Finite Group Databasebeta

← #34060605

Subgroups — #34060605

Order 19072.

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

normal subgroups only

This group has 236 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
1C2×#18011972C212yesmaximal
2#23750506C214yesmaximal
3#23750102C211yesmaximal, characteristic
4C2×#14558745C2214yes—
5#18011972—22no—
6#18011972—22no—
7C22×Dic298C2211yescharacteristic
8C4×Dic298—22no—
9#18011876—22no—
10#18011870C411yescharacteristic
11#18011867C412yes—
12#18011867C2212yes—
13#117×C149C411yescharacteristic
14#14558745—24no—
15#14558745—24no—
16C2×#11924753—24no—
17C2×Dic298—24no—
18C2×Dic298D412yes—
19C2×Dic298D412yes—
20C22×Dic149C2×C411yescharacteristic
21C22×Dic149C2311yescharacteristic
22C4⋊Dic149—21no—
23#14558715—22no—
24#14558715—22no—
25C22⋊Dic149C2×C412yes—
26C4×Dic149—22no—
27C4×Dic149—22no—
28C4×Dic149—21no—
29C22×C4×C149C2×C411yescharacteristic
30C4⋊C4×C149—21no—
31C22⋊C4×C149C2×C412yes—
32C42×C149—21no—
33#11924753—44no—
34Dic298—24no—
35Dic298—24no—
36C2×Dic149—22no—
37C2×Dic149—22no—
38C2×Dic149C22⋊C412yes—
39C2×Dic149C2×D412yes—
40C2×Dic149#4114yes—
41C23×C149C22×C411yescharacteristic
42C2×C4×C149—22no—
43C2×C4×C149—22no—
44C2×C4×C149C22⋊C411yescharacteristic
45C2×C4×C149C22⋊C411yescharacteristic
46C22×C149—41no—
47C22×C149C2×C22⋊C411yescharacteristic
48C22×C149#11712yes—
49C4×C149—21no—
50C4×C149—21no—
51C4×C149—42no—
52Dic149—22no—
53Dic149—42no—
54Dic149#12314yes—
55C2×C149—21no—
56C2×C149—22no—
57C2×C149#38111yescharacteristic
58C149#183011yescharacteristic, complemented, Sylow
59#1830—1491nomaximal, Sylow
60#519—1491no—
61C2×#101—1492no—
62#344—1494no—
63C22×Q8—1491no—
64C2×M16—1494no—
65C4×Q8—2982no—
66C4×Q8—2982no—
67#117—1491no—
68#117—1492no—
69#117—1492no—
70#117#1059701011yescharacteristic
71#101—2982no—
72#101—2982no—
73C2×Q8—2984no—
74C2×Q8—1492no—
75C2×Q8—1492no—
76C22×C4—1491no—
77C22×C4—1491no—
78C22×C4C2×#1059701011yescharacteristic
79M16—2984no—
80M16—2984no—
81C2×C8—2984no—
82C4⋊C4—21no—
83C4⋊C4—2982no—
84C4⋊C4—2982no—
85C4⋊C4—2981no—
86C22⋊C4—1492no—
87C22⋊C4C2×#1059701012yes—
88C42—21no—
89C42—2982no—
90C42—2982no—
91C42—2981no—
92C23C22×#1059701011yescharacteristic
93Q8—2984no—
94Q8—2984no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—2982no—
98C2×C4—2982no—
99C2×C4—1492no—
100C2×C4—1492no—
101C2×C4—1494no—
102C2×C4C22⋊#1059701011yescharacteristic
103C2×C4C22⋊#1059701011yescharacteristic
104C8—5964no—
105C22—41no—
106C22C2×C22⋊#1059701011yescharacteristic
107C22#1801199012yes—
108C4—21no—
109C4—21no—
110C4—42no—
111C4—2982no—
112C4—5962no—
113C4—1494no—
114C2—21no—
115C2—22no—
116C2#2375056811yescharacteristic
subgroupG/H
centerC2#23750568
commutator, prime radicalC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting#117×C149C4
socleC2×C149#381
cosocleC22×Dic149C23
hypercenter#117#10597010
hypocenterC149#1830
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ #117

Complements

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

NH ≅ G/Ntype
58. C149#1830semidirect

Maximal subgroups

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

subgroupindex
C2×#180119722
#237505062
#237501022
#1830149