Finite Group Databasebeta

← #21461280

Subgroups — #21461280

Order 7808.

264 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840783C211yesmaximal, characteristic, complemented
2C4×#11758217C211yesmaximal, characteristic, complemented
3#16840618C214yesmaximal, complemented
4C2×#14519766C211yesmaximal, characteristic
5C2×#11758217—21no—
6C4⋊#92420—21no—
7C22⋊#92420—21no—
8#14519832C2212yescomplemented
9#14519832C2212yescomplemented
10C4×#92420—21no—
11C22×D244C411yescharacteristic
12#14519766—21no—
13#14519766—21no—
14#14519766C412yes—
15#14519766C2212yes—
16C2×#11758198—21no—
17C2×#11758198—21no—
18C2×C4×Dic61C2211yescharacteristic
19C22×Q8×C61C411yescharacteristic
20C23×D61—21no—
21C2×Q8×C61—21no—
22C2×Q8×C61—42no—
23C2×Q8×C61C2×C412yes—
24C22×C4×C61—21no—
25C22×C4×C61C2×C411yescharacteristic
26C22×Dic61D411yescharacteristic
27C22×Dic61D411yescharacteristic
28C2×D244—21no—
29C2×D244—42no—
30C2×D244C2×C412yes—
31#11758217—24no—
32C2×#92420—22no—
33C2×#92420—22no—
34#11758198—22no—
35#11758198—22no—
36#11758198—22no—
37#11758198—22no—
38C4×Dic61C2×C411yescharacteristic
39C4×Dic61D411yescharacteristic
40C4×Dic61D411yescharacteristic
41C4×Dic61C2311yescharacteristic
42C23×C61C22⋊C411yescharacteristic
43C22×D61—22no—
44C22×D61—42no—
45C22×D61—42no—
46C22×D61—42no—
47Q8×C61—42no—
48Q8×C61—42no—
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61—42no—
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22×C411yescharacteristic
54C2×Dic61—22no—
55C2×Dic61—41no—
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59C2×Dic61C2×D411yescharacteristic
60D244—42no—
61D244—42no—
62#92420—24no—
63#92420—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#10412yes—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—42no—
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—84no—
72C4×C61—21no—
73C4×C61—42no—
74C4×C61#10012yes—
75Dic61—21no—
76Dic61—21no—
77Dic61—21no—
78Dic61—21no—
79#1527—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61C2×#10011yescharacteristic
82C2×C61C2×#10411yescharacteristic
83C2×C61#42111yescharacteristic
84D61—82no—
85C2×#124—611no—
86#432—611no—
87C4×M16—611no—
88#329—614no—
89C61#152711yescharacteristic, complemented, Sylow
90C22×Q8#692311yescharacteristic
91C22×D4—611no—
92C2×M16—1221no—
93#124—612no—
94#124—612no—
95#124—1221no—
96#124—1221no—
97C2×C22⋊C4—1221no—
98C2×C22⋊C4—1221no—
99C2×C42—611no—
100C4⋊C8—1221no—
101C22⋊C8—1221no—
102#97—612no—
103#97—612no—
104C4×C8—1221no—
105C24—1221no—
106C2×Q8—21no—
107C2×Q8—42no—
108C2×Q8C2×#692312yes—
109C2×D4—612no—
110C2×D4—1221no—
111C2×D4—2442no—
112C22×C4—21no—
113C22×C4—611no—
114C22×C4—611no—
115C22×C4C2×#692311yescharacteristic
116M16—1224no—
117C2×C8—1222no—
118C2×C8—1222no—
119C22⋊C4—1222no—
120C22⋊C4—1222no—
121C22⋊C4—1222no—
122C22⋊C4—1222no—
123C42—611no—
124C42—611no—
125C42—611no—
126C42—611no—
127C23—1222no—
128C23—2442no—
129C23—2442no—
130C23—2442no—
131C23C22⋊#692311yescharacteristic
132Q8—42no—
133Q8—42no—
134D4—2442no—
135D4—2442no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—611no—
140C2×C4—611no—
141C2×C4—611no—
142C2×C4—611no—
143C2×C4—1222no—
144C2×C4—2441no—
145C2×C4C22⋊#692311yescharacteristic
146C2×C4C22×#692311yescharacteristic
147C8—1224no—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—4884no—
152C22—2442no—
153C22—2442no—
154C22—2442no—
155C22#1451984212yes—
156C22C2×C22⋊#692311yescharacteristic
157C4—21no—
158C4—42no—
159C4—1221no—
160C4—1221no—
161C4—1221no—
162C4—1221no—
163C4#1451983712yes—
164C2—22no—
165C2—4882no—
166C2C2×#1451983711yescharacteristic
167C2C2×#1451984211yescharacteristic
168C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×Q8#6923
hypocenterC61#1527
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
1. #16840783C2semidirect
2. C4×#11758217C2semidirect
3. #16840618C2semidirect
8. #14519832C22semidirect
9. #14519832C22semidirect
89. C61#1527semidirect