Finite Group Databasebeta

← #34068194

Subgroups — #34068194

Order 19328.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#23752928C211yesmaximal, characteristic, complemented
2#23752586C211yesmaximal, characteristic, complemented
3#23752408C212yesmaximal, complemented
4#23751939C212yesmaximal, complemented
5#333×C151C211yesmaximal, characteristic, complemented
6C2×#14558991—22no—
7C2×D1208—22no—
8#18012736C2211yescharacteristic
9#18012728—22no—
10#18012714—22no—
11C4×D604C2212yes—
12#18012697—22no—
13#18012661—22no—
14C4×C151⋊C8C2211yescharacteristic
15C4⋊Q8×C151C2211yescharacteristic
16C4⋊C8×C151C2212yes—
17C2×D604—22no—
18C2×D604—22no—
19C2×D604—21no—
20C2×D604D412yes—
21C2×C4×D151—22no—
22#14558991—44no—
23D1208—44no—
24C2×C151⋊C8—21no—
25C4⋊Dic151D412yes—
26(C2×D151)⋊C4—24no—
27(C2×D151)⋊C4—22no—
28C4×Dic151—22no—
29C2×Q8×C151D412yes—
30C2×C8×C151—22no—
31C4⋊C4×C151—22no—
32C42×C151C2311yescharacteristic
33C22×D151—22no—
34C22×D151—41no—
35D604—22no—
36D604—22no—
37D604—42no—
38D604—42no—
39D604—42no—
40D604—82no—
41C2×Dic151—22no—
42C4×D151—42no—
43C4×D151—42no—
44C151⋊C8—22no—
45Q8×C151—42no—
46C2×C4×C151—22no—
47C2×C4×C151C2×D412yes—
48C2×C4×C151C2×D411yescharacteristic
49C8×C151—42no—
50C22×C151#12011yescharacteristic
51C2×D151—42no—
52C2×D151—42no—
53C2×D151—42no—
54C2×D151—82no—
55C2×D151—81no—
56C4×C151—21no—
57C4×C151—42no—
58C4×C151#13512yes—
59C4×C151AGL(1,ℤ/8)12yes—
60Dic151—42no—
61C2×C151#44912yes—
62C2×C151#45311yescharacteristic
63D151—82no—
64D151—161no—
65C151#162411yescharacteristic, complemented, Sylow
66#1624—1511nomaximal, Sylow
67#555—1511no—
68#492—1511no—
69#459—1512no—
70#333D15111yescharacteristic, complemented
71D4⋊C8—1512no—
72C2×SD16—3022no—
73C2×D8—3022no—
74C4⋊Q8C2×D15111yescharacteristic
75#127—1511no—
76#124—3022no—
77#121—3022no—
78C4×D4—1512no—
79#117—3022no—
80C4⋊C8C2×D15112yes—
81#102—3022no—
82C4×C8—1511no—
83C2×Q8D60412yes—
84C2×D4—3022no—
85C2×D4—3022no—
86C2×D4—3021no—
87C2×D4—1512no—
88C22×C4—3022no—
89SD16—6044no—
90D8—6044no—
91C2×C8—22no—
92C2×C8—3021no—
93C4⋊C4—22no—
94C4⋊C4—1512no—
95C22⋊C4—3024no—
96C22⋊C4—3022no—
97C42—3022no—
98C42C22×D15111yescharacteristic
99C23—3022no—
100C23—6041no—
101Q8—42no—
102D4—3022no—
103D4—3022no—
104D4—6042no—
105D4—6042no—
106D4—6042no—
107D4—12082no—
108C2×C4—22no—
109C2×C4—3022no—
110C2×C4—6042no—
111C2×C4—6042no—
112C2×C4D4×D15112yes—
113C2×C4C2×D60411yescharacteristic
114C8—42no—
115C8—3022no—
116C22—6042no—
117C22—6042no—
118C22—6042no—
119C22—12082no—
120C22—12081no—
121C22#1801270911yescharacteristic
122C4—21no—
123C4—42no—
124C4—6042no—
125C4#1801276212yes—
126C4#1801276612yes—
127C2—24161no—
128C2—12082no—
129C2#2375236012yes—
130C2#2375238211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#333×C151C2
socleC22×C151#120
hypercenter#333D151
hypocenterC151#1624
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #23752928C2semidirect
2. #23752586C2semidirect
3. #23752408C2semidirect
4. #23751939C2semidirect
5. #333×C151C2semidirect
65. C151#1624semidirect
70. #333D151semidirect

Maximal subgroups

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

subgroupindex
#237529282
#237525862
#237524082
#237519392
#333×C1512
#1624151