Finite Group Databasebeta

← #31827030

Subgroups — #31827030

Order 18112.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#17985391C211yesmaximal, characteristic, complemented
2C22×C22⋊D283C211yesmaximal, characteristic, complemented
3#22583606C212yesmaximal, complemented
4#22583596C212yesmaximal, complemented
5#22583583C212yesmaximal, complemented
6#22583582C212yesmaximal, complemented
7#22583580C211yesmaximal, characteristic, complemented
8#22583579C211yesmaximal, characteristic, complemented
9#22583578C211yesmaximal, characteristic, complemented
10#22583566C211yesmaximal, characteristic, complemented
11#120×C283C211yesmaximal, characteristic, complemented
12C23×D283C2211yescharacteristic
13#17985391—24no—
14C2×Dic566C2211yescharacteristic, complemented
15C2×D1132C2212yescomplemented
16C2×C22⋊D283—24no—
17C2×C22⋊D283C2211yescharacteristic
18C2×C22⋊D283C2212yes—
19C2×C22⋊D283C2212yes—
20C2×C22⋊D283C2211yescharacteristic, complemented
21C2×C22⋊D283C2212yescomplemented
22C2×C22⋊D283C2212yescomplemented
23C22×Dic283C2211yescharacteristic
24C22×Dic283C2211yescharacteristic, complemented
25C2×C4×D283C2211yescharacteristic, complemented
26Dic283⋊C4C2212yescomplemented
27C22⋊Dic283C2211yescharacteristic
28C22⋊Dic283C2212yescomplemented
29(C2×D283)⋊C4C2212yescomplemented
30(C2×D283)⋊C4C2212yescomplemented
31C4×Dic283C2212yescomplemented
32C24×C283C2211yescharacteristic
33C2×D4×C283C2211yescharacteristic
34C2×D4×C283C2212yescomplemented
35C22⋊C4×C283C2211yescharacteristic
36C22⋊C4×C283C2212yescomplemented
37C22×D283—22no—
38C22×D283—42no—
39C22×D283C2312yes—
40C22×D283C2311yescharacteristic
41Dic566—22no—
42D1132—42no—
43C22⋊D283—22no—
44C22⋊D283—24no—
45C22⋊D283—24no—
46C22⋊D283—22no—
47C22⋊D283—42no—
48C22⋊D283—42no—
49C2×Dic283—22no—
50C2×Dic283D414yescomplemented
51C2×Dic283C2312yes—
52C2×Dic283C2311yescharacteristic
53C2×Dic283C2311yescharacteristic
54C2×Dic283C2311yescharacteristic
55C4×D283—22no—
56C23×C283—22no—
57C23×C283—42no—
58C23×C283C2312yes—
59C23×C283C2311yescharacteristic
60C23×C283C2311yescharacteristic
61D4×C283—22no—
62D4×C283—42no—
63C2×C4×C283C2312yes—
64C2×C4×C283C2311yescharacteristic
65C22×C283—22no—
66C22×C283—21no—
67C22×C283—22no—
68C22×C283—22no—
69C22×C283—22no—
70C22×C283—22no—
71C22×C283—44no—
72C22×C283C2×D412yes—
73C22×C283C2411yescharacteristic
74C2×D283—21no—
75C2×D283—22no—
76C2×D283—22no—
77C2×D283—22no—
78C2×D283—22no—
79C2×D283—44no—
80C4×C283—21no—
81C4×C283—22no—
82Dic283—21no—
83Dic283—22no—
84Dic283C2×D412yes—
85Dic283C2×D412yes—
86C2×C283—22no—
87C2×C283—41no—
88C2×C283—42no—
89C2×C283C22×D411yescharacteristic
90C2×C283H(5,𝔽2)12yes—
91D283—41no—
92D283—42no—
93C283#53511yescharacteristic, complemented, Sylow
94#535—2831nomaximal, Sylow
95C2×#41—2831no—
96C22×D4—2831no—
97#127—2832no—
98#124—2832no—
99#121—2832no—
100#121—2832no—
101#120—2831no—
102#120—2831no—
103#120—2831no—
104#120D28311yescharacteristic, complemented
105#117—2831no—
106C24—2831no—
107C24C2×D28311yescharacteristic
108#41—5664no—
109C2×Q8—2831no—
110C2×D4—2831no—
111C2×D4—2832no—
112C2×D4—2832no—
113C2×D4—2831no—
114C2×D4—2832no—
115C2×D4—2832no—
116C2×D4—2832no—
117C2×D4—5664no—
118C2×D4C2×D28311yescharacteristic
119C2×D4C2×D28312yescomplemented
120C22×C4—2831no—
121C22×C4—2831no—
122C22×C4—2831no—
123C4⋊C4—2832no—
124C22⋊C4—2831no—
125C22⋊C4—2832no—
126C22⋊C4—2832no—
127C22⋊C4—2832no—
128C22⋊C4C2×D28311yescharacteristic
129C22⋊C4C2×D28312yescomplemented
130C42—2832no—
131C23—22no—
132C23—42no—
133C23—2832no—
134C23—2831no—
135C23—5662no—
136C23—11322no—
137C23C22×D28312yes—
138C23C22×D28311yescharacteristic
139C23C22×D28311yescharacteristic
140Q8—5662no—
141D4—22no—
142D4—42no—
143D4—5664no—
144D4—5664no—
145D4—5662no—
146D4—5662no—
147D4—11322no—
148D4—11322no—
149D4—11322no—
150C2×C4—2834no—
151C2×C4—2831no—
152C2×C4—2831no—
153C2×C4—2832no—
154C2×C4—2831no—
155C2×C4—5662no—
156C2×C4—5662no—
157C2×C4C22×D28312yes—
158C2×C4C22×D28311yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—5661no—
167C22—5662no—
168C22—5662no—
169C22—5662no—
170C22—5662no—
171C22—11324no—
172C22D4×D28312yes—
173C22C23×D28311yescharacteristic
174C4—21no—
175C4—22no—
176C4—2832no—
177C4—2832no—
178C4—5661no—
179C4—5662no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—11322no—
184C2—11321no—
185C2C2×D4×D28311yescharacteristic
186C2#2258365512yes—
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, cosocleC22×C283C24
Fitting#120×C283C2
hypercenter#120D283
hypocenterC283#535
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#17985391C2semidirect
2. C22×C22⋊D283C2semidirect
3. #22583606C2semidirect
4. #22583596C2semidirect
5. #22583583C2semidirect
6. #22583582C2semidirect
7. #22583580C2semidirect
8. #22583579C2semidirect
9. #22583578C2semidirect
10. #22583566C2semidirect
11. #120×C283C2semidirect
14. C2×Dic566C22semidirect
15. C2×D1132C22semidirect
20. C2×C22⋊D283C22semidirect
21. C2×C22⋊D283C22semidirect
22. C2×C22⋊D283C22semidirect
24. C22×Dic283C22semidirect
25. C2×C4×D283C22semidirect
26. Dic283⋊C4C22semidirect
28. C22⋊Dic283C22semidirect
29. (C2×D283)⋊C4C22semidirect
30. (C2×D283)⋊C4C22semidirect
31. C4×Dic283C22semidirect
34. C2×D4×C283C22semidirect
36. C22⋊C4×C283C22semidirect
50. C2×Dic283D4semidirect
93. C283#535semidirect
104. #120D283semidirect
119. C2×D4C2×D283semidirect
129. C22⋊C4C2×D283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179853912
C22×C22⋊D2832
#225836062
#225835962
#225835832
#225835822
#225835802
#225835792
#225835782
#225835662
#120×C2832
#535283