Finite Group Databasebeta

← #34060147

Subgroups — #34060147

Order 19072.

270 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C4×#14558746C212yesmaximal, complemented
2#23750481C214yesmaximal, complemented
3#23750176C211yesmaximal, characteristic
4C2×#14558746—22no—
5#18011966C2214yes—
6C4×#11924753—22no—
7C2×#14558737C412yes—
8#18011908C411yescharacteristic
9#18011900C2212yes—
10#18011886—22no—
11#18011873—22no—
12C42×D149C2211yescharacteristic
13C4⋊Q8×C149C411yescharacteristic
14#14558746—28no—
15C2×#11924753—24no—
16#14558737—44no—
17C2×D596—22no—
18C2×D596—22no—
19C2×D596C2×C412yes—
20C2×C4×D149—22no—
21C2×C4×D149C2×C411yescharacteristic
22C2×C4×D149D412yes—
23#14558713—24no—
24C4×Dic149D412yes—
25C4×Dic149C2311yescharacteristic
26C2×Q8×C149C2×C412yes—
27C4⋊C4×C149—22no—
28C42×C149C2×C411yescharacteristic
29#11924753—28no—
30C22×D149—22no—
31C22×D149C22⋊C411yescharacteristic
32D596—42no—
33D596—44no—
34D596—44no—
35C2×Dic149C22⋊C411yescharacteristic
36C2×Dic149C2×D412yes—
37C4×D149—24no—
38C4×D149—22no—
39C4×D149—44no—
40Q8×C149—42no—
41C2×C4×C149—22no—
42C2×C4×C149C22⋊C412yes—
43C2×C4×C149C22×C411yescharacteristic
44C22×C149C2×C22⋊C411yescharacteristic
45C2×D149—21no—
46C2×D149—22no—
47C2×D149—42no—
48C2×D149—44no—
49C4×C149—21no—
50C4×C149—42no—
51C4×C149#10414yes—
52Dic149—22no—
53Dic149#10012yes—
54C2×C149C2×#10011yescharacteristic
55C2×C149C2×#10412yes—
56D149—41no—
57D149—82no—
58C149#152511yescharacteristic, complemented, Sylow
59#1525—1491nomaximal, Sylow
60#532—1491no—
61C4×M16—1492no—
62#329—1494no—
63C2×#41—1492no—
64C2×M16—2982no—
65C4⋊Q8#1059701011yescharacteristic
66#127—1491no—
67#124—1492no—
68#121—2982no—
69C4×D4—2982no—
70C2×C42—1491no—
71#97—1494no—
72C4×C8—2982no—
73#41—5964no—
74C2×Q8C2×#1059701012yes—
75C2×D4—2982no—
76C2×D4—2982no—
77C2×D4—1492no—
78C22×C4—2982no—
79C22×C4—1492no—
80C22×C4—1491no—
81M16—2988no—
82C2×C8—2984no—
83C4⋊C4—22no—
84C22⋊C4—2984no—
85C42—1492no—
86C42—1491no—
87C42C2×#1059701011yescharacteristic
88C23—2982no—
89C23—1491no—
90Q8—42no—
91D4—5962no—
92D4—5964no—
93D4—5964no—
94C2×C4—22no—
95C2×C4—2982no—
96C2×C4—2984no—
97C2×C4—5964no—
98C2×C4—1492no—
99C2×C4—1491no—
100C2×C4C22⋊#1059701012yes—
101C2×C4C22×#1059701011yescharacteristic
102C8—2988no—
103C22—2981no—
104C22—2982no—
105C22—5962no—
106C22—5964no—
107C22C2×C22⋊#1059701011yescharacteristic
108C4—21no—
109C4—42no—
110C4—2982no—
111C4—1492no—
112C4#1801197614yes—
113C2—5961no—
114C2—11922no—
115C2D149⋊#10011yescharacteristic
116C2C2×#1801197612yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750176C2
cosocleC4×Dic149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1525
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C4×#14558746C2semidirect
2. #23750481C2semidirect
58. C149#1525semidirect

Maximal subgroups

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

subgroupindex
C4×#145587462
#237504812
#237501762
#1525149