Finite Group Databasebeta

← #37588909

Subgroups — #37588909

Order 24512.

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

normal subgroups only

This group has 346 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×D4×D383C212yesmaximal, complemented
2#27133826C212yesmaximal, complemented
3#27133823C212yesmaximal, complemented
4#27133815C211yesmaximal, characteristic, complemented
5#27133813C212yesmaximal, complemented
6#27133811C212yesmaximal, complemented
7#27133809C212yesmaximal, complemented
8C2×(C2×D383)⋊C4C211yesmaximal, characteristic, complemented
9#121×C383C211yesmaximal, characteristic, complemented
10C23×D383C2211yescharacteristic
11C23×D383C2212yescomplemented
12C2×D1532C2212yes—
13C2×D1532C2211yescharacteristic, complemented
14C2×C22⋊D383C2212yes—
15C2×C22⋊D383C2212yescomplemented
16C2×C22⋊D383C2212yescomplemented
17D4×D383—28no—
18C22×Dic383C2211yescharacteristic, complemented
19C2×C4×D383C2212yescomplemented
20C4⋊Dic383C2211yescharacteristic, complemented
21Dic383⋊C4C2212yescomplemented
22C22⋊Dic383C2212yescomplemented
23(C2×D383)⋊C4C2212yescomplemented
24(C2×D383)⋊C4C2212yescomplemented
25(C2×D383)⋊C4C2212yescomplemented
26(C2×D383)⋊C4C2212yescomplemented
27C2×D4×C383C2212yescomplemented
28C2×D4×C383C2211yescharacteristic, complemented
29C22×C4×C383C2211yescharacteristic, complemented
30C4⋊C4×C383C2211yescharacteristic, complemented
31C22⋊C4×C383C2212yescomplemented
32C22×D383—24no—
33C22×D383—41no—
34C22×D383—41no—
35C22×D383—42no—
36C22×D383—42no—
37C22×D383D414yescomplemented
38C22×D383C2312yes—
39C22×D383C2312yes—
40D1532—24no—
41D1532—41no—
42C22⋊D383—24no—
43C22⋊D383—24no—
44C22⋊D383—42no—
45C2×Dic383—41no—
46C2×Dic383C2312yes—
47C2×Dic383C2312yes—
48C4×D383—24no—
49C23×C383C2312yes—
50C23×C383C2311yescharacteristic
51D4×C383—24no—
52D4×C383—41no—
53C2×C4×C383—41no—
54C2×C4×C383C2311yescharacteristic
55C2×C4×C383C2312yes—
56C2×C4×C383C2311yescharacteristic
57C22×C383—21no—
58C22×C383—21no—
59C22×C383—22no—
60C22×C383—22no—
61C22×C383—22no—
62C22×C383C2×D412yes—
63C22×C383C2411yescharacteristic
64C2×D383—22no—
65C2×D383—22no—
66C2×D383—22no—
67C2×D383—22no—
68C2×D383—22no—
69C2×D383—44no—
70C2×D383—48no—
71C2×D383C2×D414yes—
72C4×C383—22no—
73C4×C383—21no—
74C4×C383—21no—
75Dic383—22no—
76Dic383—22no—
77C2×C383—22no—
78C2×C383—42no—
79C2×C383C22×D411yescharacteristic
80C2×C383H(5,𝔽2)11yescharacteristic
81C2×C383H(5,𝔽2)11yescharacteristic
82D383—24no—
83D383—42no—
84C383#53411yescharacteristic, complemented, Sylow
85#534—3831nomaximal, Sylow
86C22×D4—3832no—
87#123—3832no—
88#123—3832no—
89#121—3832no—
90#121—3831no—
91#121D38311yescharacteristic, complemented
92#120—3832no—
93#120—3832no—
94C2×C22⋊C4—3831no—
95C24—3831no—
96C24—3832no—
97C2×D4—3832no—
98C2×D4—3832no—
99C2×D4—3832no—
100C2×D4—3831no—
101C2×D4—3832no—
102C2×D4—7668no—
103C2×D4C2×D38312yescomplemented
104C2×D4C2×D38311yescharacteristic, complemented
105C22×C4—3831no—
106C22×C4—3832no—
107C22×C4C2×D38311yescharacteristic, complemented
108C4⋊C4—3832no—
109C4⋊C4—3831no—
110C4⋊C4C2×D38311yescharacteristic, complemented
111C22⋊C4—3832no—
112C22⋊C4—3832no—
113C22⋊C4—3832no—
114C22⋊C4—3832no—
115C22⋊C4—3832no—
116C22⋊C4C2×D38312yescomplemented
117C23—3834no—
118C23—3832no—
119C23—3832no—
120C23—15321no—
121C23—15321no—
122C23—15322no—
123C23—15322no—
124C23—7664no—
125C23C22×D38312yes—
126C23C22×D38311yescharacteristic
127D4—24no—
128D4—41no—
129D4—15321no—
130D4—15322no—
131D4—7664no—
132D4—7664no—
133D4—7664no—
134C2×C4—41no—
135C2×C4—3832no—
136C2×C4—3832no—
137C2×C4—15321no—
138C2×C4—7664no—
139C2×C4C22×D38311yescharacteristic
140C2×C4C22×D38311yescharacteristic
141C2×C4C22×D38312yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—3834no—
148C22—15324no—
149C22—15328no—
150C22—7662no—
151C22—7662no—
152C22—7662no—
153C22—7662no—
154C22—7662no—
155C22D4×D38312yes—
156C22C23×D38311yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—7662no—
161C4—7662no—
162C2—22no—
163C2—42no—
164C2—15322no—
165C2—7664no—
166C2C2×D4×D38311yescharacteristic
167C2#2713388611yescharacteristic
168C2#2713388711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D383
commutator, socle, cosocleC22×C383C24
Fitting#121×C383C2
hypercenter#121D383
hypocenterC383#534
LCSG ▷ C22×C383 ▷ C383
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D383C2semidirect
2. #27133826C2semidirect
3. #27133823C2semidirect
4. #27133815C2semidirect
5. #27133813C2semidirect
6. #27133811C2semidirect
7. #27133809C2semidirect
8. C2×(C2×D383)⋊C4C2semidirect
9. #121×C383C2semidirect
11. C23×D383C22semidirect
13. C2×D1532C22semidirect
15. C2×C22⋊D383C22semidirect
16. C2×C22⋊D383C22semidirect
18. C22×Dic383C22semidirect
19. C2×C4×D383C22semidirect
20. C4⋊Dic383C22semidirect
21. Dic383⋊C4C22semidirect
22. C22⋊Dic383C22semidirect
23. (C2×D383)⋊C4C22semidirect
24. (C2×D383)⋊C4C22semidirect
25. (C2×D383)⋊C4C22semidirect
26. (C2×D383)⋊C4C22semidirect
27. C2×D4×C383C22semidirect
28. C2×D4×C383C22semidirect
29. C22×C4×C383C22semidirect
30. C4⋊C4×C383C22semidirect
31. C22⋊C4×C383C22semidirect
37. C22×D383D4semidirect
84. C383#534semidirect
91. #121D383semidirect
103. C2×D4C2×D383semidirect
104. C2×D4C2×D383semidirect
107. C22×C4C2×D383semidirect
110. C4⋊C4C2×D383semidirect
116. C22⋊C4C2×D383semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D3832
#271338262
#271338232
#271338152
#271338132
#271338112
#271338092
C2×(C2×D383)⋊C42
#121×C3832
#534383