Finite Group Databasebeta

← #34068434

Subgroups — #34068434

Order 19328.

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

normal subgroups only

This group has 196 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
2#23752582C211yesmaximal, characteristic, complemented
3#23752572C212yesmaximal, complemented
4#23751951C212yesmaximal, complemented
5#330×C151C211yesmaximal, characteristic, complemented
6#18012739C2211yescharacteristic
7#18012727C2212yes—
8#18012724—22no—
9#18012717—22no—
10#18012714—22no—
11#18012664—22no—
12#18012662—22no—
13#18012661—22no—
14#18012650C2211yescharacteristic
15#125×C151C2211yescharacteristic
16#97×C151C2212yes—
17C2×Dic302—21no—
18C2×Dic302D412yes—
19C2×D604—22no—
20C2×D604D412yes—
21C2×C4×D151—22no—
22C2×C151⋊C8—21no—
23C4⋊Dic151—22no—
24Dic151⋊C4—22no—
25(C2×D151)⋊C4—22no—
26(C2×D151)⋊C4—22no—
27(C2×D151)⋊C4—22no—
28C2×C8×C151—22no—
29C4⋊C4×C151—22no—
30C4⋊C4×C151D412yes—
31C42×C151C2311yescharacteristic
32C22×D151—22no—
33Dic302—42no—
34Dic302—42no—
35D604—42no—
36D604—82no—
37C2×Dic151—22no—
38C2×Dic151—41no—
39C4×D151—82no—
40C151⋊C8—41no—
41C2×C4×C151—22no—
42C2×C4×C151C2×D412yes—
43C2×C4×C151C2×D411yescharacteristic
44C8×C151—42no—
45C22×C151#12011yescharacteristic
46C2×D151—42no—
47C2×D151—42no—
48C2×D151—42no—
49C4×C151—21no—
50C4×C151—22no—
51C4×C151—42no—
52Dic151—42no—
53Dic151—81no—
54C2×C151#45411yescharacteristic
55C2×C151#45512yes—
56D151—82no—
57C151#166211yescharacteristic, complemented, Sylow
58#1662—1511nomaximal, Sylow
59#562—1511no—
60#491—1511no—
61#489—1512no—
62#330D15111yescharacteristic, complemented
63#329—1512no—
64C4⋊Q8—1511no—
65#125C2×D15111yescharacteristic
66#124—1512no—
67#123—3022no—
68C22⋊Q8—3022no—
69#121—3022no—
70#103—3022no—
71#103—3022no—
72#102—3022no—
73#97—1511no—
74#97C2×D15112yes—
75C2×Q8—3021no—
76C2×Q8—1512no—
77C2×D4—3022no—
78C2×D4—1512no—
79C22×C4—3022no—
80C2×C8—22no—
81C2×C8—3021no—
82C4⋊C4—22no—
83C4⋊C4—3022no—
84C4⋊C4—3022no—
85C4⋊C4D60412yes—
86C22⋊C4—3022no—
87C22⋊C4—3022no—
88C22⋊C4—3022no—
89C42C22×D15111yescharacteristic
90C23—3022no—
91Q8—6042no—
92Q8—6042no—
93D4—6042no—
94D4—12082no—
95C2×C4—22no—
96C2×C4—3022no—
97C2×C4—6041no—
98C2×C4—12082no—
99C2×C4D4×D15112yes—
100C2×C4C2×D60411yescharacteristic
101C8—42no—
102C8—6041no—
103C22—6042no—
104C22—6042no—
105C22—6042no—
106C22#1801270911yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—6042no—
111C4—12081no—
112C2—12082no—
113C2#2375238711yescharacteristic
114C2#2375239112yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#330×C151C2
socleC22×C151#120
prime radical#23752960C2
hypercenter#330D151
hypocenterC151#1662
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #23752582C2semidirect
3. #23752572C2semidirect
4. #23751951C2semidirect
5. #330×C151C2semidirect
57. C151#1662semidirect
62. #330D151semidirect

Maximal subgroups

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

subgroupindex
#237529602
#237525822
#237525722
#237519512
#330×C1512
#1662151