Finite Group Databasebeta

← #37588859

Subgroups — #37588859

Order 24512.

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

normal subgroups only

This group has 330 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×#20259456C211yesmaximal, characteristic, complemented
2C22×C4×D383C211yesmaximal, characteristic, complemented
3#27133824C211yesmaximal, characteristic, complemented
4#27133819C212yesmaximal, complemented
5#27133814C212yesmaximal, complemented
6#27133811C211yesmaximal, characteristic, complemented
7#27133809C211yesmaximal, characteristic, complemented
8#27133803C212yesmaximal, complemented
9(C22⋊D383)⋊C4C212yesmaximal, complemented
10#27133797C211yesmaximal, characteristic, complemented
11#123×C383C211yesmaximal, characteristic, complemented
12C23×D383C2211yescharacteristic
13#20259456—24no—
14C2×Dic766C2211yescharacteristic, complemented
15C2×D1532C2212yes—
16C2×C22⋊D383C2212yes—
17C2×C22⋊D383C2211yescharacteristic
18C2×C22⋊D383C2211yescharacteristic, complemented
19C22×Dic383C2211yescharacteristic
20C22×Dic383C2211yescharacteristic, complemented
21C2×C4×D383—24no—
22C2×C4×D383C2212yes—
23C2×C4×D383C2212yes—
24C2×C4×D383C2211yescharacteristic, complemented
25Dic383⋊C4C2212yescomplemented
26Dic383⋊C4C2212yescomplemented
27C22⋊Dic383C2211yescharacteristic
28(C2×D383)⋊C4C2212yes—
29(C2×D383)⋊C4C2212yes—
30(C2×D383)⋊C4C2212yescomplemented
31C4×Dic383C2212yescomplemented
32C2×D4×C383C2211yescharacteristic
33C22×C4×C383C2211yescharacteristic
34C4⋊C4×C383C2212yescomplemented
35C22⋊C4×C383C2211yescharacteristic
36C22⋊C4×C383C2212yescomplemented
37C22×D383—22no—
38C22×D383—24no—
39C22×D383C2311yescharacteristic
40C22×D383C2312yes—
41Dic766—22no—
42D1532—24no—
43C22⋊D383—22no—
44C22⋊D383—24no—
45C22⋊D383—22no—
46C2×Dic383—22no—
47C2×Dic383D414yescomplemented
48C2×Dic383C2312yes—
49C2×Dic383C2311yescharacteristic
50C2×Dic383C2311yescharacteristic
51C2×Dic383C2311yescharacteristic
52C4×D383—24no—
53C4×D383—24no—
54C4×D383—22no—
55C23×C383C2311yescharacteristic
56C23×C383C2311yescharacteristic
57D4×C383—22no—
58C2×C4×C383—22no—
59C2×C4×C383C2312yes—
60C2×C4×C383C2312yes—
61C2×C4×C383C2311yescharacteristic
62C22×C383—22no—
63C22×C383—21no—
64C22×C383—22no—
65C22×C383C2×D412yes—
66C22×C383C2411yescharacteristic
67C2×D383—28no—
68C2×D383—22no—
69C2×D383—22no—
70C2×D383—21no—
71C2×D383—22no—
72C2×D383#4114yescomplemented
73C4×C383—22no—
74C4×C383—21no—
75C4×C383—22no—
76Dic383—21no—
77Dic383—22no—
78Dic383C2×D412yes—
79Dic383C2×D412yes—
80C2×C383—22no—
81C2×C383—41no—
82C2×C383C22×D411yescharacteristic
83C2×C383C2×#4112yes—
84D383—24no—
85D383—41no—
86C383#52511yescharacteristic, complemented, Sylow
87#525—3831nomaximal, Sylow
88C2×#41—3831no—
89C23×C4—3831no—
90#123—3831no—
91#123D38311yescharacteristic, complemented
92C22⋊Q8—3832no—
93#121—3832no—
94#120—3831no—
95#120—3831no—
96C4×D4—3832no—
97C4×D4—3832no—
98#117—3831no—
99C24—3831no—
100#41—7664no—
101C2×Q8—3831no—
102C2×D4—3832no—
103C2×D4—3831no—
104C2×D4—3831no—
105C2×D4—3832no—
106C2×D4C2×D38311yescharacteristic
107C22×C4—3831no—
108C22×C4—3831no—
109C22×C4—3832no—
110C22×C4—3831no—
111C22×C4—3832no—
112C22×C4—7664no—
113C22×C4C2×D38311yescharacteristic
114C4⋊C4—3832no—
115C4⋊C4—3832no—
116C4⋊C4C2×D38312yescomplemented
117C22⋊C4—3831no—
118C22⋊C4—3832no—
119C22⋊C4—3832no—
120C22⋊C4—3832no—
121C22⋊C4C2×D38311yescharacteristic
122C22⋊C4C2×D38312yescomplemented
123C42—3832no—
124C23—3832no—
125C23—3831no—
126C23—7664no—
127C23—7662no—
128C23C22×D38311yescharacteristic
129C23C22×D38311yescharacteristic
130Q8—7662no—
131D4—22no—
132D4—7664no—
133D4—7662no—
134D4—7664no—
135D4—7662no—
136C2×C4—22no—
137C2×C4—3834no—
138C2×C4—3831no—
139C2×C4—3831no—
140C2×C4—3832no—
141C2×C4—3831no—
142C2×C4—7664no—
143C2×C4—7664no—
144C2×C4—7662no—
145C2×C4—7662no—
146C2×C4C22×D38312yes—
147C2×C4C22×D38311yescharacteristic
148C2×C4C22×D38312yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—3834no—
153C22—7668no—
154C22—7661no—
155C22—7662no—
156C22—7662no—
157C22—7662no—
158C22D4×D38312yes—
159C22C23×D38311yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—3832no—
164C4—3832no—
165C4—7661no—
166C4—7662no—
167C2—22no—
168C2—41no—
169C2—15321no—
170C2—7664no—
171C2C2×D4×D38311yescharacteristic
172C2#41×D38312yes—
subgroupG/H
center, FrattiniC22C23×D383
commutator, socle, cosocleC22×C383C24
Fitting#123×C383C2
hypercenter#123D383
hypocenterC383#525
LCSG ▷ C22×C383 ▷ C383
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#20259456C2semidirect
2. C22×C4×D383C2semidirect
3. #27133824C2semidirect
4. #27133819C2semidirect
5. #27133814C2semidirect
6. #27133811C2semidirect
7. #27133809C2semidirect
8. #27133803C2semidirect
9. (C22⋊D383)⋊C4C2semidirect
10. #27133797C2semidirect
11. #123×C383C2semidirect
14. C2×Dic766C22semidirect
18. C2×C22⋊D383C22semidirect
20. C22×Dic383C22semidirect
24. C2×C4×D383C22semidirect
25. Dic383⋊C4C22semidirect
26. Dic383⋊C4C22semidirect
30. (C2×D383)⋊C4C22semidirect
31. C4×Dic383C22semidirect
34. C4⋊C4×C383C22semidirect
36. C22⋊C4×C383C22semidirect
47. C2×Dic383D4semidirect
72. C2×D383#41semidirect
86. C383#525semidirect
91. #123D383semidirect
116. C4⋊C4C2×D383semidirect
122. C22⋊C4C2×D383semidirect

Maximal subgroups

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

subgroupindex
C2×#202594562
C22×C4×D3832
#271338242
#271338192
#271338142
#271338112
#271338092
#271338032
(C22⋊D383)⋊C42
#271337972
#123×C3832
#525383