Finite Group Databasebeta

← #21461240

Subgroups — #21461240

Order 7808.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#16840785C211yesmaximal, characteristic, complemented
2#16840707C211yesmaximal, characteristic, complemented
3#16840614C214yesmaximal, complemented
4#16840313C211yesmaximal, characteristic
5#14519844—21no—
6#14519834C2212yes—
7#14519832—21no—
8(C2×#6923)⋊C4—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⋊C4×C61—21no—
33C4⋊C4×C61C2×C412yes—
34C42×C61C2×C411yescharacteristic
35#11758198—22no—
36#11758198—22no—
37C4×Dic61C2×C411yescharacteristic
38C4×Dic61D411yescharacteristic
39C4×Dic61D411yescharacteristic
40C22×D61—22no—
41C22×D61C2×D411yescharacteristic
42C2×#6923—42no—
43C2×#6923—42no—
44C2×#6923—42no—
45Q8×C61—42no—
46C2×C4×C61—22no—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22×C411yescharacteristic
50C2×Dic61C22⋊C411yescharacteristic
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61C2×D411yescharacteristic
53D244—42no—
54D244—42no—
55D244—42no—
56D244—44no—
57C4×D61—22no—
58C4×D61—41no—
59C4×D61—41no—
60C4×D61—44no—
61#92420—42no—
62C22×C61C2×C22⋊C411yescharacteristic
63C2×D61—21no—
64C2×D61—21no—
65C2×D61—42no—
66C2×D61—42no—
67C2×D61—42no—
68C2×D61AGL(1,ℤ/8)12yes—
69#6923—82no—
70C4×C61—21no—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—42no—
74Dic61—21no—
75Dic61—21no—
76Dic61—21no—
77#1514—611nomaximal, Sylow
78C2×C61#41011yescharacteristic
79C2×C61#41811yescharacteristic
80C2×C61#42111yescharacteristic
81D61—22no—
82D61—82no—
83#532—611no—
84#432—611no—
85#383—611no—
86#327—614no—
87C61#151411yescharacteristic, complemented, Sylow
88C2×#41—1221no—
89C4⋊Q8#692311yescharacteristic, complemented
90#127—611no—
91#124—1221no—
92#121—612no—
93#121—1221no—
94C4×D4—612no—
95C4×D4—1221no—
96C2×C42—611no—
97C4⋊C8—1221no—
98C22⋊C8—612no—
99#97—1221no—
100#95—612no—
101#95—1221no—
102#95—1221no—
103#41—2444no—
104C2×Q8—21no—
105C2×D4—612no—
106C2×D4—1222no—
107C2×D4—1221no—
108C2×D4—1221no—
109C22×C4—611no—
110C22×C4—611no—
111C22×C4—611no—
112C22×C4—1222no—
113C22×C4—1222no—
114C2×C8—1222no—
115C4⋊C4—21no—
116C4⋊C4C2×#692312yes—
117C22⋊C4—1222no—
118C22⋊C4—1222no—
119C42—611no—
120C42—611no—
121C42—611no—
122C42C2×#692311yescharacteristic
123C23—611no—
124C23—1222no—
125Q8—42no—
126D4—2442no—
127D4—2442no—
128D4—2442no—
129D4—2444no—
130C2×C4—22no—
131C2×C4—611no—
132C2×C4—611no—
133C2×C4—611no—
134C2×C4—1222no—
135C2×C4—2441no—
136C2×C4—2441no—
137C2×C4—2444no—
138C2×C4—2442no—
139C2×C4—2442no—
140C2×C4—2442no—
141C2×C4C22⋊#692311yescharacteristic
142C2×C4C22⋊#692311yescharacteristic
143C2×C4C22×#692311yescharacteristic
144C8—2442no—
145C22—612no—
146C22—1221no—
147C22—1221no—
148C22—2442no—
149C22—2442no—
150C22—2442no—
151C22C2×C22⋊#692311yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—42no—
156C4—1221no—
157C4—1221no—
158C4—1221no—
159C4—4882no—
160C2—1222no—
161C2—4882no—
162C2#1684074311yescharacteristic
163C2#1684075411yescharacteristic
164C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1514
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. #16840785C2semidirect
2. #16840707C2semidirect
3. #16840614C2semidirect
12. #14519774C4semidirect
17. #14519739C4semidirect
19. C4⋊Q8×C61C4semidirect
87. C61#1514semidirect
89. C4⋊Q8#6923semidirect