Subgroups — #19134201

Order 5504.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583279	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583276	C₂	1	1	yes	maximal, characteristic
3	#14583246	C₂	1	4	yes	maximal, complemented
4	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₁₇₂	—	2	2	no	—
6	C₂×D₃₄₄	—	2	2	no	—
7	#13063325	C₂²	1	2	yes	—
8	#13063322	C₂²	1	2	yes	—
9	#13063247	—	2	8	no	—
10	C₄×C₈×C₄₃	C₂²	1	2	yes	—
11	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×D₁₇₂	—	2	4	no	—
13	C₂×D₁₇₂	—	2	2	no	—
14	C₂×Dic₈₆	—	2	2	no	—
15	C₂×C₈×C₄₃	D₄	1	4	yes	—
16	C₂×C₈×C₄₃	D₄	1	2	yes	—
17	C₄²×C₄₃	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₄₃	—	2	4	no	—
19	Dic₁₇₂	—	4	4	no	—
20	D₃₄₄	—	4	4	no	—
21	C₂²×D₄₃	—	4	2	no	—
22	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
24	C₂×Dic₄₃	—	4	2	no	—
25	D₁₇₂	—	4	4	no	—
26	D₁₇₂	—	4	8	no	—
27	Dic₈₆	—	4	4	no	—
28	C₈×C₄₃	—	2	4	no	—
29	C₈×C₄₃	D₈	1	4	yes	—
30	C₂²×C₄₃	#127	1	1	yes	characteristic
31	C₂×D₄₃	—	8	2	no	—
32	C₂×D₄₃	—	8	4	no	—
33	C₄×C₄₃	C₂×D₈	1	2	yes	—
34	C₄×C₄₃	#135	1	4	yes	—
35	Dic₄₃	—	8	2	no	—
36	#1709	—	43	1	no	maximal, Sylow
37	C₂×C₄₃	#493	1	1	yes	characteristic
38	C₂×C₄₃	#495	1	2	yes	—
39	D₄₃	—	16	2	no	—
40	#494	—	43	1	no	—
41	#493	—	43	1	no	—
42	#486	—	43	4	no	—
43	C₈²	D₄₃	1	1	yes	characteristic, complemented
44	C₄₃	#1709	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	86	2	no	—
46	C₂×D₈	—	86	2	no	—
47	C₄⋊Q₈	—	43	2	no	—
48	#127	—	43	2	no	—
49	#102	—	86	8	no	—
50	C₄×C₈	C₂×D₄₃	1	2	yes	—
51	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
52	C₂×Q₈	—	86	2	no	—
53	C₂×D₄	—	86	4	no	—
54	C₂×D₄	—	86	2	no	—
55	Q₁₆	—	172	4	no	—
56	D₈	—	172	4	no	—
57	C₂×C₈	D₁₇₂	1	4	yes	—
58	C₂×C₈	D₁₇₂	1	2	yes	—
59	C₄⋊C₄	—	86	4	no	—
60	C₄²	C₂²×D₄₃	1	1	yes	characteristic
61	C₂³	—	172	2	no	—
62	Q₈	—	172	4	no	—
63	D₄	—	172	4	no	—
64	D₄	—	172	8	no	—
65	C₂×C₄	—	172	2	no	—
66	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
67	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
68	C₈	—	2	4	no	—
69	C₈	D₃₄₄	1	4	yes	—
70	C₂²	—	344	2	no	—
71	C₂²	—	344	4	no	—
72	C₂²	#13063322	1	1	yes	characteristic
73	C₄	—	344	2	no	—
74	C₄	C₂×D₃₄₄	1	2	yes	—
75	C₄	#13063347	1	4	yes	—
76	C₂	—	688	2	no	—
77	C₂	#14583276	1	1	yes	characteristic
78	C₂	#14583283	1	2	yes	—

	subgroup	G/H
center	C₂²	#13063322
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₈²×C₄₃	C₂
socle	C₂²×C₄₃	#127
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	#1709
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #14583279	C₂	semidirect
3. #14583246	C₂	semidirect
4. C₈²×C₄₃	C₂	semidirect
43. C₈²	D₄₃	semidirect
44. C₄₃	#1709	semidirect