Finite Group Databasebeta

← #15672703

Subgroups — #15672703

Order 2944.

228 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 49 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#13092812C211yesmaximal, characteristic, complemented
2#13092776C212yesmaximal, complemented
3#13092157C212yesmaximal, complemented
4#13092157C211yesmaximal, characteristic, complemented
5C23×H(3,𝔽4)C211yesmaximal, characteristic
6C23×#124—21no—
7C23×#124—22no—
8C23×#124C2212yes—
9C23×#124C2211yescharacteristic
10C23×#120—21no—
11C23×#120—22no—
12C2×#67275—21no—
13C2×#67273—21no—
14#10625040C2211yescharacteristic, complemented
15#10625017—22no—
16#10625014—22no—
17#10624985C2212yescomplemented
18#10624985C2211yescharacteristic, complemented
19C24×C23—21no—
20C2×Q8×C23D411yescharacteristic
21C2×Q8×C23D412yes—
22C2×D4×C23—21no—
23C2×D4×C23—22no—
24C2×D4×C23D411yescharacteristic
25C2×D4×C23D412yes—
26C2×Dic46—21no—
27C22⋊C4×C23—22no—
28C22⋊C4×C23—21no—
29C22⋊C4×C23—22no—
30C22⋊C4×C23—22no—
31C22⋊C4×C23—22no—
32C42×C23—21no—
33C42×C23C2311yescharacteristic
34#67275—42no—
35#67273—42no—
36C4⋊Dic23—22no—
37C2×C23⋊C8—21no—
38C2×C23⋊C8—22no—
39C23×C23—21no—
40C23×C23—22no—
41C23×C23—81no—
42C23×C23—82no—
43Q8×C23—41no—
44Q8×C23—42no—
45D4×C23—41no—
46D4×C23—42no—
47D4×C23—81no—
48D4×C23—82no—
49C2×C4×C23—21no—
50C2×C4×C23—22no—
51C2×C4×C23C2×D412yes—
52C2×C4×C23C2×D411yescharacteristic
53C2×Dic23—41no—
54Dic46—41no—
55Dic46—41no—
56C23⋊C8—22no—
57C23⋊C8—42no—
58#1659—231nomaximal, Sylow
59C22×C23—41no—
60C22×C23—42no—
61C22×C23—42no—
62C22×C23—42no—
63C22×C23—42no—
64C22×C23—84no—
65C22×C23#12011yescharacteristic
66C4×C23—21no—
67C4×C23—22no—
68C4×C23—41no—
69C4×C23—42no—
70Dic23—81no—
71H(3,𝔽4)D2311yescharacteristic
72#497—231no—
73#489—232no—
74#329—231no—
75#329—232no—
76C2×C23—81no—
77C2×C23—82no—
78C2×C23#45311yescharacteristic
79C2×C23#45512yes—
80C2×Q16—461no—
81C2×SD16—461no—
82C4⋊Q8—231no—
83#124—22no—
84#124—21no—
85#124C2×D2312yes—
86#124C2×D2311yescharacteristic
87#120—22no—
88#120—21no—
89#103—462no—
90#102—462no—
91#97—232no—
92#97—231no—
93C23#165911yescharacteristic, complemented, Sylow
94C24—21no—
95C2×Q8—461no—
96C2×Q8C22⋊D2312yes—
97C2×Q8C22⋊D2311yescharacteristic
98C2×D4—21no—
99C2×D4—22no—
100C2×D4C22⋊D2312yes—
101C2×D4C22⋊D2311yescharacteristic
102Q16—922no—
103SD16—922no—
104C2×C8—461no—
105C2×C8—462no—
106C4⋊C4—462no—
107C22⋊C4—22no—
108C22⋊C4—21no—
109C22⋊C4—22no—
110C22⋊C4—22no—
111C22⋊C4—22no—
112C42—21no—
113C42C22×D2311yescharacteristic
114C23—21no—
115C23—22no—
116C23—81no—
117C23—82no—
118Q8—41no—
119Q8—42no—
120Q8—921no—
121Q8—921no—
122D4—41no—
123D4—42no—
124D4—81no—
125D4—82no—
126C2×C4—21no—
127C2×C4—22no—
128C2×C4—921no—
129C2×C4C2×C22⋊D2312yes—
130C2×C4C2×C22⋊D2311yescharacteristic
131C8—462no—
132C8—922no—
133C22—41no—
134C22—42no—
135C22—42no—
136C22—42no—
137C22—42no—
138C22—84no—
139C22#1062512411yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—42no—
144C4—1841no—
145C2—81no—
146C2—82no—
147C2#1309258511yescharacteristic
148C2#1309259512yes—
subgroupG/H
centerC22#10625124
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
Fitting, prime radicalC23×H(3,𝔽4)C2
socleC22×C23#120
hypercenterH(3,𝔽4)D23
hypocenterC23#1659
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #13092812C2semidirect
2. #13092776C2semidirect
3. #13092157C2semidirect
4. #13092157C2semidirect
14. #10625040C22semidirect
17. #10624985C22semidirect
18. #10624985C22semidirect
93. C23#1659semidirect

Maximal subgroups

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

subgroupindex
#130928122
#130927762
#130921572
C23×H(3,𝔽4)2
#165923