Finite Group Databasebeta

← #24985426

Subgroups — #24985426

Order 11008.

468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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#19141627C211yesmaximal, characteristic
2#19135924C212yesmaximal
3#19135694C211yesmaximal, characteristic
4#19132417C212yesmaximal
5C43×#1272C211yesmaximal, characteristic
6C22×#10621885—21no—
7C2×#13063325C2211yescharacteristic
8C2×#13063323—21no—
9C2×#13063259—22no—
10C2×#13063248—21no—
11#14582829—21no—
12#14582820—22no—
13#14582797C2212yes—
14#14582784—22no—
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C22×Dic86—21no—
21C2×#10621885—42no—
22C2×#10621885—42no—
23C2×#10621885—42no—
24C22×C43⋊C8—21no—
25#13063325—42no—
26#13063323—42no—
27#13063323—42no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43D412yes—
31C2×C4⋊Dic43D412yes—
32C2×Dic43⋊C4—22no—
33C2×Dic43⋊C4—22no—
34C2×C4×Dic43—21no—
35#13063259—44no—
36#13063248—42no—
37C43⋊#95—21no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C22×Q8×C43D411yescharacteristic
41C22×C8×C43—22no—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C42×C43C2311yescharacteristic
44#95×C43—22no—
45C2×Q8×C43—21no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×Q8×C43D812yes—
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43C2×D412yes—
53C22×Dic43—22no—
54C22×Dic43—22no—
55C22×Dic43—41no—
56C2×Dic86—22no—
57C2×Dic86—41no—
58C2×Dic86—41no—
59C2×Dic86—41no—
60C2×Dic86—41no—
61C2×Dic86—42no—
62C2×Dic86—41no—
63C2×Dic86—81no—
64C2×Dic86—81no—
65C2×C8×C43—24no—
66C2×C8×C43—42no—
67C2×C8×C43—42no—
68C4⋊C4×C43—41no—
69C42×C43—41no—
70#10621885—48no—
71C4⋊Dic43—22no—
72C4⋊Dic43—24no—
73C4⋊Dic43—42no—
74C4⋊Dic43—42no—
75C4⋊Dic43—81no—
76C4⋊Dic43Q1614yescomplemented
77Dic43⋊C4—44no—
78Dic43⋊C4—42no—
79Dic43⋊C4—42no—
80C4×Dic43—42no—
81C2×C43⋊C8—22no—
82C2×C43⋊C8—41no—
83C2×C43⋊C8—41no—
84C23×C43#12011yescharacteristic
85Q8×C43—42no—
86Q8×C43—81no—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—42no—
96C2×C4×C43C2×D811yescharacteristic
97C2×C4×C43C2×Q1612yes—
98C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C43#13712yes—
100C2×Dic43—24no—
101C2×Dic43—42no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—81no—
108C2×Dic43—81no—
109Dic86—42no—
110Dic86—42no—
111Dic86—81no—
112Dic86—81no—
113Dic86—84no—
114C8×C43—44no—
115C43⋊C8—42no—
116#7757—431nomaximal, Sylow
117C22×C43#44711yescharacteristic
118C22×C43#45112yes—
119C22×C43#45311yescharacteristic
120C22×C43#45612yes—
121C22×C43B(4,𝔽2)11yescharacteristic
122C4×C43—21no—
123C4×C43—21no—
124C4×C43—22no—
125C4×C43—22no—
126C4×C43—42no—
127C4×C43—81no—
128Dic43—44no—
129Dic43—82no—
130Dic43—82no—
131#2734—431no—
132#2057—432no—
133#2016—431no—
134#1272D4311yescharacteristic
135#1271—432no—
136C2×C43#159511yescharacteristic
137C2×C43#160512yes—
138C2×C43#163311yescharacteristic
139C2×C43#164912yes—
140C2×C43#166011yescharacteristic
141C22×Q16—861no—
142C2×C4⋊Q8—431no—
143C2×C4⋊Q8—861no—
144C2×#107—862no—
145C2×#103—861no—
146#398—861no—
147#395—862no—
148#391C2×D4311yescharacteristic
149#389—432no—
150#387—862no—
151#340—862no—
152#336—431no—
153#336C2×D4312yes—
154C43#775711yescharacteristic, complemented, Sylow
155C22×Q8—861no—
156C22×Q8—861no—
157C22×Q8D17211yescharacteristic
158C2×Q16—1722no—
159C2×Q16—1722no—
160C2×Q16—1722no—
161C22×C8—22no—
162C22×C8—861no—
163C4⋊Q8—1722no—
164C4⋊Q8—1722no—
165C4⋊Q8—1722no—
166C2×C4⋊C4—432no—
167C2×C4⋊C4—432no—
168C2×C4⋊C4—862no—
169C2×C4⋊C4—861no—
170C2×C4⋊C4—862no—
171C2×C4⋊C4—862no—
172C2×C4⋊C4D17211yescharacteristic
173C2×C42—861no—
174C2×C42C22×D4311yescharacteristic
175#107—1724no—
176#103—1722no—
177#95—22no—
178#95—861no—
179#95—862no—
180#95—862no—
181C2×Q8—21no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—862no—
185C2×Q8—3441no—
186C2×Q8—3441no—
187C2×Q8—1721no—
188C2×Q8—1721no—
189C2×Q8—1721no—
190C2×Q8—1722no—
191C2×Q8—1721no—
192C2×Q8—1721no—
193C2×Q8D34412yes—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—862no—
197C22×C4—862no—
198C22×C4—1721no—
199C22×C4C2×D17211yescharacteristic
200C22×C4D4×D4312yes—
201Q16—1728no—
202C2×C8—24no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—862no—
206C2×C8—1721no—
207C2×C8—1721no—
208C4⋊C4—41no—
209C4⋊C4—434no—
210C4⋊C4—864no—
211C4⋊C4—862no—
212C4⋊C4—3441no—
213C4⋊C4—1722no—
214C4⋊C4—1724no—
215C4⋊C4—1722no—
216C4⋊C4—1722no—
217C4⋊C4—1722no—
218C42—41no—
219C42—1722no—
220C23#1306329511yescharacteristic
221Q8—42no—
222Q8—81no—
223Q8—3441no—
224Q8—3441no—
225Q8—3444no—
226Q8—1722no—
227Q8—1722no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—864no—
238C2×C4—3441no—
239C2×C4—3441no—
240C2×C4—1722no—
241C2×C4—1722no—
242C2×C4—1722no—
243C2×C4—1722no—
244C2×C4—1722no—
245C2×C4—1722no—
246C2×C4C2×D34411yescharacteristic
247C2×C4Q16×D4312yes—
248C2×C4#1306335311yescharacteristic
249C2×C4#1306335412yes—
250C8—44no—
251C8—1722no—
252C22#1458303511yescharacteristic
253C22#1458305612yes—
254C22#1458306911yescharacteristic
255C22#1458308312yes—
256C22#1458308711yescharacteristic
257C4—21no—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—81no—
263C4—3442no—
264C4—3442no—
265C4—1724no—
266C2#1913351511yescharacteristic
267C2#1913357012yes—
268C2#1913373611yescharacteristic
269C2#1913384612yes—
270C2#1913390711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socle, prime radicalC23×C43#120
hypercenter#1272D43
hypocenterC43#7757
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
76. C4⋊Dic43Q16semidirect
154. C43#7757semidirect

Maximal subgroups

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

subgroupindex
#191416272
#191359242
#191356942
#191324172
C43×#12722
#775743