Finite Group Databasebeta

← #23749813

Subgroups — #23749813

Order 9536.

198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 39 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#18011956C211yesmaximal, characteristic, complemented
2#18011881C212yesmaximal, complemented
3#18011879C211yesmaximal, characteristic, complemented
4#18011825C212yesmaximal, complemented
5#99×C149C211yesmaximal, characteristic, complemented
6C23×D149C2211yescharacteristic, complemented
7#14558736—21no—
8#14558735—22no—
9C2×D596—22no—
10C2×C22⋊D149—21no—
11C2×C22⋊D149—21no—
12C2×C22⋊D149C2212yes—
13D4×D149—22no—
14C22⋊Dic149C2211yescharacteristic, complemented
15#14558713—22no—
16#14558713—21no—
17C2×D4×C149C2211yescharacteristic
18C22⋊C4×C149C2212yescomplemented
19C22×D149—21no—
20C22×D149—22no—
21C22×D149—21no—
22C22×D149—42no—
23C22×D149D412yescomplemented
24Dic298—21no—
25D596—21no—
26D596—44no—
27C22⋊D149—22no—
28C22⋊D149—22no—
29C22⋊D149—22no—
30C22⋊D149—42no—
31C2×Dic149—21no—
32C2×Dic149—21no—
33C2×Dic149D412yescomplemented
34C4×D149—22no—
35C23×C149D411yescharacteristic, complemented
36C23×C149C2311yescharacteristic
37D4×C149—22no—
38C2×C4×C149—22no—
39C2×C4×C149D411yescharacteristic, complemented
40C22×C149—21no—
41C22×C149—41no—
42C22×C149—41no—
43C22×C149C2×D412yes—
44C22×C149C2×D411yescharacteristic
45C2×D149—22no—
46C2×D149—24no—
47C2×D149—22no—
48C2×D149—41no—
49C2×D149—42no—
50C2×D149—41no—
51C2×D149—42no—
52C2×D149—81no—
53C4×C149—21no—
54C4×C149—42no—
55Dic149—22no—
56Dic149—41no—
57C2×C149—21no—
58C2×C149—22no—
59C2×C149—41no—
60C2×C149#12011yescharacteristic
61D149—42no—
62D149—42no—
63C149B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—1491nomaximal, Sylow
65H(5,𝔽2)—1491no—
66#120—1491no—
67#120—1492no—
68#99—1492no—
69#99D14911yescharacteristic, complemented
70C24—1491no—
71#41—2982no—
72#41—2981no—
73C2×D4—2982no—
74C2×D4—2982no—
75C2×D4—2981no—
76C2×D4—2981no—
77C2×D4—1492no—
78C2×D4C2×D14911yescharacteristic
79C22⋊C4—2982no—
80C22⋊C4—2981no—
81C22⋊C4—1491no—
82C22⋊C4C2×D14912yescomplemented
83C23—2981no—
84C23—2982no—
85C23—2981no—
86C23—5962no—
87C23—1492no—
88C23D59611yescharacteristic, complemented
89C23C22×D14911yescharacteristic
90Q8—2981no—
91D4—22no—
92D4—2981no—
93D4—2982no—
94D4—2982no—
95D4—2982no—
96D4—5964no—
97D4—5962no—
98C2×C4—22no—
99C2×C4—2982no—
100C2×C4—2981no—
101C2×C4—2981no—
102C2×C4—1492no—
103C2×C4D59611yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—2984no—
108C22—2982no—
109C22—2982no—
110C22—5962no—
111C22—5962no—
112C22—5961no—
113C22—5961no—
114C22—11921no—
115C22D4×D14912yes—
116C22C2×D59611yescharacteristic
117C4—21no—
118C4—42no—
119C4—2982no—
120C4—5961no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—5962no—
125C2—5962no—
126C2#1801188111yescharacteristic
subgroupG/H
centerC2#18011881
commutator, cosocleC23×C149C23
FrattiniC23C22×D149
Fitting#99×C149C2
socleC2×C149#120
hypercenter#99D149
hypocenterC149B(4,𝔽2)
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #18011956C2semidirect
2. #18011881C2semidirect
3. #18011879C2semidirect
4. #18011825C2semidirect
5. #99×C149C2semidirect
6. C23×D149C22semidirect
14. C22⋊Dic149C22semidirect
18. C22⋊C4×C149C22semidirect
23. C22×D149D4semidirect
33. C2×Dic149D4semidirect
35. C23×C149D4semidirect
39. C2×C4×C149D4semidirect
63. C149B(4,𝔽2)semidirect
69. #99D149semidirect
82. C22⋊C4C2×D149semidirect
88. C23D596semidirect
103. C2×C4D596semidirect