Finite Group Databasebeta

← #14910251

Subgroups — #14910251

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2C22×#66864C211yesmaximal, characteristic, complemented
3#13080359C211yesmaximal, characteristic, complemented
4D4×D88C211yesmaximal, characteristic, complemented
5#13070882C211yesmaximal, characteristic, complemented
6#13070729C211yesmaximal, characteristic, complemented
7#13070702C211yesmaximal, characteristic, complemented
8#13070672C211yesmaximal, characteristic, complemented
9#13070657C211yesmaximal, characteristic, complemented
10#13070547C211yesmaximal, characteristic, complemented
11#13070541C211yesmaximal, characteristic, complemented
12#13070535C211yesmaximal, characteristic, complemented
13#13070530C211yesmaximal, characteristic, complemented
14#13070482C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic, complemented
17C2×#66957C2211yescharacteristic, complemented
18C22×D88C2211yescharacteristic
19C22×D88C2211yescharacteristic
20#10623083—21no—
21D4×D44—21no—
22C2×C11×M32C2211yescharacteristic, complemented
23C22×C11×C16C2211yescharacteristic, complemented
24C8×D4×C11C2211yescharacteristic
25#10622729C2211yescharacteristic, complemented
26#10622728C2211yescharacteristic
27#10622728C2211yescharacteristic
28#10622728C2211yescharacteristic, complemented
29#10622521—24no—
30C2×#66864—24no—
31C2×#66864C2211yescharacteristic
32C2×#66864C2211yescharacteristic
33C2×#66864C2211yescharacteristic, complemented
34C2×#66864C2211yescharacteristic, complemented
35C2×#66864C2211yescharacteristic, complemented
36C2×#66864C2211yescharacteristic, complemented
37C2×D176C2211yescharacteristic
38C2×D176C2211yescharacteristic, complemented
39C2×D176C2211yescharacteristic, complemented
40#10622458—21no—
41#10622456—21no—
42#10622351—21no—
43#10622346—21no—
44#10622345—21no—
45#10622345—21no—
46C4×Dic44C2211yescharacteristic, complemented
47#10622309C2211yescharacteristic, complemented
48#10622308C2211yescharacteristic
49C4×D88C2211yescharacteristic
50C11×C4⋊C16C2211yescharacteristic, complemented
51C11×C22⋊C16C2211yescharacteristic, complemented
52C11×C22⋊C16C2211yescharacteristic, complemented
53C11×#346C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622147C2211yescharacteristic, complemented
56#10622147C2211yescharacteristic, complemented
57#10622147C2211yescharacteristic, complemented
58#10622142C2211yescharacteristic, complemented
59#10622141C2211yescharacteristic, complemented
60#10622141C2211yescharacteristic, complemented
61C2×D4×D11—41no—
62C2×#4339—21no—
63C22×D44—21no—
64C22×D44—21no—
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×D4×C11D411yescharacteristic
69#66992—41no—
70#66983—21no—
71#66983—21no—
72#66983—21no—
73#66977—21no—
74C2×Dic44—22no—
75C2×Dic44—21no—
76C2×Dic44—41no—
77C2×Dic44C2311yescharacteristic
78C2×Dic44C2311yescharacteristic
79#66957—22no—
80#66957—41no—
81C2×D88—22no—
82C2×D88—22no—
83C2×D88—21no—
84C2×D88—21no—
85C2×D88—21no—
86C2×D88—41no—
87C2×D88—41no—
88C2×D88C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×D88C2311yescharacteristic
91C2×D88C2311yescharacteristic
92C2×#4314—21no—
93C2×#4314—21no—
94#66949—41no—
95#66948—41no—
96#66938—41no—
97#66935—41no—
98#66935—41no—
99(C22⋊D11)⋊C4—41no—
100#66928—21no—
101#66927—21no—
102C4×D44—21no—
103C4×Dic22—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#66885—21no—
118#66882C2311yescharacteristic
119#66882C2311yescharacteristic
120#66880—21no—
121#66880—21no—
122#66864—22no—
123#66864—22no—
124#66864—22no—
125#66864—22no—
126#66864—41no—
127#66864D414yescomplemented
128D176—22no—
129D176—22no—
130D176—41no—
131#33831—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C2×D4×C11D811yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C22×Dic11—41no—
142D4×D11—84no—
143#4339—42no—
144#4339—81no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—41no—
152C2×D44—41no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—81no—
156C2×D44—81no—
157C2×C4×D11—41no—
158C2×C4×D11—41no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—42no—
162C2×Dic22—41no—
163C2×Dic22—81no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2411yescharacteristic
172C11×C4⋊C4D811yescharacteristic
173C11×C22⋊C4D811yescharacteristic
174C11×C22⋊C4D811yescharacteristic
175C42×C11C2×D411yescharacteristic
176C22⋊Dic11—41no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185Dic11⋊C4—41no—
186Dic11⋊C4—41no—
187C4×Dic11—41no—
188Dic44—21no—
189Dic44—21no—
190Dic44—21no—
191Dic44—42no—
192Dic44C2×D412yescomplemented
193D88—21no—
194D88—21no—
195D88—21no—
196D88—21no—
197D88—21no—
198D88—21no—
199D88—21no—
200D88—42no—
201D88—42no—
202D88—81no—
203D88C2×D412yes—
204#4314—42no—
205#4314—81no—
206C11×C16—21no—
207C11×C16—21no—
208C11×C16—21no—
209C11×C16C2×D412yescomplemented
210C2×#509—111no—
211C22×SD32—111no—
212#3285—111no—
213D4×D8—111no—
214#2250—111no—
215#2220—111no—
216#2215—111no—
217#2210—111no—
218#2207—111no—
219#2187—111no—
220#2186—111no—
221#2185—111no—
222#2184—111no—
223#2175—111no—
224#2168D1111yescharacteristic, complemented
225C23×C11C2×D811yescharacteristic
226C23×C11C2×D811yescharacteristic
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—82no—
235C22×D11—161no—
236C22×D11—161no—
237D4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11C2×D811yescharacteristic
243C2×C4×C11C2×D811yescharacteristic
244C2×C4×C11C2×D811yescharacteristic
245C2×C4×C11C2×D811yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C22⋊D11—82no—
248C22⋊D11—82no—
249C22⋊D11—82no—
250C22⋊D11—82no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—82no—
256D44—22no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—82no—
265D44—82no—
266D44—82no—
267D44—161no—
268C4×D11—82no—
269C4×D11—82no—
270Dic22—22no—
271Dic22—41no—
272Dic22—41no—
273Dic22—41no—
274Dic22—82no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11C22×D411yescharacteristic
279C8×C11H(5,𝔽2)11yescharacteristic
280C2×#135—111no—
281C22×Q16—111no—
282C22×D8—111no—
283C22×D8—111no—
284#548—221no—
285D42—221no—
286#509—224no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32—111no—
293C2×SD32—224no—
294C2×D16—111no—
295C2×D16—111no—
296C2×D16—111no—
297C2×M32C2×D1111yescharacteristic, complemented
298C22×C16C2×D1111yescharacteristic, complemented
299#495—111no—
300#493—111no—
301#467—111no—
302#466—111no—
303#466—111no—
304#466—111no—
305#464—221no—
306#459—221no—
307#452—221no—
308#448—221no—
309#447—221no—
310#447—221no—
311C4×Q16—111no—
312C4×D8—111no—
313C8×D4C2×D1111yescharacteristic
314#366—111no—
315C4⋊C16C2×D1111yescharacteristic, complemented
316#358—111no—
317#358—111no—
318#357—111no—
319#357—111no—
320#357—111no—
321#357—111no—
322C22⋊C16C2×D1111yescharacteristic, complemented
323C22⋊C16C2×D1111yescharacteristic, complemented
324#346C2×D1111yescharacteristic, complemented
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11#50912yescomplemented
331C22×C11C22×D811yescharacteristic
332C2×D11—42no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—164no—
345C2×D11—164no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11D4211yescharacteristic
351C4×C11#57611yescharacteristic
352Dic11—42no—
353Dic11—81no—
354Dic11—81no—
355Dic11—81no—
356C2×#41—221no—
357C22×Q8—221no—
358C22×D4—221no—
359C22×D4—221no—
360C22×D4—441no—
361#135—222no—
362#135—441no—
363C2×Q16—111no—
364C2×Q16—111no—
365C2×Q16—222no—
366C2×Q16—221no—
367C2×Q16—441no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×D8—111no—
371C2×D8—111no—
372C2×D8—111no—
373C2×D8—111no—
374C2×D8—222no—
375C2×D8—222no—
376C2×D8—221no—
377C2×D8—221no—
378C2×D8—221no—
379C2×D8—441no—
380C2×D8—441no—
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383#127—221no—
384#124—221no—
385#124—441no—
386C22⋊Q8—221no—
387C22⋊Q8—441no—
388#121—221no—
389#121—221no—
390#121—221no—
391#121—441no—
392#121—441no—
393#120—441no—
394#120—441no—
395C4×Q8—221no—
396C4×D4—221no—
397C4×D4—441no—
398C4×D4D4411yescharacteristic
399SD32—114no—
400SD32—222no—
401SD32—222no—
402SD32—222no—
403SD32—222no—
404SD32—441no—
405D16—222no—
406D16—222no—
407D16—441no—
408M32—22no—
409C2×C16—22no—
410C2×C16C22×D1111yescharacteristic
411C2×C16C22×D1111yescharacteristic
412C2×C16C22×D1111yescharacteristic
413C2×C16C22×D1111yescharacteristic
414#107—111no—
415#107—111no—
416C4⋊C8D4411yescharacteristic
417#103—221no—
418#103—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423C22⋊C8D4411yescharacteristic
424C22⋊C8D4411yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C2×C11—22no—
427C2×C11—41no—
428C2×C11D4×D811yescharacteristic
429C2×C11C2×#50911yescharacteristic
430C2×C11#341611yescharacteristic
431D11—82no—
432D11—161no—
433D11—161no—
434D11—161no—
435C24—441no—
436C24—441no—
437#41—442no—
438#41—881no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—442no—
442C2×Q8—441no—
443C2×Q8—881no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—442no—
449C2×D4—442no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—441no—
456C2×D4—441no—
457C2×D4—441no—
458C2×D4—881no—
459C2×D4—881no—
460C2×D4—884no—
461C2×D4D8811yescharacteristic
462C22×C4—441no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467Q16—112no—
468Q16—221no—
469Q16—221no—
470Q16—221no—
471Q16—442no—
472SD16—442no—
473SD16—881no—
474D8—112no—
475D8—221no—
476D8—221no—
477D8—221no—
478D8—221no—
479D8—221no—
480D8—221no—
481D8—221no—
482D8—442no—
483D8—442no—
484D8—881no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8C2×D4411yescharacteristic
490C2×C8C2×D4411yescharacteristic
491C2×C8C2×D4411yescharacteristic
492C2×C8C23×D1111yescharacteristic
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—441no—
496C4⋊C4—441no—
497C4⋊C4D8811yescharacteristic
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C22⋊C4—441no—
505C22⋊C4D8811yescharacteristic
506C22⋊C4D8811yescharacteristic
507C42—441no—
508C42C2×D4411yescharacteristic
509C16—21no—
510C16—21no—
511C16—21no—
512C16D4×D1112yescomplemented
513C11#3383111yescharacteristic, complemented, Sylow
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—882no—
519C23—882no—
520C23—882no—
521C23—882no—
522C23—1761no—
523C23—1761no—
524C23C2×D8811yescharacteristic
525C23C2×D8811yescharacteristic
526Q8—222no—
527Q8—441no—
528Q8—441no—
529Q8—441no—
530Q8—882no—
531D4—22no—
532D4—222no—
533D4—441no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—882no—
541D4—882no—
542D4—882no—
543D4—882no—
544D4—882no—
545D4—882no—
546D4—882no—
547D4—1761no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—882no—
557C2×C4—882no—
558C2×C4—882no—
559C2×C4C2×D8811yescharacteristic
560C2×C4C2×D8811yescharacteristic
561C2×C4C2×D8811yescharacteristic
562C2×C4C2×D8811yescharacteristic
563C2×C4C22×D4411yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8C2×D4×D1111yescharacteristic
568C8#6704211yescharacteristic
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—442no—
575C22—881no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22—881no—
586C22—1764no—
587C22—1764no—
588C22#1062252112yescomplemented
589C22C22×D8811yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—442no—
595C4—881no—
596C4—881no—
597C4—881no—
598C4D4×D4411yescharacteristic
599C4#1062328311yescharacteristic
600C2—22no—
601C2—41no—
602C2—882no—
603C2—1761no—
604C2—1761no—
605C2—1761no—
606C2D4×D8811yescharacteristic
607C2C2×#1062252111yescharacteristic
608C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33831
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. C22×#66864C2semidirect
3. #13080359C2semidirect
4. D4×D88C2semidirect
5. #13070882C2semidirect
6. #13070729C2semidirect
7. #13070702C2semidirect
8. #13070672C2semidirect
9. #13070657C2semidirect
10. #13070547C2semidirect
11. #13070541C2semidirect
12. #13070535C2semidirect
13. #13070530C2semidirect
14. #13070482C2semidirect
15. C11×#2168C2semidirect
16. C22×Dic44C22semidirect
17. C2×#66957C22semidirect
22. C2×C11×M32C22semidirect
23. C22×C11×C16C22semidirect
25. #10622729C22semidirect
28. #10622728C22semidirect
33. C2×#66864C22semidirect
34. C2×#66864C22semidirect
35. C2×#66864C22semidirect
36. C2×#66864C22semidirect
38. C2×D176C22semidirect
39. C2×D176C22semidirect
46. C4×Dic44C22semidirect
47. #10622309C22semidirect
50. C11×C4⋊C16C22semidirect
51. C11×C22⋊C16C22semidirect
52. C11×C22⋊C16C22semidirect
53. C11×#346C22semidirect
55. #10622147C22semidirect
56. #10622147C22semidirect
57. #10622147C22semidirect
58. #10622142C22semidirect
59. #10622141C22semidirect
60. #10622141C22semidirect
127. #66864D4semidirect
192. Dic44C2×D4semidirect
209. C11×C16C2×D4semidirect
224. #2168D11semidirect
297. C2×M32C2×D11semidirect
298. C22×C16C2×D11semidirect
315. C4⋊C16C2×D11semidirect
322. C22⋊C16C2×D11semidirect
323. C22⋊C16C2×D11semidirect
324. #346C2×D11semidirect
330. C22×C11#509semidirect
512. C16D4×D11semidirect
513. C11#33831semidirect
588. C22#10622521semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
C22×#668642
#130803592
D4×D882
#130708822
#130707292
#130707022
#130706722
#130706572
#130705472
#130705412
#130705352
#130705302
#130704822
C11×#21682
#3383111