Finite Group Databasebeta

← #25008802

Subgroups — #25008802

Order 11008.

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

normal subgroups only

This group has 470 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#19133547C212yesmaximal
3#19132615C212yesmaximal, complemented
4#19132525C211yesmaximal, characteristic, complemented
5C43×#2022C211yesmaximal, characteristic
6#14583037—22no—
7#14582835—21no—
8#14582811C2212yes—
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×Dic86D412yes—
20C2×#10621883—42no—
21C2×C4⋊Dic43—21no—
22C2×Dic43⋊C4—22no—
23C2×C22⋊Dic43—22no—
24C2×C4×Dic43—21no—
25C2×C4×Dic43—21no—
26#13063248—42no—
27C22⋊(C43⋊C8)—22no—
28C43⋊#95—22no—
29C43⋊#95—21no—
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×C43SD1612yescomplemented
63C22×C4×C43C2×D412yes—
64C22×Dic43—22no—
65C22×Dic43—22no—
66C2×Dic86—42no—
67C2×Dic86—44no—
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—
77#10621883—84no—
78C4⋊Dic43—81no—
79Dic43⋊C4—44no—
80C4×Dic43—81no—
81C4×Dic43—81no—
82C2×C43⋊C8—42no—
83C23×C43—21no—
84C23×C43—21no—
85C23×C43—42no—
86C23×C43—41no—
87C23×C43—41no—
88C23×C43—41no—
89C23×C43—82no—
90C23×C43#12011yescharacteristic
91C23×C43C2×SD1611yescharacteristic
92C23×C43#13711yescharacteristic
93D4×C43—82no—
94D4×C43—81no—
95D4×C43—81no—
96D4×C43—81no—
97D4×C43—81no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—81no—
111C2×C4×C43—82no—
112C2×Dic43—24no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—42no—
118Dic86—44no—
119Dic86—82no—
120C43⋊C8—82no—
121#12121—431nomaximal, Sylow
122C22×C43—22no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43—42no—
128C22×C43—81no—
129C22×C43—82no—
130C22×C43—81no—
131C22×C43—82no—
132C22×C43—161no—
133C22×C43#44811yescharacteristic
134C22×C43#45311yescharacteristic
135C22×C43B(4,𝔽2)11yescharacteristic
136C4×C43—42no—
137C4×C43—42no—
138C4×C43—81no—
139C4×C43—82no—
140C4×C43—81no—
141Dic43—44no—
142Dic43—82no—
143#2607—431no—
144#2022D4311yescharacteristic
145#1601—432no—
146#1351—432no—
147#1317—431no—
148C2×C43—21no—
149C2×C43—21no—
150C2×C43—41no—
151C2×C43—41no—
152C2×C43—161no—
153C2×C43#159611yescharacteristic
154C2×C43#219712yes—
155#534C2×D4311yescharacteristic
156C2×#123—21no—
157#448—862no—
158C2×#99—21no—
159#399—861no—
160#393—432no—
161#391—862no—
162#387—862no—
163#381C2×D4311yescharacteristic
164C4×C22⋊C4—861no—
165#342C2×D4311yescharacteristic
166#327—862no—
167#323—432no—
168C43#1212111yescharacteristic, complemented, Sylow
169C22×Q8—432no—
170C22×D4—21no—
171C23×C4C22⋊D4311yescharacteristic
172C2×SD16—1722no—
173#123—42no—
174#123—41no—
175#123—42no—
176#121—22no—
177#120—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—861no—
180C2×C4⋊C4—862no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—862no—
184C2×C22⋊C4C22⋊D4311yescharacteristic
185C2×C22⋊C4C22×D4311yescharacteristic
186C2×C42—861no—
187C2×C42—861no—
188#103—1722no—
189#99—42no—
190C22⋊C8—862no—
191#95—22no—
192#95—432no—
193#95—862no—
194#95—861no—
195#95—862no—
196C24—21no—
197C24C2×C22⋊D4311yescharacteristic
198C2×Q8—1722no—
199C2×Q8—1724no—
200C2×D4—22no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—41no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—862no—
215C22×C4—862no—
216C22×C4#1062188312yescomplemented
217C22×C4D4×D4312yes—
218SD16—3444no—
219C2×C8—1722no—
220C4⋊C4—22no—
221C4⋊C4—44no—
222C4⋊C4—3441no—
223C4⋊C4—1724no—
224C22⋊C4—22no—
225C22⋊C4—41no—
226C22⋊C4—42no—
227C22⋊C4—44no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—1724no—
231C42—3441no—
232C42—3441no—
233C23—21no—
234C23—21no—
235C23—42no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—82no—
240C23#1306329311yescharacteristic
241C23C2×#1062188311yescharacteristic
242C23#1306335511yescharacteristic
243Q8—3442no—
244Q8—1724no—
245D4—82no—
246D4—81no—
247D4—81no—
248D4—81no—
249D4—81no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—82no—
264C2×C4—864no—
265C2×C4—1722no—
266C2×C4—1722no—
267C2×C4—1722no—
268C2×C4—1722no—
269C2×C4—1722no—
270C8—3442no—
271C22—22no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—81no—
278C22—82no—
279C22—82no—
280C22—81no—
281C22—161no—
282C22#1458303711yescharacteristic
283C22#1458306611yescharacteristic
284C22#1458308511yescharacteristic
285C4—42no—
286C4—42no—
287C4—81no—
288C4—82no—
289C4—81no—
290C4—3442no—
291C4—1724no—
292C2—21no—
293C2—21no—
294C2—41no—
295C2—41no—
296C2—161no—
297C2#1913351711yescharacteristic
298C2#1913658212yes—
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#12121
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. #19132615C2semidirect
4. #19132525C2semidirect
62. C22×C4×C43SD16semidirect
168. C43#12121semidirect
216. C22×C4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191402602
#191335472
#191326152
#191325252
C43×#20222
#1212143