Finite Group Databasebeta

← #34060878

Subgroups — #34060878

Order 19072.

244 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 70 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#23750629C211yesmaximal, characteristic
2#23750561C211yesmaximal, characteristic
3#23750495C214yesmaximal
4#23750181C211yesmaximal, characteristic
5C2×#14558746C2212yes—
6C2×C4×#10597010C2212yes—
7C4⋊#11924753—22no—
8(C2×#10597010)⋊C4—22no—
9#18011910C412yescomplemented
10#18011903C411yescharacteristic, complemented
11#18011889—22no—
12#18011876—22no—
13#18011869C2212yes—
14C42×D149C2211yescharacteristic
15#125×C149C411yescharacteristic, complemented
16C22×#10597010—22no—
17#14558746—24no—
18C2×#11924753—22no—
19C4×#10597010—22no—
20C4×#10597010Q814yescomplemented
21C2×Dic298—22no—
22C2×C4×D149D412yes—
23C2×C4×D149C2311yescharacteristic
24C4⋊Dic149C2×C412yes—
25#14558715—22no—
26#14558715—22no—
27#14558713—22no—
28C4×Dic149—22no—
29C4×Dic149C2×C411yescharacteristic
30C4×Dic149D412yes—
31C4⋊C4×C149—22no—
32C4⋊C4×C149C2×C412yes—
33C42×C149C2×C411yescharacteristic
34C2×#10597010—24no—
35C2×#10597010—44no—
36#11924753—42no—
37C22×D149C2×D411yescharacteristic
38Dic298—44no—
39C2×Dic149—22no—
40C2×Dic149C22⋊C412yes—
41C2×Dic149C2×D411yescharacteristic
42C4×D149—42no—
43C4×D149C2×Q812yes—
44C4×D149#4112yes—
45C2×C4×C149—22no—
46C2×C4×C149C22⋊C412yes—
47C2×C4×C149C22×C411yescharacteristic
48C22×C149C2×C22⋊C411yescharacteristic
49C2×D149—22no—
50C2×D149C22⋊Q812yes—
51#10597010—44no—
52C4×C149—22no—
53C4×C149—42no—
54C4×C149C4×Q812yes—
55Dic149—22no—
56Dic149—42no—
57Dic149#12411yescharacteristic
58Dic149C4⋊Q811yescharacteristic
59C2×C149#39111yescharacteristic
60C2×C149#42112yes—
61D149—22no—
62C149#199511yescharacteristic, complemented, Sylow
63#1995—1491nomaximal, Sylow
64#533—1491no—
65#423—1491no—
66#376—1491no—
67#339—1494no—
68C2×M16—1492no—
69C4⋊Q8—1492no—
70#125—1491no—
71#125#1059701011yescharacteristic, complemented
72C22⋊Q8—2982no—
73C4×Q8—2982no—
74#117—1492no—
75C2×C42—1492no—
76C2×C42—1491no—
77C4⋊C8—2982no—
78#95—2982no—
79C2×Q8—2982no—
80C22×C4—2982no—
81C22×C4—1492no—
82C22×C4—1491no—
83M16—2984no—
84C2×C8—2982no—
85C4⋊C4—22no—
86C4⋊C4—2982no—
87C4⋊C4—2982no—
88C4⋊C4—1492no—
89C4⋊C4C2×#1059701012yes—
90C22⋊C4—2982no—
91C42—2982no—
92C42—2982no—
93C42—1494no—
94C42—1492no—
95C42—1491no—
96C42C2×#1059701011yescharacteristic
97C23—1491no—
98Q8—5964no—
99C2×C4—22no—
100C2×C4—2984no—
101C2×C4—2982no—
102C2×C4—5962no—
103C2×C4—5964no—
104C2×C4—1492no—
105C2×C4—1491no—
106C2×C4—1492no—
107C2×C4—1492no—
108C2×C4C22⋊#1059701012yes—
109C2×C4C22×#1059701011yescharacteristic
110C8—5962no—
111C22—2982no—
112C22—1492no—
113C22C2×C22⋊#1059701011yescharacteristic
114C4—22no—
115C4—42no—
116C4—2982no—
117C4—5964no—
118C4—5962no—
119C4—1491no—
120C4—1491no—
121C4Q8×#1059701012yes—
122C2—2982no—
123C2(C2×#10597010)⋊Q811yescharacteristic
124C2#2375062212yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenter#125#10597010
hypocenterC149#1995
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. #18011910C4semidirect
10. #18011903C4semidirect
15. #125×C149C4semidirect
20. C4×#10597010Q8semidirect
62. C149#1995semidirect
71. #125#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506292
#237505612
#237504952
#237501812
#1995149