Finite Group Databasebeta

← #34060604

Subgroups — #34060604

Order 19072.

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

normal subgroups only

This group has 272 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×#18011971C212yesmaximal
2#23750506C214yesmaximal, complemented
3#23750098C211yesmaximal, characteristic
4C2×#14558745C2214yes—
5#18011971—22no—
6#18011971—22no—
7C22×C22⋊D149C2211yescharacteristic
8C4×C22⋊D149—22no—
9#18011871—22no—
10#18011867C2212yes—
11C2×C22⋊Dic149C411yescharacteristic
12C22⋊C4×D149C412yes—
13C2×C22⋊C4×C149C411yescharacteristic
14#14558745—24no—
15#14558745—24no—
16C2×#11924753—24no—
17C23×D149C2×C411yescharacteristic
18C2×C22⋊D149—24no—
19C2×C22⋊D149D412yes—
20C2×C22⋊D149D412yes—
21C22×Dic149—21no—
22C22×Dic149C2311yescharacteristic
23C2×C4×D149—22no—
24#14558715—22no—
25C22⋊Dic149—21no—
26C22⋊Dic149C2×C412yes—
27#14558713—22no—
28C4×Dic149—22no—
29C24×C149C2×C411yescharacteristic
30C22×C4×C149—21no—
31C22⋊C4×C149—21no—
32C22⋊C4×C149C2×C412yes—
33#11924753—44no—
34C22×D149—22no—
35C22×D149—81no—
36C22×D149C22⋊C412yes—
37C22⋊D149—24no—
38C22⋊D149—24no—
39C2×Dic149—22no—
40C2×Dic149—81no—
41C2×Dic149C2×D412yes—
42C2×Dic149#4114yes—
43C4×D149—82no—
44C23×C149—22no—
45C23×C149—81no—
46C23×C149C22⋊C411yescharacteristic
47C23×C149C22⋊C411yescharacteristic
48C23×C149C22×C411yescharacteristic
49C2×C4×C149—22no—
50C2×C4×C149—81no—
51C22×C149—21no—
52C22×C149—21no—
53C22×C149—41no—
54C22×C149—41no—
55C22×C149—41no—
56C22×C149—82no—
57C22×C149C2×C22⋊C411yescharacteristic
58C22×C149#11712yes—
59C2×D149—22no—
60C2×D149—42no—
61C2×D149—82no—
62C4×C149—42no—
63Dic149—42no—
64Dic149#12314yes—
65C2×C149—21no—
66C2×C149—22no—
67C2×C149—41no—
68C2×C149—41no—
69C2×C149#38111yescharacteristic
70D149—42no—
71C149#182911yescharacteristic, complemented, Sylow
72#1829—1491nomaximal, Sylow
73#518—1491no—
74C2×#100—1492no—
75#344—1494no—
76C22×D4—1491no—
77C2×M16—1494no—
78C4×D4—2982no—
79C4×D4—2982no—
80#117—1492no—
81C2×C22⋊C4—1491no—
82C2×C22⋊C4—1492no—
83C2×C22⋊C4#1059701011yescharacteristic
84#100—2982no—
85#100—2982no—
86C24—1491no—
87C24C2×#1059701011yescharacteristic
88C2×D4—2984no—
89C2×D4—1492no—
90C2×D4—1492no—
91C22×C4—21no—
92C22×C4—2982no—
93C22×C4—2981no—
94C22×C4—1491no—
95M16—2984no—
96M16—2984no—
97C2×C8—2984no—
98C4⋊C4—2982no—
99C22⋊C4—21no—
100C22⋊C4—2982no—
101C22⋊C4—2981no—
102C22⋊C4—1492no—
103C22⋊C4C2×#1059701012yes—
104C42—2982no—
105C23—22no—
106C23—81no—
107C23—2982no—
108C23—1492no—
109C23—11921no—
110C23C22⋊#1059701011yescharacteristic
111C23C22⋊#1059701011yescharacteristic
112C23C22×#1059701011yescharacteristic
113D4—2984no—
114D4—2984no—
115C2×C4—22no—
116C2×C4—81no—
117C2×C4—2982no—
118C2×C4—1492no—
119C2×C4—1494no—
120C2×C4—11922no—
121C2×C4—11921no—
122C8—5964no—
123C22—21no—
124C22—21no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22—82no—
129C22—2982no—
130C22—5962no—
131C22—11922no—
132C22C2×C22⋊#1059701011yescharacteristic
133C22#1801199012yes—
134C4—42no—
135C4—5962no—
136C4—1494no—
137C2—21no—
138C2—22no—
139C2—41no—
140C2—41no—
141C2—5962no—
142C2#2375056811yescharacteristic
subgroupG/H
centerC2#23750568
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC2×C149#381
prime radicalC22×C22⋊D149C22
cosocleC22×Dic149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1829
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #23750506C2semidirect
71. C149#1829semidirect

Maximal subgroups

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

subgroupindex
C2×#180119712
#237505062
#237500982
#1829149