Subgroups — #19134202

Order 5504.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583276	C₂	1	1	yes	maximal, characteristic
2	#14583247	C₂	1	4	yes	maximal, complemented
3	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₄₄	—	2	2	no	—
6	#13063322	C₂²	1	2	yes	—
7	#13063245	—	2	8	no	—
8	C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₄₃	—	2	2	no	—
10	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
11	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₄₃	—	2	2	no	—
13	C₂×D₁₇₂	—	2	4	no	—
14	C₂×D₁₇₂	—	2	2	no	—
15	Q₁₆×C₄₃	—	4	4	no	—
16	C₂×C₈×C₄₃	D₄	1	2	yes	—
17	C₄⋊C₄×C₄₃	—	2	4	no	—
18	C₄²×C₄₃	C₂³	1	1	yes	characteristic
19	C₂×C₄₃⋊C₈	D₄	1	4	yes	—
20	D₃₄₄	—	4	4	no	—
21	C₂²×D₄₃	—	4	2	no	—
22	Q₈×C₄₃	—	4	4	no	—
23	C₂×C₄×C₄₃	—	4	2	no	—
24	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
26	D₁₇₂	—	4	4	no	—
27	D₁₇₂	—	4	8	no	—
28	C₈×C₄₃	D₈	1	4	yes	—
29	C₄₃⋊C₈	—	2	4	no	—
30	C₂²×C₄₃	#127	1	1	yes	characteristic
31	C₂×D₄₃	—	8	2	no	—
32	C₂×D₄₃	—	8	4	no	—
33	C₄×C₄₃	—	8	2	no	—
34	C₄×C₄₃	C₂×D₈	1	2	yes	—
35	C₄×C₄₃	#135	1	4	yes	—
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	D₄₃	1	1	yes	characteristic, complemented
41	#493	—	43	1	no	—
42	#486	—	43	4	no	—
43	C₈²	—	43	1	no	—
44	C₄₃	#1709	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	2	2	no	—
46	C₂×D₈	—	86	2	no	—
47	C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
48	#127	—	43	2	no	—
49	#102	—	86	8	no	—
50	C₄×C₈	—	43	2	no	—
51	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
52	C₂×Q₈	—	2	2	no	—
53	C₂×D₄	—	86	4	no	—
54	C₂×D₄	—	86	2	no	—
55	Q₁₆	—	4	4	no	—
56	D₈	—	172	4	no	—
57	C₂×C₈	—	43	4	no	—
58	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
59	C₄⋊C₄	—	2	4	no	—
60	C₄²	C₂²×D₄₃	1	1	yes	characteristic
61	C₂³	—	172	2	no	—
62	Q₈	—	4	4	no	—
63	D₄	—	172	4	no	—
64	D₄	—	172	8	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	D₄×D₄₃	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
68	C₈	—	86	4	no	—
69	C₈	#10621882	1	4	yes	—
70	C₂²	—	344	2	no	—
71	C₂²	—	344	4	no	—
72	C₂²	#13063321	1	1	yes	characteristic
73	C₄	—	8	2	no	—
74	C₄	C₂×#10621882	1	2	yes	—
75	C₄	#13063348	1	4	yes	—
76	C₂	—	688	2	no	—
77	C₂	#14583275	1	1	yes	characteristic
78	C₂	#14583284	1	2	yes	—

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#494	C₂
socle	C₂²×C₄₃	#127
hypercenter	#494	D₄₃
hypocenter	C₄₃	#1709
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
2. #14583247	C₂	semidirect
3. C₈×C₄₃⋊C₈	C₂	semidirect
4. C₄₃×#494	C₂	semidirect
40. #494	D₄₃	semidirect
44. C₄₃	#1709	semidirect