Subgroups — C₄₃×#28460 #24948477

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#495	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1968	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#124×C₄₃	C₂²	1	2	yes	—
20	C₂×#124×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#495	—	2	8	no	—
24	C₄₃×#492	—	2	4	no	—
25	C₄₃×#462	—	2	4	no	—
26	C₄₃×#459	—	2	4	no	—
27	C₄×SD₁₆×C₄₃	—	2	4	no	—
28	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₄₃	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#397	—	2	2	no	—
37	C₄₃×#394	—	2	2	no	—
38	C₄₃×#391	C₂²	1	2	yes	—
39	C₄₃×#390	—	2	2	no	—
40	C₄₃×#390	C₂²	1	2	yes	—
41	C₄₃×#380	—	2	2	no	—
42	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	—	2	1	no	—
51	C₂×Q₁₆×C₄₃	—	2	4	no	—
52	C₂×Q₁₆×C₄₃	—	2	4	no	—
53	C₂×Q₁₆×C₄₃	—	4	2	no	—
54	C₂×SD₁₆×C₄₃	—	2	2	no	—
55	C₂×SD₁₆×C₄₃	—	2	4	no	—
56	C₂×SD₁₆×C₄₃	—	2	4	no	—
57	C₂×SD₁₆×C₄₃	—	2	4	no	—
58	C₂×SD₁₆×C₄₃	—	2	2	no	—
59	C₂×SD₁₆×C₄₃	—	2	4	no	—
60	C₂×SD₁₆×C₄₃	—	4	2	no	—
61	C₂×SD₁₆×C₄₃	—	4	2	no	—
62	C₂×SD₁₆×C₄₃	D₄	1	4	yes	complemented
63	C₂×D₈×C₄₃	—	2	4	no	—
64	C₂×D₈×C₄₃	—	2	4	no	—
65	C₂×D₈×C₄₃	—	4	2	no	—
66	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₃	—	2	2	no	—
70	C₄⋊Q₈×C₄₃	—	2	2	no	—
71	#127×C₄₃	—	2	2	no	—
72	#127×C₄₃	—	2	2	no	—
73	#124×C₄₃	—	2	4	no	—
74	#124×C₄₃	—	2	4	no	—
75	#124×C₄₃	—	4	2	no	—
76	#124×C₄₃	—	4	2	no	—
77	C₄×Q₈×C₄₃	—	2	2	no	—
78	C₄×Q₈×C₄₃	—	2	2	no	—
79	C₄×D₄×C₄₃	—	2	2	no	—
80	C₄×D₄×C₄₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
91	C₂×C₄²×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	#106×C₄₃	—	2	2	no	—
95	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
96	#103×C₄₃	—	2	2	no	—
97	#103×C₄₃	—	2	4	no	—
98	#102×C₄₃	—	2	2	no	—
99	#102×C₄₃	—	2	4	no	—
100	C₄×C₈×C₄₃	—	2	4	no	—
101	C₄×C₈×C₄₃	D₄	1	4	yes	—
102	#95×C₄₃	—	2	4	no	—
103	#95×C₄₃	D₄	1	2	yes	—
104	C₂⁴×C₄₃	—	2	1	no	—
105	C₂⁴×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	1	no	—
108	C₂×Q₈×C₄₃	—	2	1	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	—	2	2	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×Q₈×C₄₃	—	2	1	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₄₃	—	2	1	no	—
119	C₂×D₄×C₄₃	—	2	1	no	—
120	C₂×D₄×C₄₃	—	2	1	no	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	1	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	2	1	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	4	2	no	—
130	C₂×D₄×C₄₃	—	4	2	no	—
131	C₂×D₄×C₄₃	—	4	4	no	—
132	C₂×D₄×C₄₃	—	8	2	no	—
133	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₃	—	2	1	no	—
135	C₂²×C₄×C₄₃	—	2	1	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	—	4	2	no	—
139	C₂²×C₄×C₄₃	—	4	4	no	—
140	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
144	Q₁₆×C₄₃	—	4	8	no	—
145	SD₁₆×C₄₃	—	2	8	no	—
146	SD₁₆×C₄₃	—	4	8	no	—
147	SD₁₆×C₄₃	—	4	8	no	—
148	D₈×C₄₃	—	4	8	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	—	2	1	no	—
152	C₂×C₈×C₄₃	—	2	1	no	—
153	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
155	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₄₃	#41	1	2	yes	—
158	C₄⋊C₄×C₄₃	—	2	4	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	2	1	no	—
162	C₄⋊C₄×C₄₃	—	2	1	no	—
163	C₄⋊C₄×C₄₃	—	4	2	no	—
164	C₄⋊C₄×C₄₃	—	4	2	no	—
165	C₄⋊C₄×C₄₃	—	4	2	no	—
166	C₂²⋊C₄×C₄₃	—	4	8	no	—
167	C₂²⋊C₄×C₄₃	—	4	8	no	—
168	C₂²⋊C₄×C₄₃	—	4	2	no	—
169	C₂²⋊C₄×C₄₃	—	8	4	no	—
170	C₄²×C₄₃	—	2	2	no	—
171	C₄²×C₄₃	—	2	2	no	—
172	C₄²×C₄₃	—	4	2	no	—
173	C₄²×C₄₃	C₂×D₄	1	2	yes	—
174	C₄²×C₄₃	C₂×D₄	1	2	yes	—
175	C₂³×C₄₃	—	2	2	no	—
176	C₂³×C₄₃	—	4	1	no	—
177	C₂³×C₄₃	—	4	1	no	—
178	C₂³×C₄₃	—	4	2	no	—
179	C₂³×C₄₃	—	4	2	no	—
180	C₂³×C₄₃	—	4	2	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	4	no	—
184	C₂³×C₄₃	—	4	4	no	—
185	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₄₃	—	2	2	no	—
187	Q₈×C₄₃	—	2	2	no	—
188	Q₈×C₄₃	—	4	1	no	—
189	Q₈×C₄₃	—	4	1	no	—
190	Q₈×C₄₃	—	4	2	no	—
191	Q₈×C₄₃	—	4	2	no	—
192	Q₈×C₄₃	—	4	2	no	—
193	Q₈×C₄₃	—	4	2	no	—
194	D₄×C₄₃	—	2	2	no	—
195	D₄×C₄₃	—	2	2	no	—
196	D₄×C₄₃	—	4	2	no	—
197	D₄×C₄₃	—	4	1	no	—
198	D₄×C₄₃	—	4	2	no	—
199	D₄×C₄₃	—	4	2	no	—
200	D₄×C₄₃	—	4	1	no	—
201	D₄×C₄₃	—	4	2	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	4	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	8	4	no	—
219	C₂×C₄×C₄₃	#127	1	2	yes	—
220	C₂×C₄×C₄₃	#127	1	2	yes	—
221	C₂×C₄×C₄₃	#135	1	4	yes	—
222	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
228	C₈×C₄₃	—	2	2	no	—
229	C₈×C₄₃	—	2	4	no	—
230	C₈×C₄₃	#121	1	4	yes	—
231	#28460	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₄₃	—	4	4	no	—
233	C₂²×C₄₃	—	4	2	no	—
234	C₂²×C₄₃	—	8	2	no	—
235	C₂²×C₄₃	—	8	1	no	—
236	C₂²×C₄₃	—	8	1	no	—
237	C₂²×C₄₃	—	8	4	no	—
238	C₂²×C₄₃	—	8	2	no	—
239	C₂²×C₄₃	—	8	2	no	—
240	C₂²×C₄₃	—	8	4	no	—
241	C₂²×C₄₃	—	8	2	no	—
242	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
243	C₂²×C₄₃	D₄²	1	1	yes	characteristic
244	C₂²×C₄₃	#550	1	1	yes	characteristic
245	C₂²×C₄₃	C₂×#135	1	2	yes	—
246	C₂²×C₄₃	#577	1	2	yes	—
247	C₄×C₄₃	—	2	2	no	—
248	C₄×C₄₃	—	4	4	no	—
249	C₄×C₄₃	—	4	2	no	—
250	C₄×C₄₃	—	8	1	no	—
251	C₄×C₄₃	—	8	1	no	—
252	C₄×C₄₃	—	8	2	no	—
253	C₄×C₄₃	#495	1	4	yes	complemented
254	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
255	C₄×C₄₃	#535	1	1	yes	characteristic
256	C₄×C₄₃	D₄²	1	1	yes	characteristic
257	C₄×C₄₃	#550	1	1	yes	characteristic
258	C₂×#495	C₂×C₄₃	1	2	yes	complemented
259	C₂×#492	C₂×C₄₃	1	1	yes	characteristic, complemented
260	C₂×#462	C₂×C₄₃	1	1	yes	characteristic, complemented
261	C₂×#459	C₂×C₄₃	1	1	yes	characteristic
262	C₂×C₄×SD₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
263	#2548	C₂×C₄₃	1	1	yes	characteristic, complemented
264	#2547	C₂×C₄₃	1	1	yes	characteristic, complemented
265	#2015	C₂×C₄₃	1	2	yes	complemented
266	#2012	C₂×C₄₃	1	2	yes	complemented
267	#1968	C₂×C₄₃	1	2	yes	complemented
268	C₈×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
269	C₂×C₄₃	—	8	2	no	—
270	C₂×C₄₃	—	16	2	no	—
271	C₂×C₄₃	#2541	1	1	yes	characteristic
272	C₂×C₄₃	C₂×#495	1	1	yes	characteristic
273	C₂×C₄₃	#3154	1	1	yes	characteristic
274	C₂×C₄₃	#3284	1	2	yes	—
275	C₂×C₄₃	#3394	1	2	yes	—
276	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
277	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
278	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
279	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
280	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
281	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
282	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
283	C₂×#124	C₂²×C₄₃	1	2	yes	—
284	C₂×#124	C₂²×C₄₃	1	2	yes	—
285	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
287	#495	—	2	8	no	—
288	#492	—	2	4	no	—
289	#462	—	2	4	no	—
290	#459	—	2	4	no	—
291	C₄×SD₁₆	—	2	4	no	—
292	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
294	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
295	C₂×#103	C₂²×C₄₃	1	2	yes	—
296	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×#102	C₂²×C₄₃	1	2	yes	—
298	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
299	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
300	#397	—	2	2	no	—
301	#394	—	2	2	no	—
302	#391	C₂²×C₄₃	1	2	yes	—
303	#390	—	2	2	no	—
304	#390	C₂²×C₄₃	1	2	yes	—
305	#380	—	2	2	no	—
306	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
307	#336	C₂²×C₄₃	1	2	yes	—
308	C₄₃	#28460	1	1	yes	characteristic, direct product factor, Sylow
309	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
310	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
314	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂×Q₁₆	—	2	4	no	—
317	C₂×Q₁₆	—	2	4	no	—
318	C₂×Q₁₆	—	4	2	no	—
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×SD₁₆	—	2	4	no	—
321	C₂×SD₁₆	—	2	4	no	—
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×SD₁₆	—	4	2	no	—
326	C₂×SD₁₆	—	4	2	no	—
327	C₂×SD₁₆	D₄×C₄₃	1	4	yes	complemented
328	C₂×D₈	—	2	4	no	—
329	C₂×D₈	—	2	4	no	—
330	C₂×D₈	—	4	2	no	—
331	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
332	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	—	2	2	no	—
336	#127	—	2	2	no	—
337	#127	—	2	2	no	—
338	#124	—	2	4	no	—
339	#124	—	2	4	no	—
340	#124	—	4	2	no	—
341	#124	—	4	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	4	no	—
354	C₂×C₂²⋊C₄	—	2	4	no	—
355	C₂×C₂²⋊C₄	—	2	4	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
358	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
359	#106	—	2	2	no	—
360	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
361	#103	—	2	2	no	—
362	#103	—	2	4	no	—
363	#102	—	2	2	no	—
364	#102	—	2	4	no	—
365	C₄×C₈	—	2	4	no	—
366	C₄×C₈	D₄×C₄₃	1	4	yes	—
367	#95	—	2	4	no	—
368	#95	D₄×C₄₃	1	2	yes	—
369	C₂⁴	—	2	1	no	—
370	C₂⁴	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	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	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	8	2	no	—
398	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	4	no	—
405	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
406	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
409	Q₁₆	—	4	8	no	—
410	SD₁₆	—	2	8	no	—
411	SD₁₆	—	4	8	no	—
412	SD₁₆	—	4	8	no	—
413	D₈	—	4	8	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
419	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
420	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
421	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
422	C₂×C₈	#41×C₄₃	1	2	yes	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	4	2	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	4	8	no	—
432	C₂²⋊C₄	—	4	8	no	—
433	C₂²⋊C₄	—	4	2	no	—
434	C₂²⋊C₄	—	8	4	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	4	2	no	—
438	C₄²	C₂×D₄×C₄₃	1	2	yes	—
439	C₄²	C₂×D₄×C₄₃	1	2	yes	—
440	C₂³	—	2	2	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	4	no	—
450	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	4	1	no	—
454	Q₈	—	4	1	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	2	no	—
467	D₄	—	8	4	no	—
468	D₄	—	8	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	8	4	no	—
484	C₂×C₄	#127×C₄₃	1	2	yes	—
485	C₂×C₄	#127×C₄₃	1	2	yes	—
486	C₂×C₄	#135×C₄₃	1	4	yes	—
487	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
491	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
492	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
493	C₈	—	2	2	no	—
494	C₈	—	2	4	no	—
495	C₈	#121×C₄₃	1	4	yes	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	4	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	4	no	—
505	C₂²	—	8	2	no	—
506	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
507	C₂²	D₄²×C₄₃	1	1	yes	characteristic
508	C₂²	C₄₃×#550	1	1	yes	characteristic
509	C₂²	C₂×#135×C₄₃	1	2	yes	—
510	C₂²	C₄₃×#577	1	2	yes	—
511	C₄	—	2	2	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	2	no	—
517	C₄	C₄₃×#495	1	4	yes	complemented
518	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
519	C₄	C₄₃×#535	1	1	yes	characteristic
520	C₄	D₄²×C₄₃	1	1	yes	characteristic
521	C₄	C₄₃×#550	1	1	yes	characteristic
522	C₂	—	8	2	no	—
523	C₂	—	16	2	no	—
524	C₂	C₄₃×#2541	1	1	yes	characteristic
525	C₂	C₂×C₄₃×#495	1	1	yes	characteristic
526	C₂	C₄₃×#3154	1	1	yes	characteristic
527	C₂	C₄₃×#3284	1	2	yes	—
528	C₂	C₄₃×#3394	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄×C₄⋊C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#495	C₂	semidirect
2. C₂×C₄₃×#492	C₂	semidirect
3. C₂×C₄₃×#462	C₂	semidirect
5. C₂×C₄×SD₁₆×C₄₃	C₂	semidirect
6. C₄₃×#2548	C₂	semidirect
7. C₄₃×#2547	C₂	semidirect
8. C₄₃×#2015	C₂	semidirect
9. C₄₃×#2012	C₂	semidirect
10. C₄₃×#1968	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₃	C₂	semidirect
62. C₂×SD₁₆×C₄₃	D₄	semidirect
231. #28460	C₄₃	direct (N × H)
253. C₄×C₄₃	#495	semidirect
258. C₂×#495	C₂×C₄₃	semidirect
259. C₂×#492	C₂×C₄₃	semidirect
260. C₂×#462	C₂×C₄₃	semidirect
262. C₂×C₄×SD₁₆	C₂×C₄₃	semidirect
263. #2548	C₂×C₄₃	semidirect
264. #2547	C₂×C₄₃	semidirect
265. #2015	C₂×C₄₃	semidirect
266. #2012	C₂×C₄₃	semidirect
267. #1968	C₂×C₄₃	semidirect
268. C₈×C₄⋊C₄	C₂×C₄₃	semidirect
308. C₄₃	#28460	direct (N × H)
327. C₂×SD₁₆	D₄×C₄₃	semidirect
517. C₄	C₄₃×#495	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#495	2
C₂×C₄₃×#492	2
C₂×C₄₃×#462	2
C₂×C₄₃×#459	2
C₂×C₄×SD₁₆×C₄₃	2
C₄₃×#2548	2
C₄₃×#2547	2
C₄₃×#2015	2
C₄₃×#2012	2
C₄₃×#1968	2
C₈×C₄⋊C₄×C₄₃	2
#28460	43

Subgroups — C43×#28460 #24948477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28460 #24948477