Finite Group Databasebeta

← #15672441

Subgroups — #15672441

Order 2944.

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

normal subgroups only

This group has 202 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#13092753C212yesmaximal
3#13092356C211yesmaximal, characteristic
4#13092155C212yesmaximal
5C23×#324C211yesmaximal, characteristic
6C2×C4⋊C4×C23C2211yescharacteristic
7#10625097—21no—
8C2×C4⋊Dic23C2211yescharacteristic
9#10625095—21no—
10#10625095C2212yes—
11#10625061—22no—
12#10625059—22no—
13C23×C22⋊C8C2212yes—
14C23⋊#95—21no—
15C23⋊#95—21no—
16C23⋊#95C2211yescharacteristic
17#10625000—22no—
18#10624998—22no—
19C22×C4×C23D411yescharacteristic
20C22×C4×C23D411yescharacteristic
21C22×C4×C23C2311yescharacteristic
22C22×Dic23—21no—
23C22×Dic23—21no—
24C2×Dic46—21no—
25C2×Dic46D412yes—
26C2×C8×C23—22no—
27C4⋊C4×C23—22no—
28C22⋊Dic23—22no—
29C4⋊Dic23—21no—
30C4⋊Dic23—21no—
31C4⋊Dic23—21no—
32C4⋊Dic23—22no—
33C4⋊Dic23D412yes—
34Dic23⋊C4—22no—
35Dic23⋊C4—22no—
36C4×Dic23—22no—
37C23×C23C2×D411yescharacteristic
38C2×C4×C23—21no—
39C2×C4×C23—21no—
40C2×C4×C23—21no—
41C2×C4×C23—41no—
42C2×C4×C23—41no—
43C2×C4×C23Q1612yes—
44C2×C4×C23C2×D412yes—
45C2×Dic23—22no—
46C2×Dic23—22no—
47C2×Dic23—41no—
48C2×Dic23—41no—
49C2×Dic23—42no—
50C2×Dic23—41no—
51C2×Dic23—41no—
52Dic46—42no—
53Dic46—81no—
54C8×C23—42no—
55#1617—231nomaximal, Sylow
56C22×C23—21no—
57C22×C23—21no—
58C22×C23#12011yescharacteristic
59C22×C23C2×Q1611yescharacteristic
60C22×C23#13711yescharacteristic
61C4×C23—22no—
62C4×C23—22no—
63C4×C23—41no—
64Dic23—42no—
65Dic23—42no—
66Dic23—81no—
67Dic23—81no—
68#544—231no—
69#484—232no—
70#400—231no—
71#328—232no—
72#324D2311yescharacteristic
73C2×C23—21no—
74C2×C23—21no—
75C2×C23#45111yescharacteristic
76C2×C23#45411yescharacteristic
77C2×C23#45811yescharacteristic
78C4⋊Q8—462no—
79#125—462no—
80C22⋊Q8—232no—
81C22⋊Q8—461no—
82#117—461no—
83C2×C4⋊C4—231no—
84C2×C4⋊C4C2×D2311yescharacteristic
85#107—462no—
86#103—462no—
87C22⋊C8C2×D2312yes—
88#95—231no—
89#95—461no—
90#95—461no—
91C23#161711yescharacteristic, complemented, Sylow
92C2×Q8—232no—
93C2×Q8—461no—
94C22×C4—461no—
95C22×C4—461no—
96C22×C4D9211yescharacteristic
97C22×C4D9211yescharacteristic
98C22×C4C22×D2311yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—232no—
102C4⋊C4—461no—
103C4⋊C4—461no—
104C4⋊C4—461no—
105C4⋊C4—462no—
106C4⋊C4—462no—
107C4⋊C4—462no—
108C22⋊C4—462no—
109C42—462no—
110C23C2×D9211yescharacteristic
111Q8—922no—
112Q8—1841no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—462no—
119C2×C4—462no—
120C2×C4—921no—
121C2×C4—921no—
122C2×C4—922no—
123C2×C4—921no—
124C2×C4—921no—
125C2×C4Dic9212yes—
126C2×C4D4×D2312yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1062505311yescharacteristic
131C22C2×Dic9211yescharacteristic
132C22#1062508011yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—922no—
137C4—922no—
138C4—1841no—
139C4—1841no—
140C2—21no—
141C2—21no—
142C2#1309257511yescharacteristic
143C2#1309259211yescharacteristic
144C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#324D23
hypocenterC23#1617
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
91. C23#1617semidirect

Maximal subgroups

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

subgroupindex
#130930482
#130927532
#130923562
#130921552
C23×#3242
#161723