Finite Group Databasebeta

← C22⋊Q8×D43 #14583393

Subgroups — C22⋊Q8×D43 #14583393

Order 2752.

322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×D43C211yesmaximal, characteristic, complemented
2C22×C4×D43C211yesmaximal, characteristic
3#13063305C211yesmaximal, characteristic, complemented
4#13063304C211yesmaximal, characteristic, complemented
5#13063303C212yesmaximal, complemented
6#13063302C212yesmaximal, complemented
7#13063301C211yesmaximal, characteristic, complemented
8C4⋊C4×D43C212yesmaximal, complemented
9C4⋊C4×D43C211yesmaximal, characteristic, complemented
10C22⋊C4×D43C212yesmaximal
11C22⋊Q8×C43C211yesmaximal, characteristic, complemented
12C23×D43C2211yescharacteristic
13C2×Q8×C43C2211yescharacteristic, complemented
14C22×C4×C43C2211yescharacteristic
15C22×Dic43C2211yescharacteristic
16Q8×D43—24no—
17C2×C4×D43—24no—
18C2×C4×D43C2212yes—
19C2×C4×D43C2212yes—
20C2×C4×D43C2211yescharacteristic
21C2×C4×D43C2211yescharacteristic
22C2×C4×D43C2211yescharacteristic
23C2×C4×D43C2211yescharacteristic
24C2×Dic86C2212yescomplemented
25C2×Dic86C2211yescharacteristic, complemented
26C4⋊C4×C43C2212yescomplemented
27C4⋊C4×C43C2211yescharacteristic, complemented
28C22⋊C4×C43C2212yes—
29C22⋊Dic43C2212yes—
30(C2×D43)⋊C4C2212yes—
31(C2×D43)⋊C4C2212yes—
32C4⋊Dic43C2211yescharacteristic, complemented
33C4⋊Dic43C2212yescomplemented
34Dic43⋊C4C2212yescomplemented
35Dic43⋊C4C2212yescomplemented
36Dic43⋊C4C2212yescomplemented
37C23×C43C2311yescharacteristic
38C22×D43—22no—
39C22×D43—22no—
40C22×D43Q814yescomplemented
41C22×D43C2311yescharacteristic
42C22×D43C2311yescharacteristic
43Q8×C43—22no—
44C2×C4×C43—22no—
45C2×C4×C43C2311yescharacteristic
46C2×C4×C43C2312yes—
47C2×C4×C43C2312yes—
48C2×C4×C43C2311yescharacteristic
49C2×Dic43—22no—
50C2×Dic43C2312yes—
51C2×Dic43C2311yescharacteristic
52C2×Dic43C2312yes—
53C2×Dic43C2311yescharacteristic
54C4×D43—22no—
55C4×D43—24no—
56C4×D43—24no—
57C4×D43—22no—
58C4×D43—22no—
59C4×D43D414yes—
60Dic86—22no—
61Dic86—24no—
62C22×C43—21no—
63C22×C43—21no—
64C22×C43C2×Q812yescomplemented
65C22×C43C2411yescharacteristic
66C2×D43—21no—
67C2×D43—21no—
68C2×D43—28no—
69C2×D43C2×D412yes—
70C2×D43C2×Q812yes—
71C2×D43C2×Q812yescomplemented
72C2×D43#4112yes—
73C4×C43—22no—
74C4×C43—21no—
75C4×C43—22no—
76C4×C43C2×D412yes—
77Dic43—22no—
78Dic43—21no—
79Dic43—22no—
80Dic43C2×D412yes—
81C2×C43—22no—
82C2×C43C22×D411yescharacteristic
83C2×C43C22×Q811yescharacteristic
84C2×C43C2×#4111yescharacteristic
85D43—22no—
86D43C22⋊Q814yesdirect product factor
87C2×C22⋊Q8—431nomaximal, Sylow
88C43C2×C22⋊Q811yescharacteristic, complemented, Sylow
89C22×Q8—431no—
90C23×C4—431no—
91C22⋊Q8—431no—
92C22⋊Q8—431no—
93C22⋊Q8—432no—
94C22⋊Q8—431no—
95C22⋊Q8—432no—
96C22⋊Q8D4311yescharacteristic, direct product factor
97C2×C4⋊C4—431no—
98C2×C4⋊C4—432no—
99C2×C22⋊C4—432no—
100C24—431no—
101C2×Q8—432no—
102C2×Q8—431no—
103C2×Q8—864no—
104C2×Q8C2×D4311yescharacteristic, complemented
105C22×C4—431no—
106C22×C4—431no—
107C22×C4—432no—
108C22×C4—432no—
109C22×C4—431no—
110C22×C4—431no—
111C22×C4—431no—
112C22×C4—864no—
113C22×C4C2×D4311yescharacteristic
114C4⋊C4—432no—
115C4⋊C4—432no—
116C4⋊C4—432no—
117C4⋊C4—431no—
118C4⋊C4—432no—
119C4⋊C4C2×D4311yescharacteristic, complemented
120C4⋊C4C2×D4312yescomplemented
121C22⋊C4—432no—
122C22⋊C4—432no—
123C22⋊C4—432no—
124C22⋊C4C2×D4312yes—
125C23—431no—
126C23—434no—
127C23—431no—
128C23—862no—
129C23—862no—
130C23C22×D4311yescharacteristic
131Q8—22no—
132Q8—864no—
133Q8—862no—
134C2×C4—22no—
135C2×C4—431no—
136C2×C4—434no—
137C2×C4—432no—
138C2×C4—432no—
139C2×C4—431no—
140C2×C4—862no—
141C2×C4—862no—
142C2×C4—864no—
143C2×C4—864no—
144C2×C4—862no—
145C2×C4—862no—
146C2×C4C22×D4312yes—
147C2×C4C22×D4312yes—
148C2×C4C22×D4311yescharacteristic
149C2×C4C22×D4311yescharacteristic
150C22—21no—
151C22—21no—
152C22—432no—
153C22—432no—
154C22—432no—
155C22—432no—
156C22—868no—
157C22—861no—
158C22—861no—
159C22Q8×D4312yescomplemented
160C22C23×D4311yescharacteristic
161C4—21no—
162C4—22no—
163C4—22no—
164C4—432no—
165C4—861no—
166C4—862no—
167C4—862no—
168C4D4×D4312yes—
169C2—22no—
170C2—434no—
171C2—862no—
172C2C2×D4×D4311yescharacteristic
173C2C2×Q8×D4311yescharacteristic
174C2#41×D4311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
FittingC22⋊Q8×C43C2
prime radicalC23×D43C22
hypercenterC22⋊Q8D43
hypocenterC43C2×C22⋊Q8
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D43C2semidirect
3. #13063305C2semidirect
4. #13063304C2semidirect
5. #13063303C2semidirect
6. #13063302C2semidirect
7. #13063301C2semidirect
8. C4⋊C4×D43C2semidirect
9. C4⋊C4×D43C2semidirect
11. C22⋊Q8×C43C2semidirect
13. C2×Q8×C43C22semidirect
24. C2×Dic86C22semidirect
25. C2×Dic86C22semidirect
26. C4⋊C4×C43C22semidirect
27. C4⋊C4×C43C22semidirect
32. C4⋊Dic43C22semidirect
33. C4⋊Dic43C22semidirect
34. Dic43⋊C4C22semidirect
35. Dic43⋊C4C22semidirect
36. Dic43⋊C4C22semidirect
40. C22×D43Q8semidirect
64. C22×C43C2×Q8semidirect
71. C2×D43C2×Q8semidirect
86. D43C22⋊Q8direct (N × H)
88. C43C2×C22⋊Q8semidirect
96. C22⋊Q8D43direct (N × H)
104. C2×Q8C2×D43semidirect
119. C4⋊C4C2×D43semidirect
120. C4⋊C4C2×D43semidirect
159. C22Q8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D432
C22×C4×D432
#130633052
#130633042
#130633032
#130633022
#130633012
C4⋊C4×D432
C22⋊C4×D432
C22⋊Q8×C432
C2×C22⋊Q843