Finite Group Databasebeta

← #20290137

Subgroups — #20290137

Order 6784.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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#16811645C211yesmaximal, characteristic
2#16811568C211yesmaximal, characteristic
3#16811477C212yesmaximal
4#16811476C212yesmaximal
5#16811177C211yesmaximal, characteristic
6C4⋊#88324—21no—
7#13133274C2212yes—
8#13133272—21no—
9(C2×#6157)⋊C4—21no—
10(C2×#6157)⋊C4—21no—
11(C2×#6157)⋊C4C2212yes—
12#13133216C411yescharacteristic, complemented
13#13133215C411yescharacteristic, complemented
14#13133207—21no—
15#13133197C2211yescharacteristic
16#13133195—21no—
17#13133193C2211yescharacteristic
18C4×Dic106—21no—
19C4×Dic106C411yescharacteristic, complemented
20#13133174—21no—
21C42×D53C2211yescharacteristic
22C4×Q8×C53C411yescharacteristic, complemented
23C22×#6157—22no—
24C2×Q8×C53C2×C411yescharacteristic
25C2×C4×D53D411yescharacteristic
26C2×C4×D53D411yescharacteristic
27C2×C4×D53C2311yescharacteristic
28C2×Dic106—21no—
29C2×Dic106C2×C411yescharacteristic
30C2×#88324—22no—
31C4⋊C4×C53—21no—
32C4⋊C4×C53C2×C411yescharacteristic
33C42×C53—21no—
34C42×C53C2×C411yescharacteristic
35#11719921—21no—
36#11719921—21no—
37C4⋊Dic53—21no—
38C4⋊Dic53C2×C411yescharacteristic
39#11719919—21no—
40#11719919—21no—
41#11719919—21no—
42#11719919—21no—
43#11719919—21no—
44C4×Dic53—21no—
45C4×Dic53C2×C411yescharacteristic
46C4×Dic53D411yescharacteristic
47C4×Dic53D411yescharacteristic
48C22×D53C2×D411yescharacteristic
49C2×#6157—42no—
50C2×#6157—42no—
51C2×#6157—42no—
52Q8×C53—41no—
53C2×C4×C53—21no—
54C2×C4×C53—21no—
55C2×C4×C53C22⋊C411yescharacteristic
56C2×C4×C53C22⋊C411yescharacteristic
57C2×C4×C53C22×C411yescharacteristic
58C2×Dic53—21no—
59C2×Dic53—21no—
60C2×Dic53C22⋊C411yescharacteristic
61C2×Dic53C22⋊C411yescharacteristic
62C2×Dic53C2×D411yescharacteristic
63C4×D53—22no—
64C4×D53—41no—
65C4×D53—41no—
66Dic106—42no—
67Dic106—41no—
68#88324—42no—
69C22×C53C2×C22⋊C411yescharacteristic
70C2×D53—21no—
71C2×D53—21no—
72C2×D53#13712yes—
73#6157—82no—
74C4×C53—21no—
75C4×C53—21no—
76C4×C53—21no—
77C4×C53—41no—
78C4×C53—41no—
79Dic53—21no—
80Dic53—21no—
81Dic53—21no—
82Dic53—41no—
83Dic53—41no—
84#1515—531nomaximal, Sylow
85C2×C53#41011yescharacteristic
86C2×C53#41911yescharacteristic
87C2×C53#42111yescharacteristic
88D53—22no—
89#533—531no—
90#432—531no—
91#383—531no—
92#328—532no—
93#328—532no—
94C53#151511yescharacteristic, complemented, Sylow
95C4⋊Q8—531no—
96C4⋊Q8—531no—
97#125—1061no—
98C22⋊Q8—531no—
99C22⋊Q8—531no—
100C22⋊Q8—1061no—
101C4×Q8—531no—
102C4×Q8—1061no—
103C4×Q8#615711yescharacteristic, complemented
104#117—1061no—
105C2×C42—531no—
106C4⋊C8—1061no—
107C22⋊C8—532no—
108#97—1061no—
109#95—532no—
110#95—1061no—
111#95—1061no—
112C2×Q8—531no—
113C2×Q8—1061no—
114C2×Q8C2×#615711yescharacteristic
115C22×C4—531no—
116C22×C4—531no—
117C22×C4—531no—
118C22×C4—1062no—
119C2×C8—1062no—
120C4⋊C4—21no—
121C4⋊C4—531no—
122C4⋊C4—1061no—
123C4⋊C4—1061no—
124C4⋊C4—1061no—
125C4⋊C4—1061no—
126C4⋊C4—1061no—
127C4⋊C4—1061no—
128C4⋊C4C2×#615711yescharacteristic
129C22⋊C4—1061no—
130C22⋊C4—1061no—
131C42—21no—
132C42—531no—
133C42—531no—
134C42—531no—
135C42—1061no—
136C42C2×#615711yescharacteristic
137C23—531no—
138Q8—41no—
139Q8—2121no—
140Q8—2122no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—531no—
144C2×C4—531no—
145C2×C4—531no—
146C2×C4—1062no—
147C2×C4—1061no—
148C2×C4—1061no—
149C2×C4—2121no—
150C2×C4—2121no—
151C2×C4—2122no—
152C2×C4—2122no—
153C2×C4—2122no—
154C2×C4C22⋊#615711yescharacteristic
155C2×C4C22⋊#615711yescharacteristic
156C2×C4C22×#615711yescharacteristic
157C8—2122no—
158C22—532no—
159C22—1061no—
160C22—1061no—
161C22C2×C22⋊#615711yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—1061no—
168C4—1061no—
169C4—1061no—
170C4—4242no—
171C4—2121no—
172C4—2121no—
173C2—1062no—
174C2#1681160211yescharacteristic
175C2#1681161611yescharacteristic
176C2#1681162011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6157
commutatorC2×C4×C53C22×C4
FrattiniC2×C4C22×#6157
FittingC4×Q8×C53C4
socleC22×C53C2×C22⋊C4
hypercenterC4×Q8#6157
hypocenterC53#1515
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #13133216C4semidirect
13. #13133215C4semidirect
19. C4×Dic106C4semidirect
22. C4×Q8×C53C4semidirect
94. C53#1515semidirect
103. C4×Q8#6157semidirect