Finite Group Databasebeta

← #34043992

Subgroups — #34043992

Order 19072.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C149⋊#564C211yesmaximal, characteristic, complemented
2#23749989C212yesmaximal
3#23749367C211yesmaximal, characteristic, complemented
4#23749366C212yesmaximal, complemented
5#490×C149C211yesmaximal, characteristic
6#18011903C2212yes—
7#18011902—22no—
8#18011901—22no—
9#18011901—22no—
10#18011832—22no—
11#18011832—22no—
12#18011822C2212yes—
13#127×C149C2211yescharacteristic
14#125×C149C2211yescharacteristic
15#102×C149—22no—
16#97×C149C2211yescharacteristic
17C2×#11924746—22no—
18C4⋊Dic149—22no—
19C4⋊Dic149D412yes—
20C4⋊Dic149D412yes—
21#14558715—22no—
22#14558715—22no—
23#14558715—22no—
24#14558715—22no—
25C4×Dic149—22no—
26C2×D4×C149—21no—
27C2×D4×C149—22no—
28C2×C8×C149—21no—
29C4⋊C4×C149—22no—
30C4⋊C4×C149D412yes—
31C42×C149C2311yescharacteristic
32C2×Dic149—22no—
33C2×Dic149—22no—
34#11924746—42no—
35C23×C149—41no—
36D4×C149—42no—
37D4×C149—44no—
38C2×C4×C149—22no—
39C2×C4×C149C2×D412yes—
40C2×C4×C149C2×D411yescharacteristic
41C8×C149—41no—
42C22×C149—82no—
43C22×C149—81no—
44C22×C149#12011yescharacteristic
45C4×C149—21no—
46C4×C149—22no—
47C4×C149—42no—
48Dic149—42no—
49Dic149—42no—
50C2×C149—161no—
51C2×C149#45412yes—
52C2×C149#45411yescharacteristic
53C149#165811yescharacteristic, complemented, Sylow
54#1658—1491nomaximal, Sylow
55#564—1491no—
56#490—1492no—
57#490D14911yescharacteristic
58#330—1491no—
59#330—1492no—
60#127C2×D14911yescharacteristic
61#125—2982no—
62#125—2982no—
63#125—2982no—
64#125—1492no—
65#125C2×D14911yescharacteristic
66#102—22no—
67#102—2982no—
68#102—2982no—
69#97—1492no—
70#97C2×D14911yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—2982no—
75C4⋊C4—22no—
76C4⋊C4—2982no—
77C4⋊C4—2982no—
78C4⋊C4—2982no—
79C4⋊C4—2982no—
80C4⋊C4—2982no—
81C4⋊C4—1492no—
82C4⋊C4—1492no—
83C4⋊C4C22⋊D14912yes—
84C42—2982no—
85C42C22×D14911yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—2982no—
91C2×C4—2982no—
92C2×C4D4×D14912yes—
93C2×C4C2×C22⋊D14911yescharacteristic
94C8—41no—
95C8—5962no—
96C22—82no—
97C22—81no—
98C22#1801187911yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—5962no—
103C4—5962no—
104C2—161no—
105C2#2374979612yes—
106C2#2374979711yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#490×C149C2
socleC22×C149#120
prime radical#127×C149C22
hypercenter#490D149
hypocenterC149#1658
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C149⋊#564C2semidirect
3. #23749367C2semidirect
4. #23749366C2semidirect
53. C149#1658semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C149⋊#5642
#237499892
#237493672
#237493662
#490×C1492
#1658149