Finite Group Databasebeta

← #34059811

Subgroups — #34059811

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#23749795C211yesmaximal, characteristic
4#18011978—21no—
5#18011970—21no—
6#18011956C411yescharacteristic, complemented
7#18011939—21no—
8#18011907C2211yescharacteristic
9#18011837—21no—
10#100×C149C411yescharacteristic, complemented
11C2×#11924753—41no—
12C22⋊#10597010—41no—
13#14558736—21no—
14#14558735—41no—
15C2×D596D411yescharacteristic
16C2×C22⋊D149—41no—
17C2×C22⋊D149—41no—
18D4×D149—41no—
19#14558725—41no—
20D1192—41no—
21C4×Dic149D411yescharacteristic
22C2×D4×C149C2×C411yescharacteristic
23M16×C149—21no—
24C2×#10597010—81no—
25#11924753—81no—
26C22×D149—21no—
27C22×D149—41no—
28Dic298—21no—
29D596—21no—
30D596—41no—
31C22⋊D149—42no—
32C22⋊D149—41no—
33C22⋊D149—81no—
34C22⋊D149—81no—
35C2×Dic149—21no—
36C2×Dic149—41no—
37C4×D149—41no—
38C23×C149—21no—
39D4×C149—41no—
40C2×C4×C149C22⋊C411yescharacteristic
41C8×C149—41no—
42C22×C149—41no—
43C22×C149—81no—
44C22×C149#9911yescharacteristic
45C2×D149—41no—
46C2×D149—41no—
47C2×D149—81no—
48C2×D149—161no—
49#10597010—161no—
50C4×C149—21no—
51Dic149—21no—
52Dic149—21no—
53Dic149—41no—
54C2×C149—21no—
55C2×C149—81no—
56C2×C149AΣL(1,𝔽16)11yescharacteristic
57D149—81no—
58D149—81no—
59C149#140211yescharacteristic, complemented, Sylow
60#1402—1491nomaximal, Sylow
61#453—1491no—
62#353—1491no—
63#331—1491no—
64H(5,𝔽2)—1491no—
65AGL(1,ℤ/8)—2981no—
66#127—1491no—
67C4⋊C8—2981no—
68#104—2981no—
69#100#1059701011yescharacteristic, complemented
70#99—2981no—
71#41—2981no—
72#41—5961no—
73C2×D4—5961no—
74C2×D4—5961no—
75C2×D4—5961no—
76C2×D4—1491no—
77C2×D4C2×#1059701011yescharacteristic
78SD16—5961no—
79D8—5961no—
80M16—21no—
81C2×C8—5961no—
82C22⋊C4—5961no—
83C42—1491no—
84C23—21no—
85C23—2981no—
86C23—5961no—
87Q8—2981no—
88D4—41no—
89D4—2981no—
90D4—5961no—
91D4—5962no—
92D4—5961no—
93D4—11921no—
94D4—11921no—
95C2×C4—2981no—
96C2×C4—5961no—
97C2×C4—5961no—
98C2×C4—11921no—
99C2×C4C22⋊#1059701011yescharacteristic
100C8—41no—
101C8—11921no—
102C22—41no—
103C22—81no—
104C22—23841no—
105C22—5961no—
106C22—5961no—
107C22—11921no—
108C22#1801197011yescharacteristic
109C4—21no—
110C4—2981no—
111C4—2981no—
112C4—23841no—
113C4—5961no—
114C2—21no—
115C2—81no—
116C2—11921no—
117C2—11921no—
118C2#2375052611yescharacteristic
subgroupG/H
centerC2#23750526
commutatorC2×D4×C149C2×C4
FrattiniC2×D4C2×#10597010
Fitting#100×C149C4
socleC2×C149AΣL(1,𝔽16)
prime radical#23749795C2
cosocle#18011907C22
hypercenter#100#10597010
hypocenterC149#1402
LCSG ▷ C2×D4×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #23750529C2semidirect
2. #23750483C2semidirect
6. #18011956C4semidirect
10. #100×C149C4semidirect
59. C149#1402semidirect
69. #100#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505292
#237504832
#237497952
#1402149