Finite Group Databasebeta

← #13092978

Subgroups — #13092978

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×D23C211yesmaximal, characteristic, complemented
2C22×D92C211yesmaximal, characteristic, complemented
3C23×#123C211yesmaximal, characteristic, complemented
4#10625108C211yesmaximal, characteristic, complemented
5#10625100C211yesmaximal, characteristic, complemented
6#10625066C212yesmaximal, complemented
7#10625065C212yesmaximal, complemented
8#10625055C212yesmaximal, complemented
9#10625053C212yesmaximal, complemented
10#10625053C211yesmaximal, characteristic, complemented
11C22⋊C4×D23C211yesmaximal, characteristic, complemented
12C23×D23C2211yescharacteristic
13C23×D23C2211yescharacteristic, complemented
14C23×D23C2211yescharacteristic, complemented
15C2×D4×C23C2211yescharacteristic
16C22×C4×C23C2211yescharacteristic, complemented
17C2×C22⋊D23C2211yescharacteristic
18C2×C22⋊D23C2211yescharacteristic, complemented
19C2×C22⋊D23C2212yescomplemented
20D4×D23—24no—
21C2×D92—24no—
22C2×D92C2212yes—
23C2×D92C2212yescomplemented
24C2×D92C2211yescharacteristic, complemented
25C2×D92C2212yescomplemented
26C2×C4×D23C2211yescharacteristic, complemented
27C2×C4×D23C2212yescomplemented
28C4⋊C4×C23C2212yescomplemented
29C22⋊C4×C23C2211yescharacteristic, complemented
30C22⋊C4×C23C2212yescomplemented
31C22⋊Dic23C2211yescharacteristic, complemented
32(C2×D23)⋊C4C2212yescomplemented
33(C2×D23)⋊C4C2212yescomplemented
34(C2×D23)⋊C4C2212yescomplemented
35(C2×D23)⋊C4C2212yescomplemented
36Dic23⋊C4C2212yescomplemented
37C23×C23C2311yescharacteristic
38C23×C23C2311yescharacteristic
39C22×D23—22no—
40C22×D23—22no—
41C22×D23—42no—
42C22×D23—42no—
43C22×D23—42no—
44C22×D23D414yescomplemented
45C22×D23C2312yes—
46C22×D23C2311yescharacteristic
47C22×D23C2311yescharacteristic
48C22×D23C2311yescharacteristic
49D4×C23—22no—
50C2×C4×C23—22no—
51C2×C4×C23C2312yes—
52C2×C4×C23C2312yes—
53C2×C4×C23C2311yescharacteristic
54C22⋊D23—22no—
55C22⋊D23—22no—
56C22⋊D23—42no—
57C2×Dic23C2311yescharacteristic
58C2×Dic23C2312yes—
59D92—24no—
60D92—24no—
61D92—22no—
62D92—42no—
63C4×D23—22no—
64C4×D23—42no—
65C22×C23—22no—
66C22×C23—21no—
67C22×C23—22no—
68C22×C23C2×D412yes—
69C22×C23C2411yescharacteristic
70C2×D23—22no—
71C2×D23—22no—
72C2×D23—22no—
73C2×D23—21no—
74C2×D23—22no—
75C2×D23—22no—
76C2×D23—22no—
77C2×D23—44no—
78C2×D23—44no—
79C2×D23—44no—
80C2×D23C2×D412yes—
81C2×D23C2×D412yes—
82C4×C23—21no—
83C4×C23—22no—
84C4×C23—22no—
85Dic23—21no—
86Dic23—22no—
87#534—231nomaximal, Sylow
88C2×C23—22no—
89C2×C23—41no—
90C2×C23C22×D411yescharacteristic
91C2×C23H(5,𝔽2)12yes—
92D23—22no—
93D23—22no—
94D23—42no—
95D23—41no—
96C22×D4—231no—
97C22×D4—231no—
98#123—231no—
99#123—232no—
100#123D2311yescharacteristic, complemented
101#121—232no—
102#121—232no—
103#120—231no—
104#120—232no—
105#120—231no—
106C2×C22⋊C4—231no—
107C23#53411yescharacteristic, complemented, Sylow
108C24—231no—
109C24—231no—
110C24—231no—
111C2×D4—231no—
112C2×D4—231no—
113C2×D4—232no—
114C2×D4—232no—
115C2×D4—231no—
116C2×D4—232no—
117C2×D4—232no—
118C2×D4—464no—
119C2×D4—464no—
120C2×D4C2×D2311yescharacteristic
121C22×C4—231no—
122C22×C4—232no—
123C22×C4C2×D2311yescharacteristic, complemented
124C4⋊C4—232no—
125C4⋊C4C2×D2312yescomplemented
126C22⋊C4—231no—
127C22⋊C4—232no—
128C22⋊C4—232no—
129C22⋊C4—232no—
130C22⋊C4—232no—
131C22⋊C4C2×D2311yescharacteristic, complemented
132C22⋊C4C2×D2312yescomplemented
133C23—231no—
134C23—231no—
135C23—234no—
136C23—231no—
137C23—232no—
138C23—462no—
139C23—462no—
140C23—922no—
141C23—922no—
142C23—922no—
143C23C22×D2311yescharacteristic
144C23C22×D2311yescharacteristic
145D4—22no—
146D4—464no—
147D4—464no—
148D4—462no—
149D4—462no—
150D4—462no—
151D4—922no—
152D4—922no—
153C2×C4—22no—
154C2×C4—232no—
155C2×C4—231no—
156C2×C4—462no—
157C2×C4—922no—
158C2×C4C22×D2312yes—
159C2×C4C22×D2311yescharacteristic
160C2×C4C22×D2312yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—232no—
165C22—232no—
166C22—462no—
167C22—462no—
168C22—462no—
169C22—461no—
170C22—462no—
171C22—462no—
172C22—462no—
173C22—924no—
174C22—924no—
175C22—924no—
176C22D4×D2312yes—
177C22C23×D2311yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—461no—
182C4—462no—
183C2—22no—
184C2—41no—
185C2—462no—
186C2—462no—
187C2—922no—
188C2—921no—
189C2C2×D4×D2311yescharacteristic
190C2#1062516012yes—
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC23×#123C2
hypercenter#123D23
hypocenterC23#534
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×D4×D23C2semidirect
2. C22×D92C2semidirect
3. C23×#123C2semidirect
4. #10625108C2semidirect
5. #10625100C2semidirect
6. #10625066C2semidirect
7. #10625065C2semidirect
8. #10625055C2semidirect
9. #10625053C2semidirect
10. #10625053C2semidirect
11. C22⋊C4×D23C2semidirect
13. C23×D23C22semidirect
14. C23×D23C22semidirect
16. C22×C4×C23C22semidirect
18. C2×C22⋊D23C22semidirect
19. C2×C22⋊D23C22semidirect
23. C2×D92C22semidirect
24. C2×D92C22semidirect
25. C2×D92C22semidirect
26. C2×C4×D23C22semidirect
27. C2×C4×D23C22semidirect
28. C4⋊C4×C23C22semidirect
29. C22⋊C4×C23C22semidirect
30. C22⋊C4×C23C22semidirect
31. C22⋊Dic23C22semidirect
32. (C2×D23)⋊C4C22semidirect
33. (C2×D23)⋊C4C22semidirect
34. (C2×D23)⋊C4C22semidirect
35. (C2×D23)⋊C4C22semidirect
36. Dic23⋊C4C22semidirect
44. C22×D23D4semidirect
100. #123D23semidirect
107. C23#534semidirect
123. C22×C4C2×D23semidirect
125. C4⋊C4C2×D23semidirect
131. C22⋊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
C22×D922
C23×#1232
#106251082
#106251002
#106250662
#106250652
#106250552
#106250532
C22⋊C4×D232
#53423