Subgroups — C₂×#14583711 #19149356

Order 5504.

1460 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063372	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063371	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583711	C₂	1	16	yes	maximal, direct product factor
4	C₂×#13063358	C₂	1	3	yes	maximal, complemented
5	C₂×#13063353	C₂	1	3	yes	maximal, complemented
6	C₂×#13063347	C₂	1	3	yes	maximal, complemented
7	C₂²×#10621873	C₂	1	3	yes	maximal, complemented
8	C₂×#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#13063372	—	2	4	no	—
10	#13063372	C₂²	1	8	yes	complemented
11	#13063371	—	2	4	no	—
12	#13063371	C₂²	1	8	yes	complemented
13	C₂×#10621902	—	2	1	no	—
14	C₂×#10621898	C₂²	1	3	yes	—
15	C₂×#10621898	C₂²	1	3	yes	complemented
16	C₂×#10621900	—	2	3	no	—
17	C₂²×Dic₈₆	C₂²	1	3	yes	complemented
18	C₂×Q₈×D₄₃	—	2	1	no	—
19	C₂²×D₁₇₂	C₂²	1	3	yes	—
20	C₂×D₄×D₄₃	—	2	3	no	—
21	#13063358	C₂²	1	24	yes	complemented
22	#13063353	C₂²	1	24	yes	complemented
23	#13063347	C₂²	1	24	yes	complemented
24	C₂×Dic₁₇₂	C₂²	1	3	yes	complemented
25	C₂×#10621873	C₂²	1	3	yes	complemented
26	C₂×#10621873	C₂²	1	6	yes	complemented
27	C₂×#10621873	C₂²	1	1	yes	characteristic, complemented
28	C₂×#10621873	C₂²	1	24	yes	complemented
29	C₂×D₃₄₄	C₂²	1	3	yes	complemented
30	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
31	#131×C₄₃	C₂²	1	8	yes	complemented
32	C₂×M₁₆×C₄₃	C₂²	1	3	yes	complemented
33	C₂²×C₈×C₄₃	C₂²	1	3	yes	complemented
34	C₂³×D₄₃	—	2	3	no	—
35	#41×C₄₃	D₄	1	4	yes	—
36	#41×C₄₃	C₂³	1	4	yes	—
37	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
38	C₂×D₄×C₄₃	D₄	1	3	yes	—
39	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
40	C₂×C₂²⋊D₄₃	—	2	3	no	—
41	C₂×C₂²⋊D₄₃	—	2	3	no	—
42	C₂²×Dic₄₃	—	2	3	no	—
43	#10621902	—	2	8	no	—
44	Q₈×D₄₃	—	2	8	no	—
45	#10621900	—	2	24	no	—
46	D₄×D₄₃	—	2	24	no	—
47	#10621898	—	2	6	no	—
48	#10621898	—	2	6	no	—
49	#10621898	C₂³	1	12	yes	—
50	#10621898	C₂³	1	12	yes	complemented
51	C₂×D₁₇₂	—	2	3	no	—
52	C₂×D₁₇₂	—	2	6	no	—
53	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
54	C₂×D₁₇₂	C₂³	1	3	yes	—
55	C₂×D₁₇₂	C₂³	1	12	yes	—
56	C₂×C₄×D₄₃	—	2	3	no	—
57	C₂×C₄×D₄₃	—	2	3	no	—
58	C₂×Dic₈₆	—	2	3	no	—
59	C₂×Dic₈₆	—	2	6	no	—
60	C₂×Dic₈₆	C₂³	1	3	yes	—
61	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
62	C₂×Dic₈₆	C₂³	1	12	yes	complemented
63	M₁₆×C₄₃	C₂³	1	12	yes	complemented
64	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₈×C₄₃	C₂³	1	3	yes	—
66	C₂×C₈×C₄₃	C₂³	1	12	yes	complemented
67	Dic₁₇₂	C₂³	1	12	yes	complemented
68	D₃₄₄	C₂³	1	12	yes	complemented
69	#10621873	C₂³	1	12	yes	complemented
70	#10621873	C₂³	1	24	yes	complemented
71	#10621873	C₂³	1	4	yes	complemented
72	C₂³×C₄₃	C₂×D₄	1	3	yes	—
73	C₂²×D₄₃	—	2	1	no	—
74	C₂²×D₄₃	—	2	3	no	—
75	C₂²×D₄₃	—	2	12	no	—
76	C₂²×D₄₃	—	8	6	no	—
77	Q₈×C₄₃	C₂×D₄	1	4	yes	—
78	D₄×C₄₃	C₂×D₄	1	12	yes	—
79	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
80	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
81	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
82	C₂×C₄×C₄₃	C₂⁴	1	6	yes	—
83	C₂²⋊D₄₃	—	2	12	no	—
84	C₂²⋊D₄₃	—	2	12	no	—
85	C₂×Dic₄₃	—	2	3	no	—
86	C₂×Dic₄₃	—	2	12	no	—
87	C₂×Dic₄₃	—	2	1	no	—
88	D₁₇₂	—	2	3	no	—
89	D₁₇₂	—	2	12	no	—
90	D₁₇₂	—	2	1	no	—
91	D₁₇₂	C₂⁴	1	6	yes	—
92	D₁₇₂	C₂⁴	1	2	yes	—
93	C₄×D₄₃	—	2	12	no	—
94	C₄×D₄₃	—	2	12	no	—
95	Dic₈₆	—	2	3	no	—
96	Dic₈₆	—	2	12	no	—
97	Dic₈₆	—	2	1	no	—
98	Dic₈₆	C₂⁴	1	6	yes	—
99	Dic₈₆	C₂⁴	1	2	yes	—
100	C₈×C₄₃	C₂⁴	1	2	yes	—
101	C₈×C₄₃	C₂⁴	1	6	yes	—
102	C₂²×C₄₃	—	2	6	no	—
103	C₂²×C₄₃	C₂²×D₄	1	6	yes	—
104	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
105	C₂×D₄₃	—	2	6	no	—
106	C₂×D₄₃	—	2	2	no	—
107	C₂×D₄₃	—	4	2	no	—
108	C₂×D₄₃	—	4	6	no	—
109	C₂×D₄₃	—	8	12	no	—
110	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
111	C₄×C₄₃	C₂²×D₄	1	6	yes	—
112	C₄×C₄₃	C₂⁵	1	1	yes	characteristic
113	Dic₄₃	—	2	6	no	—
114	Dic₄₃	—	2	2	no	—
115	C₂×#577	—	43	1	no	maximal, Sylow
116	C₂×C₄₃	—	2	6	no	—
117	C₂×C₄₃	#577	1	2	yes	complemented
118	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
119	D₄₃	—	4	2	no	—
120	D₄₃	—	4	6	no	—
121	C₂×2₋¹⁺⁴	—	43	1	no	—
122	C₂×H(5,𝔽₂)	—	43	1	no	—
123	#577	—	43	16	no	—
124	C₂×#137	—	43	3	no	—
125	C₂×AGL(1,ℤ/8)	—	43	3	no	—
126	C₂×#135	—	43	3	no	—
127	C₂²×SD₁₆	—	43	3	no	—
128	C₂×#131	D₄₃	1	1	yes	characteristic, complemented
129	C₄₃	C₂×#577	1	1	yes	characteristic, complemented, Sylow
130	2₋¹⁺⁴	—	43	8	no	—
131	2₋¹⁺⁴	—	86	4	no	—
132	H(5,𝔽₂)	—	43	8	no	—
133	H(5,𝔽₂)	—	86	4	no	—
134	C₂×#41	—	43	3	no	—
135	C₂×#41	—	43	3	no	—
136	C₂×#41	—	86	1	no	—
137	C₂×#41	—	86	3	no	—
138	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
139	C₂²×Q₈	—	43	3	no	—
140	C₂²×Q₈	—	86	1	no	—
141	C₂²×D₄	—	43	3	no	—
142	C₂²×D₄	—	86	3	no	—
143	#137	—	43	24	no	—
144	AGL(1,ℤ/8)	—	43	24	no	—
145	#135	—	43	24	no	—
146	C₂×Q₁₆	—	43	3	no	—
147	C₂×SD₁₆	—	43	3	no	—
148	C₂×SD₁₆	—	43	6	no	—
149	C₂×SD₁₆	—	43	1	no	—
150	C₂×SD₁₆	—	43	24	no	—
151	C₂×D₈	—	43	3	no	—
152	#131	C₂×D₄₃	1	8	yes	complemented
153	C₂×M₁₆	C₂×D₄₃	1	3	yes	complemented
154	C₂²×C₈	C₂×D₄₃	1	3	yes	complemented
155	C₂⁴	—	86	3	no	—
156	#41	—	43	12	no	—
157	#41	—	43	12	no	—
158	#41	—	86	8	no	—
159	#41	—	86	24	no	—
160	#41	—	86	6	no	—
161	#41	—	86	6	no	—
162	#41	D₁₇₂	1	4	yes	—
163	#41	C₂²×D₄₃	1	4	yes	—
164	C₂×Q₈	—	43	3	no	—
165	C₂×Q₈	—	43	12	no	—
166	C₂×Q₈	—	43	1	no	—
167	C₂×Q₈	—	86	8	no	—
168	C₂×Q₈	—	86	3	no	—
169	C₂×Q₈	—	86	6	no	—
170	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
171	C₂×D₄	—	43	1	no	—
172	C₂×D₄	—	43	3	no	—
173	C₂×D₄	—	43	12	no	—
174	C₂×D₄	—	86	3	no	—
175	C₂×D₄	—	86	3	no	—
176	C₂×D₄	—	86	24	no	—
177	C₂×D₄	—	86	3	no	—
178	C₂×D₄	—	86	6	no	—
179	C₂×D₄	D₁₇₂	1	3	yes	—
180	C₂²×C₄	—	86	3	no	—
181	C₂²×C₄	—	86	3	no	—
182	C₂²×C₄	—	86	3	no	—
183	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
184	Q₁₆	—	43	12	no	—
185	SD₁₆	—	43	12	no	—
186	SD₁₆	—	43	24	no	—
187	SD₁₆	—	43	4	no	—
188	D₈	—	43	12	no	—
189	M₁₆	C₂²×D₄₃	1	12	yes	complemented
190	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
191	C₂×C₈	C₂²×D₄₃	1	3	yes	—
192	C₂×C₈	C₂²×D₄₃	1	12	yes	complemented
193	C₂³	—	86	12	no	—
194	C₂³	—	86	1	no	—
195	C₂³	—	86	3	no	—
196	C₂³	—	344	6	no	—
197	C₂³	C₂×D₁₇₂	1	3	yes	—
198	Q₈	—	43	6	no	—
199	Q₈	—	43	2	no	—
200	Q₈	—	86	12	no	—
201	Q₈	—	86	3	no	—
202	Q₈	—	86	1	no	—
203	Q₈	C₂×D₁₇₂	1	4	yes	—
204	D₄	—	43	2	no	—
205	D₄	—	43	6	no	—
206	D₄	—	86	12	no	—
207	D₄	—	86	12	no	—
208	D₄	—	86	12	no	—
209	D₄	—	86	3	no	—
210	D₄	—	86	1	no	—
211	D₄	C₂×D₁₇₂	1	12	yes	—
212	C₂×C₄	—	86	12	no	—
213	C₂×C₄	—	86	1	no	—
214	C₂×C₄	—	86	3	no	—
215	C₂×C₄	—	86	12	no	—
216	C₂×C₄	—	86	12	no	—
217	C₂×C₄	C₂×D₁₇₂	1	6	yes	—
218	C₂×C₄	C₂×D₁₇₂	1	3	yes	—
219	C₂×C₄	C₂³×D₄₃	1	6	yes	—
220	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
221	C₈	C₂³×D₄₃	1	2	yes	—
222	C₈	C₂³×D₄₃	1	6	yes	—
223	C₂²	—	2	6	no	—
224	C₂²	—	86	2	no	—
225	C₂²	—	86	6	no	—
226	C₂²	—	344	12	no	—
227	C₂²	—	172	6	no	—
228	C₂²	—	172	2	no	—
229	C₂²	C₂²×D₁₇₂	1	6	yes	—
230	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
231	C₄	—	86	2	no	—
232	C₄	—	86	6	no	—
233	C₄	C₂²×D₁₇₂	1	6	yes	—
234	C₄	C₂²×D₁₇₂	1	1	yes	characteristic
235	C₄	C₂⁴×D₄₃	1	1	yes	characteristic
236	C₂	—	2	6	no	—
237	C₂	—	172	6	no	—
238	C₂	—	172	2	no	—
239	C₂	#14583711	1	2	yes	direct product factor
240	C₂	C₂³×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₄×C₄₃	C₂⁵
Frattini	C₄	C₂⁴×D₄₃
Fitting	C₂×#131×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	C₂×#131	D₄₃
hypocenter	C₄₃	C₂×#577
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. C₂×#13063372	C₂	semidirect
2. C₂×#13063371	C₂	semidirect
3. #14583711	C₂	direct (N × H)
4. C₂×#13063358	C₂	semidirect
5. C₂×#13063353	C₂	semidirect
6. C₂×#13063347	C₂	semidirect
7. C₂²×#10621873	C₂	semidirect
8. C₂×#131×C₄₃	C₂	semidirect
10. #13063372	C₂²	semidirect
12. #13063371	C₂²	semidirect
15. C₂×#10621898	C₂²	semidirect
17. C₂²×Dic₈₆	C₂²	semidirect
21. #13063358	C₂²	semidirect
22. #13063353	C₂²	semidirect
23. #13063347	C₂²	semidirect
24. C₂×Dic₁₇₂	C₂²	semidirect
25. C₂×#10621873	C₂²	semidirect
26. C₂×#10621873	C₂²	semidirect
27. C₂×#10621873	C₂²	semidirect
28. C₂×#10621873	C₂²	semidirect
29. C₂×D₃₄₄	C₂²	semidirect
31. #131×C₄₃	C₂²	semidirect
32. C₂×M₁₆×C₄₃	C₂²	semidirect
33. C₂²×C₈×C₄₃	C₂²	semidirect
50. #10621898	C₂³	semidirect
62. C₂×Dic₈₆	C₂³	semidirect
63. M₁₆×C₄₃	C₂³	semidirect
66. C₂×C₈×C₄₃	C₂³	semidirect
67. Dic₁₇₂	C₂³	semidirect
68. D₃₄₄	C₂³	semidirect
69. #10621873	C₂³	semidirect
70. #10621873	C₂³	semidirect
71. #10621873	C₂³	semidirect
117. C₂×C₄₃	#577	semidirect
128. C₂×#131	D₄₃	semidirect
129. C₄₃	C₂×#577	semidirect
152. #131	C₂×D₄₃	semidirect
153. C₂×M₁₆	C₂×D₄₃	semidirect
154. C₂²×C₈	C₂×D₄₃	semidirect
189. M₁₆	C₂²×D₄₃	semidirect
192. C₂×C₈	C₂²×D₄₃	semidirect
239. C₂	#14583711	direct (N × H)

Subgroups — C2×#14583711 #19149356

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583711 #19149356