Subgroups — C₄₃×#23532 #24943549

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#101×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2879	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#2052	C₂	1	8	yes	maximal, complemented
8	C₄₃×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×#137×C₄₃	—	2	2	no	—
12	C₂×#137×C₄₃	—	2	4	no	—
13	C₂×#137×C₄₃	—	2	4	no	—
14	C₂×#137×C₄₃	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₄₃	—	2	1	no	—
16	C₂²×SD₁₆×C₄₃	—	2	1	no	—
17	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#430	—	2	4	no	—
23	C₂×#108×C₄₃	C₂²	1	4	yes	complemented
24	C₄₃×#419	—	2	1	no	—
25	C₄₃×#419	—	2	2	no	—
26	C₄₃×#419	—	2	2	no	—
27	C₄₃×#418	—	2	1	no	—
28	C₄₃×#417	C₂²	1	4	yes	—
29	C₄₃×#416	—	2	2	no	—
30	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
31	C₂×#101×C₄₃	—	2	4	no	—
32	C₂×#101×C₄₃	C₂²	1	4	yes	complemented
33	C₄₃×#408	—	2	2	no	—
34	C₄₃×#408	C₂²	1	4	yes	—
35	C₄₃×#407	—	2	2	no	—
36	C₄₃×#343	C₂²	1	4	yes	complemented
37	C₂×#41×C₄₃	—	2	1	no	—
38	C₂×#41×C₄₃	—	2	1	no	—
39	C₂×#41×C₄₃	—	2	2	no	—
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	—	2	2	no	—
42	C₂×#41×C₄₃	—	2	2	no	—
43	C₂×#41×C₄₃	D₄	1	2	yes	—
44	C₂×#41×C₄₃	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₃	—	2	2	no	—
46	C₂²×Q₈×C₄₃	—	2	1	no	—
47	C₂²×Q₈×C₄₃	—	2	1	no	—
48	C₂²×Q₈×C₄₃	—	2	1	no	—
49	C₂²×Q₈×C₄₃	—	2	2	no	—
50	C₂²×Q₈×C₄₃	—	2	1	no	—
51	C₂²×Q₈×C₄₃	—	2	1	no	—
52	C₂²×Q₈×C₄₃	—	2	2	no	—
53	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
55	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×D₄×C₄₃	—	2	1	no	—
57	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	—	2	1	no	—
59	C₂³×C₄×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	#137×C₄₃	—	2	16	no	—
62	#137×C₄₃	—	2	8	no	—
63	#137×C₄₃	—	2	8	no	—
64	C₂×Q₁₆×C₄₃	—	2	8	no	—
65	C₂×Q₁₆×C₄₃	—	2	4	no	—
66	C₂×SD₁₆×C₄₃	—	2	8	no	—
67	C₂×SD₁₆×C₄₃	—	2	4	no	—
68	C₂×M₁₆×C₄₃	—	2	2	no	—
69	C₂×M₁₆×C₄₃	—	2	1	no	—
70	C₂×M₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	—	2	1	no	—
73	C₂×M₁₆×C₄₃	—	2	1	no	—
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂×M₁₆×C₄₃	—	2	2	no	—
76	C₂×M₁₆×C₄₃	—	2	2	no	—
77	C₂×M₁₆×C₄₃	—	2	2	no	—
78	C₂×M₁₆×C₄₃	D₄	1	4	yes	—
79	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
80	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
81	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
82	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
83	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₃	—	2	1	no	—
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	C₂²×C₈×C₄₃	—	2	1	no	—
87	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
88	#117×C₄₃	—	2	1	no	—
89	#117×C₄₃	—	2	1	no	—
90	#117×C₄₃	—	2	1	no	—
91	#117×C₄₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	—	2	1	no	—
95	#108×C₄₃	—	2	8	no	—
96	#103×C₄₃	—	2	4	no	—
97	#103×C₄₃	—	2	8	no	—
98	#102×C₄₃	—	2	4	no	—
99	#101×C₄₃	—	2	8	no	—
100	C₂²⋊C₈×C₄₃	—	2	8	no	—
101	C₂⁴×C₄₃	—	2	1	no	—
102	C₂⁴×C₄₃	#41	1	1	yes	characteristic
103	#41×C₄₃	—	2	4	no	—
104	#41×C₄₃	—	2	4	no	—
105	#41×C₄₃	—	2	2	no	—
106	#41×C₄₃	—	2	2	no	—
107	#41×C₄₃	—	2	2	no	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	4	2	no	—
110	#41×C₄₃	—	4	2	no	—
111	#41×C₄₃	—	4	2	no	—
112	#41×C₄₃	—	4	2	no	—
113	C₂×Q₈×C₄₃	—	2	1	no	—
114	C₂×Q₈×C₄₃	—	2	4	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	4	no	—
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	4	no	—
119	C₂×Q₈×C₄₃	—	2	4	no	—
120	C₂×Q₈×C₄₃	—	2	4	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	4	1	no	—
127	C₂×Q₈×C₄₃	—	4	1	no	—
128	C₂×Q₈×C₄₃	—	4	2	no	—
129	C₂×Q₈×C₄₃	—	4	2	no	—
130	C₂×Q₈×C₄₃	—	4	2	no	—
131	C₂×Q₈×C₄₃	—	4	2	no	—
132	C₂×Q₈×C₄₃	—	4	2	no	—
133	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
134	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₄₃	—	2	1	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	4	2	no	—
141	C₂×D₄×C₄₃	—	4	2	no	—
142	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	1	no	—
146	C₂²×C₄×C₄₃	—	2	4	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	2	no	—
149	C₂²×C₄×C₄₃	—	4	2	no	—
150	C₂²×C₄×C₄₃	—	4	2	no	—
151	C₂²×C₄×C₄₃	—	4	1	no	—
152	C₂²×C₄×C₄₃	—	4	1	no	—
153	C₂²×C₄×C₄₃	—	4	2	no	—
154	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₄₃	#41	1	2	yes	—
161	C₂²×C₄×C₄₃	#41	1	2	yes	—
162	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
164	Q₁₆×C₄₃	—	2	16	no	—
165	SD₁₆×C₄₃	—	2	16	no	—
166	M₁₆×C₄₃	—	2	4	no	—
167	M₁₆×C₄₃	—	2	4	no	—
168	M₁₆×C₄₃	—	2	4	no	—
169	M₁₆×C₄₃	—	2	2	no	—
170	M₁₆×C₄₃	—	2	2	no	—
171	M₁₆×C₄₃	—	2	2	no	—
172	M₁₆×C₄₃	—	2	2	no	—
173	M₁₆×C₄₃	—	2	2	no	—
174	M₁₆×C₄₃	—	4	2	no	—
175	M₁₆×C₄₃	—	4	2	no	—
176	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
177	C₂×C₈×C₄₃	—	2	4	no	—
178	C₂×C₈×C₄₃	—	2	2	no	—
179	C₂×C₈×C₄₃	—	2	2	no	—
180	C₂×C₈×C₄₃	—	2	2	no	—
181	C₂×C₈×C₄₃	—	2	2	no	—
182	C₂×C₈×C₄₃	—	2	2	no	—
183	C₂×C₈×C₄₃	—	4	2	no	—
184	C₂×C₈×C₄₃	—	4	2	no	—
185	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
186	C₄⋊C₄×C₄₃	—	2	2	no	—
187	C₄⋊C₄×C₄₃	—	2	2	no	—
188	C₂²⋊C₄×C₄₃	—	4	1	no	—
189	C₂²⋊C₄×C₄₃	—	4	1	no	—
190	C₄²×C₄₃	—	4	1	no	—
191	C₄²×C₄₃	—	4	1	no	—
192	C₂³×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	—	4	2	no	—
195	C₂³×C₄₃	—	8	2	no	—
196	C₂³×C₄₃	#121	1	1	yes	characteristic
197	C₂³×C₄₃	#121	1	1	yes	characteristic
198	C₂³×C₄₃	#123	1	2	yes	—
199	C₂³×C₄₃	#124	1	2	yes	—
200	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
201	Q₈×C₄₃	—	2	4	no	—
202	Q₈×C₄₃	—	2	2	no	—
203	Q₈×C₄₃	—	2	4	no	—
204	Q₈×C₄₃	—	2	2	no	—
205	Q₈×C₄₃	—	4	2	no	—
206	Q₈×C₄₃	—	4	2	no	—
207	Q₈×C₄₃	—	4	4	no	—
208	Q₈×C₄₃	—	4	4	no	—
209	Q₈×C₄₃	—	4	2	no	—
210	D₄×C₄₃	—	2	2	no	—
211	D₄×C₄₃	—	2	2	no	—
212	D₄×C₄₃	—	4	2	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	4	4	no	—
215	D₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	4	4	no	—
222	C₂×C₄×C₄₃	—	4	4	no	—
223	C₂×C₄×C₄₃	—	4	2	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	4	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	8	2	no	—
228	C₂×C₄×C₄₃	#120	1	2	yes	—
229	C₂×C₄×C₄₃	#120	1	2	yes	—
230	C₂×C₄×C₄₃	#121	1	2	yes	—
231	C₂×C₄×C₄₃	#121	1	2	yes	—
232	C₂×C₄×C₄₃	#121	1	2	yes	—
233	C₂×C₄×C₄₃	#121	1	2	yes	—
234	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
235	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#123	1	2	yes	—
237	C₂×C₄×C₄₃	#123	1	2	yes	—
238	C₂×C₄×C₄₃	#123	1	2	yes	—
239	C₂×C₄×C₄₃	#124	1	2	yes	—
240	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
246	C₈×C₄₃	—	2	4	no	—
247	C₈×C₄₃	—	2	4	no	—
248	C₈×C₄₃	—	4	2	no	—
249	C₈×C₄₃	—	4	2	no	—
250	#23532	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂²×C₄₃	—	2	2	no	—
252	C₂²×C₄₃	—	2	2	no	—
253	C₂²×C₄₃	—	2	2	no	—
254	C₂²×C₄₃	—	4	2	no	—
255	C₂²×C₄₃	—	4	2	no	—
256	C₂²×C₄₃	—	4	2	no	—
257	C₂²×C₄₃	—	4	4	no	—
258	C₂²×C₄₃	—	8	4	no	—
259	C₂²×C₄₃	#394	1	2	yes	—
260	C₂²×C₄₃	#394	1	2	yes	—
261	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
262	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
263	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
264	C₄×C₄₃	—	4	2	no	—
265	C₄×C₄₃	—	4	4	no	—
266	C₄×C₄₃	—	8	2	no	—
267	C₄×C₄₃	#394	1	2	yes	—
268	C₄×C₄₃	#394	1	2	yes	—
269	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
270	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
271	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
272	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
273	C₂²×#137	C₂×C₄₃	1	1	yes	characteristic
274	C₂×#430	C₂×C₄₃	1	1	yes	characteristic, complemented
275	#2896	C₂×C₄₃	1	1	yes	characteristic
276	C₂×#419	C₂×C₄₃	1	1	yes	characteristic, complemented
277	C₂²×#101	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#2879	C₂×C₄₃	1	1	yes	characteristic
279	#2052	C₂×C₄₃	1	8	yes	complemented
280	#1742	C₂×C₄₃	1	1	yes	characteristic, complemented
281	C₂×C₄₃	—	2	2	no	—
282	C₂×C₄₃	—	2	1	no	—
283	C₂×C₄₃	—	2	1	no	—
284	C₂×C₄₃	—	2	2	no	—
285	C₂×C₄₃	—	8	2	no	—
286	C₂×C₄₃	C₂×#394	1	1	yes	characteristic
287	C₂×C₄₃	#3069	1	2	yes	—
288	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
289	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
290	C₂×#137	—	2	2	no	—
291	C₂×#137	—	2	4	no	—
292	C₂×#137	—	2	4	no	—
293	C₂×#137	C₂²×C₄₃	1	4	yes	—
294	C₂²×Q₁₆	—	2	1	no	—
295	C₂²×SD₁₆	—	2	1	no	—
296	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
297	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
298	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
299	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
300	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
301	#430	—	2	4	no	—
302	C₂×#108	C₂²×C₄₃	1	4	yes	complemented
303	#419	—	2	1	no	—
304	#419	—	2	2	no	—
305	#419	—	2	2	no	—
306	#418	—	2	1	no	—
307	#417	C₂²×C₄₃	1	4	yes	—
308	#416	—	2	2	no	—
309	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
310	C₂×#101	—	2	4	no	—
311	C₂×#101	C₂²×C₄₃	1	4	yes	complemented
312	#408	—	2	2	no	—
313	#408	C₂²×C₄₃	1	4	yes	—
314	#407	—	2	2	no	—
315	#343	C₂²×C₄₃	1	4	yes	complemented
316	C₄₃	#23532	1	1	yes	characteristic, direct product factor, Sylow
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	2	1	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	D₄×C₄₃	1	2	yes	—
324	C₂×#41	C₂³×C₄₃	1	2	yes	—
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	—	2	1	no	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×Q₈	—	2	2	no	—
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
334	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
335	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
341	#137	—	2	16	no	—
342	#137	—	2	8	no	—
343	#137	—	2	8	no	—
344	C₂×Q₁₆	—	2	8	no	—
345	C₂×Q₁₆	—	2	4	no	—
346	C₂×SD₁₆	—	2	8	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×M₁₆	—	2	2	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	—	2	2	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	2	no	—
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	D₄×C₄₃	1	4	yes	—
359	C₂×M₁₆	D₄×C₄₃	1	2	yes	—
360	C₂×M₁₆	D₄×C₄₃	1	2	yes	—
361	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
362	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
363	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	#108	—	2	8	no	—
376	#103	—	2	4	no	—
377	#103	—	2	8	no	—
378	#102	—	2	4	no	—
379	#101	—	2	8	no	—
380	C₂²⋊C₈	—	2	8	no	—
381	C₂⁴	—	2	1	no	—
382	C₂⁴	#41×C₄₃	1	1	yes	characteristic
383	#41	—	2	4	no	—
384	#41	—	2	4	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	4	2	no	—
390	#41	—	4	2	no	—
391	#41	—	4	2	no	—
392	#41	—	4	2	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	1	no	—
407	C₂×Q₈	—	4	1	no	—
408	C₂×Q₈	—	4	2	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	—	4	2	no	—
413	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
414	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
436	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
440	C₂²×C₄	#41×C₄₃	1	2	yes	—
441	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
442	C₂²×C₄	#41×C₄₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
444	Q₁₆	—	2	16	no	—
445	SD₁₆	—	2	16	no	—
446	M₁₆	—	2	4	no	—
447	M₁₆	—	2	4	no	—
448	M₁₆	—	2	4	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	4	2	no	—
455	M₁₆	—	4	2	no	—
456	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
457	C₂×C₈	—	2	4	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	4	2	no	—
464	C₂×C₈	—	4	2	no	—
465	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₄²	—	4	1	no	—
471	C₄²	—	4	1	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	8	2	no	—
476	C₂³	#121×C₄₃	1	1	yes	characteristic
477	C₂³	#121×C₄₃	1	1	yes	characteristic
478	C₂³	#123×C₄₃	1	2	yes	—
479	C₂³	#124×C₄₃	1	2	yes	—
480	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
481	Q₈	—	2	4	no	—
482	Q₈	—	2	2	no	—
483	Q₈	—	2	4	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	Q₈	—	4	4	no	—
488	Q₈	—	4	4	no	—
489	Q₈	—	4	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	8	2	no	—
508	C₂×C₄	#120×C₄₃	1	2	yes	—
509	C₂×C₄	#120×C₄₃	1	2	yes	—
510	C₂×C₄	#121×C₄₃	1	2	yes	—
511	C₂×C₄	#121×C₄₃	1	2	yes	—
512	C₂×C₄	#121×C₄₃	1	2	yes	—
513	C₂×C₄	#121×C₄₃	1	2	yes	—
514	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
515	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
516	C₂×C₄	#123×C₄₃	1	2	yes	—
517	C₂×C₄	#123×C₄₃	1	2	yes	—
518	C₂×C₄	#123×C₄₃	1	2	yes	—
519	C₂×C₄	#124×C₄₃	1	2	yes	—
520	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
524	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
525	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
526	C₈	—	2	4	no	—
527	C₈	—	2	4	no	—
528	C₈	—	4	2	no	—
529	C₈	—	4	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	8	4	no	—
538	C₂²	C₄₃×#394	1	2	yes	—
539	C₂²	C₄₃×#394	1	2	yes	—
540	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
541	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
542	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	8	2	no	—
546	C₄	C₄₃×#394	1	2	yes	—
547	C₄	C₄₃×#394	1	2	yes	—
548	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
549	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
550	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
551	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
552	C₂	—	2	2	no	—
553	C₂	—	2	1	no	—
554	C₂	—	2	1	no	—
555	C₂	—	2	2	no	—
556	C₂	—	8	2	no	—
557	C₂	C₂×C₄₃×#394	1	1	yes	characteristic
558	C₂	C₄₃×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#430	C₂	semidirect
4. C₂×C₄₃×#419	C₂	semidirect
5. C₂²×#101×C₄₃	C₂	semidirect
7. C₄₃×#2052	C₂	semidirect
8. C₄₃×#1742	C₂	semidirect
23. C₂×#108×C₄₃	C₂²	semidirect
30. C₂×#103×C₄₃	C₂²	semidirect
32. C₂×#101×C₄₃	C₂²	semidirect
36. C₄₃×#343	C₂²	semidirect
250. #23532	C₄₃	direct (N × H)
274. C₂×#430	C₂×C₄₃	semidirect
276. C₂×#419	C₂×C₄₃	semidirect
277. C₂²×#101	C₂×C₄₃	semidirect
279. #2052	C₂×C₄₃	semidirect
280. #1742	C₂×C₄₃	semidirect
302. C₂×#108	C₂²×C₄₃	semidirect
309. C₂×#103	C₂²×C₄₃	semidirect
311. C₂×#101	C₂²×C₄₃	semidirect
315. #343	C₂²×C₄₃	semidirect
316. C₄₃	#23532	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₃	2
C₂×C₄₃×#430	2
C₄₃×#2896	2
C₂×C₄₃×#419	2
C₂²×#101×C₄₃	2
C₄₃×#2879	2
C₄₃×#2052	2
C₄₃×#1742	2
#23532	43

Subgroups — C43×#23532 #24943549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#23532 #24943549