Finite Group Databasebeta

← #15672366

Subgroups — #15672366

Order 2944.

282 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#13092555C212yesmaximal, complemented
2#13092337C211yesmaximal, characteristic, complemented
3#13092151C212yesmaximal, complemented
4#13092143C211yesmaximal, characteristic, complemented
5C23×#537C211yesmaximal, characteristic
6C2×#41×C23—21no—
7C22×Dic46C2211yescharacteristic
8C23×C22⋊Q8—22no—
9C23×#121—22no—
10C23×#121—21no—
11C23×#121C2212yes—
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×#67273—22no—
14C2×Dic23⋊C4—21no—
15C23⋊#95—21no—
16C23⋊#95C2211yescharacteristic
17C22⋊(C23⋊C8)C2212yes—
18#10624992—22no—
19#41×C23—42no—
20#41×C23—42no—
21C2×Q8×C23—21no—
22C2×D4×C23—21no—
23C2×D4×C23—22no—
24C2×D4×C23—21no—
25C2×D4×C23D412yes—
26C22×C4×C23—22no—
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23—21no—
32C2×Dic46—22no—
33C2×Dic46—42no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—22no—
36C4⋊C4×C23D412yes—
37C22⋊C4×C23—22no—
38C22⋊C4×C23—22no—
39#67273—44no—
40Dic23⋊C4—42no—
41C2×C23⋊C8—22no—
42C23×C23—22no—
43C23×C23C2×D411yescharacteristic
44Q8×C23—42no—
45D4×C23—42no—
46D4×C23—42no—
47D4×C23—42no—
48D4×C23—42no—
49D4×C23—81no—
50C2×C4×C23—21no—
51C2×C4×C23—21no—
52C2×C4×C23—21no—
53C2×C4×C23—22no—
54C2×C4×C23—41no—
55C2×C4×C23—44no—
56C2×C4×C23—41no—
57C2×C4×C23SD1612yescomplemented
58C2×C4×C23C2×D412yes—
59C2×Dic23—22no—
60C2×Dic23—22no—
61C2×Dic23—41no—
62C2×Dic23—41no—
63C2×Dic23—41no—
64C2×Dic23—41no—
65Dic46—24no—
66Dic46—42no—
67C23⋊C8—42no—
68#1604—231nomaximal, Sylow
69C22×C23—21no—
70C22×C23—21no—
71C22×C23—42no—
72C22×C23—42no—
73C22×C23—42no—
74C22×C23#12011yescharacteristic
75C22×C23C2×SD1611yescharacteristic
76C22×C23AGL(1,ℤ/8)11yescharacteristic
77C4×C23—22no—
78C4×C23—22no—
79C4×C23—42no—
80C4×C23—41no—
81Dic23—42no—
82Dic23—42no—
83#537D2311yescharacteristic
84#448—232no—
85#395—231no—
86#327—232no—
87#324—231no—
88C2×C23—21no—
89C2×C23—21no—
90C2×C23—82no—
91C2×C23#45011yescharacteristic
92C2×C23#45611yescharacteristic
93C2×C23B(4,𝔽2)11yescharacteristic
94C2×#41—21no—
95C22×Q8—231no—
96C2×SD16—462no—
97C22⋊Q8—22no—
98#121—22no—
99#121—21no—
100#121C2×D2312yes—
101C2×C4⋊C4—461no—
102C2×C4⋊C4C2×D2311yescharacteristic
103#103—462no—
104C22⋊C8—232no—
105#95—231no—
106#95—461no—
107C23#160411yescharacteristic, complemented, Sylow
108#41—42no—
109#41—42no—
110C2×Q8—21no—
111C2×Q8—462no—
112C2×Q8—922no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4—21no—
116C2×D4C22⋊D2312yes—
117C22×C4—22no—
118C22×C4—461no—
119C22×C4—461no—
120C22×C4C22⋊D2311yescharacteristic
121C22×C4C22⋊D2311yescharacteristic
122C22×C4C22×D2311yescharacteristic
123SD16—924no—
124C2×C8—462no—
125C4⋊C4—21no—
126C4⋊C4—22no—
127C4⋊C4—922no—
128C4⋊C4C22⋊D2312yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C23—22no—
132C23C2×C22⋊D2311yescharacteristic
133Q8—42no—
134Q8—464no—
135Q8—922no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—44no—
147C2×C4—41no—
148C2×C4—462no—
149C2×C4—462no—
150C2×C4—921no—
151C2×C4—921no—
152C2×C4—921no—
153C2×C4—921no—
154C2×C4#6727312yescomplemented
155C2×C4C2×C22⋊D2312yes—
156C8—922no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22#1062510311yescharacteristic
163C22C2×#6727311yescharacteristic
164C22#1062512411yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—41no—
169C4—922no—
170C4—922no—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1309256811yescharacteristic
175C2#1309260011yescharacteristic
176C2#1309260411yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#537C2
socleC22×C23#120
hypercenter#537D23
hypocenterC23#1604
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #13092555C2semidirect
2. #13092337C2semidirect
3. #13092151C2semidirect
4. #13092143C2semidirect
57. C2×C4×C23SD16semidirect
107. C23#1604semidirect
154. C2×C4#67273semidirect

Maximal subgroups

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

subgroupindex
#130925552
#130923372
#130921512
#130921432
C23×#5372
#160423