Finite Group Databasebeta

← #15672731

Subgroups — #15672731

Order 2944.

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

normal subgroups only

This group has 184 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#13092827C211yesmaximal, characteristic, complemented
2#13092787C211yesmaximal, characteristic, complemented
3#13092776C211yesmaximal, characteristic
4#13092159C211yesmaximal, characteristic, complemented
5#13092159C211yesmaximal, characteristic, complemented
6#13092157C211yesmaximal, characteristic
7C23×#563C211yesmaximal, characteristic
8C23×C4⋊Q8—21no—
9C23×#126—21no—
10C23×#126—21no—
11C23×#125C2211yescharacteristic
12C23×#125C2211yescharacteristic
13C23×#124C2211yescharacteristic
14C23×#123—21no—
15C23×C22⋊Q8—21no—
16C23×C22⋊Q8—21no—
17#10625040C2211yescharacteristic
18#10625017—21no—
19#10625014—21no—
20#10624992—21no—
21#10624992—21no—
22#10624990—21no—
23#10624989—21no—
24#10624985C2211yescharacteristic
25#10624985C2211yescharacteristic
26#10624985C2211yescharacteristic
27C2×Q8×C23—21no—
28C2×Q8×C23D411yescharacteristic
29C2×D4×C23D411yescharacteristic
30C22×C4×C23—21no—
31C2×Dic46—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23D411yescharacteristic
39C4⋊C4×C23D411yescharacteristic
40C4⋊C4×C23D411yescharacteristic
41C4⋊C4×C23D411yescharacteristic
42C22⋊C4×C23—21no—
43C22⋊C4×C23—21no—
44C22⋊C4×C23—21no—
45C22⋊C4×C23—21no—
46C22⋊C4×C23—21no—
47C42×C23—21no—
48C42×C23C2311yescharacteristic
49C4⋊Dic23—21no—
50C4⋊Dic23—21no—
51C2×C23⋊C8—21no—
52C2×C23⋊C8—21no—
53C2×C23⋊C8—21no—
54C23×C23—21no—
55Q8×C23—41no—
56Q8×C23—81no—
57D4×C23—41no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—81no—
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×Dic23—41no—
68Dic46—42no—
69C23⋊C8—22no—
70C23⋊C8—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—
81C4×C23—41no—
82C4×C23—41no—
83C4×C23—41no—
84C4×C23—41no—
85Dic23—81no—
86#563D2311yescharacteristic
87#501—231no—
88#491—231no—
89#489—231no—
90#330—231no—
91#330—231no—
92#329—231no—
93C2×C23—81no—
94C2×C23#45411yescharacteristic
95C2×C23#45511yescharacteristic
96C2×C23#45611yescharacteristic
97C4⋊Q8—21no—
98C4⋊Q8—231no—
99#126—21no—
100#126—21no—
101#125C2×D2311yescharacteristic
102#125C2×D2311yescharacteristic
103#124C2×D2311yescharacteristic
104#123—21no—
105C22⋊Q8—21no—
106C22⋊Q8—21no—
107#107—461no—
108#106—461no—
109#103—461no—
110#103—461no—
111#103—461no—
112#102—461no—
113#97—231no—
114#97—231no—
115#97—231no—
116C23#166411yescharacteristic, complemented, Sylow
117C2×Q8—21no—
118C2×Q8—461no—
119C2×Q8C22⋊D2311yescharacteristic
120C2×D4C22⋊D2311yescharacteristic
121C22×C4—21no—
122C2×C8—461no—
123C2×C8—461no—
124C2×C8—461no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—461no—
132C4⋊C4—461no—
133C4⋊C4C22⋊D2311yescharacteristic
134C4⋊C4C22⋊D2311yescharacteristic
135C4⋊C4C22⋊D2311yescharacteristic
136C4⋊C4C22⋊D2311yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C22×D2311yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—81no—
147Q8—922no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—81no—
155C2×C4—921no—
156C2×C4C2×C22⋊D2311yescharacteristic
157C2×C4C2×C22⋊D2311yescharacteristic
158C2×C4C2×C22⋊D2311yescharacteristic
159C8—462no—
160C8—921no—
161C8—921no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1062512411yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—1841no—
175C2—81no—
176C2#1309259011yescharacteristic
177C2#1309259511yescharacteristic
178C2#1309260011yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#563C2
socleC22×C23#120
prime radicalC2×D4×C23D4
hypercenter#563D23
hypocenterC23#1664
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #13092827C2semidirect
2. #13092787C2semidirect
4. #13092159C2semidirect
5. #13092159C2semidirect
116. C23#1664semidirect

Maximal subgroups

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

subgroupindex
#130928272
#130927872
#130927762
#130921592
#130921572
C23×#5632
#166423