Finite Group Databasebeta

← #44445306

Subgroups — #44445306

Order 29632.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#20301791C211yesmaximal, characteristic, complemented
2C22×C4×D463C211yesmaximal, characteristic, complemented
3#28414643C212yesmaximal, complemented
4#28414634C211yesmaximal, characteristic, complemented
5#28414633C211yesmaximal, characteristic, complemented
6#28414632C211yesmaximal, characteristic, complemented
7#28414628C212yesmaximal, complemented
8#28414620C212yesmaximal, complemented
9(C22⋊D463)⋊C4C212yesmaximal, complemented
10#28414616C211yesmaximal, characteristic, complemented
11C22⋊Q8×C463C211yesmaximal, characteristic, complemented
12C23×D463C2211yescharacteristic
13#20301791—24no—
14C2×D1852C2212yes—
15C2×D1852C2212yes—
16C2×D1852C2211yescharacteristic, complemented
17C2×C22⋊D463C2212yes—
18C22×Dic463C2211yescharacteristic
19C2×C4×D463—24no—
20C2×C4×D463C2211yescharacteristic
21C2×C4×D463C2211yescharacteristic
22C2×C4×D463C2211yescharacteristic
23C2×C4×D463C2211yescharacteristic
24C2×C4×D463C2212yescomplemented
25C4⋊Dic463C2211yescharacteristic, complemented
26Dic463⋊C4C2212yescomplemented
27(C2×D463)⋊C4C2212yes—
28(C2×D463)⋊C4C2212yes—
29(C2×D463)⋊C4C2212yescomplemented
30(C2×D463)⋊C4C2212yescomplemented
31C4×Dic463C2212yescomplemented
32C2×Q8×C463C2211yescharacteristic, complemented
33C22×C4×C463C2211yescharacteristic
34C4⋊C4×C463C2211yescharacteristic, complemented
35C4⋊C4×C463C2212yescomplemented
36C22⋊C4×C463C2212yes—
37C22×D463—22no—
38C22×D463—22no—
39C22×D463—22no—
40C22×D463C2312yes—
41C22×D463C2311yescharacteristic
42C22×D463C2311yescharacteristic
43D1852—24no—
44D1852—24no—
45D1852—22no—
46C22⋊D463—24no—
47C2×Dic463—22no—
48C2×Dic463C2312yes—
49C2×Dic463C2311yescharacteristic
50C2×Dic463C2311yescharacteristic
51C4×D463—22no—
52C4×D463—22no—
53C4×D463—22no—
54C4×D463—24no—
55C4×D463D414yescomplemented
56C23×C463C2311yescharacteristic
57Q8×C463—22no—
58C2×C4×C463—22no—
59C2×C4×C463C2312yes—
60C2×C4×C463C2312yes—
61C2×C4×C463C2311yescharacteristic
62C2×C4×C463C2311yescharacteristic
63C22×C463—21no—
64C22×C463—21no—
65C22×C463#4112yescomplemented
66C22×C463C2411yescharacteristic
67C2×D463—28no—
68C2×D463—21no—
69C2×D463—21no—
70C2×D463—21no—
71C2×D463—21no—
72C2×D463—22no—
73C2×D463—22no—
74C2×D463—22no—
75C2×D463C2×D412yes—
76C2×D463#4112yescomplemented
77C4×C463—21no—
78C4×C463—22no—
79C4×C463—22no—
80C4×C463C2×D412yes—
81Dic463—21no—
82Dic463—22no—
83Dic463C2×D412yes—
84C2×C463—22no—
85C2×C463C22×D411yescharacteristic
86C2×C463C2×#4111yescharacteristic
87C2×C463C2×#4111yescharacteristic
88D463—22no—
89D463—22no—
90D463—42no—
91C463#52511yescharacteristic, complemented, Sylow
92#525—4631nomaximal, Sylow
93C2×#41—4631no—
94C23×C4—4631no—
95#123—4632no—
96C22⋊Q8—4631no—
97C22⋊Q8D46311yescharacteristic, complemented
98#121—4631no—
99#121—4631no—
100#120—4632no—
101C4×D4—4632no—
102C4×D4—4632no—
103#117—4631no—
104C24—4631no—
105#41—9264no—
106C2×Q8C2×D46311yescharacteristic, complemented
107C2×D4—4632no—
108C2×D4—4632no—
109C2×D4—4632no—
110C2×D4—4631no—
111C22×C4—9264no—
112C22×C4—4631no—
113C22×C4—4631no—
114C22×C4—4632no—
115C22×C4—4631no—
116C22×C4—4631no—
117C22×C4—4631no—
118C22×C4C2×D46311yescharacteristic
119C4⋊C4—4631no—
120C4⋊C4—4632no—
121C4⋊C4C2×D46311yescharacteristic, complemented
122C4⋊C4C2×D46312yescomplemented
123C22⋊C4—4632no—
124C22⋊C4—4632no—
125C22⋊C4—4632no—
126C22⋊C4—4632no—
127C22⋊C4C2×D46312yes—
128C42—4632no—
129C23—9262no—
130C23—9262no—
131C23—9262no—
132C23—4632no—
133C23—4631no—
134C23—4631no—
135C23C22×D46311yescharacteristic
136Q8—22no—
137D4—9264no—
138D4—9264no—
139D4—9264no—
140D4—9262no—
141C2×C4—22no—
142C2×C4—9262no—
143C2×C4—9262no—
144C2×C4—9264no—
145C2×C4—9262no—
146C2×C4—9262no—
147C2×C4—4632no—
148C2×C4—4631no—
149C2×C4—4631no—
150C2×C4—4634no—
151C2×C4C22×D46312yes—
152C2×C4C22×D46311yescharacteristic
153C2×C4C22×D46312yes—
154C2×C4C22×D46311yescharacteristic
155C22—21no—
156C22—21no—
157C22—9268no—
158C22—9262no—
159C22—9262no—
160C22—9262no—
161C22—9261no—
162C22—9261no—
163C22—9261no—
164C22—9261no—
165C22—4632no—
166C22—4632no—
167C22#2030179112yescomplemented
168C22C23×D46311yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—9261no—
173C4—9262no—
174C4—4632no—
175C4D4×D46312yes—
176C2—22no—
177C2—18522no—
178C2—9262no—
179C2—9262no—
180C2C2×D4×D46311yescharacteristic
181C2#41×D46311yescharacteristic
182C2C2×#2030179111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D463
commutator, socle, cosocleC22×C463C24
FittingC22⋊Q8×C463C2
hypercenterC22⋊Q8D463
hypocenterC463#525
LCSG ▷ C22×C463 ▷ C463
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#20301791C2semidirect
2. C22×C4×D463C2semidirect
3. #28414643C2semidirect
4. #28414634C2semidirect
5. #28414633C2semidirect
6. #28414632C2semidirect
7. #28414628C2semidirect
8. #28414620C2semidirect
9. (C22⋊D463)⋊C4C2semidirect
10. #28414616C2semidirect
11. C22⋊Q8×C463C2semidirect
16. C2×D1852C22semidirect
24. C2×C4×D463C22semidirect
25. C4⋊Dic463C22semidirect
26. Dic463⋊C4C22semidirect
29. (C2×D463)⋊C4C22semidirect
30. (C2×D463)⋊C4C22semidirect
31. C4×Dic463C22semidirect
32. C2×Q8×C463C22semidirect
34. C4⋊C4×C463C22semidirect
35. C4⋊C4×C463C22semidirect
55. C4×D463D4semidirect
65. C22×C463#41semidirect
76. C2×D463#41semidirect
91. C463#525semidirect
97. C22⋊Q8D463semidirect
106. C2×Q8C2×D463semidirect
121. C4⋊C4C2×D463semidirect
122. C4⋊C4C2×D463semidirect
167. C22#20301791semidirect

Maximal subgroups

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

subgroupindex
C2×#203017912
C22×C4×D4632
#284146432
#284146342
#284146332
#284146322
#284146282
#284146202
(C22⋊D463)⋊C42
#284146162
C22⋊Q8×C4632
#525463