Finite Group Databasebeta

← #34042845

Subgroups — #34042845

Order 19072.

106 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 25 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#23749424C211yesmaximal, characteristic, complemented
2#23749374C211yesmaximal, characteristic, complemented
3#456×C149C211yesmaximal, characteristic
4C4⋊#11924746—21no—
5#18011830—21no—
62−1+4×C149C411yescharacteristic
7#137×C149—21no—
8C4⋊Q8×C149C2211yescharacteristic
9#104×C149—21no—
10#101×C149C411yescharacteristic
11#14558720—41no—
12C2×#11924746—41no—
13#41×C149—21no—
14#41×C149—41no—
15#41×C149—41no—
16C2×Q8×C149—41no—
17C2×Q8×C149C2×C411yescharacteristic
18C2×Q8×C149D411yescharacteristic
19Q16×C149—41no—
20SD16×C149—41no—
21M16×C149—21no—
22C4⋊C4×C149—41no—
23C42×C149D411yescharacteristic
24#11924746—81no—
25#11924746—81no—
26Q8×C149—21no—
27Q8×C149—41no—
28Q8×C149—41no—
29Q8×C149—41no—
30D4×C149—21no—
31D4×C149—41no—
32D4×C149—41no—
33C2×C4×C149—21no—
34C2×C4×C149—21no—
35C2×C4×C149—21no—
36C2×C4×C149—41no—
37C2×C4×C149—42no—
38C2×C4×C149C22⋊C411yescharacteristic
39C8×C149—41no—
40C22×C149—41no—
41C22×C149#9911yescharacteristic
42C4×C149—21no—
43C4×C149—21no—
44C4×C149—21no—
45C4×C149—41no—
46C4×C149—41no—
47C4×C149—41no—
48C2×C149—21no—
49C2×C149—81no—
50C2×C149AΣL(1,𝔽16)11yescharacteristic
51C149#140511yescharacteristic, complemented, Sylow
52#1405—1491nomaximal, Sylow
53#456D14911yescharacteristic
54#356—1491no—
55#333—1491no—
562−1+4Dic14911yescharacteristic
57#137—21no—
58C4⋊Q8C2×D14911yescharacteristic
59C4⋊C8—2981no—
60#104—21no—
61#101—2981no—
62#101Dic14911yescharacteristic
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8C2×Dic14911yescharacteristic
68C2×Q8C22⋊D14911yescharacteristic
69Q16—41no—
70SD16—41no—
71M16—21no—
72M16—5961no—
73C2×C8—5961no—
74C4⋊C4—41no—
75C42C22⋊D14911yescharacteristic
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—41no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—41no—
87C2×C4—42no—
88C2×C4C22⋊Dic14911yescharacteristic
89C8—41no—
90C8—11921no—
91C8—11921no—
92C22—41no—
93C22#1801182611yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—41no—
100C2—21no—
101C2—81no—
102C2#2374941211yescharacteristic
subgroupG/H
centerC2#23749412
commutatorC2×Q8×C149C2×C4
FrattiniC4⋊Q8C2×D149
Fitting#456×C149C2
socleC2×C149AΣL(1,𝔽16)
prime radical2−1+4×C149C4
cosocleC4⋊Q8×C149C22
hypercenter#456D149
hypocenterC149#1405
LCSG ▷ C2×Q8×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #23749424C2semidirect
2. #23749374C2semidirect
51. C149#1405semidirect

Maximal subgroups

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

subgroupindex
#237494242
#237493742
#456×C1492
#1405149