Finite Group Databasebeta

← #34068439

Subgroups — #34068439

Order 19328.

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

normal subgroups only

This group has 172 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
2#23752621C212yesmaximal
3#23752582C211yesmaximal, characteristic
4#23751953C212yesmaximal
5#330×C151C211yesmaximal, characteristic
6#18012739C2211yescharacteristic
7#18012731C2212yes—
8#18012730—22no—
9#18012729—22no—
10#18012729—22no—
11#18012673—22no—
12#18012671—22no—
13#18012662—22no—
14#18012650C2211yescharacteristic
15#125×C151C2211yescharacteristic
16#97×C151C2212yes—
17C2×Dic302—21no—
18C2×C151⋊C8—21no—
19C4⋊Dic151—22no—
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
32Dic302—42no—
33C2×Dic151—22no—
34C2×Dic151—22no—
35C2×Dic151—41no—
36C151⋊C8—41no—
37C2×C4×C151—22no—
38C2×C4×C151C2×D412yes—
39C2×C4×C151C2×D411yescharacteristic
40C8×C151—24no—
41C22×C151#12011yescharacteristic
42C4×C151—21no—
43C4×C151—22no—
44C4×C151—42no—
45Dic151—42no—
46Dic151—42no—
47Dic151—81no—
48C2×C151#45411yescharacteristic
49C2×C151#45612yes—
50C151#166311yescharacteristic, complemented, Sylow
51#1663—1511nomaximal, Sylow
52#564—1511no—
53#501—1512no—
54#491—1511no—
55#330—1512no—
56#330D15111yescharacteristic
57C4⋊Q8—1511no—
58#125—3022no—
59#125—3022no—
60#125—3022no—
61#125—1512no—
62#125C2×D15111yescharacteristic
63#107—3022no—
64#106—3022no—
65#103—3022no—
66#97—1511no—
67#97C2×D15112yes—
68C2×Q8—3021no—
69C2×C8—22no—
70C2×C8—3021no—
71C4⋊C4—22no—
72C4⋊C4—3022no—
73C4⋊C4—3022no—
74C4⋊C4—3022no—
75C4⋊C4—3022no—
76C4⋊C4—3022no—
77C4⋊C4—3022no—
78C4⋊C4—1512no—
79C4⋊C4—1512no—
80C4⋊C4D60412yes—
81C42—3022no—
82C42C22×D15111yescharacteristic
83Q8—6042no—
84C2×C4—22no—
85C2×C4—3022no—
86C2×C4—3022no—
87C2×C4—6041no—
88C2×C4D4×D15112yes—
89C2×C4C2×D60411yescharacteristic
90C8—24no—
91C8—6041no—
92C22#1801270911yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—6042no—
97C4—6042no—
98C4—12081no—
99C2#2375238711yescharacteristic
100C2#2375239612yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#330×C151C2
socle, prime radicalC22×C151#120
hypercenter#330D151
hypocenterC151#1663
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
50. C151#1663semidirect

Maximal subgroups

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

subgroupindex
C151⋊#5642
#237526212
#237525822
#237519532
#330×C1512
#1663151