Finite Group Databasebeta

← #15672728

Subgroups — #15672728

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#13093171C211yesmaximal, characteristic
2#13092823C211yesmaximal, characteristic, complemented
3#13092779C211yesmaximal, characteristic
4#13092159C211yesmaximal, characteristic, complemented
5#13092158C211yesmaximal, characteristic, complemented
6#13092156C211yesmaximal, characteristic
7C23×#491C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C23×#125C2211yescharacteristic
10#10625069—21no—
11#10625069—21no—
12#10625068—21no—
13#10625067—21no—
14#10625065—21no—
15#10625059—21no—
16#10625046C2211yescharacteristic
17#10625041C2211yescharacteristic
18C23×#103—21no—
19C23×#103—21no—
20C23×#97C2211yescharacteristic
21#10624992—21no—
22#10624991—21no—
23#10624990—21no—
24#10624989—21no—
25#10624985C2211yescharacteristic
26#10624985C2211yescharacteristic
27C2×Q8×C23—21no—
28C2×D92D411yescharacteristic
29C2×C4×D23—21no—
30C2×Dic46—21no—
31C2×Dic46D411yescharacteristic
32C2×C8×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23D411yescharacteristic
38C4⋊C4×C23D411yescharacteristic
39C42×C23C2311yescharacteristic
40(C2×D23)⋊C4—21no—
41(C2×D23)⋊C4—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23D411yescharacteristic
47C4⋊Dic23D411yescharacteristic
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51C4×Dic23—21no—
52C2×C23⋊C8—21no—
53C2×C23⋊C8—21no—
54C22×D23—21no—
55Q8×C23—42no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—41no—
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C2×Dic23—21no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65D92—41no—
66C4×D23—81no—
67Dic46—41no—
68Dic46—81no—
69C8×C23—41no—
70C23⋊C8—22no—
71C23⋊C8—41no—
72#1664—231nomaximal, Sylow
73C22×C23#12011yescharacteristic
74C2×D23—41no—
75C2×D23—41no—
76C2×D23—41no—
77C4×C23—21no—
78C4×C23—21no—
79C4×C23—21no—
80C4×C23—41no—
81C4×C23—41no—
82C4×C23—81no—
83Dic23—41no—
84Dic23—41no—
85Dic23—41no—
86#563—231no—
87#501—231no—
88#491D2311yescharacteristic, complemented
89#489—231no—
90#330—231no—
91#330—231no—
92#329—231no—
93C2×C23#45411yescharacteristic
94C2×C23#45511yescharacteristic
95C2×C23#45611yescharacteristic
96D23—81no—
97C4⋊Q8—461no—
98C4⋊Q8C2×D2311yescharacteristic
99#126—461no—
100#126—461no—
101#125—231no—
102#125C2×D2311yescharacteristic
103#124—231no—
104#123—461no—
105C22⋊Q8—461no—
106C22⋊Q8—461no—
107#107—461no—
108#106—461no—
109#103—21no—
110#103—21no—
111#103—461no—
112#102—461no—
113#97—231no—
114#97—231no—
115#97C2×D2311yescharacteristic
116C23#166411yescharacteristic, complemented, Sylow
117C2×Q8—21no—
118C2×Q8—231no—
119C2×Q8—461no—
120C2×D4—231no—
121C22×C4—461no—
122C2×C8—21no—
123C2×C8—461no—
124C2×C8—461no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—231no—
130C4⋊C4—231no—
131C4⋊C4—461no—
132C4⋊C4—461no—
133C4⋊C4—461no—
134C4⋊C4—461no—
135C4⋊C4C22⋊D2311yescharacteristic
136C4⋊C4C22⋊D2311yescharacteristic
137C22⋊C4—461no—
138C22⋊C4—461no—
139C22⋊C4—461no—
140C22⋊C4—461no—
141C22⋊C4—461no—
142C42—461no—
143C42C22×D2311yescharacteristic
144C23—461no—
145Q8—42no—
146Q8—921no—
147Q8—1841no—
148D4—921no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—461no—
153C2×C4—461no—
154C2×C4—461no—
155C2×C4—1841no—
156C2×C4D4×D2311yescharacteristic
157C2×C4D4×D2311yescharacteristic
158C2×C4C2×C22⋊D2311yescharacteristic
159C8—41no—
160C8—462no—
161C8—921no—
162C22—921no—
163C22—921no—
164C22—921no—
165C22#1062510811yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—921no—
173C4—921no—
174C4—921no—
175C2—1841no—
176C2#1309258911yescharacteristic
177C2#1309259311yescharacteristic
178C2#1309259811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#491C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenter#491D23
hypocenterC23#1664
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #13092823C2semidirect
4. #13092159C2semidirect
5. #13092158C2semidirect
7. C23×#491C2semidirect
88. #491D23semidirect
116. C23#1664semidirect

Maximal subgroups

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

subgroupindex
#130931712
#130928232
#130927792
#130921592
#130921582
#130921562
C23×#4912
#166423