Finite Group Databasebeta

← #21461253

Subgroups — #21461253

Order 7808.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840780C211yesmaximal, characteristic
2#16840706C211yesmaximal, characteristic
3#16840616C214yesmaximal
4#16840317C211yesmaximal, characteristic
5C2×C4⋊#6923—21no—
6#14519844—21no—
7#14519834C2212yes—
8C4×#92420—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4C2212yes—
11#14519777C411yescharacteristic, complemented
12#14519768—21no—
13#14519757—21no—
14#14519753C2212yes—
15Q8×Dic61C412yescomplemented
16#14519742—21no—
17#14519735—21no—
18C42×D61C2211yescharacteristic
19C4⋊Q8×C61C411yescharacteristic, complemented
20C22×#6923—22no—
21C2×Q8×C61C2×C412yes—
22C2×C4×D61D411yescharacteristic
23C2×C4×D61D411yescharacteristic
24C2×C4×D61C2311yescharacteristic
25C2×Dic122—21no—
26C2×#92420—22no—
27C4⋊#6923—42no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61—21no—
30C42×C61C2×C411yescharacteristic
31#11758198—22no—
32C4⋊Dic61—21no—
33C4⋊Dic61—22no—
34C4⋊Dic61C2×C412yes—
35#11758196—22no—
36C4×Dic61—22no—
37C4×Dic61C2×C411yescharacteristic
38C4×Dic61D411yescharacteristic
39C4×Dic61D411yescharacteristic
40C22×D61C2×D411yescharacteristic
41C2×#6923—42no—
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—41no—
54C4×D61—41no—
55C4×D61SD1612yes—
56C4×D61Q1612yes—
57Dic122—42no—
58#92420—42no—
59C22×C61C2×C22⋊C411yescharacteristic
60C2×D61—21no—
61C2×D61—21no—
62C2×D61C2×SD1611yescharacteristic
63C2×D61C2×Q1611yescharacteristic
64#6923—82no—
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—42no—
68C4×C61#10312yes—
69Dic61—21no—
70Dic61—21no—
71Dic61—42no—
72Dic61#10312yes—
73#1518—611nomaximal, Sylow
74C2×C61#41011yescharacteristic
75C2×C61C2×#10311yescharacteristic
76C2×C61#42111yescharacteristic
77D61—21no—
78D61—21no—
79#533—611no—
80#431—611no—
81#382—611no—
82#328—614no—
83C61#151811yescharacteristic, complemented, Sylow
84C4⋊Q8—611no—
85C4⋊Q8#692311yescharacteristic, complemented
86#125—1221no—
87C22⋊Q8—612no—
88C22⋊Q8—1221no—
89C4×Q8—612no—
90C4×Q8—1221no—
91#117—1221no—
92C2×C4⋊C4—1221no—
93C2×C42—611no—
94C4⋊C8—1221no—
95C22⋊C8—612no—
96C4×C8—1221no—
97#95—612no—
98#95—1221no—
99C2×Q8—1221no—
100C2×Q8C2×#692312yes—
101C22×C4—611no—
102C22×C4—611no—
103C22×C4—611no—
104C22×C4—1222no—
105C2×C8—1222no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—612no—
109C4⋊C4—1222no—
110C4⋊C4—1222no—
111C4⋊C4—1221no—
112C4⋊C4—2442no—
113C22⋊C4—1222no—
114C42—611no—
115C42—611no—
116C42—611no—
117C42—1222no—
118C42C2×#692311yescharacteristic
119C23—611no—
120Q8—42no—
121Q8—2442no—
122C2×C4—22no—
123C2×C4—611no—
124C2×C4—612no—
125C2×C4—612no—
126C2×C4—611no—
127C2×C4—611no—
128C2×C4—1222no—
129C2×C4—2441no—
130C2×C4—2441no—
131C2×C4—2442no—
132C2×C4—2442no—
133C2×C4—2442no—
134C2×C4C22⋊#692311yescharacteristic
135C2×C4C22⋊#692311yescharacteristic
136C2×C4C22×#692311yescharacteristic
137C8—2442no—
138C22—611no—
139C22—611no—
140C22—1221no—
141C22—1221no—
142C22C2×C22⋊#692311yescharacteristic
143C4—21no—
144C4—21no—
145C4—42no—
146C4—612no—
147C4—1221no—
148C4—1221no—
149C4—4882no—
150C4—2442no—
151C4#1451984012yes—
152C2—1221no—
153C2—1221no—
154C2#1684074211yescharacteristic
155C2C2×#1451984011yescharacteristic
156C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1518
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
15. Q8×Dic61C4semidirect
19. C4⋊Q8×C61C4semidirect
83. C61#1518semidirect
85. C4⋊Q8#6923semidirect