Finite Group Databasebeta

← #21461260

Subgroups — #21461260

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#16840781C211yesmaximal, characteristic, complemented
2#16840707C211yesmaximal, characteristic, complemented
3#16840616C212yesmaximal, complemented
4#16840613C212yesmaximal
5#16840291C211yesmaximal, characteristic
6C4⋊#92420—21no—
7#14519834C2212yes—
8C4×#92420—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12#14519770—21no—
13#14519769C411yescharacteristic, complemented
14#14519759—21no—
15#14519753C2211yescharacteristic
16#14519748C2211yescharacteristic
17Q8×Dic61C411yescharacteristic, complemented
18D4×Dic61C411yescharacteristic, complemented
19#14519737—21no—
20#14519733—21no—
21C42×D61C2211yescharacteristic
22#124×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×Q8×C61C2×C411yescharacteristic
25C2×D4×C61C2×C411yescharacteristic
26C2×C22⋊D61—21no—
27C22×Dic61—21no—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C2×#92420—22no—
32C22⋊C4×C61—21no—
33C22⋊C4×C61—21no—
34C42×C61C2×C411yescharacteristic
35C22⋊Dic61—21no—
36C22⋊Dic61—21no—
37#11758198—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61C2×C411yescharacteristic
40C4⋊Dic61C2×C411yescharacteristic
41#11758196—21no—
42#11758196—21no—
43#11758196—21no—
44C4×Dic61—21no—
45C4×Dic61C2×C411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C23×C61—21no—
49C22×D61C2×D411yescharacteristic
50C2×#6923—42no—
51C2×#6923—42no—
52C2×#6923—42no—
53Q8×C61—41no—
54D4×C61—41no—
55C2×C4×C61—21no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C22⋊D61—42no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—42no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C4×D61—22no—
67C4×D61—41no—
68C4×D61—41no—
69#92420—42no—
70C22×C61—41no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61C2×C22⋊C411yescharacteristic
74C2×D61—21no—
75C2×D61—21no—
76C2×D61#13512yes—
77#6923—82no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—41no—
82Dic61—21no—
83Dic61—21no—
84Dic61—21no—
85Dic61—41no—
86Dic61—41no—
87#1521—611nomaximal, Sylow
88C2×C61—81no—
89C2×C61#41011yescharacteristic
90C2×C61#41611yescharacteristic
91C2×C61#42111yescharacteristic
92D61—22no—
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#692311yescharacteristic, complemented
102#123—1221no—
103C22⋊Q8—611no—
104#121—611no—
105C4×Q8—611no—
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—1221no—
118C2×D4C2×#692311yescharacteristic
119C22×C4—611no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—1221no—
123C22×C4—1222no—
124C2×C8—1222no—
125C4⋊C4—611no—
126C4⋊C4—611no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C42—611no—
137C42—611no—
138C42—611no—
139C42—1221no—
140C42C2×#692311yescharacteristic
141C23—21no—
142C23—611no—
143Q8—41no—
144D4—41no—
145D4—2442no—
146C2×C4—21no—
147C2×C4—611no—
148C2×C4—611no—
149C2×C4—611no—
150C2×C4—1222no—
151C2×C4—1221no—
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—41no—
164C22—41no—
165C22—41no—
166C22—612no—
167C22—1221no—
168C22—1221no—
169C22C2×C22⋊#692311yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—1221no—
175C4—1221no—
176C4—1221no—
177C4—4882no—
178C4—2441no—
179C4—2441no—
180C2—81no—
181C2—1222no—
182C2#1684074211yescharacteristic
183C2#1684075211yescharacteristic
184C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1521
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840781C2semidirect
2. #16840707C2semidirect
3. #16840616C2semidirect
13. #14519769C4semidirect
17. Q8×Dic61C4semidirect
18. D4×Dic61C4semidirect
22. #124×C61C4semidirect
98. C61#1521semidirect
101. #124#6923semidirect