Finite Group Databasebeta

← #34060225

Subgroups — #34060225

Order 19072.

228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750648C212yesmaximal
2#23750485C214yesmaximal, complemented
3C4⋊Q8×D149C211yesmaximal, characteristic
4#18011978C2214yes—
5#18011968—22no—
6#18011966—22no—
7C2×Q8×D149C412yes—
8#18011911C411yescharacteristic
9#18011910—22no—
10#18011909C2212yes—
11C4⋊C4×D149—22no—
12C42×D149C2211yescharacteristic
13C4⋊Q8×C149C411yescharacteristic
14C2×#11924753—24no—
15C2×Dic298—22no—
16C2×Dic298C2×C412yes—
17Q8×D149—44no—
18C2×C4×D149—22no—
19C2×C4×D149C2×C411yescharacteristic
20C2×C4×D149D412yes—
21C4⋊Dic149—22no—
22#14558715—24no—
23C4×Dic149D412yes—
24C4×Dic149C2311yescharacteristic
25C2×Q8×C149C2×C412yes—
26C4⋊C4×C149—22no—
27C42×C149C2×C411yescharacteristic
28#11924753—44no—
29C22×D149C22⋊C411yescharacteristic
30Dic298—44no—
31Dic298—42no—
32C2×Dic149—22no—
33C2×Dic149C22⋊C411yescharacteristic
34C2×Dic149C2×D412yes—
35C4×D149—22no—
36C4×D149—24no—
37C4×D149—44no—
38Q8×C149—42no—
39C2×C4×C149—22no—
40C2×C4×C149C22⋊C412yes—
41C2×C4×C149C22×C411yescharacteristic
42C22×C149C2×C22⋊C411yescharacteristic
43C2×D149—22no—
44C2×D149#10012yes—
45C4×C149—21no—
46C4×C149—22no—
47C4×C149—42no—
48Dic149—21no—
49Dic149—42no—
50Dic149#13714yes—
51C2×C149C2×#10011yescharacteristic
52C2×C149#41912yes—
53D149—22no—
54C149#155811yescharacteristic, complemented, Sylow
55#1558—1491nomaximal, Sylow
56C2×C4⋊Q8—1491no—
57#432—1492no—
58#333—1494no—
59C22×Q8—1492no—
60C4⋊Q8—2982no—
61C4⋊Q8—1492no—
62C4⋊Q8—1491no—
63C4⋊Q8#1059701011yescharacteristic
64C2×C4⋊C4—2982no—
65C2×C42—1491no—
66C4⋊C8—1494no—
67C22⋊C8—2982no—
68#97—2982no—
69C2×Q8—2982no—
70C2×Q8—5964no—
71C2×Q8—1492no—
72C2×Q8C2×#1059701012yes—
73C22×C4—2982no—
74C22×C4—1492no—
75C22×C4—1491no—
76C2×C8—2984no—
77C4⋊C4—22no—
78C4⋊C4—2984no—
79C4⋊C4—2982no—
80C42—1492no—
81C42—1491no—
82C42C2×#1059701011yescharacteristic
83C23—1491no—
84Q8—42no—
85Q8—5962no—
86Q8—5964no—
87C2×C4—22no—
88C2×C4—2982no—
89C2×C4—2984no—
90C2×C4—2982no—
91C2×C4—5964no—
92C2×C4—1491no—
93C2×C4—1492no—
94C2×C4C22⋊#1059701012yes—
95C2×C4C22×#1059701011yescharacteristic
96C8—5964no—
97C22—2982no—
98C22—1492no—
99C22C2×C22⋊#1059701011yescharacteristic
100C4—21no—
101C4—22no—
102C4—42no—
103C4—2981no—
104C4—5962no—
105C4—1494no—
106C2—2982no—
107C2D149⋊#10011yescharacteristic
108C2#2375061812yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1558
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
2. #23750485C2semidirect
54. C149#1558semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237504852
C4⋊Q8×D1492
#1558149