Subgroups — #19134266

Order 5504.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583304	C₂	1	2	yes	maximal, complemented
2	#14583279	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583272	C₂	1	1	yes	maximal, characteristic
4	#14583246	C₂	1	2	yes	maximal
5	C₄₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₇₂	—	2	2	no	—
7	C₂×#10621873	—	2	2	no	—
8	#13063325	C₂²	1	1	yes	characteristic
9	#13063325	C₂²	1	2	yes	—
10	#13063322	C₂²	1	1	yes	characteristic
11	#13063259	—	2	4	no	—
12	#13063247	—	2	4	no	—
13	C₄×C₈×C₄₃	C₂²	1	2	yes	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×D₁₇₂	—	2	2	no	—
16	C₂×D₁₇₂	—	2	1	no	—
17	C₂×Dic₈₆	—	2	1	no	—
18	C₂×Dic₈₆	—	2	2	no	—
19	C₂×C₈×C₄₃	D₄	1	4	yes	—
20	C₂×C₈×C₄₃	D₄	1	2	yes	—
21	C₄²×C₄₃	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₄₃	—	2	2	no	—
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	—	2	2	no	—
25	Dic₁₇₂	—	4	4	no	—
26	#10621873	—	4	4	no	—
27	C₂²×D₄₃	—	4	1	no	—
28	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
30	C₂×Dic₄₃	—	4	2	no	—
31	C₂×Dic₄₃	—	4	1	no	—
32	D₁₇₂	—	4	2	no	—
33	D₁₇₂	—	4	4	no	—
34	Dic₈₆	—	4	2	no	—
35	Dic₈₆	—	4	4	no	—
36	C₈×C₄₃	—	2	4	no	—
37	C₈×C₄₃	D₈	1	4	yes	—
38	C₂²×C₄₃	#127	1	1	yes	characteristic
39	C₂×D₄₃	—	8	1	no	—
40	C₂×D₄₃	—	8	2	no	—
41	C₄×C₄₃	C₂×D₈	1	2	yes	—
42	C₄×C₄₃	#137	1	4	yes	—
43	Dic₄₃	—	8	1	no	—
44	Dic₄₃	—	8	2	no	—
45	#1722	—	43	1	no	maximal, Sylow
46	C₂×C₄₃	#493	1	1	yes	characteristic
47	C₂×C₄₃	#497	1	2	yes	—
48	D₄₃	—	16	1	no	—
49	#500	—	43	2	no	—
50	#494	—	43	1	no	—
51	#492	—	43	1	no	—
52	#486	—	43	2	no	—
53	#322	D₄₃	1	1	yes	characteristic, complemented
54	C₄₃	#1722	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	86	2	no	—
56	C₂×SD₁₆	—	86	2	no	—
57	C₄⋊Q₈	—	43	2	no	—
58	C₄⋊Q₈	—	43	1	no	—
59	#127	—	43	1	no	—
60	#107	—	86	4	no	—
61	#102	—	86	4	no	—
62	C₄×C₈	C₂×D₄₃	1	2	yes	—
63	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
64	C₂×Q₈	—	86	1	no	—
65	C₂×Q₈	—	86	2	no	—
66	C₂×D₄	—	86	2	no	—
67	C₂×D₄	—	86	1	no	—
68	Q₁₆	—	172	4	no	—
69	SD₁₆	—	172	4	no	—
70	C₂×C₈	D₁₇₂	1	4	yes	—
71	C₂×C₈	D₁₇₂	1	2	yes	—
72	C₄⋊C₄	—	86	2	no	—
73	C₄⋊C₄	—	86	2	no	—
74	C₄⋊C₄	—	86	2	no	—
75	C₄²	C₂²×D₄₃	1	1	yes	characteristic
76	C₂³	—	172	1	no	—
77	Q₈	—	172	2	no	—
78	Q₈	—	172	4	no	—
79	D₄	—	172	2	no	—
80	D₄	—	172	4	no	—
81	C₂×C₄	—	172	2	no	—
82	C₂×C₄	—	172	1	no	—
83	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
84	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
85	C₈	—	2	4	no	—
86	C₈	D₃₄₄	1	4	yes	—
87	C₂²	—	344	1	no	—
88	C₂²	—	344	2	no	—
89	C₂²	#13063322	1	1	yes	characteristic
90	C₄	—	344	1	no	—
91	C₄	—	344	2	no	—
92	C₄	C₂×D₃₄₄	1	2	yes	—
93	C₄	#13063358	1	4	yes	—
94	C₂	—	688	1	no	—
95	C₂	#14583276	1	1	yes	characteristic
96	C₂	#14583293	1	2	yes	—

	subgroup	G/H
center	C₂²	#13063322
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#322	C₂
socle	C₂²×C₄₃	#127
hypercenter	#322	D₄₃
hypocenter	C₄₃	#1722
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
1. #14583304	C₂	semidirect
2. #14583279	C₂	semidirect
5. C₄₃×#322	C₂	semidirect
53. #322	D₄₃	semidirect
54. C₄₃	#1722	semidirect