Subgroups — #14643148

Order 2816.

582 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#66879	C₂	1	3	yes	maximal
2	C₂×#10622093	C₂	1	3	yes	maximal
3	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
5	C₂×#66879	C₄	1	12	yes	—
6	C₄²×Dic₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₁⋊C₈	C₂²	1	3	yes	—
8	C₈²×C₁₁	C₄	1	4	yes	complemented
9	#10622093	C₄	1	12	yes	complemented
10	C₂²×C₈×C₁₁	C₂×C₄	1	6	yes	—
11	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
12	C₂×C₄×Dic₁₁	C₂×C₄	1	6	yes	—
13	C₂²×C₁₁⋊C₈	C₂×C₄	1	6	yes	—
14	C₄×C₈×C₁₁	C₂×C₄	1	6	yes	—
15	C₄×C₈×C₁₁	C₂×C₄	1	6	yes	—
16	#66879	—	2	24	no	—
17	C₄×C₁₁⋊C₈	C₂×C₄	1	12	yes	—
18	#7846	—	11	1	no	maximal, Sylow
19	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
20	C₂²×Dic₁₁	C₄²	1	4	yes	—
21	C₂×C₈×C₁₁	C₄²	1	12	yes	—
22	C₂×C₈×C₁₁	M₁₆	1	24	yes	—
23	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
24	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
25	C₄×Dic₁₁	—	2	12	no	—
26	C₂×C₁₁⋊C₈	—	2	12	no	—
27	C₂×C₁₁⋊C₈	C₄²	1	12	yes	—
28	C₄×#97	—	11	3	no	—
29	C₂×#322	—	11	3	no	—
30	C₂×C₈²	D₁₁	1	1	yes	characteristic
31	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
33	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
34	C₂×C₄×C₁₁	C₂×M₁₆	1	12	yes	—
35	C₂×Dic₁₁	—	2	12	no	—
36	C₈×C₁₁	#97	1	24	yes	complemented
37	C₁₁⋊C₈	—	2	12	no	—
38	C₂×#97	—	11	12	no	—
39	C₂×C₄×C₈	—	11	3	no	—
40	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
41	C₄³	—	11	1	no	—
42	#322	—	11	12	no	—
43	C₈²	Dic₁₁	1	4	yes	complemented
44	C₂²×C₁₁	C₄³	1	1	yes	characteristic
45	C₂²×C₁₁	C₄×M₁₆	1	6	yes	—
46	C₄×C₁₁	C₂×#97	1	6	yes	—
47	C₄×C₁₁	C₄×M₁₆	1	6	yes	—
48	Dic₁₁	—	4	4	no	—
49	C₂²×C₈	—	11	6	no	—
50	C₂²×C₈	C₄×D₁₁	1	6	yes	—
51	C₂×C₄²	—	11	6	no	—
52	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
53	#97	—	22	24	no	—
54	C₄×C₈	—	11	12	no	—
55	C₄×C₈	C₄×D₁₁	1	6	yes	—
56	C₄×C₈	C₂×Dic₁₁	1	6	yes	—
57	C₂×C₁₁	#1455	1	4	yes	—
58	C₂×C₁₁	C₄×#97	1	3	yes	—
59	C₂²×C₄	—	11	4	no	—
60	C₂²×C₄	C₂×C₄×D₁₁	1	3	yes	—
61	C₂×C₈	—	11	12	no	—
62	C₂×C₈	—	22	12	no	—
63	C₂×C₈	#4313	1	24	yes	—
64	C₂×C₈	C₄×Dic₁₁	1	12	yes	—
65	C₄²	—	22	12	no	—
66	C₄²	C₂×C₄×D₁₁	1	3	yes	—
67	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
68	C₁₁	#7846	1	1	yes	characteristic, complemented, Sylow
69	C₂³	C₄²×D₁₁	1	1	yes	characteristic
70	C₂×C₄	—	22	12	no	—
71	C₂×C₄	C₄²×D₁₁	1	3	yes	—
72	C₂×C₄	C₂×#4313	1	12	yes	—
73	C₂×C₄	C₂×C₄×Dic₁₁	1	3	yes	—
74	C₈	—	22	12	no	—
75	C₈	#66879	1	24	yes	complemented
76	C₂²	C₄×#4313	1	6	yes	—
77	C₂²	C₄²×Dic₁₁	1	1	yes	characteristic
78	C₄	—	44	4	no	—
79	C₄	C₄×#4313	1	6	yes	—
80	C₄	C₂×#66879	1	6	yes	—
81	C₂	#13066918	1	4	yes	—
82	C₂	C₄×#66879	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator	C₂²×C₁₁	C₄³
Fitting	C₂×C₈²×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₈²	D₁₁
hypocenter	C₁₁	#7846
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
8. C₈²×C₁₁	C₄	semidirect
9. #10622093	C₄	semidirect
36. C₈×C₁₁	#97	semidirect
43. C₈²	Dic₁₁	semidirect
68. C₁₁	#7846	semidirect
75. C₈	#66879	semidirect

Maximal subgroups

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

subgroup	index
C₄×#66879	2
C₂×#10622093	2
C₂×C₈²×C₁₁	2
#7846	11