Finite Group Databasebeta

← #34060972

Subgroups — #34060972

Order 19072.

270 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 54 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#23750604C212yesmaximal, complemented
2#23750530C214yesmaximal, complemented
3#23750194C211yesmaximal, characteristic
4#18011990—22no—
5#18011970C2214yescomplemented
6#18011969—22no—
7C2×#14558736C2211yescharacteristic
8C22×D596C411yescharacteristic, complemented
9#18011908C2212yes—
10#18011899C412yescomplemented
11#18011886—22no—
12#18011881—22no—
13#117×C149C411yescharacteristic, complemented
14C4⋊#10597010—42no—
15C22⋊#10597010—24no—
16C4×#10597010—42no—
17C23×D149—21no—
18#14558736—42no—
19C2×Dic298C2×C411yescharacteristic
20C2×D596—24no—
21C2×D596—21no—
22C2×D596—42no—
23C2×D596C2×C412yes—
24C2×D596C2311yescharacteristic
25C2×C22⋊D149D412yes—
26C2×C4×D149D412yes—
27#14558713—24no—
28C22×C4×C149C2×C411yescharacteristic
29C4⋊C4×C149—21no—
30C22⋊C4×C149—21no—
31C42×C149C2×C412yes—
32C2×#10597010—44no—
33C22×D149—22no—
34C22×D149—42no—
35C22×D149—82no—
36C22×D149C2×D412yes—
37Dic298—41no—
38D596—41no—
39D596—42no—
40D596—42no—
41D596—84no—
42C22⋊D149—42no—
43C2×Dic149C22⋊C412yes—
44C4×D149—22no—
45C4×D149—22no—
46C23×C149C22⋊C411yescharacteristic
47C2×C4×C149—22no—
48C2×C4×C149—22no—
49C2×C4×C149C22⋊C411yescharacteristic
50C2×C4×C149C22×C411yescharacteristic
51C22×C149—21no—
52C22×C149—41no—
53C22×C149C2×C22⋊C411yescharacteristic
54C2×D149—22no—
55C2×D149—42no—
56C2×D149—44no—
57C2×D149—42no—
58C2×D149—84no—
59#10597010—84no—
60C4×C149—21no—
61C4×C149—42no—
62C4×C149#9912yes—
63Dic149—22no—
64C2×C149—21no—
65C2×C149—41no—
66C2×C149C2×#9911yescharacteristic
67D149—42no—
68D149—82no—
69C149#212811yescharacteristic, complemented, Sylow
70#2128—1491nomaximal, Sylow
71#535—1491no—
72#410—1492no—
73#353—1494no—
74C2×#41—1491no—
75C22×D4—1491no—
76#127—1492no—
77#124—1492no—
78#121—2982no—
79#120—2982no—
80#117—2982no—
81#117#1059701011yescharacteristic, complemented
82#99—2982no—
83#99—1494no—
84C24—2981no—
85#41—5962no—
86C2×Q8—1491no—
87C2×D4—2984no—
88C2×D4—2981no—
89C2×D4—5962no—
90C2×D4—1492no—
91C2×D4—1492no—
92C2×D4—1491no—
93C22×C4—1492no—
94C22×C4C2×#1059701011yescharacteristic
95C4⋊C4—21no—
96C4⋊C4—5962no—
97C22⋊C4—21no—
98C22⋊C4—2984no—
99C22⋊C4—2984no—
100C42—5962no—
101C42C2×#1059701012yes—
102C23—2982no—
103C23—5962no—
104C23—1492no—
105C23—11922no—
106C23C22⋊#1059701011yescharacteristic
107Q8—5961no—
108D4—5961no—
109D4—5962no—
110D4—5962no—
111D4—5962no—
112D4—11924no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—2982no—
116C2×C4—2982no—
117C2×C4—5964no—
118C2×C4—1492no—
119C2×C4C22⋊#1059701011yescharacteristic
120C2×C4C22×#1059701011yescharacteristic
121C22—21no—
122C22—41no—
123C22—2982no—
124C22—5962no—
125C22—5964no—
126C22—5962no—
127C22—11924no—
128C22C2×C22⋊#1059701011yescharacteristic
129C4—21no—
130C4—42no—
131C4—2982no—
132C4—11924no—
133C4#1801197012yes—
134C2—21no—
135C2—41no—
136C2—5962no—
137C2—11922no—
138C2C2×#1801197011yescharacteristic
subgroupG/H
centerC2C2×#18011970
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#117×C149C4
socleC2×C149C2×#99
prime radical#23750194C2
cosocleC2×D596C23
hypercenter#117#10597010
hypocenterC149#2128
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #23750604C2semidirect
2. #23750530C2semidirect
5. #18011970C22semidirect
8. C22×D596C4semidirect
10. #18011899C4semidirect
13. #117×C149C4semidirect
69. C149#2128semidirect
81. #117#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506042
#237505302
#237501942
#2128149