Subgroups — C₂×C₄₃×#1869 #24940910

Order 11008.

2438 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊C₈×C₄₃	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1869	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₃×#336	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₄₃	—	2	4	no	—
11	C₂³×C₈×C₄₃	—	2	8	no	—
12	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
13	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
14	C₂³×C₈×C₄₃	C₂²	1	4	yes	complemented
15	C₂×C₄×D₄×C₄₃	—	2	4	no	—
16	C₂×C₄×D₄×C₄₃	—	2	4	no	—
17	C₂×C₄×D₄×C₄₃	C₄	1	4	yes	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
19	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₄₃	C₄	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₄₃	C₄	1	1	yes	characteristic
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊C₈×C₄₃	—	2	4	no	—
24	C₂×C₂²⋊C₈×C₄₃	—	2	8	no	—
25	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	8	yes	complemented
27	C₄₃×#336	C₂²	1	8	yes	complemented
28	C₂⁵×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂⁵×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₄₃	—	2	4	no	—
31	C₂²×D₄×C₄₃	—	2	4	no	—
32	C₂²×D₄×C₄₃	C₈	1	8	yes	complemented
33	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₄₃	—	2	4	no	—
35	C₂³×C₄×C₄₃	—	2	4	no	—
36	C₂³×C₄×C₄₃	—	2	2	no	—
37	C₂³×C₄×C₄₃	—	2	2	no	—
38	C₂³×C₄×C₄₃	—	2	4	no	—
39	C₂³×C₄×C₄₃	—	2	4	no	—
40	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	D₄	1	4	yes	—
47	C₂³×C₄×C₄₃	D₄	1	4	yes	—
48	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₃	—	2	32	no	—
52	C₂²×C₈×C₄₃	—	2	4	no	—
53	C₂²×C₈×C₄₃	—	2	4	no	—
54	C₂²×C₈×C₄₃	—	2	8	no	—
55	C₂²×C₈×C₄₃	—	2	16	no	—
56	C₂²×C₈×C₄₃	—	2	4	no	—
57	C₂²×C₈×C₄₃	—	2	4	no	—
58	C₂²×C₈×C₄₃	—	2	4	no	—
59	C₂²×C₈×C₄₃	D₄	1	8	yes	complemented
60	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
61	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
62	C₄×D₄×C₄₃	—	2	16	no	—
63	C₄×D₄×C₄₃	—	2	8	no	—
64	C₄×D₄×C₄₃	—	2	8	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
70	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
71	C₂×C₄²×C₄₃	—	2	2	no	—
72	C₂×C₄²×C₄₃	—	2	2	no	—
73	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
75	C₂²⋊C₈×C₄₃	—	2	8	no	—
76	C₂²⋊C₈×C₄₃	—	2	16	no	—
77	C₂⁴×C₄₃	—	2	4	no	—
78	C₂⁴×C₄₃	—	2	4	no	—
79	C₂⁴×C₄₃	—	2	2	no	—
80	C₂⁴×C₄₃	—	2	4	no	—
81	C₂⁴×C₄₃	—	2	2	no	—
82	C₂⁴×C₄₃	—	2	4	no	—
83	C₂⁴×C₄₃	C₂²⋊C₄	1	4	yes	—
84	C₂⁴×C₄₃	C₂×C₈	1	4	yes	—
85	C₂⁴×C₄₃	C₂×C₈	1	4	yes	complemented
86	C₂⁴×C₄₃	M₁₆	1	4	yes	—
87	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
88	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
89	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
90	C₂×D₄×C₄₃	—	2	32	no	—
91	C₂×D₄×C₄₃	—	2	8	no	—
92	C₂×D₄×C₄₃	—	2	8	no	—
93	C₂×D₄×C₄₃	C₂×C₈	1	16	yes	complemented
94	C₂²×C₄×C₄₃	—	2	8	no	—
95	C₂²×C₄×C₄₃	—	2	8	no	—
96	C₂²×C₄×C₄₃	—	2	16	no	—
97	C₂²×C₄×C₄₃	—	2	8	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	2	8	no	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	—	2	4	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	4	4	no	—
114	C₂²×C₄×C₄₃	—	4	8	no	—
115	C₂²×C₄×C₄₃	—	4	4	no	—
116	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
117	C₂²×C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
118	C₂²×C₄×C₄₃	C₂×C₈	1	4	yes	complemented
119	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₃	#41	1	4	yes	—
130	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₄₃	—	2	32	no	—
132	C₂×C₈×C₄₃	—	2	16	no	—
133	C₂×C₈×C₄₃	—	2	4	no	—
134	C₂×C₈×C₄₃	—	2	4	no	—
135	C₂×C₈×C₄₃	—	2	4	no	—
136	C₂×C₈×C₄₃	—	2	4	no	—
137	C₂×C₈×C₄₃	—	2	4	no	—
138	C₂×C₈×C₄₃	—	4	8	no	—
139	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	complemented
140	C₄⋊C₄×C₄₃	—	2	8	no	—
141	C₂²⋊C₄×C₄₃	—	2	8	no	—
142	C₂²⋊C₄×C₄₃	—	2	8	no	—
143	C₄²×C₄₃	—	2	4	no	—
144	C₄²×C₄₃	—	2	2	no	—
145	C₄²×C₄₃	—	2	2	no	—
146	C₂³×C₄₃	—	2	4	no	—
147	C₂³×C₄₃	—	2	4	no	—
148	C₂³×C₄₃	—	2	8	no	—
149	C₂³×C₄₃	—	2	8	no	—
150	C₂³×C₄₃	—	2	16	no	—
151	C₂³×C₄₃	—	2	16	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	2	4	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	4	no	—
156	C₂³×C₄₃	—	2	8	no	—
157	C₂³×C₄₃	—	2	16	no	—
158	C₂³×C₄₃	—	4	4	no	—
159	C₂³×C₄₃	—	4	4	no	—
160	C₂³×C₄₃	—	4	8	no	—
161	C₂³×C₄₃	C₂²⋊C₈	1	16	yes	complemented
162	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
163	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂³×C₄₃	C₄×D₄	1	4	yes	—
165	C₂³×C₄₃	C₂²×C₈	1	4	yes	—
166	C₂³×C₄₃	C₂²×C₈	1	2	yes	—
167	C₂³×C₄₃	C₂²×C₈	1	4	yes	complemented
168	C₂³×C₄₃	C₂×M₁₆	1	4	yes	—
169	C₂³×C₄₃	C₂×M₁₆	1	2	yes	—
170	C₂³×C₄₃	#131	1	4	yes	—
171	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
172	D₄×C₄₃	—	2	32	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	8	no	—
177	C₂×C₄×C₄₃	—	2	8	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	8	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	16	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	4	no	—
186	C₂×C₄×C₄₃	—	4	4	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	4	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	8	no	—
192	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
193	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
195	C₂×C₄×C₄₃	#120	1	4	yes	—
196	C₂×C₄×C₄₃	#121	1	8	yes	—
197	C₂×C₄×C₄₃	#123	1	4	yes	—
198	C₂×C₄×C₄₃	C₂²×C₈	1	4	yes	complemented
199	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
203	C₈×C₄₃	—	2	8	no	—
204	C₈×C₄₃	—	4	4	no	—
205	C₂×#1869	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₄₃	—	2	4	no	—
207	C₂²×C₄₃	—	2	32	no	—
208	C₂²×C₄₃	—	2	8	no	—
209	C₂²×C₄₃	—	2	8	no	—
210	C₂²×C₄₃	—	2	4	no	—
211	C₂²×C₄₃	—	2	4	no	—
212	C₂²×C₄₃	—	2	8	no	—
213	C₂²×C₄₃	—	4	2	no	—
214	C₂²×C₄₃	—	4	16	no	—
215	C₂²×C₄₃	—	4	4	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	#386	1	4	yes	—
218	C₂²×C₄₃	C₂×C₂²⋊C₈	1	4	yes	—
219	C₂²×C₄₃	C₂×C₂²⋊C₈	1	8	yes	complemented
220	C₂²×C₄₃	#408	1	4	yes	—
221	C₂²×C₄₃	C₈×D₄	1	8	yes	—
222	C₂²×C₄₃	#435	1	8	yes	—
223	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
225	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
226	C₂²×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
227	C₂²×C₄₃	C₂×#131	1	2	yes	—
228	C₄×C₄₃	—	2	4	no	—
229	C₄×C₄₃	—	2	4	no	—
230	C₄×C₄₃	—	4	2	no	—
231	C₄×C₄₃	—	4	2	no	—
232	C₄×C₄₃	#386	1	4	yes	—
233	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
234	C₄×C₄₃	C₂×#121	1	2	yes	—
235	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
236	C₂⁴×C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
237	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
238	C₂²×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
239	C₂²×C₂²⋊C₈	C₂×C₄₃	1	2	yes	complemented
240	#1869	C₂×C₄₃	1	8	yes	direct product factor
241	C₂×#336	C₂×C₄₃	1	2	yes	complemented
242	C₂×C₄₃	—	2	8	no	—
243	C₂×C₄₃	—	4	4	no	—
244	C₂×C₄₃	#1869	1	8	yes	direct product factor
245	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
246	C₂×C₄₃	C₂²×C₂²⋊C₈	1	1	yes	characteristic
247	C₂×C₄₃	C₂×#408	1	1	yes	characteristic
248	C₂×C₄₃	C₂×C₈×D₄	1	2	yes	—
249	C₂×C₄₃	C₂×#435	1	2	yes	—
250	C₂³×D₄	C₄×C₄₃	1	1	yes	characteristic
251	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
252	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
253	C₂³×C₈	—	2	4	no	—
254	C₂³×C₈	—	2	8	no	—
255	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
256	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
257	C₂³×C₈	C₂²×C₄₃	1	4	yes	complemented
258	C₂×C₄×D₄	—	2	4	no	—
259	C₂×C₄×D₄	—	2	4	no	—
260	C₂×C₄×D₄	C₄×C₄₃	1	4	yes	—
261	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
262	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic
263	C₂²×C₂²⋊C₄	C₄×C₄₃	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₄×C₄₃	1	1	yes	characteristic
265	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×C₂²⋊C₈	—	2	4	no	—
267	C₂×C₂²⋊C₈	—	2	8	no	—
268	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	complemented
269	C₂×C₂²⋊C₈	C₂²×C₄₃	1	8	yes	complemented
270	#336	C₂²×C₄₃	1	8	yes	complemented
271	C₄₃	C₂×#1869	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁵	C₂×C₄×C₄₃	1	1	yes	characteristic
273	C₂⁵	C₂×C₄×C₄₃	1	1	yes	characteristic
274	C₂²×D₄	—	2	4	no	—
275	C₂²×D₄	—	2	4	no	—
276	C₂²×D₄	C₈×C₄₃	1	8	yes	complemented
277	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
278	C₂³×C₄	—	2	4	no	—
279	C₂³×C₄	—	2	4	no	—
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	—	2	2	no	—
282	C₂³×C₄	—	2	4	no	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
285	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
286	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
287	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
288	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
289	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
290	C₂³×C₄	D₄×C₄₃	1	4	yes	—
291	C₂³×C₄	D₄×C₄₃	1	4	yes	—
292	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
293	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
294	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
295	C₂²×C₈	—	2	32	no	—
296	C₂²×C₈	—	2	4	no	—
297	C₂²×C₈	—	2	4	no	—
298	C₂²×C₈	—	2	8	no	—
299	C₂²×C₈	—	2	16	no	—
300	C₂²×C₈	—	2	4	no	—
301	C₂²×C₈	—	2	4	no	—
302	C₂²×C₈	—	2	4	no	—
303	C₂²×C₈	D₄×C₄₃	1	8	yes	complemented
304	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
305	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
306	C₄×D₄	—	2	16	no	—
307	C₄×D₄	—	2	8	no	—
308	C₄×D₄	—	2	8	no	—
309	C₂×C₄⋊C₄	—	2	4	no	—
310	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
318	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
319	C₂²⋊C₈	—	2	8	no	—
320	C₂²⋊C₈	—	2	16	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	2	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	2	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	C₂²⋊C₄×C₄₃	1	4	yes	—
328	C₂⁴	C₂×C₈×C₄₃	1	4	yes	—
329	C₂⁴	C₂×C₈×C₄₃	1	4	yes	complemented
330	C₂⁴	M₁₆×C₄₃	1	4	yes	—
331	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
332	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
333	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
334	C₂×D₄	—	2	32	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	C₂×C₈×C₄₃	1	16	yes	complemented
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	16	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	—	4	8	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
361	C₂²×C₄	C₂²⋊C₄×C₄₃	1	8	yes	—
362	C₂²×C₄	C₂×C₈×C₄₃	1	4	yes	complemented
363	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
365	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
366	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
367	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
369	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
370	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
373	C₂²×C₄	#41×C₄₃	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
375	C₂×C₈	—	2	32	no	—
376	C₂×C₈	—	2	16	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	2	4	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	4	8	no	—
383	C₂×C₈	C₂×D₄×C₄₃	1	8	yes	complemented
384	C₄⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	2	8	no	—
394	C₂³	—	2	16	no	—
395	C₂³	—	2	16	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	8	no	—
401	C₂³	—	2	16	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	8	no	—
405	C₂³	C₂²⋊C₈×C₄₃	1	16	yes	complemented
406	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
407	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
408	C₂³	C₄×D₄×C₄₃	1	4	yes	—
409	C₂³	C₂²×C₈×C₄₃	1	4	yes	—
410	C₂³	C₂²×C₈×C₄₃	1	2	yes	—
411	C₂³	C₂²×C₈×C₄₃	1	4	yes	complemented
412	C₂³	C₂×M₁₆×C₄₃	1	4	yes	—
413	C₂³	C₂×M₁₆×C₄₃	1	2	yes	—
414	C₂³	#131×C₄₃	1	4	yes	—
415	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
416	D₄	—	2	32	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	16	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
438	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
439	C₂×C₄	#120×C₄₃	1	4	yes	—
440	C₂×C₄	#121×C₄₃	1	8	yes	—
441	C₂×C₄	#123×C₄₃	1	4	yes	—
442	C₂×C₄	C₂²×C₈×C₄₃	1	4	yes	complemented
443	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
444	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
447	C₈	—	2	8	no	—
448	C₈	—	4	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	32	no	—
451	C₂²	—	2	8	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	8	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	16	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	2	no	—
460	C₂²	C₄₃×#386	1	4	yes	—
461	C₂²	C₂×C₂²⋊C₈×C₄₃	1	4	yes	—
462	C₂²	C₂×C₂²⋊C₈×C₄₃	1	8	yes	complemented
463	C₂²	C₄₃×#408	1	4	yes	—
464	C₂²	C₈×D₄×C₄₃	1	8	yes	—
465	C₂²	C₄₃×#435	1	8	yes	—
466	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
467	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
468	C₂²	C₂³×C₈×C₄₃	1	1	yes	characteristic
469	C₂²	C₂²×M₁₆×C₄₃	1	1	yes	characteristic
470	C₂²	C₂×#131×C₄₃	1	2	yes	—
471	C₄	—	2	4	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	C₄₃×#386	1	4	yes	—
476	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
477	C₄	C₂×#121×C₄₃	1	2	yes	—
478	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
479	C₂	—	2	8	no	—
480	C₂	—	4	4	no	—
481	C₂	C₄₃×#1869	1	8	yes	direct product factor
482	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
483	C₂	C₂²×C₂²⋊C₈×C₄₃	1	1	yes	characteristic
484	C₂	C₂×C₄₃×#408	1	1	yes	characteristic
485	C₂	C₂×C₈×D₄×C₄₃	1	2	yes	—
486	C₂	C₂×C₄₃×#435	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₃	C₂³
commutator	C₂²	C₂³×C₈×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂⁴×C₄₃	C₂²×C₄
prime radical	C₂³×D₄×C₄₃	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₈×C₄₃	C₂	semidirect
3. C₂²×C₂²⋊C₈×C₄₃	C₂	semidirect
4. C₂²×C₂²⋊C₈×C₄₃	C₂	semidirect
5. C₄₃×#1869	C₂	direct (N × H)
6. C₂×C₄₃×#336	C₂	semidirect
14. C₂³×C₈×C₄₃	C₂²	semidirect
25. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
26. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
27. C₄₃×#336	C₂²	semidirect
32. C₂²×D₄×C₄₃	C₈	semidirect
59. C₂²×C₈×C₄₃	D₄	semidirect
85. C₂⁴×C₄₃	C₂×C₈	semidirect
93. C₂×D₄×C₄₃	C₂×C₈	semidirect
118. C₂²×C₄×C₄₃	C₂×C₈	semidirect
139. C₂×C₈×C₄₃	C₂×D₄	semidirect
161. C₂³×C₄₃	C₂²⋊C₈	semidirect
167. C₂³×C₄₃	C₂²×C₈	semidirect
198. C₂×C₄×C₄₃	C₂²×C₈	semidirect
205. C₂×#1869	C₄₃	direct (N × H)
219. C₂²×C₄₃	C₂×C₂²⋊C₈	semidirect
236. C₂⁴×C₈	C₂×C₄₃	semidirect
238. C₂²×C₂²⋊C₈	C₂×C₄₃	semidirect
239. C₂²×C₂²⋊C₈	C₂×C₄₃	semidirect
240. #1869	C₂×C₄₃	direct (N × H)
241. C₂×#336	C₂×C₄₃	semidirect
244. C₂×C₄₃	#1869	direct (N × H)
257. C₂³×C₈	C₂²×C₄₃	semidirect
268. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
269. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
270. #336	C₂²×C₄₃	semidirect
271. C₄₃	C₂×#1869	direct (N × H)
276. C₂²×D₄	C₈×C₄₃	semidirect
303. C₂²×C₈	D₄×C₄₃	semidirect
329. C₂⁴	C₂×C₈×C₄₃	semidirect
337. C₂×D₄	C₂×C₈×C₄₃	semidirect
362. C₂²×C₄	C₂×C₈×C₄₃	semidirect
383. C₂×C₈	C₂×D₄×C₄₃	semidirect
405. C₂³	C₂²⋊C₈×C₄₃	semidirect
411. C₂³	C₂²×C₈×C₄₃	semidirect
442. C₂×C₄	C₂²×C₈×C₄₃	semidirect
462. C₂²	C₂×C₂²⋊C₈×C₄₃	semidirect
481. C₂	C₄₃×#1869	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×C₈×C₄₃	2
C₂²×C₄×D₄×C₄₃	2
C₂²×C₂²⋊C₈×C₄₃	2
C₄₃×#1869	2
C₂×C₄₃×#336	2
C₂×#1869	43

Subgroups — C2×C43×#1869 #24940910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1869 #24940910