Finite Group Databasebeta

← #15671910

Subgroups — #15671910

Order 2944.

228 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 73 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#13092974C211yesmaximal, characteristic
2#13092263C211yesmaximal, characteristic
3#13092155C214yesmaximal
4C23×#432C211yesmaximal, characteristic
5C2×C42×C23C2211yescharacteristic
6#10625097—21no—
7#10625095—21no—
8#10625095C2212yes—
9C2×C4×Dic23—21no—
10#10625041—21no—
11#10625040C411yescharacteristic, complemented
12#10625040C411yescharacteristic, complemented
13C4×Dic46—21no—
14C4×Dic46C412yescomplemented
15C23×C4⋊C8—21no—
16C23×C22⋊C8C2212yes—
17C23×#97—21no—
18C23⋊#95—21no—
19C23⋊#95C2212yes—
20C22×C4×C23D411yescharacteristic
21C22×C4×C23D411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C22×Dic23—22no—
24C2×Dic46—21no—
25C2×Dic46C2×C412yes—
26C2×C8×C23—22no—
27C42×C23C2×C411yescharacteristic
28C42×C23C2×C411yescharacteristic
29C42×C23D411yescharacteristic
30C42×C23D411yescharacteristic
31C22⋊Dic23—22no—
32C4⋊Dic23—21no—
33C4⋊Dic23—21no—
34C4⋊Dic23—21no—
35C4⋊Dic23C2×C412yes—
36Dic23⋊C4—22no—
37Dic23⋊C4—22no—
38C4×Dic23—24no—
39C4×Dic23—22no—
40C23×C23C2×D411yescharacteristic
41C2×C4×C23—22no—
42C2×C4×C23—22no—
43C2×C4×C23—41no—
44C2×C4×C23C22⋊C411yescharacteristic
45C2×C4×C23C22⋊C411yescharacteristic
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23C22⋊C411yescharacteristic
48C2×C4×C23C22×C411yescharacteristic
49C2×C4×C23C2×D411yescharacteristic
50C2×Dic23—24no—
51C2×Dic23—22no—
52C2×Dic23—22no—
53C2×Dic23—42no—
54C2×Dic23—42no—
55Dic46—42no—
56Dic46—42no—
57C8×C23—42no—
58#1506—231nomaximal, Sylow
59C22×C23—21no—
60C22×C23—21no—
61C22×C23C2×C22⋊C411yescharacteristic
62C22×C23#13712yes—
63C4×C23—21no—
64C4×C23—21no—
65C4×C23—21no—
66C4×C23—21no—
67C4×C23—21no—
68C4×C23#10412yes—
69Dic23—44no—
70Dic23—42no—
71Dic23—42no—
72#533—231no—
73#432D2311yescharacteristic
74#376—231no—
75#328—234no—
76C2×C23—22no—
77C2×C23#41011yescharacteristic
78C2×C23#41911yescharacteristic
79C2×C23C2×#10411yescharacteristic
80C4⋊Q8—231no—
81C4⋊Q8—231no—
82#125—461no—
83C22⋊Q8—232no—
84C22⋊Q8—461no—
85C4×Q8—232no—
86C4×Q8—461no—
87#117—461no—
88C2×C42—461no—
89C2×C42C2×D2311yescharacteristic
90C4⋊C8—21no—
91C22⋊C8C2×D2312yes—
92#97—21no—
93#95—232no—
94#95—461no—
95C23#150611yescharacteristic, complemented, Sylow
96C2×Q8—232no—
97C2×Q8—461no—
98C22×C4—462no—
99C22×C4D9211yescharacteristic
100C22×C4D9211yescharacteristic
101C22×C4C22×D2311yescharacteristic
102C2×C8—22no—
103C4⋊C4—232no—
104C4⋊C4—461no—
105C4⋊C4—461no—
106C4⋊C4—462no—
107C4⋊C4—461no—
108C4⋊C4—462no—
109C22⋊C4—462no—
110C42—464no—
111C42—462no—
112C42C4×D2311yescharacteristic
113C42C4×D2311yescharacteristic
114C42C22⋊D2311yescharacteristic
115C42C22⋊D2311yescharacteristic
116C23C2×D9211yescharacteristic
117Q8—922no—
118Q8—922no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4—464no—
123C2×C4—462no—
124C2×C4—462no—
125C2×C4—922no—
126C2×C4—922no—
127C2×C4(C2×D23)⋊C411yescharacteristic
128C2×C4(C2×D23)⋊C411yescharacteristic
129C2×C4(C2×D23)⋊C411yescharacteristic
130C2×C4(C2×D23)⋊C411yescharacteristic
131C2×C4C2×C4×D2311yescharacteristic
132C2×C4C2×C22⋊D2311yescharacteristic
133C8—42no—
134C22—21no—
135C22—21no—
136C22#1062508012yes—
137C22C2×(C2×D23)⋊C411yescharacteristic
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—21no—
143C4—924no—
144C4—922no—
145C4—922no—
146C4#1062500712yes—
147C2—22no—
148C2#1309239011yescharacteristic
149C2#1309242711yescharacteristic
150C2C2×#1062500711yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#432C2
socleC22×C23C2×C22⋊C4
prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenter#432D23
hypocenterC23#1506
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
11. #10625040C4semidirect
12. #10625040C4semidirect
14. C4×Dic46C4semidirect
95. C23#1506semidirect

Maximal subgroups

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

subgroupindex
#130929742
#130922632
#130921552
C23×#4322
#150623