Finite Group Databasebeta

← #34068405

Subgroups — #34068405

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#23752601C212yesmaximal, complemented
3#23752578C211yesmaximal, characteristic, complemented
4#23751951C212yesmaximal, complemented
5#330×C151C211yesmaximal, characteristic, complemented
6C2×#14558993—22no—
7C2×D1208—22no—
8#18012736C2211yescharacteristic
9#18012727C2212yes—
10#18012724—22no—
11#18012717—22no—
12#18012714—22no—
13#18012659—22no—
14#18012650C2211yescharacteristic
15#125×C151C2211yescharacteristic
16#97×C151C2212yes—
17C2×Dic302D412yes—
18C2×D604—22no—
19C2×D604—22no—
20C2×D604—21no—
21C2×D604D412yes—
22C2×C4×D151—22no—
23#14558993—44no—
24D1208—44no—
25C2×C151⋊C8—21no—
26Dic151⋊C4—22no—
27(C2×D151)⋊C4—22no—
28(C2×D151)⋊C4—22no—
29(C2×D151)⋊C4—22no—
30C2×C8×C151—22no—
31C4⋊C4×C151—22no—
32C4⋊C4×C151D412yes—
33C42×C151C2311yescharacteristic
34C22×D151—22no—
35C22×D151—41no—
36Dic302—42no—
37D604—42no—
38D604—42no—
39D604—42no—
40D604—42no—
41D604—82no—
42C2×Dic151—22no—
43C4×D151—82no—
44C151⋊C8—41no—
45C2×C4×C151—22no—
46C2×C4×C151C2×D412yes—
47C2×C4×C151C2×D411yescharacteristic
48C8×C151—24no—
49C22×C151#12011yescharacteristic
50C2×D151—42no—
51C2×D151—42no—
52C2×D151—42no—
53C2×D151—82no—
54C2×D151—81no—
55C4×C151—22no—
56C4×C151—21no—
57C4×C151—42no—
58Dic151—42no—
59C2×C151#45312yes—
60C2×C151#45411yescharacteristic
61D151—82no—
62D151—161no—
63C151#165611yescharacteristic, complemented, Sylow
64#1656—1511nomaximal, Sylow
65#562—1511no—
66#496—1512no—
67#490—1511no—
68#330D15111yescharacteristic, complemented
69#329—1512no—
70C2×SD16—3022no—
71C2×D8—3022no—
72#127—1511no—
73#125C2×D15111yescharacteristic
74#124—1512no—
75#123—3022no—
76C22⋊Q8—3022no—
77#121—3022no—
78#102—3022no—
79#97—1511no—
80#97C2×D15112yes—
81C2×Q8—1512no—
82C2×D4—3022no—
83C2×D4—3022no—
84C2×D4—3021no—
85C2×D4—1512no—
86C22×C4—3022no—
87SD16—6044no—
88D8—6044no—
89C2×C8—22no—
90C2×C8—3021no—
91C4⋊C4—22no—
92C4⋊C4—3022no—
93C4⋊C4D60412yes—
94C22⋊C4—3022no—
95C22⋊C4—3022no—
96C22⋊C4—3022no—
97C42C22×D15111yescharacteristic
98C23—3022no—
99C23—6041no—
100Q8—6042no—
101D4—6042no—
102D4—6042no—
103D4—6042no—
104D4—6042no—
105D4—12082no—
106C2×C4—22no—
107C2×C4—3022no—
108C2×C4—12082no—
109C2×C4D4×D15112yes—
110C2×C4C2×D60411yescharacteristic
111C8—24no—
112C8—6041no—
113C22—6042no—
114C22—6042no—
115C22—6042no—
116C22—12082no—
117C22—12081no—
118C22#1801270911yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—6042no—
123C2—24161no—
124C2—12082no—
125C2#2375238112yes—
126C2#2375238711yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#330×C151C2
socleC22×C151#120
hypercenter#330D151
hypocenterC151#1656
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. #23752960C2semidirect
2. #23752601C2semidirect
3. #23752578C2semidirect
4. #23751951C2semidirect
5. #330×C151C2semidirect
63. C151#1656semidirect
68. #330D151semidirect

Maximal subgroups

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

subgroupindex
#237529602
#237526012
#237525782
#237519512
#330×C1512
#1656151