Finite Group Databasebeta

← #23752406

Subgroups — #23752406

Order 9664.

140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C2×D1208C211yesmaximal, characteristic, complemented
2C2×#14558989C211yesmaximal, characteristic, complemented
3#18012735C211yesmaximal, characteristic, complemented
4#18012701C211yesmaximal, characteristic, complemented
5Dic151⋊C8C211yesmaximal, characteristic, complemented
6#18012659C211yesmaximal, characteristic, complemented
7#102×C151C211yesmaximal, characteristic, complemented
8C2×D604C2211yescharacteristic
9C2×D604C2211yescharacteristic
10C2×C22⋊D151—21no—
11C2×C22⋊D151—21no—
12C2×C4×D151—21no—
13D1208—22no—
14#14558989—22no—
15C2×C151⋊C8C2211yescharacteristic
16(C2×D151)⋊C4—21no—
17C4×Dic151C2211yescharacteristic
18C2×D4×C151C2211yescharacteristic
19C2×C8×C151C2211yescharacteristic
20C4⋊C4×C151C2211yescharacteristic
21C22×D151—21no—
22C22×D151—21no—
23D604—21no—
24D604—21no—
25D604—21no—
26D604D412yescomplemented
27C22⋊D151—42no—
28C22⋊D151—42no—
29C2×Dic151D411yescharacteristic
30C2×Dic151D411yescharacteristic
31C4×D151—42no—
32C151⋊C8—21no—
33C23×C151—21no—
34D4×C151—21no—
35D4×C151—21no—
36C2×C4×C151—21no—
37C2×C4×C151C2311yescharacteristic
38C8×C151—21no—
39C22×C151—41no—
40C22×C151—41no—
41C22×C151—41no—
42C22×C151C2×D411yescharacteristic
43C2×D151—22no—
44C2×D151—41no—
45C2×D151—41no—
46C2×D151—41no—
47C2×D151—41no—
48C2×D151—41no—
49C4×C151—41no—
50C4×C151C2×D411yescharacteristic
51C4×C151#4111yescharacteristic
52Dic151—21no—
53Dic151D812yescomplemented
54C2×C151—81no—
55C2×C151#12111yescharacteristic
56C2×C151C2×D811yescharacteristic
57C2×C151AGL(1,ℤ/8)11yescharacteristic
58D151—42no—
59D151—81no—
60C151#45911yescharacteristic, complemented, Sylow
61#459—1511nomaximal, Sylow
62C2×D8—1511no—
63C2×D8—1511no—
64#127—1511no—
65C4×D4—1511no—
66C4⋊C8—1511no—
67#102—1511no—
68#102D15111yescharacteristic, complemented
69C2×D4—3021no—
70C2×D4—3021no—
71C2×D4—1511no—
72C2×D4—1511no—
73C2×D4C2×D15111yescharacteristic
74C22×C4—3021no—
75D8—3022no—
76D8—3022no—
77C2×C8—1511no—
78C2×C8C2×D15111yescharacteristic
79C4⋊C4C2×D15111yescharacteristic
80C22⋊C4—3021no—
81C42—1511no—
82C23—21no—
83C23—3021no—
84C23—3021no—
85D4—21no—
86D4—21no—
87D4—3021no—
88D4—3021no—
89D4—3021no—
90D4—6042no—
91D4—6042no—
92D4—1512no—
93C2×C4—21no—
94C2×C4—6042no—
95C2×C4—1511no—
96C2×C4—1511no—
97C2×C4C22×D15111yescharacteristic
98C8—21no—
99C8—3021no—
100C22—41no—
101C22—41no—
102C22—41no—
103C22—3022no—
104C22—6041no—
105C22—6041no—
106C22—6041no—
107C22—6041no—
108C22—6041no—
109C22D4×D15111yescharacteristic
110C4—41no—
111C4—3021no—
112C4—1512no—
113C4D4×D15111yescharacteristic
114C4#1455900411yescharacteristic
115C2—81no—
116C2—6042no—
117C2—12081no—
118C2#1801271211yescharacteristic
119C2D8×D15111yescharacteristic
120C2#1801276611yescharacteristic
subgroupG/H
centerC22D4×D151
commutator, cosocleC2×C4×C151C23
FrattiniC2×C4C22×D151
Fitting#102×C151C2
socleC22×C151C2×D4
hypercenter#102D151
hypocenterC151#459
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×D1208C2semidirect
2. C2×#14558989C2semidirect
3. #18012735C2semidirect
4. #18012701C2semidirect
5. Dic151⋊C8C2semidirect
6. #18012659C2semidirect
7. #102×C151C2semidirect
26. D604D4semidirect
53. Dic151D8semidirect
60. C151#459semidirect
68. #102D151semidirect