Subgroups — #14583503

Order 2752.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063317	C₂	1	1	yes	maximal, characteristic, complemented
2	#13063306	C₂	1	4	yes	maximal, complemented
3	#13063297	C₂	1	4	yes	maximal, complemented
4	#13063296	C₂	1	2	yes	maximal, complemented
5	D₄×Dic₄₃	C₂	1	2	yes	maximal, complemented
6	#13063282	C₂	1	1	yes	maximal, characteristic, complemented
7	#127×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₄₃	C₂²	1	2	yes	—
9	C₂×D₄×C₄₃	C₂²	1	4	yes	—
10	C₂×C₂²⋊D₄₃	C₂²	1	4	yes	—
11	C₂²×Dic₄₃	C₂²	1	4	yes	—
12	C₂×C₄×D₄₃	C₂²	1	1	yes	characteristic
13	C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²⋊Dic₄₃	C₂²	1	4	yes	—
15	C₂²⋊Dic₄₃	C₂²	1	4	yes	—
16	(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
17	C₄⋊Dic₄₃	C₂²	1	2	yes	—
18	Dic₄₃⋊C₄	C₂²	1	2	yes	—
19	Dic₄₃⋊C₄	C₂²	1	4	yes	—
20	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
21	C₂³×C₄₃	C₂³	1	4	yes	—
22	C₂²×D₄₃	C₂³	1	1	yes	characteristic
23	D₄×C₄₃	—	2	4	no	—
24	D₄×C₄₃	—	4	4	no	—
25	C₂×C₄×C₄₃	C₂³	1	2	yes	—
26	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂²⋊D₄₃	—	4	4	no	—
28	C₂×Dic₄₃	—	4	4	no	—
29	C₂×Dic₄₃	C₂³	1	2	yes	—
30	C₂×Dic₄₃	C₂³	1	4	yes	—
31	C₂×Dic₄₃	C₂³	1	1	yes	characteristic
32	C₄×D₄₃	—	2	2	no	—
33	C₂²×C₄₃	—	2	4	no	—
34	C₂²×C₄₃	—	2	4	no	—
35	C₂²×C₄₃	—	2	4	no	—
36	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
37	C₂×D₄₃	—	2	1	no	—
38	C₂×D₄₃	—	2	2	no	—
39	C₄×C₄₃	—	2	2	no	—
40	C₄×C₄₃	#41	1	2	yes	—
41	Dic₄₃	—	2	1	no	—
42	Dic₄₃	—	2	2	no	—
43	Dic₄₃	—	2	4	no	—
44	C₂×C₄₃	—	4	4	no	—
45	C₂×C₄₃	C₂×#41	1	1	yes	characteristic
46	C₂×C₄₃	H(5,𝔽₂)	1	2	yes	—
47	D₄₃	—	4	1	no	—
48	#540	—	43	1	no	maximal, Sylow
49	C₄₃	#540	1	1	yes	characteristic, complemented, Sylow
50	#127	D₄₃	1	1	yes	characteristic, complemented
51	#125	—	43	1	no	—
52	#123	—	43	4	no	—
53	#121	—	43	2	no	—
54	#121	—	43	4	no	—
55	C₄×D₄	—	43	2	no	—
56	#117	—	43	1	no	—
57	C₂×D₄	—	43	4	no	—
58	C₂×D₄	C₂×D₄₃	1	2	yes	—
59	C₂×D₄	C₂×D₄₃	1	4	yes	—
60	C₂²×C₄	—	43	4	no	—
61	C₂²×C₄	—	43	1	no	—
62	C₄⋊C₄	—	43	2	no	—
63	C₄⋊C₄	—	43	2	no	—
64	C₄⋊C₄	—	43	4	no	—
65	C₂²⋊C₄	—	43	4	no	—
66	C₂²⋊C₄	—	43	4	no	—
67	C₂²⋊C₄	—	43	2	no	—
68	C₄²	—	43	1	no	—
69	C₄²	C₂×D₄₃	1	1	yes	characteristic
70	C₂³	—	43	1	no	—
71	C₂³	C₂²×D₄₃	1	4	yes	—
72	D₄	—	2	4	no	—
73	D₄	—	4	4	no	—
74	D₄	—	172	4	no	—
75	C₂×C₄	—	43	2	no	—
76	C₂×C₄	—	43	1	no	—
77	C₂×C₄	—	43	4	no	—
78	C₂×C₄	—	86	2	no	—
79	C₂×C₄	—	172	4	no	—
80	C₂×C₄	C₂²×D₄₃	1	2	yes	—
81	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
82	C₂²	—	2	4	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	2	4	no	—
85	C₂²	—	86	1	no	—
86	C₂²	—	86	2	no	—
87	C₂²	C₂³×D₄₃	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	86	1	no	—
90	C₄	—	86	2	no	—
91	C₄	—	86	4	no	—
92	C₄	#10621900	1	2	yes	—
93	C₂	—	4	4	no	—
94	C₂	—	172	1	no	—
95	C₂	C₂×#10621900	1	1	yes	characteristic
96	C₂	#13063370	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁴
Fitting	#127×C₄₃	C₂
hypercenter	#127	D₄₃
hypocenter	C₄₃	#540
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. #13063317	C₂	semidirect
2. #13063306	C₂	semidirect
3. #13063297	C₂	semidirect
4. #13063296	C₂	semidirect
5. D₄×Dic₄₃	C₂	semidirect
6. #13063282	C₂	semidirect
7. #127×C₄₃	C₂	semidirect
49. C₄₃	#540	semidirect
50. #127	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063317	2
#13063306	2
#13063297	2
#13063296	2
D₄×Dic₄₃	2
#13063282	2
#127×C₄₃	2
#540	43