Finite Group Databasebeta

← #25008807

Subgroups — #25008807

Order 11008.

458 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 59 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#19140260C211yesmaximal, characteristic, complemented
2#19133615C212yesmaximal
3#19132618C212yesmaximal, complemented
4#19132525C211yesmaximal, characteristic, complemented
5C43×#2022C211yesmaximal, characteristic
6#14583215—22no—
7#14582835C2212yes—
8#14582811—21no—
9#14582803—22no—
10#14582786—22no—
11C4×C22⋊Dic43—21no—
12#14582633—22no—
13#14582623C2212yes—
14C43×#534C2211yescharacteristic
15C2×#123×C43—21no—
16C2×#99×C43—21no—
17C43×#381C2211yescharacteristic
18C43×#342C2211yescharacteristic
19C22×Dic86—21no—
20C2×C4⋊Dic43D412yes—
21C2×Dic43⋊C4—22no—
22C2×C22⋊Dic43—22no—
23C2×C4×Dic43—21no—
24C2×C4×Dic43—21no—
25#13063256—42no—
26#13063246—42no—
27C22⋊(C43⋊C8)—22no—
28C43⋊#95—21no—
29C43⋊#95—22no—
30C43⋊#95—22no—
31C43⋊#95D412yes—
32C22×D4×C43—21no—
33C23×C4×C43D411yescharacteristic
34#123×C43—42no—
35#123×C43—41no—
36#123×C43—42no—
37#121×C43—22no—
38#120×C43—41no—
39C2×C4⋊C4×C43—41no—
40C2×C22⋊C4×C43—21no—
41C2×C22⋊C4×C43—41no—
42C2×C22⋊C4×C43D411yescharacteristic
43C2×C22⋊C4×C43C2311yescharacteristic
44#99×C43—42no—
45#95×C43—22no—
46C24×C43—21no—
47C24×C43C2×D411yescharacteristic
48C2×D4×C43—22no—
49C2×D4×C43—41no—
50C2×D4×C43—41no—
51C2×D4×C43—41no—
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43SD1612yes—
63C22×C4×C43C2×D412yes—
64C22×Dic43—22no—
65C22×Dic43—22no—
66C2×Dic86—44no—
67C2×Dic86—81no—
68C4⋊C4×C43—22no—
69C4⋊C4×C43—44no—
70C22⋊C4×C43—22no—
71C22⋊C4×C43—41no—
72C22⋊C4×C43—41no—
73C22⋊C4×C43—42no—
74C22⋊C4×C43—44no—
75C22⋊C4×C43—41no—
76C22⋊Dic43—44no—
77C4⋊Dic43—42no—
78Dic43⋊C4—44no—
79C4×Dic43—81no—
80C4×Dic43—81no—
81C2×C43⋊C8—42no—
82C23×C43—21no—
83C23×C43—21no—
84C23×C43—42no—
85C23×C43—41no—
86C23×C43—41no—
87C23×C43—41no—
88C23×C43—82no—
89C23×C43#12011yescharacteristic
90C23×C43C2×SD1611yescharacteristic
91C23×C43#13711yescharacteristic
92D4×C43—82no—
93D4×C43—81no—
94D4×C43—81no—
95D4×C43—81no—
96D4×C43—81no—
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—41no—
105C2×C4×C43—42no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—81no—
110C2×C4×C43—82no—
111C2×Dic43—24no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117Dic86—84no—
118C43⋊C8—82no—
119#12122—431nomaximal, Sylow
120C22×C43—22no—
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—41no—
124C22×C43—41no—
125C22×C43—42no—
126C22×C43—81no—
127C22×C43—82no—
128C22×C43—81no—
129C22×C43—82no—
130C22×C43—161no—
131C22×C43#44811yescharacteristic
132C22×C43#45311yescharacteristic
133C22×C43B(4,𝔽2)11yescharacteristic
134C4×C43—42no—
135C4×C43—42no—
136C4×C43—81no—
137C4×C43—82no—
138C4×C43—81no—
139Dic43—44no—
140Dic43—82no—
141#2607—431no—
142#2022D4311yescharacteristic
143#1613—432no—
144#1352—432no—
145#1317—431no—
146C2×C43—21no—
147C2×C43—21no—
148C2×C43—41no—
149C2×C43—41no—
150C2×C43—161no—
151C2×C43#159611yescharacteristic
152C2×C43#219812yes—
153#534C2×D4311yescharacteristic
154C2×#123—21no—
155#481—862no—
156C2×#99—21no—
157#399—432no—
158#393—861no—
159#391—862no—
160#387—862no—
161#381C2×D4311yescharacteristic
162C4×C22⋊C4—861no—
163#342C2×D4311yescharacteristic
164#327—862no—
165#323—432no—
166C43#1212211yescharacteristic, complemented, Sylow
167C22×Q8—861no—
168C22×D4—21no—
169C23×C4C22⋊D4311yescharacteristic
170#123—42no—
171#123—41no—
172#123—42no—
173#121—22no—
174#120—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—432no—
177C2×C4⋊C4—862no—
178C2×C22⋊C4—21no—
179C2×C22⋊C4—41no—
180C2×C22⋊C4—862no—
181C2×C22⋊C4C22⋊D4311yescharacteristic
182C2×C22⋊C4C22×D4311yescharacteristic
183C2×C42—861no—
184C2×C42—861no—
185#106—1722no—
186#102—1722no—
187#99—42no—
188C22⋊C8—862no—
189#95—22no—
190#95—432no—
191#95—862no—
192#95—861no—
193#95—862no—
194C24—21no—
195C24C2×C22⋊D4311yescharacteristic
196C2×Q8—3441no—
197C2×Q8—1724no—
198C2×D4—22no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—862no—
213C22×C4—862no—
214C22×C4#1062188312yes—
215C22×C4D4×D4312yes—
216C2×C8—1722no—
217C4⋊C4—22no—
218C4⋊C4—44no—
219C4⋊C4—1722no—
220C4⋊C4—1724no—
221C22⋊C4—22no—
222C22⋊C4—41no—
223C22⋊C4—42no—
224C22⋊C4—44no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—1724no—
228C42—3441no—
229C42—3441no—
230C23—21no—
231C23—21no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23—41no—
236C23—82no—
237C23#1306329311yescharacteristic
238C23C2×#1062188311yescharacteristic
239C23#1306335511yescharacteristic
240Q8—3444no—
241D4—82no—
242D4—81no—
243D4—81no—
244D4—81no—
245D4—81no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—864no—
261C2×C4—1722no—
262C2×C4—1722no—
263C2×C4—1722no—
264C2×C4—1722no—
265C2×C4—1722no—
266C8—3442no—
267C22—22no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22—81no—
274C22—82no—
275C22—82no—
276C22—81no—
277C22—161no—
278C22#1458303711yescharacteristic
279C22#1458306611yescharacteristic
280C22#1458308511yescharacteristic
281C4—42no—
282C4—42no—
283C4—81no—
284C4—82no—
285C4—81no—
286C4—3442no—
287C4—1724no—
288C2—21no—
289C2—21no—
290C2—41no—
291C2—41no—
292C2—161no—
293C2#1913351711yescharacteristic
294C2#1913658912yes—
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2022C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#534C22
hypercenter#2022D43
hypocenterC43#12122
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #19140260C2semidirect
3. #19132618C2semidirect
4. #19132525C2semidirect
166. C43#12122semidirect

Maximal subgroups

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

subgroupindex
#191402602
#191336152
#191326182
#191325252
C43×#20222
#1212243