Finite Group Databasebeta

← #21461229

Subgroups — #21461229

Order 7808.

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

normal subgroups only

This group has 274 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#16840734C211yesmaximal, characteristic
2#16840705C211yesmaximal, characteristic
3#16840616C214yesmaximal, complemented
4C2×#14519753C211yesmaximal, characteristic
5C2×#11758217—21no—
6C2×C22⋊#6923—21no—
7#14519834—21no—
8#14519834C2212yes—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4C2212yes—
11C22×C4×D61C2211yescharacteristic
12#14519753—21no—
13#14519753—21no—
14#14519753C412yescomplemented
15#14519753C2212yes—
16C2×C4⋊Dic61C411yescharacteristic, complemented
17C2×#11758196—21no—
18C2×#11758198—21no—
19C22×Q8×C61C411yescharacteristic, complemented
20C23×D61D411yescharacteristic
21C22×#6923—22no—
22C2×Q8×C61—21no—
23C2×Q8×C61—42no—
24C2×Q8×C61C2×C412yes—
25C22×C4×C61—21no—
26C22×C4×C61C2×C411yescharacteristic
27C22×Dic61—21no—
28C22×Dic61D411yescharacteristic
29C2×C4×D61—42no—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61C2311yescharacteristic
34C22⋊#6923—42no—
35#11758217—42no—
36C2×#92420—22no—
37#11758198—22no—
38#11758198—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41#11758196—22no—
42#11758196—22no—
43C23×C61C22⋊C411yescharacteristic
44C22×D61—22no—
45C22×D61—22no—
46C22×D61—41no—
47C22×D61C22⋊C411yescharacteristic
48C22×D61C2×D411yescharacteristic
49C2×#6923—42no—
50C2×#6923—42no—
51C2×#6923—42no—
52Q8×C61—42no—
53Q8×C61—42no—
54C2×C4×C61—22no—
55C2×C4×C61—22no—
56C2×C4×C61—42no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C2×Dic61—22no—
60C2×Dic61—22no—
61C2×Dic61—42no—
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C4×D61—41no—
65C4×D61—41no—
66C4×D61—41no—
67C4×D61—41no—
68#92420—42no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61#9912yes—
72C22×C61C2×C22⋊C411yescharacteristic
73C2×D61—21no—
74C2×D61—21no—
75C2×D61—21no—
76C2×D61—21no—
77C2×D61—21no—
78C2×D61—44no—
79C2×D61#13712yes—
80#6923—82no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—42no—
84Dic61—21no—
85Dic61—21no—
86Dic61—42no—
87#1511—611nomaximal, Sylow
88C2×C61—22no—
89C2×C61C2×#9911yescharacteristic
90C2×C61#41911yescharacteristic
91C2×C61#42111yescharacteristic
92D61—22no—
93D61—41no—
94C2×C22⋊Q8—611no—
95#407—611no—
96#381—611no—
97#328—614no—
98C61#151111yescharacteristic, complemented, Sylow
99C22×Q8#692311yescharacteristic, complemented
100C23×C4—611no—
101C2×M16—1221no—
102C22⋊Q8—612no—
103C22⋊Q8—612no—
104C22⋊Q8—1221no—
105C22⋊Q8—1221no—
106C2×C4⋊C4—611no—
107C2×C4⋊C4—1221no—
108C2×C22⋊C4—1221no—
109C2×C22⋊C4—1221no—
110C22⋊C8—612no—
111C22⋊C8—1221no—
112#95—612no—
113#95—1221no—
114C24—611no—
115C2×Q8—21no—
116C2×Q8—42no—
117C2×Q8C2×#692312yes—
118C22×C4—21no—
119C22×C4—611no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—611no—
124C22×C4—1221no—
125C22×C4—1222no—
126C22×C4—2442no—
127C22×C4C2×#692311yescharacteristic
128M16—2442no—
129C2×C8—1222no—
130C4⋊C4—612no—
131C4⋊C4—1222no—
132C4⋊C4—1222no—
133C4⋊C4—1221no—
134C22⋊C4—1222no—
135C22⋊C4—1222no—
136C22⋊C4—2442no—
137C23—611no—
138C23—611no—
139C23—1222no—
140C23—1222no—
141C23—2441no—
142C23C22⋊#692311yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—42no—
148C2×C4—611no—
149C2×C4—611no—
150C2×C4—1222no—
151C2×C4—1222no—
152C2×C4—2441no—
153C2×C4—2441no—
154C2×C4—2441no—
155C2×C4—2441no—
156C2×C4—2442no—
157C2×C4—2442no—
158C2×C4—2442no—
159C2×C4—2442no—
160C2×C4C22⋊#692311yescharacteristic
161C2×C4C22×#692311yescharacteristic
162C8—2442no—
163C22—21no—
164C22—21no—
165C22—612no—
166C22—1221no—
167C22—1221no—
168C22—1221no—
169C22—1221no—
170C22—1221no—
171C22—2444no—
172C22#1451983512yes—
173C22C2×C22⋊#692311yescharacteristic
174C4—21no—
175C4—21no—
176C4—42no—
177C4—1221no—
178C4—1221no—
179C4—4882no—
180C4—2442no—
181C2—22no—
182C2—1222no—
183C2—2441no—
184C2C2×#1451983511yescharacteristic
185C2#1684075511yescharacteristic
186C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×Q8#6923
hypocenterC61#1511
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #16840616C2semidirect
14. #14519753C4semidirect
16. C2×C4⋊Dic61C4semidirect
19. C22×Q8×C61C4semidirect
98. C61#1511semidirect
99. C22×Q8#6923semidirect