Finite Group Databasebeta

← #34060172

Subgroups — #34060172

Order 19072.

248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750645C212yesmaximal, complemented
2#23750481C214yesmaximal, complemented
3C2×#18011900C211yesmaximal, characteristic
4#18011978—22no—
5C22⋊#11924753—22no—
6#18011966C2214yescomplemented
7C22×D596C411yescharacteristic
8#18011900—22no—
9#18011900C412yes—
10#18011900C2212yes—
11C2×#14558713—22no—
12C2×C4×Dic149C2211yescharacteristic
13C22×Q8×C149C411yescharacteristic
14C2×#11924753—24no—
15C23×D149—21no—
16C2×D596—21no—
17C2×D596—42no—
18C2×D596C2×C412yes—
19C22×Dic149D412yes—
20#14558713—24no—
21#14558713—24no—
22C4×Dic149C2×C411yescharacteristic
23C4×Dic149D412yes—
24C4×Dic149C2311yescharacteristic
25C2×Q8×C149—21no—
26C2×Q8×C149—42no—
27C2×Q8×C149C2×C412yes—
28C22×C4×C149—21no—
29C22×C4×C149C2×C411yescharacteristic
30#11924753—44no—
31C22×D149—22no—
32C22×D149—44no—
33C22×D149—42no—
34D596—42no—
35D596—42no—
36C2×Dic149—42no—
37C2×Dic149C22⋊C412yes—
38C2×Dic149C2×D412yes—
39C23×C149C22⋊C411yescharacteristic
40Q8×C149—42no—
41Q8×C149—42no—
42C2×C4×C149—22no—
43C2×C4×C149—22no—
44C2×C4×C149—42no—
45C2×C4×C149C22⋊C411yescharacteristic
46C2×C4×C149C22×C411yescharacteristic
47C22×C149—22no—
48C22×C149#10012yes—
49C22×C149C2×C22⋊C411yescharacteristic
50C2×D149—42no—
51C2×D149—44no—
52C2×D149—84no—
53C4×C149—21no—
54C4×C149—21no—
55C4×C149—42no—
56Dic149—22no—
57Dic149—22no—
58C2×C149—22no—
59C2×C149C2×#10011yescharacteristic
60C2×C149#42112yes—
61D149—82no—
62C149#153311yescharacteristic, complemented, Sylow
63#1533—1491nomaximal, Sylow
64C2×#124—1491no—
65#432—1492no—
66#329—1494no—
67C22×Q8#1059701011yescharacteristic
68C22×D4—1491no—
69#124—2982no—
70#124—1492no—
71#124—1492no—
72C2×C22⋊C4—2982no—
73C2×C42—1491no—
74C4⋊C8—2982no—
75C22⋊C8—2982no—
76#97—1494no—
77C24—2981no—
78C2×Q8—21no—
79C2×Q8—42no—
80C2×Q8C2×#1059701012yes—
81C2×D4—2981no—
82C2×D4—5962no—
83C2×D4—1492no—
84C22×C4—21no—
85C22×C4—1492no—
86C22×C4C2×#1059701011yescharacteristic
87C2×C8—2984no—
88C22⋊C4—2984no—
89C22⋊C4—2984no—
90C42—1492no—
91C42—1491no—
92C42—1491no—
93C23—2982no—
94C23—5964no—
95C23—5962no—
96C23C22⋊#1059701011yescharacteristic
97Q8—42no—
98Q8—42no—
99D4—5962no—
100D4—5962no—
101C2×C4—22no—
102C2×C4—22no—
103C2×C4—42no—
104C2×C4—5962no—
105C2×C4—1492no—
106C2×C4—1492no—
107C2×C4C22⋊#1059701011yescharacteristic
108C2×C4C22×#1059701011yescharacteristic
109C8—5964no—
110C22—22no—
111C22—5962no—
112C22—5964no—
113C22—11924no—
114C22#1801197112yes—
115C22C2×C22⋊#1059701011yescharacteristic
116C4—21no—
117C4—21no—
118C4—42no—
119C4—2982no—
120C4—2982no—
121C2—22no—
122C2—11922no—
123C2C2×#1801197111yescharacteristic
124C2#2375062412yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D596C4
cosocleC4×Dic149C23
hypercenterC22×Q8#10597010
hypocenterC149#1533
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #23750645C2semidirect
2. #23750481C2semidirect
6. #18011966C22semidirect
62. C149#1533semidirect

Maximal subgroups

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

subgroupindex
#237506452
#237504812
C2×#180119002
#1533149