Finite Group Databasebeta

← #23749841

Subgroups — #23749841

Order 9536.

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

normal subgroups only

This group has 124 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×#14558725C211yesmaximal, characteristic, complemented
2C2×D1192C211yesmaximal, characteristic
3#18011899C211yesmaximal, characteristic, complemented
4C4×D596C211yesmaximal, characteristic, complemented
5#18011836C211yesmaximal, characteristic, complemented
6#18011833C211yesmaximal, characteristic, complemented
7C4⋊C8×C149C211yesmaximal, characteristic, complemented
8C2×Dic298C2211yescharacteristic
9C2×D596C2211yescharacteristic
10C2×D596C2211yescharacteristic
11C2×C4×D149—21no—
12#14558725—22no—
13D1192—22no—
14C4⋊Dic149C2211yescharacteristic
15#14558713—21no—
16#14558713—21no—
17#14558713—21no—
18C2×C8×C149C2211yescharacteristic
19C2×C8×C149C2211yescharacteristic
20C42×C149C2211yescharacteristic
21C22×D149—21no—
22C22×D149—21no—
23Dic298—21no—
24Dic298—21no—
25D596—21no—
26D596—21no—
27D596—21no—
28D596D412yes—
29C2×Dic149—21no—
30C2×Dic149—21no—
31C4×D149—42no—
32C2×C4×C149D411yescharacteristic
33C2×C4×C149D411yescharacteristic
34C2×C4×C149C2311yescharacteristic
35C8×C149—21no—
36C8×C149—21no—
37C22×C149C2×D411yescharacteristic
38C2×D149—22no—
39C2×D149—41no—
40C2×D149—41no—
41C2×D149—41no—
42C2×D149—41no—
43C2×D149—41no—
44C4×C149—21no—
45C4×C149—21no—
46C4×C149C2×D411yescharacteristic
47C4×C149#4111yescharacteristic
48Dic149—41no—
49Dic149—41no—
50C2×C149#12111yescharacteristic
51C2×C149#13511yescharacteristic
52C2×C149AGL(1,ℤ/8)11yescharacteristic
53D149—42no—
54D149—81no—
55C149#46311yescharacteristic, complemented, Sylow
56#463—1491nomaximal, Sylow
57C2×SD16—1491no—
58C2×D8—1491no—
59#124—1491no—
60C4×D4—1491no—
61C4⋊C8D14911yescharacteristic, complemented
62#103—1491no—
63#102—1491no—
64C2×Q8—1491no—
65C2×D4—1491no—
66C2×D4—1491no—
67C22×C4—2981no—
68SD16—2982no—
69D8—2982no—
70C2×C8C2×D14911yescharacteristic
71C2×C8C2×D14911yescharacteristic
72C4⋊C4—1491no—
73C22⋊C4—2981no—
74C22⋊C4—2981no—
75C22⋊C4—2981no—
76C42C2×D14911yescharacteristic
77C23—2981no—
78C23—2981no—
79Q8—2981no—
80Q8—2981no—
81D4—2981no—
82D4—2981no—
83D4—2981no—
84D4—1492no—
85C2×C4—2981no—
86C2×C4—2981no—
87C2×C4—5962no—
88C2×C4D59611yescharacteristic
89C2×C4D59611yescharacteristic
90C2×C4C22×D14911yescharacteristic
91C8—21no—
92C8—21no—
93C22—2982no—
94C22—5961no—
95C22—5961no—
96C22—5961no—
97C22—5961no—
98C22—5961no—
99C22C2×D59611yescharacteristic
100C4—21no—
101C4—21no—
102C4—5961no—
103C4—5961no—
104C4D4×D14911yescharacteristic
105C4#1455873711yescharacteristic
106C2—5962no—
107C2—11921no—
108C2#1801188611yescharacteristic
109C2#1801193311yescharacteristic
110C2#1801193911yescharacteristic
subgroupG/H
centerC22C2×D596
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
FittingC4⋊C8×C149C2
socleC22×C149C2×D4
prime radicalC2×D1192C2
hypercenterC4⋊C8D149
hypocenterC149#463
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#14558725C2semidirect
3. #18011899C2semidirect
4. C4×D596C2semidirect
5. #18011836C2semidirect
6. #18011833C2semidirect
7. C4⋊C8×C149C2semidirect
55. C149#463semidirect
61. C4⋊C8D149semidirect