Finite Group Databasebeta

← #24985423

Subgroups — #24985423

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#19135920C212yesmaximal
3#19132421C211yesmaximal, characteristic
4#19132419C212yesmaximal
5C43×#2016C211yesmaximal, characteristic
6C2×#13063323—21no—
7C2×#13063258—22no—
8#14582829—21no—
9#14582820—22no—
10#14582797C2212yes—
11#14582784—22no—
12#14582661—22no—
13#14582654C2212yes—
14C22×Q16×C43—21no—
15C2×C4⋊Q8×C43C2211yescharacteristic
16C2×#103×C43—21no—
17C43×#391C2211yescharacteristic
18C43×#336C2211yescharacteristic
19C22×Dic86—21no—
20C22×C43⋊C8—22no—
21#13063323—42no—
22#13063323—42no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43D412yes—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—22no—
28C2×C4×Dic43—21no—
29#13063258—44no—
30C43⋊#95—21no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C22×Q8×C43—21no—
34C22×Q8×C43D411yescharacteristic
35C2×Q16×C43—42no—
36C2×Q16×C43—42no—
37C2×Q16×C43—42no—
38C22×C8×C43—21no—
39C4⋊Q8×C43—42no—
40C2×C4⋊C4×C43—22no—
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C42×C43C2311yescharacteristic
43#103×C43—42no—
44#95×C43—22no—
45C2×Q8×C43—21no—
46C2×Q8×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43—41no—
53C2×Q8×C43—41no—
54C2×Q8×C43D812yes—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—41no—
58C22×C4×C43C2×D412yes—
59C22×C4×C43C2×D411yescharacteristic
60C22×Dic43—22no—
61C22×Dic43—22no—
62C2×Dic86—42no—
63C2×Dic86—81no—
64C2×Dic86—81no—
65Q16×C43—48no—
66C2×C8×C43—22no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C4⋊C4×C43—24no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—42no—
72C42×C43—41no—
73C4⋊Dic43—22no—
74C4⋊Dic43—42no—
75C4⋊Dic43—81no—
76C4⋊Dic43Q1614yescomplemented
77Dic43⋊C4—44no—
78Dic43⋊C4—42no—
79Dic43⋊C4—42no—
80C4×Dic43—42no—
81C2×C43⋊C8—24no—
82C2×C43⋊C8—42no—
83C2×C43⋊C8—42no—
84C23×C43#12011yescharacteristic
85Q8×C43—42no—
86Q8×C43—42no—
87Q8×C43—42no—
88Q8×C43—81no—
89Q8×C43—81no—
90Q8×C43—81no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—81no—
102C2×C4×C43—81no—
103C2×C4×C43C2×D811yescharacteristic
104C2×C4×C43C2×Q1612yes—
105C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C43#13712yes—
107C2×Dic43—24no—
108C2×Dic43—42no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—42no—
113Dic86—84no—
114C8×C43—42no—
115C43⋊C8—44no—
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—82no—
128C4×C43—81no—
129Dic43—44no—
130Dic43—82no—
131#2734—431no—
132#2057—432no—
133#2016D4311yescharacteristic
134#1272—431no—
135#1271—432no—
136C2×C43#159511yescharacteristic
137C2×C43#160512yes—
138C2×C43#163311yescharacteristic
139C2×C43#164912yes—
140C2×C43#166011yescharacteristic
141C22×Q16—21no—
142C2×C4⋊Q8—861no—
143C2×C4⋊Q8C2×D4311yescharacteristic
144C2×#107—862no—
145C2×#103—21no—
146#398—861no—
147#395—862no—
148#391C2×D4311yescharacteristic
149#389—432no—
150#387—862no—
151#340—862no—
152#336—432no—
153#336C2×D4311yescharacteristic
154C43#775711yescharacteristic, complemented, Sylow
155C22×Q8—21no—
156C22×Q8—861no—
157C22×Q8C22⋊D4311yescharacteristic
158C2×Q16—42no—
159C2×Q16—42no—
160C2×Q16—42no—
161C22×C8—21no—
162C22×C8—862no—
163C4⋊Q8—42no—
164C4⋊Q8—1722no—
165C4⋊Q8—1722no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—432no—
168C2×C4⋊C4—432no—
169C2×C4⋊C4—861no—
170C2×C4⋊C4—862no—
171C2×C4⋊C4—862no—
172C2×C4⋊C4C22⋊D4311yescharacteristic
173C2×C42—861no—
174C2×C42C22×D4311yescharacteristic
175#107—1724no—
176#103—42no—
177#95—22no—
178#95—861no—
179#95—862no—
180#95—862no—
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—3441no—
191C2×Q8—3441no—
192C2×Q8—1722no—
193C2×Q8#1062188212yes—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—862no—
198C22×C4—862no—
199C22×C4D4×D4312yes—
200C22×C4C2×C22⋊D4311yescharacteristic
201Q16—48no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—864no—
206C2×C8—1722no—
207C2×C8—1722no—
208C4⋊C4—24no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—434no—
212C4⋊C4—862no—
213C4⋊C4—3441no—
214C4⋊C4—1722no—
215C4⋊C4—1724no—
216C4⋊C4—1722no—
217C4⋊C4—1722no—
218C42—41no—
219C42—1722no—
220C23#1306329311yescharacteristic
221Q8—42no—
222Q8—42no—
223Q8—42no—
224Q8—81no—
225Q8—81no—
226Q8—81no—
227Q8—3444no—
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—42no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—864no—
241C2×C4—1722no—
242C2×C4—1722no—
243C2×C4—1722no—
244C2×C4—1722no—
245C2×C4—1722no—
246C2×C4C2×#1062188211yescharacteristic
247C2×C4Q16×D4312yes—
248C2×C4#1306335011yescharacteristic
249C2×C4#1306335712yes—
250C8—42no—
251C8—1724no—
252C22#1458303211yescharacteristic
253C22#1458305312yes—
254C22#1458306611yescharacteristic
255C22#1458308012yes—
256C22#1458308511yescharacteristic
257C4—21no—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—82no—
263C4—81no—
264C4—3442no—
265C4—1724no—
266C2#1913351211yescharacteristic
267C2#1913356712yes—
268C2#1913373311yescharacteristic
269C2#1913384212yes—
270C2#1913390411yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2016C2
socle, prime radicalC23×C43#120
hypercenter#2016D43
hypocenterC43#7757
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2016

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
#191359202
#191324212
#191324192
C43×#20162
#775743