Subgroups — #19135700

Order 5504.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583699	C₂	1	3	yes	maximal, complemented
2	#14582867	C₂	1	3	yes	maximal, complemented
3	C₄₃×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10621898	C₂²	1	3	yes	—
5	#13063358	—	2	6	no	—
6	#13063353	—	2	6	no	—
7	#13063347	—	2	6	no	—
8	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	(C₂×D₄₃)⋊C₈	—	2	6	no	—
10	C₂×M₁₆×C₄₃	C₂²	1	3	yes	—
11	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
12	C₂×C₂²⋊D₄₃	—	2	3	no	—
13	#10621898	—	2	6	no	—
14	#10621898	—	2	6	no	—
15	C₂×D₁₇₂	D₄	1	3	yes	—
16	C₂×C₄×D₄₃	—	2	3	no	—
17	C₂×Dic₈₆	D₄	1	3	yes	—
18	M₁₆×C₄₃	—	2	6	no	—
19	C₂×C₈×C₄₃	D₄	1	6	yes	—
20	C₂×C₄₃⋊C₈	—	2	3	no	—
21	Dic₁₇₂	—	2	6	no	—
22	D₃₄₄	—	2	6	no	—
23	#10621873	—	2	12	no	—
24	C₂³×C₄₃	#41	1	1	yes	characteristic
25	C₂²×D₄₃	—	2	3	no	—
26	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
27	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
28	C₂²⋊D₄₃	—	4	6	no	—
29	C₂×Dic₄₃	—	2	3	no	—
30	D₁₇₂	—	2	6	no	—
31	C₄×D₄₃	—	4	3	no	—
32	C₄×D₄₃	—	4	3	no	—
33	Dic₈₆	—	2	6	no	—
34	C₈×C₄₃	—	2	6	no	—
35	C₄₃⋊C₈	—	4	1	no	—
36	C₂²×C₄₃	—	4	1	no	—
37	C₂²×C₄₃	#121	1	3	yes	—
38	C₂×D₄₃	—	4	6	no	—
39	C₂×D₄₃	—	4	3	no	—
40	C₄×C₄₃	#120	1	3	yes	—
41	C₄×C₄₃	#127	1	1	yes	characteristic
42	Dic₄₃	—	4	3	no	—
43	#2017	—	43	1	no	maximal, Sylow
44	C₂×C₄₃	—	2	3	no	—
45	C₂×C₄₃	#392	1	1	yes	characteristic
46	D₄₃	—	8	3	no	—
47	#575	—	43	3	no	—
48	#408	—	43	3	no	—
49	#338	D₄₃	1	1	yes	characteristic, complemented
50	C₄₃	#2017	1	1	yes	characteristic, complemented, Sylow
51	C₂×#41	—	43	3	no	—
52	#137	—	86	6	no	—
53	AGL(1,ℤ/8)	—	86	6	no	—
54	#135	—	86	6	no	—
55	C₂×M₁₆	C₂×D₄₃	1	3	yes	—
56	C₂²×C₈	—	43	1	no	—
57	C₂²⋊C₈	—	86	6	no	—
58	#41	—	86	6	no	—
59	#41	—	86	6	no	—
60	C₂×Q₈	—	43	3	no	—
61	C₂×D₄	—	43	3	no	—
62	C₂×D₄	—	86	3	no	—
63	C₂²×C₄	—	86	3	no	—
64	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
65	Q₁₆	—	86	6	no	—
66	SD₁₆	—	86	12	no	—
67	D₈	—	86	6	no	—
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	86	3	no	—
70	C₂×C₈	D₁₇₂	1	6	yes	—
71	C₂³	—	86	3	no	—
72	C₂³	#10621902	1	1	yes	characteristic
73	Q₈	—	86	6	no	—
74	D₄	—	86	6	no	—
75	D₄	—	172	6	no	—
76	C₂×C₄	—	86	3	no	—
77	C₂×C₄	—	172	3	no	—
78	C₂×C₄	—	172	3	no	—
79	C₂×C₄	C₂×D₁₇₂	1	3	yes	—
80	C₂×C₄	D₄×D₄₃	1	3	yes	—
81	C₈	—	2	6	no	—
82	C₈	—	172	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	172	6	no	—
85	C₂²	—	172	3	no	—
86	C₂²	#13063300	1	3	yes	—
87	C₄	—	172	3	no	—
88	C₄	#13063295	1	3	yes	—
89	C₄	#13063322	1	1	yes	characteristic
90	C₂	—	2	3	no	—
91	C₂	—	344	3	no	—
92	C₂	#14582809	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13063322
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#338	C₂
socle	C₂×C₄₃	#392
hypercenter	#338	D₄₃
hypocenter	C₄₃	#2017
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #14583699	C₂	semidirect
2. #14582867	C₂	semidirect
3. C₄₃×#338	C₂	semidirect
49. #338	D₄₃	semidirect
50. C₄₃	#2017	semidirect