Finite Group Databasebeta

← #13093063

Subgroups — #13093063

Order 1472.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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×#67288C211yesmaximal, characteristic, complemented
2C22×D92C211yesmaximal, characteristic, complemented
3C4×D4×C23C211yesmaximal, characteristic, complemented
4#10625108C212yesmaximal, complemented
5#10625101C211yesmaximal, characteristic, complemented
6#10625095C211yesmaximal, characteristic, complemented
7#10625065C212yesmaximal, complemented
8#10625055C212yesmaximal, complemented
9C22⋊C4×D23C212yesmaximal, complemented
10#10625046C211yesmaximal, characteristic, complemented
11C4×D92C211yesmaximal, characteristic, complemented
12C23×D23C2212yes—
13C2×D4×C23C2211yescharacteristic
14C22×C4×C23C2211yescharacteristic
15C22×C4×C23C2211yescharacteristic, complemented
16C2×C22⋊D23C2212yescomplemented
17C2×C22⋊D23C2212yescomplemented
18#67288—24no—
19C2×D92—24no—
20C2×D92C2211yescharacteristic
21C2×D92C2212yes—
22C2×D92C2211yescharacteristic
23C2×C4×D23C2212yescomplemented
24C2×C4×D23C2212yescomplemented
25C2×Dic46C2211yescharacteristic, complemented
26C4⋊C4×C23C2211yescharacteristic, complemented
27C22⋊C4×C23C2211yescharacteristic
28C22⋊C4×C23C2211yescharacteristic, complemented
29C42×C23C2211yescharacteristic, complemented
30C22⋊Dic23C2212yes—
31(C2×D23)⋊C4C2212yescomplemented
32(C2×D23)⋊C4C2212yescomplemented
33(C2×D23)⋊C4C2212yescomplemented
34(C2×D23)⋊C4C2212yescomplemented
35C4⋊Dic23C2211yescharacteristic, complemented
36Dic23⋊C4C2212yescomplemented
37C23×C23C2311yescharacteristic
38C23×C23C2311yescharacteristic
39C22×D23—24no—
40C22×D23—24no—
41C22×D23—42no—
42C22×D23C2312yes—
43C22×D23C2312yes—
44D4×C23—22no—
45C2×C4×C23—22no—
46C2×C4×C23—22no—
47C2×C4×C23C2311yescharacteristic
48C2×C4×C23C2311yescharacteristic
49C2×C4×C23C2311yescharacteristic
50C2×C4×C23C2311yescharacteristic
51C2×C4×C23C2311yescharacteristic
52C22⋊D23—24no—
53C22⋊D23—42no—
54C2×Dic23C2312yes—
55C2×Dic23C2312yes—
56D92—24no—
57D92—22no—
58D92D414yescomplemented
59C4×D23—24no—
60C4×D23—42no—
61Dic46—22no—
62C22×C23—21no—
63C22×C23—21no—
64C22×C23—21no—
65C22×C23—21no—
66C22×C23—21no—
67C22×C23#4112yescomplemented
68C22×C23C2411yescharacteristic
69C2×D23—22no—
70C2×D23—22no—
71C2×D23—22no—
72C2×D23—22no—
73C2×D23—22no—
74C2×D23—48no—
75C2×D23C2×D414yes—
76C4×C23—21no—
77C4×C23—21no—
78C4×C23—21no—
79C4×C23—21no—
80C4×C23C2×D412yes—
81Dic23—22no—
82Dic23—22no—
83#546—231nomaximal, Sylow
84C2×C23—22no—
85C2×C23—41no—
86C2×C23C22×D411yescharacteristic
87C2×C23C2×#4111yescharacteristic
88C2×C23H(5,𝔽2)11yescharacteristic
89D23—24no—
90D23—42no—
91C2×#41—231no—
92C22×D4—231no—
93#124—231no—
94#123—232no—
95C22⋊Q8—231no—
96#121—231no—
97#121—232no—
98#120—232no—
99C4×D4—231no—
100C4×D4D2311yescharacteristic, complemented
101C2×C22⋊C4—232no—
102C23#54611yescharacteristic, complemented, Sylow
103C24—232no—
104#41—464no—
105C2×Q8—231no—
106C2×D4—232no—
107C2×D4—232no—
108C2×D4—231no—
109C2×D4—232no—
110C2×D4—231no—
111C2×D4—464no—
112C2×D4C2×D2311yescharacteristic
113C22×C4—232no—
114C22×C4—232no—
115C22×C4C2×D2311yescharacteristic
116C22×C4C2×D2311yescharacteristic, complemented
117C4⋊C4—231no—
118C4⋊C4—232no—
119C4⋊C4C2×D2311yescharacteristic, complemented
120C22⋊C4—232no—
121C22⋊C4—232no—
122C22⋊C4—232no—
123C22⋊C4—232no—
124C22⋊C4—232no—
125C22⋊C4C2×D2311yescharacteristic
126C22⋊C4C2×D2311yescharacteristic, complemented
127C42C2×D2311yescharacteristic, complemented
128C23—232no—
129C23—232no—
130C23—464no—
131C23—464no—
132C23—922no—
133C23C22×D2311yescharacteristic
134C23C22×D2311yescharacteristic
135Q8—462no—
136D4—22no—
137D4—234no—
138D4—464no—
139D4—464no—
140D4—462no—
141D4—922no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—232no—
145C2×C4—232no—
146C2×C4—464no—
147C2×C4—922no—
148C2×C4C22×D2311yescharacteristic
149C2×C4C22×D2311yescharacteristic
150C2×C4C22×D2311yescharacteristic
151C2×C4C22×D2311yescharacteristic
152C2×C4C22×D2311yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—234no—
159C22—462no—
160C22—462no—
161C22—462no—
162C22—462no—
163C22—462no—
164C22—928no—
165C22#6728812yescomplemented
166C22C23×D2311yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—462no—
172C4—462no—
173C4D4×D2312yes—
174C2—22no—
175C2—41no—
176C2—464no—
177C2—922no—
178C2C2×#6728811yescharacteristic
179C2C2×D4×D2311yescharacteristic
180C2#1062516011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC4×D4×C23C2
hypercenterC4×D4D23
hypocenterC23#546
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#67288C2semidirect
2. C22×D92C2semidirect
3. C4×D4×C23C2semidirect
4. #10625108C2semidirect
5. #10625101C2semidirect
6. #10625095C2semidirect
7. #10625065C2semidirect
8. #10625055C2semidirect
9. C22⋊C4×D23C2semidirect
10. #10625046C2semidirect
11. C4×D92C2semidirect
15. C22×C4×C23C22semidirect
16. C2×C22⋊D23C22semidirect
17. C2×C22⋊D23C22semidirect
23. C2×C4×D23C22semidirect
24. C2×C4×D23C22semidirect
25. C2×Dic46C22semidirect
26. C4⋊C4×C23C22semidirect
28. C22⋊C4×C23C22semidirect
29. C42×C23C22semidirect
31. (C2×D23)⋊C4C22semidirect
32. (C2×D23)⋊C4C22semidirect
33. (C2×D23)⋊C4C22semidirect
34. (C2×D23)⋊C4C22semidirect
35. C4⋊Dic23C22semidirect
36. Dic23⋊C4C22semidirect
58. D92D4semidirect
67. C22×C23#41semidirect
100. C4×D4D23semidirect
102. C23#546semidirect
116. C22×C4C2×D23semidirect
119. C4⋊C4C2×D23semidirect
126. C22⋊C4C2×D23semidirect
127. C42C2×D23semidirect
165. C22#67288semidirect

Maximal subgroups

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

subgroupindex
C2×#672882
C22×D922
C4×D4×C232
#106251082
#106251012
#106250952
#106250652
#106250552
C22⋊C4×D232
#106250462
C4×D922
#54623