Finite Group Databasebeta

← #15672570

Subgroups — #15672570

Order 2944.

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

normal subgroups only

This group has 194 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#13093141C211yesmaximal, characteristic
2#13092769C211yesmaximal, characteristic, complemented
3#13092713C211yesmaximal, characteristic, complemented
4#13092708C211yesmaximal, characteristic
5#13092147C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic
7C23×#332C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9#10625118—21no—
10Q8×Dic23—21no—
11#10625069—22no—
12#10625068—21no—
13#10625063—21no—
14C4×D92C2211yescharacteristic
15#10625040C2211yescharacteristic
16C4×Dic46C2211yescharacteristic
17C23×C4⋊C8C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19#10625003—21no—
20#10625000—21no—
21#10624999—21no—
22#10624998—21no—
23#10624992—22no—
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×D92D411yescharacteristic
27C2×C4×D23—21no—
28C2×Dic46—21no—
29C2×Dic46D411yescharacteristic
30C2×C8×C23—21no—
31C2×C8×C23—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23D412yes—
34C42×C23C2311yescharacteristic
35(C2×D23)⋊C4—22no—
36(C2×D23)⋊C4—22no—
37(C2×D23)⋊C4—21no—
38C4⋊Dic23—22no—
39C4⋊Dic23—21no—
40C4⋊Dic23—21no—
41C4⋊Dic23D411yescharacteristic
42C4⋊Dic23D411yescharacteristic
43Dic23⋊C4—21no—
44C4×Dic23—22no—
45C4×Dic23—21no—
46C2×C23⋊C8—21no—
47C22×D23—21no—
48Q8×C23—41no—
49Q8×C23—41no—
50C2×C4×C23—22no—
51C2×C4×C23C2×D411yescharacteristic
52C2×C4×C23C2×D411yescharacteristic
53C2×C4×C23C2×D411yescharacteristic
54C2×Dic23—21no—
55C2×Dic23—21no—
56C2×Dic23—21no—
57C2×Dic23—41no—
58D92—21no—
59D92—21no—
60C4×D23—41no—
61C4×D23—41no—
62Dic46—21no—
63Dic46—21no—
64Dic46—42no—
65C8×C23—41no—
66C8×C23—41no—
67C23⋊C8—41no—
68#1638—231nomaximal, Sylow
69C22×C23#12011yescharacteristic
70C2×D23—41no—
71C2×D23—41no—
72C2×D23—41no—
73C4×C23—21no—
74C4×C23—42no—
75C4×C23#13511yescharacteristic
76C4×C23#13511yescharacteristic
77C4×C23#13711yescharacteristic
78C4×C23#13711yescharacteristic
79Dic23—41no—
80Dic23—41no—
81Dic23—41no—
82Dic23—81no—
83#556—231no—
84#487—231no—
85#477—231no—
86#476—231no—
87#332D2311yescharacteristic, complemented
88Q8⋊C8—231no—
89D4⋊C8—231no—
90C2×C23#45211yescharacteristic
91C2×C23#45211yescharacteristic
92C2×C23#45411yescharacteristic
93D23—81no—
94C4⋊Q8—231no—
95C4⋊Q8C2×D2311yescharacteristic
96#126—462no—
97#124—461no—
98C22⋊Q8—461no—
99C4×Q8—231no—
100C4×Q8—461no—
101C4×D4—231no—
102#117—461no—
103#107—461no—
104#106—461no—
105C4⋊C8C2×D2311yescharacteristic
106C4⋊C8C2×D2311yescharacteristic
107#103—461no—
108#103—462no—
109#102—461no—
110C4×C8—231no—
111C23#163811yescharacteristic, complemented, Sylow
112C2×Q8—21no—
113C2×Q8—231no—
114C2×Q8—461no—
115C2×D4—231no—
116C22×C4—461no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—461no—
120C4⋊C4—21no—
121C4⋊C4—231no—
122C4⋊C4—231no—
123C4⋊C4—462no—
124C4⋊C4—461no—
125C4⋊C4—461no—
126C4⋊C4—461no—
127C4⋊C4D9212yes—
128C22⋊C4—462no—
129C22⋊C4—462no—
130C22⋊C4—461no—
131C42—462no—
132C42—461no—
133C42C22×D2311yescharacteristic
134C23—461no—
135Q8—41no—
136Q8—41no—
137Q8—461no—
138Q8—461no—
139Q8—922no—
140D4—461no—
141D4—461no—
142C2×C4—22no—
143C2×C4—461no—
144C2×C4—461no—
145C2×C4—461no—
146C2×C4—921no—
147C2×C4—921no—
148C2×C4—921no—
149C2×C4C2×D9211yescharacteristic
150C2×C4D4×D2311yescharacteristic
151C2×C4D4×D2311yescharacteristic
152C8—41no—
153C8—41no—
154C8—921no—
155C22—921no—
156C22—921no—
157C22—921no—
158C22#1062505311yescharacteristic
159C4—21no—
160C4—42no—
161C4—921no—
162C4—921no—
163C4—921no—
164C4—1841no—
165C4#1062508311yescharacteristic
166C4#1062508611yescharacteristic
167C4#1062508711yescharacteristic
168C4#1062508911yescharacteristic
169C2—1841no—
170C2#1309258011yescharacteristic
171C2#1309258211yescharacteristic
172C2#1309259211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#332C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenter#332D23
hypocenterC23#1638
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #13092769C2semidirect
3. #13092713C2semidirect
5. #13092147C2semidirect
7. C23×#332C2semidirect
87. #332D23semidirect
111. C23#1638semidirect

Maximal subgroups

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

subgroupindex
#130931412
#130927692
#130927132
#130927082
#130921472
#130921442
C23×#3322
#163823