Subgroups — #19140705

Order 5504.

612 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063325	C₂	1	3	yes	maximal, complemented
2	C₂×#13063313	C₂	1	3	yes	maximal
3	#14582836	C₂	1	8	yes	maximal, complemented
4	C₄₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Dic₈₆	C₂²	1	3	yes	—
6	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
7	#13063325	—	2	12	no	—
8	#13063313	—	2	12	no	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	12	yes	—
10	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
12	#95×C₄₃	C₂²	1	4	yes	—
13	C₂³×D₄₃	C₂³	1	2	yes	—
14	C₂²×C₄×C₄₃	C₂³	1	6	yes	—
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₃	C₂³	1	6	yes	—
17	C₂×D₁₇₂	—	2	6	no	—
18	C₂×Dic₈₆	—	2	6	no	—
19	C₂×Dic₈₆	—	2	12	no	—
20	C₄²×C₄₃	D₄	1	12	yes	—
21	(C₂×D₄₃)⋊C₄	—	2	24	no	—
22	C₄⋊Dic₄₃	—	2	24	no	—
23	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
24	C₂²×D₄₃	—	2	6	no	—
25	C₂²×D₄₃	—	2	8	no	—
26	C₂×C₄×C₄₃	—	2	12	no	—
27	C₂×C₄×C₄₃	C₂×D₄	1	12	yes	—
28	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
29	C₂×Dic₄₃	—	2	12	no	—
30	C₂×Dic₄₃	—	2	6	no	—
31	D₁₇₂	—	4	4	no	—
32	Dic₈₆	—	4	12	no	—
33	C₂²×C₄₃	C₂²×D₄	1	3	yes	—
34	C₂²×C₄₃	2₋¹⁺⁴	1	4	yes	—
35	C₂×D₄₃	—	4	2	no	—
36	C₂×D₄₃	—	4	12	no	—
37	C₄×C₄₃	—	2	12	no	—
38	C₄×C₄₃	#127	1	4	yes	—
39	Dic₄₃	—	4	6	no	—
40	#2658	—	43	1	no	maximal, Sylow
41	C₂×C₄₃	C₂×#127	1	1	yes	characteristic
42	C₂×C₄₃	#536	1	6	yes	—
43	D₄₃	—	8	2	no	—
44	C₂×C₄⋊Q₈	—	43	3	no	—
45	C₂×#124	—	43	3	no	—
46	#399	—	43	8	no	—
47	#376	D₄₃	1	1	yes	characteristic, complemented
48	C₄₃	#2658	1	1	yes	characteristic, complemented, Sylow
49	C₂²×Q₈	—	43	3	no	—
50	C₂²×D₄	—	43	1	no	—
51	C₄⋊Q₈	—	86	12	no	—
52	#124	—	86	12	no	—
53	C₂×C₄⋊C₄	—	43	12	no	—
54	C₂×C₂²⋊C₄	—	43	12	no	—
55	C₂×C₄²	C₂×D₄₃	1	3	yes	—
56	#95	C₂×D₄₃	1	4	yes	—
57	C₂⁴	—	43	2	no	—
58	C₂×Q₈	—	86	6	no	—
59	C₂×Q₈	—	86	12	no	—
60	C₂×D₄	—	86	6	no	—
61	C₂²×C₄	—	43	6	no	—
62	C₂²×C₄	C₂²×D₄₃	1	6	yes	—
63	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
64	C₄⋊C₄	—	86	24	no	—
65	C₂²⋊C₄	—	86	24	no	—
66	C₄²	D₁₇₂	1	12	yes	—
67	C₂³	—	86	6	no	—
68	C₂³	—	86	8	no	—
69	C₂³	C₂³×D₄₃	1	1	yes	characteristic
70	Q₈	—	172	12	no	—
71	D₄	—	172	4	no	—
72	C₂×C₄	—	2	12	no	—
73	C₂×C₄	—	86	6	no	—
74	C₂×C₄	—	86	12	no	—
75	C₂×C₄	C₂×D₁₇₂	1	12	yes	—
76	C₂×C₄	C₂×D₁₇₂	1	6	yes	—
77	C₂²	—	172	2	no	—
78	C₂²	—	172	12	no	—
79	C₂²	C₂²×D₁₇₂	1	3	yes	—
80	C₂²	#13063372	1	4	yes	—
81	C₄	—	2	12	no	—
82	C₄	—	172	6	no	—
83	C₄	#13063322	1	4	yes	—
84	C₂	—	344	2	no	—
85	C₂	C₂×#13063322	1	1	yes	characteristic
86	C₂	#14583475	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#376	C₂
hypercenter	#376	D₄₃
hypocenter	C₄₃	#2658
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
1. C₂×#13063325	C₂	semidirect
3. #14582836	C₂	semidirect
4. C₄₃×#376	C₂	semidirect
47. #376	D₄₃	semidirect
48. C₄₃	#2658	semidirect