Finite Group Databasebeta

← #34059812

Subgroups — #34059812

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#23750533C211yesmaximal, characteristic, complemented
2#23750480C211yesmaximal, characteristic, complemented
3#23749803C211yesmaximal, characteristic
4#18011972—21no—
5#18011966—21no—
6#18011941—21no—
7#18011898C2211yescharacteristic
8#18011838—21no—
9#18011828C411yescharacteristic
10H(5,𝔽2)×C149C411yescharacteristic
11#14558745—41no—
12C2×#11924753—41no—
13C2×Dic298D411yescharacteristic
14#14558726—41no—
15#14558724—41no—
16#14558720—21no—
17C22⋊Dic149—41no—
18C4×Dic149D411yescharacteristic
19#41×C149—21no—
20#41×C149—41no—
21C2×D4×C149—41no—
22C2×D4×C149—41no—
23C2×D4×C149C2×C411yescharacteristic
24#11924753—42no—
25#11924753—81no—
26Dic298—41no—
27C2×Dic149—21no—
28C2×Dic149—21no—
29#11924746—41no—
30C23×C149—21no—
31C23×C149—41no—
32Q8×C149—21no—
33D4×C149—21no—
34D4×C149—41no—
35D4×C149—42no—
36D4×C149—41no—
37C2×C4×C149—41no—
38C2×C4×C149—41no—
39C2×C4×C149C22⋊C411yescharacteristic
40C22×C149—41no—
41C22×C149—41no—
42C22×C149—81no—
43C22×C149—161no—
44C22×C149#9911yescharacteristic
45C4×C149—21no—
46C4×C149—41no—
47Dic149—41no—
48Dic149—41no—
49C2×C149—21no—
50C2×C149—81no—
51C2×C149—81no—
52C2×C149AΣL(1,𝔽16)11yescharacteristic
53C149#140311yescharacteristic, complemented, Sylow
54#1403—1491nomaximal, Sylow
55#455—1491no—
56#355—1491no—
57#329—1491no—
58H(5,𝔽2)#1059701011yescharacteristic
59#137—2981no—
60#124—1491no—
61#104—2981no—
62#101—2981no—
63#100—1491no—
64#97—2981no—
65#41—21no—
66#41—41no—
67C2×Q8—1491no—
68C2×D4—41no—
69C2×D4—41no—
70C2×D4C2×#1059701011yescharacteristic
71Q16—5961no—
72SD16—5961no—
73M16—2981no—
74M16—5961no—
75C2×C8—5961no—
76C22⋊C4—5961no—
77C42—1491no—
78C23—21no—
79C23—41no—
80Q8—21no—
81Q8—5961no—
82D4—21no—
83D4—41no—
84D4—42no—
85D4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—2981no—
89C2×C4—2981no—
90C2×C4C22⋊#1059701011yescharacteristic
91C8—5961no—
92C8—5962no—
93C8—11921no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22—161no—
98C22#1801196911yescharacteristic
99C4—21no—
100C4—41no—
101C4—5961no—
102C4—5961no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#2375052511yescharacteristic
subgroupG/H
centerC2#23750525
commutatorC2×D4×C149C2×C4
FrattiniC2×D4C2×#10597010
Fitting, prime radicalH(5,𝔽2)×C149C4
socleC2×C149AΣL(1,𝔽16)
cosocle#18011898C22
hypercenterH(5,𝔽2)#10597010
hypocenterC149#1403
LCSG ▷ C2×D4×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #23750533C2semidirect
2. #23750480C2semidirect
53. C149#1403semidirect

Maximal subgroups

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

subgroupindex
#237505332
#237504802
#237498032
#1403149