Finite Group Databasebeta

← #25084525

Subgroups — #25084525

Order 11008.

1050 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145509C212yesmaximal, complemented
2#19145172C211yesmaximal, characteristic, complemented
3#19145046C212yesmaximal, complemented
4#493×D43C211yesmaximal, characteristic, complemented
5#19134262C212yesmaximal, complemented
6#19134260C212yesmaximal, complemented
7#19134209C211yesmaximal, characteristic, complemented
8#19134187C211yesmaximal, characteristic, complemented
9#19134184C211yesmaximal, characteristic, complemented
10C8×#10621872C211yesmaximal, characteristic, complemented
11C43×#1712C211yesmaximal, characteristic, complemented
12C2×#13063349—24no—
13C2×D8×D43—22no—
14#14583447C2212yes—
15#127×D43C2212yes—
16#14583304C2211yescharacteristic, complemented
17#14583287—24no—
18#14583276C2211yescharacteristic
19#14583275C2212yes—
20#14583275C2212yescomplemented
21#14583275C2212yescomplemented
22#14583274—22no—
23#14583272C2212yescomplemented
24#14583271C2212yescomplemented
25#14583246C2212yescomplemented
26#14583245C2212yescomplemented
27#14583245C2212yescomplemented
28#14583132—22no—
29#14583092—24no—
30#14583031—24no—
31D8×Dic43—22no—
32#14582950C2211yescharacteristic
33C4×#10621872C2211yescharacteristic
34C4×C8×D43C2211yescharacteristic
35#14582621C2211yescharacteristic, complemented
36#14582620C2211yescharacteristic, complemented
37C8×C43⋊C8C2211yescharacteristic, complemented
38C43×#493C2211yescharacteristic
39C43×#493C2211yescharacteristic, complemented
40C43×#493C2212yescomplemented
41C43×#493C2212yescomplemented
42C82×C43C2211yescharacteristic, complemented
43C2×#10621900—22no—
44C2×D4×D43—22no—
45C2×D4×D43—22no—
46C2×D4×D43—22no—
47#13063349—416no—
48C2×#10621873—24no—
49C2×#10621883—24no—
50C2×D344—22no—
51C2×#10621882—24no—
52C2×#10621882—24no—
53C2×#10621882—24no—
54D8×D43—48no—
55C2×#10621872D412yes—
56C2×C8×D43D412yes—
57#13063325C2312yes—
58#13063322C2312yes—
59#13063321—22no—
60#13063321—22no—
61#13063321—22no—
62#13063312—22no—
63#13063296—22no—
64#13063296—22no—
65D4×Dic43—22no—
66D4×Dic43—22no—
67C42×D43C2311yescharacteristic
68#13063259—22no—
69Dic43⋊C8D412yes—
70#13063247—24no—
71#13063246—24no—
72#13063246—24no—
73(C2×D43)⋊C8D412yes—
74#13063235D412yes—
75C4×C43⋊C8C2311yescharacteristic
76C4×C43⋊C8C2311yescharacteristic
77C4×C43⋊C8C2311yescharacteristic
78C8×Dic43D412yes—
79C2×D8×C43—22no—
80C2×D8×C43—22no—
81C2×D8×C43—24no—
82C2×D8×C43—24no—
83#127×C43C2312yes—
84#127×C43C2312yes—
85C4×C8×C43C2311yescharacteristic
86C4×C8×C43C2311yescharacteristic
87C4×C8×C43C2311yescharacteristic
88C23×D43—42no—
89C2×D4×C43—22no—
90C2×D4×C43—22no—
91C2×D4×C43—22no—
92C2×D4×C43—22no—
93C2×D4×C43—22no—
94C2×D4×C43—22no—
95C2×C22⋊D43—42no—
96C2×C22⋊D43—42no—
97C2×C22⋊D43—42no—
98C2×C22⋊D43—42no—
99C22×Dic43—42no—
100#10621900—48no—
101D4×D43—48no—
102D4×D43—48no—
103D4×D43—84no—
104C2×D172—22no—
105C2×D172—22no—
106C2×D172—22no—
107C2×C4×D43C2×D411yescharacteristic
108C2×C4×D43C2×D411yescharacteristic
109C2×C4×D43C2×D411yescharacteristic
110C2×Dic86—22no—
111D8×C43—48no—
112D8×C43—44no—
113D8×C43—44no—
114D8×C43—84no—
115C2×C8×C43C2×D412yes—
116C2×C8×C43C2×D412yes—
117C2×C8×C43C2×D412yes—
118C42×C43C2411yescharacteristic
119C22⋊Dic43—42no—
120C22⋊Dic43—42no—
121#10621883—48no—
122#10621882—48no—
123#10621882—48no—
124#10621882—84no—
125C4⋊Dic43—22no—
126C4⋊Dic43—22no—
127C4×Dic43C2×D411yescharacteristic
128C4×Dic43C2×D411yescharacteristic
129C4×Dic43C2×D411yescharacteristic
130C2×C43⋊C8C2×D412yes—
131C2×C43⋊C8C2×D412yes—
132C2×C43⋊C8C2×D412yes—
133D344—44no—
134#10621873—48no—
135#10621872D818yescomplemented
136C8×D43—24no—
137C23×C43—42no—
138C23×C43—42no—
139C22×D43—42no—
140C22×D43—84no—
141C22×D43—84no—
142C22×D43—84no—
143C22×D43#12711yescharacteristic
144D4×C43—44no—
145D4×C43—44no—
146D4×C43—44no—
147D4×C43—44no—
148D4×C43—44no—
149D4×C43—44no—
150C2×C4×C43C22×D411yescharacteristic
151C2×C4×C43C22×D411yescharacteristic
152C2×C4×C43C22×D411yescharacteristic
153C22⋊D43—84no—
154C22⋊D43—84no—
155C22⋊D43—84no—
156C22⋊D43—84no—
157C2×Dic43—42no—
158C2×Dic43—84no—
159C2×Dic43#12711yescharacteristic
160C2×Dic43#12711yescharacteristic
161C2×Dic43#12711yescharacteristic
162D172—44no—
163D172—44no—
164D172—44no—
165C4×D43—22no—
166C4×D43—22no—
167C4×D43C2×D814yes—
168Dic86—44no—
169C8×C43—22no—
170C8×C43C2×D814yescomplemented
171C8×C43AGL(1,ℤ/8)14yescomplemented
172C43⋊C8—22no—
173C43⋊C8—22no—
174C43⋊C8C2×D814yescomplemented
175#19629—431nomaximal, Sylow
176C22×C43—82no—
177C22×C43—82no—
178C22×C43—82no—
179C22×C43—82no—
180C22×C43—82no—
181C22×C43—82no—
182C22×C43C2×#12711yescharacteristic
183C2×D43—21no—
184C2×D43—21no—
185C2×D43—82no—
186C2×D43—82no—
187C2×D43—82no—
188C2×D43—168no—
189C2×D43#49312yes—
190C4×C43C22×D812yes—
191C4×C43C2×AGL(1,ℤ/8)12yes—
192C4×C43#57612yes—
193Dic43—21no—
194Dic43—21no—
195Dic43—82no—
196Dic43#49312yes—
197#3205—432no—
198#3169—431no—
199#3151—432no—
200C2×#493—431no—
201#1721—432no—
202#1721—432no—
203#1712—431no—
204#1712D4311yescharacteristic, complemented
205#1706—431no—
206#1706—431no—
207C8×M16—431no—
208C2×C43—162no—
209C2×C43—162no—
210C2×C43C2×#49311yescharacteristic
211C2×C43#315111yescharacteristic
212C2×C43#315511yescharacteristic
213D43—22no—
214D43—162no—
215C2×AGL(1,ℤ/8)—864no—
216C22×D8—862no—
217#532—432no—
218C2×#127—432no—
219#500—431no—
220#496—864no—
221#493—432no—
222#493—432no—
223#493—432no—
224#493—431no—
225#493—862no—
226#493C2×D4311yescharacteristic
227#493C2×D4312yescomplemented
228#493C2×D4311yescharacteristic, complemented
229#493C2×D4312yescomplemented
230#492—432no—
231#492—432no—
232#486—432no—
233#486—432no—
234#486—432no—
235#466—862no—
236#459—864no—
237#447—864no—
238C4×D8—862no—
239#431—431no—
240C4×M16—431no—
241C2×C4×C8—431no—
242#322—431no—
243#322—431no—
244C82—431no—
245C82C2×D4311yescharacteristic, complemented
246C43#1962911yescharacteristic, complemented, Sylow
247C2×#41—862no—
248C22×D4—862no—
249C22×D4—862no—
250C22×D4—862no—
251AGL(1,ℤ/8)—17216no—
252C2×SD16—864no—
253C2×SD16—864no—
254C2×D8—22no—
255C2×D8—24no—
256C2×D8—22no—
257C2×D8—24no—
258C2×D8—864no—
259C2×D8—864no—
260C2×D8—864no—
261C2×D8—862no—
262C2×D8—1728no—
263C2×M16—432no—
264C22×C8—432no—
265C4⋊Q8—432no—
266#127—432no—
267#127—862no—
268#127—862no—
269#127—862no—
270#127C22×D4312yes—
271#127C22×D4312yes—
272#124—862no—
273#121—862no—
274#121—862no—
275C4×D4—862no—
276C4×D4—862no—
277C2×C42—431no—
278#107—862no—
279C4⋊C8—432no—
280#102—864no—
281#102—864no—
282#102—864no—
283C22⋊C8—432no—
284#97—432no—
285C4×C8—432no—
286C4×C8—431no—
287C4×C8—431no—
288C4×C8—431no—
289C4×C8C22×D4311yescharacteristic
290C4×C8C22×D4311yescharacteristic
291C4×C8C22×D4311yescharacteristic
292C24—1722no—
293#41—1728no—
294C2×Q8—862no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—862no—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—3444no—
305C2×D4—1728no—
306C2×D4—1722no—
307C2×D4—1722no—
308C2×D4—1722no—
309C2×D4—1728no—
310C2×D4—1722no—
311C22×C4—431no—
312C22×C4—431no—
313C22×C4—431no—
314C22×C4—1722no—
315SD16—1728no—
316SD16—1728no—
317D8—48no—
318D8—44no—
319D8—44no—
320D8—84no—
321D8—3444no—
322D8—1728no—
323D8—1728no—
324D8—1724no—
325M16—438no—
326C2×C8—432no—
327C2×C8—432no—
328C2×C8—432no—
329C2×C8—864no—
330C2×C8D4×D4312yes—
331C2×C8D4×D4312yes—
332C2×C8D4×D4312yes—
333C4⋊C4—862no—
334C4⋊C4—862no—
335C22⋊C4—1722no—
336C22⋊C4—1722no—
337C42—431no—
338C42—431no—
339C42—431no—
340C42C23×D4311yescharacteristic
341C23—42no—
342C23—42no—
343C23—431no—
344C23—3444no—
345C23—3444no—
346C23—3444no—
347C23—1722no—
348Q8—1724no—
349D4—44no—
350D4—44no—
351D4—44no—
352D4—44no—
353D4—44no—
354D4—44no—
355D4—3444no—
356D4—3444no—
357D4—3444no—
358D4—3444no—
359D4—1724no—
360D4—1724no—
361D4—1724no—
362C2×C4—431no—
363C2×C4—434no—
364C2×C4—431no—
365C2×C4—431no—
366C2×C4—862no—
367C2×C4—862no—
368C2×C4—3444no—
369C2×C4—1722no—
370C2×C4C2×D4×D4311yescharacteristic
371C2×C4C2×D4×D4311yescharacteristic
372C2×C4C2×D4×D4311yescharacteristic
373C8—22no—
374C8—434no—
375C8—862no—
376C8—862no—
377C8D8×D4314yescomplemented
378C8#1306334914yescomplemented
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—432no—
386C22—861no—
387C22—861no—
388C22—3442no—
389C22—3442no—
390C22—3442no—
391C22—6888no—
392C22#127×D4311yescharacteristic
393C4—432no—
394C4—861no—
395C4—861no—
396C4—3442no—
397C4C2×D8×D4312yes—
398C4C2×#1306334912yes—
399C4#1458370012yes—
400C2—162no—
401C2—162no—
402C2—862no—
403C2—6882no—
404C2#493×D4311yescharacteristic
405C2#1914504611yescharacteristic
406C2#1914507511yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1712C2
socleC22×C43C2×#127
hypercenter#1712D43
hypocenterC43#19629
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1712

Complements

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

NH ≅ G/Ntype
1. #19145509C2semidirect
2. #19145172C2semidirect
3. #19145046C2semidirect
4. #493×D43C2semidirect
5. #19134262C2semidirect
6. #19134260C2semidirect
7. #19134209C2semidirect
8. #19134187C2semidirect
9. #19134184C2semidirect
10. C8×#10621872C2semidirect
11. C43×#1712C2semidirect
16. #14583304C22semidirect
20. #14583275C22semidirect
21. #14583275C22semidirect
23. #14583272C22semidirect
24. #14583271C22semidirect
25. #14583246C22semidirect
26. #14583245C22semidirect
27. #14583245C22semidirect
35. #14582621C22semidirect
36. #14582620C22semidirect
37. C8×C43⋊C8C22semidirect
39. C43×#493C22semidirect
40. C43×#493C22semidirect
41. C43×#493C22semidirect
42. C82×C43C22semidirect
135. #10621872D8semidirect
170. C8×C43C2×D8semidirect
171. C8×C43AGL(1,ℤ/8)semidirect
174. C43⋊C8C2×D8semidirect
204. #1712D43semidirect
227. #493C2×D43semidirect
228. #493C2×D43semidirect
229. #493C2×D43semidirect
245. C82C2×D43semidirect
246. C43#19629semidirect
377. C8D8×D43semidirect
378. C8#13063349semidirect

Maximal subgroups

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

subgroupindex
#191455092
#191451722
#191450462
#493×D432
#191342622
#191342602
#191342092
#191341872
#191341842
C8×#106218722
C43×#17122
#1962943