Finite Group Databasebeta

← #13092975

Subgroups — #13092975

Order 1472.

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×D23C212yesmaximal, complemented
2C23×#121C211yesmaximal, characteristic, complemented
3#10625110C212yesmaximal, complemented
4#10625108C212yesmaximal, complemented
5#10625101C211yesmaximal, characteristic, complemented
6C2×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
7#10625065C212yesmaximal, complemented
8#10625054C212yesmaximal, complemented
9#10625053C212yesmaximal, complemented
10C23×D23C2211yescharacteristic
11C23×D23C2212yescomplemented
12C2×D4×C23C2212yescomplemented
13C2×D4×C23C2211yescharacteristic, complemented
14C22×C4×C23C2211yescharacteristic, complemented
15C2×C22⋊D23C2212yes—
16C2×C22⋊D23C2212yescomplemented
17C2×C22⋊D23C2212yescomplemented
18C22×Dic23C2211yescharacteristic, complemented
19D4×D23—28no—
20C2×D92C2212yes—
21C2×D92C2211yescharacteristic, complemented
22C2×C4×D23C2212yescomplemented
23C4⋊C4×C23C2211yescharacteristic, complemented
24C22⋊C4×C23C2212yescomplemented
25C22⋊Dic23C2212yescomplemented
26(C2×D23)⋊C4C2212yescomplemented
27(C2×D23)⋊C4C2212yescomplemented
28(C2×D23)⋊C4C2212yescomplemented
29(C2×D23)⋊C4C2212yescomplemented
30C4⋊Dic23C2211yescharacteristic, complemented
31Dic23⋊C4C2212yescomplemented
32C23×C23C2312yes—
33C23×C23C2311yescharacteristic
34C22×D23—24no—
35C22×D23—41no—
36C22×D23—41no—
37C22×D23—42no—
38C22×D23—42no—
39C22×D23D414yescomplemented
40C22×D23C2312yes—
41C22×D23C2312yes—
42D4×C23—24no—
43D4×C23—41no—
44C2×C4×C23—41no—
45C2×C4×C23C2312yes—
46C2×C4×C23C2311yescharacteristic
47C2×C4×C23C2311yescharacteristic
48C22⋊D23—24no—
49C22⋊D23—24no—
50C22⋊D23—42no—
51C2×Dic23—41no—
52C2×Dic23C2312yes—
53C2×Dic23C2312yes—
54D92—24no—
55D92—41no—
56C4×D23—24no—
57C22×C23—21no—
58C22×C23—21no—
59C22×C23—22no—
60C22×C23—22no—
61C22×C23—22no—
62C22×C23C2×D412yes—
63C22×C23C2411yescharacteristic
64C2×D23—22no—
65C2×D23—22no—
66C2×D23—22no—
67C2×D23—22no—
68C2×D23—22no—
69C2×D23—44no—
70C2×D23—48no—
71C2×D23C2×D414yes—
72C4×C23—22no—
73C4×C23—21no—
74C4×C23—21no—
75Dic23—22no—
76Dic23—22no—
77#534—231nomaximal, Sylow
78C2×C23—22no—
79C2×C23—42no—
80C2×C23C22×D411yescharacteristic
81C2×C23H(5,𝔽2)11yescharacteristic
82C2×C23H(5,𝔽2)11yescharacteristic
83D23—24no—
84D23—42no—
85C22×D4—232no—
86#123—232no—
87#123—232no—
88#121—232no—
89#121—231no—
90#121D2311yescharacteristic, complemented
91#120—232no—
92#120—232no—
93C2×C22⋊C4—231no—
94C23#53411yescharacteristic, complemented, Sylow
95C24—231no—
96C24—232no—
97C2×D4—232no—
98C2×D4—232no—
99C2×D4—232no—
100C2×D4—232no—
101C2×D4—231no—
102C2×D4—468no—
103C2×D4C2×D2312yescomplemented
104C2×D4C2×D2311yescharacteristic, complemented
105C22×C4—231no—
106C22×C4—232no—
107C22×C4C2×D2311yescharacteristic, complemented
108C4⋊C4—232no—
109C4⋊C4—231no—
110C4⋊C4C2×D2311yescharacteristic, complemented
111C22⋊C4—232no—
112C22⋊C4—232no—
113C22⋊C4—232no—
114C22⋊C4—232no—
115C22⋊C4—232no—
116C22⋊C4C2×D2312yescomplemented
117C23—232no—
118C23—234no—
119C23—232no—
120C23—464no—
121C23—921no—
122C23—921no—
123C23—922no—
124C23—922no—
125C23C22×D2312yes—
126C23C22×D2311yescharacteristic
127D4—24no—
128D4—41no—
129D4—464no—
130D4—464no—
131D4—464no—
132D4—921no—
133D4—922no—
134C2×C4—41no—
135C2×C4—232no—
136C2×C4—232no—
137C2×C4—464no—
138C2×C4—921no—
139C2×C4C22×D2311yescharacteristic
140C2×C4C22×D2311yescharacteristic
141C2×C4C22×D2312yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—234no—
148C22—462no—
149C22—462no—
150C22—462no—
151C22—462no—
152C22—462no—
153C22—924no—
154C22—928no—
155C22D4×D2312yes—
156C22C23×D2311yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—462no—
161C4—462no—
162C2—22no—
163C2—42no—
164C2—464no—
165C2—922no—
166C2C2×D4×D2311yescharacteristic
167C2#1062515511yescharacteristic
168C2#1062516011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC23×#121C2
hypercenter#121D23
hypocenterC23#534
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D23C2semidirect
2. C23×#121C2semidirect
3. #10625110C2semidirect
4. #10625108C2semidirect
5. #10625101C2semidirect
6. C2×(C2×D23)⋊C4C2semidirect
7. #10625065C2semidirect
8. #10625054C2semidirect
9. #10625053C2semidirect
11. C23×D23C22semidirect
12. C2×D4×C23C22semidirect
13. C2×D4×C23C22semidirect
14. C22×C4×C23C22semidirect
16. C2×C22⋊D23C22semidirect
17. C2×C22⋊D23C22semidirect
18. C22×Dic23C22semidirect
21. C2×D92C22semidirect
22. C2×C4×D23C22semidirect
23. C4⋊C4×C23C22semidirect
24. C22⋊C4×C23C22semidirect
25. C22⋊Dic23C22semidirect
26. (C2×D23)⋊C4C22semidirect
27. (C2×D23)⋊C4C22semidirect
28. (C2×D23)⋊C4C22semidirect
29. (C2×D23)⋊C4C22semidirect
30. C4⋊Dic23C22semidirect
31. Dic23⋊C4C22semidirect
39. C22×D23D4semidirect
90. #121D23semidirect
94. C23#534semidirect
103. C2×D4C2×D23semidirect
104. C2×D4C2×D23semidirect
107. C22×C4C2×D23semidirect
110. C4⋊C4C2×D23semidirect
116. C22⋊C4C2×D23semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D232
C23×#1212
#106251102
#106251082
#106251012
C2×(C2×D23)⋊C42
#106250652
#106250542
#106250532
#53423