Subgroups — C₄₃×#20898 #24940915

Order 11008.

2230 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#407	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1870	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1869	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1728	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₃	—	2	4	no	—
12	C₂²×M₁₆×C₄₃	—	2	8	no	—
13	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	complemented
16	C₂³×C₈×C₄₃	C₂²	1	2	yes	complemented
17	C₂×C₄×D₄×C₄₃	—	2	4	no	—
18	C₂×C₄×D₄×C₄₃	—	2	4	no	—
19	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
20	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
21	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₄₃	C₄	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₄₃	C₄	1	1	yes	characteristic
26	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#407	—	2	4	no	—
28	C₄₃×#407	—	2	8	no	—
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊C₈×C₄₃	C₂²	1	8	yes	complemented
31	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	complemented
32	C₄₃×#336	C₂²	1	8	yes	complemented
33	C₂⁵×C₄₃	C₂×C₄	1	1	yes	characteristic
34	C₂⁵×C₄₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₄₃	—	2	4	no	—
36	C₂²×D₄×C₄₃	—	2	8	no	—
37	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₄₃	—	2	4	no	—
40	C₂³×C₄×C₄₃	—	2	4	no	—
41	C₂³×C₄×C₄₃	—	2	2	no	—
42	C₂³×C₄×C₄₃	—	2	2	no	—
43	C₂³×C₄×C₄₃	—	2	4	no	—
44	C₂³×C₄×C₄₃	—	2	4	no	—
45	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	D₄	1	4	yes	—
53	C₂³×C₄×C₄₃	D₄	1	4	yes	—
54	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₄₃	—	2	32	no	—
59	C₂×M₁₆×C₄₃	—	2	4	no	—
60	C₂×M₁₆×C₄₃	—	2	4	no	—
61	C₂×M₁₆×C₄₃	—	2	4	no	—
62	C₂×M₁₆×C₄₃	—	2	4	no	—
63	C₂×M₁₆×C₄₃	—	2	4	no	—
64	C₂×M₁₆×C₄₃	—	2	4	no	—
65	C₂×M₁₆×C₄₃	—	2	8	no	—
66	C₂×M₁₆×C₄₃	D₄	1	8	yes	complemented
67	C₂²×C₈×C₄₃	—	2	4	no	—
68	C₂²×C₈×C₄₃	—	2	8	no	—
69	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
70	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
71	C₄×D₄×C₄₃	—	2	8	no	—
72	C₄×D₄×C₄₃	—	2	8	no	—
73	C₄×D₄×C₄₃	—	2	4	no	—
74	C₄×D₄×C₄₃	—	2	4	no	—
75	C₄×D₄×C₄₃	—	2	4	no	—
76	C₄×D₄×C₄₃	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
78	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₄₃	—	2	2	no	—
87	C₂×C₄²×C₄₃	—	2	2	no	—
88	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
89	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
90	C₂²⋊C₈×C₄₃	—	2	4	no	—
91	C₂²⋊C₈×C₄₃	—	2	4	no	—
92	C₂²⋊C₈×C₄₃	—	2	16	no	—
93	C₂⁴×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	—	2	4	no	—
95	C₂⁴×C₄₃	—	2	4	no	—
96	C₂⁴×C₄₃	—	2	4	no	—
97	C₂⁴×C₄₃	—	2	4	no	—
98	C₂⁴×C₄₃	—	4	2	no	—
99	C₂⁴×C₄₃	—	4	2	no	—
100	C₂⁴×C₄₃	C₂²⋊C₄	1	4	yes	—
101	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
103	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×D₄×C₄₃	—	2	32	no	—
106	C₂×D₄×C₄₃	—	2	4	no	—
107	C₂×D₄×C₄₃	—	2	4	no	—
108	C₂×D₄×C₄₃	—	2	4	no	—
109	C₂×D₄×C₄₃	—	2	4	no	—
110	C₂×D₄×C₄₃	—	2	4	no	—
111	C₂×D₄×C₄₃	M₁₆	1	8	yes	complemented
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	2	8	no	—
115	C₂²×C₄×C₄₃	—	2	16	no	—
116	C₂²×C₄×C₄₃	—	2	8	no	—
117	C₂²×C₄×C₄₃	—	2	4	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	4	no	—
123	C₂²×C₄×C₄₃	—	2	8	no	—
124	C₂²×C₄×C₄₃	—	2	4	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	2	no	—
127	C₂²×C₄×C₄₃	—	2	4	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	4	no	—
132	C₂²×C₄×C₄₃	—	2	4	no	—
133	C₂²×C₄×C₄₃	—	4	2	no	—
134	C₂²×C₄×C₄₃	—	4	4	no	—
135	C₂²×C₄×C₄₃	—	4	8	no	—
136	C₂²×C₄×C₄₃	—	4	4	no	—
137	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
138	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
139	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
140	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₄₃	#41	1	4	yes	—
154	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₄₃	—	2	16	no	—
156	M₁₆×C₄₃	—	2	16	no	—
157	M₁₆×C₄₃	—	4	8	no	—
158	C₂×C₈×C₄₃	—	2	16	no	—
159	C₂×C₈×C₄₃	—	2	4	no	—
160	C₂×C₈×C₄₃	—	2	4	no	—
161	C₂×C₈×C₄₃	—	2	4	no	—
162	C₂×C₈×C₄₃	—	2	4	no	—
163	C₂×C₈×C₄₃	—	2	4	no	—
164	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	complemented
165	C₄⋊C₄×C₄₃	—	2	4	no	—
166	C₄⋊C₄×C₄₃	—	2	4	no	—
167	C₂²⋊C₄×C₄₃	—	2	4	no	—
168	C₂²⋊C₄×C₄₃	—	2	4	no	—
169	C₂²⋊C₄×C₄₃	—	2	4	no	—
170	C₂²⋊C₄×C₄₃	—	2	4	no	—
171	C₄²×C₄₃	—	2	4	no	—
172	C₄²×C₄₃	—	2	2	no	—
173	C₄²×C₄₃	—	2	2	no	—
174	C₂³×C₄₃	—	2	2	no	—
175	C₂³×C₄₃	—	2	2	no	—
176	C₂³×C₄₃	—	2	2	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	2	8	no	—
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	2	4	no	—
181	C₂³×C₄₃	—	2	2	no	—
182	C₂³×C₄₃	—	2	2	no	—
183	C₂³×C₄₃	—	2	2	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	2	4	no	—
186	C₂³×C₄₃	—	2	8	no	—
187	C₂³×C₄₃	—	2	8	no	—
188	C₂³×C₄₃	—	4	4	no	—
189	C₂³×C₄₃	—	4	16	no	—
190	C₂³×C₄₃	—	4	16	no	—
191	C₂³×C₄₃	—	4	4	no	—
192	C₂³×C₄₃	—	4	4	no	—
193	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂³×C₄₃	C₄×D₄	1	4	yes	—
197	C₂³×C₄₃	C₂×M₁₆	1	4	yes	—
198	C₂³×C₄₃	C₂×M₁₆	1	4	yes	complemented
199	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
200	D₄×C₄₃	—	2	16	no	—
201	D₄×C₄₃	—	2	16	no	—
202	C₂×C₄×C₄₃	—	2	8	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	8	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	2	4	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	8	no	—
215	C₂×C₄×C₄₃	—	2	8	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	2	4	no	—
220	C₂×C₄×C₄₃	—	4	4	no	—
221	C₂×C₄×C₄₃	—	4	4	no	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	4	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	8	no	—
226	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
230	C₂×C₄×C₄₃	#120	1	4	yes	—
231	C₂×C₄×C₄₃	#121	1	8	yes	—
232	C₂×C₄×C₄₃	#123	1	4	yes	—
233	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	complemented
234	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
238	C₈×C₄₃	—	2	8	no	—
239	C₈×C₄₃	—	4	4	no	—
240	#20898	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂²×C₄₃	—	2	2	no	—
242	C₂²×C₄₃	—	2	2	no	—
243	C₂²×C₄₃	—	2	2	no	—
244	C₂²×C₄₃	—	2	8	no	—
245	C₂²×C₄₃	—	2	8	no	—
246	C₂²×C₄₃	—	2	2	no	—
247	C₂²×C₄₃	—	2	2	no	—
248	C₂²×C₄₃	—	2	4	no	—
249	C₂²×C₄₃	—	2	2	no	—
250	C₂²×C₄₃	—	2	8	no	—
251	C₂²×C₄₃	—	2	2	no	—
252	C₂²×C₄₃	—	4	16	no	—
253	C₂²×C₄₃	—	4	16	no	—
254	C₂²×C₄₃	—	4	2	no	—
255	C₂²×C₄₃	—	4	4	no	—
256	C₂²×C₄₃	—	4	4	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	#386	1	4	yes	—
259	C₂²×C₄₃	#407	1	4	yes	complemented
260	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
262	C₂²×C₄₃	C₂²×M₁₆	1	2	yes	—
263	C₂²×C₄₃	#568	1	2	yes	—
264	C₄×C₄₃	—	2	4	no	—
265	C₄×C₄₃	—	2	2	no	—
266	C₄×C₄₃	—	2	2	no	—
267	C₄×C₄₃	—	4	2	no	—
268	C₄×C₄₃	—	4	2	no	—
269	C₄×C₄₃	#386	1	4	yes	—
270	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
271	C₄×C₄₃	C₂×#121	1	2	yes	—
272	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
273	C₂³×M₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
274	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
275	C₂×#407	C₂×C₄₃	1	1	yes	characteristic, complemented
276	C₂×#407	C₂×C₄₃	1	2	yes	complemented
277	#1870	C₂×C₄₃	1	4	yes	complemented
278	#1869	C₂×C₄₃	1	4	yes	complemented
279	#1728	C₂×C₄₃	1	2	yes	complemented
280	C₂×C₄₃	—	2	4	no	—
281	C₂×C₄₃	—	2	4	no	—
282	C₂×C₄₃	—	4	2	no	—
283	C₂×C₄₃	—	4	4	no	—
284	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
285	C₂×C₄₃	C₂×#407	1	1	yes	characteristic
286	C₂×C₄₃	#2879	1	1	yes	characteristic
287	C₂×C₄₃	D₄×M₁₆	1	4	yes	—
288	C₂³×D₄	C₄×C₄₃	1	1	yes	characteristic
289	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
290	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
291	C₂²×M₁₆	—	2	4	no	—
292	C₂²×M₁₆	—	2	8	no	—
293	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
294	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
295	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	complemented
296	C₂³×C₈	C₂²×C₄₃	1	2	yes	complemented
297	C₂×C₄×D₄	—	2	4	no	—
298	C₂×C₄×D₄	—	2	4	no	—
299	C₂×C₄×D₄	C₄×C₄₃	1	2	yes	—
300	C₂×C₄×D₄	C₄×C₄₃	1	2	yes	—
301	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
302	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
303	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic
304	C₂²×C₂²⋊C₄	C₄×C₄₃	1	1	yes	characteristic
305	C₂²×C₂²⋊C₄	C₄×C₄₃	1	1	yes	characteristic
306	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
307	#407	—	2	4	no	—
308	#407	—	2	8	no	—
309	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	complemented
310	C₂×C₂²⋊C₈	C₂²×C₄₃	1	8	yes	complemented
311	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	complemented
312	#336	C₂²×C₄₃	1	8	yes	complemented
313	C₄₃	#20898	1	1	yes	characteristic, direct product factor, Sylow
314	C₂⁵	C₂×C₄×C₄₃	1	1	yes	characteristic
315	C₂⁵	C₂×C₄×C₄₃	1	1	yes	characteristic
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	—	2	8	no	—
318	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
319	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
320	C₂³×C₄	—	2	4	no	—
321	C₂³×C₄	—	2	4	no	—
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	—	2	4	no	—
325	C₂³×C₄	—	2	4	no	—
326	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
327	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
328	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
329	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
330	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
331	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
332	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
333	C₂³×C₄	D₄×C₄₃	1	4	yes	—
334	C₂³×C₄	D₄×C₄₃	1	4	yes	—
335	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
336	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
339	C₂×M₁₆	—	2	32	no	—
340	C₂×M₁₆	—	2	4	no	—
341	C₂×M₁₆	—	2	4	no	—
342	C₂×M₁₆	—	2	4	no	—
343	C₂×M₁₆	—	2	4	no	—
344	C₂×M₁₆	—	2	4	no	—
345	C₂×M₁₆	—	2	4	no	—
346	C₂×M₁₆	—	2	8	no	—
347	C₂×M₁₆	D₄×C₄₃	1	8	yes	complemented
348	C₂²×C₈	—	2	4	no	—
349	C₂²×C₈	—	2	8	no	—
350	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
351	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
352	C₄×D₄	—	2	8	no	—
353	C₄×D₄	—	2	8	no	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	2	4	no	—
356	C₄×D₄	—	2	4	no	—
357	C₄×D₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
360	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
361	C₂×C₂²⋊C₄	—	2	4	no	—
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	—	2	2	no	—
369	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
370	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
371	C₂²⋊C₈	—	2	4	no	—
372	C₂²⋊C₈	—	2	4	no	—
373	C₂²⋊C₈	—	2	16	no	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	4	no	—
378	C₂⁴	—	2	4	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	—	4	2	no	—
381	C₂⁴	C₂²⋊C₄×C₄₃	1	4	yes	—
382	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
383	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
384	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
385	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
386	C₂×D₄	—	2	32	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	M₁₆×C₄₃	1	8	yes	complemented
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	8	no	—
398	C₂²×C₄	—	2	16	no	—
399	C₂²×C₄	—	2	8	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	8	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
419	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
420	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
421	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
422	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
423	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
426	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
434	C₂²×C₄	#41×C₄₃	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
436	M₁₆	—	2	16	no	—
437	M₁₆	—	2	16	no	—
438	M₁₆	—	4	8	no	—
439	C₂×C₈	—	2	16	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	4	no	—
442	C₂×C₈	—	2	4	no	—
443	C₂×C₈	—	2	4	no	—
444	C₂×C₈	—	2	4	no	—
445	C₂×C₈	C₂×D₄×C₄₃	1	8	yes	complemented
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	8	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	2	8	no	—
468	C₂³	—	2	8	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	16	no	—
471	C₂³	—	4	16	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	4	no	—
474	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
475	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
476	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
477	C₂³	C₄×D₄×C₄₃	1	4	yes	—
478	C₂³	C₂×M₁₆×C₄₃	1	4	yes	—
479	C₂³	C₂×M₁₆×C₄₃	1	4	yes	complemented
480	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
481	D₄	—	2	16	no	—
482	D₄	—	2	16	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	8	no	—
507	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
508	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
509	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
510	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
511	C₂×C₄	#120×C₄₃	1	4	yes	—
512	C₂×C₄	#121×C₄₃	1	8	yes	—
513	C₂×C₄	#123×C₄₃	1	4	yes	—
514	C₂×C₄	C₂×M₁₆×C₄₃	1	4	yes	complemented
515	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
519	C₈	—	2	8	no	—
520	C₈	—	4	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	8	no	—
525	C₂²	—	2	8	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	8	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	16	no	—
533	C₂²	—	4	16	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	2	no	—
538	C₂²	C₄₃×#386	1	4	yes	—
539	C₂²	C₄₃×#407	1	4	yes	complemented
540	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
541	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
542	C₂²	C₂²×M₁₆×C₄₃	1	2	yes	—
543	C₂²	C₄₃×#568	1	2	yes	—
544	C₄	—	2	4	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	C₄₃×#386	1	4	yes	—
550	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
551	C₄	C₂×#121×C₄₃	1	2	yes	—
552	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
553	C₂	—	2	4	no	—
554	C₂	—	2	4	no	—
555	C₂	—	4	2	no	—
556	C₂	—	4	4	no	—
557	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
558	C₂	C₂×C₄₃×#407	1	1	yes	characteristic
559	C₂	C₄₃×#2879	1	1	yes	characteristic
560	C₂	D₄×M₁₆×C₄₃	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×M₁₆×C₄₃	C₂	semidirect
3. C₂×C₄₃×#407	C₂	semidirect
4. C₂×C₄₃×#407	C₂	semidirect
5. C₄₃×#1870	C₂	semidirect
6. C₄₃×#1869	C₂	semidirect
7. C₄₃×#1728	C₂	semidirect
15. C₂²×M₁₆×C₄₃	C₂²	semidirect
16. C₂³×C₈×C₄₃	C₂²	semidirect
29. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
30. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
31. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
32. C₄₃×#336	C₂²	semidirect
66. C₂×M₁₆×C₄₃	D₄	semidirect
111. C₂×D₄×C₄₃	M₁₆	semidirect
164. C₂×C₈×C₄₃	C₂×D₄	semidirect
198. C₂³×C₄₃	C₂×M₁₆	semidirect
233. C₂×C₄×C₄₃	C₂×M₁₆	semidirect
240. #20898	C₄₃	direct (N × H)
259. C₂²×C₄₃	#407	semidirect
273. C₂³×M₁₆	C₂×C₄₃	semidirect
275. C₂×#407	C₂×C₄₃	semidirect
276. C₂×#407	C₂×C₄₃	semidirect
277. #1870	C₂×C₄₃	semidirect
278. #1869	C₂×C₄₃	semidirect
279. #1728	C₂×C₄₃	semidirect
295. C₂²×M₁₆	C₂²×C₄₃	semidirect
296. C₂³×C₈	C₂²×C₄₃	semidirect
309. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
310. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
311. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
312. #336	C₂²×C₄₃	semidirect
313. C₄₃	#20898	direct (N × H)
347. C₂×M₁₆	D₄×C₄₃	semidirect
392. C₂×D₄	M₁₆×C₄₃	semidirect
445. C₂×C₈	C₂×D₄×C₄₃	semidirect
479. C₂³	C₂×M₁₆×C₄₃	semidirect
514. C₂×C₄	C₂×M₁₆×C₄₃	semidirect
539. C₂²	C₄₃×#407	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₄₃	2
C₂²×C₄×D₄×C₄₃	2
C₂×C₄₃×#407	2
C₄₃×#1870	2
C₄₃×#1869	2
C₄₃×#1728	2
#20898	43

Subgroups — C43×#20898 #24940915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20898 #24940915