Subgroups — C₄×#13063261 #19134497

Order 5504.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063261	C₂	1	2	yes	maximal
2	C₄×#10621877	C₂	1	2	yes	maximal
3	#14582664	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#10621877	C₂²	1	4	yes	—
6	#13063261	C₄	1	8	yes	direct product factor
7	#13063236	—	2	2	no	—
8	C₄×C₄₃⋊C₈	—	2	2	no	—
9	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₄₃	C₄	1	4	yes	—
13	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
14	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₄₃	—	2	2	no	—
16	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
19	C₄²×C₄₃	C₂×C₄	1	2	yes	—
20	C₄²×C₄₃	D₄	1	1	yes	characteristic
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	#10621877	—	2	4	no	—
23	#10621877	C₂×C₄	1	8	yes	—
24	C₂×C₄₃⋊C₈	—	2	4	no	—
25	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₄₃	—	2	4	no	—
27	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
30	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	#41	1	2	yes	—
33	C₈×C₄₃	—	2	2	no	—
34	C₈×C₄₃	C₄²	1	4	yes	—
35	C₄₃⋊C₈	—	2	8	no	—
36	C₂²×C₄₃	—	2	2	no	—
37	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₄₃	C₄×Q₈	1	2	yes	—
39	C₄×C₄₃	—	2	2	no	—
40	C₄×C₄₃	#108	1	4	yes	complemented
41	C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₄₃	#117	1	1	yes	characteristic
43	C₄×C₄₃	C₄×D₄	1	2	yes	—
44	C₄×#108	—	43	1	no	maximal, Sylow
45	C₂×C₄₃	—	2	2	no	—
46	C₂×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₄₃	C₂×#108	1	2	yes	—
48	C₂×#108	—	43	2	no	—
49	C₄×M₁₆	—	43	2	no	—
50	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
51	#341	—	43	2	no	—
52	C₄₃	C₄×#108	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	43	4	no	—
54	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
56	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
57	#108	—	43	8	no	—
58	#97	—	86	2	no	—
59	C₄×C₈	—	86	2	no	—
60	C₄×C₈	Dic₄₃	1	4	yes	—
61	C₂²×C₄	Dic₈₆	1	2	yes	—
62	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
63	M₁₆	—	43	8	no	—
64	M₁₆	—	86	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	86	4	no	—
67	C₂×C₈	C₄×D₄₃	1	4	yes	—
68	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
69	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
70	C₄²	D₁₇₂	1	1	yes	characteristic
71	C₄²	D₁₇₂	1	1	yes	characteristic
72	C₄²	C₂×Dic₄₃	1	2	yes	—
73	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
78	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
79	C₂×C₄	#10621898	1	2	yes	—
80	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	86	8	no	—
83	C₈	C₄×Dic₄₃	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
86	C₂²	C₄×Dic₈₆	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#13063261	1	4	yes	direct product factor
89	C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
90	C₄	#13063284	1	1	yes	characteristic
91	C₄	C₄×D₁₇₂	1	2	yes	—
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₄₃	1	1	yes	characteristic
94	C₂	C₂×#13063261	1	2	yes	—

	subgroup	G/H
center	C₄²	D₁₇₂
commutator	C₄×C₄₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	C₄×#108
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #13063261	C₄	direct (N × H)
40. C₄×C₄₃	#108	semidirect
52. C₄₃	C₄×#108	semidirect
88. C₄	#13063261	direct (N × H)

Subgroups — C4×#13063261 #19134497

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063261 #19134497