Finite Group Databasebeta

← #34060586

Subgroups — #34060586

Order 19072.

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

normal subgroups only

This group has 504 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#23750566C212yesmaximal
2#23750503C214yesmaximal, complemented
3C22×#14558713C211yesmaximal, characteristic
4C2×C22⋊#10597010—22no—
5C2×C22⋊#10597010—22no—
6C2×C22⋊#10597010C2214yes—
7C24×D149C2211yescharacteristic
8C23×Dic149C411yescharacteristic, complemented
9C2×#14558713—22no—
10C2×#14558713—22no—
11C2×#14558713C412yescomplemented
12C2×#14558713C2212yes—
13C23×C4×C149C411yescharacteristic, complemented
14C22×#10597010—24no—
15C22⋊#10597010—28no—
16C22⋊#10597010—44no—
17C22⋊#10597010—44no—
18C23×D149—24no—
19C23×D149—42no—
20C23×D149—42no—
21C23×D149C2×C411yescharacteristic
22C23×D149D412yes—
23C23×D149D412yes—
24C23×D149C2311yescharacteristic
25C22×Dic149—21no—
26C22×Dic149—21no—
27C22×Dic149—42no—
28C22×Dic149C2×C412yes—
29#14558713—24no—
30#14558713—24no—
31C24×C149C2×C411yescharacteristic
32C22×C4×C149—21no—
33C22×C4×C149—21no—
34C22×C4×C149—42no—
35C22×C4×C149C2×C412yes—
36C2×#10597010—44no—
37C2×#10597010—44no—
38C2×#10597010—44no—
39C22×D149—24no—
40C22×D149—24no—
41C22×D149—22no—
42C22×D149—24no—
43C22×D149—24no—
44C22×D149—41no—
45C22×D149—41no—
46C22×D149—42no—
47C22×D149—42no—
48C22×D149—41no—
49C22×D149—41no—
50C22×D149—416no—
51C22×D149C22⋊C412yes—
52C22×D149C2×D412yes—
53C22×D149#4114yes—
54C2×Dic149—22no—
55C2×Dic149—42no—
56C2×Dic149—42no—
57C2×Dic149—42no—
58C23×C149—22no—
59C23×C149—22no—
60C23×C149—22no—
61C23×C149C22⋊C411yescharacteristic
62C23×C149C22⋊C411yescharacteristic
63C23×C149C22×C411yescharacteristic
64C2×C4×C149—22no—
65C2×C4×C149—42no—
66C2×C4×C149—42no—
67C2×C4×C149—42no—
68C22×C149—28no—
69C22×C149—21no—
70C22×C149—21no—
71C22×C149—21no—
72C22×C149—21no—
73C22×C149—21no—
74C22×C149—21no—
75C22×C149#9912yes—
76C22×C149#9912yes—
77C22×C149C2×C22⋊C411yescharacteristic
78C22×C149#11712yes—
79C2×D149—22no—
80C2×D149—22no—
81C2×D149—22no—
82C2×D149—22no—
83C2×D149—22no—
84C2×D149—44no—
85C2×D149—48no—
86C2×D149—48no—
87C2×D149—44no—
88C2×D149#12314yes—
89#10597010—84no—
90C4×C149—42no—
91Dic149—42no—
92C2×C149—22no—
93C2×C149—22no—
94C2×C149—22no—
95C2×C149#38111yescharacteristic
96C2×C149C2×#9911yescharacteristic
97C2×C149C2×#9911yescharacteristic
98D149—24no—
99D149—42no—
100C149#181911yescharacteristic, complemented, Sylow
101#1819—1491nomaximal, Sylow
102C22×C22⋊C4—1491no—
103#379—1492no—
104#342—1494no—
105C25—1491no—
106C23×C4—1491no—
107C23×C4#1059701011yescharacteristic, complemented
108C2×C22⋊C4—2982no—
109C2×C22⋊C4—2982no—
110C2×C22⋊C4—2982no—
111C2×C22⋊C4—2982no—
112C2×C22⋊C4—1494no—
113C2×C22⋊C4—1492no—
114C2×C22⋊C4—1492no—
115C24—2984no—
116C24—5962no—
117C24—5962no—
118C24—1492no—
119C24—1492no—
120C24—1491no—
121C24—1491no—
122C24C2×#1059701011yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—42no—
126C22×C4—2981no—
127C22×C4—2981no—
128C22×C4—2984no—
129C22×C4—5962no—
130C22×C4—1492no—
131C22×C4C2×#1059701012yes—
132C22⋊C4—2984no—
133C22⋊C4—2984no—
134C22⋊C4—2988no—
135C22⋊C4—5964no—
136C22⋊C4—5964no—
137C23—22no—
138C23—22no—
139C23—22no—
140C23—2984no—
141C23—2984no—
142C23—2984no—
143C23—2984no—
144C23—2982no—
145C23—5962no—
146C23—5961no—
147C23—5961no—
148C23—5962no—
149C23—5961no—
150C23—5961no—
151C23—59616no—
152C23—1492no—
153C23—1492no—
154C23—1494no—
155C23C22⋊#1059701011yescharacteristic
156C23C22⋊#1059701011yescharacteristic
157C23C22×#1059701011yescharacteristic
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—2982no—
163C2×C4—5962no—
164C2×C4—5962no—
165C2×C4—5962no—
166C2×C4—5964no—
167C2×C4—5964no—
168C2×C4—5964no—
169C22—28no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—2982no—
177C22—2982no—
178C22—2982no—
179C22—2982no—
180C22—2982no—
181C22—5964no—
182C22—5968no—
183C22—5968no—
184C22—5964no—
185C22—1494no—
186C22#1801196912yes—
187C22#1801197012yes—
188C22C2×C22⋊#1059701011yescharacteristic
189C22#1801199012yes—
190C4—42no—
191C4—5962no—
192C4—11924no—
193C2—22no—
194C2—22no—
195C2—22no—
196C2—2984no—
197C2—5962no—
198C2#2375056811yescharacteristic
199C2C2×#1801196911yescharacteristic
200C2C2×#1801197011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC23×C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC24×D149C22
cosocleC23×D149C23
hypercenterC23×C4#10597010
hypocenterC149#1819
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #23750503C2semidirect
8. C23×Dic149C4semidirect
11. C2×#14558713C4semidirect
13. C23×C4×C149C4semidirect
100. C149#1819semidirect
107. C23×C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505662
#237505032
C22×#145587132
#1819149