Subgroups — #19132635

Order 5504.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583272	C₂	1	1	yes	maximal, characteristic
2	#14582720	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10621873	—	2	1	no	—
5	C₂×#10621873	—	2	1	no	—
6	#13063325	C₄	1	1	yes	characteristic
7	#13063322	C₄	1	1	yes	characteristic
8	#13063265	—	2	1	no	—
9	M₃₂×C₄₃	—	2	1	no	—
10	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×D₁₇₂	—	2	1	no	—
12	C₂×D₁₇₂	—	4	1	no	—
13	C₂×Dic₈₆	—	2	1	no	—
14	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₄⋊Dic₄₃	—	4	1	no	—
18	#10621873	—	4	1	no	—
19	#10621873	—	4	1	no	—
20	#10621873	—	4	1	no	—
21	#10621873	—	4	1	no	—
22	C₁₆×C₄₃	—	4	1	no	—
23	C₄₃⋊C₁₆	—	4	1	no	—
24	C₂²×D₄₃	—	4	1	no	—
25	C₂×C₄×C₄₃	—	2	1	no	—
26	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₄₃	—	4	1	no	—
28	D₁₇₂	—	4	1	no	—
29	D₁₇₂	—	4	1	no	—
30	D₁₇₂	—	8	2	no	—
31	Dic₈₆	—	4	1	no	—
32	Dic₈₆	—	4	1	no	—
33	C₈×C₄₃	D₈	1	1	yes	characteristic
34	C₈×C₄₃	D₈	1	1	yes	characteristic
35	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
36	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
37	C₂²×C₄₃	#100	1	1	yes	characteristic
38	C₂×D₄₃	—	8	2	no	—
39	C₂×D₄₃	—	8	1	no	—
40	C₄×C₄₃	—	2	2	no	—
41	C₄×C₄₃	#102	1	1	yes	characteristic
42	C₄×C₄₃	#102	1	1	yes	characteristic
43	Dic₄₃	—	8	1	no	—
44	#1359	—	43	1	no	maximal, Sylow
45	C₂×C₄₃	—	2	1	no	—
46	C₂×C₄₃	#331	1	1	yes	characteristic
47	D₄₃	—	16	1	no	—
48	#492	—	43	1	no	—
49	#364	—	43	1	no	—
50	#364	D₄₃	1	1	yes	characteristic, complemented
51	C₄₃	#1359	1	1	yes	characteristic, complemented, Sylow
52	C₂×SD₁₆	—	86	1	no	—
53	C₂×SD₁₆	—	86	1	no	—
54	C₄⋊Q₈	—	43	1	no	—
55	#127	—	43	1	no	—
56	M₃₂	—	2	1	no	—
57	M₃₂	—	86	1	no	—
58	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
59	C₂×Q₈	—	86	1	no	—
60	C₂×D₄	—	86	1	no	—
61	C₂×D₄	—	172	1	no	—
62	SD₁₆	—	172	1	no	—
63	SD₁₆	—	172	1	no	—
64	SD₁₆	—	172	1	no	—
65	SD₁₆	—	172	1	no	—
66	C₂×C₈	D₁₇₂	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
68	C₄⋊C₄	—	172	1	no	—
69	C₄²	C₄×D₄₃	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	172	1	no	—
72	C₂³	—	172	1	no	—
73	Q₈	—	172	1	no	—
74	Q₈	—	172	1	no	—
75	D₄	—	344	2	no	—
76	D₄	—	172	1	no	—
77	D₄	—	172	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	172	1	no	—
80	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
81	C₈	#10621873	1	1	yes	characteristic
82	C₈	D₃₄₄	1	1	yes	characteristic
83	C₈	#10621882	1	1	yes	characteristic
84	C₈	#10621884	1	1	yes	characteristic
85	C₂²	—	344	2	no	—
86	C₂²	—	344	1	no	—
87	C₂²	#13063241	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	344	1	no	—
90	C₄	#13063245	1	1	yes	characteristic
91	C₄	#13063247	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	688	1	no	—
94	C₂	#14582642	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582642
commutator	C₄²×C₄₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#364	C₂
socle	C₂×C₄₃	#331
hypercenter	#364	D₄₃
hypocenter	C₄₃	#1359
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #14582720	C₂	semidirect
3. C₄₃×#364	C₂	semidirect
50. #364	D₄₃	semidirect
51. C₄₃	#1359	semidirect