Subgroups — #19143012

Order 5504.

564 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₄₃	C₂	1	2	yes	maximal
2	C₂×#13063282	C₂	1	1	yes	maximal, characteristic
3	#14582856	C₂	1	4	yes	maximal, complemented
4	#14582853	C₂	1	4	yes	maximal, complemented
5	C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
6	M₁₆×Dic₄₃	C₂	1	2	yes	maximal, complemented
7	C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
9	C₂×#10621877	C₂²	1	2	yes	—
10	C₂×#10621872	C₂²	1	4	yes	—
11	M₁₆×D₄₃	C₄	1	16	yes	complemented
12	C₂×C₈×D₄₃	C₂²	1	4	yes	—
13	#13063282	C₄	1	4	yes	—
14	#13063282	C₂²	1	2	yes	—
15	#13063282	C₂²	1	2	yes	—
16	C₂×Dic₄₃⋊C₄	C₄	1	2	yes	—
17	C₂×(C₂×D₄₃)⋊C₄	C₄	1	2	yes	—
18	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
19	#13063236	C₂²	1	2	yes	complemented
20	#13063235	C₂²	1	4	yes	complemented
21	C₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
22	C₈×Dic₄₃	C₂²	1	4	yes	complemented
23	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
24	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
25	#97×C₄₃	C₂²	1	2	yes	complemented
26	C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
27	C₂³×D₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
30	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
31	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×D₄₃	C₂×C₄	1	8	yes	—
33	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₄₃	C₂³	1	2	yes	—
35	M₁₆×C₄₃	C₂×C₄	1	8	yes	—
36	C₂×C₈×C₄₃	C₂³	1	4	yes	—
37	C₄²×C₄₃	C₂×C₄	1	2	yes	—
38	C₄²×C₄₃	C₂³	1	1	yes	characteristic
39	C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	—
41	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	—
42	Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
43	Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
44	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
45	C₄×Dic₄₃	C₂³	1	2	yes	—
46	#10621877	C₂×C₄	1	8	yes	—
47	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
48	#10621872	C₂×C₄	1	16	yes	complemented
49	C₈×D₄₃	C₂×C₄	1	16	yes	complemented
50	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²×D₄₃	—	4	2	no	—
52	C₂²×D₄₃	C₄²	1	4	yes	—
53	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
54	C₂×C₄×C₄₃	—	4	2	no	—
55	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
56	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
60	C₂×Dic₄₃	—	4	2	no	—
61	C₂×Dic₄₃	C₄²	1	4	yes	—
62	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
63	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
64	C₄×D₄₃	C₄²	1	8	yes	—
65	C₄×D₄₃	C₂²×C₄	1	4	yes	—
66	C₄×D₄₃	C₂²×C₄	1	4	yes	—
67	C₈×C₄₃	C₂²×C₄	1	8	yes	—
68	C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
69	C₂²×C₄₃	—	2	2	no	—
70	C₂²×C₄₃	C₂×C₄²	1	2	yes	—
71	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
72	C₂×D₄₃	—	2	4	no	—
73	C₂×D₄₃	—	4	4	no	—
74	C₂×D₄₃	C₂×C₄²	1	4	yes	—
75	C₄×C₄₃	—	2	2	no	—
76	C₄×C₄₃	—	2	2	no	—
77	C₄×C₄₃	C₂×C₄²	1	2	yes	—
78	C₄×C₄₃	C₂³×C₄	1	2	yes	—
79	Dic₄₃	—	2	4	no	—
80	Dic₄₃	C₂×C₄²	1	4	yes	—
81	#2873	—	43	1	no	maximal, Sylow
82	C₂×C₄₃	—	2	2	no	—
83	C₂×C₄₃	C₂²×C₄²	1	1	yes	characteristic
84	C₂×C₄₃	#568	1	2	yes	—
85	D₄₃	—	2	4	no	—
86	C₂²×M₁₆	—	43	2	no	—
87	C₂×#117	—	43	1	no	—
88	#405	—	43	4	no	—
89	#405	—	43	4	no	—
90	C₄×M₁₆	—	43	2	no	—
91	C₄×M₁₆	—	43	1	no	—
92	C₄×M₁₆	D₄₃	1	1	yes	characteristic, complemented
93	C₄₃	#2873	1	1	yes	characteristic, complemented, Sylow
94	C₂³×C₄	—	43	1	no	—
95	C₂×M₁₆	—	43	2	no	—
96	C₂×M₁₆	—	43	16	no	—
97	C₂×M₁₆	—	43	4	no	—
98	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
99	C₂²×C₈	—	43	4	no	—
100	#117	—	43	2	no	—
101	#117	—	43	2	no	—
102	#117	—	43	4	no	—
103	C₂×C₄⋊C₄	—	43	2	no	—
104	C₂×C₂²⋊C₄	—	43	2	no	—
105	C₂×C₄²	—	43	1	no	—
106	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
107	#97	—	43	4	no	—
108	#97	—	43	2	no	—
109	#97	C₂×D₄₃	1	2	yes	complemented
110	C₄×C₈	—	43	4	no	—
111	C₄×C₈	—	43	2	no	—
112	C₄×C₈	C₂×D₄₃	1	2	yes	complemented
113	C₂⁴	—	43	1	no	—
114	C₂²×C₄	—	43	1	no	—
115	C₂²×C₄	—	43	2	no	—
116	C₂²×C₄	—	43	8	no	—
117	C₂²×C₄	—	43	2	no	—
118	C₂²×C₄	—	43	2	no	—
119	C₂²×C₄	C₄×D₄₃	1	2	yes	—
120	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
121	M₁₆	—	43	8	no	—
122	M₁₆	—	43	16	no	—
123	M₁₆	C₄×D₄₃	1	8	yes	—
124	C₂×C₈	—	43	4	no	—
125	C₂×C₈	—	43	16	no	—
126	C₂×C₈	C₂²×D₄₃	1	4	yes	—
127	C₄⋊C₄	—	43	4	no	—
128	C₄⋊C₄	—	43	4	no	—
129	C₂²⋊C₄	—	43	4	no	—
130	C₂²⋊C₄	—	43	4	no	—
131	C₄²	—	43	2	no	—
132	C₄²	—	43	2	no	—
133	C₄²	C₄×D₄₃	1	2	yes	—
134	C₄²	C₂²×D₄₃	1	1	yes	characteristic
135	C₄²	C₂²×D₄₃	1	1	yes	characteristic
136	C₂³	—	43	2	no	—
137	C₂³	—	43	4	no	—
138	C₂³	—	172	2	no	—
139	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	43	4	no	—
142	C₂×C₄	—	43	2	no	—
143	C₂×C₄	—	43	8	no	—
144	C₂×C₄	—	43	4	no	—
145	C₂×C₄	—	43	4	no	—
146	C₂×C₄	—	43	4	no	—
147	C₂×C₄	—	172	2	no	—
148	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
149	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
150	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
151	C₂×C₄	C₂×C₄×D₄₃	1	4	yes	—
152	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
153	C₈	—	43	8	no	—
154	C₈	C₂×C₄×D₄₃	1	8	yes	—
155	C₂²	—	2	2	no	—
156	C₂²	—	43	4	no	—
157	C₂²	—	86	4	no	—
158	C₂²	—	172	4	no	—
159	C₂²	C₄²×D₄₃	1	2	yes	—
160	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
161	C₄	—	2	2	no	—
162	C₄	—	2	2	no	—
163	C₄	—	43	4	no	—
164	C₄	—	86	4	no	—
165	C₄	C₄²×D₄₃	1	2	yes	—
166	C₄	C₂²×C₄×D₄₃	1	2	yes	—
167	C₂	—	2	2	no	—
168	C₂	—	86	4	no	—
169	C₂	C₂×C₄²×D₄₃	1	1	yes	characteristic
170	C₂	#14583665	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator	C₂×C₄₃	C₂²×C₄²
Fitting	C₄×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×C₄
hypercenter	C₄×M₁₆	D₄₃
hypocenter	C₄₃	#2873
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #14582856	C₂	semidirect
4. #14582853	C₂	semidirect
5. C₄×#10621877	C₂	semidirect
6. M₁₆×Dic₄₃	C₂	semidirect
7. C₄×M₁₆×C₄₃	C₂	semidirect
11. M₁₆×D₄₃	C₄	semidirect
19. #13063236	C₂²	semidirect
20. #13063235	C₂²	semidirect
21. C₄×C₄₃⋊C₈	C₂²	semidirect
22. C₈×Dic₄₃	C₂²	semidirect
25. #97×C₄₃	C₂²	semidirect
26. C₄×C₈×C₄₃	C₂²	semidirect
48. #10621872	C₂×C₄	semidirect
49. C₈×D₄₃	C₂×C₄	semidirect
92. C₄×M₁₆	D₄₃	semidirect
93. C₄₃	#2873	semidirect
109. #97	C₂×D₄₃	semidirect
112. C₄×C₈	C₂×D₄₃	semidirect