Finite Group Databasebeta

← #15672492

Subgroups — #15672492

Order 2944.

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

normal subgroups only

This group has 210 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#13093146C211yesmaximal, characteristic, complemented
2#13092763C211yesmaximal, characteristic
3#13092614C211yesmaximal, characteristic
4#13092162C211yesmaximal, characteristic, complemented
5Q8⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092147C211yesmaximal, characteristic, complemented
7C23×#460C211yesmaximal, characteristic
8C2×SD16×C23—21no—
9C23×#127C2211yescharacteristic
10C4×Q8×C23C2211yescharacteristic
11Q8×Dic23—21no—
12C2×#67273—21no—
13#10625061—21no—
14#10625061—22no—
15#10625040—21no—
16#10625040C2211yescharacteristic
17C4×Dic46—21no—
18C4×Dic46C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C23×#102—21no—
21#10625014—21no—
22#10625014—22no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23D411yescharacteristic
26C2×D4×C23—21no—
27C2×D4×C23—21no—
28C2×D4×C23—21no—
29C2×Dic46—21no—
30C2×Dic46D411yescharacteristic
31SD16×C23—42no—
32C2×C8×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23D411yescharacteristic
35C42×C23—21no—
36C42×C23C2311yescharacteristic
37#67273—42no—
38C4⋊Dic23—22no—
39C4⋊Dic23—22no—
40C4⋊Dic23—21no—
41C4⋊Dic23D411yescharacteristic
42C4⋊Dic23D412yes—
43Dic23⋊C4—22no—
44Dic23⋊C4—21no—
45C4×Dic23—22no—
46C4×Dic23—21no—
47C2×C23⋊C8—21no—
48C2×C23⋊C8—21no—
49C23×C23—41no—
50Q8×C23—21no—
51Q8×C23SD1612yescomplemented
52D4×C23—42no—
53D4×C23—41no—
54D4×C23—41no—
55D4×C23—41no—
56D4×C23—41no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C2×Dic23—21no—
63C2×Dic23—21no—
64C2×Dic23—22no—
65Dic46—21no—
66Dic46—21no—
67Dic46—41no—
68Dic46—41no—
69C8×C23—41no—
70C23⋊C8—41no—
71C23⋊C8—41no—
72#1626—231nomaximal, Sylow
73C22×C23—81no—
74C22×C23—81no—
75C22×C23—81no—
76C22×C23#12011yescharacteristic
77C4×C23—22no—
78C4×C23—21no—
79C4×C23—41no—
80C4×C23C2×SD1611yescharacteristic
81C4×C23#13511yescharacteristic
82C4×C23AGL(1,ℤ/8)11yescharacteristic
83C4×C23#13711yescharacteristic
84Dic23—41no—
85Dic23—42no—
86Dic23—41no—
87#557—231no—
88#486—231no—
89#460—231no—
90#460D2311yescharacteristic
91#332—231no—
92Q8⋊C8—231no—
93Q8⋊C8—231no—
94C2×C23—161no—
95C2×C23#44811yescharacteristic
96C2×C23#44911yescharacteristic
97C2×C23#45411yescharacteristic
98C2×SD16—21no—
99C2×SD16—461no—
100C4⋊Q8—231no—
101C4⋊Q8—461no—
102#127C2×D2311yescharacteristic
103#125—462no—
104#125—461no—
105C4×Q8—231no—
106C4×Q8—461no—
107C4×Q8—461no—
108C4×Q8C2×D2311yescharacteristic
109C4⋊C8—231no—
110C4⋊C8C2×D2311yescharacteristic
111#102—21no—
112#102—461no—
113#102—462no—
114C4×C8—231no—
115C23#162611yescharacteristic, complemented, Sylow
116C2×Q8—231no—
117C2×Q8—461no—
118C2×Q8C22⋊D2311yescharacteristic
119C2×D4—21no—
120C2×D4—21no—
121C2×D4—21no—
122SD16—42no—
123SD16—922no—
124C2×C8—21no—
125C2×C8—461no—
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⋊C4C22⋊D2311yescharacteristic
136C42—21no—
137C42—462no—
138C42—461no—
139C42C22×D2311yescharacteristic
140C23—41no—
141Q8—21no—
142Q8—461no—
143Q8—461no—
144Q8—921no—
145Q8—921no—
146Q8#6727312yescomplemented
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—461no—
155C2×C4—462no—
156C2×C4—461no—
157C2×C4D4×D2311yescharacteristic
158C2×C4D4×D2311yescharacteristic
159C2×C4C2×C22⋊D2311yescharacteristic
160C8—41no—
161C8—921no—
162C8—921no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#1062510811yescharacteristic
167C4—22no—
168C4—21no—
169C4—41no—
170C4—921no—
171C4—922no—
172C4—921no—
173C4#1062508511yescharacteristic
174C4#1062508711yescharacteristic
175C4C2×#6727311yescharacteristic
176C4#1062512211yescharacteristic
177C2—161no—
178C2#1309255511yescharacteristic
179C2#1309256111yescharacteristic
180C2#1309258811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#460C2
socleC22×C23#120
prime radicalC23×#127C22
hypercenter#460D23
hypocenterC23#1626
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #13093146C2semidirect
4. #13092162C2semidirect
5. Q8⋊(C23⋊C8)C2semidirect
6. #13092147C2semidirect
51. Q8×C23SD16semidirect
115. C23#1626semidirect
146. Q8#67273semidirect

Maximal subgroups

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

subgroupindex
#130931462
#130927632
#130926142
#130921622
Q8⋊(C23⋊C8)2
#130921472
C23×#4602
#162623