Subgroups — #14583635

Order 2752.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063312	C₂	1	4	yes	maximal, complemented
2	#13063306	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₈₆	C₂	1	2	yes	maximal, complemented
4	D₄×Dic₄₃	C₂	1	4	yes	maximal, complemented
5	#127×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×C₄₃	C₂²	1	4	yes	—
7	C₂×D₄×C₄₃	C₂²	1	2	yes	—
8	C₂²×Dic₄₃	C₂²	1	4	yes	—
9	C₂×Dic₈₆	C₂²	1	2	yes	—
10	C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₄₃	C₂²	1	8	yes	—
12	C₂²⋊Dic₄₃	C₂²	1	4	yes	—
13	C₄⋊Dic₄₃	C₂²	1	2	yes	—
14	Dic₄₃⋊C₄	C₂²	1	4	yes	—
15	C₄×Dic₄₃	C₂²	1	4	yes	—
16	C₂³×C₄₃	C₂³	1	4	yes	—
17	D₄×C₄₃	—	2	8	no	—
18	D₄×C₄₃	—	4	2	no	—
19	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₄₃	C₂³	1	2	yes	—
21	C₂×Dic₄₃	—	4	4	no	—
22	C₂×Dic₄₃	C₂³	1	4	yes	—
23	C₂×Dic₄₃	C₂³	1	4	yes	—
24	Dic₈₆	—	2	4	no	—
25	C₂²×C₄₃	—	2	8	no	—
26	C₂²×C₄₃	—	2	4	no	—
27	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
28	C₄×C₄₃	—	2	1	no	—
29	C₄×C₄₃	#41	1	4	yes	—
30	Dic₄₃	—	2	4	no	—
31	Dic₄₃	—	2	4	no	—
32	C₂×C₄₃	—	4	4	no	—
33	C₂×C₄₃	C₂×#41	1	2	yes	—
34	C₂×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
35	#559	—	43	1	no	maximal, Sylow
36	C₄₃	#559	1	1	yes	characteristic, complemented, Sylow
37	#127	D₄₃	1	1	yes	characteristic
38	#124	—	43	4	no	—
39	#123	—	43	4	no	—
40	C₄×Q₈	—	43	2	no	—
41	C₄×D₄	—	43	4	no	—
42	C₂×Q₈	—	43	2	no	—
43	C₂×D₄	C₂×D₄₃	1	4	yes	—
44	C₂×D₄	C₂×D₄₃	1	2	yes	—
45	C₂²×C₄	—	43	4	no	—
46	C₄⋊C₄	—	43	2	no	—
47	C₄⋊C₄	—	43	4	no	—
48	C₂²⋊C₄	—	43	8	no	—
49	C₂²⋊C₄	—	43	4	no	—
50	C₄²	—	43	4	no	—
51	C₄²	C₂×D₄₃	1	1	yes	characteristic
52	C₂³	C₂²×D₄₃	1	4	yes	—
53	Q₈	—	86	4	no	—
54	D₄	—	2	8	no	—
55	D₄	—	4	2	no	—
56	C₂×C₄	—	43	4	no	—
57	C₂×C₄	—	43	4	no	—
58	C₂×C₄	—	172	4	no	—
59	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₄₃	1	2	yes	—
61	C₂²	—	2	8	no	—
62	C₂²	—	2	4	no	—
63	C₂²	C₂³×D₄₃	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	86	4	no	—
66	C₄	—	86	4	no	—
67	C₄	#10621900	1	4	yes	—
68	C₂	—	4	4	no	—
69	C₂	C₂×#10621900	1	2	yes	—
70	C₂	#13063370	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁴
Fitting, prime radical	#127×C₄₃	C₂
hypercenter	#127	D₄₃
hypocenter	C₄₃	#559
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #13063312	C₂	semidirect
2. #13063306	C₂	semidirect
3. C₄×Dic₈₆	C₂	semidirect
4. D₄×Dic₄₃	C₂	semidirect
36. C₄₃	#559	semidirect

Maximal subgroups

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

subgroup	index
#13063312	2
#13063306	2
C₄×Dic₈₆	2
D₄×Dic₄₃	2
#127×C₄₃	2
#559	43