Finite Group Databasebeta

← #34068433

Subgroups — #34068433

Order 19328.

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

normal subgroups only

This group has 196 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#23752582C211yesmaximal, characteristic, complemented
2#23752571C212yesmaximal, complemented
3#23751954C211yesmaximal, characteristic, complemented
4#23751952C212yesmaximal, complemented
5#562×C151C211yesmaximal, characteristic
6#18012739C2211yescharacteristic
7#18012663—22no—
8#18012662—22no—
9#18012660—22no—
10#18012650C2211yescharacteristic
11#18012650C2212yes—
12#125×C151C2211yescharacteristic
13#124×C151C2212yes—
14#123×C151—22no—
15C22⋊Q8×C151—22no—
16#121×C151—22no—
17C2×Dic302—21no—
18C2×C151⋊C8—22no—
19C2×C151⋊C8—21no—
20C4⋊Dic151—22no—
21C2×Q8×C151D412yes—
22C2×D4×C151—22no—
23C2×D4×C151D412yes—
24C22×C4×C151—22no—
25C4⋊C4×C151—22no—
26C4⋊C4×C151—22no—
27C4⋊C4×C151D412yes—
28C22⋊C4×C151—22no—
29C22⋊C4×C151—22no—
30C22⋊C4×C151—22no—
31C42×C151C2311yescharacteristic
32Dic302—42no—
33C2×Dic151—41no—
34C151⋊C8—41no—
35C151⋊C8—42no—
36C23×C151—22no—
37Q8×C151—42no—
38D4×C151—42no—
39D4×C151—82no—
40C2×C4×C151—22no—
41C2×C4×C151—22no—
42C2×C4×C151—82no—
43C2×C4×C151C2×D412yes—
44C2×C4×C151C2×D411yescharacteristic
45C22×C151—42no—
46C22×C151—42no—
47C22×C151—42no—
48C22×C151#12011yescharacteristic
49C4×C151—21no—
50C4×C151—22no—
51C4×C151—42no—
52C4×C151—42no—
53Dic151—81no—
54C2×C151—82no—
55C2×C151#45411yescharacteristic
56C2×C151#45512yes—
57C151#166211yescharacteristic, complemented, Sylow
58#1662—1511nomaximal, Sylow
59#562D15111yescharacteristic
60#491—1511no—
61#489—1512no—
62#330—1511no—
63#329—1512no—
64C4⋊Q8—1511no—
65#125C2×D15111yescharacteristic
66#124C2×D15112yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—3022no—
71#103—3022no—
72#102—3022no—
73#97—1511no—
74#97—1512no—
75C2×Q8—3021no—
76C2×Q8C22⋊D15112yes—
77C2×D4—22no—
78C2×D4C22⋊D15112yes—
79C22×C4—22no—
80C2×C8—3022no—
81C2×C8—3021no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—3022no—
85C4⋊C4C22⋊D15112yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D15111yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—6042no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—6041no—
99C2×C4C2×C22⋊D15111yescharacteristic
100C2×C4C2×C22⋊D15112yes—
101C8—6041no—
102C8—6042no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1801270811yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—12081no—
112C2—82no—
113C2#2375238511yescharacteristic
114C2#2375239012yes—
subgroupG/H
centerC22#18012708
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting, prime radical#562×C151C2
socleC22×C151#120
hypercenter#562D151
hypocenterC151#1662
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. #23752582C2semidirect
2. #23752571C2semidirect
3. #23751954C2semidirect
4. #23751952C2semidirect
57. C151#1662semidirect

Maximal subgroups

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

subgroupindex
#237525822
#237525712
#237519542
#237519522
#562×C1512
#1662151