Finite Group Databasebeta

← #34059936

Subgroups — #34059936

Order 19072.

440 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 74 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#23750595C212yesmaximal, complemented
2#23750468C214yesmaximal, complemented
3C22×C22⋊Dic149C211yesmaximal, characteristic
4C2×#14558745—22no—
5C22⋊#11924753—22no—
6C22⋊#11924753C2214yescomplemented
7C23×Dic149C411yescharacteristic
8C23×Dic149C2211yescharacteristic
9C2×C22⋊Dic149—22no—
10C2×C22⋊Dic149—22no—
11C2×C22⋊Dic149C412yes—
12C2×C22⋊Dic149C2212yes—
13C25×C149C411yescharacteristic
14#14558745—44no—
15C2×#11924753—24no—
16C22×Dic149—21no—
17C22×Dic149—21no—
18C22×Dic149—42no—
19C22×Dic149—42no—
20C22×Dic149C2×C412yes—
21C22×Dic149C2×C411yescharacteristic
22C22×Dic149D412yes—
23C22×Dic149D412yes—
24C22×Dic149C2311yescharacteristic
25C22⋊Dic149—24no—
26C22⋊Dic149—24no—
27C24×C149—21no—
28C24×C149—21no—
29C24×C149—24no—
30C24×C149—42no—
31C24×C149—42no—
32C24×C149C2×C411yescharacteristic
33C24×C149C2×C412yes—
34#11924753—44no—
35C2×Dic149—24no—
36C2×Dic149—22no—
37C2×Dic149—41no—
38C2×Dic149—42no—
39C2×Dic149—41no—
40C2×Dic149—42no—
41C2×Dic149—42no—
42C2×Dic149—42no—
43C2×Dic149C22⋊C412yes—
44C2×Dic149C2×D412yes—
45C23×C149—22no—
46C23×C149—22no—
47C23×C149—22no—
48C23×C149—24no—
49C23×C149—24no—
50C23×C149—22no—
51C23×C149—22no—
52C23×C149—42no—
53C23×C149—42no—
54C23×C149—416no—
55C23×C149—42no—
56C23×C149—42no—
57C23×C149—42no—
58C23×C149—42no—
59C23×C149C22⋊C411yescharacteristic
60C23×C149C22⋊C411yescharacteristic
61C23×C149M1614yescomplemented
62C23×C149C22×C411yescharacteristic
63C22×C149—28no—
64C22×C149—21no—
65C22×C149—21no—
66C22×C149—21no—
67C22×C149—21no—
68C22×C149—21no—
69C22×C149—21no—
70C22×C149—24no—
71C22×C149—44no—
72C22×C149—48no—
73C22×C149—48no—
74C22×C149—44no—
75C22×C149—42no—
76C22×C149—42no—
77C22×C149#9912yes—
78C22×C149#10012yes—
79C22×C149C2×C22⋊C411yescharacteristic
80C22×C149C2×M1612yes—
81Dic149—22no—
82Dic149—22no—
83Dic149—42no—
84C2×C149—22no—
85C2×C149—22no—
86C2×C149—22no—
87C2×C149—44no—
88C2×C149#40711yescharacteristic
89C2×C149C2×#9911yescharacteristic
90C2×C149C2×#10011yescharacteristic
91C149#146211yescharacteristic, complemented, Sylow
92#1462—1491nomaximal, Sylow
93C22×C22⋊C4—1491no—
94#407—1492no—
95#323—1494no—
96C25#1059701011yescharacteristic
97C23×C4—1491no—
98C23×C4—1491no—
99C2×M16—2982no—
100C2×C22⋊C4—2982no—
101C2×C22⋊C4—2982no—
102C2×C22⋊C4—1492no—
103C2×C22⋊C4—1492no—
104C22⋊C8—2982no—
105C22⋊C8—1494no—
106C24—21no—
107C24—21no—
108C24—24no—
109C24—42no—
110C24—42no—
111C24C2×#1059701012yes—
112C24C2×#1059701011yescharacteristic
113C22×C4—2981no—
114C22×C4—2981no—
115C22×C4—5962no—
116C22×C4—5962no—
117C22×C4—1492no—
118C22×C4—1492no—
119C22×C4—1492no—
120C22×C4—1491no—
121C22×C4—1491no—
122M16—5964no—
123C2×C8—2984no—
124C22⋊C4—2984no—
125C22⋊C4—2984no—
126C23—22no—
127C23—22no—
128C23—22no—
129C23—24no—
130C23—24no—
131C23—22no—
132C23—22no—
133C23—42no—
134C23—42no—
135C23—416no—
136C23—42no—
137C23—42no—
138C23—42no—
139C23—42no—
140C23C22⋊#1059701011yescharacteristic
141C23C22⋊#1059701011yescharacteristic
142C23#1455874514yescomplemented
143C23C22×#1059701011yescharacteristic
144C2×C4—2984no—
145C2×C4—2982no—
146C2×C4—5961no—
147C2×C4—5962no—
148C2×C4—5961no—
149C2×C4—5962no—
150C2×C4—5962no—
151C2×C4—5962no—
152C2×C4—1492no—
153C2×C4—1492no—
154C8—5964no—
155C22—28no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—24no—
163C22—44no—
164C22—48no—
165C22—48no—
166C22—44no—
167C22—42no—
168C22—42no—
169C22#1801196912yes—
170C22#1801197112yes—
171C22C2×C22⋊#1059701011yescharacteristic
172C22C2×#1455874512yes—
173C4—2982no—
174C4—2982no—
175C4—5962no—
176C2—22no—
177C2—22no—
178C2—22no—
179C2—44no—
180C2#2375059511yescharacteristic
181C2C2×#1801196911yescharacteristic
182C2C2×#1801197111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting, prime radicalC25×C149C4
socleC22×C149C2×C22⋊C4
cosocleC22×Dic149C23
hypercenterC25#10597010
hypocenterC149#1462
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
1. #23750595C2semidirect
2. #23750468C2semidirect
6. C22⋊#11924753C22semidirect
61. C23×C149M16semidirect
91. C149#1462semidirect
142. C23#14558745semidirect

Maximal subgroups

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

subgroupindex
#237505952
#237504682
C22×C22⋊Dic1492
#1462149