Finite Group Databasebeta

← #15672722

Subgroups — #15672722

Order 2944.

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

normal subgroups only

This group has 196 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#13093161C211yesmaximal, characteristic
2#13092786C211yesmaximal, characteristic, complemented
3#13092777C211yesmaximal, characteristic, complemented
4#13092776C211yesmaximal, characteristic, complemented
5#13092158C211yesmaximal, characteristic, complemented
6#13092156C211yesmaximal, characteristic, complemented
7C23×#329C211yesmaximal, characteristic, complemented
8C23×#124C2211yescharacteristic
9#10625117—21no—
10#10625110—21no—
11#10625057—21no—
12#10625055—21no—
13#10625054—21no—
14#10625049—21no—
15#10625046C2211yescharacteristic
16#10625041C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×#97C2211yescharacteristic
19C23×#97C2211yescharacteristic
20#10625017—21no—
21#10625014—21no—
22#10625003—21no—
23#10624998—21no—
24#10624998—21no—
25#10624998—21no—
26#10624985C2211yescharacteristic
27C2×Q8×C23D411yescharacteristic
28C2×D4×C23D411yescharacteristic
29C2×C22⋊D23—21no—
30C2×C22⋊D23—21no—
31C22×Dic23—21no—
32C2×D92D411yescharacteristic
33C2×C4×D23—21no—
34C2×Dic46—21no—
35C2×Dic46D411yescharacteristic
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C22⋊C4×C23—21no—
39C22⋊C4×C23—21no—
40C42×C23C2311yescharacteristic
41C22⋊Dic23—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23—21no—
47C4⋊Dic23—21no—
48C4⋊Dic23D411yescharacteristic
49C4⋊Dic23D411yescharacteristic
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53C2×C23⋊C8—21no—
54C23×C23—21no—
55C22×D23—21no—
56Q8×C23—41no—
57D4×C23—41no—
58C2×C4×C23—21no—
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C22⋊D23—81no—
63C22⋊D23—81no—
64C2×Dic23—21no—
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23—41no—
68C2×Dic23—81no—
69D92—41no—
70C4×D23—81no—
71Dic46—41no—
72Dic46—42no—
73C8×C23—41no—
74C8×C23—41no—
75C23⋊C8—41no—
76#1662—231nomaximal, Sylow
77C22×C23—41no—
78C22×C23—41no—
79C22×C23—41no—
80C22×C23#12011yescharacteristic
81C2×D23—41no—
82C2×D23—41no—
83C2×D23—41no—
84C4×C23—21no—
85C4×C23—21no—
86C4×C23—21no—
87C4×C23—41no—
88Dic23—41no—
89Dic23—41no—
90Dic23—41no—
91Dic23—81no—
92#562—231no—
93#491—231no—
94#489—231no—
95#489—231no—
96#330—231no—
97#329—231no—
98#329D2311yescharacteristic, complemented
99C2×C23—81no—
100C2×C23#45411yescharacteristic
101C2×C23#45511yescharacteristic
102C2×C23#45511yescharacteristic
103D23—81no—
104C4⋊Q8—231no—
105#125—231no—
106#124—231no—
107#124C2×D2311yescharacteristic
108#123—461no—
109#123—461no—
110C22⋊Q8—461no—
111C22⋊Q8—461no—
112#121—461no—
113#121—461no—
114#103—461no—
115#103—461no—
116#103—461no—
117#103—461no—
118#102—461no—
119#102—461no—
120#97—231no—
121#97C2×D2311yescharacteristic
122#97C2×D2311yescharacteristic
123C23#166211yescharacteristic, complemented, Sylow
124C2×Q8—231no—
125C2×Q8—461no—
126C2×Q8D9211yescharacteristic
127C2×D4—231no—
128C2×D4—461no—
129C2×D4—461no—
130C2×D4D9211yescharacteristic
131C22×C4—461no—
132C22×C4—461no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—461no—
136C4⋊C4—231no—
137C4⋊C4—231no—
138C4⋊C4—461no—
139C4⋊C4—461no—
140C4⋊C4—461no—
141C4⋊C4—461no—
142C4⋊C4—461no—
143C4⋊C4—461no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—461no—
147C22⋊C4—461no—
148C22⋊C4—461no—
149C22⋊C4—461no—
150C42C22×D2311yescharacteristic
151C23—21no—
152C23—461no—
153Q8—41no—
154Q8—921no—
155Q8—922no—
156D4—41no—
157D4—921no—
158D4—1841no—
159D4—1841no—
160C2×C4—21no—
161C2×C4—461no—
162C2×C4—461no—
163C2×C4—461no—
164C2×C4—921no—
165C2×C4—1841no—
166C2×C4—1841no—
167C2×C4C2×D9211yescharacteristic
168C2×C4D4×D2311yescharacteristic
169C2×C4D4×D2311yescharacteristic
170C8—41no—
171C8—41no—
172C8—921no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—921no—
177C22—921no—
178C22—921no—
179C22#1062505311yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—921no—
185C4—921no—
186C4—921no—
187C4—1841no—
188C2—81no—
189C2—1841no—
190C2#1309259111yescharacteristic
191C2#1309259611yescharacteristic
192C2#1309259711yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#329C2
socleC22×C23#120
prime radical#13093161C2
hypercenter#329D23
hypocenterC23#1662
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. #13092786C2semidirect
3. #13092777C2semidirect
4. #13092776C2semidirect
5. #13092158C2semidirect
6. #13092156C2semidirect
7. C23×#329C2semidirect
98. #329D23semidirect
123. C23#1662semidirect

Maximal subgroups

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

subgroupindex
#130931612
#130927862
#130927772
#130927762
#130921582
#130921562
C23×#3292
#166223