Finite Group Databasebeta

← #23749598

Subgroups — #23749598

Order 9536.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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×#14558736C211yesmaximal, characteristic
2#18011870C211yesmaximal, characteristic, complemented
3#18011825C214yesmaximal, complemented
4#117×C149C211yesmaximal, characteristic, complemented
5#14558736—21no—
6#14558736—21no—
7#14558736—21no—
8#14558736—21no—
9C2×Dic298C411yescharacteristic, complemented
10C2×D596C411yescharacteristic, complemented
11C2×C22⋊D149C2212yes—
12C2×C4×D149C412yescomplemented
13C4⋊Dic149—21no—
14C22⋊Dic149C2212yes—
15C4×Dic149—21no—
16C22×C4×C149C2211yescharacteristic
17C4⋊C4×C149—21no—
18C22⋊C4×C149C2212yes—
19C42×C149—21no—
20C22×D149C2×C412yes—
21Dic298—21no—
22Dic298—21no—
23D596—21no—
24D596—21no—
25C22⋊D149—22no—
26C22⋊D149—22no—
27C2×Dic149—22no—
28C2×Dic149C2×C412yes—
29C4×D149—22no—
30C4×D149—22no—
31C23×C149C2311yescharacteristic
32C2×C4×C149—22no—
33C2×C4×C149C2×C411yescharacteristic
34C2×C4×C149C2×C411yescharacteristic
35C2×C4×C149D411yescharacteristic
36C2×C4×C149D411yescharacteristic
37C2×C4×C149D411yescharacteristic
38C2×C4×C149D411yescharacteristic
39C22×C149—41no—
40C22×C149C22×C411yescharacteristic
41C22×C149C2×D411yescharacteristic
42C22×C149C2×D411yescharacteristic
43C2×D149—22no—
44C2×D149—42no—
45C4×C149—42no—
46C4×C149C22⋊C411yescharacteristic
47C4×C149C22⋊C411yescharacteristic
48C4×C149C22⋊C411yescharacteristic
49C4×C149C22⋊C411yescharacteristic
50Dic149—22no—
51Dic149—42no—
52C2×C149—21no—
53C2×C149—21no—
54C2×C149—21no—
55C2×C149C2×C22⋊C411yescharacteristic
56D149—42no—
57C149#41011yescharacteristic, complemented, Sylow
58#410—1491nomaximal, Sylow
59C2×#41—1491no—
60#117—1491no—
61#117D14911yescharacteristic, complemented
62#99—1494no—
63#41—2981no—
64#41—2981no—
65#41—2981no—
66#41—2981no—
67C2×Q8—1491no—
68C2×D4—1492no—
69C2×D4—1491no—
70C22×C4—1492no—
71C22×C4C2×D14911yescharacteristic
72C4⋊C4—21no—
73C4⋊C4—2981no—
74C22⋊C4—1492no—
75C22⋊C4C2×D14912yes—
76C42—21no—
77C42—2981no—
78C23—1492no—
79C23C22×D14911yescharacteristic
80Q8—2981no—
81Q8—2981no—
82D4—2982no—
83D4—2982no—
84D4—2981no—
85D4—2981no—
86C2×C4—22no—
87C2×C4—2982no—
88C2×C4—2982no—
89C2×C4—2982no—
90C2×C4—1492no—
91C2×C4C4×D14911yescharacteristic
92C2×C4C4×D14911yescharacteristic
93C2×C4C22⋊D14911yescharacteristic
94C2×C4C22⋊D14911yescharacteristic
95C2×C4D59611yescharacteristic
96C2×C4D59611yescharacteristic
97C22—41no—
98C22—2982no—
99C22—5962no—
100C22C2×C4×D14911yescharacteristic
101C22C2×C22⋊D14911yescharacteristic
102C22C2×D59611yescharacteristic
103C4—42no—
104C4—2982no—
105C4—5962no—
106C4#1455871311yescharacteristic
107C4#1455871311yescharacteristic
108C4#1455871311yescharacteristic
109C4#1455871311yescharacteristic
110C2—21no—
111C2—21no—
112C2—21no—
113C2—5962no—
114C2C2×#1455871311yescharacteristic
subgroupG/H
centerC4#14558713
commutatorC22×C149C22×C4
FrattiniC23C22×D149
Fitting#117×C149C2
socleC2×C149C2×C22⋊C4
prime radicalC2×#14558736C2
cosocleC23×C149C23
hypercenter#117D149
hypocenterC149#410
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #18011870C2semidirect
3. #18011825C2semidirect
4. #117×C149C2semidirect
9. C2×Dic298C4semidirect
10. C2×D596C4semidirect
12. C2×C4×D149C4semidirect
57. C149#410semidirect
61. #117D149semidirect