Finite Group Databasebeta

← #13093055

Subgroups — #13093055

Order 1472.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×#41×C23C211yesmaximal, characteristic, complemented
2C2×D4×D23C211yesmaximal, characteristic, complemented
3#10625118C211yesmaximal, characteristic, complemented
4#10625117C211yesmaximal, characteristic, complemented
5#10625110C212yesmaximal, complemented
6#10625108C212yesmaximal, complemented
7D4×Dic23C211yesmaximal, characteristic, complemented
8#10625101C211yesmaximal, characteristic, complemented
9#10625100C212yesmaximal, complemented
10C4×C22⋊D23C211yesmaximal, characteristic, complemented
11C2×(C2×D23)⋊C4C212yesmaximal, complemented
12C23×D23C2212yes—
13#41×C23—24no—
14C2×Q8×C23C2211yescharacteristic, complemented
15C2×D4×C23C2211yescharacteristic
16C2×D4×C23C2212yescomplemented
17C22×C4×C23C2212yescomplemented
18C22×C4×C23C2211yescharacteristic, complemented
19C2×C22⋊D23C2211yescharacteristic
20C2×C22⋊D23C2212yes—
21C2×C22⋊D23C2212yescomplemented
22C22×Dic23C2212yescomplemented
23D4×D23—24no—
24C2×D92C2211yescharacteristic
25C2×C4×D23C2211yescharacteristic
26C22⋊Dic23C2211yescharacteristic, complemented
27C22⋊Dic23C2212yescomplemented
28(C2×D23)⋊C4C2211yescharacteristic
29(C2×D23)⋊C4C2212yes—
30(C2×D23)⋊C4C2212yescomplemented
31(C2×D23)⋊C4C2212yescomplemented
32(C2×D23)⋊C4C2212yescomplemented
33C4⋊Dic23C2211yescharacteristic, complemented
34Dic23⋊C4C2211yescharacteristic, complemented
35Dic23⋊C4C2212yescomplemented
36C4×Dic23C2211yescharacteristic, complemented
37C23×C23C2311yescharacteristic
38C23×C23C2312yes—
39C22×D23—24no—
40C22×D23—24no—
41C22×D23—42no—
42C22×D23C2312yes—
43C22×D23C2311yescharacteristic
44Q8×C23—22no—
45D4×C23—24no—
46D4×C23D414yescomplemented
47C2×C4×C23—24no—
48C2×C4×C23—22no—
49C2×C4×C23C2311yescharacteristic
50C2×C4×C23C2312yes—
51C2×C4×C23C2311yescharacteristic
52C22⋊D23—24no—
53C22⋊D23—22no—
54C22⋊D23—42no—
55C2×Dic23—42no—
56C2×Dic23C2311yescharacteristic
57C2×Dic23C2311yescharacteristic
58C2×Dic23C2311yescharacteristic
59C2×Dic23C2312yes—
60D92—22no—
61C4×D23—22no—
62C22×C23—22no—
63C22×C23—22no—
64C22×C23—21no—
65C22×C23—21no—
66C22×C23—21no—
67C22×C23C2×D414yes—
68C22×C23C2411yescharacteristic
69C2×D23—21no—
70C2×D23—21no—
71C2×D23—22no—
72C2×D23—22no—
73C2×D23—22no—
74C2×D23—48no—
75C2×D23#4112yescomplemented
76C4×C23—21no—
77C4×C23—22no—
78C4×C23C2×D412yes—
79Dic23—21no—
80Dic23—21no—
81Dic23—21no—
82Dic23—22no—
83#546—231nomaximal, Sylow
84C2×C23—24no—
85C2×C23—41no—
86C2×C23C22×D411yescharacteristic
87C2×C23C2×#4111yescharacteristic
88C2×C23H(5,𝔽2)11yescharacteristic
89D23—22no—
90D23—42no—
91C2×#41D2311yescharacteristic, complemented
92C22×D4—231no—
93#124—231no—
94#123—232no—
95C22⋊Q8—231no—
96#121—232no—
97#121—231no—
98#120—232no—
99C4×D4—231no—
100C4×D4—231no—
101C2×C22⋊C4—232no—
102C23#54611yescharacteristic, complemented, Sylow
103C24—232no—
104#41—24no—
105C2×Q8C2×D2311yescharacteristic, complemented
106C2×D4—231no—
107C2×D4—232no—
108C2×D4—232no—
109C2×D4—231no—
110C2×D4—464no—
111C2×D4C2×D2311yescharacteristic
112C2×D4C2×D2312yescomplemented
113C22×C4—232no—
114C22×C4—231no—
115C22×C4C2×D2312yescomplemented
116C22×C4C2×D2311yescharacteristic, complemented
117C4⋊C4—231no—
118C4⋊C4—231no—
119C4⋊C4—232no—
120C22⋊C4—232no—
121C22⋊C4—231no—
122C22⋊C4—231no—
123C22⋊C4—232no—
124C22⋊C4—232no—
125C22⋊C4—232no—
126C22⋊C4—232no—
127C42—231no—
128C23—231no—
129C23—232no—
130C23—464no—
131C23—464no—
132C23—922no—
133C23C22×D2311yescharacteristic
134C23C22×D2312yes—
135Q8—22no—
136D4—24no—
137D4—462no—
138D4—464no—
139D4—462no—
140D4—922no—
141D4C22⋊D2314yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—231no—
145C2×C4—231no—
146C2×C4—232no—
147C2×C4—231no—
148C2×C4—462no—
149C2×C4—922no—
150C2×C4C22×D2311yescharacteristic
151C2×C4C22×D2312yes—
152C2×C4C22×D2311yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—232no—
159C22—461no—
160C22—461no—
161C22—462no—
162C22—462no—
163C22—462no—
164C22—928no—
165C22C2×C22⋊D2314yes—
166C22C23×D2311yescharacteristic
167C4—21no—
168C4—22no—
169C4—461no—
170C4—461no—
171C4—462no—
172C4—461no—
173C4C2×C22⋊D2312yes—
174C2—24no—
175C2—41no—
176C2—462no—
177C2—922no—
178C2#41×D2311yescharacteristic
179C2#1062516011yescharacteristic
180C2C22×C22⋊D2311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC2×#41×C23C2
hypercenterC2×#41D23
hypocenterC23#546
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C23C2semidirect
2. C2×D4×D23C2semidirect
3. #10625118C2semidirect
4. #10625117C2semidirect
5. #10625110C2semidirect
6. #10625108C2semidirect
7. D4×Dic23C2semidirect
8. #10625101C2semidirect
9. #10625100C2semidirect
10. C4×C22⋊D23C2semidirect
11. C2×(C2×D23)⋊C4C2semidirect
14. C2×Q8×C23C22semidirect
16. C2×D4×C23C22semidirect
17. C22×C4×C23C22semidirect
18. C22×C4×C23C22semidirect
21. C2×C22⋊D23C22semidirect
22. C22×Dic23C22semidirect
26. C22⋊Dic23C22semidirect
27. C22⋊Dic23C22semidirect
30. (C2×D23)⋊C4C22semidirect
31. (C2×D23)⋊C4C22semidirect
32. (C2×D23)⋊C4C22semidirect
33. C4⋊Dic23C22semidirect
34. Dic23⋊C4C22semidirect
35. Dic23⋊C4C22semidirect
36. C4×Dic23C22semidirect
46. D4×C23D4semidirect
75. C2×D23#41semidirect
91. C2×#41D23semidirect
102. C23#546semidirect
105. C2×Q8C2×D23semidirect
112. C2×D4C2×D23semidirect
115. C22×C4C2×D23semidirect
116. C22×C4C2×D23semidirect
141. D4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C232
C2×D4×D232
#106251182
#106251172
#106251102
#106251082
D4×Dic232
#106251012
#106251002
C4×C22⋊D232
C2×(C2×D23)⋊C42
#54623