Finite Group Databasebeta

← #21461167

Subgroups — #21461167

Order 7808.

232 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 72 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#16840765C211yesmaximal, characteristic
2C2×C4×#92420C211yesmaximal, characteristic
3#16840612C212yesmaximal, complemented
4Q8⋊#92420C212yesmaximal, complemented
5#16840314C211yesmaximal, characteristic
6C2×#11758217—21no—
7C22×#92420—21no—
8#14519844—21no—
9C4⋊#92420C2212yes—
10C4×#92420—21no—
11C4×#92420C2212yes—
12#14519776C411yescharacteristic
13#14519775C411yescharacteristic
14#14519767—21no—
15#14519756C411yescharacteristic
16#14519754—21no—
17Q8×Dic61C2211yescharacteristic
18#14519742—21no—
19#14519742C2211yescharacteristic
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
29#11758217—42no—
30C2×#92420—24no—
31C2×#92420—22no—
32C2×#92420—22no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C411yescharacteristic
35C22⋊C4×C61—21no—
36C22⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61C2×C411yescharacteristic
39#11758196—21no—
40#11758196—21no—
41#11758196—21no—
42#11758196—21no—
43#11758196—21no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C23×C61C22⋊C411yescharacteristic
51Q8×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C2×Dic61—22no—
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61SD1612yes—
63C2×Dic61Q1612yes—
64C2×Dic61C2×D411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66Dic122—22no—
67Dic122—42no—
68#92420—24no—
69#92420—42no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61#10312yes—
73C22×C61C2×C22⋊C411yescharacteristic
74C4×C61—21no—
75C4×C61—41no—
76C4×C61—41no—
77C4×C61#13112yes—
78Dic61—21no—
79Dic61—41no—
80Dic61—41no—
81Dic61#10312yes—
82Dic61#10412yes—
83Dic61C2×SD1611yescharacteristic
84Dic61C2×Q1611yescharacteristic
85#1493—611nomaximal, Sylow
86C2×C61—22no—
87C2×C61#40811yescharacteristic
88C2×C61C2×#10311yescharacteristic
89C2×C61C2×#10411yescharacteristic
90#533—611no—
91#423—611no—
92C2×C4×C8—611no—
93Q8⋊C8—612no—
94Q8⋊C8—612no—
95C61#149311yescharacteristic, complemented, Sylow
96C2×M16—1221no—
97C22×C8—1221no—
98C4⋊Q8—611no—
99C4⋊Q8—611no—
100#125—1221no—
101C22⋊Q8—611no—
102C22⋊Q8—1221no—
103C22⋊Q8#692311yescharacteristic
104C4×Q8—611no—
105C4×Q8—611no—
106C4×Q8—1221no—
107#117—1221no—
108C2×C42—611no—
109C4⋊C8—612no—
110C4⋊C8—1221no—
111C4×C8—612no—
112C4×C8—1221no—
113C2×Q8—611no—
114C2×Q8—1221no—
115C2×Q8C2×#692311yescharacteristic
116C22×C4—611no—
117C22×C4—611no—
118C22×C4C2×#692311yescharacteristic
119M16—2442no—
120C2×C8—1222no—
121C2×C8—1224no—
122C2×C8—1222no—
123C4⋊C4—21no—
124C4⋊C4—611no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4C2×#692311yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—1221no—
134C42—611no—
135C42—611no—
136C42—611no—
137C42—611no—
138C42—1221no—
139C42—1221no—
140C23C22⋊#692311yescharacteristic
141Q8—22no—
142Q8—1222no—
143Q8—2442no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—612no—
148C2×C4—612no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—611no—
153C2×C4—1222no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4C22⋊#692311yescharacteristic
157C2×C4C22×#692311yescharacteristic
158C8—1224no—
159C8—2442no—
160C22—21no—
161C22—21no—
162C22#1451984012yes—
163C22C2×C22⋊#692311yescharacteristic
164C4—21no—
165C4—41no—
166C4—41no—
167C4—612no—
168C4—611no—
169C4—611no—
170C4—612no—
171C4—1221no—
172C4—2441no—
173C4—2441no—
174C4#1451986412yes—
175C2—22no—
176C2#1684073511yescharacteristic
177C2C2×#1451984011yescharacteristic
178C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #16840612C2semidirect
4. Q8⋊#92420C2semidirect
95. C61#1493semidirect