Finite Group Databasebeta

← #14583409

Subgroups — #14583409

Order 2752.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10621900C211yesmaximal, characteristic, complemented
2C22×C4×D43C211yesmaximal, characteristic, complemented
3#13063307C212yesmaximal, complemented
4#13063305C211yesmaximal, characteristic, complemented
5#13063304C211yesmaximal, characteristic, complemented
6#13063296C211yesmaximal, characteristic, complemented
7#13063293C212yesmaximal, complemented
8D4×Dic43C212yesmaximal, complemented
9(C22⋊D43)⋊C4C212yesmaximal, complemented
10#13063283C211yesmaximal, characteristic, complemented
11#121×C43C211yesmaximal, characteristic, complemented
12C23×D43C2211yescharacteristic
13C2×D4×C43C2212yes—
14C2×D4×C43C2211yescharacteristic, complemented
15C22×C4×C43C2211yescharacteristic
16C2×C22⋊D43C2212yes—
17C2×C22⋊D43C2212yes—
18C22×Dic43C2211yescharacteristic
19C22×Dic43C2212yescomplemented
20#10621900—24no—
21C2×C4×D43—24no—
22C2×C4×D43C2211yescharacteristic
23C2×C4×D43C2211yescharacteristic
24C2×C4×D43C2211yescharacteristic
25C2×C4×D43C2211yescharacteristic
26C2×Dic86C2211yescharacteristic, complemented
27C4⋊C4×C43C2211yescharacteristic, complemented
28C22⋊C4×C43C2212yescomplemented
29C22⋊Dic43C2212yes—
30C22⋊Dic43C2212yescomplemented
31(C2×D43)⋊C4C2212yes—
32(C2×D43)⋊C4C2212yes—
33C4⋊Dic43C2211yescharacteristic, complemented
34C4⋊Dic43C2212yescomplemented
35Dic43⋊C4C2212yescomplemented
36C4×Dic43C2212yescomplemented
37C23×C43C2312yes—
38C23×C43C2311yescharacteristic
39C22×D43—22no—
40C22×D43—22no—
41C22×D43—22no—
42C22×D43C2311yescharacteristic
43C22×D43C2311yescharacteristic
44D4×C43—24no—
45D4×C43—22no—
46C2×C4×C43—22no—
47C2×C4×C43C2312yes—
48C2×C4×C43C2311yescharacteristic
49C2×C4×C43C2311yescharacteristic
50C22⋊D43—24no—
51C22⋊D43—24no—
52C2×Dic43—22no—
53C2×Dic43—24no—
54C2×Dic43C2312yes—
55C2×Dic43C2312yes—
56C2×Dic43C2311yescharacteristic
57C2×Dic43C2311yescharacteristic
58C4×D43—22no—
59C4×D43—22no—
60C4×D43—22no—
61C4×D43D414yescomplemented
62Dic86—22no—
63C22×C43—21no—
64C22×C43—21no—
65C22×C43—22no—
66C22×C43—22no—
67C22×C43—22no—
68C22×C43#4112yescomplemented
69C22×C43C2411yescharacteristic
70C2×D43—28no—
71C2×D43—21no—
72C2×D43—21no—
73C2×D43—21no—
74C2×D43—21no—
75C2×D43C2×D412yes—
76C2×D43#4112yescomplemented
77C4×C43—21no—
78C4×C43—22no—
79C4×C43C2×D412yes—
80Dic43—22no—
81Dic43—21no—
82Dic43—22no—
83Dic43C2×D412yes—
84C2×C43—22no—
85C2×C43—42no—
86C2×C43C22×D411yescharacteristic
87C2×C43C2×#4111yescharacteristic
88C2×C43C2×#4111yescharacteristic
89D43—22no—
90D43—22no—
91#525—431nomaximal, Sylow
92C43#52511yescharacteristic, complemented, Sylow
93C2×#41—431no—
94C23×C4—431no—
95#123—432no—
96C22⋊Q8—431no—
97C22⋊Q8—431no—
98#121—431no—
99#121D4311yescharacteristic, complemented
100#120—432no—
101C4×D4—432no—
102C4×D4—432no—
103#117—431no—
104C24—431no—
105#41—864no—
106C2×Q8—431no—
107C2×D4—432no—
108C2×D4—432no—
109C2×D4C2×D4312yes—
110C2×D4C2×D4311yescharacteristic, complemented
111C22×C4—431no—
112C22×C4—431no—
113C22×C4—432no—
114C22×C4—431no—
115C22×C4—431no—
116C22×C4—431no—
117C22×C4—864no—
118C22×C4C2×D4311yescharacteristic
119C4⋊C4—431no—
120C4⋊C4—432no—
121C4⋊C4—432no—
122C4⋊C4C2×D4311yescharacteristic, complemented
123C22⋊C4—432no—
124C22⋊C4—432no—
125C22⋊C4—432no—
126C22⋊C4—432no—
127C22⋊C4C2×D4312yescomplemented
128C42—432no—
129C23—431no—
130C23—431no—
131C23—862no—
132C23—862no—
133C23—862no—
134C23C22×D4312yes—
135C23C22×D4311yescharacteristic
136Q8—862no—
137D4—24no—
138D4—22no—
139D4—864no—
140D4—864no—
141C2×C4—22no—
142C2×C4—431no—
143C2×C4—434no—
144C2×C4—432no—
145C2×C4—431no—
146C2×C4—432no—
147C2×C4—862no—
148C2×C4—862no—
149C2×C4—862no—
150C2×C4—864no—
151C2×C4—862no—
152C2×C4C22×D4312yes—
153C2×C4C22×D4311yescharacteristic
154C2×C4C22×D4311yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—432no—
161C22—432no—
162C22—868no—
163C22—861no—
164C22—861no—
165C22—861no—
166C22—861no—
167C22#1062190012yescomplemented
168C22C23×D4311yescharacteristic
169C4—21no—
170C4—22no—
171C4—432no—
172C4—861no—
173C4—862no—
174C4—862no—
175C4D4×D4312yes—
176C2—22no—
177C2—42no—
178C2—862no—
179C2—862no—
180C2C2×D4×D4311yescharacteristic
181C2#41×D4311yescharacteristic
182C2C2×#1062190011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#121×C43C2
hypercenter#121D43
hypocenterC43#525
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#10621900C2semidirect
2. C22×C4×D43C2semidirect
3. #13063307C2semidirect
4. #13063305C2semidirect
5. #13063304C2semidirect
6. #13063296C2semidirect
7. #13063293C2semidirect
8. D4×Dic43C2semidirect
9. (C22⋊D43)⋊C4C2semidirect
10. #13063283C2semidirect
11. #121×C43C2semidirect
14. C2×D4×C43C22semidirect
19. C22×Dic43C22semidirect
26. C2×Dic86C22semidirect
27. C4⋊C4×C43C22semidirect
28. C22⋊C4×C43C22semidirect
30. C22⋊Dic43C22semidirect
33. C4⋊Dic43C22semidirect
34. C4⋊Dic43C22semidirect
35. Dic43⋊C4C22semidirect
36. C4×Dic43C22semidirect
61. C4×D43D4semidirect
68. C22×C43#41semidirect
76. C2×D43#41semidirect
92. C43#525semidirect
99. #121D43semidirect
110. C2×D4C2×D43semidirect
122. C4⋊C4C2×D43semidirect
127. C22⋊C4C2×D43semidirect
167. C22#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#106219002
C22×C4×D432
#130633072
#130633052
#130633042
#130632962
#130632932
D4×Dic432
(C22⋊D43)⋊C42
#130632832
#121×C432
#52543