Subgroups — C₂²×#13063331 #19149299

Order 5504.

1504 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10621898	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063331	C₂	1	24	yes	maximal, direct product factor
3	C₂²×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#10621872	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×D₄₃	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10621898	C₄	1	12	yes	—
8	C₂×#10621898	C₂²	1	12	yes	—
9	C₂²×Dic₈₆	C₄	1	1	yes	characteristic
10	C₂²×D₁₇₂	C₄	1	1	yes	characteristic
11	C₂²×C₂²⋊D₄₃	C₄	1	2	yes	—
12	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
13	#13063331	C₂²	1	64	yes	direct product factor
14	C₂×#10621877	C₂²	1	12	yes	complemented
15	C₂×#10621872	C₂²	1	24	yes	complemented
16	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
17	C₂×C₈×D₄₃	C₂²	1	24	yes	complemented
18	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₄₃	C₂²	1	12	yes	complemented
22	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×D₄₃	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂×C₄	1	6	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₄₃	C₂³	1	6	yes	—
28	C₂×C₂²⋊D₄₃	C₂×C₄	1	24	yes	—
29	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
30	#10621898	C₂×C₄	1	48	yes	—
31	#10621898	C₂³	1	16	yes	—
32	C₂×D₁₇₂	C₂×C₄	1	12	yes	—
33	C₂×C₄×D₄₃	C₂×C₄	1	12	yes	—
34	C₂×C₄×D₄₃	C₂³	1	12	yes	—
35	C₂×Dic₈₆	C₂×C₄	1	12	yes	—
36	C₂×C₈×C₄₃	C₂³	1	6	yes	—
37	C₂×C₈×C₄₃	C₂³	1	6	yes	—
38	C₂×C₈×C₄₃	C₂³	1	16	yes	complemented
39	#10621877	C₂³	1	16	yes	complemented
40	C₂×C₄₃⋊C₈	C₂³	1	12	yes	—
41	#10621872	C₂³	1	32	yes	complemented
42	C₈×D₄₃	C₂³	1	32	yes	complemented
43	C₂³×C₄₃	—	2	4	no	—
44	C₂³×C₄₃	C₂²×C₄	1	6	yes	—
45	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
46	C₂²×D₄₃	—	2	8	no	—
47	C₂²×D₄₃	C₂²×C₄	1	12	yes	—
48	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
49	C₂×C₄×C₄₃	C₂²×C₄	1	3	yes	—
50	C₂×C₄×C₄₃	C₂²×C₄	1	12	yes	—
51	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
52	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
53	C₂²⋊D₄₃	C₂²×C₄	1	32	yes	—
54	C₂×Dic₄₃	C₂²×C₄	1	12	yes	—
55	D₁₇₂	C₂²×C₄	1	16	yes	—
56	C₄×D₄₃	C₂²×C₄	1	24	yes	—
57	C₄×D₄₃	C₂⁴	1	8	yes	—
58	Dic₈₆	C₂²×C₄	1	16	yes	—
59	C₈×C₄₃	C₂⁴	1	4	yes	—
60	C₈×C₄₃	C₂⁴	1	4	yes	—
61	C₄₃⋊C₈	C₂⁴	1	8	yes	—
62	C₂²×C₄₃	—	2	12	no	—
63	C₂²×C₄₃	#131	1	4	yes	complemented
64	C₂²×C₄₃	C₂³×C₄	1	4	yes	—
65	C₂²×C₄₃	C₂³×C₄	1	3	yes	—
66	C₂×D₄₃	—	2	24	no	—
67	C₂×D₄₃	C₂³×C₄	1	8	yes	—
68	C₄×C₄₃	C₂³×C₄	1	4	yes	—
69	C₄×C₄₃	C₂³×C₄	1	3	yes	—
70	C₄×C₄₃	C₂⁵	1	1	yes	characteristic
71	Dic₄₃	C₂³×C₄	1	8	yes	—
72	C₂²×#131	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	—	2	4	no	—
74	C₂×C₄₃	C₂×#131	1	6	yes	complemented
75	C₂×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
76	D₄₃	—	2	8	no	—
77	C₂²×#41	—	43	1	no	—
78	C₂×#131	—	43	24	no	—
79	C₂²×M₁₆	—	43	1	no	—
80	C₂²×M₁₆	—	43	2	no	—
81	C₂³×C₈	—	43	2	no	—
82	C₂³×C₈	D₄₃	1	1	yes	characteristic, complemented
83	C₄₃	C₂²×#131	1	1	yes	characteristic, complemented, Sylow
84	C₂×#41	—	43	12	no	—
85	C₂×#41	—	43	12	no	—
86	C₂²×Q₈	—	43	1	no	—
87	C₂²×D₄	—	43	2	no	—
88	C₂²×D₄	—	43	1	no	—
89	C₂³×C₄	—	43	2	no	—
90	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
91	#131	—	43	64	no	—
92	C₂×M₁₆	—	43	12	no	—
93	C₂×M₁₆	—	43	24	no	—
94	C₂²×C₈	—	43	2	no	—
95	C₂²×C₈	—	43	24	no	—
96	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
97	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
98	C₂²×C₈	C₂×D₄₃	1	12	yes	complemented
99	C₂⁴	—	43	2	no	—
100	C₂⁴	C₄×D₄₃	1	1	yes	characteristic
101	#41	—	43	48	no	—
102	#41	—	43	16	no	—
103	C₂×Q₈	—	43	12	no	—
104	C₂×D₄	—	43	24	no	—
105	C₂×D₄	—	43	12	no	—
106	C₂²×C₄	—	43	2	no	—
107	C₂²×C₄	—	43	12	no	—
108	C₂²×C₄	—	43	12	no	—
109	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
110	C₂²×C₄	C₄×D₄₃	1	6	yes	—
111	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
112	C₂²×C₄	C₂²×D₄₃	1	6	yes	—
113	M₁₆	—	43	16	no	—
114	M₁₆	—	43	32	no	—
115	C₂×C₈	—	43	12	no	—
116	C₂×C₈	—	43	32	no	—
117	C₂×C₈	C₂²×D₄₃	1	6	yes	—
118	C₂×C₈	C₂²×D₄₃	1	6	yes	—
119	C₂×C₈	C₂²×D₄₃	1	16	yes	complemented
120	C₂³	—	2	4	no	—
121	C₂³	—	43	12	no	—
122	C₂³	—	86	8	no	—
123	C₂³	C₂×C₄×D₄₃	1	6	yes	—
124	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
125	Q₈	—	43	16	no	—
126	D₄	—	43	32	no	—
127	D₄	—	43	16	no	—
128	C₂×C₄	—	43	12	no	—
129	C₂×C₄	—	43	24	no	—
130	C₂×C₄	—	43	8	no	—
131	C₂×C₄	C₂×C₄×D₄₃	1	3	yes	—
132	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
133	C₂×C₄	C₂×C₄×D₄₃	1	12	yes	—
134	C₂×C₄	C₂³×D₄₃	1	3	yes	—
135	C₂×C₄	C₂³×D₄₃	1	4	yes	—
136	C₈	—	43	8	no	—
137	C₈	C₂³×D₄₃	1	4	yes	—
138	C₈	C₂³×D₄₃	1	4	yes	—
139	C₂²	—	2	12	no	—
140	C₂²	—	43	8	no	—
141	C₂²	—	86	24	no	—
142	C₂²	#13063331	1	4	yes	direct product factor
143	C₂²	C₂²×C₄×D₄₃	1	4	yes	—
144	C₂²	C₂²×C₄×D₄₃	1	3	yes	—
145	C₄	—	43	8	no	—
146	C₄	C₂²×C₄×D₄₃	1	3	yes	—
147	C₄	C₂²×C₄×D₄₃	1	4	yes	—
148	C₄	C₂⁴×D₄₃	1	1	yes	characteristic
149	C₂	—	2	4	no	—
150	C₂	—	86	8	no	—
151	C₂	C₂×#13063331	1	6	yes	direct product factor
152	C₂	C₂³×C₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₂⁴×C₄
Frattini	C₄	C₂⁴×D₄₃
Fitting	C₂³×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	C₂³×C₈	D₄₃
hypocenter	C₄₃	C₂²×#131
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#13063331	C₂	direct (N × H)
3. C₂²×#10621877	C₂	semidirect
4. C₂²×#10621872	C₂	semidirect
5. C₂²×C₈×D₄₃	C₂	semidirect
6. C₂³×C₈×C₄₃	C₂	semidirect
13. #13063331	C₂²	direct (N × H)
14. C₂×#10621877	C₂²	semidirect
15. C₂×#10621872	C₂²	semidirect
17. C₂×C₈×D₄₃	C₂²	semidirect
21. C₂²×C₈×C₄₃	C₂²	semidirect
38. C₂×C₈×C₄₃	C₂³	semidirect
39. #10621877	C₂³	semidirect
41. #10621872	C₂³	semidirect
42. C₈×D₄₃	C₂³	semidirect
63. C₂²×C₄₃	#131	semidirect
74. C₂×C₄₃	C₂×#131	semidirect
82. C₂³×C₈	D₄₃	semidirect
83. C₄₃	C₂²×#131	semidirect
98. C₂²×C₈	C₂×D₄₃	semidirect
119. C₂×C₈	C₂²×D₄₃	semidirect
142. C₂²	#13063331	direct (N × H)
151. C₂	C₂×#13063331	direct (N × H)

Subgroups — C22×#13063331 #19149299

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13063331 #19149299