Finite Group Databasebeta

← #15672533

Subgroups — #15672533

Order 2944.

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

normal subgroups only

This group has 214 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#13093124C211yesmaximal, characteristic
2#13092797C211yesmaximal, characteristic, complemented
3#13092713C211yesmaximal, characteristic, complemented
4#13092707C211yesmaximal, characteristic
5#13092165C211yesmaximal, characteristic, complemented
6#13092149C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic
8C4×D4×C23C2211yescharacteristic
9D4×Dic23—21no—
10C2×C4⋊Dic23—21no—
11#10625095—21no—
12C2×Dic92—22no—
13#10625061—21no—
14#10625049—22no—
15#10625040C2211yescharacteristic
16#10625040C2211yescharacteristic
17C4×Dic46C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C4×C8×C23C2211yescharacteristic
20#10625014—21no—
21#10625000—21no—
22#10624998—21no—
23#10624990—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×D4×C23D411yescharacteristic
26C22×C4×C23—21no—
27C22×Dic23—22no—
28C2×Dic46—21no—
29C2×Dic46D411yescharacteristic
30C2×Dic46D412yes—
31C2×C8×C23—21no—
32C2×C8×C23—21no—
33C4⋊C4×C23D411yescharacteristic
34C22⋊C4×C23—21no—
35C42×C23C2311yescharacteristic
36C22⋊Dic23—22no—
37C4⋊Dic23—22no—
38C4⋊Dic23—21no—
39C4⋊Dic23—21no—
40C4⋊Dic23—21no—
41C4⋊Dic23—21no—
42C4⋊Dic23D411yescharacteristic
43Dic23⋊C4—22no—
44Dic23⋊C4—21no—
45C4×Dic23—21no—
46C2×C23⋊C8—21no—
47Dic92—44no—
48C23×C23—21no—
49D4×C23—21no—
50D4×C23Q1612yescomplemented
51C2×C4×C23—21no—
52C2×C4×C23—41no—
53C2×C4×C23—41no—
54C2×C4×C23C2×D411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×Dic23—21no—
58C2×Dic23—21no—
59C2×Dic23—22no—
60C2×Dic23—41no—
61C2×Dic23—82no—
62Dic46—21no—
63Dic46—21no—
64Dic46—42no—
65Dic46—42no—
66C8×C23—22no—
67C8×C23—41no—
68C23⋊C8—41no—
69#1632—231nomaximal, Sylow
70C22×C23—22no—
71C22×C23—41no—
72C22×C23—41no—
73C22×C23#12011yescharacteristic
74C4×C23—21no—
75C4×C23—41no—
76C4×C23C2×Q1611yescharacteristic
77C4×C23#13511yescharacteristic
78C4×C23#13711yescharacteristic
79C4×C23#13711yescharacteristic
80Dic23—41no—
81Dic23—42no—
82Dic23—41no—
83Dic23—81no—
84#554—231no—
85#494—231no—
86#477—231no—
87#476—231no—
88#333—231no—
89Q8⋊C8—231no—
90D4⋊C8D2311yescharacteristic
91C2×C23—42no—
92C2×C23#45111yescharacteristic
93C2×C23#45211yescharacteristic
94C2×C23#45311yescharacteristic
95C2×Q16—462no—
96C4⋊Q8—231no—
97C4⋊Q8—231no—
98#125—461no—
99C22⋊Q8—462no—
100C22⋊Q8—461no—
101C4×Q8—231no—
102C4×D4—461no—
103C4×D4C2×D2311yescharacteristic
104C2×C4⋊C4—461no—
105#107—461no—
106#106—461no—
107C4⋊C8—231no—
108C4⋊C8C2×D2311yescharacteristic
109#103—461no—
110#102—461no—
111C4×C8C2×D2311yescharacteristic
112C23#163211yescharacteristic, complemented, Sylow
113C2×Q8—231no—
114C2×Q8—232no—
115C2×Q8—461no—
116C2×D4D9211yescharacteristic
117C22×C4—21no—
118C22×C4—462no—
119Q16—924no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—461no—
123C4⋊C4—231no—
124C4⋊C4—462no—
125C4⋊C4—462no—
126C4⋊C4—461no—
127C4⋊C4—461no—
128C4⋊C4—461no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C4⋊C4D9211yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—462no—
134C42—461no—
135C42C22×D2311yescharacteristic
136C23—21no—
137Q8—461no—
138Q8—461no—
139Q8—922no—
140Q8—922no—
141D4—21no—
142D4Dic9212yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—461no—
147C2×C4—461no—
148C2×C4—462no—
149C2×C4—921no—
150C2×C4—1842no—
151C2×C4C2×D9211yescharacteristic
152C2×C4D4×D2311yescharacteristic
153C2×C4D4×D2311yescharacteristic
154C8—22no—
155C8—41no—
156C8—921no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1062505311yescharacteristic
161C4—21no—
162C4—41no—
163C4—921no—
164C4—921no—
165C4—922no—
166C4—1841no—
167C4C2×Dic9211yescharacteristic
168C4#1062508011yescharacteristic
169C4#1062508311yescharacteristic
170C4#1062508611yescharacteristic
171C2—42no—
172C2#1309257511yescharacteristic
173C2#1309258011yescharacteristic
174C2#1309258611yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23#120
prime radicalC2×D4×C23D4
hypercenterD4⋊C8D23
hypocenterC23#1632
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13092797C2semidirect
3. #13092713C2semidirect
5. #13092165C2semidirect
6. #13092149C2semidirect
50. D4×C23Q16semidirect
112. C23#1632semidirect
142. D4Dic92semidirect

Maximal subgroups

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

subgroupindex
#130931242
#130927972
#130927132
#130927072
#130921652
#130921492
C23×D4⋊C82
#163223