1612yes—
58C2×Dic61C2×D411yescharacteristic
59C2×Dic61C2×D411yescharacteristic
60D244—24no—
61D244—22no—
62D244M1614yescomplemented
63C4×D61—44no—
64C4×D61—42no—
65C4×D61—42no—
66#92420—42no—
67#92420—42no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61#10212yes—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—24no—
73C2×D61—48no—
74C2×D61—42no—
75C2×D61—42no—
76C4×C61—21no—
77C4×C61—42no—
78C4×C61C2×M1612yes—
79Dic61—21no—
80Dic61—21no—
81Dic61#10212yes—
82Dic61C2×D811yescharacteristic
83Dic61C2×SD1611yescharacteristic
84#1486—611nomaximal, Sylow
85C2×C61—22no—
86C2×C61#40711yescharacteristic
87C2×C61C2×#10211yescharacteristic
88C2×C61#42111yescharacteristic
89D61—44no—
90C2×C4×D4—611no—
91#431—611no—
92#423—611no—
93D4⋊C8—614no—
94C61#148611yescharacteristic, complemented, Sylow
95C22×D4—611no—
96C23×C4—1221no—
97C2×M16—1221no—
98C4×D4—612no—
99C4×D4—612no—
100C4×D4—1221no—
101C4×D4—1221no—
102C2×C4⋊C4#692311yescharacteristic
103C2×C22⋊C4—1221no—
104C2×C42—611no—
105C4⋊C8—612no—
106C4⋊C8—1221no—
107C4⋊C8—1221no—
108C22⋊C8—1221no—
109C4×C8—612no—
110C24—1221no—
111C2×D4—612no—
112C2×D4—1224no—
113C2×D4—1221no—
114C22×C4—21no—
115C22×C4—611no—
116C22×C4—611no—
117C22×C4—1222no—
118C22×C4—1222no—
119C22×C4—2442no—
120C22×C4—2442no—
121C22×C4C2×#692311yescharacteristic
122M16—2442no—
123C2×C8—1222no—
124C2×C8—1222no—
125C4⋊C4—21no—
126C4⋊C4C2×#692312yes—
127C22⋊C4—1222no—
128C22⋊C4—1222no—
129C42—611no—
130C42—611no—
131C42—611no—
132C42—611no—
133C23—1224no—
134C23—1222no—
135C23—2442no—
136C23—2442no—
137C23C22⋊#692311yescharacteristic
138D4—614no—
139D4—1224no—
140D4—1222no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—612no—
145C2×C4—612no—
146C2×C4—611no—
147C2×C4—611no—
148C2×C4—611no—
149C2×C4—611no—
150C2×C4—2444no—
151C2×C4—2442no—
152C2×C4—2442no—
153C2×C4—2441no—
154C2×C4C22⋊#692311yescharacteristic
155C2×C4C22×#692311yescharacteristic
156C8—2442no—
157C8—2442no—
158C22—21no—
159C22—21no—
160C22—1224no—
161C22—2448no—
162C22—2442no—
163C22—2442no—
164C22#1451983912yes—
165C22C2×C22⋊#692311yescharacteristic
166C4—21no—
167C4—42no—
168C4—612no—
169C4—611no—
170C4—611no—
171C4—1221no—
172C4—1221no—
173C4D61⋊M1612yes—
174C2—22no—
175C2—2444no—
176C2#1684073411yescharacteristic
177C2C2×#1451983911yescharacteristic
178C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1486
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #16840779C2semidirect
2. #16840765C2semidirect
3. #16840610C2semidirect
8. C4⋊#92420C22semidirect
10. C4×#92420C22semidirect
62. D244M16semidirect
94. C61#1486semidirect