Finite Group Databasebeta

← #23750655

Subgroups — #23750655

Order 9536.

124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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×#14558746C211yesmaximal, characteristic, complemented
2C2×D149⋊C8C211yesmaximal, characteristic, complemented
3#18011978C211yesmaximal, characteristic, complemented
4#18011968C211yesmaximal, characteristic, complemented
5#18011968C211yesmaximal, characteristic, complemented
6#18011966C211yesmaximal, characteristic, complemented
7#18011873C211yesmaximal, characteristic
8#14558746—22no—
9D149⋊C8—22no—
10C2×#11924753C2211yescharacteristic
11C2×#11924753C2211yescharacteristic
12C2×#11924753C2211yescharacteristic
13C2×#11924753C2211yescharacteristic
14C2×D596C411yescharacteristic
15C2×C4×D149C2211yescharacteristic
16C2×C4×D149C2211yescharacteristic
17#14558713C411yescharacteristic
18#14558713C411yescharacteristic
19C4×Dic149C2211yescharacteristic
20C4⋊C4×C149C411yescharacteristic
21#11924753—21no—
22#11924753—21no—
23#11924753—21no—
24#11924753D412yescomplemented
25C22×D149C2×C411yescharacteristic
26C22×D149C2×C411yescharacteristic
27D596—22no—
28C2×Dic149C2×C411yescharacteristic
29C2×Dic149C2311yescharacteristic
30C4×D149—21no—
31C4×D149—21no—
32C4×D149—21no—
33C4×D149—21no—
34C2×C4×C149C2×C411yescharacteristic
35C2×C4×C149C2×C411yescharacteristic
36C2×C4×C149C2×C411yescharacteristic
37C22×C149C22×C411yescharacteristic
38C2×D149—21no—
39C2×D149—21no—
40C2×D149—21no—
41C2×D149—21no—
42C2×D149—21no—
43C2×D149M1612yescomplemented
44C4×C149—21no—
45C4×C149—21no—
46C4×C149—21no—
47Dic149—21no—
48Dic149C2×D411yescharacteristic
49Dic149#4111yescharacteristic
50C2×C149C4×D411yescharacteristic
51C2×C149C2×M1611yescharacteristic
52C2×C149#13111yescharacteristic
53D149—22no—
54D149—41no—
55C149#43511yescharacteristic, complemented, Sylow
56#435—1491nomaximal, Sylow
57C2×M16—1491no—
58C22×C8—1491no—
59C4×D4—1491no—
60C4⋊C8—1491no—
61C22⋊C8—1491no—
62C22⋊C8—1491no—
63#97—1491no—
64C2×D4—1491no—
65C22×C4—1491no—
66C22×C4—1491no—
67M16—2982no—
68C2×C8—2982no—
69C2×C8—1491no—
70C2×C8—1491no—
71C2×C8—1491no—
72C2×C8—1491no—
73C4⋊C4#1059701011yescharacteristic
74C22⋊C4—1491no—
75C22⋊C4—1491no—
76C42—1491no—
77C23—1491no—
78C23—1491no—
79D4—2982no—
80C2×C4—2981no—
81C2×C4—2981no—
82C2×C4—2981no—
83C2×C4—2981no—
84C2×C4—1491no—
85C2×C4—1491no—
86C2×C4C2×#1059701011yescharacteristic
87C2×C4C2×#1059701011yescharacteristic
88C2×C4C2×#1059701011yescharacteristic
89C8—2981no—
90C8—2981no—
91C8—2981no—
92C8—1492no—
93C22—2981no—
94C22—2981no—
95C22—2981no—
96C22—2981no—
97C22—2981no—
98C22—1492no—
99C22C22×#1059701011yescharacteristic
100C4—21no—
101C4—21no—
102C4—21no—
103C4—2981no—
104C4—1491no—
105C4—1491no—
106C2—2982no—
107C2—5961no—
108C2D4×#1059701011yescharacteristic
109C2D149⋊M1611yescharacteristic
110C2#1801199911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#10597010
commutator, socleC22×C149C22×C4
FittingC4⋊C4×C149C4
prime radicalC2×D596C4
cosocleC2×Dic149C23
hypercenterC4⋊C4#10597010
hypocenterC149#435
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14558746C2semidirect
2. C2×D149⋊C8C2semidirect
3. #18011978C2semidirect
4. #18011968C2semidirect
5. #18011968C2semidirect
6. #18011966C2semidirect
24. #11924753D4semidirect
43. C2×D149M16semidirect
55. C149#435semidirect