Finite Group Databasebeta

← #15675565

Subgroups — #15675565

Order 2944.

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

normal subgroups only

This group has 126 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#13092535C211yesmaximal, characteristic
2#13092239C212yesmaximal, complemented
3#13092238C211yesmaximal, characteristic, complemented
4#13092226C212yesmaximal
5C23×#498C211yesmaximal, characteristic, complemented
6C23×C4⋊Q8—21no—
7#10625075C2211yescharacteristic
8#10625072—21no—
9C23×#106—21no—
10C23×#106C2212yes—
11C4×C8×C23C2211yescharacteristic
12#10625001C2211yescharacteristic
13#10624994C2212yes—
14#10624987—21no—
15C2×Q8×C23—41no—
16#67288—21no—
17C2×C8×C23D411yescharacteristic
18C2×C8×C23C2311yescharacteristic
19C4⋊C4×C23—22no—
20C4⋊C4×C23—41no—
21C42×C23D411yescharacteristic
22#67267—21no—
23Dic92Q811yescharacteristic, complemented
24D184Q811yescharacteristic, complemented
25#67263—21no—
26#67262—41no—
27C8×D23—41no—
28C23⋊C16—22no—
29Q8×C23—82no—
30C2×C4×C23—21no—
31C2×C4×C23—42no—
32C2×C4×C23C2×D411yescharacteristic
33C22⋊D23—41no—
34D92—21no—
35C4×D23—41no—
36Dic46—21no—
37C8×C23SD1611yescharacteristic
38C8×C23SD1611yescharacteristic
39C8×C23C2×Q811yescharacteristic
40C8×C23#4111yescharacteristic
41C23⋊C8—41no—
42#2230—231nomaximal, Sylow
43C22×C23AGL(1,ℤ/8)11yescharacteristic
44C2×D23—41no—
45C4×C23—22no—
46C4×C23—82no—
47C4×C23C22⋊Q811yescharacteristic
48C4×C23C2×SD1611yescharacteristic
49Dic23—41no—
50#498D2311yescharacteristic, complemented
51#443—231no—
52#365—232no—
53#364—231no—
54#360—232no—
55C2×C23—21no—
56C2×C23#47611yescharacteristic
57D23—81no—
58#135—231no—
59#131—461no—
60C4⋊Q8—21no—
61M32—232no—
62#108—231no—
63#106—21no—
64#106C2×D2312yes—
65#104—461no—
66C4×C8C2×D2311yescharacteristic
67C23#223011yescharacteristic, complemented, Sylow
68#41—461no—
69C2×Q8—41no—
70Q16—231no—
71SD16—461no—
72D8—231no—
73M16—461no—
74M16—921no—
75C2×C8—921no—
76C2×C8C22⋊D2311yescharacteristic
77C2×C8C22×D2311yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C42C22⋊D2311yescharacteristic
81C16—462no—
82Q8—82no—
83Q8—461no—
84D4—461no—
85D4—921no—
86C2×C4—21no—
87C2×C4—42no—
88C2×C4—921no—
89C2×C4C2×C22⋊D2311yescharacteristic
90C8—921no—
91C8#6727411yescharacteristic
92C8#6727411yescharacteristic
93C8Q8×D2311yescharacteristic
94C8#6729211yescharacteristic
95C22—921no—
96C22#1062510311yescharacteristic
97C4—22no—
98C4—82no—
99C4—921no—
100C4C2×#6727411yescharacteristic
101C4#1062511711yescharacteristic
102C2—21no—
103C2—1841no—
104C2#1309270411yescharacteristic
subgroupG/H
centerC2#13092704
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#498C2
socleC2×C23#476
prime radical#10625075C22
hypercenter#498D23
hypocenterC23#2230
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #13092239C2semidirect
3. #13092238C2semidirect
5. C23×#498C2semidirect
23. Dic92Q8semidirect
24. D184Q8semidirect
50. #498D23semidirect
67. C23#2230semidirect

Maximal subgroups

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

subgroupindex
#130925352
#130922392
#130922382
#130922262
C23×#4982
#223023