Finite Group Databasebeta

← #34068413

Subgroups — #34068413

Order 19328.

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
1C151⋊#564C211yesmaximal, characteristic, complemented
2#23752578C211yesmaximal, characteristic
3#23752577C212yesmaximal
4#23751953C212yesmaximal, complemented
5#330×C151C211yesmaximal, characteristic, complemented
6#18012736C2211yescharacteristic
7#18012731C2212yes—
8#18012730—22no—
9#18012729—22no—
10#18012729—22no—
11#18012661—22no—
12#18012661—22no—
13#18012659—22no—
14#18012650C2211yescharacteristic
15#125×C151C2211yescharacteristic
16#97×C151C2212yes—
17C2×D604—21no—
18C2×D604—22no—
19C2×C151⋊C8—21no—
20C4⋊Dic151—22no—
21C4⋊Dic151D412yes—
22C4⋊Dic151D412yes—
23Dic151⋊C4—22no—
24Dic151⋊C4—22no—
25Dic151⋊C4—22no—
26Dic151⋊C4—22no—
27C4×Dic151—22no—
28C2×C8×C151—22no—
29C4⋊C4×C151—22no—
30C4⋊C4×C151D412yes—
31C42×C151C2311yescharacteristic
32C22×D151—41no—
33D604—44no—
34D604—42no—
35C2×Dic151—22no—
36C2×Dic151—22no—
37C151⋊C8—41no—
38C2×C4×C151—22no—
39C2×C4×C151C2×D412yes—
40C2×C4×C151C2×D411yescharacteristic
41C8×C151—42no—
42C22×C151#12011yescharacteristic
43C2×D151—82no—
44C2×D151—81no—
45C4×C151—22no—
46C4×C151—21no—
47C4×C151—42no—
48Dic151—42no—
49Dic151—42no—
50C2×C151#45412yes—
51C2×C151#45411yescharacteristic
52D151—161no—
53C151#165811yescharacteristic, complemented, Sylow
54#1658—1511nomaximal, Sylow
55#564—1511no—
56#490—1511no—
57#490—1512no—
58#330—1512no—
59#330D15111yescharacteristic, complemented
60#127—1511no—
61#125—3022no—
62#125—3022no—
63#125—3022no—
64#125—1512no—
65#125C2×D15111yescharacteristic
66#102—3022no—
67#102—3022no—
68#102—3022no—
69#97—1511no—
70#97C2×D15112yes—
71C2×D4—3022no—
72C2×D4—3021no—
73C2×C8—22no—
74C2×C8—3021no—
75C4⋊C4—22no—
76C4⋊C4—3022no—
77C4⋊C4—3022no—
78C4⋊C4—3022no—
79C4⋊C4—3022no—
80C4⋊C4—3022no—
81C4⋊C4—1512no—
82C4⋊C4—1512no—
83C4⋊C4D60412yes—
84C42—3022no—
85C42C22×D15111yescharacteristic
86C23—6041no—
87D4—6044no—
88D4—6042no—
89C2×C4—22no—
90C2×C4—3022no—
91C2×C4—3022no—
92C2×C4D4×D15112yes—
93C2×C4C2×D60411yescharacteristic
94C8—42no—
95C8—6041no—
96C22—12082no—
97C22—12081no—
98C22#1801270911yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—6042no—
103C4—6042no—
104C2—24161no—
105C2#2375238612yes—
106C2#2375238711yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#330×C151C2
socleC22×C151#120
prime radical#18012736C22
hypercenter#330D151
hypocenterC151#1658
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. C151⋊#564C2semidirect
4. #23751953C2semidirect
5. #330×C151C2semidirect
53. C151#1658semidirect
59. #330D151semidirect

Maximal subgroups

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

subgroupindex
C151⋊#5642
#237525782
#237525772
#237519532
#330×C1512
#1658151