Finite Group Databasebeta

← #25010707

Subgroups — #25010707

Order 11008.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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#19147565C211yesmaximal, characteristic
2#19136882C211yesmaximal, characteristic
3#19136748C211yesmaximal, characteristic
4#19134114C211yesmaximal, characteristic
5#19132576C211yesmaximal, characteristic
6#19132564C211yesmaximal, characteristic
7C43×#1363C211yesmaximal, characteristic
8#14583626—21no—
9#14583306—21no—
10#14583304C2211yescharacteristic
11#14583205—21no—
12#14583203—21no—
13#14583193—21no—
14#14583110—21no—
15#14583029C2211yescharacteristic
16#14583005—21no—
17C4×Dic172C2211yescharacteristic
18#14582726—21no—
19#14582725—21no—
20#14582724—21no—
21#14582704—21no—
22#14582675C2211yescharacteristic
23#14582646—21no—
24C43×#499C2211yescharacteristic
25C43×C4⋊C16C2211yescharacteristic
26C43×#334C2211yescharacteristic
27C2×Dic172—41no—
28C2×Dic172D411yescharacteristic
29#13063325—21no—
30#13063324—21no—
31#13063324—41no—
32#13063316—21no—
33#13063315—41no—
34#13063315—41no—
35C4×Dic86—21no—
36C4×Dic86D411yescharacteristic
37#13063290—21no—
38#13063290—21no—
39#13063290—41no—
40C2×C43⋊C16—21no—
41#13063259—21no—
42#13063259—21no—
43#13063259D411yescharacteristic
44#13063258—21no—
45#13063256—21no—
46C4⋊(C43⋊C8)D411yescharacteristic
47Dic43⋊C8—21no—
48#13063250—21no—
49#13063250—41no—
50#13063248—21no—
51#13063248—21no—
52#13063235—21no—
53#125×C43—21no—
54C2×C16×C43—21no—
55#107×C43D411yescharacteristic
56#107×C43D411yescharacteristic
57#106×C43—21no—
58C4⋊C8×C43—21no—
59C4×C8×C43C2311yescharacteristic
60C2×Dic86—21no—
61C2×Dic86—41no—
62C2×Dic86—41no—
63C2×Dic86D811yescharacteristic
64C2×C8×C43—41no—
65C2×C8×C43C2×D411yescharacteristic
66C2×C8×C43C2×D411yescharacteristic
67C4⋊C4×C43—21no—
68C4⋊C4×C43—21no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C42×C43C2×D411yescharacteristic
72C4⋊Dic43—21no—
73C4⋊Dic43—41no—
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76C4⋊Dic43D811yescharacteristic
77Dic43⋊C4—21no—
78Dic43⋊C4—41no—
79Dic43⋊C4—41no—
80Dic43⋊C4—41no—
81Dic43⋊C4—41no—
82Dic43⋊C4—41no—
83C4×Dic43—21no—
84C4×Dic43—41no—
85C4×Dic43—41no—
86C4×Dic43—41no—
87C2×C43⋊C8—21no—
88Dic172—21no—
89Dic172—82no—
90Dic172Q1612yescomplemented
91C16×C43—41no—
92C43⋊C16—22no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43#12011yescharacteristic
96C2×C4×C43C2×D811yescharacteristic
97C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—41no—
101C2×Dic43—41no—
102C2×Dic43—81no—
103Dic86—22no—
104Dic86—41no—
105Dic86—41no—
106Dic86—82no—
107Dic86—81no—
108Dic86—81no—
109C8×C43—21no—
110C8×C43—81no—
111C8×C43C2×Q1611yescharacteristic
112C8×C43#13711yescharacteristic
113C43⋊C8—41no—
114#12415—431nomaximal, Sylow
115C22×C43#44711yescharacteristic
116C4×C43—21no—
117C4×C43—21no—
118C4×C43—81no—
119C4×C43—81no—
120C4×C43#45111yescharacteristic
121C4×C43#45611yescharacteristic
122Dic43—42no—
123Dic43—41no—
124Dic43—41no—
125Dic43—81no—
126Dic43—161no—
127#3390—431no—
128#2255—431no—
129#2227—431no—
130#1694—431no—
131#1363D4311yescharacteristic
132#1338—431no—
133#1334—431no—
134C2×C43#164911yescharacteristic
135C2×C43#219011yescharacteristic
136C2×C43#219511yescharacteristic
137#557—861no—
138#501—861no—
139#500—431no—
140#499C2×D4311yescharacteristic
141#479—861no—
142#479—861no—
143#477—861no—
144#462—861no—
145#446—431no—
146#441—861no—
147C4×Q16—431no—
148#367—861no—
149#366—861no—
150#366—861no—
151C4⋊C16C2×D4311yescharacteristic
152#358—861no—
153#346—431no—
154#334C2×D4311yescharacteristic
155#332—861no—
156C43#1241511yescharacteristic, complemented, Sylow
157C2×Q16—431no—
158C2×Q16—1721no—
159C4⋊Q8—861no—
160C4⋊Q8—861no—
161C4⋊Q8—1721no—
162#125—21no—
163#125—861no—
164#125—1721no—
165#125—1721no—
166C4×Q8—431no—
167C4×Q8—861no—
168C4×Q8—861no—
169C4×Q8—861no—
170C4×Q8—1721no—
171C2×C16—21no—
172C2×C16—861no—
173#107—431no—
174#107—861no—
175#107—861no—
176#107—861no—
177#107D17211yescharacteristic
178#107D17211yescharacteristic
179#106—21no—
180#106—861no—
181C4⋊C8—21no—
182C4⋊C8—431no—
183C4⋊C8—861no—
184#103—861no—
185#103—861no—
186#103—861no—
187#103—1721no—
188#97—861no—
189C4×C8C22×D4311yescharacteristic
190C2×Q8—431no—
191C2×Q8—861no—
192C2×Q8—1721no—
193C2×Q8—1721no—
194Q16—432no—
195Q16—861no—
196Q16—3442no—
197C2×C8—41no—
198C2×C8—861no—
199C2×C8C2×D17211yescharacteristic
200C2×C8D4×D4311yescharacteristic
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—431no—
206C4⋊C4—861no—
207C4⋊C4—861no—
208C4⋊C4—1721no—
209C4⋊C4—1721no—
210C4⋊C4—1721no—
211C4⋊C4—1721no—
212C4⋊C4—1721no—
213C4⋊C4—1721no—
214C4⋊C4—1721no—
215C4⋊C4—1721no—
216C42—861no—
217C42—1721no—
218C42—1721no—
219C42—1721no—
220C42D4×D4311yescharacteristic
221C16—41no—
222C16—862no—
223Q8—862no—
224Q8—3441no—
225Q8—3441no—
226Q8—3442no—
227Q8—1721no—
228Q8—1721no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—861no—
232C2×C4—861no—
233C2×C4—3441no—
234C2×C4—1721no—
235C2×C4—1721no—
236C2×C4#1306329511yescharacteristic
237C2×C4D8×D4311yescharacteristic
238C2×C4#1306335211yescharacteristic
239C8—21no—
240C8—81no—
241C8—1721no—
242C8Q16×D4311yescharacteristic
243C8#1306335411yescharacteristic
244C22#1458303411yescharacteristic
245C4—21no—
246C4—21no—
247C4—81no—
248C4—81no—
249C4—3441no—
250C4—1721no—
251C4—1721no—
252C4—1722no—
253C4—6881no—
254C4#1458305611yescharacteristic
255C4#1458308411yescharacteristic
256C2#1913384511yescharacteristic
257C2#1913654211yescharacteristic
258C2#1913657411yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1363C2
socle, prime radicalC22×C43#447
hypercenter#1363D43
hypocenterC43#12415
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1363

Complements

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

NH ≅ G/Ntype
90. Dic172Q16semidirect
156. C43#12415semidirect

Maximal subgroups

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

subgroupindex
#191475652
#191368822
#191367482
#191341142
#191325762
#191325642
C43×#13632
#1241543