Finite Group Databasebeta

← #24989220

Subgroups — #24989220

Order 11008.

1198 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 147 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#19134516C212yesmaximal
2#19132925C214yesmaximal, complemented
3C22×#123×C43C211yesmaximal, characteristic
4C2×#13063242—24no—
5#14582863C2214yes—
6#14582625—28no—
7C23×D4×C43C2211yescharacteristic
8C24×C4×C43C411yescharacteristic
9C2×#123×C43—24no—
10C2×#123×C43—28no—
11C22×C4⋊C4×C43C2212yes—
12C22×C22⋊C4×C43C411yescharacteristic
13C22×C22⋊C4×C43C412yes—
14C2×#10621877—24no—
15#13063242—48no—
16C22⋊(C43⋊C8)—28no—
17C25×C43C2×C411yescharacteristic
18C25×C43C2×C411yescharacteristic
19C22×D4×C43—24no—
20C22×D4×C43—44no—
21C22×D4×C43D414yes—
22C23×C4×C43—22no—
23C23×C4×C43—24no—
24C23×C4×C43—44no—
25C23×C4×C43C2×C412yes—
26C23×C4×C43C2×C412yes—
27C23×C4×C43C2311yescharacteristic
28#123×C43—232no—
29C2×C4⋊C4×C43—24no—
30C2×C4⋊C4×C43—24no—
31C2×C4⋊C4×C43D418yes—
32C2×C22⋊C4×C43—22no—
33C2×C22⋊C4×C43—24no—
34C2×C22⋊C4×C43—24no—
35C2×C22⋊C4×C43—24no—
36C2×C22⋊C4×C43—24no—
37C24×C43—24no—
38C24×C43—22no—
39C24×C43—22no—
40C24×C43—42no—
41C24×C43—44no—
42C24×C43—44no—
43C24×C43C22⋊C412yes—
44C24×C43C22⋊C412yes—
45C24×C43C22×C411yescharacteristic
46C2×D4×C43—28no—
47C2×D4×C43—28no—
48C2×D4×C43—44no—
49C2×D4×C43—416no—
50C22×C4×C43—28no—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—44no—
56C22×C4×C43—42no—
57C22×C4×C43—44no—
58C22×C4×C43—416no—
59C22×C4×C43—44no—
60C22×C4×C43—44no—
61C22×C4×C43C22⋊C414yes—
62C22×C4×C43C22⋊C414yes—
63C22×C4×C43C2×D412yes—
64C22×C4×C43C2×D414yes—
65C4⋊C4×C43—216no—
66C22⋊C4×C43—28no—
67C22⋊C4×C43—216no—
68#10621877—48no—
69C2×C43⋊C8—44no—
70C23×C43—22no—
71C23×C43—24no—
72C23×C43—28no—
73C23×C43—22no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—24no—
77C23×C43—44no—
78C23×C43—416no—
79C23×C43—44no—
80C23×C43—44no—
81C23×C43—44no—
82C23×C43—44no—
83C23×C43—44no—
84C23×C43—44no—
85C23×C43—88no—
86C23×C43#9914yes—
87C23×C43C2×C22⋊C411yescharacteristic
88C23×C43C2×C22⋊C412yes—
89D4×C43—416no—
90C2×C4×C43—24no—
91C2×C4×C43—24no—
92C2×C4×C43—24no—
93C2×C4×C43—28no—
94C2×C4×C43—44no—
95C2×C4×C43—44no—
96C2×C4×C43—44no—
97C2×C4×C43—44no—
98C2×C4×C43—416no—
99C2×C4×C43—44no—
100C2×C4×C43—44no—
101C2×C4×C43#12014yes—
102C43⋊C8—84no—
103#8548—431nomaximal, Sylow
104C22×C43—28no—
105C22×C43—22no—
106C22×C43—22no—
107C22×C43—22no—
108C22×C43—24no—
109C22×C43—44no—
110C22×C43—44no—
111C22×C43—416no—
112C22×C43—44no—
113C22×C43—42no—
114C22×C43—44no—
115C22×C43—84no—
116C22×C43—88no—
117C22×C43#37911yescharacteristic
118C22×C43C2×#9912yes—
119C22×C43#41314yes—
120C4×C43—24no—
121C4×C43—44no—
122C4×C43—44no—
123C22×#123D4311yescharacteristic
124#1783—432no—
125#1463—434no—
126C2×C43—22no—
127C2×C43—24no—
128C2×C43—44no—
129C2×C43—82no—
130C2×C43#178111yescharacteristic
131C2×C43#178512yes—
132C23×D4C2×D4311yescharacteristic
133C24×C4Dic4311yescharacteristic
134C2×#123—24no—
135C2×#123—28no—
136C22×C4⋊C4C2×D4312yes—
137C22×C22⋊C4Dic4311yescharacteristic
138C22×C22⋊C4Dic4312yes—
139C2×#100—864no—
140#407—434no—
141#324—868no—
142C43#854811yescharacteristic, complemented, Sylow
143C25C2×Dic4311yescharacteristic
144C25C2×Dic4311yescharacteristic
145C22×D4—24no—
146C22×D4—44no—
147C22×D4C22⋊D4314yes—
148C23×C4—22no—
149C23×C4—24no—
150C23×C4—44no—
151C23×C4C2×Dic4312yes—
152C23×C4C2×Dic4312yes—
153C23×C4C22×D4311yescharacteristic
154C2×M16—864no—
155#123—232no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4C22⋊D4318yes—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4—24no—
162C2×C22⋊C4—24no—
163C2×C22⋊C4—24no—
164#100—1728no—
165C22⋊C8—868no—
166C24—24no—
167C24—22no—
168C24—22no—
169C24—42no—
170C24—44no—
171C24—44no—
172C24C22⋊Dic4312yes—
173C24C22⋊Dic4312yes—
174C24C22×Dic4311yescharacteristic
175C2×D4—28no—
176C2×D4—28no—
177C2×D4—44no—
178C2×D4—416no—
179C22×C4—28no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4—44no—
186C22×C4—416no—
187C22×C4—44no—
188C22×C4—44no—
189C22×C4—44no—
190C22×C4C22⋊Dic4314yes—
191C22×C4C22⋊Dic4314yes—
192C22×C4C2×C22⋊D4312yes—
193C22×C4C2×C22⋊D4314yes—
194M16—1728no—
195C2×C8—1724no—
196C4⋊C4—216no—
197C22⋊C4—28no—
198C22⋊C4—216no—
199C23—22no—
200C23—24no—
201C23—28no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—24no—
206C23—44no—
207C23—416no—
208C23—44no—
209C23—44no—
210C23—44no—
211C23—44no—
212C23—44no—
213C23—44no—
214C23—88no—
215C23#1306324014yes—
216C23C2×C22⋊Dic4311yescharacteristic
217C23C2×C22⋊Dic4312yes—
218D4—416no—
219C2×C4—24no—
220C2×C4—28no—
221C2×C4—24no—
222C2×C4—24no—
223C2×C4—44no—
224C2×C4—44no—
225C2×C4—416no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—44no—
229C2×C4—44no—
230C2×C4#1306329414yes—
231C8—3444no—
232C22—28no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22—24no—
237C22—44no—
238C22—44no—
239C22—416no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—84no—
244C22—88no—
245C22#1458275511yescharacteristic
246C22C2×#1306324012yes—
247C22#1458288314yes—
248C4—24no—
249C4—44no—
250C4—44no—
251C2—22no—
252C2—24no—
253C2—44no—
254C2—82no—
255C2#1913451011yescharacteristic
256C2#1913452312yes—
subgroupG/H
centerC22#14582755
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#123×C43C2
socleC22×C43#379
prime radicalC23×D4×C43C22
cosocleC23×C4×C43C23
hypercenterC22×#123D43
hypocenterC43#8548
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. #19132925C2semidirect
142. C43#8548semidirect

Maximal subgroups

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

subgroupindex
#191345162
#191329252
C22×#123×C432
#854843