Finite Group Databasebeta

← #14583412

Subgroups — #14583412

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×#10621902C211yesmaximal, characteristic, complemented
2C22×C4×D43C211yesmaximal, characteristic, complemented
3#13063310C212yesmaximal, complemented
4#13063301C211yesmaximal, characteristic, complemented
5#13063300C211yesmaximal, characteristic, complemented
6#13063299C211yesmaximal, characteristic, complemented
7#13063295C212yesmaximal, complemented
8#13063287C212yesmaximal, complemented
9(C22⋊D43)⋊C4C212yesmaximal, complemented
10#13063283C211yesmaximal, characteristic, complemented
11C22⋊Q8×C43C211yesmaximal, characteristic, complemented
12C23×D43C2211yescharacteristic
13C2×Q8×C43C2211yescharacteristic, complemented
14C22×C4×C43C2211yescharacteristic
15C2×C22⋊D43C2212yes—
16C22×Dic43C2211yescharacteristic
17#10621902—24no—
18C2×D172C2212yes—
19C2×D172C2212yes—
20C2×D172C2211yescharacteristic, complemented
21C2×C4×D43—24no—
22C2×C4×D43C2211yescharacteristic
23C2×C4×D43C2211yescharacteristic
24C2×C4×D43C2211yescharacteristic
25C2×C4×D43C2211yescharacteristic
26C2×C4×D43C2212yescomplemented
27C4⋊C4×C43C2211yescharacteristic, complemented
28C4⋊C4×C43C2212yescomplemented
29C22⋊C4×C43C2212yes—
30(C2×D43)⋊C4C2212yes—
31(C2×D43)⋊C4C2212yes—
32(C2×D43)⋊C4C2212yescomplemented
33(C2×D43)⋊C4C2212yescomplemented
34C4⋊Dic43C2211yescharacteristic, complemented
35Dic43⋊C4C2212yescomplemented
36C4×Dic43C2212yescomplemented
37C23×C43C2311yescharacteristic
38C22×D43—22no—
39C22×D43—22no—
40C22×D43—22no—
41C22×D43C2312yes—
42C22×D43C2311yescharacteristic
43C22×D43C2311yescharacteristic
44Q8×C43—22no—
45C2×C4×C43—22no—
46C2×C4×C43C2312yes—
47C2×C4×C43C2312yes—
48C2×C4×C43C2311yescharacteristic
49C2×C4×C43C2311yescharacteristic
50C22⋊D43—24no—
51C2×Dic43—22no—
52C2×Dic43C2312yes—
53C2×Dic43C2311yescharacteristic
54C2×Dic43C2311yescharacteristic
55D172—24no—
56D172—24no—
57D172—22no—
58C4×D43—22no—
59C4×D43—22no—
60C4×D43—22no—
61C4×D43—24no—
62C4×D43D414yescomplemented
63C22×C43—21no—
64C22×C43—21no—
65C22×C43#4112yescomplemented
66C22×C43C2411yescharacteristic
67C2×D43—28no—
68C2×D43—21no—
69C2×D43—21no—
70C2×D43—21no—
71C2×D43—21no—
72C2×D43—22no—
73C2×D43—22no—
74C2×D43—22no—
75C2×D43C2×D412yes—
76C2×D43#4112yescomplemented
77C4×C43—21no—
78C4×C43—22no—
79C4×C43—22no—
80C4×C43C2×D412yes—
81Dic43—21no—
82Dic43—22no—
83Dic43C2×D412yes—
84C2×C43—22no—
85C2×C43C22×D411yescharacteristic
86C2×C43C2×#4111yescharacteristic
87C2×C43C2×#4111yescharacteristic
88D43—22no—
89D43—22no—
90D43—42no—
91#525—431nomaximal, Sylow
92C43#52511yescharacteristic, complemented, Sylow
93C2×#41—431no—
94C23×C4—431no—
95#123—432no—
96C22⋊Q8—431no—
97C22⋊Q8D4311yescharacteristic, complemented
98#121—431no—
99#121—431no—
100#120—432no—
101C4×D4—432no—
102C4×D4—432no—
103#117—431no—
104C24—431no—
105#41—864no—
106C2×Q8C2×D4311yescharacteristic, complemented
107C2×D4—432no—
108C2×D4—432no—
109C2×D4—432no—
110C2×D4—431no—
111C22×C4—431no—
112C22×C4—431no—
113C22×C4—431no—
114C22×C4—432no—
115C22×C4—431no—
116C22×C4—431no—
117C22×C4—864no—
118C22×C4C2×D4311yescharacteristic
119C4⋊C4—431no—
120C4⋊C4—432no—
121C4⋊C4C2×D4311yescharacteristic, complemented
122C4⋊C4C2×D4312yescomplemented
123C22⋊C4—432no—
124C22⋊C4—432no—
125C22⋊C4—432no—
126C22⋊C4—432no—
127C22⋊C4C2×D4312yes—
128C42—432no—
129C23—431no—
130C23—431no—
131C23—432no—
132C23—862no—
133C23—862no—
134C23—862no—
135C23C22×D4311yescharacteristic
136Q8—22no—
137D4—864no—
138D4—864no—
139D4—864no—
140D4—862no—
141C2×C4—22no—
142C2×C4—431no—
143C2×C4—434no—
144C2×C4—432no—
145C2×C4—431no—
146C2×C4—862no—
147C2×C4—864no—
148C2×C4—862no—
149C2×C4—862no—
150C2×C4—862no—
151C2×C4C22×D4312yes—
152C2×C4C22×D4311yescharacteristic
153C2×C4C22×D4312yes—
154C2×C4C22×D4311yescharacteristic
155C22—21no—
156C22—21no—
157C22—432no—
158C22—432no—
159C22—868no—
160C22—861no—
161C22—861no—
162C22—861no—
163C22—861no—
164C22—862no—
165C22—862no—
166C22—862no—
167C22#1062190212yescomplemented
168C22C23×D4311yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—432no—
173C4—861no—
174C4—862no—
175C4D4×D4312yes—
176C2—22no—
177C2—862no—
178C2—862no—
179C2—1722no—
180C2C2×D4×D4311yescharacteristic
181C2#41×D4311yescharacteristic
182C2C2×#1062190211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
FittingC22⋊Q8×C43C2
hypercenterC22⋊Q8D43
hypocenterC43#525
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10621902C2semidirect
2. C22×C4×D43C2semidirect
3. #13063310C2semidirect
4. #13063301C2semidirect
5. #13063300C2semidirect
6. #13063299C2semidirect
7. #13063295C2semidirect
8. #13063287C2semidirect
9. (C22⋊D43)⋊C4C2semidirect
10. #13063283C2semidirect
11. C22⋊Q8×C43C2semidirect
13. C2×Q8×C43C22semidirect
20. C2×D172C22semidirect
26. C2×C4×D43C22semidirect
27. C4⋊C4×C43C22semidirect
28. C4⋊C4×C43C22semidirect
32. (C2×D43)⋊C4C22semidirect
33. (C2×D43)⋊C4C22semidirect
34. C4⋊Dic43C22semidirect
35. Dic43⋊C4C22semidirect
36. C4×Dic43C22semidirect
62. C4×D43D4semidirect
65. C22×C43#41semidirect
76. C2×D43#41semidirect
92. C43#525semidirect
97. C22⋊Q8D43semidirect
106. C2×Q8C2×D43semidirect
121. C4⋊C4C2×D43semidirect
122. C4⋊C4C2×D43semidirect
167. C22#10621902semidirect

Maximal subgroups

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

subgroupindex
C2×#106219022
C22×C4×D432
#130633102
#130633012
#130633002
#130632992
#130632952
#130632872
(C22⋊D43)⋊C42
#130632832
C22⋊Q8×C432
#52543