Finite Group Databasebeta

← #25253415

Subgroups — #25253415

Order 11008.

654 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146939C211yesmaximal, characteristic, complemented
2#19146269C211yesmaximal, characteristic, complemented
3#19136817C211yesmaximal, characteristic, complemented
4#19136777C211yesmaximal, characteristic, complemented
5#19136773C211yesmaximal, characteristic, complemented
6#19136731C211yesmaximal, characteristic, complemented
7#19136680C211yesmaximal, characteristic, complemented
8#19136628C211yesmaximal, characteristic, complemented
9#19136506C211yesmaximal, characteristic, complemented
10#19136505C211yesmaximal, characteristic, complemented
11#19136439C211yesmaximal, characteristic, complemented
12C16×C22⋊D43C211yesmaximal, characteristic, complemented
13C2×#14582701C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2215C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583549—21no—
19#14583533—21no—
20C2×#13063266C2211yescharacteristic
21C2×#13063266C2211yescharacteristic, complemented
22C2×C16×D43C2211yescharacteristic, complemented
23#14583303C2211yescharacteristic, complemented
24#14583274C2211yescharacteristic
25#14583211—21no—
26#14583210—21no—
27#14583177—21no—
28#14583136C2211yescharacteristic
29#14583132C2211yescharacteristic, complemented
30#14583093—21no—
31#14583034—21no—
32#14583032—21no—
33D8×Dic43C2211yescharacteristic, complemented
34#14582981C2211yescharacteristic
35C8×C22⋊D43C2211yescharacteristic
36C2×#13063259C2211yescharacteristic, complemented
37#107×D43C2211yescharacteristic, complemented
38#14582724C2211yescharacteristic, complemented
39#14582724C2211yescharacteristic, complemented
40Dic43⋊C16C2211yescharacteristic, complemented
41#14582701C2211yescharacteristic
42#14582701C2211yescharacteristic
43#14582701C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic, complemented
46#14582700C2211yescharacteristic, complemented
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic, complemented
49C22⋊(C43⋊C16)C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C2×D16×C43C2211yescharacteristic, complemented
53C22×C16×C43C2211yescharacteristic, complemented
54C43×#466C2211yescharacteristic
55C43×#466C2211yescharacteristic, complemented
56C43×#366C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic, complemented
58C43×#357C2211yescharacteristic, complemented
59C2×#10621900—41no—
60C22×D172—21no—
61C2×D4×D43—21no—
62C2×D4×D43—41no—
63C2×D344—22no—
64C2×D344—21no—
65C2×D344—41no—
66C2×D344C2311yescharacteristic
67C2×D344C2311yescharacteristic
68C2×#10621882—21no—
69C2×#10621882—21no—
70D8×D43—22no—
71D8×D43—41no—
72C2×C8×D43C2311yescharacteristic
73#13063324—21no—
74#13063321—21no—
75#13063307—41no—
76#13063306—41no—
77#13063302—41no—
78#13063300—21no—
79#13063298—41no—
80#13063296—21no—
81#13063295—41no—
82#13063293—41no—
83D4×Dic43—21no—
84#13063287—21no—
85C4×C22⋊D43D411yescharacteristic
86C2×C4⋊Dic43—21no—
87C4⋊C4×D43—21no—
88#13063266—22no—
89#13063266—41no—
90C2×C43⋊C16C2311yescharacteristic
91C2×C43⋊C16C2311yescharacteristic
92C16×D43—41no—
93#13063259—21no—
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063258—21no—
97#13063258—21no—
98Dic43⋊C8D411yescharacteristic
99#13063246—21no—
100#13063246—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)D411yescharacteristic
104(C2×D43)⋊C8D411yescharacteristic
105C8×Dic43C2311yescharacteristic
106C2×D8×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#121×C43—21no—
110#121×C43—21no—
111D16×C43—41no—
112C2×C16×C43—41no—
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#102×C43—21no—
118#102×C43—21no—
119C23×D43—41no—
120C23×D43—41no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—41no—
124C2×D4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43—41no—
129C2×C22⋊D43—41no—
130C2×C22⋊D43D811yescharacteristic
131C22×Dic43—41no—
132C22×Dic43—41no—
133#10621900—84no—
134D4×D43—42no—
135D4×D43—81no—
136D4×D43—84no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—41no—
140C2×D172—41no—
141C2×D172—42no—
142C2×D172—81no—
143C2×C4×D43—41no—
144C2×C4×D43—41no—
145C2×C4×D43C2×D411yescharacteristic
146C2×Dic86—41no—
147D8×C43—21no—
148D8×C43—21no—
149D8×C43—21no—
150D8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43C2×D411yescharacteristic
154C2×C8×C43C2411yescharacteristic
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C22⋊C4×C43—41no—
158C22⋊C4×C43—41no—
159C22⋊Dic43—41no—
160C22⋊Dic43—41no—
161C22⋊Dic43D811yescharacteristic
162#10621882—42no—
163#10621882—81no—
164(C2×D43)⋊C4—41no—
165(C2×D43)⋊C4—41no—
166(C2×D43)⋊C4D811yescharacteristic
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—41no—
170Dic43⋊C4—41no—
171Dic43⋊C4—41no—
172Dic43⋊C4D811yescharacteristic
173C4×Dic43C2×D411yescharacteristic
174C2×C43⋊C8C2×D411yescharacteristic
175C2×C43⋊C8C2×D411yescharacteristic
176D344—21no—
177D344—21no—
178D344—21no—
179D344—42no—
180D344#4112yescomplemented
181C8×D43—21no—
182C8×D43—21no—
183C16×C43—21no—
184C16×C43—21no—
185C43⋊C16—21no—
186C43⋊C16—21no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43C2×D811yescharacteristic
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—82no—
193C22×D43—82no—
194C22×D43—82no—
195C22×D43—82no—
196C22×D43—161no—
197C22×D43—161no—
198C22×D43C2×D811yescharacteristic
199D4×C43—41no—
200D4×C43—41no—
201D4×C43—41no—
202D4×C43—41no—
203D4×C43—82no—
204D4×C43—82no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43C2×D811yescharacteristic
210C2×C4×C43C22×D411yescharacteristic
211C22⋊D43—82no—
212C22⋊D43—82no—
213C22⋊D43—82no—
214C22⋊D43—161no—
215C22⋊D43D1614yescomplemented
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—82no—
219C2×Dic43—82no—
220C2×Dic43C2×D811yescharacteristic
221C2×Dic43C2×D811yescharacteristic
222C2×Dic43C2×D811yescharacteristic
223D172—22no—
224D172—41no—
225D172—41no—
226D172—41no—
227D172—82no—
228D172—82no—
229C4×D43—21no—
230C4×D43—21no—
231C4×D43—82no—
232C4×D43—82no—
233Dic86—82no—
234C8×C43—21no—
235C8×C43C2×#4111yescharacteristic
236C8×C43H(5,𝔽2)11yescharacteristic
237C43⋊C8—21no—
238C43⋊C8—21no—
239#33861—431nomaximal, Sylow
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43—81no—
247C22×C43—81no—
248C22×C43C2×D1612yes—
249C22×C43C22×D811yescharacteristic
250C2×D43—21no—
251C2×D43—21no—
252C2×D43—42no—
253C2×D43—81no—
254C2×D43—81no—
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—81no—
258C2×D43—164no—
259C2×D43—164no—
260C2×D43C2×D1612yes—
261C4×C43—21no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43#54611yescharacteristic
265C4×C43#57711yescharacteristic
266Dic43—21no—
267Dic43—21no—
268Dic43—81no—
269Dic43—81no—
270Dic43C2×D1612yes—
271#3334—431no—
272D4×D8—431no—
273#2240—431no—
274#2232—431no—
275#2232—431no—
276#2224—431no—
277#2215—431no—
278#2215D4311yescharacteristic, complemented
279#2206—431no—
280#2184—431no—
281#2184—431no—
282C4×D16—431no—
283D4×C16—431no—
284C2×#357—431no—
285C2×#357—431no—
286C2×C43—22no—
287C2×C43—161no—
288C2×C43—161no—
289C2×C43#329411yescharacteristic
290C2×C43C22×D1611yescharacteristic
291C2×C43#341611yescharacteristic
292D43—22no—
293D43—82no—
294D43—161no—
295C22×D8—431no—
296C22×D8—431no—
297#547—861no—
298D42—861no—
299C2×D16—431no—
300C2×D16—431no—
301C2×D16C2×D4311yescharacteristic, complemented
302C22×C16—431no—
303C22×C16C2×D4311yescharacteristic, complemented
304#500—431no—
305#493—431no—
306#480—861no—
307#480—861no—
308#474—861no—
309#466—431no—
310#466—431no—
311#466C2×D4311yescharacteristic
312#466C2×D4311yescharacteristic, complemented
313#459—861no—
314#447—861no—
315#447—861no—
316C4×D8—431no—
317C4×D8—431no—
318C8×D4—431no—
319C2×#107—431no—
320C2×#107—431no—
321#366—431no—
322#366—431no—
323#366C2×D4311yescharacteristic, complemented
324C4⋊C16—431no—
325#357—431no—
326#357—431no—
327#357—431no—
328#357—431no—
329#357—431no—
330#357—431no—
331#357—431no—
332#357—431no—
333#357C2×D4311yescharacteristic, complemented
334#357C2×D4311yescharacteristic, complemented
335C22⋊C16—431no—
336C22⋊C16—431no—
337C4×C16—431no—
338C43#3386111yescharacteristic, complemented, Sylow
339C2×#41—1721no—
340C22×D4—861no—
341C22×D4—861no—
342C22×D4—1721no—
343C2×D8—431no—
344C2×D8—431no—
345C2×D8—862no—
346C2×D8—861no—
347C2×D8—861no—
348C2×D8—862no—
349C2×D8—861no—
350C2×D8—1721no—
351C2×D8—1721no—
352C2×D8C22×D4311yescharacteristic
353C2×D8C22×D4311yescharacteristic
354C22×C8—431no—
355C22×C8C22×D4311yescharacteristic
356C4⋊Q8—861no—
357#127—861no—
358#123—1721no—
359#123—1721no—
360C22⋊Q8—1721no—
361#121—21no—
362#121—21no—
363#121—861no—
364#121—861no—
365#121—1721no—
366#120—1721no—
367#120—1721no—
368C4×D4—431no—
369C4×D4—861no—
370C4×D4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373D16—41no—
374D16—862no—
375D16—1721no—
376C2×C16—41no—
377C2×C16—431no—
378C2×C16—431no—
379C2×C16—1721no—
380C2×C16C22×D4311yescharacteristic
381C2×C16C22×D4311yescharacteristic
382#107—431no—
383#107—431no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107C22×D4311yescharacteristic
388#107C22×D4311yescharacteristic
389C4⋊C8—431no—
390#102—21no—
391#102—21no—
392#102—861no—
393#102—861no—
394#102—861no—
395#102—861no—
396C22⋊C8—431no—
397C22⋊C8—431no—
398C4×C8—431no—
399C24—1721no—
400C24—1721no—
401#41—3444no—
402C2×Q8—1721no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—431no—
408C2×D4—861no—
409C2×D4—861no—
410C2×D4—3441no—
411C2×D4—3441no—
412C2×D4—3444no—
413C2×D4—1722no—
414C2×D4—1721no—
415C2×D4—1721no—
416C2×D4—1721no—
417C2×D4—1721no—
418C2×D4—1722no—
419C2×D4—1721no—
420C2×D4—1721no—
421C22×C4—431no—
422C22×C4—1721no—
423C22×C4—1721no—
424C22×C4—1721no—
425C22×C4—1721no—
426C22×C4D4×D4311yescharacteristic
427D8—21no—
428D8—21no—
429D8—21no—
430D8—21no—
431D8—432no—
432D8—861no—
433D8—861no—
434D8—861no—
435D8—3441no—
436D8—1722no—
437D8—1722no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—431no—
441C2×C8—431no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8D4×D4311yescharacteristic
445C2×C8C23×D4311yescharacteristic
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—431no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—1721no—
452C4⋊C4—1721no—
453C4⋊C4—1721no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—431no—
457C22⋊C4—431no—
458C22⋊C4—1721no—
459C22⋊C4—1721no—
460C22⋊C4—1721no—
461C22⋊C4—1721no—
462C42—431no—
463C16—21no—
464C16—21no—
465C16—861no—
466C16—861no—
467C23—41no—
468C23—41no—
469C23—431no—
470C23—3442no—
471C23—3442no—
472C23—3442no—
473C23—3442no—
474C23—1721no—
475C23—1721no—
476C23—6881no—
477C23—6881no—
478C23D8×D4311yescharacteristic
479Q8—3442no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—82no—
485D4—82no—
486D4—434no—
487D4—862no—
488D4—3442no—
489D4—3442no—
490D4—3442no—
491D4—3442no—
492D4—3442no—
493D4—1721no—
494D4—1721no—
495D4—1721no—
496D4—6881no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—431no—
502C2×C4—431no—
503C2×C4—431no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—3442no—
507C2×C4—3442no—
508C2×C4—3442no—
509C2×C4—3442no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4D8×D4311yescharacteristic
513C2×C4C2×D4×D4311yescharacteristic
514C8—21no—
515C8—861no—
516C8—861no—
517C8#41×D4311yescharacteristic
518C8#1306337011yescharacteristic
519C22—21no—
520C22—21no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—432no—
528C22—861no—
529C22—861no—
530C22—3441no—
531C22—3441no—
532C22—3441no—
533C22—3441no—
534C22—3441no—
535C22—1722no—
536C22—6884no—
537C22—6884no—
538C22D16×D4312yes—
539C22C2×D8×D4311yescharacteristic
540C4—21no—
541C4—81no—
542C4—81no—
543C4—432no—
544C4—861no—
545C4—861no—
546C4—3441no—
547C4—3441no—
548C4#1458353811yescharacteristic
549C4#1458370611yescharacteristic
550C2—22no—
551C2—161no—
552C2—161no—
553C2—862no—
554C2—3442no—
555C2—6881no—
556C2#1914640311yescharacteristic
557C2C2×D16×D4311yescharacteristic
558C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2215C2
socleC22×C43C22×D8
hypercenter#2215D43
hypocenterC43#33861
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. #19146939C2semidirect
2. #19146269C2semidirect
3. #19136817C2semidirect
4. #19136777C2semidirect
5. #19136773C2semidirect
6. #19136731C2semidirect
7. #19136680C2semidirect
8. #19136628C2semidirect
9. #19136506C2semidirect
10. #19136505C2semidirect
11. #19136439C2semidirect
12. C16×C22⋊D43C2semidirect
13. C2×#14582701C2semidirect
14. #357×D43C2semidirect
15. C43×#2215C2semidirect
21. C2×#13063266C22semidirect
22. C2×C16×D43C22semidirect
23. #14583303C22semidirect
29. #14583132C22semidirect
33. D8×Dic43C22semidirect
36. C2×#13063259C22semidirect
37. #107×D43C22semidirect
38. #14582724C22semidirect
39. #14582724C22semidirect
40. Dic43⋊C16C22semidirect
43. #14582701C22semidirect
44. #14582701C22semidirect
45. #14582700C22semidirect
46. #14582700C22semidirect
48. #14582699C22semidirect
49. C22⋊(C43⋊C16)C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. C16×Dic43C22semidirect
52. C2×D16×C43C22semidirect
53. C22×C16×C43C22semidirect
55. C43×#466C22semidirect
56. C43×#366C22semidirect
57. C43×#357C22semidirect
58. C43×#357C22semidirect
180. D344#41semidirect
215. C22⋊D43D16semidirect
278. #2215D43semidirect
301. C2×D16C2×D43semidirect
303. C22×C16C2×D43semidirect
312. #466C2×D43semidirect
323. #366C2×D43semidirect
333. #357C2×D43semidirect
334. #357C2×D43semidirect
338. C43#33861semidirect

Maximal subgroups

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

subgroupindex
#191469392
#191462692
#191368172
#191367772
#191367732
#191367312
#191366802
#191366282
#191365062
#191365052
#191364392
C16×C22⋊D432
C2×#145827012
#357×D432
C43×#22152
#3386143