Subgroups — C₄₃×#10979 #24930996

Order 11008.

1382 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#421	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#410	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#339	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
7	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
9	C₄₃×#532	—	2	4	no	—
10	C₄₃×#532	—	2	4	no	—
11	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
12	C₂×#127×C₄₃	C₄	1	1	yes	characteristic, complemented
13	C₂×#124×C₄₃	C₄	1	1	yes	characteristic, complemented
14	C₂×#124×C₄₃	C₄	1	1	yes	characteristic, complemented
15	C₂×#121×C₄₃	—	2	2	no	—
16	C₂×C₄×D₄×C₄₃	—	2	2	no	—
17	C₂×#117×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#421	—	2	4	no	—
20	C₄₃×#421	—	2	4	no	—
21	C₂×#104×C₄₃	—	2	4	no	—
22	C₄₃×#410	—	2	4	no	—
23	C₂×#99×C₄₃	—	2	2	no	—
24	C₄₃×#408	—	2	4	no	—
25	C₄₃×#407	—	2	2	no	—
26	C₄₃×#339	—	2	4	no	—
27	C₂×#41×C₄₃	—	2	2	no	—
28	C₂×#41×C₄₃	—	2	2	no	—
29	C₂×#41×C₄₃	—	2	2	no	—
30	C₂×#41×C₄₃	—	2	2	no	—
31	C₂×#41×C₄₃	—	2	2	no	—
32	C₂×#41×C₄₃	—	2	2	no	—
33	C₂×#41×C₄₃	—	2	2	no	—
34	C₂×#41×C₄₃	—	2	2	no	—
35	C₂×#41×C₄₃	—	2	2	no	—
36	C₂×#41×C₄₃	—	2	2	no	—
37	C₂×#41×C₄₃	—	2	2	no	—
38	C₂×#41×C₄₃	D₄	1	4	yes	—
39	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₄×C₄₃	—	2	2	no	—
42	C₂²×D₄×C₄₃	—	2	1	no	—
43	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	D₄	1	2	yes	—
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	D₄	1	2	yes	—
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₄₃	—	2	2	no	—
51	C₂×M₁₆×C₄₃	—	2	2	no	—
52	C₂×M₁₆×C₄₃	—	2	2	no	—
53	C₂×M₁₆×C₄₃	—	2	2	no	—
54	C₂×M₁₆×C₄₃	—	2	2	no	—
55	C₂×M₁₆×C₄₃	D₄	1	4	yes	complemented
56	C₂²×C₈×C₄₃	—	2	2	no	—
57	C₄⋊Q₈×C₄₃	—	2	2	no	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	#127×C₄₃	—	2	2	no	—
60	#127×C₄₃	—	2	2	no	—
61	#124×C₄₃	—	2	2	no	—
62	#124×C₄₃	—	2	2	no	—
63	#124×C₄₃	—	2	2	no	—
64	#124×C₄₃	—	2	2	no	—
65	#121×C₄₃	—	2	16	no	—
66	C₄×D₄×C₄₃	—	2	16	no	—
67	#117×C₄₃	—	2	2	no	—
68	#117×C₄₃	—	2	2	no	—
69	#117×C₄₃	—	2	2	no	—
70	#117×C₄₃	D₄	1	4	yes	complemented
71	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₄²×C₄₃	—	2	1	no	—
77	C₂×C₄²×C₄₃	—	2	2	no	—
78	C₂×C₄²×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	D₄	1	4	yes	—
82	#104×C₄₃	—	2	16	no	—
83	#99×C₄₃	—	2	8	no	—
84	C₂²⋊C₈×C₄₃	—	2	8	no	—
85	C₂⁴×C₄₃	—	2	1	no	—
86	C₂⁴×C₄₃	C₂²⋊C₄	1	2	yes	—
87	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
88	#41×C₄₃	—	2	4	no	—
89	#41×C₄₃	—	2	4	no	—
90	#41×C₄₃	—	2	4	no	—
91	#41×C₄₃	—	2	4	no	—
92	#41×C₄₃	—	4	2	no	—
93	#41×C₄₃	—	4	2	no	—
94	#41×C₄₃	—	4	2	no	—
95	#41×C₄₃	—	4	2	no	—
96	#41×C₄₃	—	4	2	no	—
97	#41×C₄₃	—	4	2	no	—
98	#41×C₄₃	—	4	2	no	—
99	#41×C₄₃	—	4	2	no	—
100	#41×C₄₃	—	4	2	no	—
101	#41×C₄₃	—	4	2	no	—
102	#41×C₄₃	—	4	2	no	—
103	#41×C₄₃	—	4	2	no	—
104	C₂×Q₈×C₄₃	—	2	1	no	—
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
112	C₂×D₄×C₄₃	—	2	8	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	4	no	—
120	C₂×D₄×C₄₃	—	2	4	no	—
121	C₂×D₄×C₄₃	—	2	4	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	4	8	no	—
126	C₂×D₄×C₄₃	—	4	1	no	—
127	C₂×D₄×C₄₃	—	4	2	no	—
128	C₂×D₄×C₄₃	—	4	1	no	—
129	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
130	C₂²×C₄×C₄₃	—	2	4	no	—
131	C₂²×C₄×C₄₃	—	2	4	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	1	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	—	2	4	no	—
139	C₂²×C₄×C₄₃	—	4	4	no	—
140	C₂²×C₄×C₄₃	—	4	1	no	—
141	C₂²×C₄×C₄₃	—	4	2	no	—
142	C₂²×C₄×C₄₃	—	4	1	no	—
143	C₂²×C₄×C₄₃	—	4	2	no	—
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	1	yes	characteristic
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	#41	1	2	yes	—
152	C₂²×C₄×C₄₃	#41	1	2	yes	—
153	M₁₆×C₄₃	—	2	4	no	—
154	M₁₆×C₄₃	—	2	4	no	—
155	M₁₆×C₄₃	—	4	2	no	—
156	M₁₆×C₄₃	—	4	2	no	—
157	C₂×C₈×C₄₃	—	2	4	no	—
158	C₂×C₈×C₄₃	—	4	2	no	—
159	C₂×C₈×C₄₃	—	4	2	no	—
160	C₄⋊C₄×C₄₃	—	2	8	no	—
161	C₄⋊C₄×C₄₃	—	2	4	no	—
162	C₄⋊C₄×C₄₃	—	4	2	no	—
163	C₂²⋊C₄×C₄₃	—	2	8	no	—
164	C₂²⋊C₄×C₄₃	—	2	8	no	—
165	C₂²⋊C₄×C₄₃	—	2	4	no	—
166	C₂²⋊C₄×C₄₃	—	4	2	no	—
167	C₄²×C₄₃	—	2	1	no	—
168	C₄²×C₄₃	—	2	1	no	—
169	C₄²×C₄₃	—	2	4	no	—
170	C₄²×C₄₃	—	2	4	no	—
171	C₄²×C₄₃	—	4	2	no	—
172	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
173	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
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	—	4	2	no	—
179	C₂³×C₄₃	—	4	4	no	—
180	C₂³×C₄₃	—	4	4	no	—
181	C₂³×C₄₃	—	4	1	no	—
182	C₂³×C₄₃	—	4	1	no	—
183	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₄₃	#120	1	2	yes	—
185	C₂³×C₄₃	#120	1	1	yes	characteristic
186	C₂³×C₄₃	#121	1	2	yes	—
187	C₂³×C₄₃	#123	1	1	yes	characteristic
188	Q₈×C₄₃	—	2	4	no	—
189	Q₈×C₄₃	—	4	2	no	—
190	Q₈×C₄₃	—	4	2	no	—
191	Q₈×C₄₃	—	4	2	no	—
192	D₄×C₄₃	—	2	4	no	—
193	D₄×C₄₃	—	4	16	no	—
194	D₄×C₄₃	—	4	4	no	—
195	D₄×C₄₃	—	4	4	no	—
196	D₄×C₄₃	—	4	4	no	—
197	D₄×C₄₃	—	4	4	no	—
198	D₄×C₄₃	—	4	2	no	—
199	D₄×C₄₃	—	4	2	no	—
200	D₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	—	2	4	no	—
202	C₂×C₄×C₄₃	—	2	2	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	2	no	—
208	C₂×C₄×C₄₃	—	4	8	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	4	no	—
213	C₂×C₄×C₄₃	—	4	4	no	—
214	C₂×C₄×C₄₃	—	4	4	no	—
215	C₂×C₄×C₄₃	—	4	4	no	—
216	C₂×C₄×C₄₃	—	4	4	no	—
217	C₂×C₄×C₄₃	—	8	4	no	—
218	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
221	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
222	C₂×C₄×C₄₃	#120	1	2	yes	—
223	C₂×C₄×C₄₃	#120	1	2	yes	—
224	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#121	1	2	yes	—
226	C₂×C₄×C₄₃	#121	1	2	yes	—
227	C₂×C₄×C₄₃	#121	1	2	yes	—
228	C₂×C₄×C₄₃	#121	1	2	yes	—
229	C₂×C₄×C₄₃	#121	1	2	yes	—
230	C₂×C₄×C₄₃	#123	1	2	yes	—
231	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
232	C₂×C₄×C₄₃	#124	1	2	yes	—
233	C₂×C₄×C₄₃	#127	1	2	yes	—
234	C₈×C₄₃	—	4	4	no	—
235	#10979	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₄₃	—	2	2	no	—
237	C₂²×C₄₃	—	2	4	no	—
238	C₂²×C₄₃	—	4	1	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	4	1	no	—
241	C₂²×C₄₃	—	4	4	no	—
242	C₂²×C₄₃	—	4	4	no	—
243	C₂²×C₄₃	—	4	4	no	—
244	C₂²×C₄₃	—	4	2	no	—
245	C₂²×C₄₃	—	4	2	no	—
246	C₂²×C₄₃	—	8	2	no	—
247	C₂²×C₄₃	—	8	2	no	—
248	C₂²×C₄₃	—	8	2	no	—
249	C₂²×C₄₃	#379	1	1	yes	characteristic
250	C₂²×C₄₃	#386	1	1	yes	characteristic
251	C₂²×C₄₃	#386	1	1	yes	characteristic
252	C₂²×C₄₃	#392	1	2	yes	—
253	C₂²×C₄₃	#394	1	2	yes	—
254	C₄×C₄₃	—	2	4	no	—
255	C₄×C₄₃	—	4	2	no	—
256	C₄×C₄₃	—	4	2	no	—
257	C₄×C₄₃	—	4	2	no	—
258	C₄×C₄₃	—	8	4	no	—
259	C₄×C₄₃	#386	1	2	yes	—
260	C₄×C₄₃	#390	1	2	yes	—
261	C₄×C₄₃	#392	1	2	yes	—
262	C₄×C₄₃	#394	1	2	yes	—
263	C₂×#532	C₂×C₄₃	1	1	yes	characteristic
264	C₂×#421	C₂×C₄₃	1	2	yes	complemented
265	C₂×#410	C₂×C₄₃	1	1	yes	characteristic, complemented
266	#2879	C₂×C₄₃	1	1	yes	characteristic, complemented
267	C₂×#339	C₂×C₄₃	1	2	yes	complemented
268	C₂×C₄₃	—	2	1	no	—
269	C₂×C₄₃	—	2	2	no	—
270	C₂×C₄₃	—	2	1	no	—
271	C₂×C₄₃	—	2	2	no	—
272	C₂×C₄₃	—	8	2	no	—
273	C₂×C₄₃	—	8	2	no	—
274	C₂×C₄₃	#1438	1	1	yes	characteristic
275	C₂×C₄₃	#1884	1	2	yes	—
276	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
277	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
278	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
279	#532	—	2	4	no	—
280	#532	—	2	4	no	—
281	C₂×C₄⋊Q₈	C₄×C₄₃	1	1	yes	characteristic, complemented
282	C₂×#127	C₄×C₄₃	1	1	yes	characteristic, complemented
283	C₂×#124	C₄×C₄₃	1	1	yes	characteristic, complemented
284	C₂×#124	C₄×C₄₃	1	1	yes	characteristic, complemented
285	C₂×#121	—	2	2	no	—
286	C₂×C₄×D₄	—	2	2	no	—
287	C₂×#117	C₂²×C₄₃	1	2	yes	—
288	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
289	#421	—	2	4	no	—
290	#421	—	2	4	no	—
291	C₂×#104	—	2	4	no	—
292	#410	—	2	4	no	—
293	C₂×#99	—	2	2	no	—
294	#408	—	2	4	no	—
295	#407	—	2	2	no	—
296	#339	—	2	4	no	—
297	C₄₃	#10979	1	1	yes	characteristic, direct product factor, Sylow
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	2	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	D₄×C₄₃	1	4	yes	—
310	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
311	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
315	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
316	C₂²×D₄	D₄×C₄₃	1	2	yes	—
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	D₄×C₄₃	1	2	yes	—
320	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	2	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₂×M₁₆	—	2	2	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	D₄×C₄₃	1	4	yes	complemented
327	C₂²×C₈	—	2	2	no	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	#127	—	2	2	no	—
331	#127	—	2	2	no	—
332	#124	—	2	2	no	—
333	#124	—	2	2	no	—
334	#124	—	2	2	no	—
335	#124	—	2	2	no	—
336	#121	—	2	16	no	—
337	C₄×D₄	—	2	16	no	—
338	#117	—	2	2	no	—
339	#117	—	2	2	no	—
340	#117	—	2	2	no	—
341	#117	D₄×C₄₃	1	4	yes	complemented
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
351	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
352	C₂×C₄²	D₄×C₄₃	1	4	yes	—
353	#104	—	2	16	no	—
354	#99	—	2	8	no	—
355	C₂²⋊C₈	—	2	8	no	—
356	C₂⁴	—	2	1	no	—
357	C₂⁴	C₂²⋊C₄×C₄₃	1	2	yes	—
358	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
359	#41	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	2	4	no	—
362	#41	—	2	4	no	—
363	#41	—	4	2	no	—
364	#41	—	4	2	no	—
365	#41	—	4	2	no	—
366	#41	—	4	2	no	—
367	#41	—	4	2	no	—
368	#41	—	4	2	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	#41	—	4	2	no	—
373	#41	—	4	2	no	—
374	#41	—	4	2	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	C₂²⋊C₄×C₄₃	1	2	yes	—
383	C₂×D₄	—	2	8	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	4	8	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	1	no	—
400	C₂×D₄	C₂²⋊C₄×C₄₃	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
416	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
422	C₂²×C₄	#41×C₄₃	1	2	yes	—
423	C₂²×C₄	#41×C₄₃	1	2	yes	—
424	M₁₆	—	2	4	no	—
425	M₁₆	—	2	4	no	—
426	M₁₆	—	4	2	no	—
427	M₁₆	—	4	2	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	4	2	no	—
430	C₂×C₈	—	4	2	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	4	2	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	4	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	4	2	no	—
443	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
444	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
455	C₂³	#120×C₄₃	1	2	yes	—
456	C₂³	#120×C₄₃	1	1	yes	characteristic
457	C₂³	#121×C₄₃	1	2	yes	—
458	C₂³	#123×C₄₃	1	1	yes	characteristic
459	Q₈	—	2	4	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	D₄	—	2	4	no	—
464	D₄	—	4	16	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	4	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	8	4	no	—
489	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
491	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
492	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
493	C₂×C₄	#120×C₄₃	1	2	yes	—
494	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
495	C₂×C₄	#120×C₄₃	1	2	yes	—
496	C₂×C₄	#121×C₄₃	1	2	yes	—
497	C₂×C₄	#121×C₄₃	1	2	yes	—
498	C₂×C₄	#121×C₄₃	1	2	yes	—
499	C₂×C₄	#121×C₄₃	1	2	yes	—
500	C₂×C₄	#121×C₄₃	1	2	yes	—
501	C₂×C₄	#123×C₄₃	1	2	yes	—
502	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
503	C₂×C₄	#124×C₄₃	1	2	yes	—
504	C₂×C₄	#127×C₄₃	1	2	yes	—
505	C₈	—	4	4	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	2	no	—
519	C₂²	C₄₃×#379	1	1	yes	characteristic
520	C₂²	C₄₃×#386	1	1	yes	characteristic
521	C₂²	C₄₃×#386	1	1	yes	characteristic
522	C₂²	C₄₃×#392	1	2	yes	—
523	C₂²	C₄₃×#394	1	2	yes	—
524	C₄	—	2	4	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	8	4	no	—
529	C₄	C₄₃×#386	1	2	yes	—
530	C₄	C₄₃×#390	1	2	yes	—
531	C₄	C₄₃×#392	1	2	yes	—
532	C₄	C₄₃×#394	1	2	yes	—
533	C₂	—	2	1	no	—
534	C₂	—	2	2	no	—
535	C₂	—	2	1	no	—
536	C₂	—	2	2	no	—
537	C₂	—	8	2	no	—
538	C₂	—	8	2	no	—
539	C₂	C₄₃×#1438	1	1	yes	characteristic
540	C₂	C₄₃×#1884	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₃	#120
commutator	C₂²×C₄	C₂²×C₄×C₄₃
Frattini, cosocle	C₂³×C₄	C₂³×C₄₃
socle	C₂²×C₄₃	#386
prime radical	C₂×C₄₃×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#421	C₂	semidirect
3. C₂×C₄₃×#410	C₂	semidirect
4. C₄₃×#2879	C₂	semidirect
5. C₂×C₄₃×#339	C₂	semidirect
11. C₂×C₄⋊Q₈×C₄₃	C₄	semidirect
12. C₂×#127×C₄₃	C₄	semidirect
13. C₂×#124×C₄₃	C₄	semidirect
14. C₂×#124×C₄₃	C₄	semidirect
55. C₂×M₁₆×C₄₃	D₄	semidirect
70. #117×C₄₃	D₄	semidirect
235. #10979	C₄₃	direct (N × H)
264. C₂×#421	C₂×C₄₃	semidirect
265. C₂×#410	C₂×C₄₃	semidirect
266. #2879	C₂×C₄₃	semidirect
267. C₂×#339	C₂×C₄₃	semidirect
281. C₂×C₄⋊Q₈	C₄×C₄₃	semidirect
282. C₂×#127	C₄×C₄₃	semidirect
283. C₂×#124	C₄×C₄₃	semidirect
284. C₂×#124	C₄×C₄₃	semidirect
297. C₄₃	#10979	direct (N × H)
326. C₂×M₁₆	D₄×C₄₃	semidirect
341. #117	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#532	2
C₂×C₄₃×#421	2
C₂×C₄₃×#410	2
C₄₃×#2879	2
C₂×C₄₃×#339	2
#10979	43

Subgroups — C43×#10979 #24930996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#10979 #24930996