Subgroups — #19136467

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	C₄×Dic₁₇₂	C₂	1	2	yes	maximal
3	#14582727	C₂	1	1	yes	maximal, characteristic
4	#14582704	C₂	1	2	yes	maximal
5	C₄₃×#346	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₂²	1	2	yes	—
7	C₄×Dic₈₆	—	2	2	no	—
8	Dic₃₄₄	C₄	1	4	yes	complemented
9	#13063259	C₂²	1	2	yes	—
10	#13063250	—	2	2	no	—
11	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₈₆	—	2	2	no	—
15	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
17	C₄²×C₄₃	D₄	1	1	yes	characteristic
18	C₄⋊Dic₄₃	—	2	2	no	—
19	Dic₄₃⋊C₄	—	4	2	no	—
20	C₄×Dic₄₃	—	4	2	no	—
21	Dic₁₇₂	—	2	2	no	—
22	Dic₁₇₂	C₂×C₄	1	4	yes	—
23	C₁₆×C₄₃	—	2	1	no	—
24	C₁₆×C₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₄₃	D₈	1	2	yes	—
26	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₄₃	—	4	2	no	—
28	C₂×Dic₄₃	—	4	2	no	—
29	Dic₈₆	—	2	4	no	—
30	Dic₈₆	—	4	2	no	—
31	C₈×C₄₃	—	2	1	no	—
32	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₄₃	#41	1	1	yes	characteristic
34	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
35	C₄×C₄₃	—	2	2	no	—
36	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
37	C₄×C₄₃	#135	1	1	yes	characteristic
38	Dic₄₃	—	4	4	no	—
39	Dic₄₃	—	8	2	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	—	43	1	no	—
46	#358	—	43	2	no	—
47	#346	D₄₃	1	1	yes	characteristic
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	C₂×D₄₃	1	1	yes	characteristic
53	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
54	#107	—	43	2	no	—
55	#103	—	86	2	no	—
56	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
57	C₂×Q₈	—	86	2	no	—
58	Q₁₆	—	43	4	no	—
59	Q₁₆	—	86	2	no	—
60	C₂×C₈	D₁₇₂	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
62	C₄⋊C₄	—	86	2	no	—
63	C₄⋊C₄	—	172	2	no	—
64	C₄²	—	172	2	no	—
65	C₄²	D₁₇₂	1	1	yes	characteristic
66	C₁₆	—	2	1	no	—
67	C₁₆	C₄×D₄₃	1	2	yes	—
68	Q₈	—	86	4	no	—
69	Q₈	—	172	2	no	—
70	C₂×C₄	—	172	2	no	—
71	C₂×C₄	—	172	2	no	—
72	C₂×C₄	D₃₄₄	1	2	yes	—
73	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
76	C₈	#10621898	1	1	yes	characteristic
77	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	344	2	no	—
80	C₄	—	172	4	no	—
81	C₄	C₄×D₁₇₂	1	1	yes	characteristic
82	C₄	#13063347	1	1	yes	characteristic
83	C₂	C₄×D₃₄₄	1	1	yes	characteristic
84	C₂	#14583342	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃₄₄
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#346	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#346	D₄₃
hypocenter	C₄₃	#2176
LCS	G ▷ 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
8. Dic₃₄₄	C₄	semidirect
48. C₄₃	#2176	semidirect