Finite Group Databasebeta

← #14910278

Subgroups — #14910278

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2C2×#10622525C211yesmaximal, characteristic, complemented
3#13080337C211yesmaximal, characteristic, complemented
4#13080302C211yesmaximal, characteristic, complemented
5#13070887C211yesmaximal, characteristic, complemented
6#13070725C211yesmaximal, characteristic, complemented
7#13070713C211yesmaximal, characteristic, complemented
8#13070671C211yesmaximal, characteristic, complemented
9#13070661C211yesmaximal, characteristic, complemented
10#13070557C211yesmaximal, characteristic, complemented
11#13070557C211yesmaximal, characteristic, complemented
12#13070546C211yesmaximal, characteristic, complemented
13#13070540C211yesmaximal, characteristic, complemented
14#13070443C211yesmaximal, characteristic, complemented
15C11×#2177C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C2×#66965C2211yescharacteristic
18C2×#66965C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic
20#10623086—21no—
21#10623085—21no—
22C2×C11×D16C2211yescharacteristic
23C4×C11×D8C2211yescharacteristic
24C4×C11×D8C2211yescharacteristic, complemented
25C2×#66891C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27C2×#66891C2211yescharacteristic, complemented
28C2×#66890C2211yescharacteristic
29#10622632—21no—
30#10622629—21no—
31#10622525—24no—
32#10622524—24no—
33C2×Dic88C2211yescharacteristic, complemented
34C2×Dic88C2211yescharacteristic, complemented
35C2×#66864C2211yescharacteristic
36C2×#66864C2211yescharacteristic
37C2×#66862C2211yescharacteristic
38C2×C16×D11C2211yescharacteristic, complemented
39#10622500C2211yescharacteristic
40#10622500C2211yescharacteristic
41#10622500C2211yescharacteristic, complemented
42#10622496C2211yescharacteristic
43#10622396—21no—
44#10622396—21no—
45#10622394—21no—
46#10622389—21no—
47#10622312C2211yescharacteristic, complemented
48#10622309C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C11×#367C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic
52C11×#357C2211yescharacteristic, complemented
53C11×#346C2211yescharacteristic, complemented
54(C2×D11)⋊C16C2211yescharacteristic
55(C2×D11)⋊C16C2211yescharacteristic, complemented
56#10622130C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×#4341—21no—
62C2×#4341—21no—
63C2×#4341—21no—
64C2×D4×D11—21no—
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C2×#4324—21no—
70C2×#4324—21no—
71C2×#4324—21no—
72C2×#4323—21no—
73#66983—41no—
74#66983—41no—
75C2×(C2×D11)⋊C4—41no—
76C2×C4⋊Dic11—41no—
77#66965—22no—
78#66965—22no—
79#66965—22no—
80#66965—41no—
81#66965—41no—
82#66965—41no—
83D8×D11—22no—
84D8×D11—41no—
85C2×Dic44—21no—
86C2×Dic44C2311yescharacteristic
87C2×Dic44C2311yescharacteristic
88C2×Dic44C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×#4314—21no—
91C2×C8×D11C2311yescharacteristic
92C2×C8×D11C2311yescharacteristic
93#66950—21no—
94#66950—21no—
95#66950—21no—
96#66948—21no—
97#66939—41no—
98#66939—41no—
99#66939—41no—
100#66935—41no—
101#66928—21no—
102C4×D44D411yescharacteristic
103#66922—21no—
104C11×D16D414yescomplemented
105C2×C11×C16C2311yescharacteristic
106C2×C11×C16C2311yescharacteristic
107C11×#107C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C11×#102—21no—
111C4×C8×C11C2311yescharacteristic
112#66891—22no—
113#66891—22no—
114#66891—22no—
115#66890—22no—
116(C2×D11)⋊C8D411yescharacteristic
117(C2×D11)⋊C8D411yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119C2×C11⋊C16C2311yescharacteristic
120#66874—21no—
121#66874—21no—
122#66874—21no—
123#66873—21no—
124C4⋊(C11⋊C8)D411yescharacteristic
125Dic88—22no—
126Dic88—41no—
127#66864—22no—
128#66864—41no—
129#66862—22no—
130C16×D11—22no—
131#33833—111nomaximal, Sylow
132C23×D11—41no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C22×Dic11—41no—
142C22×Dic11—41no—
143C22×Dic11—41no—
144#4341—42no—
145#4341—42no—
146#4341—42no—
147#4341—81no—
148#4341—81no—
149#4341—81no—
150D4×D11—42no—
151D4×D11—81no—
152C2×D44—21no—
153C2×D44—41no—
154C2×D44D811yescharacteristic
155C2×C4×D11C2×D411yescharacteristic
156C2×C4×D11C2×D411yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×D8—21no—
161C11×D8—21no—
162C11×D8C2×D412yes—
163C11×D8C2×D412yes—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C42×C11C2×D411yescharacteristic
171#4324—42no—
172#4324—42no—
173#4324—42no—
174#4323—42no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4D811yescharacteristic
182(C2×D11)⋊C4D811yescharacteristic
183C4⋊Dic11—41no—
184C4⋊Dic11—41no—
185C4⋊Dic11—41no—
186C4⋊Dic11—41no—
187C4⋊Dic11—41no—
188C4⋊Dic11D811yescharacteristic
189C2×C11⋊C8C2×D411yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191Dic44—21no—
192Dic44—21no—
193Dic44—21no—
194Dic44—21no—
195Dic44—21no—
196Dic44—21no—
197Dic44—81no—
198D88—21no—
199D88—21no—
200#4314—81no—
201C8×D11—21no—
202C8×D11—21no—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16C2×D412yes—
207C11⋊C16—21no—
208C11⋊C16—21no—
209C2×#509—111no—
210C2×#508—111no—
211#3283—111no—
212#3280—111no—
213#2251—111no—
214#2219—111no—
215#2217—111no—
216#2210—111no—
217#2208—111no—
218#2189—111no—
219#2189—111no—
220#2187—111no—
221#2186—111no—
222#2177D1111yescharacteristic, complemented
223#2168—111no—
224C23×C11—41no—
225C23×C11—41no—
226C22×D11—41no—
227C22×D11—82no—
228C22×D11—82no—
229C22×D11—161no—
230C22×D11C2×D811yescharacteristic
231C22×D11C2×D811yescharacteristic
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—41no—
235D4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—82no—
239C2×C4×C11—161no—
240C2×C4×C11C2×D811yescharacteristic
241C2×C4×C11C2×D811yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C22⋊D11—82no—
244C22⋊D11—82no—
245C22⋊D11—82no—
246C22⋊D11—82no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—82no—
251C2×Dic11—82no—
252C2×Dic11—82no—
253C2×Dic11C2×D811yescharacteristic
254C2×Dic11C2×D811yescharacteristic
255D44—41no—
256D44—41no—
257D44—41no—
258D44—161no—
259C4×D11—21no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—21no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269C8×C11—21no—
270C8×C11C22×D411yescharacteristic
271C8×C11H(5,𝔽2)11yescharacteristic
272C11⋊C8—21no—
273C11⋊C8—21no—
274C2×#135—111no—
275C2×#135—111no—
276C2×#135—111no—
277C22×D8—111no—
278#547—221no—
279#546—221no—
280#509—224no—
281#508—224no—
282C2×Q32—111no—
283C2×Q32—111no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×D16—111no—
290C2×D16C2×D1111yescharacteristic
291C2×M32—111no—
292C22×C16—111no—
293#495—111no—
294#494—111no—
295#467—111no—
296#467—111no—
297#467—111no—
298#466—111no—
299#463—221no—
300#461—221no—
301#452—221no—
302#452—221no—
303#450—221no—
304#449—221no—
305C4×D8C2×D1111yescharacteristic
306C4×D8C2×D1111yescharacteristic, complemented
307C8×D4—111no—
308#367C2×D1111yescharacteristic, complemented
309C4⋊C16—111no—
310#358—111no—
311#358—111no—
312#358—111no—
313#357—111no—
314#357C2×D1111yescharacteristic
315#357C2×D1111yescharacteristic, complemented
316C22⋊C16—111no—
317C22⋊C16—111no—
318#346C2×D1111yescharacteristic, complemented
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11C22×D811yescharacteristic
326C2×D11—21no—
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—164no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11D4211yescharacteristic
341C4×C11#57611yescharacteristic
342Dic11—21no—
343Dic11—21no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347C2×#41—221no—
348C2×#41—221no—
349C2×#41—221no—
350C22×D4—221no—
351#135—222no—
352#135—222no—
353#135—222no—
354#135—441no—
355#135—441no—
356#135—441no—
357C2×Q16—111no—
358C2×Q16—111no—
359C2×Q16—111no—
360C2×Q16—221no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×SD16—221no—
365C2×D8—111no—
366C2×D8—221no—
367C2×D8—222no—
368C2×D8—441no—
369C2×D8C22×D1111yescharacteristic
370C2×D8C22×D1111yescharacteristic
371C22×C8—111no—
372C22×C8—111no—
373C4⋊Q8—221no—
374#124—221no—
375#123—441no—
376#123—441no—
377#123—441no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380C22⋊Q8—221no—
381#121—221no—
382#121—441no—
383#121—441no—
384#120—441no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—111no—
388C2×C4⋊C4—441no—
389C2×C22⋊C4—441no—
390Q32—222no—
391Q32—441no—
392SD32—222no—
393SD32—222no—
394SD32—222no—
395SD32—222no—
396SD32—441no—
397D16—222no—
398D16D4414yescomplemented
399M32—222no—
400C2×C16—111no—
401C2×C16—111no—
402C2×C16—222no—
403C2×C16C22×D1111yescharacteristic
404C2×C16C22×D1111yescharacteristic
405#107C22×D1111yescharacteristic
406#107C22×D1111yescharacteristic
407C4⋊C8—111no—
408#103—221no—
409#103—221no—
410#103—221no—
411#102—21no—
412#102—21no—
413#102—221no—
414C22⋊C8—111no—
415C22⋊C8—111no—
416C4×C8C22×D1111yescharacteristic
417C2×C11—82no—
418C2×C11—82no—
419C2×C11D4×D811yescharacteristic
420C2×C11#341411yescharacteristic
421C2×C11#341611yescharacteristic
422D11—41no—
423D11—41no—
424D11—161no—
425C24—441no—
426#41—442no—
427#41—442no—
428#41—442no—
429#41—881no—
430#41—881no—
431#41—881no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—111no—
438C2×D4—221no—
439C2×D4—441no—
440C2×D4—441no—
441C2×D4—442no—
442C2×D4—441no—
443C2×D4—441no—
444C2×D4—441no—
445C2×D4—881no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4—441no—
453Q16—221no—
454Q16—221no—
455Q16—221no—
456Q16—221no—
457Q16—221no—
458Q16—221no—
459Q16—881no—
460SD16—442no—
461SD16—442no—
462SD16—442no—
463SD16—881no—
464D8—21no—
465D8—21no—
466D8—221no—
467D8—221no—
468D8—442no—
469D8C2×D4412yes—
470D8C2×D4412yes—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8D4×D1111yescharacteristic
478C2×C8C23×D1111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—111no—
482C4⋊C4—441no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4—441no—
486C4⋊C4—441no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—111no—
490C22⋊C4—111no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C22⋊C4—441no—
494C22⋊C4—441no—
495C22⋊C4—441no—
496C22⋊C4—441no—
497C42D4×D1111yescharacteristic
498C16—21no—
499C16—221no—
500C16—221no—
501C16C2×D4412yes—
502C11#3383311yescharacteristic, complemented, Sylow
503C23—41no—
504C23—41no—
505C23—111no—
506C23—111no—
507C23—441no—
508C23—882no—
509C23—882no—
510C23—1761no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515Q8—441no—
516Q8—441no—
517D4—22no—
518D4—22no—
519D4—41no—
520D4—41no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—882no—
525D4—882no—
526D4—882no—
527D4—882no—
528D4—1761no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—111no—
533C2×C4—111no—
534C2×C4—161no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4—882no—
544C2×C4—882no—
545C2×C4D8×D1111yescharacteristic
546C2×C4D8×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C8—21no—
549C8—221no—
550C8—221no—
551C8C22×D4411yescharacteristic
552C8#6704211yescharacteristic
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—221no—
560C22—221no—
561C22—221no—
562C22—221no—
563C22—221no—
564C22—221no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—1764no—
569C22C2×D8×D1111yescharacteristic
570C4—21no—
571C4—21no—
572C4—81no—
573C4—81no—
574C4—221no—
575C4—221no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4D4×D4411yescharacteristic
580C4#1062330011yescharacteristic
581C2—82no—
582C2—82no—
583C2—441no—
584C2—441no—
585C2—1761no—
586C2D8×D4411yescharacteristic
587C2#1308174811yescharacteristic
588C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2177C2
socleC22×C11C22×D8
hypercenter#2177D11
hypocenterC11#33833
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C2×#10622525C2semidirect
3. #13080337C2semidirect
4. #13080302C2semidirect
5. #13070887C2semidirect
6. #13070725C2semidirect
7. #13070713C2semidirect
8. #13070671C2semidirect
9. #13070661C2semidirect
10. #13070557C2semidirect
11. #13070557C2semidirect
12. #13070546C2semidirect
13. #13070540C2semidirect
14. #13070443C2semidirect
15. C11×#2177C2semidirect
18. C2×#66965C22semidirect
24. C4×C11×D8C22semidirect
27. C2×#66891C22semidirect
33. C2×Dic88C22semidirect
34. C2×Dic88C22semidirect
38. C2×C16×D11C22semidirect
41. #10622500C22semidirect
47. #10622312C22semidirect
50. C11×#367C22semidirect
52. C11×#357C22semidirect
53. C11×#346C22semidirect
55. (C2×D11)⋊C16C22semidirect
56. #10622130C22semidirect
57. #10622130C22semidirect
58. #10622130C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
104. C11×D16D4semidirect
222. #2177D11semidirect
306. C4×D8C2×D11semidirect
308. #367C2×D11semidirect
315. #357C2×D11semidirect
318. #346C2×D11semidirect
398. D16D44semidirect
502. C11#33833semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C2×#106225252
#130803372
#130803022
#130708872
#130707252
#130707132
#130706712
#130706612
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