Finite Group Databasebeta

← #15672580

Subgroups — #15672580

Order 2944.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#13093153C211yesmaximal, characteristic
2#13092699C211yesmaximal, characteristic, complemented
3#13092624C211yesmaximal, characteristic, complemented
4#13092161C211yesmaximal, characteristic
5#13092149C211yesmaximal, characteristic, complemented
6#13092149C211yesmaximal, characteristic, complemented
7C23×#486C211yesmaximal, characteristic
8C23×C4⋊Q8C2211yescharacteristic
9C23×#127C2211yescharacteristic
10C2×#67275—21no—
11#10625107—21no—
12#10625107—21no—
13#10625106—22no—
14D4×Dic23—21no—
15D4×Dic23—21no—
16C4×Dic46C2211yescharacteristic
17C4×Dic46C2211yescharacteristic
18C23×#102—22no—
19C4×C8×C23C2211yescharacteristic
20#10625017—21no—
21#10624992—21no—
22#10624990—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23—21no—
28C2×D4×C23D412yes—
29C22×Dic23—22no—
30C2×Dic46D411yescharacteristic
31C2×Dic46D411yescharacteristic
32C2×C8×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C42×C23C2311yescharacteristic
36C22⋊Dic23—22no—
37C22⋊Dic23—22no—
38C22⋊Dic23—22no—
39#67275—42no—
40C4⋊Dic23D411yescharacteristic
41C4⋊Dic23D411yescharacteristic
42Dic23⋊C4—21no—
43Dic23⋊C4—21no—
44C4×Dic23—21no—
45C4×Dic23—21no—
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48C23×C23—22no—
49Q8×C23—41no—
50Q8×C23—41no—
51D4×C23—42no—
52D4×C23—41no—
53D4×C23—41no—
54D4×C23—41no—
55D4×C23—41no—
56C2×C4×C23—41no—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C2×Dic23—21no—
61C2×Dic23—21no—
62C2×Dic23—21no—
63C2×Dic23—21no—
64C2×Dic23—82no—
65Dic46—21no—
66Dic46—21no—
67Dic46—21no—
68Dic46—21no—
69C8×C23—41no—
70C23⋊C8—41no—
71C23⋊C8—41no—
72#1640—231nomaximal, Sylow
73C22×C23—42no—
74C22×C23—42no—
75C22×C23—42no—
76C22×C23#12011yescharacteristic
77C4×C23—21no—
78C4×C23—81no—
79C4×C23#13511yescharacteristic
80C4×C23#13511yescharacteristic
81C4×C23AGL(1,ℤ/8)11yescharacteristic
82C4×C23#13711yescharacteristic
83Dic23—41no—
84Dic23—41no—
85Dic23—41no—
86Dic23—41no—
87#559—231no—
88#486D2311yescharacteristic
89#475—231no—
90#462—231no—
91#331—231no—
92Q8⋊C8—231no—
93Q8⋊C8—231no—
94C2×C23—82no—
95C2×C23#44911yescharacteristic
96C2×C23#45211yescharacteristic
97C2×C23#45511yescharacteristic
98C2×Q16—461no—
99C4⋊Q8C2×D2311yescharacteristic
100#127C2×D2311yescharacteristic
101#124—461no—
102#124—461no—
103#123—462no—
104C4×Q8—231no—
105C4×Q8—231no—
106C4×D4—461no—
107C4×D4—461no—
108#106—461no—
109C4⋊C8—231no—
110C4⋊C8—231no—
111#103—461no—
112#103—461no—
113#102—22no—
114C4×C8C2×D2311yescharacteristic
115C23#164011yescharacteristic, complemented, Sylow
116C2×Q8—21no—
117C2×Q8—231no—
118C2×Q8—231no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D2312yes—
122C22×C4—462no—
123Q16—922no—
124C2×C8—21no—
125C2×C8—461no—
126C2×C8—461no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—231no—
130C4⋊C4—231no—
131C4⋊C4—461no—
132C4⋊C4—461no—
133C22⋊C4—462no—
134C22⋊C4—462no—
135C22⋊C4—462no—
136C42—461no—
137C42—461no—
138C42C22×D2311yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—461no—
143Q8—461no—
144Q8—461no—
145Q8—461no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—461no—
153C2×C4—461no—
154C2×C4—461no—
155C2×C4—461no—
156C2×C4—1842no—
157C2×C4D4×D2311yescharacteristic
158C2×C4D4×D2311yescharacteristic
159C2×C4C2×C22⋊D2311yescharacteristic
160C8—41no—
161C8—921no—
162C8—921no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1062510811yescharacteristic
167C4—21no—
168C4—81no—
169C4—921no—
170C4—921no—
171C4—921no—
172C4—921no—
173C4#1062508211yescharacteristic
174C4#1062508311yescharacteristic
175C4#1062508611yescharacteristic
176C4#1062508711yescharacteristic
177C2—82no—
178C2#1309255911yescharacteristic
179C2#1309257611yescharacteristic
180C2#1309259411yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#486C2
socleC22×C23#120
prime radicalC23×#127C22
hypercenter#486D23
hypocenterC23#1640
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #13092699C2semidirect
3. #13092624C2semidirect
5. #13092149C2semidirect
6. #13092149C2semidirect
115. C23#1640semidirect

Maximal subgroups

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

subgroupindex
#130931532
#130926992
#130926242
#130921612
#130921492
C23×#4862
#164023