Finite Group Databasebeta

← #24995951

Subgroups — #24995951

Order 11008.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144920C211yesmaximal, characteristic
2#19134460C211yesmaximal, characteristic, complemented
3#19133341C211yesmaximal, characteristic, complemented
4#19133094C211yesmaximal, characteristic, complemented
5#19133091C211yesmaximal, characteristic
6#19132993C211yesmaximal, characteristic
7C43×#1481C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583256—21no—
10#14583256—21no—
11#14583251C411yescharacteristic, complemented
12#14583251C411yescharacteristic, complemented
13#14583247C411yescharacteristic, complemented
14#14583247C411yescharacteristic, complemented
15#14582952C2211yescharacteristic
16#14582893—21no—
17#14582893—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19C2×C8×Dic43—21no—
20C4×C4⋊Dic43C2211yescharacteristic
21#14582653—21no—
22#14582651—21no—
23#14582649—21no—
24#14582636—22no—
25#14582634—22no—
26#14582626—22no—
27C43×#533C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C2×#10621898—21no—
32C22×C43⋊C8D411yescharacteristic
33C22×C43⋊C8D411yescharacteristic
34#13063325C2×C411yescharacteristic
35#13063322C2×C411yescharacteristic
36#13063313—21no—
37#13063299—21no—
38#13063299—21no—
39C4×D172—21no—
40C4×D172—21no—
41C2×C4⋊Dic43—21no—
42C2×C4×Dic43—21no—
43C4⋊(C43⋊C8)—21no—
44#13063248—21no—
45#13063248—21no—
46#13063248—21no—
47#13063248—21no—
48#13063245—21no—
49#13063245—21no—
50#13063245—21no—
51#13063245—21no—
52C22⋊(C43⋊C8)—21no—
53C4×C43⋊C8—21no—
54C4×C43⋊C8C2×C411yescharacteristic
55C4×C43⋊C8C2×C411yescharacteristic
56C4×C43⋊C8D411yescharacteristic
57C4×C43⋊C8D411yescharacteristic
58C8×Dic43—42no—
59C43⋊#95D412yes—
60C22×C8×C43—21no—
61C4⋊Q8×C43C2×C411yescharacteristic
62C4⋊Q8×C43C2×C411yescharacteristic
63#125×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68#117×C43—21no—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43D412yes—
73C22⋊C8×C43—21no—
74C4×C8×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C2×C22⋊D43—41no—
81C22×Dic43—22no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—21no—
89C2×C4×D43—41no—
90C2×Dic86—21no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C22⋊C4×C43—41no—
102C42×C43—41no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—41no—
109C4⋊Dic43—24no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4×Dic43—41no—
113C4×Dic43—41no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8C22⋊C411yescharacteristic
120C2×C43⋊C8C22⋊C411yescharacteristic
121C2×C43⋊C8C22⋊C411yescharacteristic
122C2×C43⋊C8C22⋊C411yescharacteristic
123C23×C43#12111yescharacteristic
124C22×D43—41no—
125Q8×C43—42no—
126Q8×C43—81no—
127C2×C4×C43—22no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12411yescharacteristic
136C2×C4×C43#12711yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C22⋊D43—81no—
142C22⋊D43—81no—
143C2×Dic43—24no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43—41no—
147D172—41no—
148D172—41no—
149D172—42no—
150D172—81no—
151C4×D43—81no—
152C4×D43—81no—
153Dic86—41no—
154Dic86—41no—
155C8×C43—42no—
156C8×C43—81no—
157C43⋊C8—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C43⋊C8—81no—
162#9751—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43#39011yescharacteristic
166C22×C43#46311yescharacteristic
167C22×C43#46411yescharacteristic
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—81no—
175C4×C43—81no—
176C4×C43#41611yescharacteristic
177C4×C43#41711yescharacteristic
178C4×C43#44312yes—
179C4×C43#46311yescharacteristic
180C4×C43#46411yescharacteristic
181Dic43—44no—
182Dic43—81no—
183#3131—431no—
184C8×C4⋊C4—431no—
185#1564—431no—
186#1503—431no—
187#1502—431no—
188#1481D4311yescharacteristic, complemented
189#1480—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43#197411yescharacteristic
193C2×C43#197611yescharacteristic
194C2×C43#198311yescharacteristic
195D43—161no—
196#533C2×D4311yescharacteristic
197#532—431no—
198#488—861no—
199#488—861no—
200#487—431no—
201#487—431no—
202#486—431no—
203#486—431no—
204#431—431no—
205#431C2×D4311yescharacteristic
206C2×C4⋊C8C2×D4311yescharacteristic
207#416—861no—
208#416—861no—
209C2×C4×C8—431no—
210C2×C4×C8—861no—
211C4×C4⋊C4—431no—
212#336—861no—
213#335—861no—
214#334—861no—
215#328—862no—
216#327—862no—
217Q8⋊C8—22no—
218D4⋊C8—862no—
219C43#975111yescharacteristic, complemented, Sylow
220C2×#41—861no—
221C22×C8—21no—
222C22×C8—431no—
223C22×C8—431no—
224C4⋊Q8—431no—
225C4⋊Q8C4×D4311yescharacteristic
226C4⋊Q8C4×D4311yescharacteristic
227#127—431no—
228#125—21no—
229#124—861no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—861no—
233#121—861no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—861no—
237C4×D4—861no—
238#117—21no—
239C2×C4⋊C4—861no—
240C2×C42—861no—
241C2×C42C22×D4311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—861no—
245C4⋊C8C22⋊D4312yes—
246#103—861no—
247#103—861no—
248#103—861no—
249#103—861no—
250#102—861no—
251#102—861no—
252#102—861no—
253#102—861no—
254C22⋊C8—21no—
255C22⋊C8—861no—
256C4×C8—21no—
257C4×C8—431no—
258C4×C8—431no—
259C4×C8—431no—
260C4×C8—431no—
261C4×C8—861no—
262C4×C8—1722no—
263#95—432no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267#41—1721no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—1721no—
275C22×C4—862no—
276C22×C4—1721no—
277C22×C4#1062189811yescharacteristic
278C22×C4D4×D4311yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—431no—
285C2×C8—431no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—861no—
291C2×C8—861no—
292C2×C8—1721no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—864no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C22⋊C4—41no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C42—41no—
306C42—1721no—
307C42—1721no—
308C42C2×C4×D4311yescharacteristic
309C42D4×D4311yescharacteristic
310C42#1062190011yescharacteristic
311C42C2×C22⋊D4311yescharacteristic
312C23—1721no—
313C23#1306329811yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—1721no—
317Q8—1721no—
318D4—3441no—
319D4—3441no—
320D4—3441no—
321D4—1721no—
322D4—1721no—
323D4—1722no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—864no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—1721no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4C22⋊C4×D4311yescharacteristic
335C2×C4(C22⋊D43)⋊C411yescharacteristic
336C2×C4C4×C22⋊D4311yescharacteristic
337C2×C4#1306329711yescharacteristic
338C2×C4#1306331111yescharacteristic
339C2×C4#1306332111yescharacteristic
340C2×C4#1306334611yescharacteristic
341C2×C4#1306334811yescharacteristic
342C2×C4#1306335211yescharacteristic
343C2×C4#1306335711yescharacteristic
344C8—42no—
345C8—81no—
346C8—861no—
347C8—861no—
348C8—861no—
349C8—861no—
350C8—3441no—
351C22—21no—
352C22—21no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22#1458279911yescharacteristic
357C22#1458311711yescharacteristic
358C22#1458312411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—3441no—
365C4—1724no—
366C4#1458289411yescharacteristic
367C4#1458289911yescharacteristic
368C4#1458301412yes—
369C4#1458311611yescharacteristic
370C4#1458312311yescharacteristic
371C2—21no—
372C2—21no—
373C2—6881no—
374C2#1913548211yescharacteristic
375C2#1913549211yescharacteristic
376C2#1913552411yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1481C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1481D43
hypocenterC43#9751
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #19134460C2semidirect
3. #19133341C2semidirect
4. #19133094C2semidirect
7. C43×#1481C2semidirect
11. #14583251C4semidirect
12. #14583251C4semidirect
13. #14583247C4semidirect
14. #14583247C4semidirect
188. #1481D43semidirect
219. C43#9751semidirect

Maximal subgroups

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

subgroupindex
#191449202
#191344602
#191333412
#191330942
#191330912
#191329932
C43×#14812
#975143