Finite Group Databasebeta

← #34068403

Subgroups — #34068403

Order 19328.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#23752602C212yesmaximal, complemented
2#23752578C211yesmaximal, characteristic, complemented
3#23751954C211yesmaximal, characteristic, complemented
4#23751952C212yesmaximal, complemented
5#562×C151C211yesmaximal, characteristic, complemented
6C2×#14558991—22no—
7C2×#14558989—22no—
8#18012736C2211yescharacteristic
9#18012659—22no—
10#18012650C2211yescharacteristic
11#18012650C2212yes—
12#125×C151C2211yescharacteristic
13#124×C151C2212yes—
14#123×C151—22no—
15C22⋊Q8×C151—22no—
16#121×C151—22no—
17C2×D604—22no—
18C2×D604—21no—
19#14558991—44no—
20#14558989—44no—
21C2×C151⋊C8—22no—
22C2×C151⋊C8—21no—
23C2×Q8×C151D412yes—
24C2×D4×C151—22no—
25C2×D4×C151D412yes—
26C22×C4×C151—22no—
27C4⋊C4×C151—22no—
28C4⋊C4×C151—22no—
29C4⋊C4×C151D412yes—
30C22⋊C4×C151—22no—
31C22⋊C4×C151—22no—
32C22⋊C4×C151—22no—
33C42×C151C2311yescharacteristic
34C22×D151—41no—
35D604—42no—
36D604—42no—
37D604—42no—
38C151⋊C8—24no—
39C151⋊C8—41no—
40C23×C151—22no—
41Q8×C151—42no—
42D4×C151—42no—
43D4×C151—82no—
44C2×C4×C151—22no—
45C2×C4×C151—22no—
46C2×C4×C151—82no—
47C2×C4×C151C2×D412yes—
48C2×C4×C151C2×D411yescharacteristic
49C22×C151—42no—
50C22×C151—42no—
51C22×C151—42no—
52C22×C151#12011yescharacteristic
53C2×D151—82no—
54C2×D151—81no—
55C4×C151—22no—
56C4×C151—21no—
57C4×C151—42no—
58C4×C151—42no—
59C2×C151—82no—
60C2×C151#45312yes—
61C2×C151#45411yescharacteristic
62D151—161no—
63C151#165611yescharacteristic, complemented, Sylow
64#1656—1511nomaximal, Sylow
65#562D15111yescharacteristic, complemented
66#496—1512no—
67#490—1511no—
68#330—1511no—
69#329—1512no—
70C2×SD16—3022no—
71C2×D8—3022no—
72#127—1511no—
73#125C2×D15111yescharacteristic
74#124C2×D15112yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—3022no—
79#97—1511no—
80#97—1512no—
81C2×Q8C22⋊D15112yes—
82C2×D4—22no—
83C2×D4—3021no—
84C2×D4—3022no—
85C2×D4C22⋊D15112yes—
86C22×C4—22no—
87SD16—6044no—
88D8—6044no—
89C2×C8—3022no—
90C2×C8—3021no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D15112yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D15111yescharacteristic
98C23—22no—
99C23—6041no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—6042no—
104D4—6042no—
105D4—6042no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D15111yescharacteristic
110C2×C4C2×C22⋊D15112yes—
111C8—3024no—
112C8—6041no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—12082no—
117C22—12081no—
118C22#1801270811yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—24161no—
125C2#2375238012yes—
126C2#2375238511yescharacteristic
subgroupG/H
centerC22#18012708
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#562×C151C2
socleC22×C151#120
hypercenter#562D151
hypocenterC151#1656
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #23752602C2semidirect
2. #23752578C2semidirect
3. #23751954C2semidirect
4. #23751952C2semidirect
5. #562×C151C2semidirect
63. C151#1656semidirect
65. #562D151semidirect

Maximal subgroups

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

subgroupindex
#237526022
#237525782
#237519542
#237519522
#562×C1512
#1656151