Finite Group Databasebeta

← C4×#15689557 #26369591

Subgroups — C4×#15689557 #26369591

Order 12032.

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×#15689557C211yesmaximal, characteristic
2C4×#13094043C211yesmaximal, characteristic, complemented
3C4×D8×D47C211yesmaximal, characteristic, complemented
4#20245264C211yesmaximal, characteristic, complemented
5#20245261C211yesmaximal, characteristic, complemented
6#20245251C211yesmaximal, characteristic, complemented
7#20245249C211yesmaximal, characteristic, complemented
8C4×#13093969C211yesmaximal, characteristic, complemented
9C4×#13093968C211yesmaximal, characteristic, complemented
10C4×#13093965C211yesmaximal, characteristic, complemented
11#20245173C211yesmaximal, characteristic, complemented
12#20245102C211yesmaximal, characteristic, complemented
13#20245097C211yesmaximal, characteristic, complemented
14C4×#13093963C211yesmaximal, characteristic, complemented
15C4×D16×C47C211yesmaximal, characteristic, complemented
16C2×#13094043C2211yescharacteristic
17C2×D8×D47C2211yescharacteristic
18C4×#10625352—21no—
19C4×D4×D47—21no—
20#15689557C418yesdirect product factor
21C2×#13093969C2211yescharacteristic
22C2×#13093968C2211yescharacteristic
23C2×#13093965C2211yescharacteristic
24C2×#13093963C2211yescharacteristic
25C2×#13093963C2211yescharacteristic
26C4×Dic188C2211yescharacteristic, complemented
27#15689217C2211yescharacteristic, complemented
28#15689214—21no—
29C4×#10625335—21no—
30C4×D376C2211yescharacteristic
31D8×Dic47C2211yescharacteristic
32D8×Dic47C2211yescharacteristic, complemented
33#15689205C2211yescharacteristic
34C4×#10625334—21no—
35#15689203—21no—
36#15689160C2211yescharacteristic
37#107×D47C2211yescharacteristic
38#15689116—21no—
39#102×D47—21no—
40C4×C8×D47C2211yescharacteristic
41#15688951C2211yescharacteristic, complemented
42#15688950C2211yescharacteristic, complemented
43#15688948C2211yescharacteristic, complemented
44#15688928C2211yescharacteristic, complemented
45#15688926C2211yescharacteristic, complemented
46#15688925C2211yescharacteristic
47#15688924C2211yescharacteristic
48#15688924C2211yescharacteristic, complemented
49#15688923C2211yescharacteristic
50#15688898C2211yescharacteristic, complemented
51#15688898C2211yescharacteristic, complemented
52C4×C47⋊C16C2211yescharacteristic, complemented
53C2×D16×C47C2211yescharacteristic
54C4×D8×C47C2211yescharacteristic
55C4×D8×C47C2211yescharacteristic, complemented
56C47×#366C2211yescharacteristic, complemented
57C47×#357C2211yescharacteristic
58C47×#357C2211yescharacteristic, complemented
59C4×C16×C47C2211yescharacteristic, complemented
60C2×#10625352—21no—
61C2×D4×D47—21no—
62C22×C4×D47—41no—
63#13094043—22no—
64#13094043C2×C414yescomplemented
65C2×Dic188C2311yescharacteristic
66C2×#10625335—21no—
67C2×D376C2311yescharacteristic
68C2×#10625334—21no—
69D8×D47—22no—
70D8×D47C2×C414yescomplemented
71C2×C8×D47D411yescharacteristic
72C2×C8×D47C2311yescharacteristic
73C4×Dic94—21no—
74#13093989—21no—
75C4×D188—21no—
76D4×Dic47—21no—
77D4×Dic47—21no—
78#13093986—21no—
79C4×C22⋊D47—41no—
80C4×C22⋊D47—41no—
81(C22⋊D47)⋊C4—41no—
82(C22⋊D47)⋊C4—41no—
83#13093982—21no—
84#13093980—41no—
85C4⋊C4×D47—21no—
86C22⋊C4×D47—41no—
87C2×C4×Dic47—41no—
88C42×D47D411yescharacteristic
89#13093969C2×C414yescomplemented
90#13093968C2×C414yescomplemented
91#13093965C2×C414yescomplemented
92#13093963—22no—
93#13093963C2×C414yescomplemented
94C2×C47⋊C16C2311yescharacteristic
95C2×C47⋊C16C2311yescharacteristic
96#13093958C2311yescharacteristic
97#13093958C2311yescharacteristic
98#13093957—21no—
99#13093955—21no—
100#13093949—21no—
101#13093947—21no—
102#13093946—21no—
103#13093945—21no—
104#13093945—21no—
105#13093944—21no—
106C4×C47⋊C8D411yescharacteristic
107C8×Dic47D411yescharacteristic
108C8×Dic47C2311yescharacteristic
109C2×D8×C47C2311yescharacteristic
110C2×D8×C47C2311yescharacteristic
111C4×D4×C47—21no—
112C4×D4×C47—21no—
113D16×C47C2×C414yescomplemented
114C2×C16×C47C2311yescharacteristic
115C2×C16×C47C2311yescharacteristic
116#107×C47C2311yescharacteristic
117#107×C47C2311yescharacteristic
118#102×C47—21no—
119#102×C47—21no—
120C4×C8×C47C2311yescharacteristic
121C23×D47—41no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C2×C22⋊D47—41no—
127C2×C22⋊D47—41no—
128C22×Dic47—41no—
129C22×Dic47—41no—
130C22×Dic47—41no—
131#10625352—24no—
132#10625352—42no—
133D4×D47—24no—
134D4×D47—42no—
135C2×D188—21no—
136C2×C4×D47—41no—
137C2×C4×D47—41no—
138C2×C4×D47—41no—
139C2×C4×D47—84no—
140C2×C4×D47D811yescharacteristic
141C2×C4×D47D811yescharacteristic
142C2×C4×D47C2×D411yescharacteristic
143C2×Dic94—21no—
144D8×C47—21no—
145D8×C47—21no—
146D8×C47C22×C412yes—
147D8×C47C22×C412yescomplemented
148C2×C8×C47C2×D411yescharacteristic
149C2×C8×C47C2411yescharacteristic
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C22⋊C4×C47—41no—
153C22⋊C4×C47—41no—
154C42×C47C2×D411yescharacteristic
155C22⋊Dic47—41no—
156C22⋊Dic47—41no—
157#10625335—24no—
158#10625334—24no—
159(C2×D47)⋊C4—41no—
160(C2×D47)⋊C4—41no—
161(C2×D47)⋊C4—41no—
162C4⋊Dic47—21no—
163C4⋊Dic47—21no—
164Dic47⋊C4—41no—
165Dic47⋊C4—41no—
166Dic47⋊C4—41no—
167C4×Dic47—41no—
168C4×Dic47—41no—
169C4×Dic47—41no—
170C4×Dic47D811yescharacteristic
171C4×Dic47D811yescharacteristic
172C4×Dic47C2×D411yescharacteristic
173C2×C47⋊C8C2×D411yescharacteristic
174C2×C47⋊C8C2×D411yescharacteristic
175Dic188—21no—
176Dic188C22×C412yescomplemented
177D376—21no—
178D376C22×C412yes—
179C8×D47—22no—
180C8×D47C22×C412yes—
181C8×D47#4112yes—
182C16×C47—21no—
183C16×C47C22×C412yescomplemented
184C47⋊C16—21no—
185C47⋊C16C22×C412yescomplemented
186C23×C47—41no—
187C23×C47—41no—
188C22×D47—41no—
189C22×D47—44no—
190C22×D47—82no—
191C22×D47—82no—
192C22×D47C2×D811yescharacteristic
193D4×C47—22no—
194D4×C47—22no—
195D4×C47—41no—
196D4×C47—41no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47—82no—
200C2×C4×C47—82no—
201C2×C4×C47C2×D811yescharacteristic
202C2×C4×C47C2×D811yescharacteristic
203C2×C4×C47C22×D411yescharacteristic
204C22⋊D47—44no—
205C22⋊D47—44no—
206C2×Dic47—41no—
207C2×Dic47—44no—
208C2×Dic47—41no—
209C2×Dic47—41no—
210C2×Dic47—82no—
211C2×Dic47—82no—
212C2×Dic47C2×D811yescharacteristic
213C2×Dic47C2×D811yescharacteristic
214C2×Dic47C2×D811yescharacteristic
215D188—22no—
216D188—41no—
217C4×D47—22no—
218C4×D47—41no—
219C4×D47—82no—
220C4×D47—82no—
221C4×D47—82no—
222C4×D47C4×D412yes—
223C4×D47#13512yes—
224Dic94—22no—
225Dic94—41no—
226C8×C47—21no—
227C8×C47C23×C411yescharacteristic
228C8×C47C2×#4111yescharacteristic
229C47⋊C8—21no—
230C47⋊C8C4×D412yes—
231C4×#509—471nomaximal, Sylow
232C22×C47—42no—
233C22×C47—42no—
234C22×C47—81no—
235C22×C47—81no—
236C22×C47—81no—
237C22×C47—81no—
238C22×C47C22×D811yescharacteristic
239C2×D47—21no—
240C2×D47—21no—
241C2×D47—42no—
242C2×D47—88no—
243C2×D47—81no—
244C2×D47—81no—
245C2×D47C4×D812yes—
246C4×C47—21no—
247C4×C47—81no—
248C4×C47—81no—
249C4×C47#50912yescomplemented
250C4×C47C2×C4×D411yescharacteristic
251C4×C47C2×#13511yescharacteristic
252Dic47—21no—
253Dic47—21no—
254Dic47—42no—
255Dic47—81no—
256Dic47—81no—
257Dic47C4×D812yes—
258C2×#509—471no—
259C4×#135—471no—
260C2×C4×D8—471no—
261#2177—471no—
262#2177—471no—
263#2175—471no—
264#2175—471no—
265C4×SD32—471no—
266C4×SD32—471no—
267C4×D16—471no—
268C4×D16D4711yescharacteristic, complemented
269#2159—471no—
270#2140—471no—
271#2139—471no—
272C4×M32—471no—
273C2×C47—82no—
274C2×C47—82no—
275C2×C47C2×C4×D811yescharacteristic
276C2×C47C2×#50911yescharacteristic
277C2×C47#341411yescharacteristic
278D47—22no—
279D47—82no—
280C2×#135—471no—
281C22×D8—471no—
282C4×#41—941no—
283C2×C4×D4—941no—
284#509—478no—
285C2×SD32—471no—
286C2×SD32—471no—
287C2×D16—471no—
288C2×D16C2×D4711yescharacteristic
289C2×M32—471no—
290C2×M32—471no—
291C4×Q16—471no—
292C4×Q16—471no—
293C4×SD16—941no—
294C4×SD16—941no—
295C4×D8—471no—
296C4×D8—471no—
297C4×D8—471no—
298C4×D8—471no—
299C4×D8—941no—
300C4×D8—941no—
301C4×D8C2×D4711yescharacteristic
302C4×D8C2×D4711yescharacteristic, complemented
303#427—471no—
304C2×#107—471no—
305#416—941no—
306C2×#102—941no—
307C2×C4×C8—471no—
308#367—471no—
309#367—471no—
310#366—471no—
311#366C2×D4711yescharacteristic, complemented
312#358—471no—
313#358—471no—
314#357—471no—
315#357—471no—
316#357—471no—
317#357—471no—
318#357C2×D4711yescharacteristic
319#357C2×D4711yescharacteristic, complemented
320#346—471no—
321#346—471no—
322C4×C16—471no—
323C4×C16C2×D4711yescharacteristic, complemented
324C47C4×#50911yescharacteristic, complemented, Sylow
325C2×#41—941no—
326C22×D4—941no—
327C23×C4—1881no—
328#135—474no—
329#135—942no—
330C2×Q16—471no—
331C2×SD16—941no—
332C2×D8—474no—
333C2×D8—471no—
334C2×D8—942no—
335C2×D8—941no—
336C2×D8C22×D4711yescharacteristic
337C2×D8C22×D4711yescharacteristic
338C22×C8—471no—
339C22×C8—471no—
340C4×Q8—941no—
341C4×Q8—941no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—941no—
345C4×D4—941no—
346C4×D4—941no—
347C4×D4—941no—
348C4×D4—1881no—
349C4×D4—1881no—
350C4×D4—1881no—
351C4×D4—1881no—
352#117—941no—
353#117—1881no—
354C2×C4⋊C4—941no—
355C2×C22⋊C4—1881no—
356C2×C42—471no—
357C2×C42—1881no—
358SD32—474no—
359SD32—474no—
360D16—474no—
361D16C4×D4714yescomplemented
362M32—474no—
363M32—942no—
364C2×C16—471no—
365C2×C16—471no—
366C2×C16C22×D4711yescharacteristic
367C2×C16C22×D4711yescharacteristic
368#107—471no—
369#107—471no—
370#107—941no—
371#107C22×D4711yescharacteristic
372#107C22×D4711yescharacteristic
373#106—941no—
374#103—941no—
375#103—941no—
376#102—21no—
377#102—21no—
378#102—941no—
379#102—941no—
380#102—941no—
381#102—941no—
382C4×C8—471no—
383C4×C8—471no—
384C4×C8—471no—
385C4×C8C22×D4711yescharacteristic
386C24—1881no—
387#41—944no—
388#41—1882no—
389C2×Q8—941no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—944no—
393C2×D4—941no—
394C2×D4—1882no—
395C2×D4—1881no—
396C2×D4—1881no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—471no—
400C22×C4—471no—
401C22×C4—471no—
402C22×C4—3764no—
403C22×C4—1881no—
404C22×C4—1881no—
405C22×C4—1881no—
406C22×C4—1881no—
407C22×C4—1881no—
408C22×C4—1881no—
409Q16—472no—
410Q16—941no—
411SD16—944no—
412D8—21no—
413D8—21no—
414D8—472no—
415D8—944no—
416D8—941no—
417D8C2×C4×D4712yes—
418D8C2×C4×D4712yescomplemented
419C2×C8—471no—
420C2×C8—472no—
421C2×C8—472no—
422C2×C8—471no—
423C2×C8—942no—
424C2×C8D4×D4711yescharacteristic
425C2×C8C23×D4711yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—941no—
429C4⋊C4—941no—
430C4⋊C4—1881no—
431C4⋊C4—1881no—
432C4⋊C4—1881no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—1881no—
436C22⋊C4—1881no—
437C22⋊C4—1881no—
438C22⋊C4—1881no—
439C22⋊C4—1881no—
440C42—471no—
441C42—471no—
442C42—471no—
443C42—1881no—
444C42—1881no—
445C42—1881no—
446C42D4×D4711yescharacteristic
447C16—21no—
448C16—472no—
449C16—941no—
450C16C2×C4×D4712yescomplemented
451C23—41no—
452C23—41no—
453C23—471no—
454C23—3762no—
455C23—3762no—
456C23—1884no—
457C23—1881no—
458Q8—942no—
459Q8—1881no—
460D4—22no—
461D4—22no—
462D4—41no—
463D4—41no—
464D4—942no—
465D4—1884no—
466D4—1884no—
467D4—1881no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—471no—
473C2×C4—472no—
474C2×C4—472no—
475C2×C4—471no—
476C2×C4—471no—
477C2×C4—942no—
478C2×C4—3762no—
479C2×C4—3762no—
480C2×C4—3762no—
481C2×C4—3762no—
482C2×C4—3762no—
483C2×C4—1881no—
484C2×C4—1884no—
485C2×C4—1881no—
486C2×C4—1881no—
487C2×C4—1881no—
488C2×C4D8×D4711yescharacteristic
489C2×C4D8×D4711yescharacteristic
490C2×C4C2×D4×D4711yescharacteristic
491C8—21no—
492C8—472no—
493C8—941no—
494C8C22×C4×D4711yescharacteristic
495C8#41×D4711yescharacteristic
496C22—42no—
497C22—42no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—472no—
503C22—941no—
504C22—941no—
505C22—3768no—
506C22—3761no—
507C22—3761no—
508C22—1882no—
509C22C2×D8×D4711yescharacteristic
510C4—21no—
511C4—81no—
512C4—81no—
513C4—472no—
514C4—941no—
515C4—941no—
516C4—3761no—
517C4—3761no—
518C4—1882no—
519C4#1568955712yesdirect product factor
520C4C4×D4×D4711yescharacteristic
521C4#135×D4711yescharacteristic
522C2—82no—
523C2—82no—
524C2—942no—
525C2—3762no—
526C2C4×D8×D4711yescharacteristic
527C2C2×#1568955711yescharacteristic
528C2#2025652111yescharacteristic
subgroupG/H
centerC2×C4D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC4×D16×C47C2
socleC22×C47C22×D8
prime radicalC2×#15689557C2
cosocleC2×C8×C47C24
hypercenterC4×D16D47
hypocenterC47C4×#509
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
2. C4×#13094043C2semidirect
3. C4×D8×D47C2semidirect
4. #20245264C2semidirect
5. #20245261C2semidirect
6. #20245251C2semidirect
7. #20245249C2semidirect
8. C4×#13093969C2semidirect
9. C4×#13093968C2semidirect
10. C4×#13093965C2semidirect
11. #20245173C2semidirect
12. #20245102C2semidirect
13. #20245097C2semidirect
14. C4×#13093963C2semidirect
15. C4×D16×C47C2semidirect
20. #15689557C4direct (N × H)
26. C4×Dic188C22semidirect
27. #15689217C22semidirect
32. D8×Dic47C22semidirect
41. #15688951C22semidirect
42. #15688950C22semidirect
43. #15688948C22semidirect
44. #15688928C22semidirect
45. #15688926C22semidirect
48. #15688924C22semidirect
50. #15688898C22semidirect
51. #15688898C22semidirect
52. C4×C47⋊C16C22semidirect
55. C4×D8×C47C22semidirect
56. C47×#366C22semidirect
58. C47×#357C22semidirect
59. C4×C16×C47C22semidirect
64. #13094043C2×C4semidirect
70. D8×D47C2×C4semidirect
89. #13093969C2×C4semidirect
90. #13093968C2×C4semidirect
91. #13093965C2×C4semidirect
93. #13093963C2×C4semidirect
113. D16×C47C2×C4semidirect
147. D8×C47C22×C4semidirect
176. Dic188C22×C4semidirect
183. C16×C47C22×C4semidirect
185. C47⋊C16C22×C4semidirect
249. C4×C47#509semidirect
268. C4×D16D47semidirect
302. C4×D8C2×D47semidirect
311. #366C2×D47semidirect
319. #357C2×D47semidirect
323. C4×C16C2×D47semidirect
324. C47C4×#509semidirect
361. D16C4×D47semidirect
418. D8C2×C4×D47semidirect
450. C16C2×C4×D47semidirect
519. C4#15689557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895572
C4×#130940432
C4×D8×D472
#202452642
#202452612
#202452512
#202452492
C4×#130939692
C4×#130939682
C4×#130939652
#202451732
#202451022
#202450972
C4×#130939632
C4×D16×C472
C4×#50947