Finite Group Databasebeta

← #34042842

Subgroups — #34042842

Order 19072.

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

normal subgroups only

This group has 112 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#23749420C211yesmaximal, characteristic, complemented
2#23749365C211yesmaximal, characteristic, complemented
3#454×C149C211yesmaximal, characteristic
4#18011826—21no—
5#18011822—21no—
62−1+4×C149C411yescharacteristic, complemented
7AGL(1,ℤ/8)×C149—21no—
8#124×C149C2211yescharacteristic
9#104×C149—21no—
10#101×C149C411yescharacteristic, complemented
11C2×#11924746—41no—
12C22⋊Dic149—41no—
13#41×C149—21no—
14#41×C149—41no—
15#41×C149—41no—
16C2×Q8×C149—41no—
17C2×Q8×C149C2×C411yescharacteristic
18C2×D4×C149D411yescharacteristic
19SD16×C149—41no—
20D8×C149—41no—
21M16×C149—21no—
22C22⋊C4×C149—41no—
23C42×C149D411yescharacteristic
24C2×Dic149—81no—
25#11924746—42no—
26C23×C149—21no—
27Q8×C149—21no—
28Q8×C149—41no—
29Q8×C149—41no—
30D4×C149—21no—
31D4×C149—41no—
32D4×C149—41no—
33D4×C149—41no—
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—41no—
42C22×C149—81no—
43C22×C149#9911yescharacteristic
44C4×C149—21no—
45C4×C149—41no—
46C4×C149—41no—
47C4×C149—41no—
48Dic149—161no—
49C2×C149—21no—
50C2×C149—81no—
51C2×C149—81no—
52C2×C149AΣL(1,𝔽16)11yescharacteristic
53C149#140411yescharacteristic, complemented, Sylow
54#1404—1491nomaximal, Sylow
55#454D14911yescharacteristic
56#354—1491no—
57#329—1491no—
582−1+4Dic14911yescharacteristic, complemented
59AGL(1,ℤ/8)—21no—
60#124C2×D14911yescharacteristic
61#104—21no—
62#101Dic14911yescharacteristic, complemented
63#99—2981no—
64#97—2981no—
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×Dic14911yescharacteristic
70C2×D4C22⋊D14911yescharacteristic
71SD16—41no—
72D8—41no—
73M16—21no—
74C2×C8—5961no—
75C22⋊C4—41no—
76C22⋊C4—5961no—
77C42C22⋊D14911yescharacteristic
78C23—21no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—41no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—41no—
89C2×C4—42no—
90C2×C4—11921no—
91C2×C4C22⋊Dic14911yescharacteristic
92C8—41no—
93C8—5962no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22#1801182611yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—41no—
102C4—23841no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#2374941211yescharacteristic
subgroupG/H
centerC2#23749412
commutatorC2×Q8×C149C2×C4
Frattini#124C2×D149
Fitting, prime radical#454×C149C2
socleC2×C149AΣL(1,𝔽16)
cosocle#124×C149C22
hypercenter#454D149
hypocenterC149#1404
LCSG ▷ C2×Q8×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #23749420C2semidirect
2. #23749365C2semidirect
6. 2−1+4×C149C4semidirect
10. #101×C149C4semidirect
53. C149#1404semidirect
58. 2−1+4Dic149semidirect
62. #101Dic149semidirect

Maximal subgroups

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

subgroupindex
#237494202
#237493652
#454×C1492
#1404149