Finite Group Databasebeta

← #34059813

Subgroups — #34059813

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#23749805C211yesmaximal, characteristic
4#18011972—21no—
5#18011966—21no—
6#18011956C411yescharacteristic
7#18011944—21no—
8#18011898C2211yescharacteristic
9#18011837—21no—
10#100×C149C411yescharacteristic
11#14558745—41no—
12C2×#11924753—41no—
13#14558736—21no—
14#14558735—41no—
15C2×Dic298D411yescharacteristic
16C2×C22⋊D149—41no—
17D4×D149—41no—
18Dic596—41no—
19#14558725—41no—
20C22⋊Dic149—41no—
21C4×Dic149D411yescharacteristic
22C2×D4×C149C2×C411yescharacteristic
23M16×C149—21no—
24#11924753—42no—
25#11924753—81no—
26C22×D149—41no—
27Dic298—21no—
28Dic298—41no—
29D596—21no—
30C22⋊D149—42no—
31C22⋊D149—41no—
32C2×Dic149—21no—
33C2×Dic149—21no—
34C2×Dic149—41no—
35C4×D149—41no—
36C23×C149—21no—
37D4×C149—41no—
38C2×C4×C149C22⋊C411yescharacteristic
39C8×C149—41no—
40C22×C149—41no—
41C22×C149—81no—
42C22×C149#9911yescharacteristic
43C2×D149—41no—
44C2×D149—161no—
45C4×C149—21no—
46Dic149—41no—
47Dic149—41no—
48Dic149—41no—
49C2×C149—21no—
50C2×C149—81no—
51C2×C149AΣL(1,𝔽16)11yescharacteristic
52D149—81no—
53C149#140311yescharacteristic, complemented, Sylow
54#1403—1491nomaximal, Sylow
55#455—1491no—
56#355—1491no—
57#329—1491no—
58H(5,𝔽2)—1491no—
59#137—2981no—
60#124—1491no—
61#104—2981no—
62#101—2981no—
63#100#1059701011yescharacteristic
64#97—2981no—
65#41—2981no—
66#41—5961no—
67C2×Q8—1491no—
68C2×D4—5961no—
69C2×D4—5961no—
70C2×D4C2×#1059701011yescharacteristic
71Q16—5961no—
72SD16—5961no—
73M16—21no—
74M16—5961no—
75C2×C8—5961no—
76C22⋊C4—5961no—
77C42—1491no—
78C23—21no—
79C23—5961no—
80Q8—2981no—
81Q8—5961no—
82D4—41no—
83D4—2981no—
84D4—5962no—
85D4—5961no—
86C2×C4—2981no—
87C2×C4—2981no—
88C2×C4—5961no—
89C2×C4—5961no—
90C2×C4C22⋊#1059701011yescharacteristic
91C8—41no—
92C8—5962no—
93C8—11921no—
94C22—41no—
95C22—81no—
96C22—23841no—
97C22—5961no—
98C22#1801197011yescharacteristic
99C4—21no—
100C4—5961no—
101C4—5961no—
102C4—5961no—
103C2—21no—
104C2—81no—
105C2—11921no—
106C2#2375052611yescharacteristic
subgroupG/H
centerC2#23750526
commutatorC2×D4×C149C2×C4
FrattiniC2×D4C2×#10597010
Fitting#100×C149C4
socleC2×C149AΣL(1,𝔽16)
prime radical#18011956C4
cosocle#18011898C22
hypercenter#100#10597010
hypocenterC149#1403
LCSG ▷ C2×D4×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

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
#237498052
#1403149