Finite Group Databasebeta

← #34067254

Subgroups — #34067254

Order 19328.

122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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#23752379C211yesmaximal, characteristic
2#23751956C211yesmaximal, characteristic, complemented
3#353×C151C211yesmaximal, characteristic, complemented
4#18012784C411yescharacteristic, complemented
5#18012765—21no—
6C4⋊(C151⋊C8)—21no—
7#18012667—21no—
8#18012656C411yescharacteristic, complemented
9#127×C151C2211yescharacteristic
10#99×C151—21no—
11#14559004—21no—
12#14559003—41no—
13C2×C22⋊D151—41no—
14D4×D151—41no—
15#14558992—41no—
16#14558989—41no—
17#14558988—21no—
18C2×C151⋊C8—41no—
19C2×D4×C151—41no—
20C2×D4×C151C2×C411yescharacteristic
21C2×D4×C151D411yescharacteristic
22C22⋊C4×C151—41no—
23C42×C151D411yescharacteristic
24C22×D151—41no—
25Dic302—21no—
26D604—21no—
27C22⋊D151—42no—
28C22⋊D151—41no—
29C2×Dic151—41no—
30C4×D151—41no—
31C151⋊C8—41no—
32C151⋊C8—81no—
33C23×C151—21no—
34C23×C151—21no—
35D4×C151—41no—
36D4×C151—41no—
37D4×C151—81no—
38D4×C151—81no—
39C2×C4×C151—21no—
40C2×C4×C151—81no—
41C2×C4×C151C22⋊C411yescharacteristic
42C22×C151—41no—
43C22×C151—41no—
44C22×C151—81no—
45C22×C151—81no—
46C22×C151#9911yescharacteristic
47C2×D151—41no—
48C2×D151—161no—
49C4×C151—21no—
50C4×C151—21no—
51C4×C151—21no—
52C4×C151—161no—
53Dic151—41no—
54C2×C151—21no—
55C2×C151—81no—
56C2×C151—81no—
57C2×C151AΣL(1,𝔽16)11yescharacteristic
58D151—81no—
59C151#140211yescharacteristic, complemented, Sylow
60#1402—1511nomaximal, Sylow
61#453—1511no—
62#353D15111yescharacteristic, complemented
63#331—1511no—
64H(5,𝔽2)—1511no—
65AGL(1,ℤ/8)—3021no—
66#127C2×D15111yescharacteristic
67C4⋊C8—3021no—
68#104—3021no—
69#100—1511no—
70#99—21no—
71#41—3021no—
72#41—6041no—
73C2×D4—41no—
74C2×D4—6041no—
75C2×D4—6041no—
76C2×D4C4×D15111yescharacteristic
77C2×D4C22⋊D15111yescharacteristic
78SD16—6041no—
79D8—6041no—
80M16—3021no—
81C2×C8—6041no—
82C22⋊C4—41no—
83C42D60411yescharacteristic
84C23—21no—
85C23—21no—
86C23—6041no—
87Q8—3021no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—3021no—
93D4—6042no—
94D4—6041no—
95C2×C4—21no—
96C2×C4—81no—
97C2×C4—6041no—
98C2×C4—6041no—
99C2×C4(C2×D151)⋊C411yescharacteristic
100C8—6041no—
101C8—12081no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—6041no—
107C22—24161no—
108C22#1801265311yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—161no—
113C4—6041no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—12081no—
118C2#2375199811yescharacteristic
subgroupG/H
centerC2#23751998
commutatorC2×D4×C151C2×C4
Frattini#127C2×D151
Fitting#353×C151C2
socleC2×C151AΣL(1,𝔽16)
prime radical#23752379C2
cosocle#127×C151C22
hypercenter#353D151
hypocenterC151#1402
LCSG ▷ C2×D4×C151 ▷ C2×C4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #23751956C2semidirect
3. #353×C151C2semidirect
4. #18012784C4semidirect
8. #18012656C4semidirect
59. C151#1402semidirect
62. #353D151semidirect

Maximal subgroups

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

subgroupindex
#237523792
#237519562
#353×C1512
#1402151