Finite Group Databasebeta

← #19212067

Subgroups — #19212067

Order 5888.

146 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 25 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#15673004C211yesmaximal, characteristic
2#15671566C211yesmaximal, characteristic, complemented
3C23×#1411C211yesmaximal, characteristic, complemented
4#13092794C411yescharacteristic
5#13092765—21no—
6#13092765—21no—
7#13092216—21no—
8C8×C23⋊C8C411yescharacteristic
9C23×#494C2211yescharacteristic
10C23×#356—21no—
11C2×Q16×C23—41no—
12C23×C4⋊Q8D411yescharacteristic
13C23×C4⋊Q8D411yescharacteristic
14C2×D184—41no—
15#10625045—21no—
16C23×#101—41no—
17C4×C8×C23C2×C411yescharacteristic
18#10625018—41no—
19#10624991—42no—
20#10624991—42no—
21C4×C23⋊C8—21no—
22C2×Q8×C23—21no—
23C2×Q8×C23—21no—
24C2×D92—41no—
25C2×D92—41no—
26C2×D92—41no—
27Q16×C23—82no—
28M16×C23—81no—
29C2×C8×C23—21no—
30C4⋊C4×C23—41no—
31C4⋊C4×C23—41no—
32C42×C23C22⋊C411yescharacteristic
33#67267—81no—
34C2×C23⋊C8—22no—
35D184—82no—
36#7531—231nomaximal, Sylow
37C22×D23—81no—
38Q8×C23—81no—
39Q8×C23—81no—
40C2×C4×C23—21no—
41C2×C4×C23—41no—
42C2×C4×C23—41no—
43C2×C4×C23#9911yescharacteristic
44D92—82no—
45D92—82no—
46D92—82no—
47C8×C23—22no—
48C8×C23—161no—
49C23⋊C8—42no—
50C23⋊C8—161no—
51#1709—231no—
52#1411—231no—
53#1411D2311yescharacteristic, complemented
54C22×C23#35311yescharacteristic
55C2×D23—161no—
56C2×D23—161no—
57C2×D23—161no—
58C4×C23—22no—
59C4×C23—21no—
60C4×C23—81no—
61C4×C23—81no—
62#494C2×D2311yescharacteristic
63#493—231no—
64#486—461no—
65#486—461no—
66#356—21no—
67#356—461no—
68C82—231no—
69C2×C23—21no—
70C2×C23#140811yescharacteristic
71D23—321no—
72C2×Q16—41no—
73C2×D8—921no—
74C4⋊Q8D9211yescharacteristic
75C4⋊Q8C22⋊D2311yescharacteristic
76#127—461no—
77#102—922no—
78#102—922no—
79#101—41no—
80#101—921no—
81C4×C8—461no—
82C4×C8C4×D2311yescharacteristic
83C23#753111yescharacteristic, complemented, Sylow
84C2×Q8—21no—
85C2×Q8—21no—
86C2×D4—921no—
87C2×D4—921no—
88C2×D4—921no—
89Q16—82no—
90D8—1842no—
91M16—81no—
92M16—1841no—
93C2×C8—21no—
94C2×C8—462no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C42(C2×D23)⋊C411yescharacteristic
98C23—1841no—
99Q8—81no—
100Q8—81no—
101D4—1842no—
102D4—1842no—
103D4—1842no—
104C2×C4—21no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4#1062498811yescharacteristic
108C8—22no—
109C8—161no—
110C8—922no—
111C8—3681no—
112C22—3681no—
113C22—3681no—
114C22—3681no—
115C22#1309220911yescharacteristic
116C4—22no—
117C4—21no—
118C4—81no—
119C4—81no—
120C2—21no—
121C2—7361no—
122C2#1567155911yescharacteristic
subgroupG/H
centerC2#15671559
commutatorC4×C8×C23C2×C4
Frattini#494C2×D23
FittingC23×#1411C2
socleC2×C23#1408
hypercenter#1411D23
hypocenterC23#7531
LCSG ▷ C4×C8×C23 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
2. #15671566C2semidirect
3. C23×#1411C2semidirect
53. #1411D23semidirect
83. C23#7531semidirect