Finite Group Databasebeta

← #13092983

Subgroups — #13092983

Order 1472.

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×D4×D23C211yesmaximal, characteristic, complemented
2C2×#67288C211yesmaximal, characteristic, complemented
3C23×#121C211yesmaximal, characteristic, complemented
4#10625111C212yesmaximal, complemented
5#10625109C211yesmaximal, characteristic, complemented
6#10625108C212yesmaximal, complemented
7#10625101C211yesmaximal, characteristic, complemented
8#10625066C211yesmaximal, characteristic, complemented
9#10625063C211yesmaximal, characteristic, complemented
10#10625056C212yesmaximal, complemented
11#10625053C212yesmaximal, complemented
12C23×D23C2212yes—
13C2×D4×C23C2211yescharacteristic
14C2×D4×C23C2212yescomplemented
15C22×C4×C23C2211yescharacteristic, complemented
16C2×C22⋊D23C2212yes—
17C2×C22⋊D23C2211yescharacteristic
18C2×C22⋊D23C2211yescharacteristic, complemented
19C2×C22⋊D23C2212yescomplemented
20C2×C22⋊D23C2212yescomplemented
21D4×D23—24no—
22#67288—24no—
23C2×D92C2211yescharacteristic
24C2×D92C2211yescharacteristic
25C2×D92C2212yescomplemented
26C2×C4×D23C2211yescharacteristic
27C2×C4×D23C2211yescharacteristic, complemented
28C2×Dic46C2211yescharacteristic, complemented
29C4⋊C4×C23C2211yescharacteristic, complemented
30C22⋊C4×C23C2212yescomplemented
31C22⋊Dic23C2212yescomplemented
32(C2×D23)⋊C4C2212yes—
33(C2×D23)⋊C4C2212yescomplemented
34(C2×D23)⋊C4C2212yescomplemented
35C4⋊Dic23C2211yescharacteristic, complemented
36C4×Dic23C2212yescomplemented
37C23×C23C2312yes—
38C23×C23C2311yescharacteristic
39C22×D23—24no—
40C22×D23—42no—
41C22×D23—42no—
42C22×D23C2312yes—
43C22×D23C2311yescharacteristic
44C22×D23C2311yescharacteristic
45D4×C23—22no—
46D4×C23—42no—
47C2×C4×C23—22no—
48C2×C4×C23C2312yes—
49C2×C4×C23C2311yescharacteristic
50C2×C4×C23C2311yescharacteristic
51C22⋊D23—22no—
52C22⋊D23—22no—
53C22⋊D23—24no—
54C22⋊D23—42no—
55C22⋊D23—42no—
56C2×Dic23C2312yes—
57C2×Dic23C2311yescharacteristic
58C2×Dic23C2311yescharacteristic
59D92—22no—
60D92—22no—
61D92—42no—
62C4×D23—22no—
63C4×D23D414yescomplemented
64Dic46—22no—
65C22×C23—21no—
66C22×C23—22no—
67C22×C23—21no—
68C22×C23—22no—
69C22×C23—21no—
70C22×C23—22no—
71C22×C23C2411yescharacteristic
72C2×D23—21no—
73C2×D23—21no—
74C2×D23—21no—
75C2×D23—22no—
76C2×D23—21no—
77C2×D23—22no—
78C2×D23—21no—
79C2×D23—22no—
80C2×D23—48no—
81C2×D23C2×D412yes—
82C4×C23—21no—
83C4×C23—22no—
84C4×C23C2×D412yes—
85Dic23—21no—
86Dic23—22no—
87Dic23C2×D412yes—
88#535—231nomaximal, Sylow
89C2×C23—42no—
90C2×C23—41no—
91C2×C23C22×D411yescharacteristic
92C2×C23H(5,𝔽2)11yescharacteristic
93C2×C23H(5,𝔽2)11yescharacteristic
94D23—22no—
95D23—41no—
96D23—42no—
97C2×#41—231no—
98C22×D4—231no—
99#127—232no—
100#124—232no—
101#121—231no—
102#121—231no—
103#121—231no—
104#121D2311yescharacteristic, complemented
105#120—232no—
106#120—232no—
107#117—231no—
108C23#53511yescharacteristic, complemented, Sylow
109C24—232no—
110#41—464no—
111C2×Q8—231no—
112C2×D4—231no—
113C2×D4—232no—
114C2×D4—231no—
115C2×D4—232no—
116C2×D4—232no—
117C2×D4—231no—
118C2×D4—231no—
119C2×D4—232no—
120C2×D4—464no—
121C2×D4C2×D2311yescharacteristic
122C2×D4C2×D2312yescomplemented
123C22×C4—231no—
124C22×C4—231no—
125C22×C4C2×D2311yescharacteristic, complemented
126C4⋊C4—231no—
127C4⋊C4C2×D2311yescharacteristic, complemented
128C22⋊C4—232no—
129C22⋊C4—232no—
130C22⋊C4—232no—
131C22⋊C4—232no—
132C22⋊C4C2×D2312yescomplemented
133C42—232no—
134C23—231no—
135C23—232no—
136C23—231no—
137C23—464no—
138C23—922no—
139C23—922no—
140C23C22×D2312yes—
141C23C22×D2311yescharacteristic
142Q8—462no—
143D4—22no—
144D4—42no—
145D4—462no—
146D4—464no—
147D4—462no—
148D4—462no—
149D4—462no—
150D4—922no—
151D4—922no—
152D4—922no—
153C2×C4—22no—
154C2×C4—231no—
155C2×C4—234no—
156C2×C4—232no—
157C2×C4—231no—
158C2×C4—462no—
159C2×C4C22×D2312yes—
160C2×C4C22×D2311yescharacteristic
161C2×C4C22×D2311yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—232no—
169C22—461no—
170C22—461no—
171C22—461no—
172C22—462no—
173C22—461no—
174C22—462no—
175C22—461no—
176C22—462no—
177C22—928no—
178C22C23×D2311yescharacteristic
179C4—21no—
180C4—22no—
181C4—232no—
182C4—461no—
183C4—462no—
184C4D4×D2312yes—
185C2—42no—
186C2—41no—
187C2—462no—
188C2—922no—
189C2—921no—
190C2C2×D4×D2311yescharacteristic
191C2#1062515511yescharacteristic
192C2#1062516011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC23×#121C2
hypercenter#121D23
hypocenterC23#535
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. C2×#67288C2semidirect
3. C23×#121C2semidirect
4. #10625111C2semidirect
5. #10625109C2semidirect
6. #10625108C2semidirect
7. #10625101C2semidirect
8. #10625066C2semidirect
9. #10625063C2semidirect
10. #10625056C2semidirect
11. #10625053C2semidirect
14. C2×D4×C23C22semidirect
15. C22×C4×C23C22semidirect
18. C2×C22⋊D23C22semidirect
19. C2×C22⋊D23C22semidirect
20. C2×C22⋊D23C22semidirect
25. C2×D92C22semidirect
27. C2×C4×D23C22semidirect
28. C2×Dic46C22semidirect
29. C4⋊C4×C23C22semidirect
30. C22⋊C4×C23C22semidirect
31. C22⋊Dic23C22semidirect
33. (C2×D23)⋊C4C22semidirect
34. (C2×D23)⋊C4C22semidirect
35. C4⋊Dic23C22semidirect
36. C4×Dic23C22semidirect
63. C4×D23D4semidirect
104. #121D23semidirect
108. C23#535semidirect
122. C2×D4C2×D23semidirect
125. C22×C4C2×D23semidirect
127. C4⋊C4C2×D23semidirect
132. 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
C2×#672882
C23×#1212
#106251112
#106251092
#106251082
#106251012
#106250662
#106250632
#106250562
#106250532
#53523