Finite Group Databasebeta

← #24985346

Subgroups — #24985346

Order 11008.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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#19142583C211yesmaximal, characteristic, complemented
2#19135826C212yesmaximal
3#19132421C211yesmaximal, characteristic, complemented
4#19132417C212yesmaximal, complemented
5C43×#2014C211yesmaximal, characteristic
6C2×#13063246—22no—
7C2×#13063246—22no—
8#14582838—21no—
9#14582831—22no—
10#14582806—21no—
11#14582797C2212yes—
12#14582786—22no—
13#14582654C2212yes—
14C22×SD16×C43—21no—
15C2×#127×C43C2211yescharacteristic
16C2×#102×C43—21no—
17C43×#391C2211yescharacteristic
18C43×#336C2211yescharacteristic
19C22×C43⋊C8—22no—
20C2×C4⋊Dic43—21no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43D412yes—
23C2×C4⋊Dic43D412yes—
24C2×Dic43⋊C4—22no—
25C2×C4×Dic43—21no—
26#13063246—44no—
27#13063246—44no—
28C43⋊#95—21no—
29C43⋊#95—22no—
30C43⋊#95—22no—
31C43⋊#95—22no—
32C22×Q8×C43D411yescharacteristic
33C22×D4×C43—21no—
34C22×D4×C43—22no—
35C2×SD16×C43—42no—
36C2×SD16×C43—42no—
37C2×SD16×C43—42no—
38C22×C8×C43—21no—
39#127×C43—42no—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C42×C43C2311yescharacteristic
42#102×C43—42no—
43#95×C43—22no—
44C24×C43—41no—
45C2×Q8×C43—21no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×Q8×C43SD1612yes—
49C2×D4×C43—22no—
50C2×D4×C43—24no—
51C2×D4×C43—42no—
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C2×D4×C43—42no—
56C2×D4×C43—42no—
57C2×D4×C43—41no—
58C2×D4×C43—42no—
59C2×D4×C43—42no—
60C2×D4×C43—41no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43C2×D412yes—
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—22no—
66C22×Dic43—22no—
67SD16×C43—48no—
68C2×C8×C43—22no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C4⋊C4×C43—41no—
72C42×C43—41no—
73C4⋊Dic43—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43—42no—
76C4⋊Dic43—81no—
77C4⋊Dic43—81no—
78Dic43⋊C4—42no—
79Dic43⋊C4—42no—
80C4×Dic43—81no—
81C2×C43⋊C8—42no—
82C2×C43⋊C8—42no—
83C2×C43⋊C8—42no—
84C23×C43—42no—
85C23×C43—81no—
86C23×C43—82no—
87C23×C43—81no—
88C23×C43—82no—
89C23×C43#12011yescharacteristic
90Q8×C43—42no—
91Q8×C43—81no—
92D4×C43—42no—
93D4×C43—42no—
94D4×C43—44no—
95D4×C43—44no—
96D4×C43—81no—
97D4×C43—81no—
98D4×C43—82no—
99D4×C43—82no—
100C2×C4×C43—21no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43C2×SD1611yescharacteristic
110C2×C4×C43#13512yes—
111C2×C4×C43AGL(1,ℤ/8)12yes—
112C2×C4×C43#13711yescharacteristic
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—42no—
118C2×Dic43—42no—
119C8×C43—42no—
120C43⋊C8—82no—
121#7743—431nomaximal, Sylow
122C22×C43—82no—
123C22×C43—84no—
124C22×C43—161no—
125C22×C43—162no—
126C22×C43—161no—
127C22×C43#44811yescharacteristic
128C22×C43#44912yes—
129C22×C43#45311yescharacteristic
130C22×C43#45412yes—
131C22×C43B(4,𝔽2)11yescharacteristic
132C4×C43—21no—
133C4×C43—21no—
134C4×C43—22no—
135C4×C43—22no—
136C4×C43—42no—
137C4×C43—81no—
138Dic43—82no—
139Dic43—82no—
140#2809—431no—
141#2041—432no—
142#2014D4311yescharacteristic
143#1272—431no—
144#1271—432no—
145C2×C43—162no—
146C2×C43#159611yescharacteristic
147C2×C43#159712yes—
148C2×C43#162411yescharacteristic
149C2×C43#162612yes—
150C2×C43#165711yescharacteristic
151C22×SD16—21no—
152C2×#127C2×D4311yescharacteristic
153C2×#102—21no—
154C2×#102—862no—
155C2×#102—862no—
156#400—861no—
157#398—862no—
158#391—861no—
159#391C2×D4311yescharacteristic
160#389—432no—
161#387—862no—
162#336—432no—
163#336C2×D4311yescharacteristic
164C43#774311yescharacteristic, complemented, Sylow
165C22×Q8C22⋊D4311yescharacteristic
166C22×D4—22no—
167C22×D4—21no—
168C2×SD16—42no—
169C2×SD16—42no—
170C2×SD16—42no—
171C22×C8—21no—
172C22×C8—862no—
173#127—42no—
174C2×C4⋊C4—432no—
175C2×C4⋊C4—432no—
176C2×C4⋊C4—861no—
177C2×C4⋊C4—861no—
178C2×C4⋊C4—862no—
179C2×C4⋊C4C22⋊D4311yescharacteristic
180C2×C42—861no—
181C2×C42C22×D4311yescharacteristic
182#102—42no—
183#102—1724no—
184#102—1724no—
185#95—22no—
186#95—861no—
187#95—862no—
188#95—862no—
189#95—862no—
190C24—41no—
191C2×Q8—21no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8#1062188312yes—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—42no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—41no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—862no—
210C22×C4—862no—
211C22×C4D4×D4312yes—
212C22×C4C2×C22⋊D4311yescharacteristic
213SD16—48no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—1722no—
218C2×C8—1722no—
219C2×C8—1722no—
220C4⋊C4—41no—
221C4⋊C4—862no—
222C4⋊C4—862no—
223C4⋊C4—3441no—
224C4⋊C4—3441no—
225C4⋊C4—1722no—
226C4⋊C4—1722no—
227C4⋊C4—1722no—
228C42—41no—
229C42—3441no—
230C23—42no—
231C23—82no—
232C23—81no—
233C23—82no—
234C23—81no—
235C23#1306329311yescharacteristic
236Q8—42no—
237Q8—81no—
238D4—42no—
239D4—42no—
240D4—44no—
241D4—44no—
242D4—81no—
243D4—81no—
244D4—82no—
245D4—82no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4—1722no—
260C2×C4—1722no—
261C2×C4C2×#1062188311yescharacteristic
262C2×C4#1306334612yes—
263C2×C4#1306335212yes—
264C2×C4#1306335511yescharacteristic
265C8—42no—
266C8—3442no—
267C22—82no—
268C22—84no—
269C22—161no—
270C22—161no—
271C22—162no—
272C22#1458303711yescharacteristic
273C22#1458304312yes—
274C22#1458306611yescharacteristic
275C22#1458307012yes—
276C22#1458308511yescharacteristic
277C4—21no—
278C4—21no—
279C4—22no—
280C4—22no—
281C4—42no—
282C4—81no—
283C4—3442no—
284C4—3442no—
285C2—162no—
286C2#1913351711yescharacteristic
287C2#1913352312yes—
288C2#1913367611yescharacteristic
289C2#1913369012yes—
290C2#1913389111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2014C2
socleC23×C43#120
prime radicalC2×#127×C43C22
hypercenter#2014D43
hypocenterC43#7743
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2014

Complements

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

NH ≅ G/Ntype
1. #19142583C2semidirect
3. #19132421C2semidirect
4. #19132417C2semidirect
164. C43#7743semidirect

Maximal subgroups

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

subgroupindex
#191425832
#191358262
#191324212
#191324172
C43×#20142
#774343