Finite Group Databasebeta

← #21461250

Subgroups — #21461250

Order 7808.

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

normal subgroups only

This group has 264 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#16840780C211yesmaximal, characteristic, complemented
2#16840706C211yesmaximal, characteristic, complemented
3#16840614C214yesmaximal, complemented
4#16840313C211yesmaximal, characteristic
5C2×C4⋊#6923—21no—
6#14519844—21no—
7#14519834C2212yes—
8C4×#92420—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4C2212yes—
11C2×#11758226—21no—
12#14519774C411yescharacteristic, complemented
13#14519766—21no—
14#14519752—21no—
15#14519752C2212yes—
16#14519739—21no—
17#14519739C412yescomplemented
18C42×D61C2211yescharacteristic
19C4⋊Q8×C61C411yescharacteristic, complemented
20C22×#6923—22no—
21C2×Q8×C61—21no—
22#11758226—42no—
23#11758226—42no—
24C2×D244—22no—
25C2×D244—21no—
26C2×D244—21no—
27C2×D244C2×C412yes—
28C2×C4×D61—22no—
29C2×C4×D61D411yescharacteristic
30C2×C4×D61D411yescharacteristic
31C2×C4×D61C2311yescharacteristic
32C2×#92420—22no—
33C4⋊#6923—42no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61C2×C412yes—
36C42×C61C2×C411yescharacteristic
37#11758198—22no—
38#11758198—22no—
39C4×Dic61C2×C411yescharacteristic
40C4×Dic61D411yescharacteristic
41C4×Dic61D411yescharacteristic
42C22×D61—22no—
43C22×D61C2×D411yescharacteristic
44C2×#6923—42no—
45C2×#6923—42no—
46C2×#6923—42no—
47Q8×C61—42no—
48C2×C4×C61—22no—
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22×C411yescharacteristic
52C2×Dic61C22⋊C411yescharacteristic
53C2×Dic61C22⋊C411yescharacteristic
54C2×Dic61C2×D411yescharacteristic
55D244—42no—
56D244—42no—
57D244—42no—
58D244—42no—
59D244—42no—
60C4×D61—41no—
61C4×D61—41no—
62C4×D61—44no—
63C4×D61D812yes—
64C4×D61SD1612yes—
65#92420—42no—
66C22×C61C2×C22⋊C411yescharacteristic
67C2×D61—21no—
68C2×D61—21no—
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—42no—
72C2×D61C2×D811yescharacteristic
73C2×D61C2×SD1611yescharacteristic
74#6923—82no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—42no—
78C4×C61#10212yes—
79Dic61—21no—
80Dic61—21no—
81Dic61#10212yes—
82#1517—611nomaximal, Sylow
83C2×C61#41011yescharacteristic
84C2×C61C2×#10211yescharacteristic
85C2×C61#42111yescharacteristic
86D61—21no—
87D61—21no—
88D61—82no—
89#532—611no—
90#431—611no—
91#382—611no—
92#327—614no—
93C61#151711yescharacteristic, complemented, Sylow
94C2×#41—1221no—
95C4⋊Q8#692311yescharacteristic, complemented
96#127—611no—
97#124—1221no—
98#121—612no—
99#121—1221no—
100C4×D4—612no—
101C4×D4—1221no—
102C2×C4⋊C4—1221no—
103C2×C42—611no—
104C4⋊C8—1221no—
105C22⋊C8—612no—
106C4×C8—1221no—
107#95—612no—
108#95—1221no—
109#41—2442no—
110#41—2442no—
111C2×Q8—21no—
112C2×D4—612no—
113C2×D4—1222no—
114C2×D4—1221no—
115C2×D4—1221no—
116C22×C4—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—1222no—
120C22×C4—1222no—
121C2×C8—1222no—
122C4⋊C4—21no—
123C4⋊C4—2442no—
124C4⋊C4C2×#692312yes—
125C22⋊C4—1222no—
126C22⋊C4—1222no—
127C42—611no—
128C42—611no—
129C42—611no—
130C42C2×#692311yescharacteristic
131C23—611no—
132C23—1222no—
133Q8—42no—
134D4—2442no—
135D4—2442no—
136D4—2442no—
137D4—2442no—
138D4—2442no—
139C2×C4—22no—
140C2×C4—611no—
141C2×C4—612no—
142C2×C4—612no—
143C2×C4—611no—
144C2×C4—611no—
145C2×C4—2441no—
146C2×C4—2441no—
147C2×C4—2444no—
148C2×C4—2442no—
149C2×C4—2442no—
150C2×C4—2442no—
151C2×C4C22⋊#692311yescharacteristic
152C2×C4C22⋊#692311yescharacteristic
153C2×C4C22×#692311yescharacteristic
154C8—2442no—
155C22—611no—
156C22—611no—
157C22—1221no—
158C22—1221no—
159C22—2442no—
160C22—2442no—
161C22—2442no—
162C22C2×C22⋊#692311yescharacteristic
163C4—21no—
164C4—21no—
165C4—42no—
166C4—612no—
167C4—1221no—
168C4—1221no—
169C4—4882no—
170C4#1451983912yes—
171C2—1221no—
172C2—1221no—
173C2—4882no—
174C2#1684074311yescharacteristic
175C2C2×#1451983911yescharacteristic
176C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1517
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
1. #16840780C2semidirect
2. #16840706C2semidirect
3. #16840614C2semidirect
12. #14519774C4semidirect
17. #14519739C4semidirect
19. C4⋊Q8×C61C4semidirect
93. C61#1517semidirect
95. C4⋊Q8#6923semidirect