Finite Group Databasebeta

← #15672704

Subgroups — #15672704

Order 2944.

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

normal subgroups only

This group has 228 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#13093159C211yesmaximal, characteristic
2#13092812C211yesmaximal, characteristic, complemented
3#13092777C212yesmaximal, complemented
4#13092156C212yesmaximal, complemented
5C23×#329C211yesmaximal, characteristic, complemented
6C23×#124C2211yescharacteristic
7#10625118—21no—
8C2×#67275—21no—
9#10625108—21no—
10C2×#67273—21no—
11#10625056—22no—
12#10625053—22no—
13#10625046C2212yes—
14#10625040C2211yescharacteristic, complemented
15C23×#97C2212yescomplemented
16#10625003—22no—
17#10624998—22no—
18#10624985C2211yescharacteristic, complemented
19C23×D23—21no—
20C2×Q8×C23D411yescharacteristic
21C2×D4×C23D411yescharacteristic
22C2×C22⋊D23—22no—
23C2×D92—21no—
24C2×D92D412yes—
25C2×Dic46—21no—
26C2×Dic46D412yes—
27C2×C8×C23—22no—
28C22⋊C4×C23—22no—
29C42×C23C2311yescharacteristic
30C22⋊Dic23—21no—
31#67275—42no—
32#67273—42no—
33(C2×D23)⋊C4—22no—
34(C2×D23)⋊C4—22no—
35(C2×D23)⋊C4—22no—
36C4⋊Dic23—22no—
37C4×Dic23—21no—
38C2×C23⋊C8—21no—
39C23×C23—21no—
40C22×D23—22no—
41C22×D23—81no—
42C22×D23—82no—
43Q8×C23—41no—
44D4×C23—41no—
45C2×C4×C23—21no—
46C2×C4×C23C2×D411yescharacteristic
47C2×C4×C23C2×D412yes—
48C22⋊D23—82no—
49C2×Dic23—22no—
50C2×Dic23—41no—
51D92—42no—
52D92—81no—
53Dic46—42no—
54Dic46—41no—
55Dic46—41no—
56C8×C23—42no—
57C23⋊C8—22no—
58#1659—231nomaximal, Sylow
59C22×C23—41no—
60C22×C23—42no—
61C22×C23#12011yescharacteristic
62C2×D23—42no—
63C2×D23—42no—
64C2×D23—42no—
65C2×D23—84no—
66C4×C23—21no—
67C4×C23—22no—
68C4×C23—41no—
69Dic23—42no—
70Dic23—81no—
71H(3,𝔽4)—231no—
72#497—231no—
73#489—232no—
74#329—232no—
75#329D2311yescharacteristic, complemented
76C2×C23—81no—
77C2×C23#45311yescharacteristic
78C2×C23#45512yes—
79D23—82no—
80C2×Q16—461no—
81C2×SD16—461no—
82C4⋊Q8—231no—
83#124—232no—
84#124—462no—
85#124—461no—
86#124C2×D2311yescharacteristic
87#120—462no—
88#120—461no—
89#103—462no—
90#102—462no—
91#97—231no—
92#97C2×D2312yescomplemented
93C23#165911yescharacteristic, complemented, Sylow
94C24—461no—
95C2×Q8—232no—
96C2×Q8—461no—
97C2×Q8D9211yescharacteristic
98C2×D4—232no—
99C2×D4—461no—
100C2×D4—462no—
101C2×D4D9211yescharacteristic
102Q16—922no—
103SD16—922no—
104C2×C8—22no—
105C2×C8—461no—
106C4⋊C4—462no—
107C22⋊C4—22no—
108C22⋊C4—462no—
109C22⋊C4—461no—
110C22⋊C4—462no—
111C22⋊C4—462no—
112C42—461no—
113C42C22×D2311yescharacteristic
114C23—21no—
115C23—462no—
116C23—1841no—
117C23—1842no—
118Q8—41no—
119Q8—922no—
120Q8—921no—
121Q8—921no—
122D4—41no—
123D4—922no—
124D4—1841no—
125D4—1842no—
126C2×C4—21no—
127C2×C4—462no—
128C2×C4—921no—
129C2×C4C2×D9211yescharacteristic
130C2×C4D4×D2312yes—
131C8—42no—
132C8—462no—
133C22—41no—
134C22—42no—
135C22—922no—
136C22—922no—
137C22—922no—
138C22—1844no—
139C22#1062505311yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—922no—
144C4—1841no—
145C2—81no—
146C2—1842no—
147C2#1309258711yescharacteristic
148C2#1309259612yes—
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#329C2
socleC22×C23#120
prime radical#13093159C2
hypercenter#329D23
hypocenterC23#1659
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. #13092812C2semidirect
3. #13092777C2semidirect
4. #13092156C2semidirect
5. C23×#329C2semidirect
14. #10625040C22semidirect
15. C23×#97C22semidirect
18. #10624985C22semidirect
75. #329D23semidirect
92. #97C2×D23semidirect
93. C23#1659semidirect

Maximal subgroups

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

subgroupindex
#130931592
#130928122
#130927772
#130921562
C23×#3292
#165923