Finite Group Databasebeta

← #21461212

Subgroups — #21461212

Order 7808.

228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840785C211yesmaximal, characteristic
2#16840698C211yesmaximal, characteristic
3#16840616C212yesmaximal
4#16840615C212yesmaximal
5#16840316C211yesmaximal, characteristic
6C2×C4×#6923—21no—
7#14519844—21no—
8#14519834C2212yes—
9#14519832—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—24no—
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—24no—
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—22no—
65C4×D61—22no—
66C4×D61—41no—
67Dic122—42no—
68Dic122—41no—
69#92420—42no—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61#13712yes—
74#6923—44no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—41no—
79C4×C61—41no—
80Dic61—21no—
81Dic61—21no—
82Dic61—41no—
83Dic61—41no—
84Dic61#10412yes—
85#1506—611nomaximal, Sylow
86C2×C61#41011yescharacteristic
87C2×C61#41911yescharacteristic
88C2×C61C2×#10411yescharacteristic
89D61—22no—
90#533—611no—
91#432—611no—
92#376—611no—
93#328—612no—
94#328—612no—
95C61#150611yescharacteristic, complemented, Sylow
96C4⋊Q8—611no—
97C4⋊Q8—611no—
98#125—1221no—
99C22⋊Q8—611no—
100C22⋊Q8—611no—
101C22⋊Q8—1221no—
102C4×Q8—611no—
103C4×Q8—1221no—
104C4×Q8#692311yescharacteristic, complemented
105#117—1221no—
106C2×C42—611no—
107C2×C42—1221no—
108C4⋊C8—1221no—
109C22⋊C8—612no—
110#97—1221no—
111#95—612no—
112#95—1221no—
113C2×Q8—611no—
114C2×Q8—1221no—
115C2×Q8C2×#692311yescharacteristic
116C22×C4—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—1222no—
120C2×C8—1222no—
121C4⋊C4—21no—
122C4⋊C4—611no—
123C4⋊C4—1221no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4C2×#692311yescharacteristic
130C22⋊C4—1221no—
131C22⋊C4—1221no—
132C42—21no—
133C42—611no—
134C42—611no—
135C42—611no—
136C42—1224no—
137C42—1221no—
138C42C2×#692311yescharacteristic
139C23—611no—
140Q8—41no—
141Q8—2441no—
142Q8—2442no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—611no—
146C2×C4—611no—
147C2×C4—611no—
148C2×C4—1222no—
149C2×C4—1222no—
150C2×C4—1224no—
151C2×C4—1221no—
152C2×C4—1221no—
153C2×C4—2441no—
154C2×C4—2442no—
155C2×C4—2442no—
156C2×C4C22⋊#692311yescharacteristic
157C2×C4C22⋊#692311yescharacteristic
158C2×C4C22×#692311yescharacteristic
159C8—2442no—
160C22—612no—
161C22—1221no—
162C22—1221no—
163C22C2×C22⋊#692311yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—612no—
170C4—1221no—
171C4—1221no—
172C4—2444no—
173C4—2441no—
174C4—2441no—
175C2—1222no—
176C2#1684074111yescharacteristic
177C2#1684075511yescharacteristic
178C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1506
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
95. C61#1506semidirect
104. C4×Q8#6923semidirect