Finite Group Databasebeta

← #23749698

Subgroups — #23749698

Order 9536.

124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14558719C211yesmaximal, characteristic, complemented
2C2×C8×D149C211yesmaximal, characteristic, complemented
3C4×D596C211yesmaximal, characteristic
4C4⋊#11924746C211yesmaximal, characteristic, complemented
5#18011823C211yesmaximal, characteristic, complemented
6#18011823C211yesmaximal, characteristic, complemented
7#97×C149C211yesmaximal, characteristic, complemented
8C2×D596C411yescharacteristic
9C2×C4×D149C2211yescharacteristic
10C2×C4×D149C2211yescharacteristic
11#14558719—22no—
12C2×#11924746C2211yescharacteristic
13C2×#11924746C2211yescharacteristic
14C8×D149—22no—
15C4⋊Dic149C411yescharacteristic
16#14558713C411yescharacteristic
17#14558713C411yescharacteristic
18C2×C8×C149C2211yescharacteristic
19C2×C8×C149C2211yescharacteristic
20C42×C149C2211yescharacteristic
21C22×D149C2×C411yescharacteristic
22C22×D149C2×C411yescharacteristic
23D596—22no—
24C2×Dic149C2×C411yescharacteristic
25C2×Dic149C2×C411yescharacteristic
26C4×D149—21no—
27C4×D149—21no—
28C4×D149—21no—
29C4×D149—21no—
30#11924746—21no—
31#11924746—21no—
32C2×C4×C149C2×C411yescharacteristic
33C2×C4×C149C2×C411yescharacteristic
34C2×C4×C149C2311yescharacteristic
35C8×C149—21no—
36C8×C149D412yescomplemented
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×C149C2×D411yescharacteristic
47C4×C149#4111yescharacteristic
48Dic149—21no—
49Dic149—21no—
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#97D14911yescharacteristic, complemented
64C2×D4—1491no—
65C22×C4—1491no—
66C22×C4—1491no—
67M16—2982no—
68C2×C8—2982no—
69C2×C8—1491no—
70C2×C8—1491no—
71C2×C8C2×D14911yescharacteristic
72C2×C8C2×D14911yescharacteristic
73C4⋊C4—1491no—
74C22⋊C4—1491no—
75C22⋊C4—1491no—
76C42C2×D14911yescharacteristic
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×C4C4×D14911yescharacteristic
87C2×C4C4×D14911yescharacteristic
88C2×C4C22×D14911yescharacteristic
89C8—21no—
90C8—2981no—
91C8—2981no—
92C8D59612yescomplemented
93C22—2981no—
94C22—2981no—
95C22—2981no—
96C22—2981no—
97C22—2981no—
98C22—1492no—
99C22C2×C4×D14911yescharacteristic
100C4—21no—
101C4—21no—
102C4—2981no—
103C4—2981no—
104C4C2×D59611yescharacteristic
105C4#1455873611yescharacteristic
106C2—2982no—
107C2—5961no—
108C2C4×D59611yescharacteristic
109C2M16×D14911yescharacteristic
110C2#1801191911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D149
commutator, socleC22×C149C22×C4
Fitting#97×C149C2
prime radicalC2×D596C4
cosocleC2×C4×C149C23
hypercenter#97D149
hypocenterC149#435
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#14558719C2semidirect
2. C2×C8×D149C2semidirect
4. C4⋊#11924746C2semidirect
5. #18011823C2semidirect
6. #18011823C2semidirect
7. #97×C149C2semidirect
36. C8×C149D4semidirect
43. C2×D149M16semidirect
55. C149#435semidirect
63. #97D149semidirect
92. C8D596semidirect