Finite Group Databasebeta

← #34067262

Subgroups — #34067262

Order 19328.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#23752384C211yesmaximal, characteristic
2#23752007C211yesmaximal, characteristic, complemented
3#329×C151C211yesmaximal, characteristic, complemented
4#18012787C411yescharacteristic, complemented
5#18012765—21no—
6#18012667—21no—
7#18012658C411yescharacteristic, complemented
8#18012654—21no—
9#124×C151C2211yescharacteristic
10#97×C151—21no—
11#14559005—41no—
12#14559004—21no—
13#14559004—41no—
14Q8×D151—41no—
15#14558992—41no—
16#14558989—41no—
17#14558988—21no—
18C22⋊Dic151—41no—
19C2×Q8×C151C2×C411yescharacteristic
20C2×D4×C151D411yescharacteristic
21C2×C8×C151—41no—
22C22⋊C4×C151—41no—
23C42×C151D411yescharacteristic
24Dic302—21no—
25Dic302—41no—
26D604—21no—
27D604—41no—
28C22⋊D151—41no—
29C2×Dic151—81no—
30C4×D151—41no—
31C4×D151—42no—
32C151⋊C8—41no—
33C23×C151—21no—
34Q8×C151—41no—
35D4×C151—41no—
36C2×C4×C151—21no—
37C2×C4×C151—21no—
38C2×C4×C151C22⋊C411yescharacteristic
39C8×C151—42no—
40C22×C151—41no—
41C22×C151—81no—
42C22×C151#9911yescharacteristic
43C2×D151—41no—
44C4×C151—21no—
45C4×C151—41no—
46C4×C151—41no—
47Dic151—41no—
48Dic151—161no—
49C2×C151—21no—
50C2×C151—81no—
51C2×C151AΣL(1,𝔽16)11yescharacteristic
52D151—81no—
53C151#140411yescharacteristic, complemented, Sylow
54#1404—1511nomaximal, Sylow
55#454—1511no—
56#354—1511no—
57#329D15111yescharacteristic, complemented
582−1+4—1511no—
59AGL(1,ℤ/8)—3021no—
60#124C2×D15111yescharacteristic
61#104—3021no—
62#101—1511no—
63#99—3021no—
64#97—21no—
65#41—3021no—
66#41—6041no—
67#41—6041no—
68C2×Q8—6041no—
69C2×Q8C4×D15111yescharacteristic
70C2×D4D60411yescharacteristic
71SD16—6041no—
72D8—6041no—
73M16—3021no—
74C2×C8—41no—
75C22⋊C4—41no—
76C22⋊C4—6041no—
77C42C22⋊D15111yescharacteristic
78C23—21no—
79Q8—41no—
80Q8—3021no—
81Q8—6041no—
82D4—41no—
83D4—3021no—
84D4—6041no—
85D4—6041no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—6041no—
89C2×C4—6042no—
90C2×C4—12081no—
91C2×C4(C2×D151)⋊C411yescharacteristic
92C8—42no—
93C8—6041no—
94C22—41no—
95C22—81no—
96C22—6041no—
97C22#1801265311yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—6041no—
102C4—24161no—
103C2—21no—
104C2—81no—
105C2—12081no—
106C2#2375200011yescharacteristic
subgroupG/H
centerC2#23752000
commutatorC2×Q8×C151C2×C4
Frattini#124C2×D151
Fitting#329×C151C2
socleC2×C151AΣL(1,𝔽16)
prime radical#23752384C2
cosocle#124×C151C22
hypercenter#329D151
hypocenterC151#1404
LCSG ▷ C2×Q8×C151 ▷ C2×C4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23752007C2semidirect
3. #329×C151C2semidirect
4. #18012787C4semidirect
7. #18012658C4semidirect
53. C151#1404semidirect
57. #329D151semidirect

Maximal subgroups

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

subgroupindex
#237523842
#237520072
#329×C1512
#1404151