Finite Group Databasebeta

← #15672404

Subgroups — #15672404

Order 2944.

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

normal subgroups only

This group has 210 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#13093048C211yesmaximal, characteristic
2#13092747C212yesmaximal
3#13092153C212yesmaximal
4#13092143C211yesmaximal, characteristic
5C23×#398C211yesmaximal, characteristic
6C2×C4⋊C4×C23—21no—
7C2×C4⋊C4×C23C2211yescharacteristic
8C2×C4⋊C4×C23C2211yescharacteristic
9#10625097—21no—
10#10625095—21no—
11#10625095C2212yes—
12#10625061—22no—
13#10625059—22no—
14C23×#95—21no—
15C23×#95C2211yescharacteristic
16C22⋊(C23⋊C8)C2212yes—
17#10624992—22no—
18#10624990—22no—
19C22×C4×C23—21no—
20C22×C4×C23—21no—
21C22×C4×C23D411yescharacteristic
22C22×C4×C23D411yescharacteristic
23C22×C4×C23C2311yescharacteristic
24C2×Dic46—21no—
25C2×Dic46D412yes—
26C4⋊C4×C23—22no—
27C4⋊C4×C23—22no—
28C4⋊C4×C23—42no—
29C22⋊Dic23—22no—
30C4⋊Dic23—21no—
31C4⋊Dic23—21no—
32C4⋊Dic23—21no—
33C4⋊Dic23D412yes—
34Dic23⋊C4—22no—
35Dic23⋊C4—22no—
36C4×Dic23—22no—
37C2×C23⋊C8—22no—
38C23×C23C2×D411yescharacteristic
39C2×C4×C23—21no—
40C2×C4×C23—21no—
41C2×C4×C23—22no—
42C2×C4×C23—21no—
43C2×C4×C23—41no—
44C2×C4×C23—41no—
45C2×C4×C23—41no—
46C2×C4×C23—41no—
47C2×C4×C23—41no—
48C2×C4×C23—41no—
49C2×C4×C23—41no—
50C2×C4×C23SD1612yes—
51C2×C4×C23C2×D412yes—
52C2×Dic23—22no—
53C2×Dic23—22no—
54Dic46—42no—
55Dic46—81no—
56C23⋊C8—42no—
57#1611—231nomaximal, Sylow
58C22×C23—21no—
59C22×C23—21no—
60C22×C23#12011yescharacteristic
61C22×C23C2×SD1611yescharacteristic
62C22×C23#13711yescharacteristic
63C4×C23—22no—
64C4×C23—22no—
65C4×C23—42no—
66C4×C23—41no—
67C4×C23—81no—
68Dic23—42no—
69Dic23—42no—
70#544—231no—
71#483—232no—
72#398D2311yescharacteristic
73#328—232no—
74#324—231no—
75C2×C23—21no—
76C2×C23—21no—
77C2×C23#44811yescharacteristic
78C2×C23#45611yescharacteristic
79C2×C23#45811yescharacteristic
80C4⋊Q8—462no—
81#125—462no—
82C22⋊Q8—232no—
83C22⋊Q8—461no—
84#117—461no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4C2×D2311yescharacteristic
87C2×C4⋊C4C2×D2311yescharacteristic
88#106—462no—
89#103—462no—
90C22⋊C8—232no—
91#95—21no—
92#95C2×D2311yescharacteristic
93C23#161111yescharacteristic, complemented, Sylow
94C2×Q8—232no—
95C2×Q8—461no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D2311yescharacteristic
99C22×C4C22⋊D2311yescharacteristic
100C22×C4C22×D2311yescharacteristic
101C2×C8—462no—
102C4⋊C4—22no—
103C4⋊C4—22no—
104C4⋊C4—42no—
105C4⋊C4—232no—
106C4⋊C4—461no—
107C4⋊C4—461no—
108C4⋊C4—461no—
109C4⋊C4—462no—
110C4⋊C4—462no—
111C22⋊C4—462no—
112C42—462no—
113C23C2×C22⋊D2311yescharacteristic
114Q8—922no—
115Q8—1841no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—462no—
128C2×C4—462no—
129C2×C4#6727312yes—
130C2×C4D4×D2312yes—
131C8—922no—
132C22—21no—
133C22—21no—
134C22C2×#6727311yescharacteristic
135C22#1062510811yescharacteristic
136C22#1062512211yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—81no—
142C4—922no—
143C4—922no—
144C2—21no—
145C2—21no—
146C2#1309255511yescharacteristic
147C2#1309259911yescharacteristic
148C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#398C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#398D23
hypocenterC23#1611
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
93. C23#1611semidirect

Maximal subgroups

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

subgroupindex
#130930482
#130927472
#130921532
#130921432
C23×#3982
#161123