Finite Group Databasebeta

← #45690763

Subgroups — #45690763

Order 33472.

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×D523C212yesmaximal, complemented
2#30660358C212yesmaximal, complemented
3#30660355C212yesmaximal, complemented
4#30660347C211yesmaximal, characteristic, complemented
5#30660345C212yesmaximal, complemented
6#30660343C212yesmaximal, complemented
7#30660341C212yesmaximal, complemented
8C2×(C2×D523)⋊C4C211yesmaximal, characteristic, complemented
9#121×C523C211yesmaximal, characteristic, complemented
10C23×D523C2211yescharacteristic
11C23×D523C2212yescomplemented
12C2×D2092C2212yes—
13C2×D2092C2211yescharacteristic, complemented
14C2×C22⋊D523C2212yes—
15C2×C22⋊D523C2212yescomplemented
16C2×C22⋊D523C2212yescomplemented
17D4×D523—28no—
18C22×Dic523C2211yescharacteristic, complemented
19C2×C4×D523C2212yescomplemented
20C4⋊Dic523C2211yescharacteristic, complemented
21Dic523⋊C4C2212yescomplemented
22C22⋊Dic523C2212yescomplemented
23(C2×D523)⋊C4C2212yescomplemented
24(C2×D523)⋊C4C2212yescomplemented
25(C2×D523)⋊C4C2212yescomplemented
26(C2×D523)⋊C4C2212yescomplemented
27C2×D4×C523C2212yescomplemented
28C2×D4×C523C2211yescharacteristic, complemented
29C22×C4×C523C2211yescharacteristic, complemented
30C4⋊C4×C523C2211yescharacteristic, complemented
31C22⋊C4×C523C2212yescomplemented
32C22×D523—24no—
33C22×D523—41no—
34C22×D523—41no—
35C22×D523—42no—
36C22×D523—42no—
37C22×D523D414yescomplemented
38C22×D523C2312yes—
39C22×D523C2312yes—
40D2092—24no—
41D2092—41no—
42C22⋊D523—24no—
43C22⋊D523—24no—
44C22⋊D523—42no—
45C2×Dic523—41no—
46C2×Dic523C2312yes—
47C2×Dic523C2312yes—
48C4×D523—24no—
49C23×C523C2312yes—
50C23×C523C2311yescharacteristic
51D4×C523—24no—
52D4×C523—41no—
53C2×C4×C523—41no—
54C2×C4×C523C2311yescharacteristic
55C2×C4×C523C2312yes—
56C2×C4×C523C2311yescharacteristic
57C22×C523—21no—
58C22×C523—21no—
59C22×C523—22no—
60C22×C523—22no—
61C22×C523—22no—
62C22×C523C2×D412yes—
63C22×C523C2411yescharacteristic
64C2×D523—22no—
65C2×D523—22no—
66C2×D523—22no—
67C2×D523—22no—
68C2×D523—22no—
69C2×D523—44no—
70C2×D523—48no—
71C2×D523C2×D414yes—
72C4×C523—22no—
73C4×C523—21no—
74C4×C523—21no—
75Dic523—22no—
76Dic523—22no—
77C2×C523—22no—
78C2×C523—42no—
79C2×C523C22×D411yescharacteristic
80C2×C523H(5,𝔽2)11yescharacteristic
81C2×C523H(5,𝔽2)11yescharacteristic
82D523—24no—
83D523—42no—
84C523#53411yescharacteristic, complemented, Sylow
85#534—5231nomaximal, Sylow
86C22×D4—5232no—
87#123—5232no—
88#123—5232no—
89#121—5232no—
90#121—5231no—
91#121D52311yescharacteristic, complemented
92#120—5232no—
93#120—5232no—
94C2×C22⋊C4—5231no—
95C24—5231no—
96C24—5232no—
97C2×D4—5232no—
98C2×D4—5232no—
99C2×D4—5232no—
100C2×D4—5232no—
101C2×D4—5231no—
102C2×D4—10468no—
103C2×D4C2×D52312yescomplemented
104C2×D4C2×D52311yescharacteristic, complemented
105C22×C4—5231no—
106C22×C4—5232no—
107C22×C4C2×D52311yescharacteristic, complemented
108C4⋊C4—5232no—
109C4⋊C4—5231no—
110C4⋊C4C2×D52311yescharacteristic, complemented
111C22⋊C4—5232no—
112C22⋊C4—5232no—
113C22⋊C4—5232no—
114C22⋊C4—5232no—
115C22⋊C4—5232no—
116C22⋊C4C2×D52312yescomplemented
117C23—5232no—
118C23—5234no—
119C23—5232no—
120C23—10464no—
121C23—20921no—
122C23—20921no—
123C23—20922no—
124C23—20922no—
125C23C22×D52312yes—
126C23C22×D52311yescharacteristic
127D4—24no—
128D4—41no—
129D4—10464no—
130D4—10464no—
131D4—10464no—
132D4—20921no—
133D4—20922no—
134C2×C4—41no—
135C2×C4—5232no—
136C2×C4—5232no—
137C2×C4—10464no—
138C2×C4—20921no—
139C2×C4C22×D52311yescharacteristic
140C2×C4C22×D52311yescharacteristic
141C2×C4C22×D52312yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—5234no—
148C22—10462no—
149C22—10462no—
150C22—10462no—
151C22—10462no—
152C22—10462no—
153C22—20924no—
154C22—20928no—
155C22D4×D52312yes—
156C22C23×D52311yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—10462no—
161C4—10462no—
162C2—22no—
163C2—42no—
164C2—10464no—
165C2—20922no—
166C2C2×D4×D52311yescharacteristic
167C2#3066041811yescharacteristic
168C2#3066041911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D523
commutator, socle, cosocleC22×C523C24
Fitting#121×C523C2
hypercenter#121D523
hypocenterC523#534
LCSG ▷ C22×C523 ▷ C523
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D523C2semidirect
2. #30660358C2semidirect
3. #30660355C2semidirect
4. #30660347C2semidirect
5. #30660345C2semidirect
6. #30660343C2semidirect
7. #30660341C2semidirect
8. C2×(C2×D523)⋊C4C2semidirect
9. #121×C523C2semidirect
11. C23×D523C22semidirect
13. C2×D2092C22semidirect
15. C2×C22⋊D523C22semidirect
16. C2×C22⋊D523C22semidirect
18. C22×Dic523C22semidirect
19. C2×C4×D523C22semidirect
20. C4⋊Dic523C22semidirect
21. Dic523⋊C4C22semidirect
22. C22⋊Dic523C22semidirect
23. (C2×D523)⋊C4C22semidirect
24. (C2×D523)⋊C4C22semidirect
25. (C2×D523)⋊C4C22semidirect
26. (C2×D523)⋊C4C22semidirect
27. C2×D4×C523C22semidirect
28. C2×D4×C523C22semidirect
29. C22×C4×C523C22semidirect
30. C4⋊C4×C523C22semidirect
31. C22⋊C4×C523C22semidirect
37. C22×D523D4semidirect
84. C523#534semidirect
91. #121D523semidirect
103. C2×D4C2×D523semidirect
104. C2×D4C2×D523semidirect
107. C22×C4C2×D523semidirect
110. C4⋊C4C2×D523semidirect
116. C22⋊C4C2×D523semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D5232
#306603582
#306603552
#306603472
#306603452
#306603432
#306603412
C2×(C2×D523)⋊C42
#121×C5232
#534523