Finite Group Databasebeta

← #14910263

Subgroups — #14910263

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622528C211yesmaximal, characteristic, complemented
2C2×D11×SD32C211yesmaximal, characteristic, complemented
3Q16×D44C211yesmaximal, characteristic, complemented
4#13080302C211yesmaximal, characteristic
5#13070887C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070708C211yesmaximal, characteristic, complemented
8#13070678C211yesmaximal, characteristic, complemented
9#13070661C211yesmaximal, characteristic, complemented
10#13070557C211yesmaximal, characteristic, complemented
11#13070551C211yesmaximal, characteristic, complemented
12#13070546C211yesmaximal, characteristic, complemented
13#13070534C211yesmaximal, characteristic, complemented
14#13070443C211yesmaximal, characteristic, complemented
15C11×#2175C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic, complemented
18C2×#66965C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20Q8×D44—21no—
21#10623085—21no—
22C2×C11×SD32C2211yescharacteristic
23C4×C11×Q16C2211yescharacteristic, complemented
24C4×C11×D8C2211yescharacteristic
25C2×#66893C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29#10622644—21no—
30#10622629—21no—
31#10622528—24no—
32D11×SD32—24no—
33C2×Dic88C2211yescharacteristic, complemented
34C2×Dic88C2211yescharacteristic, complemented
35C2×#66864C2211yescharacteristic
36C2×#66864C2211yescharacteristic
37C2×#66862C2211yescharacteristic, complemented
38C2×C16×D11C2211yescharacteristic
39#10622500C2211yescharacteristic
40#10622500C2211yescharacteristic
41#10622500C2211yescharacteristic, complemented
42#10622496C2211yescharacteristic
43#10622421—21no—
44#10622421—21no—
45#10622394—21no—
46#10622389—21no—
47#10622312C2211yescharacteristic, complemented
48#10622309C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C11×#366C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic
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×Q8×D11—21no—
62C2×Q8×D11—21no—
63C2×#4341—21no—
64C2×D4×D11—21no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C4×Q8×C11—21no—
68C4×D4×C11—21no—
69C2×#4326—21no—
70C2×#4326—21no—
71C2×#4324—21no—
72C2×#4323—21no—
73#66983—41no—
74C2×(C2×D11)⋊C4—41no—
75Q16×D11—22no—
76Q16×D11—22no—
77Q16×D11—41no—
78Q16×D11—41no—
79#66965—22no—
80#66965—41no—
81D8×D11—22no—
82D8×D11—41no—
83C2×Dic44—21no—
84C2×Dic44C2311yescharacteristic
85C2×Dic44C2311yescharacteristic
86C2×Dic44C2311yescharacteristic
87C2×D88C2311yescharacteristic
88C2×#4314—21no—
89C2×C8×D11C2311yescharacteristic
90C2×C8×D11C2311yescharacteristic
91#66950—21no—
92#66950—21no—
93#66950—21no—
94#66950—41no—
95#66950—41no—
96#66948—21no—
97#66939—41no—
98#66935—41no—
99#66928—21no—
100C4×D44—41no—
101C4×D44D411yescharacteristic
102#66922—21no—
103#66922—41no—
104C11×SD32D414yescomplemented
105C2×C11×C16C2311yescharacteristic
106C2×C11×C16C2311yescharacteristic
107C11×#107C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110C11×#102—21no—
111C4×C8×C11C2311yescharacteristic
112#66893—22no—
113#66892—22no—
114#66891—22no—
115#66891—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#33832—111nomaximal, Sylow
132C23×D11—41no—
133C2×Q8×C11—21no—
134C2×D4×C11—21no—
135C22×C4×C11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C22×Dic11—41no—
139Q8×D11—42no—
140Q8×D11—42no—
141Q8×D11—81no—
142Q8×D11—81no—
143#4341—42no—
144#4341—81no—
145D4×D11—42no—
146D4×D11—81no—
147C2×D44—21no—
148C2×D44—41no—
149C2×D44D811yescharacteristic
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—41no—
158C2×Dic22—41no—
159C11×Q16—21no—
160C11×Q16C2×D412yes—
161C11×D8—21no—
162C11×D8C2×D412yes—
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C22⋊C4—41no—
169C42×C11—41no—
170C42×C11C2×D411yescharacteristic
171#4326—42no—
172#4326—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×#510—111no—
210C22×SD32—111no—
211D4×Q16—111no—
212#3280—111no—
213#2251—111no—
214#2220—111no—
215#2216—111no—
216#2211—111no—
217#2208—111no—
218#2189—111no—
219#2188—111no—
220#2187—111no—
221#2185—111no—
222#2175D1111yescharacteristic, complemented
223#2168—111no—
224C23×C11—41no—
225C22×D11—41no—
226C22×D11—82no—
227C22×D11—82no—
228C22×D11—161no—
229C22×D11C2×D811yescharacteristic
230C22×D11C2×D811yescharacteristic
231Q8×C11—22no—
232Q8×C11—41no—
233D4×C11—22no—
234D4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—161no—
239C2×C4×C11C2×D811yescharacteristic
240C2×C4×C11C2×D811yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C22⋊D11—82no—
243C22⋊D11—82no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—82no—
248C2×Dic11C2×D811yescharacteristic
249C2×Dic11C2×D811yescharacteristic
250D44—22no—
251D44—41no—
252D44—41no—
253D44—161no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—21no—
258C4×D11—82no—
259C4×D11—82no—
260Dic22—41no—
261Dic22—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—82no—
267Dic22—82no—
268C8×C11—21no—
269C8×C11C22×D411yescharacteristic
270C8×C11H(5,𝔽2)11yescharacteristic
271C11⋊C8—21no—
272C11⋊C8—21no—
273C2×#135—111no—
274C22×Q16—111no—
275C22×Q16—111no—
276C22×D8—111no—
277D4×Q8—221no—
278#546—221no—
279#510—224no—
280C2×Q32—111no—
281C2×Q32—111no—
282C2×Q32—111no—
283C2×SD32—111no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—224no—
289C2×SD32C2×D1111yescharacteristic
290C2×M32—111no—
291C22×C16—111no—
292#495—111no—
293#494—111no—
294#467—111no—
295#467—111no—
296#467—111no—
297#466—111no—
298#463—221no—
299#462—221no—
300#451—221no—
301#451—221no—
302#450—221no—
303#449—221no—
304C4×Q16C2×D1111yescharacteristic, complemented
305C4×D8C2×D1111yescharacteristic
306C8×D4—111no—
307#366C2×D1111yescharacteristic, complemented
308C4⋊C16—111no—
309#358—111no—
310#358—111no—
311#358—111no—
312#358C2×D1111yescharacteristic, complemented
313#357—111no—
314#357C2×D1111yescharacteristic
315C22⋊C16—111no—
316C22⋊C16—111no—
317#346C2×D1111yescharacteristic, complemented
318C22×C11—42no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11C22×D811yescharacteristic
322C2×D11—21no—
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—164no—
331C2×D11#51012yescomplemented
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—42no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11D4211yescharacteristic
338C4×C11#57611yescharacteristic
339Dic11—21no—
340Dic11—21no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344C2×#41—221no—
345C22×Q8—221no—
346C22×Q8—221no—
347C22×D4—221no—
348#135—222no—
349#135—441no—
350C2×Q16—111no—
351C2×Q16—111no—
352C2×Q16—111no—
353C2×Q16—221no—
354C2×Q16—221no—
355C2×Q16—222no—
356C2×Q16—222no—
357C2×Q16—221no—
358C2×Q16—441no—
359C2×Q16—441no—
360C2×Q16C22×D1111yescharacteristic
361C2×SD16—221no—
362C2×SD16—221no—
363C2×D8—111no—
364C2×D8—221no—
365C2×D8—222no—
366C2×D8—441no—
367C2×D8C22×D1111yescharacteristic
368C22×C8—111no—
369C22×C8—111no—
370C4⋊Q8—221no—
371C4⋊Q8—441no—
372#124—221no—
373#123—441no—
374C22⋊Q8—221no—
375C22⋊Q8—221no—
376C22⋊Q8—221no—
377C22⋊Q8—441no—
378C22⋊Q8—441no—
379#121—221no—
380#121—441no—
381#120—441no—
382C4×Q8—21no—
383C4×D4—21no—
384C4×D4—111no—
385C4×D4—441no—
386C2×C22⋊C4—441no—
387Q32—222no—
388Q32—222no—
389Q32—441no—
390SD32—222no—
391SD32—222no—
392SD32—222no—
393SD32—222no—
394SD32—441no—
395SD32D4414yescomplemented
396M32—222no—
397C2×C16—111no—
398C2×C16—111no—
399C2×C16—222no—
400C2×C16C22×D1111yescharacteristic
401C2×C16C22×D1111yescharacteristic
402#107C22×D1111yescharacteristic
403#107C22×D1111yescharacteristic
404C4⋊C8—111no—
405#103—21no—
406#103—221no—
407#103—221no—
408#103—221no—
409#102—21no—
410#102—221no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C4×C8C22×D1111yescharacteristic
414C2×C11—82no—
415C2×C11D4×D811yescharacteristic
416C2×C11C2×#51011yescharacteristic
417C2×C11#341611yescharacteristic
418D11—22no—
419D11—41no—
420D11—161no—
421C24—441no—
422#41—442no—
423#41—881no—
424C2×Q8—21no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—441no—
429C2×Q8—441no—
430C2×Q8—442no—
431C2×Q8—442no—
432C2×Q8—881no—
433C2×Q8—881no—
434C2×D4—21no—
435C2×D4—111no—
436C2×D4—221no—
437C2×D4—441no—
438C2×D4—441no—
439C2×D4—442no—
440C2×D4—441no—
441C2×D4—881no—
442C22×C4—41no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—441no—
448Q16—21no—
449Q16—221no—
450Q16—221no—
451Q16—221no—
452Q16—221no—
453Q16—221no—
454Q16—221no—
455Q16—442no—
456Q16—442no—
457Q16—881no—
458Q16C2×D4412yes—
459SD16—442no—
460SD16—881no—
461D8—21no—
462D8—221no—
463D8—221no—
464D8—442no—
465D8C2×D4412yes—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8D4×D1111yescharacteristic
473C2×C8C23×D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—111no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C22⋊C4—41no—
484C22⋊C4—111no—
485C22⋊C4—111no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C42—41no—
493C42D4×D1111yescharacteristic
494C16—21no—
495C16—221no—
496C16—221no—
497C16C2×D4412yes—
498C11#3383211yescharacteristic, complemented, Sylow
499C23—41no—
500C23—111no—
501C23—111no—
502C23—441no—
503C23—882no—
504C23—882no—
505C23—1761no—
506Q8—22no—
507Q8—41no—
508Q8—441no—
509Q8—441no—
510Q8—441no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—882no—
515Q8—882no—
516D4—22no—
517D4—41no—
518D4—222no—
519D4—441no—
520D4—441no—
521D4—882no—
522D4—882no—
523D4—1761no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—111no—
528C2×C4—111no—
529C2×C4—161no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—882no—
538C2×C4—882no—
539C2×C4—882no—
540C2×C4D8×D1111yescharacteristic
541C2×C4D8×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C8—21no—
544C8—221no—
545C8—221no—
546C8C22×D4411yescharacteristic
547C8#6704211yescharacteristic
548C22—42no—
549C22—81no—
550C22—81no—
551C22—112no—
552C22—221no—
553C22—221no—
554C22—221no—
555C22—221no—
556C22—221no—
557C22—881no—
558C22—881no—
559C22—881no—
560C22—1764no—
561C22C2×D8×D1111yescharacteristic
562C4—21no—
563C4—21no—
564C4—42no—
565C4—81no—
566C4—81no—
567C4—221no—
568C4—221no—
569C4—881no—
570C4—881no—
571C4—881no—
572C4D4×D4411yescharacteristic
573C4#1062330011yescharacteristic
574C2—82no—
575C2—222no—
576C2—441no—
577C2—1761no—
578C2D8×D4411yescharacteristic
579C2D11×#51011yescharacteristic
580C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2175C2
socleC22×C11C22×D8
prime radical#13080302C2
hypercenter#2175D11
hypocenterC11#33832
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. C2×#10622528C2semidirect
2. C2×D11×SD32C2semidirect
3. Q16×D44C2semidirect
5. #13070887C2semidirect
6. #13070730C2semidirect
7. #13070708C2semidirect
8. #13070678C2semidirect
9. #13070661C2semidirect
10. #13070557C2semidirect
11. #13070551C2semidirect
12. #13070546C2semidirect
13. #13070534C2semidirect
14. #13070443C2semidirect
15. C11×#2175C2semidirect
17. C2×Q16×D11C22semidirect
23. C4×C11×Q16C22semidirect
25. C2×#66893C22semidirect
33. C2×Dic88C22semidirect
34. C2×Dic88C22semidirect
37. C2×#66862C22semidirect
41. #10622500C22semidirect
47. #10622312C22semidirect
50. C11×#366C22semidirect
51. C11×#358C22semidirect
53. C11×#346C22semidirect
55. (C2×D11)⋊C16C22semidirect
56. #10622130C22semidirect
57. #10622130C22semidirect
58. #10622130C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
104. C11×SD32D4semidirect
222. #2175D11semidirect
304. C4×Q16C2×D11semidirect
307. #366C2×D11semidirect
312. #358C2×D11semidirect
317. #346C2×D11semidirect
331. C2×D11#510semidirect
395. SD32D44semidirect
498. C11#33832semidirect

Maximal subgroups

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

subgroupindex
C2×#106225282
C2×D11×SD322
Q16×D442
#130803022
#130708872
#130707302
#130707082
#130706782
#130706612
#130705572
#130705512
#130705462
#130705342
#130704432
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