Finite Group Databasebeta

← #25253413

Subgroups — #25253413

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
2D8×C22⋊D43C211yesmaximal, characteristic, complemented
3#19136817C211yesmaximal, characteristic, complemented
4#19136776C211yesmaximal, characteristic, complemented
5#19136774C211yesmaximal, characteristic, complemented
6#19136730C211yesmaximal, characteristic, complemented
7#19136679C211yesmaximal, characteristic, complemented
8#19136678C211yesmaximal, characteristic, complemented
9#19136628C211yesmaximal, characteristic, complemented
10#19136505C211yesmaximal, characteristic, complemented
11D16×Dic43C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C16C211yesmaximal, characteristic, complemented
13C2×#14582700C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2184C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583549—21no—
18D4×C22⋊D43—21no—
19C2×#13063266C2211yescharacteristic, complemented
20C22×C43⋊C16C2211yescharacteristic, complemented
21C2×C16×D43C2211yescharacteristic, complemented
22#14583303C2211yescharacteristic, complemented
23#14583274C2211yescharacteristic
24#14583211—21no—
25#14583210—21no—
26#14583177—21no—
27#14583135C2211yescharacteristic
28#14583132C2211yescharacteristic
29#14583132C2211yescharacteristic, complemented
30#14583092—21no—
31#14583033—21no—
32#14583031—21no—
33D8×Dic43C2211yescharacteristic
34D8×Dic43C2211yescharacteristic, complemented
35C8×C22⋊D43C2211yescharacteristic
36C2×#13063259C2211yescharacteristic, complemented
37#107×D43C2211yescharacteristic, complemented
38#14582725C2211yescharacteristic, complemented
39#14582725C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42#14582701C2211yescharacteristic, complemented
43#14582701C2211yescharacteristic, complemented
44#14582700C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic, complemented
48#14582700C2211yescharacteristic, complemented
49#14582699C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C22×D8×C43C2211yescharacteristic
53C2×D16×C43C2211yescharacteristic
54C2×D16×C43C2211yescharacteristic, complemented
55C43×#466C2211yescharacteristic, complemented
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic, complemented
59C2×#10621900—41no—
60C22×C22⋊D43—41no—
61C2×D4×D43—21no—
62C2×D344C2311yescharacteristic
63C2×#10621882—21no—
64C2×#10621882—21no—
65D8×D43—22no—
66D8×D43—41no—
67C2×C8×D43C2311yescharacteristic
68#13063324—21no—
69#13063321—21no—
70#13063307—41no—
71#13063306—41no—
72#13063302—41no—
73#13063299—21no—
74#13063297—41no—
75#13063296—21no—
76#13063296—21no—
77#13063294—41no—
78#13063293—41no—
79D4×Dic43—21no—
80D4×Dic43—21no—
81C4×C22⋊D43D411yescharacteristic
82C2×C4⋊Dic43—21no—
83C4⋊C4×D43—21no—
84#13063266—41no—
85C2×C43⋊C16—41no—
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88C16×D43—41no—
89#13063259—21no—
90#13063259C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95Dic43⋊C8D411yescharacteristic
96#13063247—21no—
97#13063246—21no—
98#13063246—21no—
99#13063246—21no—
100#13063246—21no—
101C22⋊(C43⋊C8)D411yescharacteristic
102(C2×D43)⋊C8D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C22×D4×C43—21no—
105C2×D8×C43—22no—
106C2×D8×C43—21no—
107C2×D8×C43—41no—
108C2×D8×C43C2311yescharacteristic
109C2×D8×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112#121×C43—21no—
113D16×C43—22no—
114D16×C43—41no—
115C2×C16×C43C2311yescharacteristic
116C2×C16×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#102×C43—21no—
119C24×C43—41no—
120C23×D43—41no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—41no—
125C2×D4×C43—41no—
126C2×D4×C43—42no—
127C2×D4×C43—81no—
128C22×C4×C43C2×D411yescharacteristic
129C2×C22⋊D43—41no—
130C2×C22⋊D43—41no—
131C2×C22⋊D43—41no—
132C2×C22⋊D43—41no—
133C2×C22⋊D43—41no—
134C2×C22⋊D43—41no—
135C2×C22⋊D43—84no—
136C2×C22⋊D43D811yescharacteristic
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43—41no—
140#10621900—84no—
141D4×D43—42no—
142D4×D43—81no—
143C2×D172—21no—
144C2×C4×D43—41no—
145C2×C4×D43C2×D411yescharacteristic
146C2×Dic86—41no—
147D8×C43—21no—
148D8×C43—21no—
149D8×C43—21no—
150D8×C43—21no—
151D8×C43—21no—
152D8×C43—42no—
153D8×C43#4112yescomplemented
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43C2×D411yescharacteristic
157C2×C8×C43C2411yescharacteristic
158C4⋊C4×C43—21no—
159C22⋊C4×C43—41no—
160C22⋊Dic43—41no—
161C22⋊Dic43—41no—
162C22⋊Dic43—41no—
163C22⋊Dic43—41no—
164C22⋊Dic43D811yescharacteristic
165#10621882—42no—
166#10621882—81no—
167(C2×D43)⋊C4—41no—
168(C2×D43)⋊C4D811yescharacteristic
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—41no—
173Dic43⋊C4—41no—
174Dic43⋊C4—41no—
175Dic43⋊C4D811yescharacteristic
176C4×Dic43C2×D411yescharacteristic
177C2×C43⋊C8C2×D411yescharacteristic
178C2×C43⋊C8C2×D411yescharacteristic
179D344—21no—
180D344—21no—
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×C43—41no—
190C23×C43—82no—
191C23×C43—82no—
192C23×C43—161no—
193C23×C43C2×D811yescharacteristic
194C22×D43—41no—
195C22×D43—82no—
196C22×D43—82no—
197C22×D43—161no—
198C22×D43C2×D811yescharacteristic
199D4×C43—22no—
200D4×C43—41no—
201D4×C43—41no—
202D4×C43—41no—
203D4×C43—41no—
204D4×C43—41no—
205D4×C43—82no—
206D4×C43—82no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—41no—
210C2×C4×C43C2×D811yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C22⋊D43—82no—
213C22⋊D43—82no—
214C22⋊D43—82no—
215C22⋊D43—82no—
216C22⋊D43—82no—
217C22⋊D43—161no—
218C22⋊D43D1614yescomplemented
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—82no—
223C2×Dic43—82no—
224C2×Dic43—82no—
225C2×Dic43C2×D811yescharacteristic
226C2×Dic43C2×D811yescharacteristic
227C2×Dic43C2×D811yescharacteristic
228D172—41no—
229D172—41no—
230C4×D43—21no—
231C4×D43—21no—
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—42no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43—81no—
247C22×C43—81no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—164no—
252C22×C43C2×D1612yes—
253C22×C43C22×D811yescharacteristic
254C2×D43—21no—
255C2×D43—21no—
256C2×D43—81no—
257C2×D43—81no—
258C2×D43—81no—
259C2×D43—164no—
260C2×D43C2×D1612yes—
261C4×C43—21no—
262C4×C43—81no—
263C4×C43#54611yescharacteristic
264C4×C43#57711yescharacteristic
265Dic43—21no—
266Dic43—21no—
267Dic43—81no—
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#2215—431no—
279#2206—431no—
280#2184—431no—
281#2184D4311yescharacteristic, complemented
282C4×D16—431no—
283D4×C16—431no—
284C2×#357—431no—
285C2×#357—431no—
286C2×C43—22no—
287C2×C43—82no—
288C2×C43—161no—
289C2×C43—161no—
290C2×C43#329411yescharacteristic
291C2×C43C22×D1611yescharacteristic
292C2×C43#341611yescharacteristic
293D43—22no—
294D43—161no—
295C22×D8—431no—
296C22×D8C2×D4311yescharacteristic
297#547—861no—
298D42—861no—
299C2×D16—431no—
300C2×D16C2×D4311yescharacteristic
301C2×D16C2×D4311yescharacteristic, complemented
302C22×C16—431no—
303C22×C16—431no—
304#500—431no—
305#493—431no—
306#480—861no—
307#480—861no—
308#474—861no—
309#466—431no—
310#466—431no—
311#466—431no—
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#366—431no—
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
334#357C2×D4311yescharacteristic, complemented
335C22⋊C16—431no—
336C22⋊C16C2×D4311yescharacteristic, complemented
337C4×C16—431no—
338C43#3386111yescharacteristic, complemented, Sylow
339C2×#41—1721no—
340C22×D4—21no—
341C22×D4—861no—
342C22×D4—1721no—
343C2×D8—22no—
344C2×D8—21no—
345C2×D8—41no—
346C2×D8—431no—
347C2×D8—861no—
348C2×D8—861no—
349C2×D8—862no—
350C2×D8—1721no—
351C2×D8C22×D4311yescharacteristic
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—861no—
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—22no—
374D16—41no—
375D16—1721no—
376C2×C16—431no—
377C2×C16—431no—
378C2×C16—1721no—
379C2×C16—1721no—
380C2×C16C22×D4311yescharacteristic
381C2×C16C22×D4311yescharacteristic
382#107—431no—
383#107—431no—
384#107—431no—
385#107—861no—
386#107—861no—
387#107—861no—
388#107C22×D4311yescharacteristic
389C4⋊C8—431no—
390#102—21no—
391#102—861no—
392#102—861no—
393#102—861no—
394#102—861no—
395#102—861no—
396C22⋊C8—431no—
397C22⋊C8—431no—
398C4×C8—431no—
399C24—41no—
400C24—1721no—
401#41—3444no—
402C2×Q8—1721no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—42no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—81no—
410C2×D4—431no—
411C2×D4—861no—
412C2×D4—3441no—
413C2×D4—3444no—
414C2×D4—1721no—
415C2×D4—1721no—
416C2×D4—1721no—
417C2×D4—1722no—
418C2×D4—1721no—
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—21no—
432D8—42no—
433D8—861no—
434D8—861no—
435D8—3441no—
436D8—1722no—
437D8#1062190012yescomplemented
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—431no—
448C4⋊C4—861no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—1721no—
452C4⋊C4—1721no—
453C4⋊C4—1721no—
454C22⋊C4—41no—
455C22⋊C4—431no—
456C22⋊C4—431no—
457C22⋊C4—1721no—
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—41no—
470C23—82no—
471C23—82no—
472C23—161no—
473C23—431no—
474C23—3442no—
475C23—3442no—
476C23—1721no—
477C23—6881no—
478C23D8×D4311yescharacteristic
479Q8—3442no—
480D4—22no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—41no—
485D4—41no—
486D4—82no—
487D4—82no—
488D4—434no—
489D4—3442no—
490D4—3442no—
491D4—3442no—
492D4—3442no—
493D4—3442no—
494D4—1721no—
495D4—1721no—
496D4—6881no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—431no—
501C2×C4—431no—
502C2×C4—431no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—3442no—
506C2×C4—3442no—
507C2×C4—3442no—
508C2×C4—3442no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4D8×D4311yescharacteristic
513C2×C4C2×D4×D4311yescharacteristic
514C8—21no—
515C8—861no—
516C8—861no—
517C8C2×#1062190011yescharacteristic
518C8#1306337011yescharacteristic
519C22—21no—
520C22—21no—
521C22—42no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—164no—
531C22—432no—
532C22—861no—
533C22—861no—
534C22—3441no—
535C22—3441no—
536C22—3441no—
537C22—6884no—
538C22D16×D4312yes—
539C22C2×D8×D4311yescharacteristic
540C4—21no—
541C4—81no—
542C4—432no—
543C4—861no—
544C4—861no—
545C4—3441no—
546C4—3441no—
547C4—3441no—
548C4#1458353611yescharacteristic
549C4#1458370911yescharacteristic
550C2—22no—
551C2—82no—
552C2—161no—
553C2—161no—
554C2—862no—
555C2—6881no—
556C2#1914640111yescharacteristic
557C2C2×D16×D4311yescharacteristic
558C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2184C2
socleC22×C43C22×D8
hypercenter#2184D43
hypocenterC43#33861
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #19146939C2semidirect
2. D8×C22⋊D43C2semidirect
3. #19136817C2semidirect
4. #19136776C2semidirect
5. #19136774C2semidirect
6. #19136730C2semidirect
7. #19136679C2semidirect
8. #19136678C2semidirect
9. #19136628C2semidirect
10. #19136505C2semidirect
11. D16×Dic43C2semidirect
12. (C22⋊D43)⋊C16C2semidirect
13. C2×#14582700C2semidirect
14. #357×D43C2semidirect
15. C43×#2184C2semidirect
19. C2×#13063266C22semidirect
20. C22×C43⋊C16C22semidirect
21. C2×C16×D43C22semidirect
22. #14583303C22semidirect
29. #14583132C22semidirect
34. D8×Dic43C22semidirect
36. C2×#13063259C22semidirect
37. #107×D43C22semidirect
38. #14582725C22semidirect
39. #14582725C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. #14582701C22semidirect
43. #14582701C22semidirect
46. #14582700C22semidirect
47. #14582700C22semidirect
48. #14582700C22semidirect
49. #14582699C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. C16×Dic43C22semidirect
54. C2×D16×C43C22semidirect
55. C43×#466C22semidirect
57. C43×#357C22semidirect
58. C43×C22⋊C16C22semidirect
153. D8×C43#41semidirect
218. C22⋊D43D16semidirect
281. #2184D43semidirect
301. C2×D16C2×D43semidirect
312. #466C2×D43semidirect
334. #357C2×D43semidirect
336. C22⋊C16C2×D43semidirect
338. C43#33861semidirect
437. D8#10621900semidirect

Maximal subgroups

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

subgroupindex
#191469392
D8×C22⋊D432
#191368172
#191367762
#191367742
#191367302
#191366792
#191366782
#191366282
#191365052
D16×Dic432
(C22⋊D43)⋊C162
C2×#145827002
#357×D432
C43×#21842
#3386143