Finite Group Databasebeta

← #34068191

Subgroups — #34068191

Order 19328.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#23752928C211yesmaximal, characteristic, complemented
2#23752404C212yesmaximal, complemented
3#23751961C211yesmaximal, characteristic, complemented
4#23751941C212yesmaximal, complemented
5#492×C151C211yesmaximal, characteristic, complemented
6C2×#14558989—22no—
7#18012728—22no—
8#18012714—22no—
9C4×D604C2212yes—
10#18012697—22no—
11C4⋊(C151⋊C8)C2212yes—
12#18012660—22no—
13C2×SD16×C151—22no—
14C4⋊Q8×C151C2211yescharacteristic
15#127×C151C2211yescharacteristic
16C4×C8×C151C2211yescharacteristic
17C2×D604—22no—
18C2×D604D412yes—
19C2×C4×D151—22no—
20#14558989—44no—
21C2×C151⋊C8—22no—
22C4⋊Dic151D412yes—
23(C2×D151)⋊C4—24no—
24(C2×D151)⋊C4—22no—
25C4×Dic151—22no—
26C2×Q8×C151D412yes—
27C2×D4×C151—22no—
28C2×D4×C151—21no—
29SD16×C151—44no—
30C2×C8×C151—21no—
31C4⋊C4×C151—22no—
32C42×C151C2311yescharacteristic
33C22×D151—22no—
34D604—22no—
35D604—22no—
36D604—82no—
37C2×Dic151—22no—
38C4×D151—42no—
39C4×D151—42no—
40C151⋊C8—42no—
41C23×C151—41no—
42Q8×C151—42no—
43D4×C151—42no—
44D4×C151—42no—
45D4×C151—42no—
46C2×C4×C151—22no—
47C2×C4×C151C2×D412yes—
48C2×C4×C151C2×D411yescharacteristic
49C8×C151—22no—
50C22×C151—82no—
51C22×C151—81no—
52C22×C151#12011yescharacteristic
53C2×D151—42no—
54C2×D151—42no—
55C2×D151—42no—
56C4×C151—21no—
57C4×C151—42no—
58C4×C151#13512yes—
59C4×C151AGL(1,ℤ/8)12yes—
60Dic151—42no—
61C2×C151—161no—
62C2×C151#44912yes—
63C2×C151#45311yescharacteristic
64D151—82no—
65C151#162411yescharacteristic, complemented, Sylow
66#1624—1511nomaximal, Sylow
67#555—1511no—
68#492D15111yescharacteristic, complemented
69#459—1512no—
70#333—1511no—
71D4⋊C8—1512no—
72C2×SD16—22no—
73C2×D8—3022no—
74C4⋊Q8C2×D15111yescharacteristic
75#127C2×D15111yescharacteristic
76#124—3022no—
77#121—3022no—
78C4×D4—1512no—
79#117—3022no—
80C4⋊C8—1512no—
81#102—3022no—
82C4×C8C2×D15111yescharacteristic
83C2×Q8C22⋊D15112yes—
84C2×D4—22no—
85C2×D4—21no—
86C2×D4—3022no—
87C2×D4—1512no—
88C22×C4—3022no—
89SD16—44no—
90D8—6044no—
91C2×C8—21no—
92C2×C8—3022no—
93C4⋊C4—22no—
94C4⋊C4—1512no—
95C22⋊C4—3024no—
96C22⋊C4—3022no—
97C42—3022no—
98C42C22×D15111yescharacteristic
99C23—41no—
100C23—3022no—
101Q8—42no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—3022no—
106D4—3022no—
107D4—12082no—
108C2×C4—22no—
109C2×C4—3022no—
110C2×C4—6042no—
111C2×C4—6042no—
112C2×C4D4×D15112yes—
113C2×C4C2×C22⋊D15111yescharacteristic
114C8—22no—
115C8—6042no—
116C22—82no—
117C22—81no—
118C22—6042no—
119C22—6042no—
120C22—6042no—
121C22#1801270711yescharacteristic
122C4—21no—
123C4—42no—
124C4—6042no—
125C4#1801276012yes—
126C4#1801276612yes—
127C2—161no—
128C2—12082no—
129C2#2375235612yes—
130C2#2375237911yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#492×C151C2
socleC22×C151#120
hypercenter#492D151
hypocenterC151#1624
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #23752928C2semidirect
2. #23752404C2semidirect
3. #23751961C2semidirect
4. #23751941C2semidirect
5. #492×C151C2semidirect
65. C151#1624semidirect
68. #492D151semidirect

Maximal subgroups

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

subgroupindex
#237529282
#237524042
#237519612
#237519412
#492×C1512
#1624151