Finite Group Databasebeta

← #21461133

Subgroups — #21461133

Order 7808.

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

normal subgroups only

This group has 212 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#16840781C211yesmaximal, characteristic, complemented
2#16840781C211yesmaximal, characteristic, complemented
3#16840612C212yesmaximal, complemented
4#16840610C212yesmaximal, complemented
5#16840297C211yesmaximal, characteristic
6C4⋊#92420—21no—
7C4⋊#92420C2212yes—
8#14519834—21no—
9#14519834—21no—
10C4×#92420—21no—
11C4×#92420C2212yes—
12#14519772—21no—
13#14519765C411yescharacteristic
14#14519762—21no—
15#14519757C411yescharacteristic
16#14519752C411yescharacteristic
17#14519742C2211yescharacteristic
18#14519739—21no—
19#14519739C2211yescharacteristic
20#14519735—21no—
21C42×D61C2211yescharacteristic
22#125×C61C411yescharacteristic
23C2×D244—21no—
24C2×D244C2×C411yescharacteristic
25C2×C4×D61—21no—
26C2×C4×D61C2×C411yescharacteristic
27C2×C4×D61D411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×Dic122C2×C411yescharacteristic
30C2×#92420—22no—
31C2×#92420—22no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C411yescharacteristic
35C4⋊C4×C61C2×C411yescharacteristic
36C42×C61C2×C411yescharacteristic
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42C4⋊Dic61—21no—
43#11758196—21no—
44C4×Dic61—21no—
45C4×Dic61D411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61C2311yescharacteristic
48C22×D61—21no—
49C22×D61C22⋊C411yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22×C411yescharacteristic
55C2×Dic61—21no—
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C2×D411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59D244—22no—
60D244—42no—
61C4×D61—22no—
62C4×D61—22no—
63C4×D61—41no—
64C4×D61—42no—
65Dic122—22no—
66#92420—42no—
67#92420—42no—
68C22×C61C2×C22⋊C411yescharacteristic
69C2×D61—21no—
70C2×D61—21no—
71C2×D61—21no—
72C2×D61—41no—
73C2×D61—41no—
74C2×D61—41no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—41no—
78C4×C61—41no—
79C4×C61#13112yes—
80Dic61—21no—
81Dic61—21no—
82Dic61—41no—
83Dic61#13512yes—
84#1482—611nomaximal, Sylow
85C2×C61#40811yescharacteristic
86C2×C61#41611yescharacteristic
87C2×C61#42111yescharacteristic
88D61—41no—
89D61—81no—
90#529—611no—
91#431—611no—
92#431—611no—
93Q8⋊C8—612no—
94D4⋊C8—612no—
95C61#148211yescharacteristic, complemented, Sylow
96#126—1221no—
97#125#692311yescharacteristic
98#124—611no—
99#123—1221no—
100C22⋊Q8—611no—
101#121—611no—
102C4×Q8—611no—
103C4×D4—611no—
104C4×D4—1221no—
105#117—1221no—
106C2×C42—611no—
107C4⋊C8—612no—
108C4⋊C8—1221no—
109C22⋊C8—1221no—
110C22⋊C8—1221no—
111C4×C8—612no—
112C4×C8—1221no—
113C2×Q8—611no—
114C2×D4—611no—
115C2×D4—1221no—
116C22×C4—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—1221no—
120C2×C8—1222no—
121C2×C8—1222no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C4⋊C4C2×#692311yescharacteristic
127C4⋊C4C2×#692311yescharacteristic
128C22⋊C4—1221no—
129C22⋊C4—1221no—
130C22⋊C4—1221no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C42—611no—
134C42—611no—
135C42—611no—
136C42—1221no—
137C42C2×#692311yescharacteristic
138C23—611no—
139C23—1221no—
140Q8—1222no—
141D4—1222no—
142D4—2442no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—611no—
146C2×C4—611no—
147C2×C4—611no—
148C2×C4—1222no—
149C2×C4—1222no—
150C2×C4—1221no—
151C2×C4—2441no—
152C2×C4—2442no—
153C2×C4C22⋊#692311yescharacteristic
154C2×C4C22⋊#692311yescharacteristic
155C2×C4C22×#692311yescharacteristic
156C8—2442no—
157C8—2442no—
158C22—1221no—
159C22—1221no—
160C22—1221no—
161C22—2441no—
162C22—2441no—
163C22—2441no—
164C22C2×C22⋊#692311yescharacteristic
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—612no—
170C4—1221no—
171C4—1221no—
172C4—2441no—
173C4#1451986512yes—
174C2—4881no—
175C2—2441no—
176C2#1684073711yescharacteristic
177C2#1684075211yescharacteristic
178C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#125×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#125#6923
hypocenterC61#1482
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #16840781C2semidirect
2. #16840781C2semidirect
3. #16840612C2semidirect
4. #16840610C2semidirect
95. C61#1482semidirect