Finite Group Databasebeta

← #34060231

Subgroups — #34060231

Order 19072.

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

normal subgroups only

This group has 210 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#23750630C212yesmaximal
2#23750484C214yesmaximal, complemented
3#23750181C211yesmaximal, characteristic
4C2×#14558746—22no—
5#18011978—22no—
6#18011978C2214yes—
7#18011910C2212yes—
8#18011903C411yescharacteristic
9#18011889—22no—
10#18011876—22no—
11#18011869C412yes—
12C42×D149C2211yescharacteristic
13#125×C149C411yescharacteristic
14#14558746—44no—
15C2×#11924753—24no—
16C2×Dic298—22no—
17C2×C4×D149C2×C411yescharacteristic
18C2×C4×D149D412yes—
19C4⋊Dic149C2×C412yes—
20#14558715—22no—
21#14558715—22no—
22#14558713—22no—
23C4×Dic149—22no—
24C4×Dic149D412yes—
25C4×Dic149C2311yescharacteristic
26C4⋊C4×C149—22no—
27C4⋊C4×C149C2×C412yes—
28C42×C149C2×C411yescharacteristic
29#11924753—44no—
30C22×D149C22⋊C411yescharacteristic
31Dic298—42no—
32Dic298—42no—
33C2×Dic149—22no—
34C2×Dic149C22⋊C411yescharacteristic
35C2×Dic149C2×D412yes—
36C4×D149—22no—
37C4×D149—22no—
38C4×D149—22no—
39C2×C4×C149—22no—
40C2×C4×C149C22⋊C412yes—
41C2×C4×C149C22×C411yescharacteristic
42C22×C149C2×C22⋊C411yescharacteristic
43C2×D149—21no—
44C2×D149—22no—
45C4×C149—21no—
46C4×C149—22no—
47C4×C149—42no—
48Dic149—42no—
49Dic149#10112yes—
50Dic149AGL(1,ℤ/8)12yes—
51Dic149#13712yes—
52C2×C149C2×#10111yescharacteristic
53C2×C149#41712yes—
54D149—41no—
55C149#156111yescharacteristic, complemented, Sylow
56#1561—1491nomaximal, Sylow
57#533—1491no—
58#423—1492no—
59#332—1494no—
60C2×M16—2982no—
61C4⋊Q8—1492no—
62#125—1491no—
63#125#1059701011yescharacteristic
64C22⋊Q8—2982no—
65C4×Q8—2982no—
66#117—1492no—
67C2×C42—1491no—
68C4⋊C8—2982no—
69C4⋊C8—1494no—
70C2×Q8—2982no—
71C22×C4—1492no—
72C22×C4—1491no—
73M16—5964no—
74C2×C8—2984no—
75C4⋊C4—22no—
76C4⋊C4—2982no—
77C4⋊C4—2982no—
78C4⋊C4—1492no—
79C4⋊C4C2×#1059701012yes—
80C22⋊C4—2982no—
81C42—2982no—
82C42—1492no—
83C42—1491no—
84C42C2×#1059701011yescharacteristic
85C23—1491no—
86Q8—5962no—
87Q8—5962no—
88C2×C4—22no—
89C2×C4—2982no—
90C2×C4—2982no—
91C2×C4—2982no—
92C2×C4—2982no—
93C2×C4—1491no—
94C2×C4—1492no—
95C2×C4C22⋊#1059701012yes—
96C2×C4C22×#1059701011yescharacteristic
97C8—5964no—
98C22—2981no—
99C22—2982no—
100C22C2×C22⋊#1059701011yescharacteristic
101C4—21no—
102C4—22no—
103C4—42no—
104C4—5962no—
105C4—1492no—
106C4—1492no—
107C4—1492no—
108C2—5961no—
109C2D149⋊#10111yescharacteristic
110C2#2375061612yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenter#125#10597010
hypocenterC149#1561
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #23750484C2semidirect
55. C149#1561semidirect

Maximal subgroups

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

subgroupindex
#237506302
#237504842
#237501812
#1561149