Finite Group Databasebeta

← #21461252

Subgroups — #21461252

Order 7808.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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
2#16840706C211yesmaximal, characteristic
3#16840616C212yesmaximal
4#16840615C212yesmaximal
5#16840316C211yesmaximal, characteristic
6C2×C4⋊#6923—21no—
7C4⋊#92420—21no—
8#14519834C2212yes—
9C4×#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12#14519776C411yescharacteristic, complemented
13#14519775C411yescharacteristic, complemented
14#14519767—21no—
15#14519757C2211yescharacteristic
16#14519755—21no—
17#14519753C2211yescharacteristic
18C4×Dic122—21no—
19C4×Dic122C411yescharacteristic, complemented
20#14519734—21no—
21C42×D61C2211yescharacteristic
22C4×Q8×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×Q8×C61C2×C411yescharacteristic
25C2×C4×D61D411yescharacteristic
26C2×C4×D61D411yescharacteristic
27C2×C4×D61C2311yescharacteristic
28C2×Dic122—21no—
29C2×Dic122C2×C411yescharacteristic
30C2×#92420—22no—
31C4⋊#6923—42no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61C2×C411yescharacteristic
34C42×C61—21no—
35C42×C61C2×C411yescharacteristic
36#11758198—21no—
37#11758198—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61C2×C411yescharacteristic
40#11758196—21no—
41#11758196—21no—
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
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×Dic61—21no—
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C4×D61—41no—
65C4×D61—41no—
66C4×D61SD1612yes—
67C4×D61Q1612yes—
68Dic122—42no—
69Dic122—41no—
70#92420—42no—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—21no—
73C2×D61—21no—
74C2×D61C2×SD1611yescharacteristic
75C2×D61C2×Q1611yescharacteristic
76#6923—82no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—41no—
80C4×C61—41no—
81C4×C61#10312yes—
82Dic61—21no—
83Dic61—21no—
84Dic61—41no—
85Dic61—41no—
86Dic61#10312yes—
87#1518—611nomaximal, Sylow
88C2×C61#41011yescharacteristic
89C2×C61C2×#10311yescharacteristic
90C2×C61#42111yescharacteristic
91D61—21no—
92D61—21no—
93#533—611no—
94#431—611no—
95#382—611no—
96#328—612no—
97#328—612no—
98C61#151811yescharacteristic, complemented, Sylow
99C4⋊Q8—611no—
100C4⋊Q8—611no—
101#125—1221no—
102C22⋊Q8—611no—
103C22⋊Q8—611no—
104C22⋊Q8—1221no—
105C4×Q8—611no—
106C4×Q8—1221no—
107C4×Q8#692311yescharacteristic, complemented
108#117—1221no—
109C2×C4⋊C4—1221no—
110C2×C42—611no—
111C4⋊C8—1221no—
112C22⋊C8—612no—
113C4×C8—1221no—
114#95—612no—
115#95—1221no—
116C2×Q8—611no—
117C2×Q8—1221no—
118C2×Q8C2×#692311yescharacteristic
119C22×C4—611no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—1222no—
123C2×C8—1222no—
124C4⋊C4—21no—
125C4⋊C4—611no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4—2442no—
133C4⋊C4C2×#692311yescharacteristic
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C42—21no—
137C42—611no—
138C42—611no—
139C42—611no—
140C42—1221no—
141C42C2×#692311yescharacteristic
142C23—611no—
143Q8—41no—
144Q8—2441no—
145Q8—2442no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—611no—
149C2×C4—612no—
150C2×C4—612no—
151C2×C4—611no—
152C2×C4—611no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4—2442no—
158C2×C4—2442no—
159C2×C4—2442no—
160C2×C4C22⋊#692311yescharacteristic
161C2×C4C22⋊#692311yescharacteristic
162C2×C4C22×#692311yescharacteristic
163C8—2442no—
164C22—611no—
165C22—611no—
166C22—1221no—
167C22—1221no—
168C22C2×C22⋊#692311yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—612no—
174C4—1221no—
175C4—1221no—
176C4—4882no—
177C4—2441no—
178C4—2441no—
179C4#1451984012yes—
180C2—1221no—
181C2—1221no—
182C2#1684074111yescharacteristic
183C2C2×#1451984011yescharacteristic
184C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1518
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
12. #14519776C4semidirect
13. #14519775C4semidirect
19. C4×Dic122C4semidirect
22. C4×Q8×C61C4semidirect
98. C61#1518semidirect
107. C4×Q8#6923semidirect