Finite Group Databasebeta

← #21461270

Subgroups — #21461270

Order 7808.

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

normal subgroups only

This group has 234 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
1C4×#11758217C211yesmaximal, characteristic, complemented
2C2×#14519832C211yesmaximal, characteristic, complemented
3#16840619C212yesmaximal, complemented
4#16840617C212yesmaximal, complemented
5#16840293C211yesmaximal, characteristic
6C2×#11758217—21no—
7C22×#92420—21no—
8#14519832—21no—
9#14519832C2212yes—
10#14519832C2212yes—
11C4×#92420—21no—
12#14519770—21no—
13#14519768C2211yescharacteristic
14#14519764C2211yescharacteristic
15#14519758—21no—
16#14519756C411yescharacteristic
17#14519742C411yescharacteristic
18D4×Dic61—21no—
19D4×Dic61C411yescharacteristic
20#14519733—21no—
21C2×C4×Dic61C2211yescharacteristic
22#121×C61C411yescharacteristic
23C2×D4×C61—21no—
24C2×D4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C22×Dic61—21no—
27C22×Dic61D411yescharacteristic
28C22×Dic61D411yescharacteristic
29C2×Dic122C2×C411yescharacteristic
30#11758217—24no—
31C2×#92420—24no—
32C2×#92420—22no—
33C2×#92420—22no—
34C4⋊C4×C61C2×C411yescharacteristic
35C22⋊C4×C61—21no—
36C22⋊Dic61—21no—
37C22⋊Dic61—21no—
38C22⋊Dic61—21no—
39C22⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C23×C61—21no—
51C23×C61C22⋊C411yescharacteristic
52D4×C61—41no—
53D4×C61—42no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C2×Dic61—22no—
59C2×Dic61—22no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—42no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67Dic122—41no—
68#92420—24no—
69#92420—24no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61#10412yes—
76C22×C61C2×C22⋊C411yescharacteristic
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—41no—
80Dic61—21no—
81Dic61—21no—
82Dic61—21no—
83Dic61—41no—
84Dic61—41no—
85Dic61#10412yes—
86#1524—611nomaximal, Sylow
87C2×C61—22no—
88C2×C61—81no—
89C2×C61#41311yescharacteristic
90C2×C61C2×#10411yescharacteristic
91C2×C61C2×#10411yescharacteristic
92#529—611no—
93C4×M16—611no—
94C2×#97—611no—
95#330—612no—
96#329—612no—
97C61#152411yescharacteristic, complemented, Sylow
98C2×M16—1221no—
99C22×C8—1221no—
100#126—1221no—
101#125—611no—
102#124—611no—
103#123—1221no—
104C22⋊Q8—611no—
105#121#692311yescharacteristic
106C4×Q8—611no—
107C4×D4—611no—
108C4×D4—1221no—
109#117—1221no—
110C2×C42—611no—
111#97—612no—
112#97—612no—
113#97—1221no—
114C4×C8—1221no—
115C2×Q8—611no—
116C2×D4—21no—
117C2×D4C2×#692311yescharacteristic
118C22×C4—611no—
119C22×C4—611no—
120C22×C4—1221no—
121C22×C4C2×#692311yescharacteristic
122M16—1224no—
123C2×C8—1222no—
124C2×C8—1222no—
125C2×C8—1224no—
126C4⋊C4—611no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4C2×#692311yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C42—611no—
138C42—611no—
139C42—611no—
140C42—611no—
141C42—1221no—
142C23—21no—
143C23C22⋊#692311yescharacteristic
144Q8—2441no—
145D4—41no—
146D4—42no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—611no—
153C2×C4—1222no—
154C2×C4—1222no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—2442no—
158C2×C4C22⋊#692311yescharacteristic
159C2×C4C22×#692311yescharacteristic
160C8—1224no—
161C8—1224no—
162C22—21no—
163C22—21no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22#1451984112yes—
168C22C2×C22⋊#692311yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—612no—
173C4—1221no—
174C4—1221no—
175C4—1221no—
176C4—2441no—
177C4—2441no—
178C2—22no—
179C2—81no—
180C2#1684074911yescharacteristic
181C2C2×#1451984111yescharacteristic
182C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1524
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C4×#11758217C2semidirect
2. C2×#14519832C2semidirect
3. #16840619C2semidirect
4. #16840617C2semidirect
97. C61#1524semidirect