Finite Group Databasebeta

← #15672452

Subgroups — #15672452

Order 2944.

336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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#13093052C211yesmaximal, characteristic, complemented
2#13092793C211yesmaximal, characteristic, complemented
3#13092613C212yesmaximal, complemented
4#13092144C212yesmaximal, complemented
5C23×#331C211yesmaximal, characteristic, complemented
6C2×D4×D23—22no—
7C23×#127C2211yescharacteristic
8#10625109—22no—
9#10625108—22no—
10C2×#67272—22no—
11C2×D184—22no—
12#10625045C2211yescharacteristic, complemented
13C4×D92C2212yes—
14C23×C4⋊C8C2212yescomplemented
15#10625003—22no—
16C4×C23⋊C8C2211yescharacteristic, complemented
17C23×D23—22no—
18C2×D4×C23—22no—
19C2×D4×C23D412yes—
20C2×C22⋊D23—24no—
21D4×D23—44no—
22D4×D23—44no—
23C2×D92—22no—
24C2×D92—21no—
25C2×D92D412yes—
26C2×C4×D23—22no—
27C2×C8×C23—22no—
28C42×C23C2311yescharacteristic
29C22⋊Dic23—22no—
30#67272—44no—
31(C2×D23)⋊C4—22no—
32C4⋊Dic23D412yes—
33C2×C23⋊C8—21no—
34D184—44no—
35C23×C23—22no—
36C22×D23—22no—
37C22×D23—48no—
38C22×D23—41no—
39C22×D23—82no—
40D4×C23—42no—
41D4×C23—42no—
42D4×C23—42no—
43C2×C4×C23C2×D411yescharacteristic
44C2×C4×C23C2×D412yes—
45C22⋊D23—48no—
46C2×Dic23—22no—
47D92—22no—
48D92—42no—
49D92—42no—
50D92—42no—
51D92D814yescomplemented
52C4×D23—42no—
53C4×D23—42no—
54C8×C23—42no—
55C23⋊C8—22no—
56#1619—231nomaximal, Sylow
57C22×C23—44no—
58C22×C23—42no—
59C22×C23#12011yescharacteristic
60C2×D23—24no—
61C2×D23—42no—
62C2×D23—42no—
63C2×D23—88no—
64C2×D23—82no—
65C2×D23—81no—
66C4×C23—21no—
67C4×C23C2×D812yes—
68C4×C23AGL(1,ℤ/8)12yes—
69Dic23—42no—
70D42—231no—
71#493—231no—
72#459—232no—
73#331D2311yescharacteristic, complemented
74D4⋊C8—232no—
75C2×C23—82no—
76C2×C23#44712yes—
77C2×C23#45311yescharacteristic
78D23—44no—
79D23—161no—
80C22×D4—462no—
81C2×D8—462no—
82C2×D8—462no—
83#127—231no—
84#127C2×D2311yescharacteristic
85#121—462no—
86#120—462no—
87C4×D4—232no—
88C4⋊C8C2×D2312yescomplemented
89#102—462no—
90C4×C8—231no—
91C23#161911yescharacteristic, complemented, Sylow
92C24—462no—
93C2×D4—22no—
94C2×D4—232no—
95C2×D4—464no—
96C2×D4—461no—
97C2×D4—462no—
98C2×D4—924no—
99C2×D4—924no—
100C2×D4D9212yes—
101C22×C4—462no—
102D8—924no—
103D8—924no—
104C2×C8—22no—
105C2×C8—461no—
106C4⋊C4—232no—
107C22⋊C4—462no—
108C22⋊C4—462no—
109C42C22×D2311yescharacteristic
110C23—22no—
111C23—462no—
112C23—928no—
113C23—921no—
114C23—1842no—
115D4—42no—
116D4—42no—
117D4—42no—
118D4—234no—
119D4—462no—
120D4—922no—
121D4—928no—
122D4—922no—
123D4—922no—
124C2×C4—462no—
125C2×C4—922no—
126C2×C4—922no—
127C2×C4C2×D9211yescharacteristic
128C2×C4D4×D2312yes—
129C8—42no—
130C8—462no—
131C22—44no—
132C22—42no—
133C22—464no—
134C22—922no—
135C22—922no—
136C22—1848no—
137C22—1842no—
138C22—1841no—
139C22#1062505311yescharacteristic
140C4—21no—
141C4—922no—
142C4D8×D2312yes—
143C4#1062508512yes—
144C2—82no—
145C2—924no—
146C2—3681no—
147C2#1309255212yes—
148C2#1309258711yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#331C2
socleC22×C23#120
hypercenter#331D23
hypocenterC23#1619
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #13093052C2semidirect
2. #13092793C2semidirect
3. #13092613C2semidirect
4. #13092144C2semidirect
5. C23×#331C2semidirect
12. #10625045C22semidirect
14. C23×C4⋊C8C22semidirect
16. C4×C23⋊C8C22semidirect
51. D92D8semidirect
73. #331D23semidirect
88. C4⋊C8C2×D23semidirect
91. C23#1619semidirect

Maximal subgroups

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

subgroupindex
#130930522
#130927932
#130926132
#130921442
C23×#3312
#161923