Finite Group Databasebeta

← C2×#13092752 #15683302

Subgroups — C2×#13092752 #15683302

Order 2944.

460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10625095C211yesmaximal, characteristic
2#13092752C218yesmaximal, direct product factor
3C2×#10624989C212yesmaximal, complemented
4C2×#10624992C212yesmaximal, complemented
5C2×C22⋊(C23⋊C8)C211yesmaximal, characteristic
6C22×C4⋊C4×C23C211yesmaximal, characteristic
7C23×C4×C23—21no—
8C23×C4×C23C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C2×C4⋊C4×C23—21no—
11C2×C4⋊C4×C23—22no—
12C2×C4⋊C4×C23C2212yes—
13C2×C4⋊C4×C23C2214yes—
14C2×C22⋊Dic23—21no—
15C2×C4⋊Dic23C2211yescharacteristic
16#10625095—22no—
17#10625095C2214yes—
18C2×Dic23⋊C4—21no—
19C22×C23⋊C8C2212yes—
20C22⋊(C23⋊C8)C2214yes—
21#10624992C2218yescomplemented
22#10624989C2218yescomplemented
23C24×C23D411yescharacteristic
24C22×C4×C23—24no—
25C22×C4×C23—24no—
26C22×C4×C23—22no—
27C22×C4×C23—44no—
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D412yes—
30C22×C4×C23C2312yes—
31C22×C4×C23C2311yescharacteristic
32C22×Dic23—21no—
33C22×Dic23—21no—
34C2×Dic46—24no—
35C2×Dic46—21no—
36C2×Dic46C2312yes—
37C4⋊C4×C23—24no—
38C4⋊C4×C23—22no—
39C4⋊C4×C23C2314yes—
40C22⋊Dic23—24no—
41C4⋊Dic23—21no—
42C4⋊Dic23C2312yes—
43Dic23⋊C4—24no—
44C2×C23⋊C8—24no—
45C2×C23⋊C8C2314yes—
46C23×C23—22no—
47C23×C23—22no—
48C23×C23Q1614yes—
49C23×C23C2×D412yes—
50C23×C23C2×D411yescharacteristic
51C2×C4×C23—22no—
52C2×C4×C23—24no—
53C2×C4×C23—24no—
54C2×C4×C23—24no—
55C2×C4×C23—48no—
56C2×C4×C23—44no—
57C2×C4×C23C2×D412yes—
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23#4114yes—
60C2×C4×C23C2411yescharacteristic
61C2×Dic23—22no—
62C2×Dic23—22no—
63C2×Dic23—42no—
64C2×Dic23—42no—
65Dic46—24no—
66Dic46—42no—
67C23⋊C8—24no—
68C2×#484—231nomaximal, Sylow
69C22×C23—22no—
70C22×C23—22no—
71C22×C23—28no—
72C22×C23#12312yes—
73C22×C23C2×Q1614yes—
74C22×C23C2×Q1612yes—
75C22×C23AGL(1,ℤ/8)12yes—
76C22×C23C22×D411yescharacteristic
77C4×C23—22no—
78C4×C23—44no—
79C4×C23#12312yes—
80C4×C23C2×#4112yes—
81Dic23—42no—
82Dic23—42no—
83C2×C22⋊Q8—231no—
84C22×C4⋊C4D2311yescharacteristic
85#484—238no—
86C2×#107—232no—
87C2×#103—232no—
88C2×C22⋊C8—231no—
89C2×C23—24no—
90C2×C23#48414yescomplemented
91C2×C23C2×#12311yescharacteristic
92C2×C23C22×Q1611yescharacteristic
93C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
94C22×Q8—231no—
95C23×C4—21no—
96C23×C4C2×D2311yescharacteristic
97C22×C8—232no—
98C22⋊Q8—234no—
99C22⋊Q8—462no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—231no—
103C2×C4⋊C4—461no—
104C2×C4⋊C4C2×D2312yes—
105C2×C4⋊C4C2×D2314yes—
106C2×C22⋊C4—461no—
107#107—238no—
108#103—238no—
109C22⋊C8—234no—
110C23C2×#48411yescharacteristic, complemented, Sylow
111C24C22⋊D2311yescharacteristic
112C2×Q8—232no—
113C2×Q8—461no—
114C2×Q8—464no—
115C22×C4—24no—
116C22×C4—24no—
117C22×C4—22no—
118C22×C4—44no—
119C22×C4—461no—
120C22×C4—461no—
121C22×C4C22⋊D2312yes—
122C22×C4C22⋊D2311yescharacteristic
123C22×C4C22×D2312yes—
124C22×C4C22×D2311yescharacteristic
125C2×C8—234no—
126C2×C8—464no—
127C4⋊C4—24no—
128C4⋊C4—22no—
129C4⋊C4—232no—
130C4⋊C4—461no—
131C4⋊C4—464no—
132C4⋊C4C22×D2314yes—
133C22⋊C4—464no—
134C23—22no—
135C23—22no—
136C23#6727514yes—
137C23C2×C22⋊D2312yes—
138C23C2×C22⋊D2311yescharacteristic
139Q8—464no—
140Q8—922no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—24no—
145C2×C4—48no—
146C2×C4—44no—
147C2×C4—462no—
148C2×C4—462no—
149C2×C4—922no—
150C2×C4—922no—
151C2×C4#6728814yes—
152C2×C4C2×C22⋊D2312yes—
153C2×C4C2×C22⋊D2311yescharacteristic
154C2×C4C23×D2311yescharacteristic
155C8—464no—
156C22—22no—
157C22—22no—
158C22—28no—
159C22#1062510012yes—
160C22#1062510312yes—
161C22C2×#6727514yes—
162C22C2×#6727512yes—
163C22C22×C22⋊D2311yescharacteristic
164C4—22no—
165C4—44no—
166C4—922no—
167C4—922no—
168C4#1062510012yes—
169C4C2×#6728812yes—
170C2—24no—
171C2#1309275214yesdirect product factor
172C2C2×#1062510011yescharacteristic
173C2C22×#6727511yescharacteristic
174C2C2×#1062510311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC22×C4⋊C4×C23C2
socleC23×C23C2×D4
prime radicalC24×C23D4
hypercenterC22×C4⋊C4D23
hypocenterC23C2×#484
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13092752C2direct (N × H)
3. C2×#10624989C2semidirect
4. C2×#10624992C2semidirect
21. #10624992C22semidirect
22. #10624989C22semidirect
90. C2×C23#484semidirect
110. C23C2×#484semidirect
171. C2#13092752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106250952
#130927522
C2×#106249892
C2×#106249922
C2×C22⋊(C23⋊C8)2
C22×C4⋊C4×C232
C2×#48423