Finite Group Databasebeta

← #23749705

Subgroups — #23749705

Order 9536.

134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14558721C211yesmaximal, characteristic
2D4×Dic149C211yesmaximal, characteristic, complemented
3#18011873C211yesmaximal, characteristic, complemented
4#18011844C211yesmaximal, characteristic, complemented
5#18011833C211yesmaximal, characteristic, complemented
6C8×Dic149C211yesmaximal, characteristic, complemented
7#102×C149C211yesmaximal, characteristic, complemented
8C2×D596C2211yescharacteristic
9C22×Dic149—21no—
10C2×C4×D149—21no—
11#14558721C414yescomplemented
12C2×#11924746C2211yescharacteristic
13C4⋊Dic149C2211yescharacteristic
14C22⋊Dic149—21no—
15#14558713—21no—
16C4×Dic149C2211yescharacteristic
17C2×D4×C149C2211yescharacteristic
18C2×C8×C149C2211yescharacteristic
19C4⋊C4×C149C2211yescharacteristic
20C22×D149—21no—
21D596—21no—
22D596C2×C412yescomplemented
23C2×Dic149—21no—
24C2×Dic149—42no—
25C2×Dic149D411yescharacteristic
26C2×Dic149D411yescharacteristic
27C4×D149—42no—
28#11924746C2×C412yescomplemented
29C23×C149—21no—
30D4×C149—21no—
31D4×C149C2×C412yescomplemented
32C2×C4×C149—21no—
33C2×C4×C149C2311yescharacteristic
34C8×C149—21no—
35C22×C149—22no—
36C22×C149—41no—
37C22×C149—41no—
38C22×C149C2×D411yescharacteristic
39C2×D149—22no—
40C2×D149—41no—
41C2×D149—41no—
42C4×C149—41no—
43C4×C149C22×C411yescharacteristic
44C4×C149#4111yescharacteristic
45Dic149—21no—
46Dic149—41no—
47Dic149D812yescomplemented
48C2×C149—42no—
49C2×C149C4×D411yescharacteristic
50C2×C149C2×D811yescharacteristic
51C2×C149#13511yescharacteristic
52D149—42no—
53C149C4×D811yescharacteristic, complemented, Sylow
54C4×D8—1491nomaximal, Sylow
55C2×D8—1491no—
56C4×D4—1491no—
57C4×D4—1491no—
58#107—1491no—
59#102—1491no—
60#102D14911yescharacteristic, complemented
61C4×C8—1491no—
62C2×D4—1491no—
63C2×D4C2×D14911yescharacteristic
64C22×C4—2981no—
65C22×C4—2981no—
66D8—1494no—
67C2×C8—1491no—
68C2×C8C2×D14911yescharacteristic
69C4⋊C4—1491no—
70C4⋊C4C2×D14911yescharacteristic
71C22⋊C4—2981no—
72C22⋊C4—2981no—
73C42—1491no—
74C23—21no—
75C23—2981no—
76D4—21no—
77D4—2981no—
78D4—1492no—
79D4C4×D14912yescomplemented
80C2×C4—21no—
81C2×C4—2981no—
82C2×C4—5962no—
83C2×C4—5962no—
84C2×C4—1491no—
85C2×C4—1491no—
86C2×C4C22×D14911yescharacteristic
87C8—21no—
88C8—1492no—
89C22—22no—
90C22—41no—
91C22—41no—
92C22—2982no—
93C22—5961no—
94C22—5961no—
95C22D4×D14911yescharacteristic
96C4—41no—
97C4—2981no—
98C4—5961no—
99C4—1492no—
100C4C2×C4×D14911yescharacteristic
101C4#1455873511yescharacteristic
102C2—42no—
103C2—5962no—
104C2#1801187111yescharacteristic
105C2D8×D14911yescharacteristic
106C2#1801193211yescharacteristic
subgroupG/H
centerC22D4×D149
commutatorC4×C149C22×C4
FrattiniC2×C4C22×D149
Fitting#102×C149C2
socleC22×C149C2×D4
prime radicalC2×#14558721C2
cosocleC2×C4×C149C23
hypercenter#102D149
hypocenterC149C4×D8
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. D4×Dic149C2semidirect
3. #18011873C2semidirect
4. #18011844C2semidirect
5. #18011833C2semidirect
6. C8×Dic149C2semidirect
7. #102×C149C2semidirect
11. #14558721C4semidirect
22. D596C2×C4semidirect
28. #11924746C2×C4semidirect
31. D4×C149C2×C4semidirect
47. Dic149D8semidirect
53. C149C4×D8semidirect
60. #102D149semidirect
79. D4C4×D149semidirect