Finite Group Databasebeta

← #25000110

Subgroups — #25000110

Order 11008.

630 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 133 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#19134751C211yesmaximal, characteristic, complemented
2#19134595C212yesmaximal, complemented
3C2×D4⋊(C43⋊C8)C212yesmaximal, complemented
4#19132478C211yesmaximal, characteristic, complemented
5C43×#2537C211yesmaximal, characteristic
6C2×#13063256—22no—
7C2×C4⋊(C43⋊C8)C2212yes—
8C2×#13063246—22no—
9C2×C4×C43⋊C8C2211yescharacteristic
10#14582769C2211yescharacteristic
11#14582661—22no—
12D4⋊(C43⋊C8)—24no—
13C2×#121×C43—22no—
14C2×C4×D4×C43C2212yes—
15C43×#394—22no—
16C43×#384C2211yescharacteristic
17C43×#380—22no—
18C22×C43⋊C8—21no—
19C22×C43⋊C8—22no—
20C2×C4⋊Dic43—22no—
21C2×C4⋊Dic43—21no—
22#13063256—44no—
23C4⋊(C43⋊C8)—22no—
24C4⋊(C43⋊C8)—22no—
25#13063246—44no—
26C4×C43⋊C8—21no—
27C4×C43⋊C8D412yescomplemented
28C22×D4×C43—22no—
29C22×D4×C43D412yes—
30C23×C4×C43—22no—
31#121×C43—44no—
32#121×C43—44no—
33C4×D4×C43—22no—
34C4×D4×C43—22no—
35C4×D4×C43—22no—
36C4×D4×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43D412yes—
39C2×C4⋊C4×C43D412yes—
40C2×C22⋊C4×C43—24no—
41C2×C22⋊C4×C43—22no—
42C2×C42×C43C2311yescharacteristic
43#95×C43—22no—
44C24×C43—22no—
45C2×D4×C43—22no—
46C2×D4×C43—22no—
47C2×D4×C43—22no—
48C2×D4×C43—22no—
49C2×D4×C43—22no—
50C2×D4×C43—48no—
51C2×D4×C43—82no—
52C2×D4×C43SD1614yes—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—42no—
56C22×C4×C43—42no—
57C22×C4×C43—42no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43—42no—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D412yes—
63C22×Dic43—41no—
64C4⋊C4×C43—22no—
65C4⋊C4×C43—22no—
66C4⋊C4×C43—42no—
67C4⋊C4×C43—42no—
68C4⋊C4×C43—42no—
69C22⋊C4×C43—48no—
70C22⋊C4×C43—42no—
71C22⋊C4×C43—42no—
72C42×C43C2×D411yescharacteristic
73C42×C43#4111yescharacteristic
74C42×C43#4112yes—
75C4⋊Dic43—42no—
76C4⋊Dic43—42no—
77C4⋊Dic43—42no—
78C2×C43⋊C8—22no—
79C2×C43⋊C8—22no—
80C2×C43⋊C8—22no—
81C2×C43⋊C8—42no—
82C2×C43⋊C8—42no—
83C2×C43⋊C8—42no—
84C23×C43—24no—
85C23×C43—42no—
86C23×C43—42no—
87C23×C43—42no—
88C23×C43—42no—
89C23×C43—42no—
90C23×C43—42no—
91C23×C43#12011yescharacteristic
92D4×C43—24no—
93D4×C43—24no—
94D4×C43—42no—
95D4×C43—42no—
96D4×C43—88no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—44no—
103C2×C4×C43—42no—
104C2×C4×C43—82no—
105C2×C4×C43—82no—
106C2×C4×C43—82no—
107C2×C4×C43—82no—
108C2×C4×C43#12111yescharacteristic
109C2×C4×C43#12112yes—
110C2×C4×C43#12312yes—
111C2×C4×C43#12411yescharacteristic
112C2×C4×C43C2×SD1612yes—
113C2×C4×C43#13512yes—
114C2×C4×C43AGL(1,ℤ/8)12yes—
115C2×C4×C43AGL(1,ℤ/8)12yes—
116C2×Dic43—82no—
117C2×Dic43—81no—
118C43⋊C8—24no—
119C43⋊C8—82no—
120#10432—431nomaximal, Sylow
121C22×C43—44no—
122C22×C43—44no—
123C22×C43—44no—
124C22×C43—82no—
125C22×C43—82no—
126C22×C43—82no—
127C22×C43—82no—
128C22×C43#39411yescharacteristic
129C22×C43#44912yes—
130C22×C43#45012yes—
131C22×C43#45311yescharacteristic
132C22×C43#45611yescharacteristic
133C4×C43—21no—
134C4×C43—21no—
135C4×C43—82no—
136C4×C43—82no—
137C4×C43#46512yes—
138C4×C43#46912yes—
139C4×C43#48112yes—
140C4×C43#48212yes—
141Dic43—161no—
142#2537D4311yescharacteristic
143#1844—431no—
144#1802—432no—
145C2×D4⋊C8—432no—
146#1296—431no—
147C2×C43—84no—
148C2×C43#162411yescharacteristic
149C2×C43#162911yescharacteristic
150C2×C43#165412yes—
151C2×C43#203412yes—
152C2×C43#203911yescharacteristic
153C2×#121—22no—
154C2×C4×D4C2×D4312yes—
155C2×#106—862no—
156C2×C4⋊C8—432no—
157C2×#102—862no—
158C2×C4×C8—431no—
159#394—22no—
160#384—431no—
161#384C2×D4311yescharacteristic
162#380—22no—
163#340—862no—
164D4⋊C8—864no—
165C43#1043211yescharacteristic, complemented, Sylow
166C22×D4—22no—
167C22×D4C22⋊D4312yes—
168C23×C4—22no—
169C22×C8—861no—
170C22×C8—862no—
171#121—44no—
172#121—44no—
173C4×D4—22no—
174C4×D4—22no—
175C4×D4—22no—
176C4×D4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—862no—
179C2×C4⋊C4—861no—
180C2×C4⋊C4C22⋊D4312yes—
181C2×C4⋊C4C22⋊D4312yes—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—22no—
184C2×C42C22×D4311yescharacteristic
185#106—1724no—
186C4⋊C8—862no—
187C4⋊C8—862no—
188#102—1724no—
189C4×C8—432no—
190C4×C8—861no—
191#95—22no—
192C24—22no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—48no—
199C2×D4—82no—
200C2×D4#1062188314yes—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—1721no—
210C22×C4C2×C22⋊D4311yescharacteristic
211C22×C4C2×C22⋊D4312yes—
212C2×C8—862no—
213C2×C8—862no—
214C2×C8—862no—
215C2×C8—1722no—
216C2×C8—1722no—
217C2×C8—1722no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—1722no—
224C4⋊C4—1722no—
225C4⋊C4—1722no—
226C22⋊C4—48no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C42D4×D4311yescharacteristic
230C42#1062190011yescharacteristic
231C42#1062190012yes—
232C23—24no—
233C23—42no—
234C23—42no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23#1306329411yescharacteristic
240D4—24no—
241D4—24no—
242D4—42no—
243D4—42no—
244D4—88no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—3442no—
257C2×C4—3441no—
258C2×C4#1306329611yescharacteristic
259C2×C4#1306329712yes—
260C2×C4#1306330612yes—
261C2×C4#1306331211yescharacteristic
262C2×C4C2×#1062188312yes—
263C2×C4#1306334512yes—
264C2×C4#1306335012yes—
265C2×C4#1306335112yes—
266C8—864no—
267C8—3442no—
268C22—44no—
269C22—44no—
270C22—44no—
271C22—82no—
272C22—82no—
273C22—82no—
274C22—82no—
275C22#1458281311yescharacteristic
276C22#1458304412yes—
277C22#1458305012yes—
278C22#1458306711yescharacteristic
279C22#1458308211yescharacteristic
280C4—21no—
281C4—21no—
282C4—82no—
283C4—82no—
284C4—6881no—
285C4#1458312612yes—
286C4#1458315012yes—
287C4#1458321512yes—
288C4#1458322012yes—
289C2—84no—
290C2#1913367811yescharacteristic
291C2#1913371111yescharacteristic
292C2#1913387912yes—
293C2#1913578112yes—
294C2#1913581611yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2537C2
socleC23×C43#120
hypercenter#2537D43
hypocenterC43#10432
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #19134751C2semidirect
2. #19134595C2semidirect
3. C2×D4⋊(C43⋊C8)C2semidirect
4. #19132478C2semidirect
27. C4×C43⋊C8D4semidirect
165. C43#10432semidirect

Maximal subgroups

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

subgroupindex
#191347512
#191345952
C2×D4⋊(C43⋊C8)2
#191324782
C43×#25372
#1043243