Finite Group Databasebeta

← #34052759

Subgroups — #34052759

Order 19072.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#18011903C212yesmaximal
2#23749565C214yesmaximal
3#23749557C214yesmaximal
4#23749555C214yesmaximal
5#382×C149C211yesmaximal, characteristic
6#18011903—28no—
7C2×C4⋊Dic149C2212yes—
8C2×C4⋊Dic149C2212yes—
9C2×C4⋊Dic149C2214yes—
10C2×#14558715C2214yes—
11C2×#14558715C2214yes—
12#18011818C2218yes—
13#18011818C2214yes—
14C2×C4⋊C4×C149C2212yes—
15C2×C42×C149C2211yescharacteristic
16#95×C149C2214yes—
17C22×Dic149C2314yes—
18C22×Dic149C2314yes—
19C4⋊Dic149—24no—
20C4⋊Dic149—24no—
21C4⋊Dic149—44no—
22#14558715—28no—
23#14558715—28no—
24C22×C4×C149C2314yes—
25C22×C4×C149C2312yes—
26C22×C4×C149C2311yescharacteristic
27C4⋊C4×C149—42no—
28C42×C149D414yes—
29C2×Dic149—24no—
30C2×Dic149—24no—
31C2×Dic149—24no—
32C2×Dic149—28no—
33C2×Dic149—24no—
34C23×C149C2411yescharacteristic
35C2×C4×C149—21no—
36C2×C4×C149—24no—
37C2×C4×C149—21no—
38C2×C4×C149—24no—
39C2×C4×C149—28no—
40C2×C4×C149C2×D412yes—
41C2×C4×C149C2×D414yes—
42C22×C149C22×D411yescharacteristic
43C22×C149H(5,𝔽2)11yescharacteristic
44C22×C1492−1+414yes—
45C22×C1492−1+411yescharacteristic
46C4×C149—24no—
47C4×C149—22no—
48C4×C149—44no—
49Dic149—44no—
50Dic149—44no—
51C2×C149#53612yes—
52C2×C149#53711yescharacteristic
53C2×C149#56312yes—
54C2×C149#56412yes—
55C149#282211yescharacteristic, complemented, Sylow
56#2822—1491nomaximal, Sylow
57C2×#125—1492no—
58#400—1494no—
59#398—1494no—
60#398—1494no—
61#382D14911yescharacteristic
62#125—2988no—
63C2×C4⋊C4—1494no—
64C2×C4⋊C4—1492no—
65C2×C4⋊C4—1494no—
66C2×C4⋊C4—1492no—
67C2×C4⋊C4—1494no—
68C2×C4⋊C4C2×D14912yes—
69C2×C42C2×D14911yescharacteristic
70#95—1498no—
71#95—1494no—
72#95C2×D14914yes—
73C22×C4—1494no—
74C22×C4—1494no—
75C22×C4C22×D14914yes—
76C22×C4C22×D14912yes—
77C22×C4C22×D14911yescharacteristic
78C4⋊C4—42no—
79C4⋊C4—2988no—
80C4⋊C4—2988no—
81C4⋊C4—2984no—
82C4⋊C4—2984no—
83C4⋊C4—5964no—
84C42D59614yes—
85C23C23×D14911yescharacteristic
86C2×C4—21no—
87C2×C4—24no—
88C2×C4—21no—
89C2×C4—24no—
90C2×C4—28no—
91C2×C4—2984no—
92C2×C4—2984no—
93C2×C4—2984no—
94C2×C4—2988no—
95C2×C4—2984no—
96C2×C4C2×D59614yes—
97C2×C4C2×D59612yes—
98C22C22×D59611yescharacteristic
99C22#1801195611yescharacteristic
100C22#1801195814yes—
101C22#1801195911yescharacteristic
102C4—24no—
103C4—22no—
104C4—44no—
105C4—5964no—
106C4—5964no—
107C2#2375020112yes—
108C2#2375020611yescharacteristic
109C2#2375037512yes—
110C2C149⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, prime radical, cosocleC23×C149C24
Fitting#382×C149C2
hypercenter#382D149
hypocenterC149#2822
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
55. C149#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#180119032
#237495652
#237495572
#237495552
#382×C1492
#2822149