Finite Group Databasebeta

← #23749874

Subgroups — #23749874

Order 9536.

120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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×#14558723C211yesmaximal, characteristic, complemented
2C2×#14558719C211yesmaximal, characteristic, complemented
3#18011887C211yesmaximal, characteristic, complemented
4#18011886C211yesmaximal, characteristic
5#18011844C211yesmaximal, characteristic, complemented
6#18011833C211yesmaximal, characteristic, complemented
7#103×C149C211yesmaximal, characteristic, complemented
8C2×D596—21no—
9C2×D596C2211yescharacteristic
10C2×C4×D149C2211yescharacteristic
11#14558723—22no—
12#14558719—22no—
13C2×#11924746C2211yescharacteristic
14C4⋊Dic149C2211yescharacteristic
15#14558715—21no—
16#14558713—21no—
17#14558713—21no—
18C2×Q8×C149C2211yescharacteristic
19C2×C8×C149C2211yescharacteristic
20C4⋊C4×C149C2211yescharacteristic
21C22×D149—21no—
22C22×D149D411yescharacteristic
23D596—21no—
24D596—21no—
25D596—42no—
26C2×Dic149—21no—
27C2×Dic149D411yescharacteristic
28C4×D149—21no—
29C4×D149—21no—
30#11924746D412yescomplemented
31Q8×C149—21no—
32Q8×C149—21no—
33C2×C4×C149—21no—
34C2×C4×C149—21no—
35C2×C4×C149C2311yescharacteristic
36C8×C149—21no—
37C22×C149C2×D411yescharacteristic
38C2×D149—21no—
39C2×D149—21no—
40C2×D149—21no—
41C2×D149—41no—
42C2×D149—41no—
43C2×D149—41no—
44C4×C149—41no—
45C4×C149—41no—
46C4×C149C2×D411yescharacteristic
47C4×C149#4111yescharacteristic
48Dic149—21no—
49Dic149—41no—
50C2×C149#12111yescharacteristic
51C2×C149AGL(1,ℤ/8)11yescharacteristic
52C2×C149#13711yescharacteristic
53D149—41no—
54D149—81no—
55C149#46811yescharacteristic, complemented, Sylow
56#468—1491nomaximal, Sylow
57C2×SD16—1491no—
58C2×M16—1491no—
59C22⋊Q8—1491no—
60#121—1491no—
61#107—1491no—
62#103D14911yescharacteristic, complemented
63#102—1491no—
64C2×Q8C2×D14911yescharacteristic
65C2×D4—2981no—
66C2×D4—1491no—
67C22×C4—1491no—
68SD16—2982no—
69M16—2982no—
70C2×C8—1491no—
71C2×C8C2×D14911yescharacteristic
72C4⋊C4—2981no—
73C4⋊C4—1491no—
74C4⋊C4C2×D14911yescharacteristic
75C22⋊C4—2981no—
76C22⋊C4—2981no—
77C23—2981no—
78C23—1491no—
79Q8—21no—
80Q8—21no—
81D4—2981no—
82D4—2981no—
83D4—5962no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—2981no—
87C2×C4—2981no—
88C2×C4—2981no—
89C2×C4—1491no—
90C2×C4C22×D14911yescharacteristic
91C8—21no—
92C8—1492no—
93C22—2981no—
94C22—2981no—
95C22—2981no—
96C22—5961no—
97C22—5961no—
98C22—5961no—
99C22D4×D14911yescharacteristic
100C4—41no—
101C4—41no—
102C4—2981no—
103C4—5961no—
104C4D4×D14911yescharacteristic
105C4#1455873611yescharacteristic
106C2—5961no—
107C2—11921no—
108C2#1801188411yescharacteristic
109C2#1801193811yescharacteristic
110C2#1801194311yescharacteristic
subgroupG/H
centerC22D4×D149
commutator, cosocleC2×C4×C149C23
FrattiniC2×C4C22×D149
Fitting#103×C149C2
socleC22×C149C2×D4
prime radical#18011886C2
hypercenter#103D149
hypocenterC149#468
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#14558723C2semidirect
2. C2×#14558719C2semidirect
3. #18011887C2semidirect
5. #18011844C2semidirect
6. #18011833C2semidirect
7. #103×C149C2semidirect
30. #11924746D4semidirect
55. C149#468semidirect
62. #103D149semidirect