Finite Group Databasebeta

← #25072677

Subgroups — #25072677

Order 11008.

1068 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C2×#14583635C211yesmaximal, characteristic, complemented
2#19144713C212yesmaximal, complemented
3#19133714C214yesmaximal, complemented
4#19133652C214yesmaximal, complemented
5#19133309C211yesmaximal, characteristic, complemented
6#19133043C212yesmaximal, complemented
7C43×#3151C211yesmaximal, characteristic
8#14583635—24no—
9#14583635—22no—
10#14583635C2214yes—
11C2×#13063312—22no—
12C2×#13063306—22no—
13C2×C4×Dic86C2212yes—
14C2×D4×Dic43—22no—
15#14583210—22no—
16#14583191C2214yescomplemented
17#14583096C2214yescomplemented
18#14583037—22no—
19#14582999—24no—
20#14582956C2212yes—
21#14582643C2214yes—
22#14582631C2218yescomplemented
23C2×AGL(1,ℤ/8)×C43—22no—
24C43×#532C2211yescharacteristic
25C2×#127×C43C2211yescharacteristic
26C43×#496—22no—
27C43×#493C2212yes—
28C43×#492C2212yes—
29C4×M16×C43C2211yescharacteristic
30C22×Dic86D412yes—
31C23×Dic43—22no—
32C2×#10621883—24no—
33#13063312—28no—
34#13063312—28no—
35#13063306—28no—
36#13063306—28no—
37C4×Dic86—22no—
38C4×Dic86—22no—
39C4×Dic86D414yes—
40C4×Dic86C2314yes—
41D4×Dic43—28no—
42D4×Dic43—28no—
43C2×C4⋊Dic43D412yes—
44C2×Dic43⋊C4—22no—
45C2×C22⋊Dic43—24no—
46C2×C22⋊Dic43—22no—
47C2×C4×Dic43—22no—
48#13063258—24no—
49C4⋊(C43⋊C8)C2314yes—
50#13063248—24no—
51#13063246—24no—
52C22⋊(C43⋊C8)—22no—
53#13063236—22no—
54C2×#41×C43—21no—
55C22×D4×C43—22no—
56C22×D4×C43D412yes—
57AGL(1,ℤ/8)×C43—48no—
58C2×SD16×C43—24no—
59C2×D8×C43—24no—
60C2×M16×C43—21no—
61C4⋊Q8×C43C2311yescharacteristic
62#127×C43—22no—
63#127×C43D412yes—
64#127×C43C2311yescharacteristic
65#127×C43C2312yes—
66#124×C43—21no—
67#121×C43—22no—
68C4×D4×C43—22no—
69C2×C42×C43C2311yescharacteristic
70#97×C43—21no—
71C4×C8×C43C2312yes—
72C24×C43—22no—
73#41×C43—44no—
74C2×Q8×C43—21no—
75C2×D4×C43—24no—
76C2×D4×C43—22no—
77C2×D4×C43—24no—
78C2×D4×C43—22no—
79C2×D4×C43—21no—
80C2×D4×C43—48no—
81C2×D4×C43—41no—
82C2×D4×C43—44no—
83C2×D4×C43C2×D414yes—
84C22×C4×C43—41no—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D411yescharacteristic
87C22×Dic43—28no—
88C22×Dic43—22no—
89C22×Dic43—22no—
90C22×Dic43—84no—
91C2×Dic86—22no—
92C2×Dic86—44no—
93C2×Dic86C2×D414yes—
94SD16×C43—48no—
95D8×C43—48no—
96M16×C43—24no—
97C2×C8×C43—22no—
98C4⋊C4×C43—22no—
99C22⋊C4×C43—42no—
100C42×C43C2×D412yes—
101C42×C43C2×D411yescharacteristic
102C42×C43C2411yescharacteristic
103C22⋊Dic43—216no—
104C22⋊Dic43—28no—
105#10621883—48no—
106C4⋊Dic43—22no—
107C4⋊Dic43C2×D414yes—
108Dic43⋊C4—24no—
109Dic43⋊C4—24no—
110C4×Dic43—24no—
111C4×Dic43—24no—
112C2×C43⋊C8—24no—
113C23×C43—24no—
114C23×C43—48no—
115C23×C43—44no—
116C23×C43—41no—
117C23×C43#12011yescharacteristic
118Q8×C43—42no—
119D4×C43—44no—
120D4×C43—48no—
121D4×C43—42no—
122D4×C43—48no—
123D4×C43—44no—
124D4×C43—82no—
125D4×C43—82no—
126C2×C4×C43—22no—
127C2×C4×C43—24no—
128C2×C4×C43—41no—
129C2×C4×C43—82no—
130C2×C4×C43#12012yes—
131C2×C4×C43#12011yescharacteristic
132C2×C4×C43C22×D412yes—
133C2×C4×C43C22×D411yescharacteristic
134C2×Dic43—24no—
135C2×Dic43—24no—
136C2×Dic43—44no—
137C2×Dic43—44no—
138C2×Dic43—88no—
139Dic86—24no—
140Dic86—24no—
141Dic86—44no—
142C8×C43—24no—
143C43⋊C8—44no—
144#18526—431nomaximal, Sylow
145C22×C43—22no—
146C22×C43—48no—
147C22×C43—44no—
148C22×C43—88no—
149C22×C43—82no—
150C22×C43—81no—
151C22×C43#45312yes—
152C22×C43C2×#12011yescharacteristic
153C4×C43—22no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—81no—
157C4×C43#57514yes—
158Dic43—44no—
159Dic43—44no—
160C2×#559—431no—
161#3151D4311yescharacteristic
162#3112—432no—
163#1630—434no—
164#1620—434no—
165#1555—431no—
166#1491—432no—
167C2×C43—22no—
168C2×C43—84no—
169C2×C43—161no—
170C2×C43#300512yes—
171C2×C43C2×#45311yescharacteristic
172C2×AGL(1,ℤ/8)—22no—
173#559—434no—
174#559—864no—
175#559—862no—
176#532C2×D4311yescharacteristic
177C2×#127C2×D4311yescharacteristic
178C2×#124—862no—
179C2×#123—862no—
180C2×C4×Q8—432no—
181C2×C4×D4—862no—
182#496—22no—
183#493C2×D4312yes—
184#492C2×D4312yes—
185#480—862no—
186#477—434no—
187#460—434no—
188#448—862no—
189#440—864no—
190#432—432no—
191C4×M16C2×D4311yescharacteristic
192#331—434no—
193Q8⋊C8—438no—
194C43#1852611yescharacteristic, complemented, Sylow
195C2×#41—21no—
196C22×Q8—432no—
197C22×D4—22no—
198C22×D4C22⋊D4312yes—
199C23×C4—862no—
200AGL(1,ℤ/8)—48no—
201C2×SD16—24no—
202C2×SD16—864no—
203C2×D8—24no—
204C2×M16—21no—
205C4⋊Q8C22×D4311yescharacteristic
206#127—22no—
207#127C22⋊D4312yes—
208#127C22×D4311yescharacteristic
209#127C22×D4312yes—
210#124—21no—
211#124—868no—
212#124—868no—
213#123—868no—
214#123—868no—
215#121—22no—
216C4×Q8—434no—
217C4×Q8—434no—
218C4×Q8—862no—
219C4×Q8—862no—
220C4×D4—22no—
221C4×D4—868no—
222C4×D4—868no—
223C2×C4⋊C4—432no—
224C2×C4⋊C4—862no—
225C2×C22⋊C4—864no—
226C2×C22⋊C4—862no—
227C2×C42—862no—
228C2×C42C22×D4311yescharacteristic
229#107—864no—
230C4⋊C8—434no—
231#103—864no—
232#102—864no—
233C22⋊C8—862no—
234#97—21no—
235#97—862no—
236C4×C8C22×D4312yes—
237C24—22no—
238#41—44no—
239C2×Q8—21no—
240C2×Q8—434no—
241C2×Q8—862no—
242C2×Q8—1724no—
243C2×D4—24no—
244C2×D4—22no—
245C2×D4—24no—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—48no—
249C2×D4—44no—
250C2×D4—41no—
251C2×D4C2×C22⋊D4314yes—
252C22×C4—41no—
253C22×C4—868no—
254C22×C4—862no—
255C22×C4—862no—
256C22×C4—3444no—
257C22×C4D4×D4312yes—
258C22×C4C2×C22⋊D4311yescharacteristic
259SD16—48no—
260SD16—1728no—
261D8—48no—
262M16—24no—
263C2×C8—22no—
264C2×C8—864no—
265C4⋊C4—22no—
266C4⋊C4—434no—
267C4⋊C4—862no—
268C4⋊C4—864no—
269C4⋊C4—864no—
270C22⋊C4—42no—
271C22⋊C4—8616no—
272C22⋊C4—868no—
273C42—864no—
274C42—864no—
275C42D4×D4312yes—
276C42C2×C22⋊D4311yescharacteristic
277C42C23×D4311yescharacteristic
278C23—24no—
279C23—48no—
280C23—44no—
281C23—41no—
282C23#1306329311yescharacteristic
283Q8—42no—
284Q8—864no—
285Q8—864no—
286Q8—1724no—
287D4—44no—
288D4—48no—
289D4—42no—
290D4—48no—
291D4—44no—
292D4—82no—
293D4—82no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—864no—
299C2×C4—864no—
300C2×C4—3448no—
301C2×C4—1724no—
302C2×C4—1724no—
303C2×C4#1306329312yes—
304C2×C4#1306329311yescharacteristic
305C2×C4C2×D4×D4312yes—
306C2×C4C22×C22⋊D4311yescharacteristic
307C8—24no—
308C8—1724no—
309C22—22no—
310C22—48no—
311C22—44no—
312C22—88no—
313C22—82no—
314C22—81no—
315C22#1458306612yes—
316C22C2×#1306329311yescharacteristic
317C4—22no—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—1724no—
322C4—1724no—
323C4#1458369514yes—
324C2—22no—
325C2—84no—
326C2—161no—
327C2#1914383412yes—
328C2C2×#1458306611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3151C2
socleC22×C43C2×#120
hypercenter#3151D43
hypocenterC43#18526
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. C2×#14583635C2semidirect
2. #19144713C2semidirect
3. #19133714C2semidirect
4. #19133652C2semidirect
5. #19133309C2semidirect
6. #19133043C2semidirect
16. #14583191C22semidirect
17. #14583096C22semidirect
22. #14582631C22semidirect
194. C43#18526semidirect

Maximal subgroups

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

subgroupindex
C2×#145836352
#191447132
#191337142
#191336522
#191333092
#191330432
C43×#31512
#1852643