Finite Group Databasebeta

← #37588917

Subgroups — #37588917

Order 24512.

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×#20259457C211yesmaximal, characteristic, complemented
2C2×D4×D383C211yesmaximal, characteristic, complemented
3#27133837C212yesmaximal, complemented
4#27133827C212yesmaximal, complemented
5#27133816C211yesmaximal, characteristic, complemented
6#27133815C211yesmaximal, characteristic, complemented
7#27133812C211yesmaximal, characteristic, complemented
8#27133811C212yesmaximal, complemented
9#27133809C212yesmaximal, complemented
10#27133799C211yesmaximal, characteristic, complemented
11#121×C383C211yesmaximal, characteristic, complemented
12C23×D383C2212yes—
13#20259457—24no—
14C2×Dic766C2211yescharacteristic, complemented
15C2×D1532C2211yescharacteristic
16C2×D1532C2211yescharacteristic
17C2×D1532C2212yescomplemented
18C2×C22⋊D383C2211yescharacteristic
19C2×C22⋊D383C2212yes—
20C2×C22⋊D383C2211yescharacteristic, complemented
21C2×C22⋊D383C2212yescomplemented
22C2×C22⋊D383C2212yescomplemented
23D4×D383—24no—
24C2×C4×D383C2211yescharacteristic
25C2×C4×D383C2211yescharacteristic, complemented
26C4⋊Dic383C2211yescharacteristic, complemented
27C22⋊Dic383C2212yescomplemented
28(C2×D383)⋊C4C2212yes—
29(C2×D383)⋊C4C2212yescomplemented
30(C2×D383)⋊C4C2212yescomplemented
31C4×Dic383C2212yescomplemented
32C2×D4×C383C2211yescharacteristic
33C2×D4×C383C2212yescomplemented
34C22×C4×C383C2211yescharacteristic, complemented
35C4⋊C4×C383C2211yescharacteristic, complemented
36C22⋊C4×C383C2212yescomplemented
37C22×D383—24no—
38C22×D383—42no—
39C22×D383—42no—
40C22×D383C2312yes—
41C22×D383C2311yescharacteristic
42C22×D383C2311yescharacteristic
43Dic766—22no—
44D1532—22no—
45D1532—22no—
46D1532—42no—
47C22⋊D383—22no—
48C22⋊D383—24no—
49C22⋊D383—22no—
50C22⋊D383—42no—
51C22⋊D383—42no—
52C2×Dic383C2312yes—
53C2×Dic383C2311yescharacteristic
54C2×Dic383C2311yescharacteristic
55C4×D383—22no—
56C4×D383D414yescomplemented
57C23×C383C2312yes—
58C23×C383C2311yescharacteristic
59D4×C383—22no—
60D4×C383—42no—
61C2×C4×C383—22no—
62C2×C4×C383C2311yescharacteristic
63C2×C4×C383C2312yes—
64C2×C4×C383C2311yescharacteristic
65C22×C383—21no—
66C22×C383—22no—
67C22×C383—21no—
68C22×C383—22no—
69C22×C383—21no—
70C22×C383—22no—
71C22×C383C2411yescharacteristic
72C2×D383—21no—
73C2×D383—21no—
74C2×D383—21no—
75C2×D383—22no—
76C2×D383—21no—
77C2×D383—22no—
78C2×D383—21no—
79C2×D383—22no—
80C2×D383—48no—
81C2×D383C2×D412yes—
82C4×C383—21no—
83C4×C383—22no—
84C4×C383C2×D412yes—
85Dic383—21no—
86Dic383—22no—
87Dic383C2×D412yes—
88C2×C383—42no—
89C2×C383—41no—
90C2×C383C22×D411yescharacteristic
91C2×C383H(5,𝔽2)11yescharacteristic
92C2×C383H(5,𝔽2)11yescharacteristic
93D383—22no—
94D383—41no—
95D383—42no—
96C383#53511yescharacteristic, complemented, Sylow
97#535—3831nomaximal, Sylow
98C2×#41—3831no—
99C22×D4—3831no—
100#127—3832no—
101#124—3832no—
102#121—3831no—
103#121—3831no—
104#121—3831no—
105#121D38311yescharacteristic, complemented
106#120—3832no—
107#120—3832no—
108#117—3831no—
109C24—3832no—
110#41—7664no—
111C2×Q8—3831no—
112C2×D4—3832no—
113C2×D4—3832no—
114C2×D4—3831no—
115C2×D4—3832no—
116C2×D4—3831no—
117C2×D4—3832no—
118C2×D4—3831no—
119C2×D4—3831no—
120C2×D4—7664no—
121C2×D4C2×D38311yescharacteristic
122C2×D4C2×D38312yescomplemented
123C22×C4—3831no—
124C22×C4—3831no—
125C22×C4C2×D38311yescharacteristic, complemented
126C4⋊C4—3831no—
127C4⋊C4C2×D38311yescharacteristic, complemented
128C22⋊C4—3832no—
129C22⋊C4—3832no—
130C22⋊C4—3832no—
131C22⋊C4—3832no—
132C22⋊C4C2×D38312yescomplemented
133C42—3832no—
134C23—3831no—
135C23—3832no—
136C23—3831no—
137C23—15322no—
138C23—15322no—
139C23—7664no—
140C23C22×D38312yes—
141C23C22×D38311yescharacteristic
142Q8—7662no—
143D4—22no—
144D4—42no—
145D4—15322no—
146D4—15322no—
147D4—15322no—
148D4—7662no—
149D4—7664no—
150D4—7662no—
151D4—7662no—
152D4—7662no—
153C2×C4—22no—
154C2×C4—3831no—
155C2×C4—3834no—
156C2×C4—3832no—
157C2×C4—3831no—
158C2×C4—7662no—
159C2×C4C22×D38312yes—
160C2×C4C22×D38311yescharacteristic
161C2×C4C22×D38311yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—3832no—
169C22—15328no—
170C22—7661no—
171C22—7662no—
172C22—7661no—
173C22—7662no—
174C22—7661no—
175C22—7662no—
176C22—7661no—
177C22—7661no—
178C22C23×D38311yescharacteristic
179C4—21no—
180C4—22no—
181C4—3832no—
182C4—7661no—
183C4—7662no—
184C4D4×D38312yes—
185C2—42no—
186C2—41no—
187C2—15322no—
188C2—15321no—
189C2—7662no—
190C2C2×D4×D38311yescharacteristic
191C2#2713388611yescharacteristic
192C2#2713388711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D383
commutator, socle, cosocleC22×C383C24
Fitting#121×C383C2
hypercenter#121D383
hypocenterC383#535
LCSG ▷ C22×C383 ▷ C383
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#20259457C2semidirect
2. C2×D4×D383C2semidirect
3. #27133837C2semidirect
4. #27133827C2semidirect
5. #27133816C2semidirect
6. #27133815C2semidirect
7. #27133812C2semidirect
8. #27133811C2semidirect
9. #27133809C2semidirect
10. #27133799C2semidirect
11. #121×C383C2semidirect
14. C2×Dic766C22semidirect
17. C2×D1532C22semidirect
20. C2×C22⋊D383C22semidirect
21. C2×C22⋊D383C22semidirect
22. C2×C22⋊D383C22semidirect
25. C2×C4×D383C22semidirect
26. C4⋊Dic383C22semidirect
27. C22⋊Dic383C22semidirect
29. (C2×D383)⋊C4C22semidirect
30. (C2×D383)⋊C4C22semidirect
31. C4×Dic383C22semidirect
33. C2×D4×C383C22semidirect
34. C22×C4×C383C22semidirect
35. C4⋊C4×C383C22semidirect
36. C22⋊C4×C383C22semidirect
56. C4×D383D4semidirect
96. C383#535semidirect
105. #121D383semidirect
122. C2×D4C2×D383semidirect
125. C22×C4C2×D383semidirect
127. C4⋊C4C2×D383semidirect
132. C22⋊C4C2×D383semidirect

Maximal subgroups

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

subgroupindex
C2×#202594572
C2×D4×D3832
#271338372
#271338272
#271338162
#271338152
#271338122
#271338112
#271338092
#271337992
#121×C3832
#535383