Finite Group Databasebeta

← #14910281

Subgroups — #14910281

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×#10622521C211yesmaximal, characteristic, complemented
2C2×#10622517C211yesmaximal, characteristic, complemented
3#13080338C211yesmaximal, characteristic, complemented
4#13080303C211yesmaximal, characteristic, complemented
5#13070887C211yesmaximal, characteristic, complemented
6#13070724C211yesmaximal, characteristic, complemented
7#13070712C211yesmaximal, characteristic, complemented
8#13070672C211yesmaximal, characteristic, complemented
9#13070662C211yesmaximal, characteristic, complemented
10#13070558C211yesmaximal, characteristic, complemented
11#13070558C211yesmaximal, characteristic, complemented
12#13070547C211yesmaximal, characteristic, complemented
13#13070541C211yesmaximal, characteristic, complemented
14#13070493C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18C2×#66957C2211yescharacteristic, complemented
19C22×D88C2211yescharacteristic
20#10623082—21no—
21#10623081—21no—
22C2×C11×M32C2211yescharacteristic
23C22×C11×C16C2211yescharacteristic, complemented
24C8×D4×C11C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622729C2211yescharacteristic
27#10622729C2211yescharacteristic, complemented
28#10622728C2211yescharacteristic
29#10622521—24no—
30C2×Dic88C2211yescharacteristic, complemented
31C2×Dic88C2211yescharacteristic, complemented
32#10622517—24no—
33C2×#66864C2211yescharacteristic
34C2×#66864C2211yescharacteristic
35C2×#66864C2211yescharacteristic
36C2×#66864C2211yescharacteristic
37C2×#66864C2211yescharacteristic, complemented
38C2×D176C2211yescharacteristic
39C2×D176C2211yescharacteristic
40#10622457—21no—
41#10622454—21no—
42#10622347—21no—
43#10622346—21no—
44#10622346—21no—
45#10622344—21no—
46#10622312C2211yescharacteristic, complemented
47#10622309C2211yescharacteristic
48C4×D88C2211yescharacteristic
49C4×D88C2211yescharacteristic, complemented
50C11×C4⋊C16C2211yescharacteristic, complemented
51C11×C22⋊C16C2211yescharacteristic
52C11×C22⋊C16C2211yescharacteristic, complemented
53C11×#346C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622147C2211yescharacteristic
56#10622147C2211yescharacteristic, complemented
57#10622143C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59#10622141C2211yescharacteristic, complemented
60#10622141C2211yescharacteristic, complemented
61C2×#4339—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C22×D44—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11D411yescharacteristic
68#66991—41no—
69#66990—41no—
70#66983—21no—
71#66977—21no—
72#66977—21no—
73#66977—21no—
74C2×Dic44—21no—
75C2×Dic44C2311yescharacteristic
76C2×Dic44C2311yescharacteristic
77C2×Dic44C2311yescharacteristic
78#66957—22no—
79#66957—22no—
80#66957—22no—
81#66957—41no—
82#66957—41no—
83#66957—41no—
84C2×D88—22no—
85C2×D88—21no—
86C2×D88—41no—
87C2×D88C2311yescharacteristic
88C2×D88C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×#4314—21no—
91C2×#4314—21no—
92C2×#4314—21no—
93C2×#4314—21no—
94#66947—41no—
95C4⋊C4×D11—41no—
96#66937—41no—
97#66936—41no—
98#66936—41no—
99C22⋊C4×D11—41no—
100#66928—21no—
101C4×D44—21no—
102C4×D44—21no—
103#66922—21no—
104C11×M32—22no—
105C2×C11×C16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C2×C11×C16C2311yescharacteristic
109C2×C11×C16C2311yescharacteristic
110C11×C4⋊C8D411yescharacteristic
111C11×C22⋊C8D411yescharacteristic
112C11×C22⋊C8D411yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66885—21no—
115#66885—21no—
116#66885—21no—
117#66882C2311yescharacteristic
118#66882C2311yescharacteristic
119#66880—21no—
120#66880—21no—
121#66880—21no—
122Dic88—22no—
123Dic88—41no—
124#66864—22no—
125#66864—22no—
126#66864—22no—
127#66864—22no—
128#66864—41no—
129D176—22no—
130D176D414yescomplemented
131#33833—111nomaximal, Sylow
132C23×D11—41no—
133C2×D4×C11D811yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140#4339—42no—
141#4339—42no—
142#4339—42no—
143#4339—81no—
144#4339—81no—
145#4339—81no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—42no—
150C2×D44—41no—
151C2×D44—81no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×C4×D11—41no—
156C2×C4×D11—41no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2411yescharacteristic
168C11×C4⋊C4D811yescharacteristic
169C11×C22⋊C4D811yescharacteristic
170C11×C22⋊C4D811yescharacteristic
171C42×C11C2×D411yescharacteristic
172C22⋊Dic11—41no—
173C22⋊Dic11—41no—
174C22⋊Dic11—41no—
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—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—41no—
183C4⋊Dic11—41no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186Dic11⋊C4—41no—
187Dic44—21no—
188Dic44—21no—
189Dic44—21no—
190Dic44—21no—
191Dic44—21no—
192Dic44—21no—
193Dic44—81no—
194D88—21no—
195D88—21no—
196D88—21no—
197D88—21no—
198D88—42no—
199D88C2×D412yes—
200D88C2×D412yes—
201#4314—42no—
202#4314—42no—
203#4314—42no—
204#4314—81no—
205C11×C16—21no—
206C11×C16—21no—
207C11×C16—21no—
208C11×C16C2×D412yes—
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#2177—111no—
223#2168D1111yescharacteristic, complemented
224C23×C11C2×D811yescharacteristic
225C23×C11C2×D811yescharacteristic
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—82no—
230C22×D11—82no—
231C22×D11—161no—
232D4×C11—41no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11C2×D811yescharacteristic
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C2×D811yescharacteristic
240C2×C4×C11C2×D811yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C22⋊D11—82no—
243C22⋊D11—82no—
244C22⋊D11—82no—
245C22⋊D11—161no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251D44—22no—
252D44—22no—
253D44—41no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—82no—
258C4×D11—82no—
259C4×D11—82no—
260C4×D11—82no—
261C4×D11—82no—
262C4×D11—161no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11C22×D411yescharacteristic
273C8×C11H(5,𝔽2)11yescharacteristic
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×D16—111no—
291C2×M32C2×D1111yescharacteristic
292C22×C16C2×D1111yescharacteristic, complemented
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×D8—111no—
306C4×D8—111no—
307C8×D4C2×D1111yescharacteristic
308#367—111no—
309C4⋊C16C2×D1111yescharacteristic, complemented
310#358—111no—
311#358—111no—
312#358—111no—
313#357—111no—
314#357—111no—
315#357—111no—
316C22⋊C16C2×D1111yescharacteristic
317C22⋊C16C2×D1111yescharacteristic, complemented
318#346C2×D1111yescharacteristic, complemented
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11C22×D811yescharacteristic
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—164no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11D4211yescharacteristic
341C4×C11#57611yescharacteristic
342Dic11—81no—
343Dic11—81no—
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—111no—
367C2×D8—111no—
368C2×D8—222no—
369C2×D8—221no—
370C2×D8—441no—
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
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—221no—
386C4×D4—221no—
387C4×D4D4411yescharacteristic
388C2×C4⋊C4—441no—
389C2×C22⋊C4—441no—
390Q32—222no—
391Q32—441no—
392SD32—222no—
393SD32—222no—
394SD32—222no—
395SD32—222no—
396SD32—441no—
397D16—114no—
398D16—222no—
399M32—22no—
400C2×C16—22no—
401C2×C16C22×D1111yescharacteristic
402C2×C16C22×D1111yescharacteristic
403C2×C16C22×D1111yescharacteristic
404C2×C16C22×D1111yescharacteristic
405#107—111no—
406#107—111no—
407C4⋊C8D4411yescharacteristic
408#103—221no—
409#103—221no—
410#103—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414C22⋊C8D4411yescharacteristic
415C22⋊C8D4411yescharacteristic
416C4×C8C22×D1111yescharacteristic
417C2×C11—41no—
418C2×C11—41no—
419C2×C11D4×D811yescharacteristic
420C2×C11#341411yescharacteristic
421C2×C11#341611yescharacteristic
422D11—82no—
423D11—82no—
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—221no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—442no—
439C2×D4—441no—
440C2×D4—441no—
441C2×D4—441no—
442C2×D4—441no—
443C2×D4—441no—
444C2×D4—881no—
445C2×D4D8811yescharacteristic
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×D4411yescharacteristic
453Q16—221no—
454Q16—221no—
455Q16—221no—
456Q16—221no—
457Q16—221no—
458Q16—221no—
459Q16—881no—
460SD16—442no—
461SD16—442no—
462SD16—442no—
463SD16—881no—
464D8—112no—
465D8—112no—
466D8—221no—
467D8—221no—
468D8—221no—
469D8—221no—
470D8—442no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×D4411yescharacteristic
476C2×C8C2×D4411yescharacteristic
477C2×C8C2×D4411yescharacteristic
478C2×C8C23×D1111yescharacteristic
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4—441no—
486C4⋊C4D8811yescharacteristic
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C22⋊C4—441no—
494C22⋊C4—441no—
495C22⋊C4D8811yescharacteristic
496C22⋊C4D8811yescharacteristic
497C42C2×D4411yescharacteristic
498C16—21no—
499C16—21no—
500C16—21no—
501C16D4×D1112yes—
502C11#3383311yescharacteristic, complemented, Sylow
503C23—441no—
504C23—441no—
505C23—441no—
506C23—882no—
507C23—882no—
508C23—1761no—
509C23C2×D8811yescharacteristic
510C23C2×D8811yescharacteristic
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515Q8—441no—
516Q8—441no—
517D4—41no—
518D4—222no—
519D4—222no—
520D4—441no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—882no—
525D4—882no—
526D4—882no—
527D4—882no—
528D4—1761no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—882no—
539C2×C4—882no—
540C2×C4—882no—
541C2×C4—882no—
542C2×C4—1761no—
543C2×C4C2×D8811yescharacteristic
544C2×C4C2×D8811yescharacteristic
545C2×C4C2×D8811yescharacteristic
546C2×C4C2×D8811yescharacteristic
547C2×C4C22×D4411yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8C2×D4×D1111yescharacteristic
552C8#6704211yescharacteristic
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—442no—
560C22—442no—
561C22—881no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—1764no—
569C22C22×D8811yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—881no—
575C4—881no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4D4×D4411yescharacteristic
580C4#1062328311yescharacteristic
581C2—41no—
582C2—41no—
583C2—882no—
584C2—882no—
585C2—1761no—
586C2D4×D8811yescharacteristic
587C2#1308175211yescharacteristic
588C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33833
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C2×#10622517C2semidirect
3. #13080338C2semidirect
4. #13080303C2semidirect
5. #13070887C2semidirect
6. #13070724C2semidirect
7. #13070712C2semidirect
8. #13070672C2semidirect
9. #13070662C2semidirect
10. #13070558C2semidirect
11. #13070558C2semidirect
12. #13070547C2semidirect
13. #13070541C2semidirect
14. #13070493C2semidirect
15. C11×#2168C2semidirect
18. C2×#66957C22semidirect
23. C22×C11×C16C22semidirect
27. #10622729C22semidirect
30. C2×Dic88C22semidirect
31. C2×Dic88C22semidirect
37. C2×#66864C22semidirect
46. #10622312C22semidirect
49. C4×D88C22semidirect
50. C11×C4⋊C16C22semidirect
52. C11×C22⋊C16C22semidirect
53. C11×#346C22semidirect
56. #10622147C22semidirect
57. #10622143C22semidirect
58. #10622141C22semidirect
59. #10622141C22semidirect
60. #10622141C22semidirect
130. D176D4semidirect
223. #2168D11semidirect
292. C22×C16C2×D11semidirect
309. C4⋊C16C2×D11semidirect
317. C22⋊C16C2×D11semidirect
318. #346C2×D11semidirect
502. C11#33833semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
C2×#106225172
#130803382
#130803032
#130708872
#130707242
#130707122
#130706722
#130706622
#130705582
#130705472
#130705412
#130704932
C11×#21682
#3383311