Finite Group Databasebeta

← #34060180

Subgroups — #34060180

Order 19072.

238 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 56 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#23750480C214yesmaximal, complemented
3#23750173C211yesmaximal, characteristic
4#18011978—22no—
5#18011968—22no—
6#18011966C2214yes—
7C2×#14558735C412yes—
8#18011911C411yescharacteristic
9#18011898C2212yes—
10#18011882—22no—
11D4×Dic149—22no—
12C42×D149C2211yescharacteristic
13#127×C149C411yescharacteristic
14C2×#11924753—24no—
15#14558735—44no—
16C2×Dic298C2×C412yes—
17C2×C22⋊D149—22no—
18C22×Dic149—22no—
19C2×C4×D149C2×C411yescharacteristic
20C2×C4×D149D412yes—
21C4⋊Dic149—22no—
22C22⋊Dic149—24no—
23C4×Dic149D412yes—
24C4×Dic149C2311yescharacteristic
25C2×D4×C149—22no—
26C2×D4×C149C2×C412yes—
27C42×C149C2×C411yescharacteristic
28#11924753—44no—
29C22×D149C22⋊C411yescharacteristic
30Dic298—42no—
31C22⋊D149—44no—
32C2×Dic149—22no—
33C2×Dic149—44no—
34C2×Dic149C22⋊C411yescharacteristic
35C2×Dic149C2×D412yes—
36C4×D149—22no—
37C4×D149—42no—
38C23×C149—22no—
39D4×C149—42no—
40D4×C149—44no—
41C2×C4×C149C22⋊C412yes—
42C2×C4×C149C22×C411yescharacteristic
43C22×C149—42no—
44C22×C149—44no—
45C22×C149C2×C22⋊C411yescharacteristic
46C2×D149—21no—
47C2×D149—22no—
48C4×C149—21no—
49C4×C149—22no—
50Dic149—22no—
51Dic149—42no—
52Dic149#10012yes—
53C2×C149—82no—
54C2×C149C2×#10011yescharacteristic
55C2×C149#42112yes—
56D149—41no—
57C149#153611yescharacteristic, complemented, Sylow
58#1536—1491nomaximal, Sylow
59#532—1491no—
60#432—1492no—
61#329—1494no—
62C2×#41—1492no—
63C4⋊Q8—1491no—
64#127#1059701011yescharacteristic
65#124—1492no—
66#121—2982no—
67C4×D4—2982no—
68C2×C42—1491no—
69C4⋊C8—2982no—
70C22⋊C8—2982no—
71#97—1494no—
72#41—5964no—
73C2×Q8—1492no—
74C2×D4—22no—
75C2×D4—2982no—
76C2×D4C2×#1059701012yes—
77C22×C4—2982no—
78C22×C4—1491no—
79C22×C4—1492no—
80C2×C8—2984no—
81C4⋊C4—2982no—
82C22⋊C4—2984no—
83C42—1492no—
84C42—1491no—
85C42C2×#1059701011yescharacteristic
86C23—22no—
87C23—1491no—
88Q8—5962no—
89D4—42no—
90D4—44no—
91D4—5964no—
92C2×C4—2982no—
93C2×C4—2982no—
94C2×C4—5962no—
95C2×C4—5964no—
96C2×C4—1492no—
97C2×C4—1491no—
98C2×C4C22⋊#1059701012yes—
99C2×C4C22×#1059701011yescharacteristic
100C8—5964no—
101C22—42no—
102C22—44no—
103C22—2981no—
104C22—2982no—
105C22C2×C22⋊#1059701011yescharacteristic
106C4—21no—
107C4—22no—
108C4—2982no—
109C4—5962no—
110C4—1492no—
111C2—82no—
112C2—5961no—
113C2D149⋊#10011yescharacteristic
114C2#2375062312yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750173C2
cosocleC4×Dic149C23
hypercenter#127#10597010
hypocenterC149#1536
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. #23750480C2semidirect
57. C149#1536semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237504802
#237501732
#1536149