Finite Group Databasebeta

← #25009614

Subgroups — #25009614

Order 11008.

454 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135945C211yesmaximal, characteristic, complemented
2#19133534C212yesmaximal, complemented
3#19132598C212yesmaximal, complemented
4#19132539C211yesmaximal, characteristic, complemented
5C43×#2819C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7#14583050—22no—
8#14582939—21no—
9#14582668C2211yescharacteristic
10#14582659—21no—
11#14582635—22no—
12#14582625C2212yes—
13C2×#124×C43—21no—
14C43×#394—21no—
15C43×#394C2212yes—
16C43×#393—22no—
17C43×#392—22no—
18C43×#382C2211yescharacteristic
19C2×#10621883—42no—
20C2×#10621877—21no—
21#13063324—41no—
22#13063316—41no—
23#13063304—22no—
24#13063284—21no—
25#13063258—41no—
26#13063256—41no—
27#13063246—42no—
28C22⋊(C43⋊C8)—22no—
29C22×Q8×C43—21no—
30C22×D4×C43—21no—
31C22×D4×C43—21no—
32C22×D4×C43D412yes—
33#124×C43—42no—
34#124×C43—42no—
35C2×C4⋊C4×C43D411yescharacteristic
36C2×C4⋊C4×C43C2311yescharacteristic
37C2×C22⋊C4×C43—22no—
38C2×C22⋊C4×C43—22no—
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43—22no—
41C2×C42×C43D411yescharacteristic
42#95×C43—21no—
43#95×C43—22no—
44#95×C43D412yes—
45C24×C43—22no—
46C2×Q8×C43—42no—
47C2×Q8×C43—81no—
48C2×Q8×C43—81no—
49C2×D4×C43—42no—
50C2×D4×C43—42no—
51C2×D4×C43—82no—
52C2×D4×C43—82no—
53C2×D4×C43—81no—
54C2×D4×C43—81no—
55C2×D4×C43—81no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—22no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D412yes—
61C2×Dic86—22no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—41no—
64C22⋊C4×C43—44no—
65C22⋊C4×C43—42no—
66C22⋊C4×C43—42no—
67C22⋊C4×C43—82no—
68C22⋊C4×C43—82no—
69C42×C43—21no—
70C42×C43SD1612yescomplemented
71C22⋊Dic43—41no—
72#10621883—84no—
73C4⋊Dic43—22no—
74C4⋊Dic43—21no—
75C4⋊Dic43—21no—
76Dic43⋊C4—42no—
77C4×Dic43—41no—
78#10621877—22no—
79#10621877—41no—
80C2×C43⋊C8—41no—
81C2×C43⋊C8—42no—
82C23×C43—42no—
83C23×C43—42no—
84C23×C43—42no—
85C23×C43—42no—
86C23×C43—42no—
87C23×C43—42no—
88C23×C43—42no—
89C23×C43#12011yescharacteristic
90Q8×C43—84no—
91D4×C43—44no—
92D4×C43—82no—
93D4×C43—84no—
94D4×C43—84no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—41no—
107C2×C4×C43C2×SD1611yescharacteristic
108C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
109C2×Dic43—41no—
110C2×Dic43—41no—
111Dic86—82no—
112C43⋊C8—42no—
113C43⋊C8—82no—
114#12250—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43—82no—
118C22×C43—82no—
119C22×C43—82no—
120C22×C43—82no—
121C22×C43—82no—
122C22×C43—82no—
123C22×C43—82no—
124C22×C43#45011yescharacteristic
125C22×C43#45611yescharacteristic
126C22×C43B(4,𝔽2)11yescharacteristic
127C4×C43—21no—
128C4×C43—21no—
129C4×C43—42no—
130C4×C43—42no—
131C4×C43—82no—
132C4×C43—81no—
133Dic43—81no—
134Dic43—81no—
135#2819D4311yescharacteristic
136#2061—431no—
137#1599—432no—
138#1345—432no—
139#1324—431no—
140C2×C43—21no—
141C2×C43—21no—
142C2×C43—162no—
143C2×C43#160411yescharacteristic
144C2×C43#219911yescharacteristic
145C2×C43#220211yescharacteristic
146#544—431no—
147C2×#124—21no—
148#450—862no—
149#428—861no—
150#394—21no—
151#394C2×D4312yes—
152#393—22no—
153#392—22no—
154#382C2×D4311yescharacteristic
155#343—431no—
156#339—861no—
157#328—862no—
158#324—432no—
159C43#1225011yescharacteristic, complemented, Sylow
160C22×Q8—21no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4C22⋊D4312yes—
164C2×SD16—1722no—
165C2×M16—861no—
166C4⋊Q8—1721no—
167#125—1721no—
168#124—42no—
169#124—42no—
170C22⋊Q8—862no—
171#117—861no—
172C2×C4⋊C4C22⋊D4311yescharacteristic
173C2×C4⋊C4C22×D4311yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C42C22⋊D4311yescharacteristic
179#107—1721no—
180#106—1721no—
181#102—1722no—
182C22⋊C8—862no—
183#95—21no—
184#95—22no—
185#95C22⋊D4312yes—
186C24—22no—
187C2×Q8—42no—
188C2×Q8—81no—
189C2×Q8—81no—
190C2×Q8—862no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—82no—
194C2×D4—81no—
195C2×D4—81no—
196C2×D4—82no—
197C2×D4—81no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4C2×C22⋊D4311yescharacteristic
202C22×C4C2×C22⋊D4312yes—
203SD16—3444no—
204M16—862no—
205M16—1721no—
206C2×C8—1722no—
207C2×C8—1721no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—862no—
211C4⋊C4—861no—
212C4⋊C4—861no—
213C4⋊C4—1722no—
214C22⋊C4—44no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—82no—
218C22⋊C4—82no—
219C22⋊C4—1721no—
220C42—21no—
221C42—1721no—
222C42#1062188312yescomplemented
223C23—42no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23#1306329411yescharacteristic
231Q8—84no—
232Q8—3442no—
233D4—44no—
234D4—82no—
235D4—84no—
236D4—84no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—1721no—
250C2×C4—1721no—
251C2×C4C2×#1062188311yescharacteristic
252C2×C4#1306335111yescharacteristic
253C8—3442no—
254C8—1722no—
255C22—21no—
256C22—21no—
257C22—82no—
258C22—82no—
259C22—82no—
260C22—82no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22#1458305011yescharacteristic
265C22#1458308211yescharacteristic
266C22#1458308611yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—82no—
272C4—81no—
273C4—3441no—
274C4—3441no—
275C2—21no—
276C2—21no—
277C2—162no—
278C2#1913356411yescharacteristic
279C2#1913659611yescharacteristic
280C2#1913661211yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
Fitting, prime radicalC43×#2819C2
socleC22×C43B(4,𝔽2)
hypercenter#2819D43
hypocenterC43#12250
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2819

Complements

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

NH ≅ G/Ntype
1. #19135945C2semidirect
2. #19133534C2semidirect
3. #19132598C2semidirect
4. #19132539C2semidirect
70. C42×C43SD16semidirect
159. C43#12250semidirect
222. C42#10621883semidirect

Maximal subgroups

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

subgroupindex
#191359452
#191335342
#191325982
#191325392
C43×#28192
#1225043