Finite Group Databasebeta

← #15672481

Subgroups — #15672481

Order 2944.

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

normal subgroups only

This group has 240 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#13093133C211yesmaximal, characteristic, complemented
2#13092791C211yesmaximal, characteristic, complemented
3#13092613C212yesmaximal, complemented
4#13092144C212yesmaximal, complemented
5C23×#333C211yesmaximal, characteristic, complemented
6C23×C4⋊Q8C2211yescharacteristic
7#10625118—22no—
8C2×#67274—22no—
9C2×D184—22no—
10#10625066—22no—
11#10625063—22no—
12#10625045C2211yescharacteristic
13C4×D92C2212yes—
14C23×C4⋊C8C2212yes—
15#10625003—22no—
16C4×C23⋊C8C2211yescharacteristic
17C2×Q8×C23D412yes—
18C2×D92—22no—
19C2×D92—21no—
20C2×D92—22no—
21C2×D92D412yes—
22C2×C4×D23—22no—
23C2×C8×C23—22no—
24C4⋊C4×C23—22no—
25C42×C23C2311yescharacteristic
26#67274—44no—
27(C2×D23)⋊C4—24no—
28(C2×D23)⋊C4—22no—
29C4⋊Dic23D412yes—
30C4×Dic23—22no—
31C2×C23⋊C8—21no—
32D184—44no—
33C22×D23—22no—
34C22×D23—41no—
35Q8×C23—42no—
36C2×C4×C23—22no—
37C2×C4×C23C2×D411yescharacteristic
38C2×C4×C23C2×D412yes—
39C2×Dic23—22no—
40D92—22no—
41D92—22no—
42D92—42no—
43D92—42no—
44D92—42no—
45D92—82no—
46C4×D23—42no—
47C4×D23—42no—
48C8×C23—42no—
49C23⋊C8—22no—
50#1624—231nomaximal, Sylow
51C22×C23#12011yescharacteristic
52C2×D23—42no—
53C2×D23—42no—
54C2×D23—42no—
55C2×D23—82no—
56C2×D23—81no—
57C4×C23—21no—
58C4×C23—42no—
59C4×C23#13512yes—
60C4×C23AGL(1,ℤ/8)12yes—
61Dic23—42no—
62#555—231no—
63#492—231no—
64#459—232no—
65#333D2311yescharacteristic, complemented
66D4⋊C8—232no—
67C2×C23#44912yes—
68C2×C23#45311yescharacteristic
69D23—82no—
70D23—161no—
71C2×SD16—462no—
72C2×D8—462no—
73C4⋊Q8C2×D2311yescharacteristic
74#127—231no—
75#124—462no—
76#121—462no—
77C4×D4—232no—
78#117—462no—
79C4⋊C8C2×D2312yes—
80#102—462no—
81C4×C8—231no—
82C23#162411yescharacteristic, complemented, Sylow
83C2×Q8D9212yes—
84C2×D4—232no—
85C2×D4—462no—
86C2×D4—461no—
87C2×D4—462no—
88C22×C4—462no—
89SD16—924no—
90D8—924no—
91C2×C8—22no—
92C2×C8—461no—
93C4⋊C4—22no—
94C4⋊C4—232no—
95C22⋊C4—464no—
96C22⋊C4—462no—
97C42—462no—
98C42C22×D2311yescharacteristic
99C23—462no—
100C23—921no—
101Q8—42no—
102D4—462no—
103D4—462no—
104D4—922no—
105D4—922no—
106D4—922no—
107D4—1842no—
108C2×C4—22no—
109C2×C4—462no—
110C2×C4—922no—
111C2×C4—922no—
112C2×C4C2×D9211yescharacteristic
113C2×C4D4×D2312yes—
114C8—42no—
115C8—462no—
116C22—922no—
117C22—922no—
118C22—922no—
119C22—1842no—
120C22—1841no—
121C22#1062505311yescharacteristic
122C4—21no—
123C4—42no—
124C4—922no—
125C4#1062508512yes—
126C4#1062509012yes—
127C2—3681no—
128C2—1842no—
129C2#1309256512yes—
130C2#1309258711yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#333C2
socleC22×C23#120
hypercenter#333D23
hypocenterC23#1624
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #13093133C2semidirect
2. #13092791C2semidirect
3. #13092613C2semidirect
4. #13092144C2semidirect
5. C23×#333C2semidirect
65. #333D23semidirect
82. C23#1624semidirect

Maximal subgroups

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

subgroupindex
#130931332
#130927912
#130926132
#130921442
C23×#3332
#162423