Finite Group Databasebeta

← #34060528

Subgroups — #34060528

Order 19072.

584 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 86 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, complemented
2C2×#18011971C212yesmaximal, complemented
3#23750595C212yesmaximal, complemented
4C22×#14558735C211yesmaximal, characteristic
5C2×#14558745C2214yes—
6#18011972—24no—
7#18011971—24no—
8C22⋊#11924753—24no—
9C2×#14558735—24no—
10C2×#14558735—24no—
11C2×#14558735—24no—
12C22×Dic298C2211yescharacteristic
13C22×C22⋊D149C411yescharacteristic
14C22×C22⋊D149C2211yescharacteristic
15C23×Dic149C411yescharacteristic
16C23×Dic149C2211yescharacteristic
17C22×C4×D149C411yescharacteristic
18C22×D4×C149C411yescharacteristic
19#14558745—24no—
20#14558745—24no—
21C2×#11924753—24no—
22C23×D149C2×C411yescharacteristic
23#14558735—232no—
24C2×Dic298—22no—
25C2×Dic298—22no—
26C2×Dic298D414yes—
27C2×C22⋊D149—22no—
28C2×C22⋊D149—22no—
29C2×C22⋊D149—22no—
30C2×C22⋊D149—22no—
31C2×C22⋊D149—22no—
32C2×C22⋊D149D414yes—
33C22×Dic149—22no—
34C22×Dic149—22no—
35C22×Dic149—22no—
36C22×Dic149—22no—
37C22×Dic149—22no—
38C22×Dic149C2×C411yescharacteristic
39C22×Dic149C2×C411yescharacteristic
40C22×Dic149D414yes—
41C22×Dic149C2311yescharacteristic
42C2×C4×D149—22no—
43C2×C4×D149—22no—
44C2×C4×D149—22no—
45C24×C149C2×C411yescharacteristic
46C24×C149C2×C411yescharacteristic
47C2×D4×C149—22no—
48C2×D4×C149—22no—
49C2×D4×C149—22no—
50C22×C4×C149C2×C411yescharacteristic
51#11924753—44no—
52C22×D149—21no—
53C22×D149—21no—
54C22×D149—42no—
55C22×D149C22⋊C412yes—
56Dic298—28no—
57C22⋊D149—28no—
58C22⋊D149—28no—
59C2×Dic149—28no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149—28no—
65C2×Dic149C22⋊C412yes—
66C2×Dic149C22⋊C412yes—
67C2×Dic149C2×D412yes—
68C2×Dic149C2×D412yes—
69C2×Dic149C2×D412yes—
70C4×D149—28no—
71C23×C149—21no—
72C23×C149—21no—
73C23×C149—21no—
74C23×C149—21no—
75C23×C149—42no—
76C23×C149—42no—
77C23×C149C22⋊C412yes—
78C23×C149C22⋊C412yes—
79C23×C149C22×C411yescharacteristic
80D4×C149—28no—
81C2×C4×C149—21no—
82C2×C4×C149—21no—
83C2×C4×C149C22⋊C412yes—
84C22×C149—22no—
85C22×C149—22no—
86C22×C149—22no—
87C22×C149—24no—
88C22×C149—42no—
89C22×C149—42no—
90C22×C149—42no—
91C22×C149—42no—
92C22×C149—42no—
93C22×C149C2×C22⋊C411yescharacteristic
94C22×C149C2×C22⋊C411yescharacteristic
95C22×C149C2×C22⋊C411yescharacteristic
96C2×D149—22no—
97C2×D149—42no—
98C2×D149—42no—
99C2×D149—42no—
100C4×C149—22no—
101Dic149—22no—
102Dic149—22no—
103Dic149#12014yes—
104C2×C149—21no—
105C2×C149—21no—
106C2×C149—42no—
107C2×C149—42no—
108C2×C149#37911yescharacteristic
109C2×C149#41312yes—
110D149—42no—
111C149#178511yescharacteristic, complemented, Sylow
112#1785—1491nomaximal, Sylow
113C22×#41—1491no—
114C2×#101—1492no—
115C2×#100—1492no—
116#407—1492no—
117C2×#41—2984no—
118C2×#41—2984no—
119C2×#41—2984no—
120C22×Q8—1491no—
121C22×D4—1491no—
122C22×D4—1491no—
123C22×D4#1059701011yescharacteristic
124C23×C4—1491no—
125C23×C4—1491no—
126C23×C4—1491no—
127C2×M16—1494no—
128#101—2984no—
129#100—2984no—
130C22⋊C8—2984no—
131C24—1491no—
132C24C2×#1059701011yescharacteristic
133C24C2×#1059701011yescharacteristic
134#41—29832no—
135C2×Q8—2982no—
136C2×Q8—2982no—
137C2×Q8—1494no—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—2982no—
142C2×D4—2982no—
143C2×D4—2982no—
144C2×D4—2982no—
145C2×D4—2982no—
146C2×D4—1494no—
147C22×C4—2982no—
148C22×C4—2982no—
149C22×C4—2982no—
150C22×C4—2982no—
151C22×C4—2982no—
152C22×C4—2982no—
153C22×C4—2982no—
154C22×C4—2982no—
155C22×C4—1494no—
156C22×C4—1491no—
157C22×C4—1491no—
158C22×C4—1491no—
159C22×C4C2×#1059701011yescharacteristic
160M16—2984no—
161M16—2984no—
162C2×C8—2984no—
163C23—21no—
164C23—21no—
165C23—21no—
166C23—21no—
167C23—42no—
168C23—42no—
169C23—2981no—
170C23—2981no—
171C23—5962no—
172C23—1492no—
173C23C22⋊#1059701012yes—
174C23C22⋊#1059701012yes—
175C23C22×#1059701011yescharacteristic
176Q8—2988no—
177D4—28no—
178D4—2988no—
179D4—2988no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—2988no—
183C2×C4—2988no—
184C2×C4—2981no—
185C2×C4—2981no—
186C2×C4—2981no—
187C2×C4—2981no—
188C2×C4—2988no—
189C2×C4—1492no—
190C2×C4—1492no—
191C2×C4—1492no—
192C2×C4—1492no—
193C2×C4—1492no—
194C2×C4C22⋊#1059701012yes—
195C8—5964no—
196C22—22no—
197C22—22no—
198C22—22no—
199C22—24no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—2982no—
206C22—5962no—
207C22—5962no—
208C22—5962no—
209C22C2×C22⋊#1059701011yescharacteristic
210C22C2×C22⋊#1059701011yescharacteristic
211C22C2×C22⋊#1059701011yescharacteristic
212C4—22no—
213C4—2982no—
214C4—2982no—
215C4—1494no—
216C2—21no—
217C2—21no—
218C2—42no—
219C2—42no—
220C2—5962no—
221C2#2375056611yescharacteristic
222C2#2375061212yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC22×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×#14558735C2
cosocleC22×Dic149C23
hypercenterC22×D4#10597010
hypocenterC149#1785
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#18011972C2semidirect
2. C2×#18011971C2semidirect
3. #23750595C2semidirect
111. C149#1785semidirect

Maximal subgroups

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

subgroupindex
C2×#180119722
C2×#180119712
#237505952
C22×#145587352
#1785149