Finite Group Databasebeta

← #34059810

Subgroups — #34059810

Order 19072.

122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 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
1#23750529C211yesmaximal, characteristic, complemented
2#23750483C211yesmaximal, characteristic, complemented
3#23749793C211yesmaximal, characteristic
4#18011978—21no—
5#18011970—21no—
6#18011936—21no—
7#18011907C2211yescharacteristic
8#18011838—21no—
9#18011828C411yescharacteristic, complemented
10H(5,𝔽2)×C149C411yescharacteristic, complemented
11C2×#11924753—41no—
12C22⋊#10597010—41no—
13C2×D596D411yescharacteristic
14C2×C22⋊D149—41no—
15#14558723—41no—
16#14558721—41no—
17#14558720—21no—
18C4×Dic149D411yescharacteristic
19#41×C149—21no—
20#41×C149—41no—
21C2×D4×C149—41no—
22C2×D4×C149—41no—
23C2×D4×C149C2×C411yescharacteristic
24C2×#10597010—81no—
25#11924753—81no—
26C22×D149—21no—
27D596—41no—
28C22⋊D149—81no—
29C22⋊D149—81no—
30C2×Dic149—21no—
31#11924746—41no—
32C23×C149—21no—
33C23×C149—41no—
34Q8×C149—21no—
35D4×C149—21no—
36D4×C149—41no—
37D4×C149—42no—
38D4×C149—41no—
39C2×C4×C149—41no—
40C2×C4×C149—41no—
41C2×C4×C149C22⋊C411yescharacteristic
42C22×C149—41no—
43C22×C149—41no—
44C22×C149—81no—
45C22×C149—161no—
46C22×C149#9911yescharacteristic
47C2×D149—41no—
48C2×D149—81no—
49#10597010—161no—
50C4×C149—21no—
51C4×C149—41no—
52Dic149—21no—
53Dic149—21no—
54C2×C149—21no—
55C2×C149—81no—
56C2×C149—81no—
57C2×C149AΣL(1,𝔽16)11yescharacteristic
58D149—81no—
59C149#140211yescharacteristic, complemented, Sylow
60#1402—1491nomaximal, Sylow
61#453—1491no—
62#353—1491no—
63#331—1491no—
64H(5,𝔽2)#1059701011yescharacteristic, complemented
65AGL(1,ℤ/8)—2981no—
66#127—1491no—
67C4⋊C8—2981no—
68#104—2981no—
69#100—1491no—
70#99—2981no—
71#41—21no—
72#41—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—5961no—
76C2×D4—1491no—
77C2×D4C2×#1059701011yescharacteristic
78SD16—5961no—
79D8—5961no—
80M16—2981no—
81C2×C8—5961no—
82C22⋊C4—5961no—
83C42—1491no—
84C23—21no—
85C23—41no—
86C23—2981no—
87Q8—21no—
88D4—21no—
89D4—41no—
90D4—42no—
91D4—41no—
92D4—5961no—
93D4—11921no—
94D4—11921no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—2981no—
98C2×C4—11921no—
99C2×C4C22⋊#1059701011yescharacteristic
100C8—5961no—
101C8—11921no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—161no—
106C22—5961no—
107C22—11921no—
108C22#1801196911yescharacteristic
109C4—21no—
110C4—41no—
111C4—2981no—
112C4—2981no—
113C4—23841no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—11921no—
118C2#2375052511yescharacteristic
subgroupG/H
centerC2#23750525
commutatorC2×D4×C149C2×C4
FrattiniC2×D4C2×#10597010
FittingH(5,𝔽2)×C149C4
socleC2×C149AΣL(1,𝔽16)
prime radical#23749793C2
cosocle#18011907C22
hypercenterH(5,𝔽2)#10597010
hypocenterC149#1402
LCSG ▷ C2×D4×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #23750529C2semidirect
2. #23750483C2semidirect
9. #18011828C4semidirect
10. H(5,𝔽2)×C149C4semidirect
59. C149#1402semidirect
64. H(5,𝔽2)#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505292
#237504832
#237497932
#1402149