Finite Group Databasebeta

← #15675470

Subgroups — #15675470

Order 2944.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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#13092853C212yesmaximal, complemented
2#13092535C211yesmaximal, characteristic, complemented
3#13092238C211yesmaximal, characteristic, complemented
4#13092230C212yesmaximal, complemented
5C23×#493C211yesmaximal, characteristic, complemented
6C2×D8×C23—21no—
7C2×D8×C23C2212yes—
8C23×#127—21no—
9#10625075C2211yescharacteristic
10#10625072—21no—
11C4×C8×C23C2211yescharacteristic
12#10625009—22no—
13#10625008—22no—
14#10625001C2211yescharacteristic
15#10624994C2212yes—
16#10624987—21no—
17C2×D4×C23—22no—
18C2×D4×C23—42no—
19#67288—21no—
20D8×C23—22no—
21D8×C23—22no—
22D8×C23—41no—
23D8×C23—41no—
24C2×C8×C23D411yescharacteristic
25C2×C8×C23C2311yescharacteristic
26C42×C23D411yescharacteristic
27#67267—21no—
28Dic92D411yescharacteristic, complemented
29D184D411yescharacteristic, complemented
30#67263—21no—
31#67262—41no—
32C8×D23—41no—
33C23⋊C16—22no—
34C23×C23—42no—
35D4×C23—42no—
36D4×C23—42no—
37D4×C23—84no—
38C2×C4×C23—21no—
39C2×C4×C23C2×D411yescharacteristic
40C22⋊D23—41no—
41D92—21no—
42C4×D23—41no—
43Dic46—21no—
44C8×C23D811yescharacteristic
45C8×C23D811yescharacteristic
46C8×C23C2×D411yescharacteristic
47C8×C23#4111yescharacteristic
48C23⋊C8—41no—
49#2213—231nomaximal, Sylow
50C22×C23—84no—
51C22×C23—82no—
52C22×C23AGL(1,ℤ/8)11yescharacteristic
53C2×D23—41no—
54C4×C23—22no—
55C4×C23#12111yescharacteristic
56C4×C23C2×D811yescharacteristic
57Dic23—41no—
58#509—232no—
59#493D2311yescharacteristic, complemented
60#443—231no—
61#364—231no—
62#361—232no—
63C2×C23—21no—
64C2×C23—162no—
65C2×C23#45911yescharacteristic
66D23—81no—
67#135—231no—
68C2×D8—21no—
69C2×D8C2×D2312yes—
70#131—461no—
71#127—21no—
72SD32—462no—
73D16—462no—
74M32—232no—
75#108—231no—
76#104—461no—
77C4×C8C2×D2311yescharacteristic
78C23#221311yescharacteristic, complemented, Sylow
79#41—461no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—231no—
83SD16—461no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—231no—
89M16—461no—
90M16—921no—
91C2×C8—921no—
92C2×C8C22⋊D2311yescharacteristic
93C2×C8C22×D2311yescharacteristic
94C42C22⋊D2311yescharacteristic
95C16—462no—
96C23—42no—
97Q8—461no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—461no—
102D4—921no—
103C2×C4—21no—
104C2×C4—921no—
105C2×C4C2×C22⋊D2311yescharacteristic
106C8—921no—
107C8#6727211yescharacteristic
108C8#6727211yescharacteristic
109C8D4×D2311yescharacteristic
110C8#6729011yescharacteristic
111C22—84no—
112C22—82no—
113C22—921no—
114C22#1062510311yescharacteristic
115C4—22no—
116C4—921no—
117C4C2×#6727211yescharacteristic
118C4#1062510911yescharacteristic
119C2—21no—
120C2—162no—
121C2—1841no—
122C2#1309260911yescharacteristic
subgroupG/H
centerC2#13092609
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#493C2
socleC2×C23#459
hypercenter#493D23
hypocenterC23#2213
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #13092853C2semidirect
2. #13092535C2semidirect
3. #13092238C2semidirect
4. #13092230C2semidirect
5. C23×#493C2semidirect
28. Dic92D4semidirect
29. D184D4semidirect
59. #493D23semidirect
78. C23#2213semidirect

Maximal subgroups

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

subgroupindex
#130928532
#130925352
#130922382
#130922302
C23×#4932
#221323