Finite Group Databasebeta

← #21461263

Subgroups — #21461263

Order 7808.

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

normal subgroups only

This group has 218 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#16840780C211yesmaximal, characteristic, complemented
2#16840707C211yesmaximal, characteristic, complemented
3#16840616C212yesmaximal, complemented
4#16840614C212yesmaximal
5#16840299C211yesmaximal, characteristic
6#14519844—21no—
7#14519834C2212yes—
8C4×#92420—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12#14519772—21no—
13#14519768C411yescharacteristic, complemented
14#14519766C411yescharacteristic, complemented
15#14519762—21no—
16#14519753C2211yescharacteristic
17#14519752C2211yescharacteristic
18C4×D244—21no—
19C4×D244C411yescharacteristic, complemented
20#14519734—21no—
21C42×D61C2211yescharacteristic
22C4×Q8×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×Q8×C61C2×C411yescharacteristic
25C2×D244—21no—
26C2×D244C2×C411yescharacteristic
27C2×C4×D61—21no—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C2×#92420—22no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61C2×C411yescharacteristic
34C42×C61—21no—
35C42×C61C2×C411yescharacteristic
36#11758198—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45C4×Dic61C2×C411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C22×D61—21no—
49C22×D61C2×D411yescharacteristic
50C2×#6923—42no—
51C2×#6923—42no—
52C2×#6923—42no—
53Q8×C61—41no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63D244—41no—
64D244—42no—
65C4×D61—22no—
66C4×D61—41no—
67C4×D61—41no—
68C4×D61—42no—
69#92420—42no—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61—41no—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61#13512yes—
77#6923—82no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—41no—
82C4×C61—41no—
83Dic61—21no—
84Dic61—21no—
85Dic61—21no—
86Dic61—41no—
87#1521—611nomaximal, Sylow
88C2×C61#41011yescharacteristic
89C2×C61#41611yescharacteristic
90C2×C61#42111yescharacteristic
91D61—22no—
92D61—81no—
93#529—611no—
94#431—611no—
95#383—611no—
96#328—612no—
97#327—612no—
98C61#152111yescharacteristic, complemented, Sylow
99#126—1221no—
100#125—611no—
101#124—611no—
102#123—1221no—
103C22⋊Q8—611no—
104#121—611no—
105C4×Q8#692311yescharacteristic, complemented
106C4×D4—611no—
107C4×D4—1221no—
108#117—1221no—
109C2×C42—611no—
110C4⋊C8—1221no—
111C22⋊C8—612no—
112C4×C8—1221no—
113#95—612no—
114#95—1221no—
115#95—1221no—
116C2×Q8C2×#692311yescharacteristic
117C2×D4—611no—
118C2×D4—1221no—
119C22×C4—611no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—1221no—
123C22×C4—1222no—
124C2×C8—1222no—
125C4⋊C4—21no—
126C4⋊C4—611no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4C2×#692311yescharacteristic
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C42—21no—
137C42—611no—
138C42—611no—
139C42—611no—
140C42C2×#692311yescharacteristic
141C23—611no—
142C23—1221no—
143Q8—41no—
144D4—2441no—
145D4—2442no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—611no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—1222no—
152C2×C4—1221no—
153C2×C4—2441no—
154C2×C4—2441no—
155C2×C4—2442no—
156C2×C4—2442no—
157C2×C4—2442no—
158C2×C4—2442no—
159C2×C4C22⋊#692311yescharacteristic
160C2×C4C22⋊#692311yescharacteristic
161C2×C4C22×#692311yescharacteristic
162C8—2442no—
163C22—612no—
164C22—1221no—
165C22—1221no—
166C22—2441no—
167C22—2441no—
168C22—2441no—
169C22C2×C22⋊#692311yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—1221no—
176C4—1221no—
177C4—1221no—
178C4—4882no—
179C4—2441no—
180C2—1222no—
181C2—4881no—
182C2#1684074111yescharacteristic
183C2#1684075211yescharacteristic
184C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1521
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. #16840780C2semidirect
2. #16840707C2semidirect
3. #16840616C2semidirect
13. #14519768C4semidirect
14. #14519766C4semidirect
19. C4×D244C4semidirect
22. C4×Q8×C61C4semidirect
98. C61#1521semidirect
105. C4×Q8#6923semidirect