Finite Group Databasebeta

← #21461210

Subgroups — #21461210

Order 7808.

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

normal subgroups only

This group has 272 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
1#16840784C211yesmaximal, characteristic, complemented
2#16840698C211yesmaximal, characteristic, complemented
3#16840614C214yesmaximal, complemented
4#16840313C211yesmaximal, characteristic
5C2×C4×#6923—21no—
6C4⋊#92420—21no—
7#14519834C2212yes—
8#14519832—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4C2212yes—
11C2×#11758226—21no—
12#14519774C411yescharacteristic, complemented
13#14519766—21no—
14#14519752—21no—
15#14519752C2212yes—
16#14519739—21no—
17#14519739C412yescomplemented
18C42×D61C2211yescharacteristic
19C4⋊Q8×C61C411yescharacteristic, complemented
20C22×#6923—22no—
21C2×Q8×C61—21no—
22#11758226—44no—
23C2×D244—22no—
24C2×D244—21no—
25C2×D244—21no—
26C2×D244C2×C412yes—
27C2×C4×D61—22no—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C2×#92420—22no—
32C4×#6923—24no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C412yes—
35C42×C61C2×C411yescharacteristic
36#11758198—22no—
37#11758198—22no—
38C4×Dic61C2×C411yescharacteristic
39C4×Dic61D411yescharacteristic
40C4×Dic61D411yescharacteristic
41C22×D61—22no—
42C22×D61C2×D411yescharacteristic
43C2×#6923—24no—
44C2×#6923—42no—
45C2×#6923—42no—
46Q8×C61—42no—
47C2×C4×C61—22no—
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22×C411yescharacteristic
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61C22⋊C411yescharacteristic
53C2×Dic61C2×D411yescharacteristic
54D244—42no—
55D244—42no—
56D244—44no—
57D244—42no—
58C4×D61—22no—
59C4×D61—22no—
60C4×D61—41no—
61C4×D61—44no—
62#92420—42no—
63C22×C61C2×C22⋊C411yescharacteristic
64C2×D61—21no—
65C2×D61—21no—
66C2×D61—42no—
67C2×D61—42no—
68C2×D61—42no—
69C2×D61AGL(1,ℤ/8)12yes—
70#6923—44no—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—42no—
74C4×C61#10412yes—
75Dic61—21no—
76Dic61—21no—
77Dic61—21no—
78#1505—611nomaximal, Sylow
79C2×C61#41011yescharacteristic
80C2×C61#41811yescharacteristic
81C2×C61C2×#10411yescharacteristic
82D61—22no—
83D61—82no—
84#532—611no—
85#432—611no—
86#376—611no—
87#327—614no—
88C61#150511yescharacteristic, complemented, Sylow
89C2×#41—1221no—
90C4⋊Q8#692311yescharacteristic, complemented
91#127—611no—
92#124—1221no—
93#121—612no—
94#121—1221no—
95C4×D4—612no—
96C4×D4—1221no—
97C2×C42—611no—
98C2×C42—1221no—
99C4⋊C8—1221no—
100C22⋊C8—612no—
101#97—1221no—
102#95—612no—
103#95—1221no—
104#41—2444no—
105C2×Q8—21no—
106C2×D4—612no—
107C2×D4—1222no—
108C2×D4—1221no—
109C2×D4—1221no—
110C22×C4—611no—
111C22×C4—611no—
112C22×C4—611no—
113C22×C4—1222no—
114C22×C4—1222no—
115C2×C8—1222no—
116C4⋊C4—21no—
117C4⋊C4C2×#692312yes—
118C22⋊C4—1222no—
119C22⋊C4—1222no—
120C42—611no—
121C42—611no—
122C42—611no—
123C42—1224no—
124C42C2×#692311yescharacteristic
125C23—611no—
126C23—1222no—
127Q8—42no—
128D4—2442no—
129D4—2442no—
130D4—2444no—
131D4—2442no—
132C2×C4—22no—
133C2×C4—611no—
134C2×C4—611no—
135C2×C4—611no—
136C2×C4—1222no—
137C2×C4—1222no—
138C2×C4—1224no—
139C2×C4—2441no—
140C2×C4—2444no—
141C2×C4—2442no—
142C2×C4—2442no—
143C2×C4C22⋊#692311yescharacteristic
144C2×C4C22⋊#692311yescharacteristic
145C2×C4C22×#692311yescharacteristic
146C8—2442no—
147C22—612no—
148C22—1221no—
149C22—1221no—
150C22—2442no—
151C22—2442no—
152C22—2442no—
153C22C2×C22⋊#692311yescharacteristic
154C4—21no—
155C4—21no—
156C4—42no—
157C4—1221no—
158C4—1221no—
159C4—1221no—
160C4—2444no—
161C4#1451984212yes—
162C2—1222no—
163C2—4882no—
164C2#1684074311yescharacteristic
165C2#1684075411yescharacteristic
166C2C2×#1451984211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1505
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #16840784C2semidirect
2. #16840698C2semidirect
3. #16840614C2semidirect
12. #14519774C4semidirect
17. #14519739C4semidirect
19. C4⋊Q8×C61C4semidirect
88. C61#1505semidirect
90. C4⋊Q8#6923semidirect