Finite Group Databasebeta

← #34060219

Subgroups — #34060219

Order 19072.

332 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750648C212yesmaximal, complemented
2#23750483C214yesmaximal, complemented
3#127×D149C211yesmaximal, characteristic
4#18011978C2214yescomplemented
5#18011968—22no—
6#18011966—22no—
7C2×D4×D149—22no—
8C2×D4×D149C412yes—
9#18011908C411yescharacteristic
10#18011907—22no—
11#18011907C2212yes—
12C42×D149C2211yescharacteristic
13#127×C149C411yescharacteristic
14C2×#11924753—24no—
15C23×D149—22no—
16C2×D596—22no—
17C2×D596C2×C412yes—
18C2×C22⋊D149—22no—
19C2×C22⋊D149—24no—
20D4×D149—48no—
21D4×D149—44no—
22C2×C4×D149C2×C411yescharacteristic
23C2×C4×D149D412yes—
24C4×Dic149D412yes—
25C4×Dic149C2311yescharacteristic
26C2×D4×C149—22no—
27C2×D4×C149C2×C412yes—
28C42×C149C2×C411yescharacteristic
29#11924753—44no—
30C22×D149—22no—
31C22×D149—48no—
32C22×D149—44no—
33C22×D149C22⋊C411yescharacteristic
34D596—42no—
35D596—44no—
36C22⋊D149—44no—
37C22⋊D149—48no—
38C2×Dic149C22⋊C411yescharacteristic
39C2×Dic149C2×D412yes—
40C4×D149—22no—
41C4×D149—24no—
42C23×C149—22no—
43D4×C149—42no—
44D4×C149—44no—
45C2×C4×C149C22⋊C412yes—
46C2×C4×C149C22×C411yescharacteristic
47C22×C149—42no—
48C22×C149—44no—
49C22×C149C2×C22⋊C411yescharacteristic
50C2×D149—22no—
51C2×D149—42no—
52C2×D149—44no—
53C2×D149—88no—
54C2×D149#10012yes—
55C4×C149—21no—
56C4×C149—22no—
57Dic149—21no—
58Dic149AGL(1,ℤ/8)14yes—
59C2×C149—82no—
60C2×C149C2×#10011yescharacteristic
61C2×C149#41812yes—
62D149—22no—
63D149—82no—
64C149#155511yescharacteristic, complemented, Sylow
65#1555—1491nomaximal, Sylow
66C2×#127—1491no—
67#432—1492no—
68#331—1494no—
69C22×D4—2982no—
70C22×D4—1492no—
71#127—2982no—
72#127—1492no—
73#127—1491no—
74#127#1059701011yescharacteristic
75C2×C42—1491no—
76C4⋊C8—1494no—
77C22⋊C8—2982no—
78#97—2982no—
79C24—2982no—
80C2×D4—22no—
81C2×D4—2982no—
82C2×D4—2984no—
83C2×D4—2982no—
84C2×D4—5964no—
85C2×D4—5968no—
86C2×D4—1492no—
87C2×D4C2×#1059701012yes—
88C22×C4—1492no—
89C22×C4—1491no—
90C2×C8—2984no—
91C42—1492no—
92C42—1491no—
93C42C2×#1059701011yescharacteristic
94C23—22no—
95C23—2982no—
96C23—5968no—
97C23—5964no—
98C23—1491no—
99D4—42no—
100D4—44no—
101D4—5962no—
102D4—5964no—
103D4—5964no—
104D4—5968no—
105C2×C4—2982no—
106C2×C4—2984no—
107C2×C4—1491no—
108C2×C4—1492no—
109C2×C4C22⋊#1059701012yes—
110C2×C4C22×#1059701011yescharacteristic
111C8—5964no—
112C22—42no—
113C22—44no—
114C22—2982no—
115C22—5962no—
116C22—5964no—
117C22—1492no—
118C22—11928no—
119C22C2×C22⋊#1059701011yescharacteristic
120C4—21no—
121C4—22no—
122C4—2981no—
123C4—1494no—
124C2—82no—
125C2—2982no—
126C2—11922no—
127C2D149⋊#10011yescharacteristic
128C2#2375061712yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC22×C149C2×C22⋊C4
prime radical#127×D149C2
cosocleC4×Dic149C23
hypercenter#127#10597010
hypocenterC149#1555
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #23750648C2semidirect
2. #23750483C2semidirect
4. #18011978C22semidirect
64. C149#1555semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237504832
#127×D1492
#1555149