Finite Group Databasebeta

← C4×#14583336 #25249916

Subgroups — C4×#14583336 #25249916

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583336C211yesmaximal, characteristic
2C4×#13063348C211yesmaximal, characteristic, complemented
3C4×D8×D43C211yesmaximal, characteristic, complemented
4#19136470C211yesmaximal, characteristic, complemented
5#19136468C211yesmaximal, characteristic, complemented
6#19136462C211yesmaximal, characteristic, complemented
7#19136460C211yesmaximal, characteristic, complemented
8C4×#13063268C211yesmaximal, characteristic, complemented
9C4×D688C211yesmaximal, characteristic, complemented
10C4×#13063266C211yesmaximal, characteristic, complemented
11#19136382C211yesmaximal, characteristic, complemented
12#19136309C211yesmaximal, characteristic, complemented
13#19136306C211yesmaximal, characteristic, complemented
14C4×#13063264C211yesmaximal, characteristic, complemented
15C4×SD32×C43C211yesmaximal, characteristic, complemented
16C2×#13063348C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18C4×#10621902—21no—
19C4×D4×D43—21no—
20#14583336C418yesdirect product factor
21C2×#13063268C2211yescharacteristic
22C2×D688C2211yescharacteristic
23C2×#13063266C2211yescharacteristic
24C2×#13063264C2211yescharacteristic
25C2×#13063264C2211yescharacteristic
26Q16×Dic43C2211yescharacteristic, complemented
27C4×#10621884—21no—
28#14582984—21no—
29C4×D344C2211yescharacteristic
30C4×D344C2211yescharacteristic, complemented
31D8×Dic43C2211yescharacteristic
32#14582981C2211yescharacteristic
33#14582981C2211yescharacteristic, complemented
34C4×#10621882—21no—
35#14582979—21no—
36#14582936C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582894—21no—
39#102×D43—21no—
40C4×C8×D43C2211yescharacteristic
41#14582726C2211yescharacteristic, complemented
42#14582725C2211yescharacteristic, complemented
43#14582724C2211yescharacteristic, complemented
44#14582703C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic
46#14582701C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic
48#14582699C2211yescharacteristic
49#14582699C2211yescharacteristic, complemented
50#14582674C2211yescharacteristic, complemented
51#14582674C2211yescharacteristic, complemented
52C4×C43⋊C16C2211yescharacteristic, complemented
53C2×SD32×C43C2211yescharacteristic
54C4×Q16×C43C2211yescharacteristic, complemented
55C4×D8×C43C2211yescharacteristic
56C43×#367C2211yescharacteristic, complemented
57C43×#358C2211yescharacteristic, complemented
58C43×#357C2211yescharacteristic
59C4×C16×C43C2211yescharacteristic, complemented
60C2×#10621902—21no—
61C2×D4×D43—21no—
62C22×C4×D43—41no—
63#13063348—22no—
64#13063348C2×C414yescomplemented
65C2×#10621884—21no—
66C2×D344C2311yescharacteristic
67C2×D344C2311yescharacteristic
68C2×#10621882—21no—
69D8×D43—22no—
70D8×D43C2×C414yescomplemented
71C2×C8×D43D411yescharacteristic
72C2×C8×D43C2311yescharacteristic
73Q8×Dic43—21no—
74C4×D172—21no—
75C4×D172—21no—
76C4×D172—41no—
77D4×Dic43—21no—
78#13063287—21no—
79#13063287—21no—
80#13063287—41no—
81C4×C22⋊D43—41no—
82(C22⋊D43)⋊C4—41no—
83#13063283—21no—
84#13063283—41no—
85C4⋊C4×D43—21no—
86C22⋊C4×D43—41no—
87C42×D43—41no—
88C42×D43D411yescharacteristic
89#13063268C2×C414yescomplemented
90D688C2×C414yescomplemented
91#13063266C2×C414yescomplemented
92#13063264—22no—
93#13063264C2×C414yescomplemented
94C2×C43⋊C16C2311yescharacteristic
95C2×C43⋊C16C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063258—21no—
99#13063256—21no—
100#13063249—21no—
101#13063247—21no—
102#13063247—21no—
103#13063246—21no—
104#13063245—21no—
105#13063245—21no—
106C4×C43⋊C8D411yescharacteristic
107C8×Dic43D411yescharacteristic
108C8×Dic43C2311yescharacteristic
109C2×Q16×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C4×Q8×C43—21no—
112C4×D4×C43—21no—
113SD32×C43C2×C414yescomplemented
114C2×C16×C43C2311yescharacteristic
115C2×C16×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#103×C43—21no—
119#102×C43—21no—
120C4×C8×C43C2311yescharacteristic
121C23×D43—41no—
122C2×Q8×C43—21no—
123C2×D4×C43—21no—
124C22×C4×C43—41no—
125C2×C22⋊D43—41no—
126C22×Dic43—41no—
127#10621902—24no—
128#10621902—42no—
129D4×D43—24no—
130D4×D43—42no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—41no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C4×D43—41no—
138C2×C4×D43—41no—
139C2×C4×D43—41no—
140C2×C4×D43—84no—
141C2×C4×D43D811yescharacteristic
142C2×C4×D43D811yescharacteristic
143C2×C4×D43C2×D411yescharacteristic
144Q16×C43—21no—
145Q16×C43C22×C412yescomplemented
146D8×C43—21no—
147D8×C43C22×C412yes—
148C2×C8×C43C2×D411yescharacteristic
149C2×C8×C43C2411yescharacteristic
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C42×C43—41no—
155C42×C43C2×D411yescharacteristic
156C22⋊Dic43—41no—
157#10621884—24no—
158#10621882—24no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163(C2×D43)⋊C4—41no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—41no—
167Dic43⋊C4—41no—
168C4×Dic43—41no—
169C4×Dic43—41no—
170C4×Dic43D811yescharacteristic
171C4×Dic43D811yescharacteristic
172C4×Dic43C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174C2×C43⋊C8C2×D411yescharacteristic
175D344—21no—
176D344—21no—
177D344C22×C412yes—
178D344C22×C412yescomplemented
179C8×D43—22no—
180C8×D43C22×C412yes—
181C8×D43#4112yes—
182C16×C43—21no—
183C16×C43C22×C412yescomplemented
184C43⋊C16—21no—
185C43⋊C16C22×C412yescomplemented
186C23×C43—41no—
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—44no—
190C22×D43—82no—
191C22×D43—82no—
192C22×D43C2×D811yescharacteristic
193Q8×C43—22no—
194Q8×C43—41no—
195D4×C43—22no—
196D4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—82no—
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C22⋊D43—44no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—82no—
208C2×Dic43C2×D811yescharacteristic
209C2×Dic43C2×D811yescharacteristic
210C2×Dic43C2×D811yescharacteristic
211D172—22no—
212D172—22no—
213D172—44no—
214D172—41no—
215D172—41no—
216C4×D43—22no—
217C4×D43—41no—
218C4×D43—44no—
219C4×D43—82no—
220C4×D43—82no—
221C4×D43—82no—
222C4×D43—82no—
223C4×D43—82no—
224C4×D43C4×D412yes—
225C4×D43#13512yes—
226C8×C43—21no—
227C8×C43C23×C411yescharacteristic
228C8×C43C2×#4111yescharacteristic
229C43⋊C8—21no—
230C43⋊C8C4×D412yes—
231C4×#509—431nomaximal, Sylow
232C22×C43—42no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43C22×D811yescharacteristic
236C2×D43—21no—
237C2×D43—21no—
238C2×D43—42no—
239C2×D43—42no—
240C2×D43—88no—
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C2×D43C4×D812yes—
246C4×C43—21no—
247C4×C43—42no—
248C4×C43—81no—
249C4×C43—81no—
250C4×C43#50912yescomplemented
251C4×C43C2×C4×D411yescharacteristic
252C4×C43C2×#13511yescharacteristic
253Dic43—21no—
254Dic43—21no—
255Dic43—81no—
256Dic43—81no—
257Dic43C4×D812yes—
258C2×#509—431no—
259C4×#135—431no—
260C2×C4×D8—431no—
261#2177—431no—
262#2177—431no—
263#2175—431no—
264#2175—431no—
265C4×SD32—431no—
266C4×SD32D4311yescharacteristic, complemented
267C4×D16—431no—
268C4×D16—431no—
269#2159—431no—
270#2140—431no—
271#2139—431no—
272C4×M32—431no—
273C2×C43—82no—
274C2×C43C2×C4×D811yescharacteristic
275C2×C43C2×#50911yescharacteristic
276C2×C43#341411yescharacteristic
277D43—22no—
278D43—82no—
279D43—82no—
280C2×#135—431no—
281C22×D8—431no—
282C4×#41—861no—
283C2×C4×D4—861no—
284#509—438no—
285C2×SD32—431no—
286C2×SD32C2×D4311yescharacteristic
287C2×D16—431no—
288C2×D16—431no—
289C2×M32—431no—
290C2×M32—431no—
291C4×Q16—431no—
292C4×Q16C2×D4311yescharacteristic, complemented
293C4×SD16—861no—
294C4×SD16—861no—
295C4×D8—431no—
296C4×D8—431no—
297C4×D8—431no—
298C4×D8—431no—
299C4×D8—431no—
300C4×D8—861no—
301C4×D8—861no—
302C4×D8C2×D4311yescharacteristic
303#427—431no—
304C2×#107—431no—
305#416—861no—
306C2×#102—861no—
307C2×C4×C8—431no—
308#367—431no—
309#367C2×D4311yescharacteristic, complemented
310#366—431no—
311#366—431no—
312#358—431no—
313#358C2×D4311yescharacteristic, complemented
314#357—431no—
315#357—431no—
316#357—431no—
317#357—431no—
318#357—431no—
319#357C2×D4311yescharacteristic
320#346—431no—
321#346—431no—
322C4×C16—431no—
323C4×C16C2×D4311yescharacteristic, complemented
324C43C4×#50911yescharacteristic, complemented, Sylow
325C2×#41—861no—
326C22×D4—861no—
327C23×C4—1721no—
328#135—434no—
329#135—862no—
330C2×Q16C22×D4311yescharacteristic
331C2×SD16—861no—
332C2×D8—434no—
333C2×D8—431no—
334C2×D8—431no—
335C2×D8—862no—
336C2×D8—861no—
337C2×D8C22×D4311yescharacteristic
338C22×C8—431no—
339C22×C8—431no—
340C4×Q8—21no—
341C4×Q8—861no—
342C4×D4—21no—
343C4×D4—861no—
344C4×D4—861no—
345C4×D4—861no—
346C4×D4—861no—
347C4×D4—861no—
348C4×D4—1721no—
349C4×D4—1721no—
350C4×D4—1721no—
351C4×D4—1721no—
352#117—861no—
353#117—1721no—
354C2×C4⋊C4—861no—
355C2×C22⋊C4—1721no—
356C2×C42—431no—
357C2×C42—1721no—
358SD32—434no—
359SD32C4×D4314yescomplemented
360D16—434no—
361D16—434no—
362M32—434no—
363M32—862no—
364C2×C16—431no—
365C2×C16—431no—
366C2×C16C22×D4311yescharacteristic
367C2×C16C22×D4311yescharacteristic
368#107—431no—
369#107—431no—
370#107—861no—
371#107C22×D4311yescharacteristic
372#107C22×D4311yescharacteristic
373#106—861no—
374#103—21no—
375#103—861no—
376#102—21no—
377#102—861no—
378#102—861no—
379#102—861no—
380#102—861no—
381#102—861no—
382C4×C8—431no—
383C4×C8—431no—
384C4×C8—431no—
385C4×C8C22×D4311yescharacteristic
386C24—1721no—
387#41—864no—
388#41—1722no—
389C2×Q8—21no—
390C2×D4—21no—
391C2×D4—864no—
392C2×D4—861no—
393C2×D4—861no—
394C2×D4—1721no—
395C2×D4—1722no—
396C2×D4—1721no—
397C22×C4—41no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—431no—
401C22×C4—3444no—
402C22×C4—1721no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4—1721no—
406C22×C4—1721no—
407C22×C4—1721no—
408C22×C4—1721no—
409Q16—21no—
410Q16C2×C4×D4312yescomplemented
411SD16—864no—
412D8—21no—
413D8—432no—
414D8—432no—
415D8—864no—
416D8—861no—
417D8—861no—
418D8C2×C4×D4312yes—
419C2×C8—431no—
420C2×C8—432no—
421C2×C8—432no—
422C2×C8—431no—
423C2×C8—862no—
424C2×C8D4×D4311yescharacteristic
425C2×C8C23×D4311yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C22⋊C4—41no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C42—41no—
441C42—431no—
442C42—431no—
443C42—431no—
444C42—1721no—
445C42—1721no—
446C42D4×D4311yescharacteristic
447C16—21no—
448C16—432no—
449C16—861no—
450C16C2×C4×D4312yescomplemented
451C23—41no—
452C23—431no—
453C23—3442no—
454C23—3442no—
455C23—1724no—
456C23—1721no—
457C23—1721no—
458Q8—22no—
459Q8—41no—
460D4—22no—
461D4—41no—
462D4—862no—
463D4—862no—
464D4—1724no—
465D4—1724no—
466D4—1721no—
467D4—1721no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—431no—
473C2×C4—432no—
474C2×C4—432no—
475C2×C4—431no—
476C2×C4—431no—
477C2×C4—862no—
478C2×C4—3442no—
479C2×C4—3442no—
480C2×C4—3442no—
481C2×C4—3442no—
482C2×C4—3442no—
483C2×C4—3442no—
484C2×C4—1721no—
485C2×C4—1724no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4D8×D4311yescharacteristic
489C2×C4D8×D4311yescharacteristic
490C2×C4C2×D4×D4311yescharacteristic
491C8—21no—
492C8—432no—
493C8—861no—
494C8C22×C4×D4311yescharacteristic
495C8#41×D4311yescharacteristic
496C22—42no—
497C22—81no—
498C22—81no—
499C22—432no—
500C22—861no—
501C22—861no—
502C22—3448no—
503C22—3441no—
504C22—3441no—
505C22—3441no—
506C22—3441no—
507C22—1722no—
508C22—1722no—
509C22C2×D8×D4311yescharacteristic
510C4—21no—
511C4—42no—
512C4—81no—
513C4—81no—
514C4—432no—
515C4—861no—
516C4—861no—
517C4—3441no—
518C4—3441no—
519C4#1458333612yesdirect product factor
520C4C4×D4×D4311yescharacteristic
521C4#135×D4311yescharacteristic
522C2—82no—
523C2—862no—
524C2—3442no—
525C2—3442no—
526C2C4×D8×D4311yescharacteristic
527C2C2×#1458333611yescharacteristic
528C2#1914772811yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC4×SD32×C43C2
socleC22×C43C22×D8
prime radicalC2×#14583336C2
cosocleC2×C8×C43C24
hypercenterC4×SD32D43
hypocenterC43C4×#509
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. C4×#13063348C2semidirect
3. C4×D8×D43C2semidirect
4. #19136470C2semidirect
5. #19136468C2semidirect
6. #19136462C2semidirect
7. #19136460C2semidirect
8. C4×#13063268C2semidirect
9. C4×D688C2semidirect
10. C4×#13063266C2semidirect
11. #19136382C2semidirect
12. #19136309C2semidirect
13. #19136306C2semidirect
14. C4×#13063264C2semidirect
15. C4×SD32×C43C2semidirect
20. #14583336C4direct (N × H)
26. Q16×Dic43C22semidirect
30. C4×D344C22semidirect
33. #14582981C22semidirect
41. #14582726C22semidirect
42. #14582725C22semidirect
43. #14582724C22semidirect
44. #14582703C22semidirect
46. #14582701C22semidirect
49. #14582699C22semidirect
50. #14582674C22semidirect
51. #14582674C22semidirect
52. C4×C43⋊C16C22semidirect
54. C4×Q16×C43C22semidirect
56. C43×#367C22semidirect
57. C43×#358C22semidirect
59. C4×C16×C43C22semidirect
64. #13063348C2×C4semidirect
70. D8×D43C2×C4semidirect
89. #13063268C2×C4semidirect
90. D688C2×C4semidirect
91. #13063266C2×C4semidirect
93. #13063264C2×C4semidirect
113. SD32×C43C2×C4semidirect
145. Q16×C43C22×C4semidirect
178. D344C22×C4semidirect
183. C16×C43C22×C4semidirect
185. C43⋊C16C22×C4semidirect
250. C4×C43#509semidirect
266. C4×SD32D43semidirect
292. C4×Q16C2×D43semidirect
309. #367C2×D43semidirect
313. #358C2×D43semidirect
323. C4×C16C2×D43semidirect
324. C43C4×#509semidirect
359. SD32C4×D43semidirect
410. Q16C2×C4×D43semidirect
450. C16C2×C4×D43semidirect
519. C4#14583336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833362
C4×#130633482
C4×D8×D432
#191364702
#191364682
#191364622
#191364602
C4×#130632682
C4×D6882
C4×#130632662
#191363822
#191363092
#191363062
C4×#130632642
C4×SD32×C432
C4×#50943