Finite Group Databasebeta

← #25007145

Subgroups — #25007145

Order 11008.

292 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 65 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#19145249C211yesmaximal, characteristic
2#19136408C211yesmaximal, characteristic
3#19134351C211yesmaximal, characteristic
4#19132588C211yesmaximal, characteristic
5#19132584C211yesmaximal, characteristic
6#19132583C211yesmaximal, characteristic
7C43×#1342C211yesmaximal, characteristic
8#14583509—21no—
9#14583299C411yescharacteristic, complemented
10#14583277C411yescharacteristic, complemented
11#14583266—21no—
12#14583157C2211yescharacteristic
13#14583138—21no—
14#14583006C411yescharacteristic, complemented
15#14583005C411yescharacteristic, complemented
16#14582991—21no—
17#14582857—21no—
18#14582857C2211yescharacteristic
19#14582719—21no—
20#14582681C2211yescharacteristic
21#14582676—21no—
22#14582656—21no—
23#14582656C2211yescharacteristic
24C43×#470C2211yescharacteristic
25C43×#349C2211yescharacteristic
26C43×#338C2211yescharacteristic
27C2×Dic172C2×C411yescharacteristic
28C2×#10621885—21no—
29C22×C43⋊C8D411yescharacteristic
30#13063323—21no—
31#13063318—41no—
32#13063318—41no—
33#13063316—21no—
34#13063316—41no—
35#13063315—41no—
36#13063304—21no—
37Q8×Dic43—21no—
38#13063290—21no—
39#13063284—21no—
40#13063284D411yescharacteristic
41#13063265—21no—
42#13063258—21no—
43#13063257C2×C411yescharacteristic
44#13063250—21no—
45#13063249—21no—
46#13063248—21no—
47#13063235—22no—
48#13063235C2×C411yescharacteristic
49#13063235D411yescharacteristic
50C8×Dic43—22no—
51C8×Dic43C2×C411yescharacteristic
52C8×Dic43D411yescharacteristic
53C2×Q16×C43C2×C411yescharacteristic
54C2×M16×C43—21no—
55C2×M16×C43C2311yescharacteristic
56C22⋊Q8×C43—21no—
57M32×C43—21no—
58#106×C43C2×C411yescharacteristic
59#103×C43—21no—
60C2×Q8×C43—21no—
61C22×C4×C43C2×D411yescharacteristic
62C2×Dic86—21no—
63Q16×C43—41no—
64M16×C43—41no—
65M16×C43—41no—
66M16×C43—41no—
67C2×C8×C43—22no—
68C2×C8×C43C22×C411yescharacteristic
69C2×C8×C43C2×D411yescharacteristic
70C4⋊C4×C43—21no—
71C4⋊C4×C43—41no—
72C22⋊C4×C43—41no—
73C22⋊Dic43—21no—
74C22⋊Dic43—41no—
75C22⋊Dic43—41no—
76#10621885—41no—
77#10621885—41no—
78C4⋊Dic43—21no—
79C4⋊Dic43—21no—
80C4⋊Dic43—41no—
81C4⋊Dic43—41no—
82C4⋊Dic43—41no—
83Dic43⋊C4—41no—
84Dic43⋊C4—41no—
85Dic43⋊C4—41no—
86Dic43⋊C4—41no—
87Dic43⋊C4—41no—
88C4×Dic43—22no—
89C4×Dic43—41no—
90C4×Dic43—41no—
91C4×Dic43C22⋊C411yescharacteristic
92C4×Dic43C22⋊C411yescharacteristic
93C2×C43⋊C8—21no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8C22⋊C411yescharacteristic
96C2×C43⋊C8C22⋊C411yescharacteristic
97Dic172—41no—
98C16×C43—41no—
99C43⋊C16—41no—
100C23×C43AGL(1,ℤ/8)11yescharacteristic
101Q8×C43—41no—
102Q8×C43—41no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43C2×C22⋊C411yescharacteristic
108C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
109C2×Dic43—21no—
110C2×Dic43—21no—
111C2×Dic43—42no—
112C2×Dic43—41no—
113C2×Dic43—41no—
114Dic86—41no—
115Dic86—41no—
116C8×C43—21no—
117C8×C43—21no—
118C8×C43—42no—
119C43⋊C8—21no—
120C43⋊C8#10411yescharacteristic
121C43⋊C8#10411yescharacteristic
122#11771—431nomaximal, Sylow
123C22×C43—21no—
124C22×C43—41no—
125C22×C43#41811yescharacteristic
126C4×C43—21no—
127C4×C43—81no—
128C4×C43—81no—
129C4×C43#41011yescharacteristic
130C4×C43C2×#10411yescharacteristic
131Dic43—41no—
132Dic43—41no—
133Dic43—81no—
134Dic43—82no—
135Dic43—81no—
136#3177—431no—
137#2166—431no—
138#1747—431no—
139#1342—431no—
140#1342D4311yescharacteristic
141#1340—431no—
142#1340—431no—
143C2×C43—21no—
144C2×C43—41no—
145C2×C43#150511yescharacteristic
146#541—861no—
147#499—431no—
148#494—431no—
149#491—861no—
150#470—431no—
151#470C2×D4311yescharacteristic
152#467—861no—
153#441—431no—
154#441—431no—
155C4×Q16—861no—
156#405—431no—
157#405—861no—
158#364—861no—
159#349—431no—
160#349C2×D4311yescharacteristic
161#347—861no—
162#338C2×D4311yescharacteristic
163H(3,ℤ/4)—431no—
164H(3,ℤ/4)—861no—
165C43#1177111yescharacteristic, complemented, Sylow
166C2×Q16—431no—
167C2×Q16—861no—
168C2×Q16C4×D4311yescharacteristic
169C2×M16—21no—
170C2×M16C22×D4311yescharacteristic
171C22×C8—431no—
172C4⋊Q8—861no—
173#126—1721no—
174#126—1721no—
175#125—861no—
176#125—1721no—
177#125—1721no—
178C22⋊Q8—21no—
179C22⋊Q8—861no—
180C4×Q8—861no—
181C4×Q8—861no—
182#117—431no—
183#117—861no—
184M32—21no—
185M32—861no—
186#107—861no—
187#106—431no—
188#106C4×D4311yescharacteristic
189#103—21no—
190#103—861no—
191#103—861no—
192#103—861no—
193#97—431no—
194#97—431no—
195#97—862no—
196C4×C8—431no—
197C4×C8—431no—
198C4×C8—862no—
199C2×Q8—21no—
200C2×Q8—861no—
201C22×C4D4×D4311yescharacteristic
202Q16—41no—
203Q16—1721no—
204Q16—1721no—
205Q16—1721no—
206M16—41no—
207M16—41no—
208M16—41no—
209C2×C8—22no—
210C2×C8—431no—
211C2×C8—431no—
212C2×C8—861no—
213C2×C8—861no—
214C2×C8C2×C4×D4311yescharacteristic
215C2×C8D4×D4311yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—861no—
219C4⋊C4—861no—
220C4⋊C4—1721no—
221C4⋊C4—1721no—
222C4⋊C4—1721no—
223C4⋊C4—1721no—
224C4⋊C4—1721no—
225C4⋊C4—1721no—
226C4⋊C4—1721no—
227C4⋊C4—1721no—
228C22⋊C4—41no—
229C22⋊C4—861no—
230C22⋊C4—1721no—
231C22⋊C4—1721no—
232C42—431no—
233C42—431no—
234C42—862no—
235C42—1721no—
236C42—1721no—
237C16—41no—
238C16—1721no—
239C23#1306335211yescharacteristic
240Q8—41no—
241Q8—41no—
242Q8—1721no—
243Q8—1721no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—861no—
249C2×C4—861no—
250C2×C4—1722no—
251C2×C4—1721no—
252C2×C4—1721no—
253C2×C4C22⋊C4×D4311yescharacteristic
254C2×C4#1306334911yescharacteristic
255C8—21no—
256C8—21no—
257C8—42no—
258C8—431no—
259C8—431no—
260C8—861no—
261C22—21no—
262C22—41no—
263C22#1458290211yescharacteristic
264C4—21no—
265C4—81no—
266C4—81no—
267C4—3441no—
268C4—3442no—
269C4—3441no—
270C4—1721no—
271C4—1721no—
272C4#1458287111yescharacteristic
273C4#104×D4311yescharacteristic
274C2—21no—
275C2—41no—
276C2#1913310111yescharacteristic
subgroupG/H
centerC2#19133101
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1342C2
socleC2×C43#1505
prime radicalC23×C43AGL(1,ℤ/8)
cosocleC2×M16×C43C23
hypercenter#1342D43
hypocenterC43#11771
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1342

Complements

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

NH ≅ G/Ntype
9. #14583299C4semidirect
10. #14583277C4semidirect
14. #14583006C4semidirect
15. #14583005C4semidirect
165. C43#11771semidirect

Maximal subgroups

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

subgroupindex
#191452492
#191364082
#191343512
#191325882
#191325842
#191325832
C43×#13422
#1177143