Finite Group Databasebeta

← #25009908

Subgroups — #25009908

Order 11008.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#19146044C211yesmaximal, characteristic
2#19136797C211yesmaximal, characteristic
3#19136101C211yesmaximal, characteristic
4#19132614C211yesmaximal, characteristic
5#19132613C211yesmaximal, characteristic
6#19132536C211yesmaximal, characteristic
7C43×#2235C211yesmaximal, characteristic
8#14583509—21no—
9#14583208—21no—
10#14583205—21no—
11#14583155—21no—
12#14583140C2211yescharacteristic
13#14583108—21no—
14#14583107—21no—
15#14582939—21no—
16#14582925C2211yescharacteristic
17#14582724—21no—
18#14582702—21no—
19C22⋊(C43⋊C16)C2211yescharacteristic
20#14582668—21no—
21#14582664C2211yescharacteristic
22C43×#467C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C43×#367—21no—
25C43×#358—21no—
26C43×C22⋊C16C2211yescharacteristic
27C2×Dic172D411yescharacteristic
28C2×#10621885—21no—
29C2×#10621877—21no—
30C2×#10621877D411yescharacteristic
31#13063323—21no—
32#13063318—41no—
33#13063318—41no—
34#13063316—21no—
35#13063316—41no—
36#13063315—41no—
37#13063304—21no—
38Q8×Dic43—21no—
39#13063290—21no—
40#13063284D411yescharacteristic
41C2×C43⋊C16—21no—
42#13063259D411yescharacteristic
43#13063258—41no—
44#13063256—21no—
45#13063256—41no—
46Dic43⋊C8—21no—
47Dic43⋊C8—21no—
48#13063250—21no—
49#13063249—21no—
50#13063248—21no—
51C2×Q16×C43D411yescharacteristic
52C22×C8×C43C2311yescharacteristic
53C22⋊Q8×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C16×C43—21no—
56#107×C43—21no—
57#107×C43—21no—
58#107×C43D411yescharacteristic
59#103×C43—21no—
60C2×Q8×C43—21no—
61C22×C4×C43—41no—
62C22×C4×C43C2×D411yescharacteristic
63C2×Dic86—21no—
64Q16×C43—41no—
65C2×C8×C43—41no—
66C2×C8×C43C2×D411yescharacteristic
67C2×C8×C43C2×D411yescharacteristic
68C4⋊C4×C43—21no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C22⋊C4×C43—41no—
73C22⋊Dic43—21no—
74C22⋊Dic43—41no—
75#10621885—81no—
76C4⋊Dic43—21no—
77C4⋊Dic43—41no—
78C4⋊Dic43—41no—
79C4⋊Dic43D811yescharacteristic
80C4⋊Dic43D811yescharacteristic
81Dic43⋊C4—41no—
82Dic43⋊C4—41no—
83Dic43⋊C4—41no—
84Dic43⋊C4—41no—
85Dic43⋊C4—41no—
86C4×Dic43—21no—
87C4×Dic43—41no—
88C4×Dic43—41no—
89#10621877—22no—
90#10621877—41no—
91#10621877—41no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—41no—
94Dic172—41no—
95C16×C43—41no—
96C43⋊C16—41no—
97C23×C43AGL(1,ℤ/8)11yescharacteristic
98Q8×C43—41no—
99Q8×C43—41no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—81no—
105C2×C4×C43—161no—
106C2×C4×C43#12011yescharacteristic
107C2×C4×C43C2×D811yescharacteristic
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—41no—
111C2×Dic43—41no—
112Dic86—41no—
113Dic86—41no—
114C8×C43—21no—
115C8×C43—21no—
116C43⋊C8—42no—
117C43⋊C8—41no—
118#12296—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43#44711yescharacteristic
123C4×C43—21no—
124C4×C43—81no—
125C4×C43—81no—
126C4×C43—161no—
127C4×C43#45611yescharacteristic
128C4×C43#45811yescharacteristic
129Dic43—41no—
130Dic43—41no—
131Dic43—81no—
132Dic43—81no—
133#3261—431no—
134#2236—431no—
135#2235D4311yescharacteristic
136#2089—431no—
137#1350—431no—
138#1350—431no—
139#1323—431no—
140C2×C43—41no—
141C2×C43#161011yescharacteristic
142C2×C43#219311yescharacteristic
143C2×C43#219511yescharacteristic
144#541—861no—
145#479—861no—
146#479—861no—
147#470—861no—
148#467—431no—
149#467C2×D4311yescharacteristic
150#462—861no—
151#462—861no—
152#428—861no—
153C2×#107C2×D4311yescharacteristic
154#424—431no—
155#367—21no—
156#366—861no—
157#358—21no—
158#358—861no—
159C22⋊C16—431no—
160C22⋊C16C2×D4311yescharacteristic
161#343—861no—
162#341—431no—
163C43#1229611yescharacteristic, complemented, Sylow
164C2×Q16—431no—
165C2×Q16—861no—
166C2×Q16C22⋊D4311yescharacteristic
167C2×M16—431no—
168C2×M16—861no—
169C22×C8C22×D4311yescharacteristic
170C4⋊Q8—861no—
171#126—1721no—
172#126—1721no—
173#125—861no—
174#125—1721no—
175#125—1721no—
176C22⋊Q8—21no—
177C22⋊Q8—861no—
178C4×Q8—861no—
179C4×Q8—861no—
180#117—431no—
181C2×C4⋊C4—21no—
182C2×C16—21no—
183C2×C16—861no—
184#107—21no—
185#107—21no—
186#107—431no—
187#107—1721no—
188#107C22⋊D4311yescharacteristic
189#106—861no—
190#106—1721no—
191C4⋊C8—861no—
192C4⋊C8—861no—
193#103—21no—
194#103—861no—
195#103—861no—
196#103—861no—
197C2×Q8—21no—
198C2×Q8—861no—
199C22×C4—41no—
200C22×C4D4×D4311yescharacteristic
201Q16—41no—
202Q16—3441no—
203Q16—1721no—
204M16—862no—
205M16—1721no—
206M16—1721no—
207C2×C8—41no—
208C2×C8—861no—
209C2×C8—1721no—
210C2×C8D4×D4311yescharacteristic
211C2×C8C2×C22⋊D4311yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—431no—
217C4⋊C4—431no—
218C4⋊C4—861no—
219C4⋊C4—1721no—
220C4⋊C4—1721no—
221C4⋊C4—1721no—
222C4⋊C4—1721no—
223C4⋊C4—1721no—
224C4⋊C4—1721no—
225C4⋊C4—1721no—
226C22⋊C4—41no—
227C22⋊C4—861no—
228C22⋊C4—1721no—
229C42—861no—
230C42—1721no—
231C42—1721no—
232C16—41no—
233C16—1721no—
234C23#1306334911yescharacteristic
235Q8—41no—
236Q8—41no—
237Q8—1721no—
238Q8—1721no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—161no—
245C2×C4—861no—
246C2×C4—861no—
247C2×C4—1721no—
248C2×C4—1721no—
249C2×C4#1306329311yescharacteristic
250C2×C4D8×D4311yescharacteristic
251C8—21no—
252C8—21no—
253C8—1722no—
254C8—1721no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22#1458303111yescharacteristic
259C4—21no—
260C4—81no—
261C4—81no—
262C4—161no—
263C4—3441no—
264C4—3441no—
265C4—1721no—
266C4—1721no—
267C4#1458308011yescharacteristic
268C4#1458308811yescharacteristic
269C2—41no—
270C2#1913359611yescharacteristic
271C2#1913655811yescharacteristic
272C2#1913657011yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2235C2
socleC22×C43#447
prime radicalC23×C43AGL(1,ℤ/8)
hypercenter#2235D43
hypocenterC43#12296
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
163. C43#12296semidirect

Maximal subgroups

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

subgroupindex
#191460442
#191367972
#191361012
#191326142
#191326132
#191325362
C43×#22352
#1229643