Finite Group Databasebeta

← #15672540

Subgroups — #15672540

Order 2944.

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

normal subgroups only

This group has 218 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
2#13092704C212yesmaximal, complemented
3#13092166C211yesmaximal, characteristic, complemented
4#13092146C212yesmaximal, complemented
5C23×#494C211yesmaximal, characteristic, complemented
6C2×Q16×C23—22no—
7C23×C4⋊Q8C2211yescharacteristic
8C23×C4⋊Q8C2211yescharacteristic
9#10625118—22no—
10#10625066—22no—
11#10625063—22no—
12C4×D92C2212yes—
13C4×C8×C23C2211yescharacteristic
14#10624991—22no—
15#10624990—22no—
16C4⋊(C23⋊C8)C2212yes—
17C2×Q8×C23—21no—
18C2×Q8×C23D412yes—
19C2×D92—22no—
20C2×D92D412yes—
21C2×C4×D23—22no—
22Q16×C23—44no—
23C2×C8×C23—21no—
24C4⋊C4×C23—22no—
25C4⋊C4×C23—22no—
26C42×C23C2311yescharacteristic
27(C2×D23)⋊C4—24no—
28(C2×D23)⋊C4—22no—
29C4⋊Dic23D412yes—
30C4×Dic23—22no—
31C2×C23⋊C8—22no—
32C22×D23—22no—
33Q8×C23—42no—
34Q8×C23—42no—
35C2×C4×C23—22no—
36C2×C4×C23—41no—
37C2×C4×C23C2×D412yes—
38C2×C4×C23C2×D411yescharacteristic
39C2×Dic23—22no—
40D92—22no—
41D92—22no—
42D92—82no—
43C4×D23—42no—
44C4×D23—42no—
45C8×C23—22no—
46C23⋊C8—42no—
47#1634—231nomaximal, Sylow
48C22×C23#12011yescharacteristic
49C2×D23—42no—
50C2×D23—42no—
51C2×D23—42no—
52C4×C23—21no—
53C4×C23—42no—
54C4×C23—81no—
55C4×C23#13512yes—
56C4×C23#13712yes—
57Dic23—42no—
58#555—231no—
59#494D2311yescharacteristic, complemented
60#476—232no—
61#333—231no—
62D4⋊C8—232no—
63C2×C23#45212yes—
64C2×C23#45311yescharacteristic
65D23—82no—
66C2×Q16—22no—
67C4⋊Q8C2×D2311yescharacteristic
68C4⋊Q8C2×D2311yescharacteristic
69#124—462no—
70#121—462no—
71C4×D4—232no—
72#117—462no—
73#106—462no—
74C4⋊C8—232no—
75#102—462no—
76C4×C8C2×D2311yescharacteristic
77C23#163411yescharacteristic, complemented, Sylow
78C2×Q8—21no—
79C2×Q8C22⋊D2312yes—
80C2×D4—232no—
81C2×D4—462no—
82C22×C4—462no—
83Q16—44no—
84C2×C8—21no—
85C2×C8—462no—
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—232no—
89C22⋊C4—464no—
90C22⋊C4—462no—
91C42—462no—
92C42C22×D2311yescharacteristic
93C23—462no—
94Q8—42no—
95Q8—42no—
96D4—462no—
97D4—462no—
98D4—1842no—
99C2×C4—22no—
100C2×C4—41no—
101C2×C4—462no—
102C2×C4—922no—
103C2×C4—922no—
104C2×C4D4×D2312yes—
105C2×C4C2×C22⋊D2311yescharacteristic
106C8—22no—
107C8—922no—
108C22—922no—
109C22—922no—
110C22—922no—
111C22#1062510811yescharacteristic
112C4—21no—
113C4—42no—
114C4—81no—
115C4—922no—
116C4#1062508912yes—
117C4#1062509012yes—
118C2—1842no—
119C2#1309257812yes—
120C2#1309258411yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#494C2
socleC22×C23#120
prime radical#13093133C2
hypercenter#494D23
hypocenterC23#1634
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #13092704C2semidirect
3. #13092166C2semidirect
4. #13092146C2semidirect
5. C23×#494C2semidirect
59. #494D23semidirect
77. C23#1634semidirect

Maximal subgroups

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

subgroupindex
#130931332
#130927042
#130921662
#130921462
C23×#4942
#163423