Finite Group Databasebeta

← #34060224

Subgroups — #34060224

Order 19072.

228 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 62 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
2#23750485C214yesmaximal, complemented
3C2×#18011909C211yesmaximal, characteristic
4#18011978C2214yes—
5C22⋊#11924753—22no—
6#18011966—22no—
7C22×Dic298C411yescharacteristic
8#18011909—22no—
9#18011909C412yes—
10#18011909C2212yes—
11C2×#14558715—22no—
12C2×C4×Dic149C2211yescharacteristic
13C22×Q8×C149C411yescharacteristic
14C2×#11924753—24no—
15C2×Dic298—21no—
16C2×Dic298—42no—
17C2×Dic298C2×C412yes—
18C22×Dic149—21no—
19C22×Dic149D412yes—
20#14558715—24no—
21#14558715—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—
31Dic298—42no—
32Dic298—42no—
33C2×Dic149—24no—
34C2×Dic149—22no—
35C2×Dic149—42no—
36C2×Dic149C22⋊C412yes—
37C2×Dic149C2×D412yes—
38C23×C149C22⋊C411yescharacteristic
39Q8×C149—42no—
40Q8×C149—42no—
41C2×C4×C149—22no—
42C2×C4×C149—22no—
43C2×C4×C149—42no—
44C2×C4×C149C22⋊C411yescharacteristic
45C2×C4×C149C22×C411yescharacteristic
46C22×C149—22no—
47C22×C149#10012yes—
48C22×C149C2×C22⋊C411yescharacteristic
49C4×C149—21no—
50C4×C149—21no—
51C4×C149—42no—
52Dic149—22no—
53Dic149—42no—
54Dic149#13714yes—
55C2×C149—22no—
56C2×C149C2×#10011yescharacteristic
57C2×C149#41912yes—
58C149#155811yescharacteristic, complemented, Sylow
59#1558—1491nomaximal, Sylow
60C2×C4⋊Q8—1491no—
61#432—1492no—
62#333—1494no—
63C22×Q8—1491no—
64C22×Q8#1059701011yescharacteristic
65C4⋊Q8—2982no—
66C4⋊Q8—1492no—
67C4⋊Q8—1492no—
68C2×C4⋊C4—2982no—
69C2×C42—1491no—
70C4⋊C8—1494no—
71C22⋊C8—2982no—
72#97—2982no—
73C2×Q8—21no—
74C2×Q8—42no—
75C2×Q8—2981no—
76C2×Q8—5962no—
77C2×Q8—1492no—
78C2×Q8C2×#1059701012yes—
79C22×C4—21no—
80C22×C4—2981no—
81C22×C4—1492no—
82C22×C4C2×#1059701011yescharacteristic
83C2×C8—2984no—
84C4⋊C4—2984no—
85C4⋊C4—2984no—
86C42—1492no—
87C42—1491no—
88C42—1491no—
89C23C22⋊#1059701011yescharacteristic
90Q8—42no—
91Q8—42no—
92Q8—5962no—
93Q8—5962no—
94C2×C4—22no—
95C2×C4—22no—
96C2×C4—42no—
97C2×C4—2984no—
98C2×C4—2982no—
99C2×C4—5962no—
100C2×C4—1492no—
101C2×C4—1492no—
102C2×C4C22⋊#1059701011yescharacteristic
103C2×C4C22×#1059701011yescharacteristic
104C8—5964no—
105C22—22no—
106C22#1801197112yes—
107C22C2×C22⋊#1059701011yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—2982no—
112C4—5962no—
113C4—1494no—
114C2—22no—
115C2C2×#1801197111yescharacteristic
116C2#2375061812yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC22×Q8#10597010
hypocenterC149#1558
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
2. #23750485C2semidirect
58. C149#1558semidirect

Maximal subgroups

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

subgroupindex
#237506452
#237504852
C2×#180119092
#1558149