Finite Group Databasebeta

← #15672628

Subgroups — #15672628

Order 2944.

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

normal subgroups only

This group has 212 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#13093132C211yesmaximal, characteristic
2#13092768C211yesmaximal, characteristic, complemented
3#13092697C211yesmaximal, characteristic, complemented
4#13092623C211yesmaximal, characteristic, complemented
5#13092165C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic, complemented
8C4×D4×C23C2211yescharacteristic
9#10625109—21no—
10#10625101—21no—
11#10625097—21no—
12C2×#67263—21no—
13#10625063—21no—
14#10625056—22no—
15C4×D92C2211yescharacteristic
16#10625040C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C4×C8×C23C2211yescharacteristic
20#10625014—21no—
21#10624998—22no—
22#10624998—21no—
23#10624989—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×D4×C23D411yescharacteristic
26C22×C4×C23—21no—
27C2×C22⋊D23—22no—
28C2×D92D411yescharacteristic
29C2×C4×D23—21no—
30C2×Dic46—21no—
31C2×Dic46D412yes—
32C2×C8×C23—21no—
33C2×C8×C23—21no—
34C4⋊C4×C23D411yescharacteristic
35C22⋊C4×C23—21no—
36C42×C23C2311yescharacteristic
37C22⋊Dic23—22no—
38(C2×D23)⋊C4—22no—
39(C2×D23)⋊C4—21no—
40C4⋊Dic23—21no—
41C4⋊Dic23—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23—21no—
44C4⋊Dic23D411yescharacteristic
45C4×Dic23—22no—
46C2×C23⋊C8—21no—
47#67263—42no—
48C23×C23—21no—
49C22×D23—21no—
50D4×C23—21no—
51D4×C23—21no—
52C2×C4×C23—21no—
53C2×C4×C23—41no—
54C2×C4×C23—41no—
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C22⋊D23—82no—
59C2×Dic23—21no—
60C2×Dic23—22no—
61C2×Dic23—41no—
62D92—21no—
63D92—21no—
64C4×D23—41no—
65C4×D23—41no—
66Dic46—42no—
67Dic46—41no—
68Dic46—41no—
69C8×C23—41no—
70C8×C23—41no—
71C23⋊C8—41no—
72#1646—231nomaximal, Sylow
73C22×C23—41no—
74C22×C23—41no—
75C22×C23—41no—
76C22×C23#12011yescharacteristic
77C2×D23—41no—
78C2×D23—41no—
79C2×D23—41no—
80C4×C23—21no—
81C4×C23—41no—
82C4×C23#13511yescharacteristic
83C4×C23#13511yescharacteristic
84C4×C23AGL(1,ℤ/8)11yescharacteristic
85C4×C23#13711yescharacteristic
86Dic23—41no—
87Dic23—42no—
88Dic23—81no—
89#555—231no—
90#487—231no—
91#474—231no—
92#461—231no—
93#333—231no—
94D4⋊C8—231no—
95D4⋊C8D2311yescharacteristic, complemented
96C2×C23—81no—
97C2×C23#44911yescharacteristic
98C2×C23#45211yescharacteristic
99C2×C23#45511yescharacteristic
100D23—81no—
101C2×SD16—461no—
102C4⋊Q8—231no—
103C4⋊Q8—231no—
104#124—462no—
105#121—461no—
106#121—461no—
107C4×D4—231no—
108C4×D4C2×D2311yescharacteristic
109#117—461no—
110#117—461no—
111#107—461no—
112C4⋊C8—231no—
113C4⋊C8C2×D2311yescharacteristic
114#103—461no—
115#103—462no—
116#102—461no—
117C4×C8C2×D2311yescharacteristic
118C23#164611yescharacteristic, complemented, Sylow
119C2×Q8—232no—
120C2×Q8—461no—
121C2×D4—231no—
122C2×D4—462no—
123C2×D4D9211yescharacteristic
124C22×C4—21no—
125C22×C4—461no—
126SD16—922no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—461no—
130C4⋊C4—231no—
131C4⋊C4—461no—
132C4⋊C4—461no—
133C4⋊C4—461no—
134C4⋊C4—461no—
135C4⋊C4D9211yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—462no—
138C22⋊C4—462no—
139C22⋊C4—461no—
140C42—462no—
141C42C22×D2311yescharacteristic
142C23—21no—
143C23—461no—
144Q8—922no—
145Q8—921no—
146Q8—921no—
147D4—21no—
148D4—21no—
149D4—461no—
150D4—461no—
151D4—1842no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—461no—
156C2×C4—462no—
157C2×C4—921no—
158C2×C4—921no—
159C2×C4—921no—
160C2×C4C2×D9211yescharacteristic
161C2×C4D4×D2311yescharacteristic
162C2×C4D4×D2311yescharacteristic
163C8—41no—
164C8—41no—
165C8—921no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—921no—
170C22—921no—
171C22—921no—
172C22#1062505311yescharacteristic
173C4—21no—
174C4—41no—
175C4—921no—
176C4—922no—
177C4—1841no—
178C4#1062507511yescharacteristic
179C4#1062508011yescharacteristic
180C4#1062508211yescharacteristic
181C4#1062508711yescharacteristic
182C2—81no—
183C2—1841no—
184C2#1309256311yescharacteristic
185C2#1309258111yescharacteristic
186C2#1309259611yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23#120
prime radical#13093132C2
hypercenterD4⋊C8D23
hypocenterC23#1646
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. #13092768C2semidirect
3. #13092697C2semidirect
4. #13092623C2semidirect
5. #13092165C2semidirect
6. #13092146C2semidirect
7. C23×D4⋊C8C2semidirect
95. D4⋊C8D23semidirect
118. C23#1646semidirect

Maximal subgroups

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

subgroupindex
#130931322
#130927682
#130926972
#130926232
#130921652
#130921462
C23×D4⋊C82
#164623