Subgroups — #14684975

Order 2816.

1278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066843	C₂	1	14	yes	maximal
2	C₂×C₄³×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄²×C₁₁	C₂²	1	7	yes	—
4	C₄³×C₁₁	C₄	1	8	yes	complemented
5	C₂×C₁₁⋊#95	C₂²	1	28	yes	—
6	C₂³×C₄×C₁₁	C₂³	1	7	yes	—
7	C₂³×Dic₁₁	C₂³	1	8	yes	—
8	C₂×C₄²×C₁₁	—	2	28	no	—
9	C₂×C₄²×C₁₁	C₂×C₄	1	28	yes	—
10	C₁₁⋊#95	—	2	56	no	—
11	#14690	—	11	1	no	maximal, Sylow
12	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
13	C₂²×C₄×C₁₁	—	2	28	no	—
14	C₂²×C₄×C₁₁	C₂²×C₄	1	14	yes	—
15	C₂²×C₄×C₁₁	#41	1	28	yes	—
16	C₂²×Dic₁₁	—	2	56	no	—
17	C₄²×C₁₁	—	2	56	no	—
18	C₂×C₄³	D₁₁	1	1	yes	characteristic
19	#1434	—	11	14	no	—
20	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
21	C₂³×C₁₁	C₂×#41	1	14	yes	—
22	C₂×C₄×C₁₁	—	2	28	no	—
23	C₂×C₄×C₁₁	—	2	56	no	—
24	C₂×C₄×C₁₁	#117	1	28	yes	—
25	C₂×Dic₁₁	—	4	56	no	—
26	C₂²×C₄²	C₂×D₁₁	1	7	yes	—
27	C₂×#95	—	11	28	no	—
28	C₄³	Dic₁₁	1	8	yes	complemented
29	C₂²×C₁₁	C₂×#117	1	7	yes	—
30	C₂²×C₁₁	#529	1	28	yes	—
31	C₄×C₁₁	—	2	28	no	—
32	Dic₁₁	—	8	8	no	—
33	C₂³×C₄	—	11	8	no	—
34	C₂³×C₄	C₂²×D₁₁	1	7	yes	—
35	C₂×C₄²	—	2	28	no	—
36	C₂×C₄²	C₂×Dic₁₁	1	28	yes	—
37	#95	—	22	56	no	—
38	C₂×C₁₁	#2283	1	7	yes	—
39	C₂×C₁₁	#2865	1	8	yes	—
40	C₂⁴	C₂³×D₁₁	1	1	yes	characteristic
41	C₂²×C₄	—	2	28	no	—
42	C₂²×C₄	—	22	56	no	—
43	C₂²×C₄	#4339	1	28	yes	—
44	C₂²×C₄	C₂²×Dic₁₁	1	14	yes	—
45	C₄²	—	2	56	no	—
46	C₁₁	#14690	1	1	yes	characteristic, complemented, Sylow
47	C₂³	C₂×#4339	1	14	yes	—
48	C₂³	C₂³×Dic₁₁	1	1	yes	characteristic
49	C₂×C₄	—	2	56	no	—
50	C₂×C₄	—	2	28	no	—
51	C₂×C₄	—	44	56	no	—
52	C₂×C₄	#66979	1	28	yes	—
53	C₂²	#10623010	1	28	yes	—
54	C₂²	C₂×#66979	1	7	yes	—
55	C₄	—	2	28	no	—
56	C₄	—	88	8	no	—
57	C₂	#13071014	1	7	yes	—
58	C₂	#13077005	1	8	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₁₁
commutator	C₂³×C₁₁	C₂³×C₄
Fitting	C₂×C₄³×C₁₁	C₂
socle, prime radical, cosocle	C₂⁴×C₁₁	C₂⁴
hypercenter	C₂×C₄³	D₁₁
hypocenter	C₁₁	#14690
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
4. C₄³×C₁₁	C₄	semidirect
28. C₄³	Dic₁₁	semidirect
46. C₁₁	#14690	semidirect

Maximal subgroups

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

subgroup	index
#13066843	2
C₂×C₄³×C₁₁	2
#14690	11