Finite Group Databasebeta

← #34059816

Subgroups — #34059816

Order 19072.

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

normal subgroups only

This group has 106 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#23750535C211yesmaximal, characteristic, complemented
2#23750485C211yesmaximal, characteristic, complemented
3#23749808C211yesmaximal, characteristic
4#18011978—21no—
5#18011972—21no—
6#18011941—21no—
7#18011909C2211yescharacteristic
8#18011838—21no—
9#18011830C411yescharacteristic
102−1+4×C149C411yescharacteristic
11#14558745—41no—
12C2×#11924753—41no—
13C2×Dic298D411yescharacteristic
14#14558726—41no—
15#14558724—41no—
16#14558720—21no—
17#14558715—41no—
18C4×Dic149D411yescharacteristic
19#41×C149—21no—
20#41×C149—41no—
21#41×C149—41no—
22C2×Q8×C149—41no—
23C2×Q8×C149C2×C411yescharacteristic
24#11924753—81no—
25#11924753—81no—
26Dic298—41no—
27C2×Dic149—21no—
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
42C4×C149—21no—
43C4×C149—41no—
44C4×C149—41no—
45Dic149—21no—
46Dic149—21no—
47Dic149—41no—
48C2×C149—21no—
49C2×C149—81no—
50C2×C149AΣL(1,𝔽16)11yescharacteristic
51C149#140511yescharacteristic, complemented, Sylow
52#1405—1491nomaximal, Sylow
53#456—1491no—
54#356—1491no—
55#333—1491no—
562−1+4#1059701011yescharacteristic
57#137—2981no—
58C4⋊Q8—1491no—
59C4⋊C8—2981no—
60#104—2981no—
61#101—2981no—
62#101—1491no—
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—1491no—
68C2×Q8C2×#1059701011yescharacteristic
69Q16—5961no—
70SD16—5961no—
71M16—2981no—
72M16—5961no—
73C2×C8—5961no—
74C4⋊C4—5961no—
75C42—1491no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—5961no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—2981no—
87C2×C4—2981no—
88C2×C4C22⋊#1059701011yescharacteristic
89C8—5961no—
90C8—11921no—
91C8—11921no—
92C22—41no—
93C22#1801196911yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—2981no—
98C4—2981no—
99C4—5961no—
100C2—21no—
101C2—81no—
102C2#2375052511yescharacteristic
subgroupG/H
centerC2#23750525
commutatorC2×Q8×C149C2×C4
FrattiniC2×Q8C2×#10597010
Fitting, prime radical2−1+4×C149C4
socleC2×C149AΣL(1,𝔽16)
cosocle#18011909C22
hypercenter2−1+4#10597010
hypocenterC149#1405
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. #23750535C2semidirect
2. #23750485C2semidirect
51. C149#1405semidirect

Maximal subgroups

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

subgroupindex
#237505352
#237504852
#237498082
#1405149