Finite Group Databasebeta

← #34044019

Subgroups — #34044019

Order 19072.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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#23750035C212yesmaximal
2#23749995C211yesmaximal, characteristic
3#23749367C211yesmaximal, characteristic
4#23749367C212yesmaximal
5#564×C149C211yesmaximal, characteristic
6#18011911C2211yescharacteristic
7#18011844—22no—
8#18011842—22no—
9#18011834—22no—
10#18011822C2211yescharacteristic
11#18011822C2212yes—
12#125×C149—22no—
13#125×C149—22no—
14#125×C149—22no—
15#125×C149C2211yescharacteristic
16#125×C149C2212yes—
17C2×Dic298—21no—
18C2×#11924746—22no—
19C2×#11924746—21no—
20C4⋊Dic149—22no—
21C4⋊C4×C149—22no—
22C4⋊C4×C149—22no—
23C4⋊C4×C149—22no—
24C4⋊C4×C149—22no—
25C4⋊C4×C149—22no—
26C4⋊C4×C149—22no—
27C4⋊C4×C149D412yes—
28C4⋊C4×C149D412yes—
29C4⋊C4×C149D412yes—
30C42×C149—22no—
31C42×C149C2311yescharacteristic
32Dic298—42no—
33C2×Dic149—41no—
34#11924746—24no—
35#11924746—41no—
36C2×C4×C149—22no—
37C2×C4×C149—22no—
38C2×C4×C149—22no—
39C2×C4×C149C2×D411yescharacteristic
40C2×C4×C149C2×D412yes—
41C22×C149#12011yescharacteristic
42C4×C149—21no—
43C4×C149—22no—
44C4×C149—42no—
45C4×C149—42no—
46C4×C149—42no—
47Dic149—81no—
48C2×C149#45411yescharacteristic
49C2×C149#45612yes—
50C149#166311yescharacteristic, complemented, Sylow
51#1663—1491nomaximal, Sylow
52#564D14911yescharacteristic
53#501—1492no—
54#491—1491no—
55#330—1492no—
56#330—1491no—
57C4⋊Q8—1491no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D14911yescharacteristic
62#125C2×D14912yes—
63#107—2982no—
64#106—2982no—
65#103—2982no—
66#97—1491no—
67#97—1492no—
68C2×Q8—2981no—
69C2×C8—2982no—
70C2×C8—2981no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—2982no—
78C4⋊C4C22⋊D14912yes—
79C4⋊C4C22⋊D14912yes—
80C4⋊C4C22⋊D14912yes—
81C42—22no—
82C42C22×D14911yescharacteristic
83Q8—5962no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—5961no—
88C2×C4C2×C22⋊D14912yes—
89C2×C4C2×C22⋊D14911yescharacteristic
90C8—2984no—
91C8—5961no—
92C22#1801188011yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—11921no—
99C2#2374979811yescharacteristic
100C2#2374980812yes—
subgroupG/H
centerC22#18011880
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#564×C149C2
socle, prime radicalC22×C149#120
hypercenter#564D149
hypocenterC149#1663
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
50. C149#1663semidirect

Maximal subgroups

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

subgroupindex
#237500352
#237499952
#237493672
#564×C1492
#1663149