Subgroups — #19132561

Order 5504.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic
2	#14582675	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₄₄	C₄	1	1	yes	characteristic
5	C₄×D₁₇₂	—	2	1	no	—
6	C₂×C₄₃⋊C₁₆	—	2	1	no	—
7	#13063259	C₄	1	1	yes	characteristic
8	#13063247	—	2	1	no	—
9	C₄⋊C₈×C₄₃	—	2	1	no	—
10	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×D₁₇₂	—	2	1	no	—
12	C₂×C₄×D₄₃	—	4	1	no	—
13	C₂×C₈×C₄₃	—	4	1	no	—
14	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₄²×C₄₃	D₄	1	1	yes	characteristic
17	(C₂×D₄₃)⋊C₄	—	4	1	no	—
18	C₄⋊Dic₄₃	—	2	1	no	—
19	D₃₄₄	—	2	1	no	—
20	D₃₄₄	C₈	1	2	yes	complemented
21	C₄₃⋊C₁₆	—	2	2	no	—
22	C₂²×D₄₃	—	4	1	no	—
23	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
25	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
26	C₂×Dic₄₃	—	4	1	no	—
27	D₁₇₂	—	2	2	no	—
28	D₁₇₂	—	4	1	no	—
29	C₄×D₄₃	—	8	2	no	—
30	C₈×C₄₃	—	2	1	no	—
31	C₈×C₄₃	—	8	1	no	—
32	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₄₃	M₁₆	1	1	yes	characteristic
34	C₂²×C₄₃	#102	1	1	yes	characteristic
35	C₂×D₄₃	—	4	2	no	—
36	C₂×D₄₃	—	8	1	no	—
37	C₂×D₄₃	—	8	1	no	—
38	C₄×C₄₃	—	2	1	no	—
39	C₄×C₄₃	—	2	1	no	—
40	C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₄₃	#104	1	1	yes	characteristic
42	Dic₄₃	—	8	1	no	—
43	#1333	—	43	1	no	maximal, Sylow
44	C₂×C₄₃	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₄₃	#360	1	1	yes	characteristic
46	C₂×C₄₃	#361	1	1	yes	characteristic
47	D₄₃	—	8	2	no	—
48	C₄×D₈	—	43	1	no	—
49	#346	—	43	1	no	—
50	#334	D₄₃	1	1	yes	characteristic, complemented
51	C₄₃	#1333	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₈	—	43	1	no	—
53	C₄×D₄	—	86	1	no	—
54	C₂×C₁₆	—	86	1	no	—
55	#107	—	43	1	no	—
56	C₄⋊C₈	—	2	1	no	—
57	#102	—	86	1	no	—
58	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
59	C₂×D₄	—	86	1	no	—
60	C₂²×C₄	—	172	1	no	—
61	D₈	—	43	2	no	—
62	D₈	—	86	1	no	—
63	C₂×C₈	—	4	1	no	—
64	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
65	C₂×C₈	D₁₇₂	1	1	yes	characteristic
66	C₄⋊C₄	—	86	1	no	—
67	C₂²⋊C₄	—	172	1	no	—
68	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
69	C₁₆	—	86	2	no	—
70	C₂³	—	172	1	no	—
71	D₄	—	86	2	no	—
72	D₄	—	172	1	no	—
73	C₂×C₄	—	344	2	no	—
74	C₂×C₄	—	172	1	no	—
75	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
76	C₂×C₄	#10621882	1	1	yes	characteristic
77	C₂×C₄	#10621884	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	8	1	no	—
80	C₈	C₈×D₄₃	1	1	yes	characteristic
81	C₈	#10621872	1	1	yes	characteristic
82	C₂²	—	344	1	no	—
83	C₂²	—	344	1	no	—
84	C₂²	—	172	2	no	—
85	C₂²	#13063245	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	1	no	—
88	C₄	—	344	1	no	—
89	C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
90	C₄	#13063251	1	1	yes	characteristic
91	C₂	—	344	2	no	—
92	C₂	#14582626	1	1	yes	characteristic
93	C₂	#14582708	1	1	yes	characteristic
94	C₂	#14582711	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063245
commutator	C₈×C₄₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	#102
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1333
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
2. #14582675	C₂	semidirect
3. C₄₃×#334	C₂	semidirect
20. D₃₄₄	C₈	semidirect
50. #334	D₄₃	semidirect
51. C₄₃	#1333	semidirect