Finite Group Databasebeta

← #15672368

Subgroups — #15672368

Order 2944.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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#13092998C211yesmaximal, characteristic
2#13092558C212yesmaximal, complemented
3#13092337C211yesmaximal, characteristic, complemented
4#13092152C212yesmaximal, complemented
5C23×#324C211yesmaximal, characteristic, complemented
6C2×#67288—21no—
7C22×Dic46C2211yescharacteristic
8C2×C4⋊C4×C23C2211yescharacteristic
9#10625101—21no—
10#10625101C2212yes—
11C2×Dic23⋊C4—21no—
12C2×#67263—22no—
13#10625068—22no—
14#10625066—22no—
15C23×C22⋊C8C2212yes—
16C23⋊#95—21no—
17C23⋊#95C2211yescharacteristic
18#10624998—22no—
19C22×C4×C23D411yescharacteristic
20C22×C4×C23D411yescharacteristic
21C22×C4×C23C2311yescharacteristic
22C2×C22⋊D23—22no—
23C22×Dic23—21no—
24C22×Dic23—21no—
25#67288—42no—
26#67288—42no—
27C2×D92—21no—
28C2×D92—21no—
29C2×D92D412yes—
30C2×C4×D23—22no—
31C2×Dic46—22no—
32C2×Dic46—21no—
33C2×Dic46—42no—
34C2×C8×C23—22no—
35C4⋊C4×C23—22no—
36(C2×D23)⋊C4—22no—
37(C2×D23)⋊C4—22no—
38C4⋊Dic23—21no—
39C4⋊Dic23D412yes—
40Dic23⋊C4—42no—
41#67263—44no—
42C23×C23C2×D411yescharacteristic
43C22×D23—22no—
44C2×C4×C23—21no—
45C2×C4×C23—21no—
46C2×C4×C23—21no—
47C2×C4×C23—41no—
48C2×C4×C23—41no—
49C2×C4×C23SD1612yescomplemented
50C2×C4×C23C2×D412yes—
51C22⋊D23—42no—
52C22⋊D23—42no—
53C2×Dic23—22no—
54C2×Dic23—22no—
55C2×Dic23—22no—
56C2×Dic23—41no—
57C2×Dic23—41no—
58C2×Dic23—41no—
59C2×Dic23—41no—
60D92—42no—
61D92—42no—
62D92—81no—
63C4×D23—44no—
64Dic46—24no—
65Dic46—42no—
66Dic46—42no—
67C8×C23—42no—
68#1604—231nomaximal, Sylow
69C22×C23—21no—
70C22×C23—21no—
71C22×C23#12011yescharacteristic
72C22×C23C2×SD1611yescharacteristic
73C22×C23AGL(1,ℤ/8)11yescharacteristic
74C2×D23—42no—
75C2×D23—42no—
76C2×D23—42no—
77C4×C23—22no—
78C4×C23—22no—
79C4×C23—41no—
80Dic23—42no—
81Dic23—42no—
82Dic23—42no—
83#537—231no—
84#448—232no—
85#395—231no—
86#327—232no—
87#324D2311yescharacteristic, complemented
88C2×C23—21no—
89C2×C23—21no—
90C2×C23#45011yescharacteristic
91C2×C23#45611yescharacteristic
92C2×C23B(4,𝔽2)11yescharacteristic
93D23—82no—
94C2×#41—461no—
95C22×Q8—231no—
96C2×SD16—462no—
97C22⋊Q8—462no—
98#121—232no—
99#121—462no—
100#121—461no—
101C2×C4⋊C4—461no—
102C2×C4⋊C4C2×D2311yescharacteristic
103#103—462no—
104C22⋊C8C2×D2312yes—
105#95—231no—
106#95—461no—
107C23#160411yescharacteristic, complemented, Sylow
108#41—922no—
109#41—922no—
110C2×Q8—461no—
111C2×Q8—462no—
112C2×Q8—922no—
113C2×D4—232no—
114C2×D4—461no—
115C2×D4—461no—
116C2×D4—462no—
117C22×C4—462no—
118C22×C4—461no—
119C22×C4—461no—
120C22×C4D9211yescharacteristic
121C22×C4D9211yescharacteristic
122C22×C4C22×D2311yescharacteristic
123SD16—924no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—232no—
127C4⋊C4—461no—
128C4⋊C4—922no—
129C22⋊C4—462no—
130C22⋊C4—462no—
131C23—462no—
132C23C2×D9211yescharacteristic
133Q8—464no—
134Q8—922no—
135Q8—922no—
136D4—922no—
137D4—922no—
138D4—922no—
139D4—922no—
140D4—1841no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—462no—
147C2×C4—462no—
148C2×C4—462no—
149C2×C4—924no—
150C2×C4—921no—
151C2×C4—921no—
152C2×C4—921no—
153C2×C4—921no—
154C2×C4#6726312yescomplemented
155C2×C4D4×D2312yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—922no—
160C22—922no—
161C22—922no—
162C22#1062505311yescharacteristic
163C22C2×#6726311yescharacteristic
164C22#1062507911yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—922no—
169C4—922no—
170C4—922no—
171C2—21no—
172C2—21no—
173C2—1842no—
174C2#1309257011yescharacteristic
175C2#1309260211yescharacteristic
176C2#1309260511yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23#120
prime radical#13092998C2
hypercenter#324D23
hypocenterC23#1604
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #13092558C2semidirect
3. #13092337C2semidirect
4. #13092152C2semidirect
5. C23×#324C2semidirect
49. C2×C4×C23SD16semidirect
87. #324D23semidirect
107. C23#1604semidirect
154. C2×C4#67263semidirect

Maximal subgroups

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

subgroupindex
#130929982
#130925582
#130923372
#130921522
C23×#3242
#160423