Subgroups — C₂×#14583712 #19149358

Order 5504.

1408 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063373	C₂	1	2	yes	maximal, complemented
2	#14583712	C₂	1	16	yes	maximal, direct product factor
3	C₂×#13063357	C₂	1	4	yes	maximal, complemented
4	C₂×#13063356	C₂	1	2	yes	maximal, complemented
5	C₂×#13063348	C₂	1	2	yes	maximal, complemented
6	C₂×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Q₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
8	C₂×#13063331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#13063373	—	2	8	no	—
11	#13063373	C₂²	1	16	yes	complemented
12	C₂×#10621902	—	2	2	no	—
13	C₂×#10621902	C₂²	1	4	yes	—
14	C₂×#10621898	—	2	4	no	—
15	C₂×#10621898	C₂²	1	1	yes	characteristic
16	C₂×#10621898	C₂²	1	2	yes	—
17	C₂×Q₈×D₄₃	—	2	2	no	—
18	C₂×Q₈×D₄₃	C₂²	1	4	yes	—
19	#13063357	C₂²	1	32	yes	complemented
20	#13063356	C₂²	1	16	yes	complemented
21	#13063348	C₂²	1	16	yes	complemented
22	#13063347	C₂²	1	8	yes	complemented
23	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
24	C₂×#10621885	C₂²	1	4	yes	—
25	Q₁₆×D₄₃	C₂²	1	16	yes	complemented
26	C₂×#10621873	C₂²	1	2	yes	—
27	C₂×#10621884	C₂²	1	4	yes	—
28	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
29	#13063331	C₂²	1	8	yes	complemented
30	C₂×#10621877	C₂²	1	1	yes	characteristic
31	C₂×#10621872	C₂²	1	2	yes	—
32	C₂×C₈×D₄₃	C₂²	1	2	yes	—
33	C₂²×Q₈×C₄₃	C₂²	1	2	yes	—
34	C₂×Q₁₆×C₄₃	C₂²	1	2	yes	—
35	C₂×Q₁₆×C₄₃	C₂²	1	2	yes	—
36	C₂×Q₁₆×C₄₃	C₂²	1	8	yes	complemented
37	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×Q₈×C₄₃	—	2	2	no	—
39	C₂×Q₈×C₄₃	—	2	4	no	—
40	C₂×Q₈×C₄₃	C₂³	1	4	yes	—
41	C₂×Q₈×C₄₃	C₂³	1	8	yes	—
42	C₂²×C₄×C₄₃	—	2	2	no	—
43	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂×C₂²⋊D₄₃	—	2	2	no	—
45	C₂×C₂²⋊D₄₃	D₄	1	2	yes	—
46	#10621902	—	2	16	no	—
47	#10621902	—	2	8	no	—
48	#10621902	C₂³	1	16	yes	—
49	Q₈×D₄₃	—	2	8	no	—
50	Q₈×D₄₃	—	2	16	no	—
51	Q₈×D₄₃	C₂³	1	16	yes	—
52	#10621898	—	2	4	no	—
53	#10621898	—	2	32	no	—
54	#10621898	D₄	1	4	yes	—
55	#10621898	C₂³	1	4	yes	—
56	#10621898	C₂³	1	8	yes	—
57	C₂×D₁₇₂	—	2	4	no	—
58	C₂×D₁₇₂	D₄	1	1	yes	characteristic
59	C₂×D₁₇₂	C₂³	1	2	yes	—
60	C₂×C₄×D₄₃	—	2	2	no	—
61	C₂×C₄×D₄₃	—	2	4	no	—
62	C₂×C₄×D₄₃	—	2	4	no	—
63	C₂×C₄×D₄₃	C₂³	1	2	yes	—
64	C₂×Dic₈₆	—	2	4	no	—
65	C₂×Dic₈₆	D₄	1	1	yes	characteristic
66	C₂×Dic₈₆	C₂³	1	2	yes	—
67	Q₁₆×C₄₃	C₂³	1	8	yes	—
68	Q₁₆×C₄₃	C₂³	1	8	yes	—
69	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₄₃	C₂³	1	4	yes	—
72	#10621885	C₂³	1	16	yes	—
73	#10621884	C₂³	1	16	yes	—
74	#10621877	C₂³	1	4	yes	—
75	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
76	Dic₁₇₂	C₂³	1	4	yes	—
77	D₃₄₄	C₂³	1	4	yes	—
78	#10621873	C₂³	1	8	yes	—
79	#10621872	C₂³	1	8	yes	—
80	C₈×D₄₃	C₂³	1	8	yes	—
81	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×D₄₃	—	2	2	no	—
83	C₂²×D₄₃	C₂×D₄	1	2	yes	—
84	Q₈×C₄₃	—	2	4	no	—
85	Q₈×C₄₃	—	2	8	no	—
86	Q₈×C₄₃	C₂⁴	1	8	yes	—
87	C₂×C₄×C₄₃	—	2	4	no	—
88	C₂×C₄×C₄₃	—	2	8	no	—
89	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
91	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
92	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
93	C₂²⋊D₄₃	—	2	8	no	—
94	C₂²⋊D₄₃	C₂×D₄	1	8	yes	—
95	C₂×Dic₄₃	—	2	2	no	—
96	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
97	D₁₇₂	—	2	16	no	—
98	D₁₇₂	—	2	2	no	—
99	D₁₇₂	C₂×D₄	1	4	yes	—
100	D₁₇₂	C₂⁴	1	4	yes	—
101	C₄×D₄₃	—	2	16	no	—
102	C₄×D₄₃	—	2	8	no	—
103	C₄×D₄₃	—	2	16	no	—
104	C₄×D₄₃	C₂×D₄	1	4	yes	—
105	C₄×D₄₃	C₂⁴	1	4	yes	—
106	Dic₈₆	—	2	2	no	—
107	Dic₈₆	—	2	16	no	—
108	Dic₈₆	C₂×D₄	1	4	yes	—
109	Dic₈₆	C₂⁴	1	4	yes	—
110	C₈×C₄₃	C₂⁴	1	2	yes	—
111	C₈×C₄₃	C₂⁴	1	2	yes	—
112	C₄₃⋊C₈	C₂⁴	1	4	yes	—
113	C₂²×C₄₃	—	2	2	no	—
114	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
115	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
116	C₂×D₄₃	—	2	4	no	—
117	C₂×D₄₃	—	2	4	no	—
118	C₂×D₄₃	—	4	4	no	—
119	C₂×D₄₃	C₂²×D₄	1	4	yes	—
120	C₄×C₄₃	—	2	8	no	—
121	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
122	C₄×C₄₃	C₂²×D₄	1	2	yes	—
123	C₄×C₄₃	C₂⁵	1	1	yes	characteristic
124	Dic₄₃	—	2	4	no	—
125	Dic₄₃	C₂²×D₄	1	4	yes	—
126	C₂×#578	—	43	1	no	maximal, Sylow
127	C₂×C₄₃	—	2	2	no	—
128	C₂×C₄₃	#578	1	2	yes	complemented
129	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
130	D₄₃	—	2	4	no	—
131	D₄₃	—	4	4	no	—
132	C₂×2₋¹⁺⁴	—	43	2	no	—
133	#578	—	43	16	no	—
134	C₂×#137	—	43	2	no	—
135	C₂×#137	—	43	4	no	—
136	C₂×#135	—	43	2	no	—
137	C₂×#135	—	43	1	no	—
138	C₂²×Q₁₆	—	43	2	no	—
139	C₂²×Q₁₆	D₄₃	1	1	yes	characteristic, complemented
140	C₂×#131	—	43	1	no	—
141	C₄₃	C₂×#578	1	1	yes	characteristic, complemented, Sylow
142	2₋¹⁺⁴	—	43	16	no	—
143	2₋¹⁺⁴	—	86	8	no	—
144	C₂×#41	—	43	1	no	—
145	C₂×#41	—	43	4	no	—
146	C₂×#41	—	43	2	no	—
147	C₂×#41	—	86	4	no	—
148	C₂×#41	—	86	2	no	—
149	C₂²×Q₈	—	43	4	no	—
150	C₂²×Q₈	—	86	2	no	—
151	C₂²×Q₈	C₂×D₄₃	1	2	yes	—
152	#137	—	43	16	no	—
153	#137	—	43	32	no	—
154	#135	—	43	16	no	—
155	#135	—	43	8	no	—
156	C₂×Q₁₆	—	43	4	no	—
157	C₂×Q₁₆	—	43	16	no	—
158	C₂×Q₁₆	—	43	1	no	—
159	C₂×Q₁₆	C₂×D₄₃	1	2	yes	—
160	C₂×Q₁₆	C₂×D₄₃	1	2	yes	—
161	C₂×Q₁₆	C₂×D₄₃	1	8	yes	complemented
162	C₂×SD₁₆	—	43	4	no	—
163	C₂×SD₁₆	—	43	2	no	—
164	C₂×D₈	—	43	1	no	—
165	#131	—	43	8	no	—
166	C₂×M₁₆	—	43	1	no	—
167	C₂×M₁₆	—	43	2	no	—
168	C₂²×C₈	—	43	2	no	—
169	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
170	#41	—	43	4	no	—
171	#41	—	43	4	no	—
172	#41	—	43	16	no	—
173	#41	—	43	8	no	—
174	#41	—	86	32	no	—
175	#41	—	86	8	no	—
176	#41	—	86	16	no	—
177	#41	—	86	4	no	—
178	C₂×Q₈	—	2	2	no	—
179	C₂×Q₈	—	2	4	no	—
180	C₂×Q₈	—	43	1	no	—
181	C₂×Q₈	—	43	16	no	—
182	C₂×Q₈	—	43	2	no	—
183	C₂×Q₈	—	86	4	no	—
184	C₂×Q₈	—	86	8	no	—
185	C₂×Q₈	—	86	16	no	—
186	C₂×Q₈	C₂²×D₄₃	1	4	yes	—
187	C₂×Q₈	C₂²×D₄₃	1	8	yes	—
188	C₂×D₄	—	43	2	no	—
189	C₂×D₄	—	43	1	no	—
190	C₂×D₄	—	43	2	no	—
191	C₂×D₄	—	86	4	no	—
192	C₂×D₄	—	86	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	43	2	no	—
195	C₂²×C₄	—	86	4	no	—
196	C₂²×C₄	—	86	4	no	—
197	C₂²×C₄	—	86	2	no	—
198	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
199	Q₁₆	—	43	16	no	—
200	Q₁₆	—	43	4	no	—
201	Q₁₆	C₂²×D₄₃	1	8	yes	—
202	Q₁₆	C₂²×D₄₃	1	8	yes	—
203	SD₁₆	—	43	16	no	—
204	SD₁₆	—	43	8	no	—
205	D₈	—	43	4	no	—
206	M₁₆	—	43	4	no	—
207	M₁₆	—	43	8	no	—
208	C₂×C₈	—	43	2	no	—
209	C₂×C₈	—	43	8	no	—
210	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
211	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
212	C₂×C₈	C₂²×D₄₃	1	4	yes	—
213	C₂³	—	43	2	no	—
214	C₂³	—	86	2	no	—
215	C₂³	D₄×D₄₃	1	1	yes	characteristic
216	Q₈	—	2	4	no	—
217	Q₈	—	2	8	no	—
218	Q₈	—	43	4	no	—
219	Q₈	—	43	4	no	—
220	Q₈	—	86	16	no	—
221	Q₈	—	86	2	no	—
222	Q₈	C₂³×D₄₃	1	8	yes	—
223	D₄	—	43	8	no	—
224	D₄	—	43	4	no	—
225	D₄	—	43	4	no	—
226	D₄	—	86	16	no	—
227	D₄	—	86	8	no	—
228	D₄	—	86	2	no	—
229	C₂×C₄	—	2	8	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	43	2	no	—
232	C₂×C₄	—	43	4	no	—
233	C₂×C₄	—	43	4	no	—
234	C₂×C₄	—	86	16	no	—
235	C₂×C₄	—	86	16	no	—
236	C₂×C₄	—	86	2	no	—
237	C₂×C₄	—	86	8	no	—
238	C₂×C₄	D₄×D₄₃	1	2	yes	—
239	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
240	C₂×C₄	C₂³×D₄₃	1	2	yes	—
241	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
242	C₈	—	43	4	no	—
243	C₈	C₂³×D₄₃	1	2	yes	—
244	C₈	C₂³×D₄₃	1	2	yes	—
245	C₂²	—	2	2	no	—
246	C₂²	—	43	4	no	—
247	C₂²	—	86	4	no	—
248	C₂²	—	86	4	no	—
249	C₂²	—	172	4	no	—
250	C₂²	C₂×D₄×D₄₃	1	2	yes	—
251	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
252	C₄	—	2	8	no	—
253	C₄	—	43	4	no	—
254	C₄	—	86	4	no	—
255	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
256	C₄	C₂×D₄×D₄₃	1	2	yes	—
257	C₄	C₂⁴×D₄₃	1	1	yes	characteristic
258	C₂	—	2	2	no	—
259	C₂	—	86	4	no	—
260	C₂	—	172	4	no	—
261	C₂	#14583712	1	2	yes	direct product factor
262	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁵
Frattini	C₄	C₂⁴×D₄₃
Fitting	C₂²×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	C₂²×Q₁₆	D₄₃
hypocenter	C₄₃	C₂×#578
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#13063373	C₂	semidirect
2. #14583712	C₂	direct (N × H)
3. C₂×#13063357	C₂	semidirect
4. C₂×#13063356	C₂	semidirect
5. C₂×#13063348	C₂	semidirect
6. C₂×#13063347	C₂	semidirect
7. C₂×Q₁₆×D₄₃	C₂	semidirect
8. C₂×#13063331	C₂	semidirect
9. C₂²×Q₁₆×C₄₃	C₂	semidirect
11. #13063373	C₂²	semidirect
19. #13063357	C₂²	semidirect
20. #13063356	C₂²	semidirect
21. #13063348	C₂²	semidirect
22. #13063347	C₂²	semidirect
25. Q₁₆×D₄₃	C₂²	semidirect
29. #13063331	C₂²	semidirect
36. C₂×Q₁₆×C₄₃	C₂²	semidirect
128. C₂×C₄₃	#578	semidirect
139. C₂²×Q₁₆	D₄₃	semidirect
141. C₄₃	C₂×#578	semidirect
161. C₂×Q₁₆	C₂×D₄₃	semidirect
261. C₂	#14583712	direct (N × H)

Subgroups — C2×#14583712 #19149358

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583712 #19149358