Finite Group Databasebeta

← #14910266

Subgroups — #14910266

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×#10622522C211yesmaximal, characteristic, complemented
2C22×#66864C211yesmaximal, characteristic, complemented
3D4×Dic44C211yesmaximal, characteristic, complemented
4#13080303C211yesmaximal, characteristic
5#13070887C211yesmaximal, characteristic, complemented
6#13070729C211yesmaximal, characteristic, complemented
7#13070707C211yesmaximal, characteristic, complemented
8#13070679C211yesmaximal, characteristic, complemented
9#13070662C211yesmaximal, characteristic, complemented
10#13070558C211yesmaximal, characteristic, complemented
11#13070552C211yesmaximal, characteristic, complemented
12#13070547C211yesmaximal, characteristic, complemented
13#13070535C211yesmaximal, characteristic, complemented
14#13070482C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic
17C22×Dic44C2211yescharacteristic, complemented
18C2×#66957C2211yescharacteristic
19C22×D88C2211yescharacteristic
20#10623081—21no—
21D4×Dic22—21no—
22C2×C11×M32C2211yescharacteristic, complemented
23C22×C11×C16C2211yescharacteristic
24C8×D4×C11C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622729C2211yescharacteristic
27#10622729C2211yescharacteristic, complemented
28#10622728C2211yescharacteristic
29#10622522—24no—
30C2×Dic88C2211yescharacteristic, complemented
31C2×Dic88C2211yescharacteristic, complemented
32C2×Dic88C2211yescharacteristic, complemented
33C2×#66864—24no—
34C2×#66864C2211yescharacteristic
35C2×#66864C2211yescharacteristic
36C2×#66864C2211yescharacteristic
37C2×#66864C2211yescharacteristic
38C2×#66864C2211yescharacteristic
39C2×#66864C2211yescharacteristic
40#10622462—21no—
41#10622457—21no—
42#10622352—21no—
43#10622352—21no—
44#10622347—21no—
45#10622344—21no—
46#10622312C2211yescharacteristic, complemented
47C4×Dic44C2211yescharacteristic, complemented
48#10622309C2211yescharacteristic
49C4×D88C2211yescharacteristic
50C11×C4⋊C16C2211yescharacteristic, complemented
51C11×C22⋊C16C2211yescharacteristic
52C11×C22⋊C16C2211yescharacteristic, complemented
53C11×#346C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622147C2211yescharacteristic
56#10622142C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59#10622141C2211yescharacteristic, complemented
60#10622141C2211yescharacteristic, complemented
61C2×#4339—21no—
62C22×D44—21no—
63C22×Dic22—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11D411yescharacteristic
68#66990—41no—
69D4×Dic11—41no—
70#66983—21no—
71#66977—21no—
72#66977—21no—
73#66977—21no—
74C2×Dic44—22no—
75C2×Dic44—22no—
76C2×Dic44—21no—
77C2×Dic44—21no—
78C2×Dic44—21no—
79C2×Dic44—41no—
80C2×Dic44—41no—
81C2×Dic44C2311yescharacteristic
82C2×Dic44C2311yescharacteristic
83C2×Dic44C2311yescharacteristic
84C2×Dic44C2311yescharacteristic
85#66957—22no—
86#66957—41no—
87C2×D88—22no—
88C2×D88—21no—
89C2×D88—41no—
90C2×D88C2311yescharacteristic
91C2×D88C2311yescharacteristic
92C2×#4314—21no—
93C2×#4314—21no—
94#66947—41no—
95#66941—41no—
96#66937—41no—
97C22⋊C4×D11—41no—
98#66931—41no—
99#66931—41no—
100#66928—21no—
101C4×D44—21no—
102#66922—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#66882C2311yescharacteristic
117#66882C2311yescharacteristic
118#66880—21no—
119#66880—21no—
120#66880—21no—
121#66880—21no—
122Dic88—22no—
123Dic88—22no—
124Dic88—41no—
125#66864—22no—
126#66864—22no—
127#66864—22no—
128#66864—22no—
129#66864—41no—
130#66864D414yescomplemented
131#33832—111nomaximal, Sylow
132C23×D11—41no—
133C2×D4×C11D811yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C22×Dic11—41no—
139C22×Dic11—41no—
140#4339—42no—
141#4339—81no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—42no—
145C2×D44—41no—
146C2×D44—81no—
147C2×C4×D11—41no—
148C2×C4×D11—41no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—42no—
154C2×Dic22—42no—
155C2×Dic22—41no—
156C2×Dic22—41no—
157C2×Dic22—81no—
158C2×Dic22—81no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2411yescharacteristic
167C11×C4⋊C4D811yescharacteristic
168C11×C22⋊C4D811yescharacteristic
169C11×C22⋊C4D811yescharacteristic
170C42×C11C2×D411yescharacteristic
171C22⋊Dic11—41no—
172C22⋊Dic11—41no—
173C22⋊Dic11—41no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—41no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—41no—
181C4⋊Dic11—41no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186C4×Dic11—41no—
187Dic44—21no—
188Dic44—21no—
189Dic44—21no—
190Dic44—21no—
191Dic44—21no—
192Dic44—21no—
193Dic44—21no—
194Dic44—42no—
195Dic44—42no—
196Dic44—81no—
197Dic44C2×D412yes—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—42no—
202D88C2×D412yes—
203#4314—42no—
204#4314—81no—
205C11×C16—21no—
206C11×C16—21no—
207C11×C16—21no—
208C11×C16C2×D412yes—
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#2175—111no—
223#2168D1111yescharacteristic, complemented
224C23×C11C2×D811yescharacteristic
225C23×C11C2×D811yescharacteristic
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—82no—
229C22×D11—82no—
230C22×D11—161no—
231D4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11C2×D811yescharacteristic
237C2×C4×C11C2×D811yescharacteristic
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C2×D811yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C22⋊D11—82no—
242C22⋊D11—161no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—82no—
250C2×Dic11—82no—
251D44—22no—
252D44—41no—
253D44—41no—
254D44—41no—
255D44—82no—
256C4×D11—82no—
257C4×D11—161no—
258Dic22—22no—
259Dic22—41no—
260Dic22—41no—
261Dic22—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—82no—
267Dic22—82no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11C22×D411yescharacteristic
272C8×C11H(5,𝔽2)11yescharacteristic
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—111no—
289C2×SD32—224no—
290C2×M32C2×D1111yescharacteristic, complemented
291C22×C16C2×D1111yescharacteristic
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×Q16—111no—
305C4×D8—111no—
306C8×D4C2×D1111yescharacteristic
307#366—111no—
308C4⋊C16C2×D1111yescharacteristic, complemented
309#358—111no—
310#358—111no—
311#358—111no—
312#358—111no—
313#357—111no—
314#357—111no—
315C22⋊C16C2×D1111yescharacteristic
316C22⋊C16C2×D1111yescharacteristic, complemented
317#346C2×D1111yescharacteristic, complemented
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11#51012yescomplemented
324C22×C11C22×D811yescharacteristic
325C2×D11—42no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—164no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11D4211yescharacteristic
337C4×C11#57611yescharacteristic
338Dic11—42no—
339Dic11—81no—
340Dic11—81no—
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—111no—
354C2×Q16—222no—
355C2×Q16—222no—
356C2×Q16—221no—
357C2×Q16—221no—
358C2×Q16—221no—
359C2×Q16—441no—
360C2×Q16—441no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×D8—111no—
364C2×D8—111no—
365C2×D8—222no—
366C2×D8—221no—
367C2×D8—441no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
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—221no—
383C4×D4—221no—
384C4×D4—441no—
385C4×D4D4411yescharacteristic
386C2×C22⋊C4—441no—
387Q32—222no—
388Q32—222no—
389Q32—441no—
390SD32—114no—
391SD32—222no—
392SD32—222no—
393SD32—222no—
394SD32—222no—
395SD32—441no—
396M32—22no—
397C2×C16—22no—
398C2×C16C22×D1111yescharacteristic
399C2×C16C22×D1111yescharacteristic
400C2×C16C22×D1111yescharacteristic
401C2×C16C22×D1111yescharacteristic
402#107—111no—
403#107—111no—
404C4⋊C8D4411yescharacteristic
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#102—221no—
410#102—221no—
411C22⋊C8D4411yescharacteristic
412C22⋊C8D4411yescharacteristic
413C4×C8C22×D1111yescharacteristic
414C2×C11—22no—
415C2×C11—41no—
416C2×C11D4×D811yescharacteristic
417C2×C11C2×#51011yescharacteristic
418C2×C11#341611yescharacteristic
419D11—82no—
420D11—161no—
421C24—441no—
422#41—442no—
423#41—881no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—442no—
429C2×Q8—442no—
430C2×Q8—441no—
431C2×Q8—441no—
432C2×Q8—881no—
433C2×Q8—881no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—442no—
437C2×D4—441no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—881no—
441C2×D4D8811yescharacteristic
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4C2×D4411yescharacteristic
447C22×C4C2×D4411yescharacteristic
448Q16—112no—
449Q16—221no—
450Q16—221no—
451Q16—221no—
452Q16—221no—
453Q16—221no—
454Q16—221no—
455Q16—221no—
456Q16—442no—
457Q16—442no—
458Q16—881no—
459SD16—442no—
460SD16—881no—
461D8—112no—
462D8—221no—
463D8—221no—
464D8—221no—
465D8—442no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×D4411yescharacteristic
471C2×C8C2×D4411yescharacteristic
472C2×C8C2×D4411yescharacteristic
473C2×C8C23×D1111yescharacteristic
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—441no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4D8811yescharacteristic
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4D8811yescharacteristic
491C22⋊C4D8811yescharacteristic
492C42—441no—
493C42C2×D4411yescharacteristic
494C16—21no—
495C16—21no—
496C16—21no—
497C16D4×D1112yes—
498C11#3383211yescharacteristic, complemented, Sylow
499C23—441no—
500C23—441no—
501C23—882no—
502C23—882no—
503C23—1761no—
504C23C2×D8811yescharacteristic
505C23C2×D8811yescharacteristic
506Q8—222no—
507Q8—441no—
508Q8—441no—
509Q8—441no—
510Q8—441no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—882no—
515Q8—882no—
516D4—22no—
517D4—222no—
518D4—441no—
519D4—441no—
520D4—441no—
521D4—882no—
522D4—882no—
523D4—1761no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—882no—
535C2×C4—882no—
536C2×C4—882no—
537C2×C4—1761no—
538C2×C4C2×D8811yescharacteristic
539C2×C4C2×D8811yescharacteristic
540C2×C4C2×D8811yescharacteristic
541C2×C4C2×D8811yescharacteristic
542C2×C4C22×D4411yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8C2×D4×D1111yescharacteristic
547C8#6704211yescharacteristic
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—442no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22—1764no—
560C22#1062252212yescomplemented
561C22C22×D8811yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—442no—
567C4—881no—
568C4—881no—
569C4—881no—
570C4—881no—
571C4—881no—
572C4D4×D4411yescharacteristic
573C4#1062328311yescharacteristic
574C2—22no—
575C2—41no—
576C2—882no—
577C2—1761no—
578C2D4×D8811yescharacteristic
579C2C2×#1062252211yescharacteristic
580C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
prime radical#13080303C2
hypercenter#2168D11
hypocenterC11#33832
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×#10622522C2semidirect
2. C22×#66864C2semidirect
3. D4×Dic44C2semidirect
5. #13070887C2semidirect
6. #13070729C2semidirect
7. #13070707C2semidirect
8. #13070679C2semidirect
9. #13070662C2semidirect
10. #13070558C2semidirect
11. #13070552C2semidirect
12. #13070547C2semidirect
13. #13070535C2semidirect
14. #13070482C2semidirect
15. C11×#2168C2semidirect
17. C22×Dic44C22semidirect
22. C2×C11×M32C22semidirect
27. #10622729C22semidirect
30. C2×Dic88C22semidirect
31. C2×Dic88C22semidirect
32. C2×Dic88C22semidirect
46. #10622312C22semidirect
47. C4×Dic44C22semidirect
50. C11×C4⋊C16C22semidirect
52. C11×C22⋊C16C22semidirect
53. C11×#346C22semidirect
56. #10622142C22semidirect
57. #10622141C22semidirect
58. #10622141C22semidirect
59. #10622141C22semidirect
60. #10622141C22semidirect
130. #66864D4semidirect
223. #2168D11semidirect
290. C2×M32C2×D11semidirect
308. C4⋊C16C2×D11semidirect
316. C22⋊C16C2×D11semidirect
317. #346C2×D11semidirect
323. C22×C11#510semidirect
498. C11#33832semidirect
560. C22#10622522semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
C22×#668642
D4×Dic442
#130803032
#130708872
#130707292
#130707072
#130706792
#130706622
#130705582
#130705522
#130705472
#130705352
#130704822
C11×#21682
#3383211