Finite Group Databasebeta

← #15672601

Subgroups — #15672601

Order 2944.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#13093128C211yesmaximal, characteristic
2#13092699C211yesmaximal, characteristic, complemented
3#13092619C211yesmaximal, characteristic
4#13092166C211yesmaximal, characteristic, complemented
5#13092149C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic
7C23×#487C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C23×C4⋊Q8C2211yescharacteristic
10#10625117—22no—
11C2×#67274—21no—
12#10625068—21no—
13#10625064—21no—
14C4⋊C4×D23—21no—
15#10625061—21no—
16C4×D92C2211yescharacteristic
17C4×Dic46C2211yescharacteristic
18C23×#103—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×Q8×C23D412yes—
27C2×D92D411yescharacteristic
28C2×C4×D23—21no—
29C2×C4×D23—22no—
30C2×Dic46D411yescharacteristic
31C2×C8×C23—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—21no—
36C42×C23C2311yescharacteristic
37#67274—42no—
38(C2×D23)⋊C4—22no—
39(C2×D23)⋊C4—21no—
40C4⋊Dic23—22no—
41C4⋊Dic23D411yescharacteristic
42C4⋊Dic23D411yescharacteristic
43Dic23⋊C4—22no—
44Dic23⋊C4—21no—
45C4×Dic23—21no—
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48C22×D23—21no—
49Q8×C23—42no—
50Q8×C23—41no—
51Q8×C23—41no—
52C2×C4×C23—22no—
53C2×C4×C23—41no—
54C2×C4×C23C2×D411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×Dic23—21no—
58C2×Dic23—21no—
59C2×Dic23—21no—
60D92—21no—
61D92SD1612yes—
62C4×D23—41no—
63C4×D23—41no—
64C4×D23—82no—
65Dic46—21no—
66Dic46—21no—
67C8×C23—41no—
68C23⋊C8—41no—
69C23⋊C8—41no—
70#1643—231nomaximal, Sylow
71C22×C23#12011yescharacteristic
72C2×D23—22no—
73C2×D23—41no—
74C2×D23—41no—
75C4×C23—21no—
76C4×C23—42no—
77C4×C23—81no—
78C4×C23C2×SD1611yescharacteristic
79C4×C23#13511yescharacteristic
80C4×C23#13711yescharacteristic
81C4×C23#13711yescharacteristic
82Dic23—41no—
83Dic23—41no—
84Dic23—41no—
85#554—231no—
86#487D2311yescharacteristic, complemented
87#475—231no—
88#461—231no—
89#333—231no—
90Q8⋊C8—231no—
91D4⋊C8—231no—
92C2×C23#44811yescharacteristic
93C2×C23#45211yescharacteristic
94C2×C23#45511yescharacteristic
95D23—42no—
96C2×SD16—461no—
97C4⋊Q8C2×D2311yescharacteristic
98C4⋊Q8C2×D2311yescharacteristic
99#125—461no—
100C22⋊Q8—461no—
101C22⋊Q8—462no—
102C4×Q8—231no—
103C4×D4—231no—
104C4×D4—461no—
105C2×C4⋊C4—461no—
106#106—461no—
107C4⋊C8—231no—
108C4⋊C8—231no—
109#103—22no—
110#103—461no—
111#103—461no—
112C4×C8C2×D2311yescharacteristic
113C23#164311yescharacteristic, complemented, Sylow
114C2×Q8—21no—
115C2×Q8—231no—
116C2×Q8C22⋊D2312yes—
117C2×D4—231no—
118C22×C4—462no—
119C22×C4—461no—
120SD16—922no—
121C2×C8—21no—
122C2×C8—461no—
123C2×C8—461no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—231no—
129C4⋊C4—231no—
130C4⋊C4—462no—
131C4⋊C4—462no—
132C4⋊C4—461no—
133C22⋊C4—462no—
134C22⋊C4—461no—
135C42—461no—
136C42C22×D2311yescharacteristic
137C23—461no—
138Q8—42no—
139Q8—41no—
140Q8—41no—
141Q8—461no—
142Q8—461no—
143D4—232no—
144D4—461no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—461no—
148C2×C4—461no—
149C2×C4—461no—
150C2×C4—921no—
151C2×C4—921no—
152C2×C4—1842no—
153C2×C4D4×D2311yescharacteristic
154C2×C4D4×D2311yescharacteristic
155C2×C4C2×C22⋊D2311yescharacteristic
156C8—41no—
157C8—921no—
158C8—921no—
159C22—462no—
160C22—921no—
161C22—921no—
162C22#1062510811yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—921no—
167C4—921no—
168C4—921no—
169C4SD16×D2311yescharacteristic
170C4#1062508611yescharacteristic
171C4#1062508911yescharacteristic
172C4#1062509011yescharacteristic
173C2—922no—
174C2#1309255411yescharacteristic
175C2#1309257811yescharacteristic
176C2#1309259411yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#487C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenter#487D23
hypocenterC23#1643
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #13092699C2semidirect
4. #13092166C2semidirect
5. #13092149C2semidirect
7. C23×#487C2semidirect
86. #487D23semidirect
113. C23#1643semidirect

Maximal subgroups

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

subgroupindex
#130931282
#130926992
#130926192
#130921662
#130921492
#130921462
C23×#4872
#164323