Subgroups — #14583157

Order 2752.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#13063304	C₂	1	2	yes	maximal
3	#13063257	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063250	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₈₆	C₂²	1	2	yes	—
8	M₁₆×C₄₃	—	2	2	no	—
9	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₄₃	—	2	2	no	—
12	C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	Dic₄₃⋊C₄	—	2	2	no	—
14	Dic₁₇₂	—	2	2	no	—
15	C₂³×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	—	2	1	no	—
17	C₂×C₄×C₄₃	—	2	1	no	—
18	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₄₃	—	2	2	no	—
21	C₂×Dic₄₃	—	2	2	no	—
22	Dic₈₆	—	2	2	no	—
23	Dic₈₆	—	2	2	no	—
24	C₈×C₄₃	—	2	1	no	—
25	C₈×C₄₃	D₄	1	2	yes	—
26	C₂²×C₄₃	—	2	1	no	—
27	C₂²×C₄₃	—	2	2	no	—
28	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₄×C₄₃	—	2	1	no	—
30	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₃	#41	1	1	yes	characteristic
32	Dic₄₃	—	4	2	no	—
33	Dic₄₃	—	4	2	no	—
34	C₂×C₄₃	—	4	1	no	—
35	C₂×C₄₃	#121	1	1	yes	characteristic
36	C₂×C₄₃	#137	1	2	yes	—
37	#470	—	43	1	no	maximal, Sylow
38	C₄₃	#470	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₁₆	—	43	1	no	—
40	C₂×M₁₆	D₄₃	1	1	yes	characteristic
41	C₂²⋊Q₈	—	43	2	no	—
42	#106	—	43	1	no	—
43	#103	—	43	2	no	—
44	C₂×Q₈	—	43	2	no	—
45	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
46	Q₁₆	—	86	2	no	—
47	M₁₆	—	2	2	no	—
48	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
49	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
50	C₄⋊C₄	—	43	2	no	—
51	C₄⋊C₄	—	86	2	no	—
52	C₂²⋊C₄	—	86	2	no	—
53	C₂³	D₁₇₂	1	1	yes	characteristic
54	Q₈	—	86	2	no	—
55	Q₈	—	86	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	86	2	no	—
59	C₂×C₄	—	86	2	no	—
60	C₂×C₄	D₁₇₂	1	1	yes	characteristic
61	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₈	C₂²⋊D₄₃	1	2	yes	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	2	no	—
66	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	172	2	no	—
69	C₄	—	172	2	no	—
70	C₄	#10621898	1	1	yes	characteristic
71	C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
72	C₂	—	4	1	no	—
73	C₂	#13063299	1	1	yes	characteristic
74	C₂	#13063358	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₂×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂³×C₄₃	D₄
hypercenter	C₂×M₁₆	D₄₃
hypocenter	C₄₃	#470
LCS	G ▷ C₂×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
1. C₂×Dic₁₇₂	C₂	semidirect
3. #13063257	C₂	semidirect
4. #13063250	C₂	semidirect
38. C₄₃	#470	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₇₂	2
#13063304	2
#13063257	2
#13063250	2
C₂×M₁₆×C₄₃	2
#470	43