Subgroups — C₂×#14582654 #19134286

Order 5504.

528 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄₃⋊C₈	C₂	1	2	yes	maximal
2	#14582654	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₈	—	2	4	no	—
5	C₂²×C₄₃⋊C₈	—	2	4	no	—
6	C₂²×C₄₃⋊C₈	C₄	1	8	yes	complemented
7	C₂²×C₄₃⋊C₈	C₂²	1	4	yes	—
8	C₂³×C₄×C₄₃	C₄	1	2	yes	—
9	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₄₃	—	2	4	no	—
11	C₂×C₄²×C₄₃	C₄	1	2	yes	—
12	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
13	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	—	2	4	no	—
15	C₂²×C₄×C₄₃	—	2	4	no	—
16	C₂²×C₄×C₄₃	C₈	1	8	yes	complemented
17	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	D₄	1	4	yes	—
21	C₂²×C₄×C₄₃	D₄	1	2	yes	—
22	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₄²×C₄₃	—	2	4	no	—
25	C₄²×C₄₃	—	2	4	no	—
26	C₂×C₄₃⋊C₈	—	2	16	no	—
27	C₂×C₄₃⋊C₈	—	2	4	no	—
28	C₂×C₄₃⋊C₈	—	2	4	no	—
29	C₂×C₄₃⋊C₈	C₂×C₄	1	8	yes	complemented
30	C₂³×C₄₃	C₄²	1	2	yes	—
31	C₂³×C₄₃	C₂²⋊C₄	1	2	yes	—
32	C₂³×C₄₃	C₄⋊C₄	1	2	yes	—
33	C₂³×C₄₃	C₂×C₈	1	4	yes	—
34	C₂³×C₄₃	M₁₆	1	4	yes	—
35	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	—	2	16	no	—
37	C₂×C₄×C₄₃	—	2	4	no	—
38	C₂×C₄×C₄₃	—	2	4	no	—
39	C₂×C₄×C₄₃	C₄²	1	2	yes	—
40	C₂×C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
41	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₄₃	C₄⋊C₄	1	8	yes	—
43	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₄₃	C₂×C₈	1	8	yes	complemented
45	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
49	C₄₃⋊C₈	—	2	8	no	—
50	C₂²×C₄₃	#95	1	4	yes	—
51	C₂²×C₄₃	C₄×C₈	1	4	yes	—
52	C₂²×C₄₃	#97	1	4	yes	—
53	C₂²×C₄₃	C₂²⋊C₈	1	8	yes	—
54	C₂²×C₄₃	C₄⋊C₈	1	8	yes	—
55	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
56	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄₃	C₂²×C₈	1	2	yes	—
59	C₂²×C₄₃	C₂×M₁₆	1	2	yes	—
60	C₄×C₄₃	—	2	8	no	—
61	C₄×C₄₃	#95	1	4	yes	—
62	C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
63	C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
64	C₂×#336	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	#336	1	8	yes	complemented
66	C₂×C₄₃	C₂×#95	1	1	yes	characteristic
67	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
68	C₂×C₄₃	C₂×#97	1	1	yes	characteristic
69	C₂×C₄₃	C₂×C₂²⋊C₈	1	2	yes	—
70	C₂×C₄₃	C₂×C₄⋊C₈	1	2	yes	—
71	C₂³×C₈	—	43	2	no	—
72	C₂²×C₄²	D₄₃	1	1	yes	characteristic
73	#336	—	43	4	no	—
74	C₄₃	C₂×#336	1	1	yes	characteristic, complemented, Sylow
75	C₂³×C₄	Dic₄₃	1	2	yes	—
76	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
77	C₂²×C₈	—	43	4	no	—
78	C₂²×C₈	—	43	8	no	—
79	C₂²×C₈	—	86	4	no	—
80	C₂²×C₈	—	86	4	no	—
81	C₂×C₄²	—	2	4	no	—
82	C₂×C₄²	Dic₄₃	1	2	yes	—
83	C₂×C₄²	C₂×D₄₃	1	2	yes	—
84	C₂⁴	C₂×Dic₄₃	1	1	yes	characteristic
85	C₂²×C₄	—	2	4	no	—
86	C₂²×C₄	—	2	4	no	—
87	C₂²×C₄	C₄₃⋊C₈	1	8	yes	complemented
88	C₂²×C₄	Dic₈₆	1	2	yes	—
89	C₂²×C₄	C₄×D₄₃	1	4	yes	—
90	C₂²×C₄	D₁₇₂	1	2	yes	—
91	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
92	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
93	C₂²×C₄	C₂²⋊D₄₃	1	4	yes	—
94	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
95	C₂×C₈	—	43	8	no	—
96	C₂×C₈	—	86	16	no	—
97	C₂×C₈	—	86	4	no	—
98	C₂×C₈	—	86	4	no	—
99	C₄²	—	2	4	no	—
100	C₄²	—	2	4	no	—
101	C₂³	C₂×C₄₃⋊C₈	1	4	yes	—
102	C₂³	#10621877	1	4	yes	—
103	C₂³	C₄×Dic₄₃	1	2	yes	—
104	C₂³	C₄⋊Dic₄₃	1	2	yes	—
105	C₂³	C₂²⋊Dic₄₃	1	2	yes	—
106	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
107	C₂×C₄	—	2	16	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	—	2	4	no	—
110	C₂×C₄	C₂×C₄₃⋊C₈	1	8	yes	complemented
111	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
112	C₂×C₄	Dic₄₃⋊C₄	1	8	yes	—
113	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
114	C₂×C₄	(C₂×D₄₃)⋊C₄	1	8	yes	—
115	C₂×C₄	C₂²⋊Dic₄₃	1	2	yes	—
116	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
117	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
118	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
119	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
120	C₈	—	86	8	no	—
121	C₂²	C₄₃⋊#95	1	4	yes	—
122	C₂²	C₄×C₄₃⋊C₈	1	4	yes	—
123	C₂²	#13063236	1	4	yes	—
124	C₂²	C₂²⋊(C₄₃⋊C₈)	1	8	yes	—
125	C₂²	C₄⋊(C₄₃⋊C₈)	1	8	yes	—
126	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
127	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
128	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
129	C₂²	C₂²×C₄₃⋊C₈	1	2	yes	—
130	C₂²	C₂×#10621877	1	2	yes	—
131	C₄	—	2	8	no	—
132	C₄	C₄₃⋊#95	1	4	yes	—
133	C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
134	C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
135	C₂	#14582654	1	8	yes	direct product factor
136	C₂	C₂×C₄₃⋊#95	1	1	yes	characteristic
137	C₂	C₂×C₄×C₄₃⋊C₈	1	1	yes	characteristic
138	C₂	C₂×#13063236	1	1	yes	characteristic
139	C₂	C₂×C₂²⋊(C₄₃⋊C₈)	1	2	yes	—
140	C₂	C₂×C₄⋊(C₄₃⋊C₈)	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂²×C₄²×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂×C₄
hypercenter	C₂²×C₄²	D₄₃
hypocenter	C₄₃	C₂×#336
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. #14582654	C₂	direct (N × H)
6. C₂²×C₄₃⋊C₈	C₄	semidirect
16. C₂²×C₄×C₄₃	C₈	semidirect
29. C₂×C₄₃⋊C₈	C₂×C₄	semidirect
44. C₂×C₄×C₄₃	C₂×C₈	semidirect
65. C₂×C₄₃	#336	semidirect
74. C₄₃	C₂×#336	semidirect
87. C₂²×C₄	C₄₃⋊C₈	semidirect
110. C₂×C₄	C₂×C₄₃⋊C₈	semidirect
135. C₂	#14582654	direct (N × H)

Subgroups — C2×#14582654 #19134286

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582654 #19134286