Finite Group Databasebeta

← #25000113

Subgroups — #25000113

Order 11008.

630 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 127 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#19139511C211yesmaximal, characteristic
2#19134592C212yesmaximal, complemented
3C2×#14582628C212yesmaximal, complemented
4#19132478C211yesmaximal, characteristic, complemented
5C43×#1844C211yesmaximal, characteristic, complemented
6C2×#13063300—22no—
7C2×C4×D172C2212yes—
8C2×C4⋊(C43⋊C8)C2212yes—
9C2×#13063245—22no—
10#14582816—22no—
11#14582756—22no—
12#14582661—22no—
13#14582628—24no—
14C2×#106×C43—22no—
15C2×C4×C8×C43C2211yescharacteristic
16C43×#384C2211yescharacteristic
17C43×#384C2211yescharacteristic
18C22×D172—22no—
19C22×D172D412yes—
20C22×C4×D43—22no—
21C22×C43⋊C8—22no—
22#13063300—44no—
23#13063300—44no—
24C4×D172—22no—
25C4×D172—22no—
26C4×D172—22no—
27C4×D172—22no—
28C2×C4⋊Dic43D412yes—
29C2×(C2×D43)⋊C4—24no—
30C2×(C2×D43)⋊C4—22no—
31C4⋊(C43⋊C8)—22no—
32C4⋊(C43⋊C8)—22no—
33#13063245—44no—
34C43⋊#95—22no—
35C22×C8×C43—21no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43D412yes—
40C2×C42×C43C2311yescharacteristic
41#106×C43—44no—
42C4×C8×C43—21no—
43C4×C8×C43D412yescomplemented
44C23×D43—22no—
45C22×C4×C43—22no—
46C22×C4×C43—41no—
47C22×C4×C43C2×D412yes—
48C22×C4×C43C2×D411yescharacteristic
49C22×Dic43—22no—
50C2×D172—22no—
51C2×D172—22no—
52C2×D172—22no—
53C2×D172—22no—
54C2×D172—22no—
55C2×D172—48no—
56C2×D172—82no—
57C2×D172SD1614yes—
58C2×C4×D43—42no—
59C2×C4×D43—42no—
60C2×C4×D43—42no—
61C2×C4×D43—42no—
62C2×C4×D43—42no—
63C2×C4×D43—42no—
64C2×C8×C43—22no—
65C2×C8×C43—22no—
66C2×C8×C43—22no—
67C4⋊C4×C43—42no—
68C4⋊C4×C43—42no—
69C4⋊C4×C43—42no—
70C4⋊C4×C43—42no—
71C4⋊C4×C43—42no—
72C4⋊C4×C43—42no—
73C42×C43C2×D411yescharacteristic
74C42×C43#4111yescharacteristic
75C42×C43#4112yes—
76(C2×D43)⋊C4—48no—
77(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—42no—
79C4⋊Dic43—22no—
80C4⋊Dic43—22no—
81C2×C43⋊C8—42no—
82C2×C43⋊C8—42no—
83C2×C43⋊C8—42no—
84C23×C43#12011yescharacteristic
85C22×D43—24no—
86C22×D43—42no—
87C22×D43—42no—
88C22×D43—42no—
89C22×D43—42no—
90C22×D43—42no—
91C22×D43—42no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—44no—
95C2×C4×C43—42no—
96C2×C4×C43—82no—
97C2×C4×C43—81no—
98C2×C4×C43#12111yescharacteristic
99C2×C4×C43#12112yes—
100C2×C4×C43#12312yes—
101C2×C4×C43#12411yescharacteristic
102C2×C4×C43C2×SD1612yes—
103C2×C4×C43#13512yes—
104C2×C4×C43AGL(1,ℤ/8)12yes—
105C2×C4×C43AGL(1,ℤ/8)12yes—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109D172—24no—
110D172—24no—
111D172—42no—
112D172—42no—
113D172—88no—
114C4×D43—82no—
115C4×D43—82no—
116C4×D43—82no—
117C4×D43—82no—
118C8×C43—24no—
119C43⋊C8—82no—
120#10432—431nomaximal, Sylow
121C22×C43#39411yescharacteristic
122C22×C43#44912yes—
123C22×C43#45012yes—
124C22×C43#45311yescharacteristic
125C22×C43#45611yescharacteristic
126C2×D43—44no—
127C2×D43—44no—
128C2×D43—44no—
129C2×D43—82no—
130C2×D43—82no—
131C2×D43—82no—
132C2×D43—82no—
133C4×C43—21no—
134C4×C43—21no—
135C4×C43—82no—
136C4×C43—161no—
137C4×C43#46512yes—
138C4×C43#46912yes—
139C4×C43#48112yes—
140C4×C43#48212yes—
141Dic43—82no—
142#2537—431no—
143#1844D4311yescharacteristic, complemented
144#1802—432no—
145C2×D4⋊C8—432no—
146#1296—431no—
147C2×C43#162411yescharacteristic
148C2×C43#162911yescharacteristic
149C2×C43#165412yes—
150C2×C43#203412yes—
151C2×C43#203911yescharacteristic
152D43—84no—
153C2×#121—862no—
154C2×C4×D4—432no—
155C2×#106—22no—
156C2×C4⋊C8—432no—
157C2×#102—862no—
158C2×C4×C8C2×D4311yescharacteristic
159#394—862no—
160#384C2×D4311yescharacteristic
161#384C2×D4311yescharacteristic
162#380—862no—
163#340—862no—
164D4⋊C8—864no—
165C43#1043211yescharacteristic, complemented, Sylow
166C22×D4—432no—
167C22×D4—862no—
168C23×C4—862no—
169C22×C8—21no—
170C22×C8—862no—
171#121—1724no—
172#121—1724no—
173C4×D4—862no—
174C4×D4—862no—
175C4×D4—862no—
176C4×D4—862no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—432no—
181C2×C4⋊C4C22⋊D4312yes—
182C2×C22⋊C4—864no—
183C2×C22⋊C4—862no—
184C2×C42C22×D4311yescharacteristic
185#106—44no—
186C4⋊C8—862no—
187C4⋊C8—862no—
188#102—1724no—
189C4×C8—21no—
190C4×C8D17212yescomplemented
191#95—862no—
192C24—862no—
193C2×D4—434no—
194C2×D4—862no—
195C2×D4—862no—
196C2×D4—862no—
197C2×D4—862no—
198C2×D4—862no—
199C2×D4—3442no—
200C2×D4—1728no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—862no—
204C22×C4—1722no—
205C22×C4—1722no—
206C22×C4—1722no—
207C22×C4—1722no—
208C22×C4—1722no—
209C22×C4—1722no—
210C22×C4D4×D4312yes—
211C22×C4C2×C22⋊D4311yescharacteristic
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—1722no—
216C2×C8—1722no—
217C2×C8—1722no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—862no—
225C4⋊C4—862no—
226C22⋊C4—1728no—
227C22⋊C4—1722no—
228C22⋊C4—1722no—
229C42C2×D17211yescharacteristic
230C42#1062189811yescharacteristic
231C42#1062190212yes—
232C23—864no—
233C23—1722no—
234C23—1722no—
235C23—1722no—
236C23—1722no—
237C23—1722no—
238C23—1722no—
239C23#1306329311yescharacteristic
240D4—864no—
241D4—864no—
242D4—3448no—
243D4—1722no—
244D4—1722no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—44no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—3442no—
252C2×C4—3442no—
253C2×C4—3442no—
254C2×C4—3442no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4#1306329911yescharacteristic
259C2×C4#1306330012yes—
260C2×C4#1306331012yes—
261C2×C4#1306331411yescharacteristic
262C2×C4SD16×D4312yes—
263C2×C4#1306334612yes—
264C2×C4#1306335212yes—
265C2×C4#1306335212yes—
266C8—24no—
267C8—3442no—
268C22—3442no—
269C22—3442no—
270C22—3442no—
271C22—3442no—
272C22—1724no—
273C22—1724no—
274C22—1724no—
275C22#1458281611yescharacteristic
276C22#1458304312yes—
277C22#1458304812yes—
278C22#1458306611yescharacteristic
279C22#1458308111yescharacteristic
280C4—21no—
281C4—21no—
282C4—82no—
283C4—161no—
284C4—3442no—
285C4#1458312912yes—
286C4#1458315312yes—
287C4#1458321912yes—
288C4#1458322512yes—
289C2—3444no—
290C2#1913367611yescharacteristic
291C2#1913370911yescharacteristic
292C2#1913387612yes—
293C2#1913578612yes—
294C2#1913581911yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1844C2
socleC23×C43#120
prime radical#19139511C2
hypercenter#1844D43
hypocenterC43#10432
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
2. #19134592C2semidirect
3. C2×#14582628C2semidirect
4. #19132478C2semidirect
5. C43×#1844C2semidirect
43. C4×C8×C43D4semidirect
143. #1844D43semidirect
165. C43#10432semidirect
190. C4×C8D172semidirect

Maximal subgroups

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

subgroupindex
#191395112
#191345922
C2×#145826282
#191324782
C43×#18442
#1043243