Subgroups — #14583647

Order 2752.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063313	C₂	1	2	yes	maximal, complemented
2	#13063310	C₂	1	4	yes	maximal, complemented
3	#13063303	C₂	1	4	yes	maximal, complemented
4	#13063300	C₂	1	4	yes	maximal, complemented
5	#125×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₇₂	C₂²	1	4	yes	—
7	C₂×D₁₇₂	C₂²	1	2	yes	—
8	C₂×C₄×D₄₃	C₂²	1	4	yes	—
9	C₂×Dic₈₆	C₂²	1	2	yes	—
10	C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
11	C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
12	C₄²×C₄₃	C₂²	1	1	yes	characteristic
13	(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
14	(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
15	(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
16	Dic₄₃⋊C₄	C₂²	1	4	yes	—
17	C₂²×D₄₃	C₂³	1	4	yes	—
18	C₂×C₄×C₄₃	C₂³	1	4	yes	—
19	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₄₃	C₂³	1	2	yes	—
21	C₂×Dic₄₃	C₂³	1	4	yes	—
22	D₁₇₂	—	4	2	no	—
23	D₁₇₂	—	4	4	no	—
24	C₄×D₄₃	—	4	4	no	—
25	Dic₈₆	—	4	2	no	—
26	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
27	C₂×D₄₃	—	2	4	no	—
28	C₂×D₄₃	—	2	4	no	—
29	C₂×D₄₃	—	2	4	no	—
30	C₄×C₄₃	—	2	2	no	—
31	C₄×C₄₃	—	2	4	no	—
32	C₄×C₄₃	—	2	1	no	—
33	Dic₄₃	—	2	4	no	—
34	C₂×C₄₃	H(5,𝔽₂)	1	2	yes	—
35	C₂×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
36	D₄₃	—	4	4	no	—
37	#562	—	43	1	no	maximal, Sylow
38	C₄₃	#562	1	1	yes	characteristic, complemented, Sylow
39	#125	D₄₃	1	1	yes	characteristic, complemented
40	#124	—	43	2	no	—
41	#123	—	43	4	no	—
42	C₂²⋊Q₈	—	43	4	no	—
43	#121	—	43	4	no	—
44	C₂×Q₈	—	43	2	no	—
45	C₂×D₄	—	43	4	no	—
46	C₂×D₄	—	43	2	no	—
47	C₂²×C₄	—	43	4	no	—
48	C₄⋊C₄	—	43	4	no	—
49	C₄⋊C₄	C₂×D₄₃	1	4	yes	—
50	C₄⋊C₄	C₂×D₄₃	1	2	yes	—
51	C₂²⋊C₄	—	43	4	no	—
52	C₂²⋊C₄	—	43	4	no	—
53	C₂²⋊C₄	—	43	4	no	—
54	C₄²	C₂×D₄₃	1	1	yes	characteristic
55	C₂³	—	43	4	no	—
56	Q₈	—	172	2	no	—
57	D₄	—	172	4	no	—
58	D₄	—	172	2	no	—
59	C₂×C₄	—	43	4	no	—
60	C₂×C₄	—	172	4	no	—
61	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₃	1	2	yes	—
63	C₂×C₄	C₂²×D₄₃	1	4	yes	—
64	C₂²	—	86	4	no	—
65	C₂²	—	86	4	no	—
66	C₂²	—	86	4	no	—
67	C₂²	C₂³×D₄₃	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	2	2	no	—
70	C₄	—	2	1	no	—
71	C₄	—	86	4	no	—
72	C₂	—	172	4	no	—
73	C₂	#13063371	1	2	yes	—
74	C₂	#13063373	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁴
Fitting	#125×C₄₃	C₂
hypercenter	#125	D₄₃
hypocenter	C₄₃	#562
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #13063313	C₂	semidirect
2. #13063310	C₂	semidirect
3. #13063303	C₂	semidirect
4. #13063300	C₂	semidirect
5. #125×C₄₃	C₂	semidirect
38. C₄₃	#562	semidirect
39. #125	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063313	2
#13063310	2
#13063303	2
#13063300	2
#125×C₄₃	2
#562	43