Subgroups — #19136881

Order 5504.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583304	C₂	1	1	yes	maximal, characteristic
2	#14583301	C₂	1	1	yes	maximal, characteristic
3	#14582727	C₂	1	2	yes	maximal
4	#14582725	C₂	1	2	yes	maximal
5	C₄₃×#346	C₂	1	1	yes	maximal, characteristic
6	#13063325	—	2	1	no	—
7	#13063317	—	2	1	no	—
8	#13063259	—	2	1	no	—
9	#13063259	C₂²	1	1	yes	characteristic
10	#13063259	C₂²	1	1	yes	characteristic
11	#13063259	C₂²	1	2	yes	—
12	#13063257	—	2	1	no	—
13	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₈₆	—	4	1	no	—
16	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
18	C₄²×C₄₃	D₄	1	1	yes	characteristic
19	C₄⋊Dic₄₃	—	2	1	no	—
20	C₄⋊Dic₄₃	—	2	1	no	—
21	C₄⋊Dic₄₃	—	2	2	no	—
22	C₄⋊Dic₄₃	—	4	1	no	—
23	Dic₄₃⋊C₄	—	4	1	no	—
24	Dic₄₃⋊C₄	—	4	1	no	—
25	C₁₆×C₄₃	Q₈	1	4	yes	complemented
26	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₄₃	—	4	1	no	—
30	C₂×Dic₄₃	—	4	1	no	—
31	C₂×Dic₄₃	—	4	2	no	—
32	Dic₈₆	—	8	2	no	—
33	C₈×C₄₃	Q₁₆	1	2	yes	—
34	C₈×C₄₃	C₂×Q₈	1	2	yes	—
35	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₄₃	—	2	1	no	—
37	C₄×C₄₃	—	2	1	no	—
38	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
39	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
40	Dic₄₃	—	8	2	no	—
41	Dic₄₃	—	8	1	no	—
42	Dic₄₃	—	8	1	no	—
43	#2255	—	43	1	no	maximal, Sylow
44	C₂×C₄₃	#500	1	1	yes	characteristic
45	C₂×C₄₃	#509	1	1	yes	characteristic
46	C₂×C₄₃	#510	1	1	yes	characteristic
47	#500	—	43	1	no	—
48	#499	—	43	1	no	—
49	#367	—	43	2	no	—
50	#366	—	43	2	no	—
51	#346	D₄₃	1	1	yes	characteristic
52	C₄₃	#2255	1	1	yes	characteristic, complemented, Sylow
53	C₄⋊Q₈	—	86	1	no	—
54	#125	—	86	1	no	—
55	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
56	#107	—	43	1	no	—
57	#107	—	43	2	no	—
58	#107	—	43	1	no	—
59	#107	—	86	1	no	—
60	#106	—	86	1	no	—
61	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
62	C₂×Q₈	—	172	1	no	—
63	C₂×C₈	D₁₇₂	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
65	C₄⋊C₄	—	86	1	no	—
66	C₄⋊C₄	—	86	1	no	—
67	C₄⋊C₄	—	86	2	no	—
68	C₄⋊C₄	—	172	1	no	—
69	C₄⋊C₄	—	172	1	no	—
70	C₄⋊C₄	—	172	1	no	—
71	C₄²	D₁₇₂	1	1	yes	characteristic
72	C₁₆	Dic₈₆	1	4	yes	complemented
73	Q₈	—	344	2	no	—
74	C₂×C₄	—	172	1	no	—
75	C₂×C₄	—	172	1	no	—
76	C₂×C₄	—	172	2	no	—
77	C₂×C₄	D₃₄₄	1	1	yes	characteristic
78	C₂×C₄	D₃₄₄	1	1	yes	characteristic
79	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
80	C₈	Dic₁₇₂	1	2	yes	—
81	C₈	C₂×Dic₈₆	1	2	yes	—
82	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	344	2	no	—
86	C₄	—	344	1	no	—
87	C₄	—	344	1	no	—
88	C₄	#13063325	1	1	yes	characteristic
89	C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
90	C₂	#14583304	1	1	yes	characteristic
91	C₂	#14583337	1	1	yes	characteristic
92	C₂	#14583342	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#346	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#346	D₄₃
hypocenter	C₄₃	#2255
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
25. C₁₆×C₄₃	Q₈	semidirect
52. C₄₃	#2255	semidirect
72. C₁₆	Dic₈₆	semidirect