Finite Group Databasebeta

← #21461215

Subgroups — #21461215

Order 7808.

346 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 64 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, complemented
2C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#16840613C214yesmaximal, complemented
4C2×#14519748C211yesmaximal, characteristic
5C2×#11758213—21no—
6C2×C22⋊#6923—21no—
7C2×C4×#6923—21no—
8#14519834C2212yescomplemented
9C22⋊#92420—21no—
10(C2×#6923)⋊C4C2212yescomplemented
11C22×C22⋊D61—21no—
12C22×C4×D61C2211yescharacteristic
13#14519748—21no—
14#14519748—21no—
15#14519748C412yescomplemented
16#14519748C2212yes—
17C2×C4⋊Dic61C411yescharacteristic, complemented
18C2×C22⋊Dic61—21no—
19C22×D4×C61C411yescharacteristic, complemented
20C24×C61—21no—
21C23×D61D411yescharacteristic
22C22×#6923—22no—
23C2×D4×C61—21no—
24C2×D4×C61—42no—
25C2×D4×C61C2×C412yes—
26C22×C4×C61C2×C411yescharacteristic
27C2×C22⋊D61—22no—
28C2×C22⋊D61—22no—
29C2×C22⋊D61—44no—
30C22×Dic61—21no—
31C22×Dic61D411yescharacteristic
32C2×C4×D61—42no—
33C2×C4×D61C2×C411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61C2311yescharacteristic
37C22⋊#6923—24no—
38C2×#92420—22no—
39C4×#6923—42no—
40#11758213—42no—
41C22⋊Dic61—22no—
42C22⋊Dic61—22no—
43C4⋊Dic61—21no—
44C4⋊Dic61C2×C412yes—
45C23×C61—22no—
46C23×C61—42no—
47C23×C61—42no—
48C23×C61—42no—
49C23×C61C22⋊C411yescharacteristic
50C22×D61—22no—
51C22×D61—22no—
52C22×D61—41no—
53C22×D61C22⋊C411yescharacteristic
54C22×D61C2×D411yescharacteristic
55C2×#6923—24no—
56C2×#6923—42no—
57C2×#6923—42no—
58D4×C61—42no—
59D4×C61—42no—
60C2×C4×C61—22no—
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C22⋊D61—44no—
64C22⋊D61—44no—
65C2×Dic61—22no—
66C2×Dic61—41no—
67C2×Dic61—42no—
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C2×D411yescharacteristic
70C4×D61—22no—
71C4×D61—22no—
72C4×D61—41no—
73C4×D61—41no—
74#92420—42no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61—42no—
80C22×C61—84no—
81C22×C61#10412yes—
82C22×C61C2×C22⋊C411yescharacteristic
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—21no—
86C2×D61—21no—
87C2×D61—21no—
88C2×D61—44no—
89C2×D61AGL(1,ℤ/8)12yes—
90#6923—44no—
91C4×C61—21no—
92C4×C61#9912yes—
93Dic61—21no—
94Dic61—21no—
95Dic61—42no—
96#1507—611nomaximal, Sylow
97C2×C61—22no—
98C2×C61—82no—
99C2×C61C2×#9911yescharacteristic
100C2×C61#41811yescharacteristic
101C2×C61C2×#10411yescharacteristic
102D61—22no—
103D61—41no—
104C2×#121—611no—
105#407—611no—
106C4×C22⋊C4—611no—
107#327—614no—
108C61#150711yescharacteristic, complemented, Sylow
109C22×D4—1221no—
110C22×D4#692311yescharacteristic, complemented
111C23×C4—611no—
112C2×M16—1221no—
113#121—612no—
114#121—612no—
115#121—1221no—
116#121—1221no—
117C2×C4⋊C4—611no—
118C2×C22⋊C4—1221no—
119C2×C22⋊C4—1221no—
120C2×C42—1221no—
121C22⋊C8—612no—
122C22⋊C8—1221no—
123#95—612no—
124C24—21no—
125C24—611no—
126C2×D4—21no—
127C2×D4—42no—
128C2×D4—1222no—
129C2×D4—1222no—
130C2×D4—2444no—
131C2×D4C2×#692312yes—
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—611no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—1222no—
138C22×C4—1221no—
139C22×C4—2442no—
140C22×C4C2×#692311yescharacteristic
141M16—2442no—
142C2×C8—1222no—
143C4⋊C4—612no—
144C4⋊C4—1221no—
145C22⋊C4—1222no—
146C22⋊C4—1222no—
147C22⋊C4—1224no—
148C42—2442no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—42no—
153C23—611no—
154C23—611no—
155C23—1222no—
156C23—1222no—
157C23—2441no—
158C23C22⋊#692311yescharacteristic
159D4—42no—
160D4—42no—
161D4—2444no—
162D4—2444no—
163C2×C4—22no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4—1224no—
169C2×C4—1222no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2442no—
174C2×C4—2442no—
175C2×C4—2442no—
176C2×C4C22⋊#692311yescharacteristic
177C2×C4C22×#692311yescharacteristic
178C8—2442no—
179C22—21no—
180C22—21no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22—84no—
185C22—612no—
186C22—1221no—
187C22—1221no—
188C22—1221no—
189C22—1221no—
190C22—1221no—
191C22—2444no—
192C22#1451984112yes—
193C22C2×C22⋊#692311yescharacteristic
194C4—21no—
195C4—1221no—
196C4—1221no—
197C4—2444no—
198C4—2442no—
199C4#1451983512yes—
200C2—22no—
201C2—82no—
202C2—1222no—
203C2—2441no—
204C2C2×#1451983511yescharacteristic
205C2#1684075411yescharacteristic
206C2C2×#1451984111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×D4#6923
hypocenterC61#1507
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #16840733C2semidirect
2. C4×C22⋊#6923C2semidirect
3. #16840613C2semidirect
8. #14519834C22semidirect
10. (C2×#6923)⋊C4C22semidirect
15. #14519748C4semidirect
17. C2×C4⋊Dic61C4semidirect
19. C22×D4×C61C4semidirect
108. C61#1507semidirect
110. C22×D4#6923semidirect