Finite Group Databasebeta

← #34068227

Subgroups — #34068227

Order 19328.

314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752847C211yesmaximal, characteristic
2#23752584C211yesmaximal, characteristic, complemented
3#23752503C212yesmaximal, complemented
4#23751939C212yesmaximal, complemented
5#331×C151C211yesmaximal, characteristic, complemented
6C2×D4×D151—22no—
7C2×#14558992—22no—
8#18012739C2211yescharacteristic, complemented
9#18012710—22no—
10#18012707—22no—
11C4×D604C2212yes—
12#18012671—22no—
13#18012661—22no—
14C4×C151⋊C8C2211yescharacteristic, complemented
15#127×C151C2211yescharacteristic
16C4⋊C8×C151C2212yescomplemented
17C23×D151—22no—
18C2×Dic302—21no—
19C2×D604D412yes—
20C2×C22⋊D151—24no—
21D4×D151—44no—
22D4×D151—44no—
23C2×C4×D151—22no—
24#14558992—44no—
25C2×C151⋊C8—21no—
26C4⋊Dic151—22no—
27C4⋊Dic151D412yes—
28C22⋊Dic151—22no—
29(C2×D151)⋊C4—22no—
30C2×D4×C151—22no—
31C2×D4×C151D412yes—
32C2×C8×C151—22no—
33C42×C151C2311yescharacteristic
34C22×D151—22no—
35C22×D151—48no—
36C22×D151—82no—
37Dic302—42no—
38D604—22no—
39D604SD1614yescomplemented
40C22⋊D151—48no—
41C2×Dic151—22no—
42C2×Dic151—41no—
43C4×D151—42no—
44C4×D151—42no—
45C151⋊C8—22no—
46C23×C151—22no—
47D4×C151—42no—
48D4×C151—42no—
49D4×C151—42no—
50C2×C4×C151C2×D412yes—
51C2×C4×C151C2×D411yescharacteristic
52C8×C151—42no—
53C22×C151—44no—
54C22×C151—42no—
55C22×C151#12011yescharacteristic
56C2×D151—24no—
57C2×D151—42no—
58C2×D151—42no—
59C2×D151—88no—
60C4×C151—21no—
61C4×C151C2×SD1612yes—
62C4×C151AGL(1,ℤ/8)12yes—
63Dic151—42no—
64Dic151—81no—
65C2×C151—82no—
66C2×C151#45012yes—
67C2×C151#45311yescharacteristic
68D151—44no—
69C151#162911yescharacteristic, complemented, Sylow
70#1629—1511nomaximal, Sylow
71D42—1511no—
72#492—1511no—
73#476—1512no—
74#331D15111yescharacteristic, complemented
75D4⋊C8—1512no—
76C22×D4—3022no—
77C2×SD16—3022no—
78C4⋊Q8—1511no—
79#127C2×D15111yescharacteristic
80#121—3022no—
81#120—3022no—
82C4×D4—1512no—
83#106—3022no—
84C4⋊C8C2×D15112yescomplemented
85#102—3022no—
86C4×C8—1511no—
87C24—3022no—
88C2×Q8—3021no—
89C2×D4—22no—
90C2×D4—3024no—
91C2×D4—6044no—
92C2×D4—6044no—
93C2×D4—1512no—
94C2×D4D60412yes—
95C22×C4—3022no—
96SD16—6044no—
97C2×C8—22no—
98C2×C8—3021no—
99C4⋊C4—3022no—
100C4⋊C4—1512no—
101C22⋊C4—3022no—
102C22⋊C4—3022no—
103C42C22×D15111yescharacteristic
104C23—22no—
105C23—3022no—
106C23—6048no—
107C23—12082no—
108Q8—6042no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—3022no—
113D4—6048no—
114D4—1514no—
115C2×C4—3022no—
116C2×C4—6042no—
117C2×C4—6042no—
118C2×C4—6041no—
119C2×C4D4×D15112yes—
120C2×C4C2×D60411yescharacteristic
121C8—42no—
122C8—3022no—
123C22—44no—
124C22—42no—
125C22—3024no—
126C22—6042no—
127C22—6042no—
128C22—12088no—
129C22#1801270911yescharacteristic
130C4—21no—
131C4—6042no—
132C4—12081no—
133C4SD16×D15112yes—
134C4#1801276312yes—
135C2—82no—
136C2—6044no—
137C2#2375236412yes—
138C2#2375238211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#331×C151C2
socleC22×C151#120
prime radical#23752847C2
hypercenter#331D151
hypocenterC151#1629
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #23752584C2semidirect
3. #23752503C2semidirect
4. #23751939C2semidirect
5. #331×C151C2semidirect
8. #18012739C22semidirect
14. C4×C151⋊C8C22semidirect
16. C4⋊C8×C151C22semidirect
39. D604SD16semidirect
69. C151#1629semidirect
74. #331D151semidirect
84. C4⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528472
#237525842
#237525032
#237519392
#331×C1512
#1629151