Finite Group Databasebeta

← #25000951

Subgroups — #25000951

Order 11008.

448 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 77 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#19145370C211yesmaximal, characteristic
2#19135061C212yesmaximal
3#19134777C211yesmaximal, characteristic
4#19133116C212yesmaximal
5C43×#1293C211yesmaximal, characteristic
6C22×#10621877C2211yescharacteristic
7C2×#13063304C2212yes—
8#14583235—22no—
9#14583140—21no—
10#14583140—21no—
11#14583057—22no—
12C2×Dic43⋊C8—21no—
13C2×#13063243—22no—
14C4×C22⋊Dic43C2211yescharacteristic
15#14582667—22no—
16#14582653—21no—
17#14582637—22no—
18#14582637—22no—
19C43×#407C2212yes—
20C2×C22⋊C8×C43C2211yescharacteristic
21C22×Dic86D412yes—
22C2×Dic172—21no—
23C2×Dic172—21no—
24C2×#10621877—22no—
25C2×#10621877—42no—
26C22×C43⋊C8—21no—
27#13063304—22no—
28#13063304—22no—
29#13063304—22no—
30#13063304—22no—
31C2×C4⋊Dic43D412yes—
32C2×Dic43⋊C4—22no—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43—21no—
35C2×C4×Dic43—21no—
36#13063259—21no—
37#13063259—21no—
38Dic43⋊C8—42no—
39#13063250—22no—
40#13063250—22no—
41#13063243—44no—
42C43⋊#95D411yescharacteristic
43C43⋊#95D411yescharacteristic
44C23×C4×C43C2311yescharacteristic
45C2×M16×C43—22no—
46C22×C8×C43D411yescharacteristic
47C22×C8×C43D411yescharacteristic
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C24×C43#4111yescharacteristic
52C22×C4×C43—41no—
53C22×C4×C43—41no—
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43C2×D412yes—
57C22×C4×C43#4112yes—
58C22×Dic43—21no—
59C22×Dic43—21no—
60C22×Dic43—22no—
61C22×Dic43—22no—
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×Dic86—42no—
65C2×Dic86—42no—
66M16×C43—42no—
67M16×C43—42no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—42no—
73C22⋊Dic43—42no—
74C22⋊Dic43—42no—
75C22⋊Dic43—42no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78Dic43⋊C4—42no—
79Dic43⋊C4—42no—
80C4×Dic43—41no—
81C4×Dic43—41no—
82#10621877—24no—
83#10621877—42no—
84C2×C43⋊C8—22no—
85C2×C43⋊C8—41no—
86C2×C43⋊C8—41no—
87Dic172—81no—
88Dic172—81no—
89C23×C43—21no—
90C23×C43—21no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43#12111yescharacteristic
94C23×C43#12312yes—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43#12011yescharacteristic
102C2×C4×C43#12112yes—
103C2×C4×C43#12411yescharacteristic
104C2×Dic43—22no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107C2×Dic43—41no—
108C2×Dic43—41no—
109C2×Dic43—44no—
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—41no—
113C2×Dic43—82no—
114Dic86—42no—
115Dic86—42no—
116Dic86—82no—
117C8×C43—41no—
118C8×C43—41no—
119C8×C43—82no—
120C43⋊C8—42no—
121#10559—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—22no—
125C22×C43—22no—
126C22×C43—22no—
127C22×C43—81no—
128C22×C43—81no—
129C22×C43#39411yescharacteristic
130C22×C43#47311yescharacteristic
131C22×C43#47311yescharacteristic
132C4×C43—22no—
133C4×C43—21no—
134C4×C43B(4,𝔽2)11yescharacteristic
135C4×C43#45811yescharacteristic
136Dic43—42no—
137Dic43—81no—
138Dic43—82no—
139Dic43—82no—
140#3189—431no—
141#1901—432no—
142#1851—431no—
143#1508—432no—
144#1293D4311yescharacteristic
145C2×C43—21no—
146C2×C43—21no—
147C2×C43—42no—
148C2×C43#204411yescharacteristic
149C2×C43#204711yescharacteristic
150C2×C43#205011yescharacteristic
151C22×M16—431no—
152C2×C22⋊Q8—432no—
153#484—862no—
154#467—861no—
155#467—861no—
156#451—862no—
157C2×C4⋊C8—861no—
158C2×#101—862no—
159#407C2×D4312yes—
160C2×C22⋊C8C2×D4311yescharacteristic
161C4×C22⋊C4—431no—
162#343—862no—
163#336—861no—
164#328—862no—
165#328—862no—
166C43#1055911yescharacteristic, complemented, Sylow
167C22×Q8—432no—
168C23×C4C22×D4311yescharacteristic
169C2×Q16—861no—
170C2×Q16—861no—
171C2×M16—22no—
172C2×M16—862no—
173C2×M16—1722no—
174C22×C8—861no—
175C22×C8D17211yescharacteristic
176C22×C8D17211yescharacteristic
177C22⋊Q8—862no—
178C22⋊Q8—862no—
179C22⋊Q8—862no—
180C22⋊Q8—862no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—862no—
183C2×C22⋊C4—862no—
184C2×C22⋊C4—861no—
185C2×C42—861no—
186#107—861no—
187#107—861no—
188C4⋊C8—1722no—
189#103—862no—
190#103—862no—
191#101—1724no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195#95—431no—
196#95—431no—
197C24#1062190211yescharacteristic
198C2×Q8—862no—
199C2×Q8—862no—
200C2×Q8—1722no—
201C2×Q8—1722no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—861no—
205C22×C4—862no—
206C22×C4—861no—
207C22×C4—862no—
208C22×C4C2×D17211yescharacteristic
209C22×C4#1062189812yes—
210C22×C4D4×D4312yes—
211C22×C4D4×D4311yescharacteristic
212Q16—3441no—
213Q16—3441no—
214M16—42no—
215M16—42no—
216M16—864no—
217M16—1722no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—42no—
223C2×C8—862no—
224C2×C8—1721no—
225C2×C8—1721no—
226C4⋊C4—862no—
227C4⋊C4—862no—
228C4⋊C4—1722no—
229C4⋊C4—1722no—
230C22⋊C4—1722no—
231C22⋊C4—1722no—
232C22⋊C4—1722no—
233C42—1721no—
234C42—1721no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#1306330011yescharacteristic
240C23#1306331012yes—
241Q8—3442no—
242Q8—1722no—
243Q8—1722no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—862no—
251C2×C4—3442no—
252C2×C4—1721no—
253C2×C4—1721no—
254C2×C4—1724no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1721no—
258C2×C4—1721no—
259C2×C4—1721no—
260C2×C4#1306329511yescharacteristic
261C2×C4#1306329812yes—
262C2×C4#1306331311yescharacteristic
263C8—41no—
264C8—41no—
265C8—82no—
266C8—1722no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—81no—
273C22—81no—
274C22#1458281711yescharacteristic
275C22#1458317511yescharacteristic
276C22#1458317511yescharacteristic
277C4—22no—
278C4—21no—
279C4—3441no—
280C4—3442no—
281C4—3442no—
282C4—1722no—
283C4#1458308711yescharacteristic
284C4#1458309011yescharacteristic
285C2—21no—
286C2—21no—
287C2—42no—
288C2#1913584711yescharacteristic
289C2#1913586411yescharacteristic
290C2#1913588311yescharacteristic
subgroupG/H
centerC22#14582817
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1293C2
socleC22×C43#394
prime radicalC24×C43#41
hypercenter#1293D43
hypocenterC43#10559
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
166. C43#10559semidirect

Maximal subgroups

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

subgroupindex
#191453702
#191350612
#191347772
#191331162
C43×#12932
#1055943