Finite Group Databasebeta

← #21461345

Subgroups — #21461345

Order 7808.

198 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840782C211yesmaximal, characteristic
2#16840779C211yesmaximal, characteristic
3#16840622C212yesmaximal, complemented
4#16840621C212yesmaximal, complemented
5#16840314C211yesmaximal, characteristic
6#14519844C2212yes—
7#14519844C2212yes—
8C22⋊#92420—21no—
9C22⋊#92420—21no—
10#14519832—21no—
11C4×#92420—21no—
12#14519776C2211yescharacteristic
13#14519775C2211yescharacteristic
14#14519767—21no—
15#14519756C411yescharacteristic
16#14519754—21no—
17Q8×Dic61C411yescharacteristic
18#14519742—21no—
19#14519742C411yescharacteristic
20#14519733—21no—
21C2×C4×Dic61C2211yescharacteristic
22C22⋊Q8×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×Dic61D411yescharacteristic
26C22×Dic61D411yescharacteristic
27C2×Dic122—21no—
28C2×Dic122C2×C411yescharacteristic
29C2×#92420—22no—
30C2×#92420—22no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61C2×C411yescharacteristic
33C22⋊C4×C61—21no—
34C22⋊Dic61—21no—
35C4⋊Dic61—21no—
36C4⋊Dic61C2×C411yescharacteristic
37#11758196—21no—
38#11758196—21no—
39#11758196—21no—
40#11758196—21no—
41#11758196—21no—
42C4×Dic61—21no—
43C4×Dic61—21no—
44C4×Dic61C2×C411yescharacteristic
45C4×Dic61D411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61C2311yescharacteristic
48C23×C61C22⋊C411yescharacteristic
49Q8×C61—41no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—41no—
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22×C411yescharacteristic
55C2×Dic61—22no—
56C2×Dic61—22no—
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61C22⋊C411yescharacteristic
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C2×D411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63Dic122—42no—
64Dic122—41no—
65#92420—42no—
66#92420—42no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61C2×C22⋊C411yescharacteristic
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—41no—
74C4×C61—41no—
75Dic61—21no—
76Dic61—21no—
77Dic61—41no—
78Dic61—41no—
79Dic61#13512yes—
80Dic61#13712yes—
81#1554—611nomaximal, Sylow
82C2×C61—41no—
83C2×C61#41311yescharacteristic
84C2×C61#41611yescharacteristic
85C2×C61#41911yescharacteristic
86#533—611no—
87#432—611no—
88#431—611no—
89#333—612no—
90#332—612no—
91C61#155411yescharacteristic, complemented, Sylow
92C4⋊Q8—611no—
93C4⋊Q8—611no—
94#125—1221no—
95C22⋊Q8—611no—
96C22⋊Q8—1221no—
97C22⋊Q8#692311yescharacteristic
98C4×Q8—611no—
99C4×Q8—611no—
100C4×Q8—1221no—
101#117—1221no—
102C2×C42—611no—
103C4⋊C8—612no—
104C4⋊C8—612no—
105C22⋊C8—1221no—
106C22⋊C8—1221no—
107#97—1221no—
108C4×C8—1221no—
109C2×Q8—611no—
110C2×Q8—1221no—
111C2×Q8C2×#692311yescharacteristic
112C22×C4—611no—
113C22×C4—611no—
114C22×C4C2×#692311yescharacteristic
115C2×C8—1222no—
116C2×C8—1222no—
117C4⋊C4—21no—
118C4⋊C4—611no—
119C4⋊C4—1221no—
120C4⋊C4—1221no—
121C4⋊C4—1221no—
122C4⋊C4—1221no—
123C4⋊C4—1221no—
124C4⋊C4—1221no—
125C4⋊C4C2×#692311yescharacteristic
126C22⋊C4—21no—
127C22⋊C4—1221no—
128C42—611no—
129C42—611no—
130C42—611no—
131C42—611no—
132C42—1221no—
133C42—1221no—
134C23C22⋊#692311yescharacteristic
135Q8—41no—
136Q8—2441no—
137Q8—2442no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—611no—
142C2×C4—611no—
143C2×C4—611no—
144C2×C4—611no—
145C2×C4—1222no—
146C2×C4—1222no—
147C2×C4—1221no—
148C2×C4—1221no—
149C2×C4C22⋊#692311yescharacteristic
150C2×C4C22×#692311yescharacteristic
151C8—2442no—
152C8—2442no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22C2×C22⋊#692311yescharacteristic
157C4—21no—
158C4—21no—
159C4—41no—
160C4—41no—
161C4—612no—
162C4—612no—
163C4—1221no—
164C4—1221no—
165C4—2441no—
166C4—2441no—
167C2—41no—
168C2#1684074911yescharacteristic
169C2#1684075211yescharacteristic
170C2#1684075511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1554
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #16840622C2semidirect
4. #16840621C2semidirect
91. C61#1554semidirect