Finite Group Databasebeta

← #31827106

Subgroups — #31827106

Order 18112.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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×#17985393C211yesmaximal, characteristic, complemented
2C22×D1132C211yesmaximal, characteristic, complemented
3#22583599C211yesmaximal, characteristic, complemented
4#22583595C212yesmaximal, complemented
5#22583585C211yesmaximal, characteristic, complemented
6#22583585C212yesmaximal, complemented
7#22583580C212yesmaximal, complemented
8#22583572C211yesmaximal, characteristic, complemented
9C4×C22⋊D283C211yesmaximal, characteristic, complemented
10C22⋊C4×D283C212yesmaximal, complemented
11C22⋊Q8×C283C211yesmaximal, characteristic, complemented
12C23×D283C2212yes—
13#17985393—24no—
14C2×D1132—24no—
15C2×D1132C2212yes—
16C2×D1132C2211yescharacteristic
17C2×D1132C2211yescharacteristic
18C2×D1132C2212yescomplemented
19C2×D1132C2212yescomplemented
20C2×C22⋊D283C2211yescharacteristic
21C2×C4×D283C2212yescomplemented
22C2×C4×D283C2211yescharacteristic, complemented
23C2×C4×D283C2212yescomplemented
24Dic283⋊C4C2211yescharacteristic, complemented
25C22⋊Dic283C2211yescharacteristic
26(C2×D283)⋊C4C2212yescomplemented
27(C2×D283)⋊C4C2212yescomplemented
28(C2×D283)⋊C4C2211yescharacteristic, complemented
29(C2×D283)⋊C4C2212yescomplemented
30(C2×D283)⋊C4C2212yescomplemented
31C4×Dic283C2211yescharacteristic, complemented
32C2×Q8×C283C2211yescharacteristic, complemented
33C22×C4×C283C2211yescharacteristic
34C4⋊C4×C283C2211yescharacteristic, complemented
35C4⋊C4×C283C2212yescomplemented
36C22⋊C4×C283C2212yes—
37C22×D283—24no—
38C22×D283—24no—
39C22×D283—42no—
40C22×D283C2312yes—
41C22×D283C2311yescharacteristic
42C22×D283C2312yes—
43D1132—24no—
44D1132—24no—
45D1132—22no—
46D1132—42no—
47D1132D414yescomplemented
48C22⋊D283—22no—
49C2×Dic283C2311yescharacteristic
50C2×Dic283C2311yescharacteristic
51C2×Dic283C2311yescharacteristic
52C4×D283—24no—
53C4×D283—22no—
54C4×D283—42no—
55C23×C283C2311yescharacteristic
56Q8×C283—22no—
57C2×C4×C283—22no—
58C2×C4×C283C2312yes—
59C2×C4×C283C2312yes—
60C2×C4×C283C2311yescharacteristic
61C2×C4×C283C2311yescharacteristic
62C22×C283—21no—
63C22×C283—21no—
64C22×C283#4112yescomplemented
65C22×C283C2411yescharacteristic
66C2×D283—22no—
67C2×D283—22no—
68C2×D283—21no—
69C2×D283—22no—
70C2×D283—21no—
71C2×D283—22no—
72C2×D283—21no—
73C2×D283—22no—
74C2×D283—48no—
75C2×D283C2×D414yes—
76C4×C283—21no—
77C4×C283—22no—
78C4×C283—22no—
79C4×C283C2×D412yes—
80Dic283—21no—
81Dic283—21no—
82Dic283—21no—
83C2×C283—22no—
84C2×C283C22×D411yescharacteristic
85C2×C283C2×#4111yescharacteristic
86C2×C283H(5,𝔽2)11yescharacteristic
87D283—24no—
88D283—41no—
89D283—42no—
90C283#54611yescharacteristic, complemented, Sylow
91#546—2831nomaximal, Sylow
92C2×#41—2831no—
93C22×D4—2831no—
94#124—2831no—
95#123—2832no—
96C22⋊Q8D28311yescharacteristic, complemented
97#121—2831no—
98#121—2832no—
99#120—2832no—
100C4×D4—2831no—
101C4×D4—2831no—
102C2×C22⋊C4—2832no—
103C24—2832no—
104#41—5664no—
105C2×Q8C2×D28311yescharacteristic, complemented
106C2×D4—2831no—
107C2×D4—2831no—
108C2×D4—2832no—
109C2×D4—2831no—
110C2×D4—2832no—
111C2×D4—2832no—
112C2×D4—5664no—
113C22×C4—2832no—
114C22×C4—2831no—
115C22×C4—2832no—
116C22×C4C2×D28311yescharacteristic
117C4⋊C4—2831no—
118C4⋊C4C2×D28311yescharacteristic, complemented
119C4⋊C4C2×D28312yescomplemented
120C22⋊C4—2831no—
121C22⋊C4—2832no—
122C22⋊C4—2832no—
123C22⋊C4—2832no—
124C22⋊C4—2831no—
125C22⋊C4—2832no—
126C22⋊C4C2×D28312yes—
127C42—2831no—
128C23—2832no—
129C23—2832no—
130C23—2831no—
131C23—5664no—
132C23—5664no—
133C23—11322no—
134C23C22×D28311yescharacteristic
135Q8—22no—
136D4—2834no—
137D4—5664no—
138D4—5664no—
139D4—5662no—
140D4—5662no—
141D4—11322no—
142C2×C4—22no—
143C2×C4—2831no—
144C2×C4—2831no—
145C2×C4—2831no—
146C2×C4—5664no—
147C2×C4—5662no—
148C2×C4—11322no—
149C2×C4C22×D28312yes—
150C2×C4C22×D28312yes—
151C2×C4C22×D28311yescharacteristic
152C2×C4C22×D28311yescharacteristic
153C22—21no—
154C22—21no—
155C22—2834no—
156C22—5662no—
157C22—5662no—
158C22—5661no—
159C22—5662no—
160C22—5661no—
161C22—5662no—
162C22—5661no—
163C22—5662no—
164C22—11328no—
165C22#1798539312yescomplemented
166C22C23×D28311yescharacteristic
167C4—21no—
168C4—22no—
169C4—22no—
170C4—5661no—
171C4—5661no—
172C4—5661no—
173C4D4×D28312yes—
174C2—22no—
175C2—5664no—
176C2—11322no—
177C2—11321no—
178C2C2×D4×D28311yescharacteristic
179C2C2×#1798539311yescharacteristic
180C2#2258365611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D283
commutator, socle, cosocleC22×C283C24
FittingC22⋊Q8×C283C2
hypercenterC22⋊Q8D283
hypocenterC283#546
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#17985393C2semidirect
2. C22×D1132C2semidirect
3. #22583599C2semidirect
4. #22583595C2semidirect
5. #22583585C2semidirect
6. #22583585C2semidirect
7. #22583580C2semidirect
8. #22583572C2semidirect
9. C4×C22⋊D283C2semidirect
10. C22⋊C4×D283C2semidirect
11. C22⋊Q8×C283C2semidirect
18. C2×D1132C22semidirect
19. C2×D1132C22semidirect
21. C2×C4×D283C22semidirect
22. C2×C4×D283C22semidirect
23. C2×C4×D283C22semidirect
24. Dic283⋊C4C22semidirect
26. (C2×D283)⋊C4C22semidirect
27. (C2×D283)⋊C4C22semidirect
28. (C2×D283)⋊C4C22semidirect
29. (C2×D283)⋊C4C22semidirect
30. (C2×D283)⋊C4C22semidirect
31. C4×Dic283C22semidirect
32. C2×Q8×C283C22semidirect
34. C4⋊C4×C283C22semidirect
35. C4⋊C4×C283C22semidirect
47. D1132D4semidirect
64. C22×C283#41semidirect
90. C283#546semidirect
96. C22⋊Q8D283semidirect
105. C2×Q8C2×D283semidirect
118. C4⋊C4C2×D283semidirect
119. C4⋊C4C2×D283semidirect
165. C22#17985393semidirect

Maximal subgroups

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

subgroupindex
C2×#179853932
C22×D11322
#225835992
#225835952
#225835852
#225835802
#225835722
C4×C22⋊D2832
C22⋊C4×D2832
C22⋊Q8×C2832
#546283