Finite Group Databasebeta

← #34068402

Subgroups — #34068402

Order 19328.

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

normal subgroups only

This group has 230 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
1#23752960C211yesmaximal, characteristic, complemented
2#23752599C212yesmaximal, complemented
3#23751954C211yesmaximal, characteristic, complemented
4#23751951C212yesmaximal, complemented
5#490×C151C211yesmaximal, characteristic, complemented
6C2×#14558992—22no—
7C2×#14558989—22no—
8#18012727C2212yes—
9#18012724—22no—
10#18012717—22no—
11#18012714—22no—
12#18012650C2212yes—
13#127×C151C2211yescharacteristic
14#125×C151C2211yescharacteristic
15#102×C151—22no—
16#97×C151C2211yescharacteristic
17C2×Dic302D412yes—
18C2×D604—22no—
19C2×D604D412yes—
20C2×C4×D151—22no—
21#14558992—44no—
22#14558989—44no—
23C2×C151⋊C8—22no—
24Dic151⋊C4—22no—
25(C2×D151)⋊C4—22no—
26(C2×D151)⋊C4—22no—
27(C2×D151)⋊C4—22no—
28C2×D4×C151—22no—
29C2×D4×C151—21no—
30C2×C8×C151—21no—
31C4⋊C4×C151—22no—
32C4⋊C4×C151D412yes—
33C42×C151C2311yescharacteristic
34C22×D151—22no—
35Dic302—42no—
36D604—42no—
37D604—82no—
38C2×Dic151—22no—
39C4×D151—82no—
40C151⋊C8—24no—
41C23×C151—41no—
42D4×C151—42no—
43D4×C151—42no—
44D4×C151—42no—
45C2×C4×C151—22no—
46C2×C4×C151C2×D412yes—
47C2×C4×C151C2×D411yescharacteristic
48C8×C151—41no—
49C22×C151—82no—
50C22×C151—81no—
51C22×C151#12011yescharacteristic
52C2×D151—42no—
53C2×D151—42no—
54C2×D151—42no—
55C4×C151—22no—
56C4×C151—21no—
57C4×C151—42no—
58Dic151—42no—
59C2×C151—161no—
60C2×C151#45312yes—
61C2×C151#45411yescharacteristic
62D151—82no—
63C151#165611yescharacteristic, complemented, Sylow
64#1656—1511nomaximal, Sylow
65#562—1511no—
66#496—1512no—
67#490D15111yescharacteristic, complemented
68#330—1511no—
69#329—1512no—
70C2×SD16—3022no—
71C2×D8—3022no—
72#127C2×D15111yescharacteristic
73#125C2×D15111yescharacteristic
74#124—1512no—
75#123—3022no—
76C22⋊Q8—3022no—
77#121—3022no—
78#102—22no—
79#97—1512no—
80#97C2×D15111yescharacteristic
81C2×Q8—1512no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—3022no—
85C2×D4—1512no—
86C22×C4—3022no—
87SD16—6044no—
88D8—6044no—
89C2×C8—21no—
90C2×C8—3022no—
91C4⋊C4—22no—
92C4⋊C4—3022no—
93C4⋊C4C22⋊D15112yes—
94C22⋊C4—3022no—
95C22⋊C4—3022no—
96C22⋊C4—3022no—
97C42C22×D15111yescharacteristic
98C23—41no—
99C23—3022no—
100Q8—6042no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—6042no—
105D4—12082no—
106C2×C4—22no—
107C2×C4—3022no—
108C2×C4—12082no—
109C2×C4D4×D15112yes—
110C2×C4C2×C22⋊D15111yescharacteristic
111C8—41no—
112C8—3024no—
113C22—82no—
114C22—81no—
115C22—6042no—
116C22—6042no—
117C22—6042no—
118C22#1801270711yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—6042no—
123C2—161no—
124C2—12082no—
125C2#2375237812yes—
126C2#2375238411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#490×C151C2
socleC22×C151#120
hypercenter#490D151
hypocenterC151#1656
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23752960C2semidirect
2. #23752599C2semidirect
3. #23751954C2semidirect
4. #23751951C2semidirect
5. #490×C151C2semidirect
63. C151#1656semidirect
67. #490D151semidirect

Maximal subgroups

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

subgroupindex
#237529602
#237525992
#237519542
#237519512
#490×C1512
#1656151