Finite Group Databasebeta

← #34059814

Subgroups — #34059814

Order 19072.

112 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 20 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#23750531C211yesmaximal, characteristic, complemented
2#23750481C211yesmaximal, characteristic, complemented
3#23749798C211yesmaximal, characteristic
4#18011970—21no—
5#18011966—21no—
6#18011936—21no—
7#18011900C2211yescharacteristic
8#18011838—21no—
9#18011830C411yescharacteristic, complemented
102−1+4×C149C411yescharacteristic, complemented
11C2×#11924753—41no—
12C22⋊#10597010—41no—
13C2×D596D411yescharacteristic
14#14558723—41no—
15#14558721—41no—
16#14558720—21no—
17#14558713—41no—
18C4×Dic149D411yescharacteristic
19#41×C149—21no—
20#41×C149—41no—
21#41×C149—41no—
22C2×Q8×C149—41no—
23C2×Q8×C149C2×C411yescharacteristic
24C2×#10597010—81no—
25#11924753—42no—
26C22×D149—21no—
27D596—41no—
28C2×Dic149—21no—
29#11924746—41no—
30Q8×C149—21no—
31Q8×C149—41no—
32Q8×C149—41no—
33D4×C149—21no—
34D4×C149—41no—
35D4×C149—41no—
36C2×C4×C149—21no—
37C2×C4×C149—41no—
38C2×C4×C149—42no—
39C2×C4×C149C22⋊C411yescharacteristic
40C22×C149—41no—
41C22×C149#9911yescharacteristic
42C2×D149—41no—
43C2×D149—81no—
44#10597010—161no—
45C4×C149—21no—
46C4×C149—41no—
47C4×C149—41no—
48Dic149—41no—
49C2×C149—21no—
50C2×C149—81no—
51C2×C149AΣL(1,𝔽16)11yescharacteristic
52D149—81no—
53C149#140411yescharacteristic, complemented, Sylow
54#1404—1491nomaximal, Sylow
55#454—1491no—
56#354—1491no—
57#329—1491no—
582−1+4#1059701011yescharacteristic, complemented
59AGL(1,ℤ/8)—2981no—
60#124—1491no—
61#104—2981no—
62#101—1491no—
63#99—2981no—
64#97—2981no—
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×#1059701011yescharacteristic
70C2×D4—1491no—
71SD16—5961no—
72D8—5961no—
73M16—2981no—
74C2×C8—5961no—
75C22⋊C4—5961no—
76C22⋊C4—5961no—
77C42—1491no—
78C23—2981no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—5961no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—42no—
89C2×C4—2981no—
90C2×C4—11921no—
91C2×C4C22⋊#1059701011yescharacteristic
92C8—5961no—
93C8—5962no—
94C22—41no—
95C22—5961no—
96C22—11921no—
97C22#1801196911yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—23841no—
102C4—5961no—
103C2—21no—
104C2—81no—
105C2—11921no—
106C2#2375052511yescharacteristic
subgroupG/H
centerC2#23750525
commutatorC2×Q8×C149C2×C4
FrattiniC2×Q8C2×#10597010
Fitting2−1+4×C149C4
socleC2×C149AΣL(1,𝔽16)
prime radical#23749798C2
cosocle#18011900C22
hypercenter2−1+4#10597010
hypocenterC149#1404
LCSG ▷ C2×Q8×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #23750531C2semidirect
2. #23750481C2semidirect
9. #18011830C4semidirect
10. 2−1+4×C149C4semidirect
53. C149#1404semidirect
58. 2−1+4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505312
#237504812
#237497982
#1404149