Subgroups — C₂×#14582921 #19143148

Order 5504.

576 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10621872	C₂	1	2	yes	maximal
2	C₂×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582921	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×D₄₃	C₄	1	1	yes	characteristic
8	C₂²×C₄×D₄₃	C₄	1	1	yes	characteristic
9	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
10	C₂×#10621872	—	2	8	no	—
11	C₂×#10621872	C₂²	1	8	yes	—
12	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄×Dic₄₃	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₄₃	C₄	1	1	yes	characteristic
15	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
16	C₄²×D₄₃	C₄	1	4	yes	—
17	C₄²×D₄₃	C₂²	1	4	yes	—
18	C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	complemented
19	Dic₄₃⋊C₈	C₂²	1	8	yes	complemented
20	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	C₂²	1	4	yes	complemented
23	C₂³×D₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₄₃	—	2	4	no	—
31	C₂×C₄×D₄₃	—	2	4	no	—
32	C₂×C₄×D₄₃	C₂×C₄	1	4	yes	—
33	C₂×C₄×D₄₃	C₂×C₄	1	4	yes	—
34	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
35	C₂×C₄×D₄₃	D₄	1	4	yes	—
36	C₂×C₄×D₄₃	Q₈	1	4	yes	—
37	C₂×C₄×D₄₃	C₂³	1	2	yes	—
38	C₂×C₈×C₄₃	—	2	4	no	—
39	C₂×C₈×C₄₃	C₂³	1	4	yes	—
40	C₄²×C₄₃	C₂×C₄	1	2	yes	—
41	C₄²×C₄₃	C₂³	1	2	yes	—
42	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
43	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
44	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
45	C₄×Dic₄₃	C₂³	1	2	yes	—
46	C₂×C₄₃⋊C₈	—	2	4	no	—
47	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
48	#10621872	—	2	16	no	—
49	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×D₄₃	—	2	2	no	—
51	C₂²×D₄₃	—	2	2	no	—
52	C₂²×D₄₃	C₄⋊C₄	1	4	yes	—
53	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
54	C₂×C₄×C₄₃	—	2	2	no	—
55	C₂×C₄×C₄₃	M₁₆	1	4	yes	complemented
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	2	yes	—
59	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
61	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
62	C₂×Dic₄₃	—	2	2	no	—
63	C₂×Dic₄₃	C₄⋊C₄	1	4	yes	—
64	C₂×Dic₄₃	M₁₆	1	4	yes	complemented
65	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
66	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
67	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
68	C₄×D₄₃	—	2	8	no	—
69	C₄×D₄₃	—	2	8	no	—
70	C₄×D₄₃	C₄⋊C₄	1	8	yes	—
71	C₄×D₄₃	C₂×D₄	1	4	yes	—
72	C₄×D₄₃	C₂×Q₈	1	4	yes	—
73	C₈×C₄₃	—	2	4	no	—
74	C₄₃⋊C₈	—	2	4	no	—
75	C₂²×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
76	C₂²×C₄₃	C₂×M₁₆	1	2	yes	—
77	C₂²×C₄₃	C₂×M₁₆	1	2	yes	—
78	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
79	C₂×D₄₃	—	2	2	no	—
80	C₂×D₄₃	—	2	2	no	—
81	C₂×D₄₃	—	2	8	no	—
82	C₂×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
83	C₄×C₄₃	—	2	2	no	—
84	C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
85	C₄×C₄₃	C₂×M₁₆	1	4	yes	complemented
86	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
87	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
88	Dic₄₃	—	2	2	no	—
89	Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
90	Dic₄₃	C₂×M₁₆	1	4	yes	complemented
91	C₂×#423	—	43	1	no	maximal, Sylow
92	C₂×C₄₃	#423	1	4	yes	complemented
93	C₂×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
95	C₂×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
96	D₄₃	—	2	4	no	—
97	C₂²×M₁₆	—	43	2	no	—
98	C₂²×C₄²	—	43	1	no	—
99	#423	—	43	8	no	—
100	C₂×C₄⋊C₈	—	43	2	no	—
101	C₂×C₄⋊C₈	—	43	1	no	—
102	C₂×C₄⋊C₈	D₄₃	1	1	yes	characteristic, complemented
103	C₄₃	C₂×#423	1	1	yes	characteristic, complemented, Sylow
104	C₂³×C₄	—	43	1	no	—
105	C₂³×C₄	—	43	1	no	—
106	C₂³×C₄	—	43	1	no	—
107	C₂×M₁₆	—	43	8	no	—
108	C₂×M₁₆	—	86	8	no	—
109	C₂²×C₈	—	43	2	no	—
110	C₂²×C₈	C₂×D₄₃	1	2	yes	—
111	C₂×C₄²	—	43	1	no	—
112	C₂×C₄²	—	43	1	no	—
113	C₂×C₄²	—	43	1	no	—
114	C₂×C₄²	—	43	4	no	—
115	C₂×C₄²	—	43	4	no	—
116	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
117	C₄⋊C₈	—	43	8	no	—
118	C₄⋊C₈	—	43	4	no	—
119	C₄⋊C₈	C₂×D₄₃	1	4	yes	complemented
120	C₂⁴	—	43	1	no	—
121	C₂²×C₄	—	43	1	no	—
122	C₂²×C₄	—	43	1	no	—
123	C₂²×C₄	—	43	2	no	—
124	C₂²×C₄	—	43	4	no	—
125	C₂²×C₄	—	43	4	no	—
126	C₂²×C₄	—	43	2	no	—
127	C₂²×C₄	—	43	1	no	—
128	C₂²×C₄	—	43	4	no	—
129	C₂²×C₄	—	43	4	no	—
130	C₂²×C₄	—	86	4	no	—
131	C₂²×C₄	—	86	4	no	—
132	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
133	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
134	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
135	M₁₆	—	86	16	no	—
136	C₂×C₈	—	2	4	no	—
137	C₂×C₈	—	43	4	no	—
138	C₂×C₈	—	86	4	no	—
139	C₂×C₈	C₂²×D₄₃	1	4	yes	—
140	C₄²	—	43	4	no	—
141	C₄²	—	43	4	no	—
142	C₄²	—	43	2	no	—
143	C₄²	—	43	2	no	—
144	C₄²	C₄×D₄₃	1	2	yes	—
145	C₄²	C₂²×D₄₃	1	2	yes	—
146	C₂³	—	43	4	no	—
147	C₂³	—	43	2	no	—
148	C₂³	—	86	2	no	—
149	C₂³	—	86	2	no	—
150	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	43	4	no	—
153	C₂×C₄	—	43	4	no	—
154	C₂×C₄	—	43	2	no	—
155	C₂×C₄	—	43	2	no	—
156	C₂×C₄	—	43	8	no	—
157	C₂×C₄	—	43	4	no	—
158	C₂×C₄	—	43	4	no	—
159	C₂×C₄	—	43	2	no	—
160	C₂×C₄	—	86	8	no	—
161	C₂×C₄	—	86	2	no	—
162	C₂×C₄	—	86	8	no	—
163	C₂×C₄	#10621872	1	4	yes	complemented
164	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
165	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
166	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
167	C₂×C₄	D₄×D₄₃	1	2	yes	—
168	C₂×C₄	Q₈×D₄₃	1	2	yes	—
169	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
170	C₈	—	2	4	no	—
171	C₈	—	86	4	no	—
172	C₂²	—	43	4	no	—
173	C₂²	—	86	2	no	—
174	C₂²	—	86	2	no	—
175	C₂²	—	86	8	no	—
176	C₂²	C₄⋊C₄×D₄₃	1	2	yes	—
177	C₂²	M₁₆×D₄₃	1	2	yes	—
178	C₂²	C₂×#10621872	1	2	yes	—
179	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
180	C₄	—	2	2	no	—
181	C₄	—	43	4	no	—
182	C₄	—	43	4	no	—
183	C₄	—	86	2	no	—
184	C₄	C₄⋊C₄×D₄₃	1	2	yes	—
185	C₄	C₂×#10621872	1	4	yes	complemented
186	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
187	C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
188	C₂	—	86	4	no	—
189	C₂	#14582921	1	4	yes	direct product factor
190	C₂	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
191	C₂	C₂×M₁₆×D₄₃	1	1	yes	characteristic
192	C₂	C₂²×#10621872	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄⋊C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	C₂×C₄⋊C₈	D₄₃
hypocenter	C₄₃	C₂×#423
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #14582921	C₂	direct (N × H)
4. C₂×C₄⋊(C₄₃⋊C₈)	C₂	semidirect
5. C₂×Dic₄₃⋊C₈	C₂	semidirect
6. C₂×C₄⋊C₈×C₄₃	C₂	semidirect
18. C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
19. Dic₄₃⋊C₈	C₂²	semidirect
22. C₄⋊C₈×C₄₃	C₂²	semidirect
55. C₂×C₄×C₄₃	M₁₆	semidirect
64. C₂×Dic₄₃	M₁₆	semidirect
85. C₄×C₄₃	C₂×M₁₆	semidirect
90. Dic₄₃	C₂×M₁₆	semidirect
92. C₂×C₄₃	#423	semidirect
102. C₂×C₄⋊C₈	D₄₃	semidirect
103. C₄₃	C₂×#423	semidirect
119. C₄⋊C₈	C₂×D₄₃	semidirect
163. C₂×C₄	#10621872	semidirect
185. C₄	C₂×#10621872	semidirect
189. C₂	#14582921	direct (N × H)

Subgroups — C2×#14582921 #19143148

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582921 #19143148