Finite Group Databasebeta

← #34046764

Subgroups — #34046764

Order 19072.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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#23750061C212yesmaximal, complemented
2#23749743C211yesmaximal, characteristic, complemented
3#23749446C211yesmaximal, characteristic, complemented
4#23749438C212yesmaximal, complemented
5#493×C149C211yesmaximal, characteristic, complemented
6#18011933C2211yescharacteristic
7#18011917—21no—
8#18011855—22no—
9#18011852—22no—
10#18011851C2212yes—
11#18011847C2211yescharacteristic
12#18011839—21no—
13C2×D8×C149—21no—
14C2×D8×C149C2212yes—
15#127×C149—21no—
16C4×C8×C149C2211yescharacteristic
17#14558736—21no—
18Dic596D411yescharacteristic, complemented
19#14558725—21no—
20D1192D411yescharacteristic, complemented
21#14558720—21no—
22#14558719—41no—
23C8×D149—41no—
24#14558711—22no—
25C2×D4×C149—22no—
26C2×D4×C149—42no—
27D8×C149—22no—
28D8×C149—22no—
29D8×C149—41no—
30D8×C149—41no—
31C2×C8×C149D411yescharacteristic
32C2×C8×C149C2311yescharacteristic
33C42×C149D411yescharacteristic
34Dic298—21no—
35D596—21no—
36C22⋊D149—41no—
37C4×D149—41no—
38#11924746—41no—
39C23×C149—42no—
40D4×C149—42no—
41D4×C149—42no—
42D4×C149—84no—
43C2×C4×C149—21no—
44C2×C4×C149C2×D411yescharacteristic
45C8×C149D811yescharacteristic
46C8×C149D811yescharacteristic
47C8×C149C2×D411yescharacteristic
48C8×C149#4111yescharacteristic
49C22×C149—84no—
50C22×C149—82no—
51C22×C149AGL(1,ℤ/8)11yescharacteristic
52C2×D149—41no—
53C4×C149—22no—
54C4×C149#12111yescharacteristic
55C4×C149C2×D811yescharacteristic
56Dic149—41no—
57C2×C149—21no—
58C2×C149—162no—
59C2×C149#45911yescharacteristic
60D149—81no—
61C149#221311yescharacteristic, complemented, Sylow
62#2213—1491nomaximal, Sylow
63#509—1492no—
64#493D14911yescharacteristic, complemented
65#443—1491no—
66#364—1491no—
67#361—1492no—
68#135—1491no—
69C2×D8—21no—
70C2×D8C2×D14912yes—
71#131—2981no—
72#127—21no—
73SD32—2982no—
74D16—2982no—
75M32—1492no—
76#108—1491no—
77#104—2981no—
78C4×C8C2×D14911yescharacteristic
79#41—2981no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—1491no—
83SD16—2981no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—1491no—
89M16—2981no—
90M16—5961no—
91C2×C8—5961no—
92C2×C8C22⋊D14911yescharacteristic
93C2×C8C22×D14911yescharacteristic
94C42C22⋊D14911yescharacteristic
95C16—2982no—
96C23—42no—
97Q8—2981no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—2981no—
102D4—5961no—
103C2×C4—21no—
104C2×C4—5961no—
105C2×C4C2×C22⋊D14911yescharacteristic
106C8—5961no—
107C8#1455872111yescharacteristic
108C8#1455872111yescharacteristic
109C8D4×D14911yescharacteristic
110C8#1455873511yescharacteristic
111C22—84no—
112C22—82no—
113C22—5961no—
114C22#1801193711yescharacteristic
115C4—22no—
116C4—5961no—
117C4#1801188211yescharacteristic
118C4C2×#1455872111yescharacteristic
119C2—21no—
120C2—162no—
121C2—11921no—
122C2#2374981711yescharacteristic
subgroupG/H
centerC2#23749817
commutator, cosocleC2×C8×C149C23
FrattiniC2×C8C22×D149
Fitting#493×C149C2
socleC2×C149#459
hypercenter#493D149
hypocenterC149#2213
LCSG ▷ C2×C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #23750061C2semidirect
2. #23749743C2semidirect
3. #23749446C2semidirect
4. #23749438C2semidirect
5. #493×C149C2semidirect
18. Dic596D4semidirect
20. D1192D4semidirect
61. C149#2213semidirect
64. #493D149semidirect

Maximal subgroups

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

subgroupindex
#237500612
#237497432
#237494462
#237494382
#493×C1492
#2213149