Finite Group Databasebeta

← #15672690

Subgroups — #15672690

Order 2944.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#13092807C212yesmaximal, complemented
2#13092783C211yesmaximal, characteristic, complemented
3#13092159C211yesmaximal, characteristic, complemented
4#13092157C212yesmaximal, complemented
5C23×#562C211yesmaximal, characteristic, complemented
6C23×#125C2211yescharacteristic
7C23×#124C2212yes—
8C23×#123—22no—
9C23×C22⋊Q8—22no—
10C23×#121—22no—
11C2×#67274—22no—
12C2×#67272—22no—
13#10625045C2211yescharacteristic
14#10624991—22no—
15#10624985C2211yescharacteristic
16#10624985C2212yes—
17C2×Q8×C23D412yes—
18C2×D4×C23—22no—
19C2×D4×C23D412yes—
20C22×C4×C23—22no—
21C2×D92—22no—
22C2×D92—21no—
23C4⋊C4×C23—22no—
24C4⋊C4×C23—22no—
25C4⋊C4×C23D412yes—
26C22⋊C4×C23—22no—
27C22⋊C4×C23—22no—
28C22⋊C4×C23—22no—
29C42×C23C2311yescharacteristic
30#67274—44no—
31#67272—44no—
32C2×C23⋊C8—22no—
33C2×C23⋊C8—21no—
34C23×C23—22no—
35C22×D23—41no—
36Q8×C23—42no—
37D4×C23—42no—
38D4×C23—82no—
39C2×C4×C23—22no—
40C2×C4×C23—22no—
41C2×C4×C23—82no—
42C2×C4×C23C2×D411yescharacteristic
43C2×C4×C23C2×D412yes—
44D92—42no—
45D92—42no—
46D92—42no—
47C23⋊C8—24no—
48C23⋊C8—41no—
49#1656—231nomaximal, Sylow
50C22×C23—42no—
51C22×C23—42no—
52C22×C23—42no—
53C22×C23#12011yescharacteristic
54C2×D23—82no—
55C2×D23—81no—
56C4×C23—22no—
57C4×C23—21no—
58C4×C23—42no—
59C4×C23—42no—
60#562D2311yescharacteristic, complemented
61#496—232no—
62#490—231no—
63#330—231no—
64#329—232no—
65C2×C23—82no—
66C2×C23#45312yes—
67C2×C23#45411yescharacteristic
68D23—161no—
69C2×SD16—462no—
70C2×D8—462no—
71#127—231no—
72#125C2×D2311yescharacteristic
73#124C2×D2312yes—
74#123—22no—
75C22⋊Q8—22no—
76#121—22no—
77#102—462no—
78#97—231no—
79#97—232no—
80C23#165611yescharacteristic, complemented, Sylow
81C2×Q8C22⋊D2312yes—
82C2×D4—22no—
83C2×D4—461no—
84C2×D4—462no—
85C2×D4C22⋊D2312yes—
86C22×C4—22no—
87SD16—924no—
88D8—924no—
89C2×C8—462no—
90C2×C8—461no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D2312yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D2311yescharacteristic
98C23—22no—
99C23—921no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—922no—
104D4—922no—
105D4—922no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D2311yescharacteristic
110C2×C4C2×C22⋊D2312yes—
111C8—464no—
112C8—921no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—1842no—
117C22—1841no—
118C22#1062512411yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—3681no—
125C2#1309258512yes—
126C2#1309259011yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#562C2
socleC22×C23#120
hypercenter#562D23
hypocenterC23#1656
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #13092807C2semidirect
2. #13092783C2semidirect
3. #13092159C2semidirect
4. #13092157C2semidirect
5. C23×#562C2semidirect
60. #562D23semidirect
80. C23#1656semidirect

Maximal subgroups

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

subgroupindex
#130928072
#130927832
#130921592
#130921572
C23×#5622
#165623