Finite Group Databasebeta

← #28417073

Subgroups — #28417073

Order 14912.

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×D4×D233C211yesmaximal, characteristic, complemented
2#21418524C211yesmaximal, characteristic, complemented
3#21418518C212yesmaximal, complemented
4#21418511C211yesmaximal, characteristic, complemented
5#21418509C211yesmaximal, characteristic, complemented
6#21418507C212yesmaximal, complemented
7#21418503C212yesmaximal, complemented
8D4×Dic233C211yesmaximal, characteristic, complemented
9C4×C22⋊D233C211yesmaximal, characteristic, complemented
10C2×#16836571C212yesmaximal, complemented
11C2×#41×C233C211yesmaximal, characteristic, complemented
12C23×D233C2212yes—
13C2×D932C2211yescharacteristic
14C2×C22⋊D233C2211yescharacteristic
15C2×C22⋊D233C2212yes—
16C2×C22⋊D233C2212yescomplemented
17D4×D233—24no—
18C22×Dic233C2212yescomplemented
19C2×C4×D233C2211yescharacteristic
20C4⋊Dic233C2211yescharacteristic, complemented
21#16836573C2211yescharacteristic, complemented
22#16836573C2212yescomplemented
23C22⋊Dic233C2211yescharacteristic, complemented
24C22⋊Dic233C2212yescomplemented
25#16836571C2211yescharacteristic
26#16836571C2212yes—
27#16836571C2212yescomplemented
28#16836571C2212yescomplemented
29#16836571C2212yescomplemented
30C4×Dic233C2211yescharacteristic, complemented
31#41×C233—24no—
32C2×Q8×C233C2211yescharacteristic, complemented
33C2×D4×C233C2211yescharacteristic
34C2×D4×C233C2212yescomplemented
35C22×C4×C233C2211yescharacteristic, complemented
36C22×C4×C233C2212yescomplemented
37C22×D233—24no—
38C22×D233—24no—
39C22×D233—42no—
40C22×D233C2312yes—
41C22×D233C2311yescharacteristic
42D932—22no—
43C22⋊D233—24no—
44C22⋊D233—22no—
45C22⋊D233—42no—
46C2×Dic233—42no—
47C2×Dic233C2311yescharacteristic
48C2×Dic233C2311yescharacteristic
49C2×Dic233C2312yes—
50C2×Dic233C2311yescharacteristic
51C4×D233—22no—
52C23×C233C2311yescharacteristic
53C23×C233C2312yes—
54Q8×C233—22no—
55D4×C233—24no—
56D4×C233D414yescomplemented
57C2×C4×C233—24no—
58C2×C4×C233—22no—
59C2×C4×C233C2311yescharacteristic
60C2×C4×C233C2312yes—
61C2×C4×C233C2311yescharacteristic
62C22×C233—22no—
63C22×C233—22no—
64C22×C233—21no—
65C22×C233—21no—
66C22×C233—21no—
67C22×C233C2×D414yes—
68C22×C233C2411yescharacteristic
69C2×D233—21no—
70C2×D233—21no—
71C2×D233—22no—
72C2×D233—22no—
73C2×D233—22no—
74C2×D233—48no—
75C2×D233#4112yescomplemented
76C4×C233—21no—
77C4×C233—22no—
78C4×C233C2×D412yes—
79Dic233—21no—
80Dic233—21no—
81Dic233—21no—
82Dic233—22no—
83C2×C233—24no—
84C2×C233—41no—
85C2×C233C22×D411yescharacteristic
86C2×C233C2×#4111yescharacteristic
87C2×C233H(5,𝔽2)11yescharacteristic
88D233—22no—
89D233—42no—
90C233#54611yescharacteristic, complemented, Sylow
91#546—2331nomaximal, Sylow
92C2×#41D23311yescharacteristic, complemented
93C22×D4—2331no—
94#124—2331no—
95#123—2332no—
96C22⋊Q8—2331no—
97#121—2332no—
98#121—2331no—
99#120—2332no—
100C4×D4—2331no—
101C4×D4—2331no—
102C2×C22⋊C4—2332no—
103C24—2332no—
104#41—24no—
105C2×Q8C2×D23311yescharacteristic, complemented
106C2×D4—4664no—
107C2×D4—2332no—
108C2×D4—2331no—
109C2×D4—2332no—
110C2×D4—2331no—
111C2×D4C2×D23311yescharacteristic
112C2×D4C2×D23312yescomplemented
113C22×C4—2332no—
114C22×C4—2331no—
115C22×C4C2×D23312yescomplemented
116C22×C4C2×D23311yescharacteristic, complemented
117C4⋊C4—2331no—
118C4⋊C4—2331no—
119C4⋊C4—2332no—
120C22⋊C4—2332no—
121C22⋊C4—2331no—
122C22⋊C4—2331no—
123C22⋊C4—2332no—
124C22⋊C4—2332no—
125C22⋊C4—2332no—
126C22⋊C4—2332no—
127C42—2331no—
128C23—9322no—
129C23—4664no—
130C23—4664no—
131C23—2332no—
132C23—2331no—
133C23C22×D23311yescharacteristic
134C23C22×D23312yes—
135Q8—22no—
136D4—24no—
137D4—9322no—
138D4—4662no—
139D4—4664no—
140D4—4662no—
141D4C22⋊D23314yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—9322no—
145C2×C4—4662no—
146C2×C4—2331no—
147C2×C4—2331no—
148C2×C4—2332no—
149C2×C4—2331no—
150C2×C4C22×D23311yescharacteristic
151C2×C4C22×D23312yes—
152C2×C4C22×D23311yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—9328no—
159C22—4662no—
160C22—4662no—
161C22—4662no—
162C22—4661no—
163C22—4661no—
164C22—2332no—
165C22C2×C22⋊D23314yes—
166C22C23×D23311yescharacteristic
167C4—21no—
168C4—22no—
169C4—4661no—
170C4—4661no—
171C4—4661no—
172C4—4662no—
173C4C2×C22⋊D23312yes—
174C2—24no—
175C2—41no—
176C2—9322no—
177C2—4662no—
178C2C22×C22⋊D23311yescharacteristic
179C2#41×D23311yescharacteristic
180C2#2141858111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D233
commutator, socle, cosocleC22×C233C24
FittingC2×#41×C233C2
hypercenterC2×#41D233
hypocenterC233#546
LCSG ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D4×D233C2semidirect
2. #21418524C2semidirect
3. #21418518C2semidirect
4. #21418511C2semidirect
5. #21418509C2semidirect
6. #21418507C2semidirect
7. #21418503C2semidirect
8. D4×Dic233C2semidirect
9. C4×C22⋊D233C2semidirect
10. C2×#16836571C2semidirect
11. C2×#41×C233C2semidirect
16. C2×C22⋊D233C22semidirect
18. C22×Dic233C22semidirect
20. C4⋊Dic233C22semidirect
21. #16836573C22semidirect
22. #16836573C22semidirect
23. C22⋊Dic233C22semidirect
24. C22⋊Dic233C22semidirect
27. #16836571C22semidirect
28. #16836571C22semidirect
29. #16836571C22semidirect
30. C4×Dic233C22semidirect
32. C2×Q8×C233C22semidirect
34. C2×D4×C233C22semidirect
35. C22×C4×C233C22semidirect
36. C22×C4×C233C22semidirect
56. D4×C233D4semidirect
75. C2×D233#41semidirect
90. C233#546semidirect
92. C2×#41D233semidirect
105. C2×Q8C2×D233semidirect
112. C2×D4C2×D233semidirect
115. C22×C4C2×D233semidirect
116. C22×C4C2×D233semidirect
141. D4C22⋊D233semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D2332
#214185242
#214185182
#214185112
#214185092
#214185072
#214185032
D4×Dic2332
C4×C22⋊D2332
C2×#168365712
C2×#41×C2332
#546233