Subgroups — #14582909

Order 2752.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	#13063284	C₂	1	1	yes	maximal, characteristic
3	#13063250	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₄₃	—	2	1	no	—
7	C₂×Dic₈₆	—	2	1	no	—
8	C₂×Dic₈₆	—	2	2	no	—
9	C₂×Dic₈₆	C₄	1	4	yes	complemented
10	C₂×Dic₈₆	C₂²	1	2	yes	—
11	M₁₆×C₄₃	—	2	2	no	—
12	C₂×C₈×C₄₃	C₂²	1	2	yes	—
13	C₂²⋊Dic₄₃	—	2	1	no	—
14	C₄⋊Dic₄₃	C₂²	1	2	yes	—
15	C₄×Dic₄₃	—	2	1	no	—
16	C₂³×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₃	D₄	1	2	yes	—
20	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₃	—	2	4	no	—
22	C₂×Dic₄₃	—	2	2	no	—
23	C₂×Dic₄₃	—	2	2	no	—
24	Dic₈₆	—	2	4	no	—
25	Dic₈₆	—	2	2	no	—
26	Dic₈₆	C₂×C₄	1	4	yes	—
27	C₈×C₄₃	—	2	2	no	—
28	C₂²×C₄₃	—	2	2	no	—
29	C₂²×C₄₃	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
32	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
34	Dic₄₃	—	2	4	no	—
35	Dic₄₃	—	4	2	no	—
36	C₂×C₄₃	—	2	2	no	—
37	C₂×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₄₃	#137	1	2	yes	—
39	#419	—	43	1	no	maximal, Sylow
40	C₄₃	#419	1	1	yes	characteristic, complemented, Sylow
41	C₂²×Q₈	—	43	1	no	—
42	C₂×M₁₆	D₄₃	1	1	yes	characteristic
43	#117	—	43	1	no	—
44	#103	—	43	4	no	—
45	C₂×Q₈	—	43	2	no	—
46	C₂×Q₈	—	43	4	no	—
47	C₂×Q₈	—	86	1	no	—
48	C₂×Q₈	—	86	2	no	—
49	C₂²×C₄	—	86	1	no	—
50	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
51	M₁₆	—	2	2	no	—
52	C₂×C₈	C₂×D₄₃	1	2	yes	—
53	C₄⋊C₄	—	43	2	no	—
54	C₂²⋊C₄	—	86	1	no	—
55	C₄²	—	86	1	no	—
56	C₂³	D₁₇₂	1	1	yes	characteristic
57	Q₈	—	43	4	no	—
58	Q₈	—	86	4	no	—
59	Q₈	—	86	2	no	—
60	C₂×C₄	—	86	4	no	—
61	C₂×C₄	—	86	2	no	—
62	C₂×C₄	—	86	2	no	—
63	C₂×C₄	C₄×D₄₃	1	2	yes	—
64	C₂×C₄	D₁₇₂	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊D₄₃	1	2	yes	—
66	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	(C₂×D₄₃)⋊C₄	1	2	yes	—
70	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
71	C₄	—	86	4	no	—
72	C₄	—	172	2	no	—
73	C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
74	C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
75	C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
76	C₂	—	2	2	no	—
77	C₂	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
78	C₂	#13063358	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₂×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂³×C₄₃	D₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	C₂×M₁₆	D₄₃
hypocenter	C₄₃	#419
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13063250	C₂	semidirect
9. C₂×Dic₈₆	C₄	semidirect
40. C₄₃	#419	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₈₆	2
#13063284	2
#13063250	2
C₂×M₁₆×C₄₃	2
#419	43