Finite Group Databasebeta

← #15672734

Subgroups — #15672734

Order 2944.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#13093167C211yesmaximal, characteristic
2#13092826C211yesmaximal, characteristic, complemented
3#13092786C211yesmaximal, characteristic, complemented
4#13092776C211yesmaximal, characteristic
5#13092158C211yesmaximal, characteristic, complemented
6#13092158C211yesmaximal, characteristic, complemented
7C23×#329C211yesmaximal, characteristic
8C23×#124C2211yescharacteristic
9#10625115—21no—
10#10625106—21no—
11#10625050—21no—
12#10625050—21no—
13#10625049—21no—
14#10625049—21no—
15#10625041C2211yescharacteristic
16#10625041C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×#97C2211yescharacteristic
19C23×#97C2211yescharacteristic
20#10625017—21no—
21#10625014—21no—
22#10625000—21no—
23#10624999—21no—
24#10624998—21no—
25#10624998—21no—
26#10624985C2211yescharacteristic
27C2×Q8×C23D411yescharacteristic
28C2×D4×C23D411yescharacteristic
29C22×Dic23—21no—
30C2×Dic46—21no—
31C2×Dic46—21no—
32C2×C8×C23—21no—
33C2×C8×C23—21no—
34C22⋊C4×C23—21no—
35C22⋊C4×C23—21no—
36C42×C23C2311yescharacteristic
37C22⋊Dic23—21no—
38C22⋊Dic23—21no—
39C22⋊Dic23—21no—
40C4⋊Dic23—21no—
41C4⋊Dic23—21no—
42C4⋊Dic23D411yescharacteristic
43C4⋊Dic23D411yescharacteristic
44C4⋊Dic23D411yescharacteristic
45C4⋊Dic23D411yescharacteristic
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52C4×Dic23—21no—
53C2×C23⋊C8—21no—
54C23×C23—21no—
55Q8×C23—41no—
56D4×C23—41no—
57C2×C4×C23—21no—
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×Dic23—21no—
62C2×Dic23—21no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—41no—
66C2×Dic23—81no—
67Dic46—42no—
68Dic46—81no—
69C8×C23—22no—
70C8×C23—41no—
71C23⋊C8—41no—
72#1664—231nomaximal, Sylow
73C22×C23—41no—
74C22×C23—41no—
75C22×C23—41no—
76C22×C23#12011yescharacteristic
77C4×C23—21no—
78C4×C23—21no—
79C4×C23—21no—
80C4×C23—41no—
81Dic23—41no—
82Dic23—41no—
83Dic23—41no—
84Dic23—41no—
85Dic23—81no—
86#563—231no—
87#501—231no—
88#491—231no—
89#489—231no—
90#330—231no—
91#330—231no—
92#329D2311yescharacteristic
93C2×C23—81no—
94C2×C23#45411yescharacteristic
95C2×C23#45511yescharacteristic
96C2×C23#45611yescharacteristic
97C4⋊Q8—231no—
98C4⋊Q8—461no—
99#126—461no—
100#126—461no—
101#125—231no—
102#125—231no—
103#124C2×D2311yescharacteristic
104#123—461no—
105C22⋊Q8—461no—
106C22⋊Q8—461no—
107#107—461no—
108#106—461no—
109#103—461no—
110#103—461no—
111#103—461no—
112#102—461no—
113#97—231no—
114#97C2×D2311yescharacteristic
115#97C2×D2311yescharacteristic
116C23#166411yescharacteristic, complemented, Sylow
117C2×Q8—461no—
118C2×Q8—461no—
119C2×Q8D9211yescharacteristic
120C2×D4D9211yescharacteristic
121C22×C4—461no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—461no—
125C4⋊C4—231no—
126C4⋊C4—231no—
127C4⋊C4—231no—
128C4⋊C4—231no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C4⋊C4—461no—
132C4⋊C4—461no—
133C4⋊C4—461no—
134C4⋊C4—461no—
135C4⋊C4—461no—
136C4⋊C4—461no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—461no—
140C22⋊C4—461no—
141C22⋊C4—461no—
142C42—461no—
143C42C22×D2311yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—922no—
147Q8—1841no—
148D4—41no—
149C2×C4—21no—
150C2×C4—461no—
151C2×C4—461no—
152C2×C4—461no—
153C2×C4—461no—
154C2×C4—921no—
155C2×C4—1841no—
156C2×C4C2×D9211yescharacteristic
157C2×C4D4×D2311yescharacteristic
158C2×C4D4×D2311yescharacteristic
159C8—22no—
160C8—41no—
161C8—921no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1062505311yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—921no—
171C4—921no—
172C4—921no—
173C4—921no—
174C4—1841no—
175C2—81no—
176C2#1309259111yescharacteristic
177C2#1309259711yescharacteristic
178C2#1309260111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#329C2
socleC22×C23#120
prime radicalC2×D4×C23D4
hypercenter#329D23
hypocenterC23#1664
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #13092826C2semidirect
3. #13092786C2semidirect
5. #13092158C2semidirect
6. #13092158C2semidirect
116. C23#1664semidirect

Maximal subgroups

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

subgroupindex
#130931672
#130928262
#130927862
#130927762
#130921582
C23×#3292
#166423