Subgroups — C₄₃×#25694 #24945711

Order 11008.

1094 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3506	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2037	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1859	C₂	1	4	yes	maximal, complemented
9	C₄×#100×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#559	—	2	2	no	—
11	C₄₃×#556	—	2	1	no	—
12	C₄₃×#555	—	2	1	no	—
13	C₄₃×#553	—	2	2	no	—
14	C₄₃×#550	—	2	1	no	—
15	C₄₃×#547	—	2	1	no	—
16	C₄₃×#538	—	2	2	no	—
17	C₄₃×#535	C₂²	1	2	yes	—
18	C₄₃×#533	C₂²	1	1	yes	characteristic
19	C₄₃×#532	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#525	—	2	2	no	—
22	C₂×C₂²⋊Q₈×C₄₃	—	2	2	no	—
23	C₄₃×#520	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#501	—	2	2	no	—
26	C₄₃×#500	—	2	1	no	—
27	C₄₃×#498	—	2	1	no	—
28	C₄₃×#489	—	2	2	no	—
29	C₄₃×#487	—	2	1	no	—
30	C₄₃×#486	—	2	1	no	—
31	C₄₃×#428	C₂²	1	4	yes	—
32	C₂×#104×C₄₃	C₂²	1	4	yes	—
33	C₄₃×#417	C₂²	1	4	yes	—
34	C₂×#100×C₄₃	C₂²	1	2	yes	—
35	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#399	—	2	2	no	—
38	C₄₃×#390	C₂²	1	2	yes	—
39	C₄₃×#384	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#343	C₂²	1	2	yes	—
42	C₄₃×#339	C₂²	1	4	yes	—
43	C₂×#41×C₄₃	—	2	2	no	—
44	C₂×#41×C₄₃	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	D₄	1	2	yes	—
48	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
49	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₄₃	—	2	1	no	—
51	C₄⋊Q₈×C₄₃	—	2	1	no	—
52	C₄⋊Q₈×C₄₃	—	2	1	no	—
53	C₄⋊Q₈×C₄₃	—	2	1	no	—
54	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
57	#127×C₄₃	—	2	2	no	—
58	#127×C₄₃	D₄	1	1	yes	characteristic
59	#126×C₄₃	—	2	4	no	—
60	#125×C₄₃	D₄	1	2	yes	—
61	#124×C₄₃	—	2	4	no	—
62	#124×C₄₃	—	2	2	no	—
63	#124×C₄₃	D₄	1	2	yes	—
64	#123×C₄₃	—	2	4	no	—
65	#123×C₄₃	—	2	4	no	—
66	C₂²⋊Q₈×C₄₃	—	2	2	no	—
67	C₂²⋊Q₈×C₄₃	—	2	1	no	—
68	C₂²⋊Q₈×C₄₃	—	2	1	no	—
69	C₂²⋊Q₈×C₄₃	—	4	8	no	—
70	#121×C₄₃	—	2	2	no	—
71	#121×C₄₃	—	2	4	no	—
72	#121×C₄₃	—	2	1	no	—
73	#121×C₄₃	—	2	1	no	—
74	#121×C₄₃	—	2	2	no	—
75	#121×C₄₃	—	2	2	no	—
76	#120×C₄₃	—	2	4	no	—
77	C₄×Q₈×C₄₃	—	2	2	no	—
78	C₄×Q₈×C₄₃	—	2	1	no	—
79	C₄×Q₈×C₄₃	—	2	1	no	—
80	C₄×D₄×C₄₃	—	2	4	no	—
81	C₄×D₄×C₄₃	—	2	2	no	—
82	C₄×D₄×C₄₃	—	2	4	no	—
83	C₄×D₄×C₄₃	—	2	1	no	—
84	C₄×D₄×C₄₃	—	2	1	no	—
85	C₄×D₄×C₄₃	—	2	1	no	—
86	C₄×D₄×C₄₃	—	2	1	no	—
87	C₄×D₄×C₄₃	—	2	1	no	—
88	C₄×D₄×C₄₃	—	2	1	no	—
89	#117×C₄₃	—	2	2	no	—
90	#117×C₄₃	—	2	2	no	—
91	#117×C₄₃	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
99	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
100	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	#107×C₄₃	—	2	4	no	—
103	#106×C₄₃	—	2	4	no	—
104	#104×C₄₃	—	2	8	no	—
105	#103×C₄₃	—	2	4	no	—
106	#102×C₄₃	—	2	4	no	—
107	#100×C₄₃	—	2	4	no	—
108	#97×C₄₃	—	2	1	no	—
109	#97×C₄₃	—	2	1	no	—
110	C₄×C₈×C₄₃	—	2	1	no	—
111	C₄×C₈×C₄₃	—	2	1	no	—
112	#95×C₄₃	—	2	1	no	—
113	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
114	#41×C₄₃	—	2	4	no	—
115	#41×C₄₃	—	2	4	no	—
116	#41×C₄₃	—	8	4	no	—
117	C₂×Q₈×C₄₃	—	2	1	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	—	4	4	no	—
120	C₂×Q₈×C₄₃	—	4	1	no	—
121	C₂×Q₈×C₄₃	—	4	1	no	—
122	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₄₃	—	2	4	no	—
124	C₂×D₄×C₄₃	—	2	4	no	—
125	C₂×D₄×C₄₃	—	2	1	no	—
126	C₂×D₄×C₄₃	—	2	1	no	—
127	C₂×D₄×C₄₃	—	2	1	no	—
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	4	4	no	—
140	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
144	M₁₆×C₄₃	—	2	2	no	—
145	M₁₆×C₄₃	—	2	2	no	—
146	M₁₆×C₄₃	—	2	2	no	—
147	M₁₆×C₄₃	#41	1	4	yes	complemented
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₄⋊C₄×C₄₃	—	2	4	no	—
151	C₄⋊C₄×C₄₃	—	2	4	no	—
152	C₄⋊C₄×C₄₃	—	2	1	no	—
153	C₄⋊C₄×C₄₃	—	2	1	no	—
154	C₄⋊C₄×C₄₃	—	2	2	no	—
155	C₄⋊C₄×C₄₃	—	2	1	no	—
156	C₄⋊C₄×C₄₃	—	2	2	no	—
157	C₄⋊C₄×C₄₃	—	2	1	no	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	2	no	—
161	C₄⋊C₄×C₄₃	—	2	2	no	—
162	C₄⋊C₄×C₄₃	—	4	8	no	—
163	C₄⋊C₄×C₄₃	—	4	1	no	—
164	C₄⋊C₄×C₄₃	—	4	1	no	—
165	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
166	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
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	2	no	—
171	C₂²⋊C₄×C₄₃	—	2	2	no	—
172	C₂²⋊C₄×C₄₃	—	2	2	no	—
173	C₂²⋊C₄×C₄₃	—	2	2	no	—
174	C₂²⋊C₄×C₄₃	—	2	2	no	—
175	C₂²⋊C₄×C₄₃	—	4	8	no	—
176	C₄²×C₄₃	—	2	4	no	—
177	C₄²×C₄₃	—	2	2	no	—
178	C₄²×C₄₃	—	2	4	no	—
179	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
183	C₂³×C₄₃	—	2	2	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	2	2	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	4	2	no	—
188	C₂³×C₄₃	—	4	2	no	—
189	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₄₃	—	2	4	no	—
191	Q₈×C₄₃	—	4	2	no	—
192	Q₈×C₄₃	—	8	1	no	—
193	Q₈×C₄₃	—	8	2	no	—
194	Q₈×C₄₃	—	8	2	no	—
195	D₄×C₄₃	—	2	4	no	—
196	D₄×C₄₃	—	4	2	no	—
197	D₄×C₄₃	—	4	2	no	—
198	D₄×C₄₃	—	4	2	no	—
199	D₄×C₄₃	—	4	2	no	—
200	D₄×C₄₃	—	4	2	no	—
201	D₄×C₄₃	—	8	1	no	—
202	D₄×C₄₃	—	8	4	no	—
203	D₄×C₄₃	—	8	4	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	4	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	4	4	no	—
214	C₂×C₄×C₄₃	—	4	4	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	4	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	8	2	no	—
219	C₂×C₄×C₄₃	—	8	4	no	—
220	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
221	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
222	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
223	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
227	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
228	C₈×C₄₃	—	2	4	no	—
229	C₈×C₄₃	—	4	2	no	—
230	#25694	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂²×C₄₃	—	2	1	no	—
232	C₂²×C₄₃	—	2	1	no	—
233	C₂²×C₄₃	—	4	4	no	—
234	C₂²×C₄₃	—	4	2	no	—
235	C₂²×C₄₃	—	4	2	no	—
236	C₂²×C₄₃	—	4	2	no	—
237	C₂²×C₄₃	—	4	2	no	—
238	C₂²×C₄₃	—	4	2	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	8	2	no	—
241	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
242	C₂²×C₄₃	#532	1	1	yes	characteristic
243	C₂²×C₄₃	#536	1	1	yes	characteristic
244	C₄×C₄₃	—	2	1	no	—
245	C₄×C₄₃	—	2	1	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	4	4	no	—
248	C₄×C₄₃	—	4	2	no	—
249	C₄×C₄₃	—	4	2	no	—
250	C₄×C₄₃	—	4	2	no	—
251	C₄×C₄₃	—	4	2	no	—
252	C₄×C₄₃	—	8	2	no	—
253	C₄×C₄₃	#453	1	2	yes	—
254	C₄×C₄₃	#547	1	2	yes	—
255	C₄×C₄₃	#548	1	2	yes	—
256	#3506	C₂×C₄₃	1	1	yes	characteristic
257	#3165	C₂×C₄₃	1	1	yes	characteristic, complemented
258	#3141	C₂×C₄₃	1	1	yes	characteristic, complemented
259	#2542	C₂×C₄₃	1	1	yes	characteristic, complemented
260	#2037	C₂×C₄₃	1	4	yes	complemented
261	#1986	C₂×C₄₃	1	1	yes	characteristic, complemented
262	#1980	C₂×C₄₃	1	1	yes	characteristic, complemented
263	#1859	C₂×C₄₃	1	4	yes	complemented
264	C₄×#100	C₂×C₄₃	1	1	yes	characteristic, complemented
265	C₂×C₄₃	—	2	1	no	—
266	C₂×C₄₃	—	2	1	no	—
267	C₂×C₄₃	—	8	2	no	—
268	C₂×C₄₃	—	8	2	no	—
269	C₂×C₄₃	#2432	1	1	yes	characteristic
270	C₂×C₄₃	C₂×#453	1	1	yes	characteristic
271	C₂×C₄₃	#3022	1	1	yes	characteristic
272	#559	—	2	2	no	—
273	#556	—	2	1	no	—
274	#555	—	2	1	no	—
275	#553	—	2	2	no	—
276	#550	—	2	1	no	—
277	#547	—	2	1	no	—
278	#538	—	2	2	no	—
279	#535	C₂²×C₄₃	1	2	yes	—
280	#533	C₂²×C₄₃	1	1	yes	characteristic
281	#532	C₂²×C₄₃	1	1	yes	characteristic
282	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
283	#525	—	2	2	no	—
284	C₂×C₂²⋊Q₈	—	2	2	no	—
285	#520	C₂²×C₄₃	1	2	yes	—
286	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
287	#501	—	2	2	no	—
288	#500	—	2	1	no	—
289	#498	—	2	1	no	—
290	#489	—	2	2	no	—
291	#487	—	2	1	no	—
292	#486	—	2	1	no	—
293	#428	C₂²×C₄₃	1	4	yes	—
294	C₂×#104	C₂²×C₄₃	1	4	yes	—
295	#417	C₂²×C₄₃	1	4	yes	—
296	C₂×#100	C₂²×C₄₃	1	2	yes	—
297	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
298	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
299	#399	—	2	2	no	—
300	#390	C₂²×C₄₃	1	2	yes	—
301	#384	C₂²×C₄₃	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
303	#343	C₂²×C₄₃	1	2	yes	—
304	#339	C₂²×C₄₃	1	4	yes	—
305	C₄₃	#25694	1	1	yes	characteristic, direct product factor, Sylow
306	C₂×#41	—	2	2	no	—
307	C₂×#41	C₂³×C₄₃	1	2	yes	—
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
310	C₂³×C₄	D₄×C₄₃	1	2	yes	—
311	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
312	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
318	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
319	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
320	#127	—	2	2	no	—
321	#127	D₄×C₄₃	1	1	yes	characteristic
322	#126	—	2	4	no	—
323	#125	D₄×C₄₃	1	2	yes	—
324	#124	—	2	4	no	—
325	#124	—	2	2	no	—
326	#124	D₄×C₄₃	1	2	yes	—
327	#123	—	2	4	no	—
328	#123	—	2	4	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	—	4	8	no	—
333	#121	—	2	2	no	—
334	#121	—	2	4	no	—
335	#121	—	2	1	no	—
336	#121	—	2	1	no	—
337	#121	—	2	2	no	—
338	#121	—	2	2	no	—
339	#120	—	2	4	no	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	#117	—	2	2	no	—
353	#117	—	2	2	no	—
354	#117	C₂³×C₄₃	1	2	yes	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	—	2	4	no	—
362	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
363	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
364	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
365	#107	—	2	4	no	—
366	#106	—	2	4	no	—
367	#104	—	2	8	no	—
368	#103	—	2	4	no	—
369	#102	—	2	4	no	—
370	#100	—	2	4	no	—
371	#97	—	2	1	no	—
372	#97	—	2	1	no	—
373	C₄×C₈	—	2	1	no	—
374	C₄×C₈	—	2	1	no	—
375	#95	—	2	1	no	—
376	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
377	#41	—	2	4	no	—
378	#41	—	2	4	no	—
379	#41	—	8	4	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂×Q₈	—	4	1	no	—
384	C₂×Q₈	—	4	1	no	—
385	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	#41×C₄₃	1	4	yes	complemented
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	8	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
429	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	4	8	no	—
439	C₄²	—	2	4	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	4	no	—
442	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
445	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
453	Q₈	—	2	4	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	8	1	no	—
456	Q₈	—	8	2	no	—
457	Q₈	—	8	2	no	—
458	D₄	—	2	4	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	8	1	no	—
465	D₄	—	8	4	no	—
466	D₄	—	8	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	8	4	no	—
483	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
484	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
485	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
486	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
490	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
491	C₈	—	2	4	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
504	C₂²	C₄₃×#532	1	1	yes	characteristic
505	C₂²	C₄₃×#536	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	2	no	—
515	C₄	C₄₃×#453	1	2	yes	—
516	C₄	C₄₃×#547	1	2	yes	—
517	C₄	C₄₃×#548	1	2	yes	—
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	—	8	2	no	—
521	C₂	—	8	2	no	—
522	C₂	C₄₃×#2432	1	1	yes	characteristic
523	C₂	C₂×C₄₃×#453	1	1	yes	characteristic
524	C₂	C₄₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#3506	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3165	C₂	semidirect
3. C₄₃×#3141	C₂	semidirect
4. C₄₃×#2542	C₂	semidirect
5. C₄₃×#2037	C₂	semidirect
6. C₄₃×#1986	C₂	semidirect
7. C₄₃×#1980	C₂	semidirect
8. C₄₃×#1859	C₂	semidirect
9. C₄×#100×C₄₃	C₂	semidirect
147. M₁₆×C₄₃	#41	semidirect
230. #25694	C₄₃	direct (N × H)
257. #3165	C₂×C₄₃	semidirect
258. #3141	C₂×C₄₃	semidirect
259. #2542	C₂×C₄₃	semidirect
260. #2037	C₂×C₄₃	semidirect
261. #1986	C₂×C₄₃	semidirect
262. #1980	C₂×C₄₃	semidirect
263. #1859	C₂×C₄₃	semidirect
264. C₄×#100	C₂×C₄₃	semidirect
305. C₄₃	#25694	direct (N × H)
410. M₁₆	#41×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3506	2
C₄₃×#3165	2
C₄₃×#3141	2
C₄₃×#2542	2
C₄₃×#2037	2
C₄₃×#1986	2
C₄₃×#1980	2
C₄₃×#1859	2
C₄×#100×C₄₃	2
#25694	43

Subgroups — C43×#25694 #24945711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25694 #24945711