Subgroups — #19136465

Order 5504.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₄₄	C₂	1	1	yes	maximal, characteristic
2	#14582993	C₂	1	2	yes	maximal
3	#14582702	C₂	1	2	yes	maximal
4	#14582674	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#367	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₂²	1	2	yes	—
7	#13063290	—	2	2	no	—
8	Dic₃₄₄	C₄	1	4	yes	complemented
9	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	#13063248	—	2	2	no	—
11	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	#107×C₄₃	C₂²	1	2	yes	—
14	C₂×Dic₈₆	—	2	2	no	—
15	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₄₃	—	2	2	no	—
17	Dic₄₃⋊C₄	—	4	2	no	—
18	C₄×Dic₄₃	—	4	2	no	—
19	C₄×Dic₄₃	D₄	1	1	yes	characteristic
20	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
21	Dic₁₇₂	—	2	2	no	—
22	Dic₁₇₂	C₂×C₄	1	4	yes	—
23	C₁₆×C₄₃	C₂×C₄	1	2	yes	—
24	C₄₃⋊C₁₆	—	2	1	no	—
25	C₂×C₄×C₄₃	—	4	2	no	—
26	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₄₃	—	4	2	no	—
28	C₂×Dic₄₃	D₈	1	2	yes	—
29	Dic₈₆	—	2	4	no	—
30	Dic₈₆	—	4	2	no	—
31	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₄₃	#41	1	1	yes	characteristic
33	C₄₃⋊C₈	—	2	1	no	—
34	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
35	C₄×C₄₃	—	8	2	no	—
36	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
37	C₄×C₄₃	#135	1	1	yes	characteristic
38	Dic₄₃	—	2	2	no	—
39	Dic₄₃	—	4	4	no	—
40	#2176	—	43	1	no	maximal, Sylow
41	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
42	C₂×C₄₃	#510	1	2	yes	—
43	C₂×Q₃₂	—	43	1	no	—
44	C₄×Q₁₆	—	43	2	no	—
45	#367	D₄₃	1	1	yes	characteristic
46	#358	—	43	2	no	—
47	#346	—	43	1	no	—
48	C₄₃	#2176	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₁₆	—	43	2	no	—
50	C₄×Q₈	—	86	2	no	—
51	Q₃₂	—	43	4	no	—
52	C₂×C₁₆	—	43	1	no	—
53	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
54	#107	C₂×D₄₃	1	2	yes	—
55	#103	—	86	2	no	—
56	C₄×C₈	—	43	1	no	—
57	C₂×Q₈	—	86	2	no	—
58	Q₁₆	—	43	4	no	—
59	Q₁₆	—	86	2	no	—
60	C₂×C₈	—	43	1	no	—
61	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	172	2	no	—
64	C₄²	—	43	1	no	—
65	C₄²	—	172	2	no	—
66	C₁₆	—	86	1	no	—
67	C₁₆	C₄×D₄₃	1	2	yes	—
68	Q₈	—	86	4	no	—
69	Q₈	—	172	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	43	2	no	—
72	C₂×C₄	—	172	2	no	—
73	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
74	C₈	—	86	1	no	—
75	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
76	C₈	#10621902	1	1	yes	characteristic
77	C₂²	D₈×D₄₃	1	1	yes	characteristic
78	C₄	—	8	2	no	—
79	C₄	—	86	2	no	—
80	C₄	—	172	4	no	—
81	C₄	#13063287	1	1	yes	characteristic
82	C₄	#13063348	1	1	yes	characteristic
83	C₂	#14582981	1	1	yes	characteristic
84	C₂	#14583338	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#367	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#367	D₄₃
hypocenter	C₄₃	#2176
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
8. Dic₃₄₄	C₄	semidirect
48. C₄₃	#2176	semidirect