Finite Group Databasebeta

← #21461211

Subgroups — #21461211

Order 7808.

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

normal subgroups only

This group has 228 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
2#16840698C211yesmaximal, characteristic
3#16840615C214yesmaximal
4#16840317C211yesmaximal, characteristic
5C2×C4×#6923—21no—
6C4⋊#92420—21no—
7#14519834C2212yes—
8#14519832—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4C2212yes—
11#14519777C411yescharacteristic, complemented
12#14519768—21no—
13#14519757C2212yes—
14#14519753—21no—
15Q8×Dic61—21no—
16#14519742C412yescomplemented
17#14519735—21no—
18C42×D61C2211yescharacteristic
19C4⋊Q8×C61C411yescharacteristic, complemented
20C22×#6923—22no—
21C2×Q8×C61—21no—
22C2×C4×D61D411yescharacteristic
23C2×C4×D61D411yescharacteristic
24C2×C4×D61C2311yescharacteristic
25C2×Dic122C2×C412yes—
26C2×#92420—22no—
27C4×#6923—24no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61C2×C412yes—
30C42×C61C2×C411yescharacteristic
31#11758198—22no—
32C4⋊Dic61—21no—
33C4⋊Dic61—21no—
34C4⋊Dic61—22no—
35#11758196—22no—
36C4×Dic61—22no—
37C4×Dic61C2×C411yescharacteristic
38C4×Dic61D411yescharacteristic
39C4×Dic61D411yescharacteristic
40C22×D61C2×D411yescharacteristic
41C2×#6923—24no—
42C2×#6923—42no—
43C2×#6923—42no—
44Q8×C61—42no—
45C2×C4×C61—22no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C2×Dic61—22no—
50C2×Dic61C22⋊C411yescharacteristic
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61C2×D411yescharacteristic
53C4×D61—22no—
54C4×D61—22no—
55C4×D61—41no—
56Dic122—42no—
57#92420—42no—
58C22×C61C2×C22⋊C411yescharacteristic
59C2×D61—21no—
60C2×D61—21no—
61C2×D61#13712yes—
62#6923—44no—
63C4×C61—21no—
64C4×C61—21no—
65C4×C61—42no—
66C4×C61#10412yes—
67Dic61—21no—
68Dic61—21no—
69Dic61—21no—
70Dic61—42no—
71#1506—611nomaximal, Sylow
72C2×C61#41011yescharacteristic
73C2×C61#41911yescharacteristic
74C2×C61C2×#10411yescharacteristic
75D61—22no—
76#533—611no—
77#432—611no—
78#376—611no—
79#328—614no—
80C61#150611yescharacteristic, complemented, Sylow
81C4⋊Q8—611no—
82C4⋊Q8#692311yescharacteristic, complemented
83#125—1221no—
84C22⋊Q8—612no—
85C22⋊Q8—1221no—
86C4×Q8—612no—
87C4×Q8—1221no—
88#117—1221no—
89C2×C42—611no—
90C2×C42—1221no—
91C4⋊C8—1221no—
92C22⋊C8—612no—
93#97—1221no—
94#95—612no—
95#95—1221no—
96C2×Q8—21no—
97C2×Q8—612no—
98C22×C4—611no—
99C22×C4—611no—
100C22×C4—611no—
101C22×C4—1222no—
102C2×C8—1222no—
103C4⋊C4—21no—
104C4⋊C4—1222no—
105C4⋊C4—1222no—
106C4⋊C4—1221no—
107C4⋊C4—1221no—
108C4⋊C4C2×#692312yes—
109C22⋊C4—1222no—
110C42—611no—
111C42—611no—
112C42—611no—
113C42—1222no—
114C42—1224no—
115C42C2×#692311yescharacteristic
116C23—611no—
117Q8—42no—
118Q8—2442no—
119C2×C4—22no—
120C2×C4—611no—
121C2×C4—611no—
122C2×C4—611no—
123C2×C4—1222no—
124C2×C4—1222no—
125C2×C4—1224no—
126C2×C4—1222no—
127C2×C4—2441no—
128C2×C4—2442no—
129C2×C4—2442no—
130C2×C4C22⋊#692311yescharacteristic
131C2×C4C22⋊#692311yescharacteristic
132C2×C4C22×#692311yescharacteristic
133C8—2442no—
134C22—612no—
135C22—1221no—
136C22—1221no—
137C22C2×C22⋊#692311yescharacteristic
138C4—21no—
139C4—21no—
140C4—42no—
141C4—1221no—
142C4—1221no—
143C4—1221no—
144C4—2444no—
145C4—2442no—
146C4#1451984112yes—
147C2—1222no—
148C2#1684074311yescharacteristic
149C2#1684075511yescharacteristic
150C2C2×#1451984111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1506
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
11. #14519777C4semidirect
16. #14519742C4semidirect
19. C4⋊Q8×C61C4semidirect
80. C61#1506semidirect
82. C4⋊Q8#6923semidirect