Finite Group Databasebeta

← #15672556

Subgroups — #15672556

Order 2944.

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

normal subgroups only

This group has 188 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#13093142C211yesmaximal, characteristic
2#13092769C211yesmaximal, characteristic
3#13092713C211yesmaximal, characteristic
4#13092713C211yesmaximal, characteristic
5#13092147C211yesmaximal, characteristic
6#13092147C211yesmaximal, characteristic
7C23×#332C211yesmaximal, characteristic
8C23×C4⋊Q8C2211yescharacteristic
9Q8×Dic23—21no—
10#10625115—21no—
11#10625061—21no—
12#10625060—22no—
13#10625058—21no—
14#10625040C2211yescharacteristic
15C4×Dic46C2211yescharacteristic
16C4×Dic46C2211yescharacteristic
17C23×C4⋊C8C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19#10625000—21no—
20#10625000—21no—
21#10624998—21no—
22#10624998—21no—
23#10624992—22no—
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×Dic46—21no—
27C2×Dic46D411yescharacteristic
28C2×Dic46D411yescharacteristic
29C2×C8×C23—21no—
30C2×C8×C23—21no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23D412yes—
33C42×C23C2311yescharacteristic
34C4⋊Dic23—22no—
35C4⋊Dic23—21no—
36C4⋊Dic23—21no—
37C4⋊Dic23D411yescharacteristic
38C4⋊Dic23D411yescharacteristic
39Dic23⋊C4—22no—
40Dic23⋊C4—22no—
41Dic23⋊C4—21no—
42Dic23⋊C4—21no—
43C4×Dic23—22no—
44C4×Dic23—21no—
45C4×Dic23—21no—
46C2×C23⋊C8—21no—
47Q8×C23—41no—
48Q8×C23—41no—
49C2×C4×C23—22no—
50C2×C4×C23C2×D411yescharacteristic
51C2×C4×C23C2×D411yescharacteristic
52C2×C4×C23C2×D411yescharacteristic
53C2×Dic23—21no—
54C2×Dic23—21no—
55C2×Dic23—21no—
56C2×Dic23—21no—
57C2×Dic23—41no—
58Dic46—21no—
59Dic46—21no—
60Dic46—21no—
61Dic46—42no—
62Dic46Q1612yes—
63C8×C23—41no—
64C8×C23—41no—
65C23⋊C8—41no—
66#1636—231nomaximal, Sylow
67C22×C23#12011yescharacteristic
68C4×C23—21no—
69C4×C23—42no—
70C4×C23C2×Q1611yescharacteristic
71C4×C23#13511yescharacteristic
72C4×C23#13711yescharacteristic
73C4×C23#13711yescharacteristic
74Dic23—22no—
75Dic23—41no—
76Dic23—41no—
77Dic23—41no—
78Dic23—81no—
79#557—231no—
80#487—231no—
81#477—231no—
82#477—231no—
83#332D2311yescharacteristic
84Q8⋊C8—231no—
85Q8⋊C8—231no—
86C2×C23#45111yescharacteristic
87C2×C23#45211yescharacteristic
88C2×C23#45411yescharacteristic
89C4⋊Q8—231no—
90C4⋊Q8—461no—
91C4⋊Q8C2×D2311yescharacteristic
92#125—461no—
93#125—462no—
94C4×Q8—231no—
95C4×Q8—231no—
96C4×Q8—461no—
97C4×Q8—461no—
98#107—461no—
99#107—461no—
100C4⋊C8C2×D2311yescharacteristic
101C4⋊C8C2×D2311yescharacteristic
102#103—461no—
103#103—461no—
104#103—462no—
105C4×C8—231no—
106C23#163611yescharacteristic, complemented, Sylow
107C2×Q8—21no—
108C2×Q8—231no—
109C2×Q8—231no—
110C2×Q8—461no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—461no—
114C4⋊C4—21no—
115C4⋊C4—231no—
116C4⋊C4—231no—
117C4⋊C4—462no—
118C4⋊C4—462no—
119C4⋊C4—462no—
120C4⋊C4—461no—
121C4⋊C4—461no—
122C4⋊C4—461no—
123C4⋊C4—461no—
124C4⋊C4D9212yes—
125C42—462no—
126C42—461no—
127C42—461no—
128C42C22×D2311yescharacteristic
129Q8—41no—
130Q8—41no—
131Q8—232no—
132Q8—461no—
133Q8—461no—
134Q8—461no—
135Q8—922no—
136C2×C4—22no—
137C2×C4—461no—
138C2×C4—461no—
139C2×C4—461no—
140C2×C4—461no—
141C2×C4—921no—
142C2×C4C2×D9211yescharacteristic
143C2×C4D4×D2311yescharacteristic
144C2×C4D4×D2311yescharacteristic
145C8—41no—
146C8—41no—
147C8—921no—
148C22#1062505311yescharacteristic
149C4—21no—
150C4—42no—
151C4—462no—
152C4—921no—
153C4—921no—
154C4—921no—
155C4—1841no—
156C4#1062508311yescharacteristic
157C4#1062508611yescharacteristic
158C4#1062508611yescharacteristic
159C4Q16×D2311yescharacteristic
160C2#1309257411yescharacteristic
161C2#1309258011yescharacteristic
162C2#1309259211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#332C2
socle, prime radicalC22×C23#120
hypercenter#332D23
hypocenterC23#1636
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
106. C23#1636semidirect

Maximal subgroups

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

subgroupindex
#130931422
#130927692
#130927132
#130921472
C23×#3322
#163623