Finite Group Databasebeta

← #24985784

Subgroups — #24985784

Order 11008.

478 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 83 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#19141621C211yesmaximal, characteristic
2#19136138C211yesmaximal, characteristic, complemented
3#19136000C212yesmaximal, complemented
4#19132415C212yesmaximal, complemented
5C43×#1272C211yesmaximal, characteristic, complemented
6C2×#13063314—21no—
7C2×#13063256—21no—
8C2×#13063249—21no—
9C2×#13063247—22no—
10#14582816—21no—
11#14582809—22no—
12#14582801C2212yes—
13#14582791—22no—
14#14582769C2211yescharacteristic
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×D172—21no—
20C22×D172—21no—
21C22×D172D412yes—
22C22×C43⋊C8—21no—
23#13063314—42no—
24#13063314—42no—
25C2×C4⋊Dic43—22no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43D412yes—
28C2×(C2×D43)⋊C4—22no—
29C2×(C2×D43)⋊C4—22no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—22no—
32C2×C4×Dic43—21no—
33#13063256—42no—
34#13063249—42no—
35#13063247—44no—
36C43⋊#95—21no—
37C22×Q8×C43D411yescharacteristic
38C22×C8×C43—22no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C42×C43C2311yescharacteristic
41#95×C43—22no—
42C23×D43—22no—
43C2×Q8×C43—21no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43SD1612yes—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—22no—
52C22×Dic43—41no—
53C2×D172—22no—
54C2×D172—22no—
55C2×D172—42no—
56C2×D172—42no—
57C2×D172—42no—
58C2×D172—81no—
59C2×D172—81no—
60C2×D172—82no—
61C2×D172—81no—
62C2×C8×C43—42no—
63C2×C8×C43—42no—
64C2×C8×C43—42no—
65C4⋊C4×C43—41no—
66C42×C43—41no—
67(C2×D43)⋊C4—44no—
68(C2×D43)⋊C4—42no—
69(C2×D43)⋊C4—42no—
70(C2×D43)⋊C4—42no—
71(C2×D43)⋊C4—42no—
72(C2×D43)⋊C4—82no—
73C4⋊Dic43—42no—
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76C4⋊Dic43—42no—
77C4⋊Dic43—42no—
78C4×Dic43—42no—
79C2×C43⋊C8—22no—
80C2×C43⋊C8—41no—
81C2×C43⋊C8—41no—
82C23×C43#12011yescharacteristic
83C22×D43—42no—
84C22×D43—42no—
85C22×D43—42no—
86C22×D43—42no—
87C22×D43—42no—
88C22×D43—42no—
89C22×D43—42no—
90Q8×C43—42no—
91Q8×C43—81no—
92C2×C4×C43—21no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43C2×SD1611yescharacteristic
102C2×C4×C43#13512yes—
103C2×C4×C43AGL(1,ℤ/8)12yes—
104C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—82no—
109C2×Dic43—81no—
110D172—44no—
111D172—82no—
112D172—84no—
113D172—84no—
114C8×C43—82no—
115C43⋊C8—42no—
116#7810—431nomaximal, Sylow
117C22×C43#44912yes—
118C22×C43#45011yescharacteristic
119C22×C43#45311yescharacteristic
120C22×C43#45512yes—
121C22×C43#45811yescharacteristic
122C2×D43—82no—
123C2×D43—82no—
124C2×D43—82no—
125C2×D43—82no—
126C2×D43—82no—
127C2×D43—82no—
128C2×D43—82no—
129C4×C43—22no—
130C4×C43—22no—
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—42no—
134C4×C43—81no—
135Dic43—82no—
136Dic43—161no—
137#2733—431no—
138#2096—431no—
139#2071—432no—
140#1272D4311yescharacteristic, complemented
141#1270—432no—
142C2×C43#161212yes—
143C2×C43#161311yescharacteristic
144C2×C43#162411yescharacteristic
145C2×C43#164212yes—
146C2×C43#165911yescharacteristic
147D43—162no—
148C2×#124—861no—
149C2×#106—861no—
150C2×#103—861no—
151C2×#102—862no—
152#394—861no—
153#392—862no—
154#391C2×D4311yescharacteristic
155#390—432no—
156#388—862no—
157#384—431no—
158#340—862no—
159#336—431no—
160#336C2×D4312yes—
161C43#781011yescharacteristic, complemented, Sylow
162C22×Q8D17211yescharacteristic
163C22×D4—432no—
164C22×D4—861no—
165C22×D4—861no—
166C22×C8—22no—
167C22×C8—861no—
168#124—1722no—
169#124—1722no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4—861no—
172C2×C4⋊C4—862no—
173C2×C4⋊C4D17211yescharacteristic
174C2×C22⋊C4—862no—
175C2×C22⋊C4—862no—
176C2×C22⋊C4—862no—
177C2×C22⋊C4—862no—
178C2×C42—861no—
179C2×C42C22×D4311yescharacteristic
180#106—1722no—
181#103—1722no—
182#102—1724no—
183#95—22no—
184#95—861no—
185C24—862no—
186C2×Q8—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8#1062187312yes—
190C2×D4—862no—
191C2×D4—862no—
192C2×D4—3441no—
193C2×D4—3441no—
194C2×D4—3441no—
195C2×D4—3442no—
196C2×D4—1722no—
197C2×D4—1722no—
198C2×D4—1722no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—862no—
202C22×C4—1721no—
203C22×C4C2×D17211yescharacteristic
204C22×C4D4×D4312yes—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—862no—
209C2×C8—1721no—
210C2×C8—1721no—
211C4⋊C4—41no—
212C4⋊C4—1721no—
213C4⋊C4—1721no—
214C4⋊C4—1722no—
215C4⋊C4—1722no—
216C4⋊C4—1722no—
217C22⋊C4—3442no—
218C22⋊C4—1724no—
219C22⋊C4—1722no—
220C22⋊C4—1722no—
221C22⋊C4—1722no—
222C22⋊C4—1722no—
223C42—41no—
224C42—1722no—
225C23—1722no—
226C23—1722no—
227C23—1722no—
228C23—1722no—
229C23—1722no—
230C23—1722no—
231C23—1722no—
232C23#1306329511yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—3442no—
236D4—3444no—
237D4—3444no—
238D4—1724no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—3442no—
249C2×C4—3441no—
250C2×C4—1722no—
251C2×C4—1722no—
252C2×C4—1722no—
253C2×C4C2×#1062187311yescharacteristic
254C2×C4#1306334812yes—
255C2×C4#1306335212yes—
256C2×C4#1306335311yescharacteristic
257C8—82no—
258C8—1722no—
259C22—3442no—
260C22—3442no—
261C22—3442no—
262C22—3442no—
263C22—3442no—
264C22—3442no—
265C22—3442no—
266C22#1458304712yes—
267C22#1458305211yescharacteristic
268C22#1458306911yescharacteristic
269C22#1458307812yes—
270C22#1458309011yescharacteristic
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—81no—
277C4—3442no—
278C4—6881no—
279C2—6882no—
280C2#1913361212yes—
281C2#1913361711yescharacteristic
282C2#1913367911yescharacteristic
283C2#1913379812yes—
284C2#1913390211yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43#120
prime radical#19141621C2
hypercenter#1272D43
hypocenterC43#7810
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #19136138C2semidirect
3. #19136000C2semidirect
4. #19132415C2semidirect
5. C43×#1272C2semidirect
140. #1272D43semidirect
161. C43#7810semidirect

Maximal subgroups

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

subgroupindex
#191416212
#191361382
#191360002
#191324152
C43×#12722
#781043