Finite Group Databasebeta

← #15672495

Subgroups — #15672495

Order 2944.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#13093145C211yesmaximal, characteristic, complemented
2#13092764C211yesmaximal, characteristic
3#13092618C211yesmaximal, characteristic
4#13092617C211yesmaximal, characteristic
5#13092162C211yesmaximal, characteristic, complemented
6#13092149C211yesmaximal, characteristic, complemented
7C23×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C23C2211yescharacteristic
9#10625115—21no—
10C2×#67274—21no—
11C2×#67263—21no—
12#10625060—22no—
13#10625058—21no—
14#10625045C2211yescharacteristic
15#10625041—21no—
16#10625040C2211yescharacteristic
17C4×Dic46—21no—
18C4×Dic46C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C4×C8×C23C2211yescharacteristic
21#10625003—21no—
22#10625003—22no—
23#10624991—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23D411yescharacteristic
26C2×D92—21no—
27C2×D92—21no—
28C2×D92—21no—
29C2×Dic46—21no—
30C2×Dic46D411yescharacteristic
31C2×C8×C23—21no—
32C2×C8×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23D411yescharacteristic
35C42×C23—21no—
36C42×C23C2311yescharacteristic
37#67274—42no—
38C4⋊Dic23—21no—
39C4⋊Dic23D411yescharacteristic
40C4⋊Dic23D412yes—
41Dic23⋊C4—22no—
42Dic23⋊C4—22no—
43Dic23⋊C4—22no—
44Dic23⋊C4—21no—
45C4×Dic23—22no—
46C4×Dic23—21no—
47C2×C23⋊C8—21no—
48#67263—42no—
49C22×D23—41no—
50Q8×C23—21no—
51Q8×C23—21no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23C2×D411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×Dic23—21no—
58C2×Dic23—21no—
59C2×Dic23—22no—
60D92—42no—
61D92—41no—
62D92—41no—
63D92—41no—
64D92—41no—
65Dic46—21no—
66Dic46—41no—
67Dic46—41no—
68Dic46SD1612yescomplemented
69C8×C23—41no—
70C8×C23—41no—
71C23⋊C8—41no—
72#1626—231nomaximal, Sylow
73C22×C23#12011yescharacteristic
74C2×D23—81no—
75C2×D23—81no—
76C2×D23—81no—
77C4×C23—21no—
78C4×C23—41no—
79C4×C23—41no—
80C4×C23C2×SD1611yescharacteristic
81C4×C23#13511yescharacteristic
82C4×C23AGL(1,ℤ/8)11yescharacteristic
83C4×C23#13711yescharacteristic
84Dic23—22no—
85Dic23—42no—
86Dic23—41no—
87#557—231no—
88#486—231no—
89#460—231no—
90#460—231no—
91#332—231no—
92Q8⋊C8—231no—
93Q8⋊C8D2311yescharacteristic, complemented
94C2×C23#44811yescharacteristic
95C2×C23#44911yescharacteristic
96C2×C23#45411yescharacteristic
97D23—161no—
98C2×SD16—461no—
99C2×SD16—461no—
100C4⋊Q8—231no—
101C4⋊Q8—461no—
102#127—231no—
103#125—461no—
104#125—462no—
105C4×Q8—231no—
106C4×Q8—461no—
107C4×Q8—461no—
108C4×Q8C2×D2311yescharacteristic
109C4⋊C8—231no—
110C4⋊C8C2×D2311yescharacteristic
111#102—461no—
112#102—462no—
113#102—461no—
114C4×C8C2×D2311yescharacteristic
115C23#162611yescharacteristic, complemented, Sylow
116C2×Q8—231no—
117C2×Q8—461no—
118C2×Q8D9211yescharacteristic
119C2×D4—461no—
120C2×D4—461no—
121C2×D4—461no—
122SD16—922no—
123SD16—922no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—461no—
127C4⋊C4—21no—
128C4⋊C4—231no—
129C4⋊C4—232no—
130C4⋊C4—462no—
131C4⋊C4—462no—
132C4⋊C4—462no—
133C4⋊C4—461no—
134C4⋊C4—461no—
135C4⋊C4D9211yescharacteristic
136C42—21no—
137C42—462no—
138C42—461no—
139C42C22×D2311yescharacteristic
140C23—921no—
141Q8—21no—
142Q8—21no—
143Q8—232no—
144Q8—461no—
145Q8—921no—
146Q8—921no—
147D4—922no—
148D4—921no—
149D4—921no—
150D4—921no—
151D4—921no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—461no—
155C2×C4—461no—
156C2×C4—462no—
157C2×C4C2×D9211yescharacteristic
158C2×C4D4×D2311yescharacteristic
159C2×C4D4×D2311yescharacteristic
160C8—41no—
161C8—41no—
162C8—921no—
163C22—1841no—
164C22—1841no—
165C22—1841no—
166C22#1062505311yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—462no—
171C4—922no—
172C4—921no—
173C4#1062507511yescharacteristic
174C4#1062507911yescharacteristic
175C4SD16×D2311yescharacteristic
176C4#1062508911yescharacteristic
177C2—3681no—
178C2#1309255711yescharacteristic
179C2#1309256411yescharacteristic
180C2#1309259111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×Q8⋊C8C2
socleC22×C23#120
prime radical#10625045C22
hypercenterQ8⋊C8D23
hypocenterC23#1626
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #13093145C2semidirect
5. #13092162C2semidirect
6. #13092149C2semidirect
7. C23×Q8⋊C8C2semidirect
68. Dic46SD16semidirect
93. Q8⋊C8D23semidirect
115. C23#1626semidirect

Maximal subgroups

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

subgroupindex
#130931452
#130927642
#130926182
#130926172
#130921622
#130921492
C23×Q8⋊C82
#162623