Subgroups — C₄₃×#29854 #24949871

Order 11008.

856 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2066	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2036	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2034	C₂	1	2	yes	maximal
9	C₄₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1959	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#489	—	2	4	no	—
19	C₄₃×#432	—	2	4	no	—
20	C₂×#107×C₄₃	C₂²	1	2	yes	—
21	C₂×#106×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#391	—	2	1	no	—
31	C₄₃×#391	C₂²	1	1	yes	characteristic
32	C₄₃×#390	C₂²	1	1	yes	characteristic
33	C₄₃×#389	—	2	1	no	—
34	C₄₃×#389	C₂²	1	2	yes	—
35	C₄₃×#388	—	2	1	no	—
36	C₄₃×#388	—	2	1	no	—
37	C₄₃×#386	—	2	1	no	—
38	C₄₃×#386	—	2	1	no	—
39	C₄₃×#384	C₂²	1	1	yes	characteristic
40	C₄₃×#382	C₂²	1	1	yes	characteristic
41	C₄₃×#380	—	2	1	no	—
42	C₄₃×#380	C₂²	1	2	yes	—
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₃	—	2	1	no	—
46	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₄₃	—	2	2	no	—
55	C₄⋊Q₈×C₄₃	—	2	2	no	—
56	#124×C₄₃	—	2	2	no	—
57	#124×C₄₃	—	2	2	no	—
58	C₂²⋊Q₈×C₄₃	—	4	2	no	—
59	C₂²⋊Q₈×C₄₃	—	4	4	no	—
60	#121×C₄₃	—	4	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄²×C₄₃	—	2	2	no	—
78	C₂×C₄²×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	#107×C₄₃	—	4	2	no	—
84	#106×C₄₃	—	4	2	no	—
85	C₄⋊C₈×C₄₃	—	2	4	no	—
86	#103×C₄₃	—	2	4	no	—
87	#103×C₄₃	—	4	2	no	—
88	#102×C₄₃	—	2	4	no	—
89	#102×C₄₃	—	4	2	no	—
90	C₂²⋊C₈×C₄₃	—	2	4	no	—
91	#97×C₄₃	—	2	2	no	—
92	#97×C₄₃	D₄	1	4	yes	complemented
93	#95×C₄₃	—	2	2	no	—
94	#95×C₄₃	—	2	2	no	—
95	#95×C₄₃	—	2	1	no	—
96	#95×C₄₃	—	2	1	no	—
97	#95×C₄₃	—	2	1	no	—
98	#95×C₄₃	—	2	1	no	—
99	C₂⁴×C₄₃	—	2	1	no	—
100	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₄₃	—	2	1	no	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	4	2	no	—
106	C₂×Q₈×C₄₃	—	4	2	no	—
107	C₂×Q₈×C₄₃	—	4	2	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	4	2	no	—
113	C₂×D₄×C₄₃	—	4	2	no	—
114	C₂×D₄×C₄₃	—	4	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	2	2	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	4	1	no	—
129	C₂²×C₄×C₄₃	—	4	1	no	—
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	2	2	no	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	2	no	—
148	C₄⋊C₄×C₄₃	—	4	2	no	—
149	C₄⋊C₄×C₄₃	—	4	2	no	—
150	C₄⋊C₄×C₄₃	—	4	2	no	—
151	C₄⋊C₄×C₄₃	—	4	2	no	—
152	C₄⋊C₄×C₄₃	—	4	4	no	—
153	C₂²⋊C₄×C₄₃	—	4	2	no	—
154	C₂²⋊C₄×C₄₃	—	4	4	no	—
155	C₂²⋊C₄×C₄₃	—	4	2	no	—
156	C₂²⋊C₄×C₄₃	—	4	2	no	—
157	C₂²⋊C₄×C₄₃	—	4	2	no	—
158	C₂²⋊C₄×C₄₃	—	4	2	no	—
159	C₂²⋊C₄×C₄₃	—	4	2	no	—
160	C₄²×C₄₃	—	2	2	no	—
161	C₄²×C₄₃	—	2	2	no	—
162	C₄²×C₄₃	—	2	1	no	—
163	C₄²×C₄₃	—	2	1	no	—
164	C₄²×C₄₃	C₂×D₄	1	2	yes	—
165	C₄²×C₄₃	#41	1	2	yes	—
166	C₂³×C₄₃	—	2	1	no	—
167	C₂³×C₄₃	—	2	1	no	—
168	C₂³×C₄₃	—	2	1	no	—
169	C₂³×C₄₃	—	2	1	no	—
170	C₂³×C₄₃	—	2	1	no	—
171	C₂³×C₄₃	—	2	1	no	—
172	C₂³×C₄₃	—	4	1	no	—
173	C₂³×C₄₃	—	4	1	no	—
174	C₂³×C₄₃	—	4	1	no	—
175	C₂³×C₄₃	—	4	1	no	—
176	C₂³×C₄₃	—	4	1	no	—
177	C₂³×C₄₃	—	4	1	no	—
178	C₂³×C₄₃	—	4	1	no	—
179	C₂³×C₄₃	#137	1	2	yes	—
180	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₄₃	—	4	2	no	—
182	Q₈×C₄₃	—	4	2	no	—
183	Q₈×C₄₃	—	8	4	no	—
184	D₄×C₄₃	—	4	2	no	—
185	D₄×C₄₃	—	4	2	no	—
186	D₄×C₄₃	—	8	4	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	4	4	no	—
200	C₂×C₄×C₄₃	—	4	4	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	4	1	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	1	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	#121	1	2	yes	—
219	C₂×C₄×C₄₃	#121	1	2	yes	—
220	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
221	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
224	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
225	C₈×C₄₃	—	2	4	no	—
226	C₈×C₄₃	—	4	2	no	—
227	#29854	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₄₃	—	2	2	no	—
229	C₂²×C₄₃	—	2	2	no	—
230	C₂²×C₄₃	—	2	2	no	—
231	C₂²×C₄₃	—	4	1	no	—
232	C₂²×C₄₃	—	4	1	no	—
233	C₂²×C₄₃	—	4	1	no	—
234	C₂²×C₄₃	—	4	1	no	—
235	C₂²×C₄₃	—	8	1	no	—
236	C₂²×C₄₃	—	8	1	no	—
237	C₂²×C₄₃	—	8	1	no	—
238	C₂²×C₄₃	—	8	1	no	—
239	C₂²×C₄₃	—	8	1	no	—
240	C₂²×C₄₃	—	8	1	no	—
241	C₂²×C₄₃	—	8	1	no	—
242	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
243	C₂²×C₄₃	#535	1	1	yes	characteristic
244	C₂²×C₄₃	#536	1	1	yes	characteristic
245	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
247	C₂²×C₄₃	#575	1	1	yes	characteristic
248	C₂²×C₄₃	#575	1	1	yes	characteristic
249	C₄×C₄₃	—	2	2	no	—
250	C₄×C₄₃	—	2	2	no	—
251	C₄×C₄₃	—	2	2	no	—
252	C₄×C₄₃	—	4	1	no	—
253	C₄×C₄₃	—	4	1	no	—
254	C₄×C₄₃	—	8	1	no	—
255	C₄×C₄₃	—	8	1	no	—
256	C₄×C₄₃	—	8	2	no	—
257	C₄×C₄₃	—	8	1	no	—
258	C₄×C₄₃	—	8	2	no	—
259	C₄×C₄₃	#537	1	2	yes	—
260	C₄×C₄₃	#542	1	2	yes	—
261	C₂×#489	C₂×C₄₃	1	1	yes	characteristic, complemented
262	C₂×#432	C₂×C₄₃	1	1	yes	characteristic, complemented
263	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
264	#2850	C₂×C₄₃	1	1	yes	characteristic
265	#2067	C₂×C₄₃	1	2	yes	complemented
266	#2066	C₂×C₄₃	1	2	yes	complemented
267	#2036	C₂×C₄₃	1	2	yes	complemented
268	#2034	C₂×C₄₃	1	2	yes	—
269	#1993	C₂×C₄₃	1	1	yes	characteristic, complemented
270	#1959	C₂×C₄₃	1	1	yes	characteristic, complemented
271	#1847	C₂×C₄₃	1	1	yes	characteristic, complemented
272	C₂×C₄₃	—	4	2	no	—
273	C₂×C₄₃	—	16	1	no	—
274	C₂×C₄₃	#2620	1	1	yes	characteristic
275	C₂×C₄₃	#3055	1	1	yes	characteristic
276	C₂×C₄₃	#3056	1	1	yes	characteristic
277	C₂×C₄₃	#3214	1	1	yes	characteristic
278	C₂×C₄₃	#3215	1	1	yes	characteristic
279	C₂×C₄₃	#3239	1	1	yes	characteristic
280	C₂×C₄₃	#3240	1	1	yes	characteristic
281	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
282	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
283	C₂×C₂²⋊Q₈	—	2	1	no	—
284	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
285	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
286	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
287	#489	—	2	4	no	—
288	#432	—	2	4	no	—
289	C₂×#107	C₂²×C₄₃	1	2	yes	—
290	C₂×#106	C₂²×C₄₃	1	2	yes	—
291	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
292	C₂×#103	C₂²×C₄₃	1	2	yes	—
293	C₂×#103	C₂²×C₄₃	1	2	yes	—
294	C₂×#102	C₂²×C₄₃	1	2	yes	—
295	C₂×#102	C₂²×C₄₃	1	2	yes	—
296	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
297	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
299	#391	—	2	1	no	—
300	#391	C₂²×C₄₃	1	1	yes	characteristic
301	#390	C₂²×C₄₃	1	1	yes	characteristic
302	#389	—	2	1	no	—
303	#389	C₂²×C₄₃	1	2	yes	—
304	#388	—	2	1	no	—
305	#388	—	2	1	no	—
306	#386	—	2	1	no	—
307	#386	—	2	1	no	—
308	#384	C₂²×C₄₃	1	1	yes	characteristic
309	#382	C₂²×C₄₃	1	1	yes	characteristic
310	#380	—	2	1	no	—
311	#380	C₂²×C₄₃	1	2	yes	—
312	#340	C₂²×C₄₃	1	2	yes	—
313	#340	C₂²×C₄₃	1	2	yes	—
314	C₄₃	#29854	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
319	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
320	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
323	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	—	2	2	no	—
326	#124	—	2	2	no	—
327	#124	—	2	2	no	—
328	C₂²⋊Q₈	—	4	2	no	—
329	C₂²⋊Q₈	—	4	4	no	—
330	#121	—	4	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
350	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
353	#107	—	4	2	no	—
354	#106	—	4	2	no	—
355	C₄⋊C₈	—	2	4	no	—
356	#103	—	2	4	no	—
357	#103	—	4	2	no	—
358	#102	—	2	4	no	—
359	#102	—	4	2	no	—
360	C₂²⋊C₈	—	2	4	no	—
361	#97	—	2	2	no	—
362	#97	D₄×C₄₃	1	4	yes	complemented
363	#95	—	2	2	no	—
364	#95	—	2	2	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	C₂⁴	—	2	1	no	—
370	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	4	2	no	—
376	C₂×Q₈	—	4	2	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	2	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	—	4	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	C₂×D₄×C₄₃	1	2	yes	—
435	C₄²	#41×C₄₃	1	2	yes	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	#137×C₄₃	1	2	yes	—
450	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
451	Q₈	—	4	2	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	8	4	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	8	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	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	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	#121×C₄₃	1	2	yes	—
489	C₂×C₄	#121×C₄₃	1	2	yes	—
490	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
492	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
493	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
494	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
495	C₈	—	2	4	no	—
496	C₈	—	4	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	1	no	—
510	C₂²	—	8	1	no	—
511	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
512	C₂²	C₄₃×#535	1	1	yes	characteristic
513	C₂²	C₄₃×#536	1	1	yes	characteristic
514	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
515	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
516	C₂²	C₄₃×#575	1	1	yes	characteristic
517	C₂²	C₄₃×#575	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	—	8	1	no	—
524	C₄	—	8	1	no	—
525	C₄	—	8	2	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	2	no	—
528	C₄	C₄₃×#537	1	2	yes	—
529	C₄	C₄₃×#542	1	2	yes	—
530	C₂	—	4	2	no	—
531	C₂	—	16	1	no	—
532	C₂	C₄₃×#2620	1	1	yes	characteristic
533	C₂	C₄₃×#3055	1	1	yes	characteristic
534	C₂	C₄₃×#3056	1	1	yes	characteristic
535	C₂	C₄₃×#3214	1	1	yes	characteristic
536	C₂	C₄₃×#3215	1	1	yes	characteristic
537	C₂	C₄₃×#3239	1	1	yes	characteristic
538	C₂	C₄₃×#3240	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#489	C₂	semidirect
2. C₂×C₄₃×#432	C₂	semidirect
3. C₄₃×#2857	C₂	semidirect
5. C₄₃×#2067	C₂	semidirect
6. C₄₃×#2066	C₂	semidirect
7. C₄₃×#2036	C₂	semidirect
9. C₄₃×#1993	C₂	semidirect
10. C₄₃×#1959	C₂	semidirect
11. C₄₃×#1847	C₂	semidirect
92. #97×C₄₃	D₄	semidirect
227. #29854	C₄₃	direct (N × H)
261. C₂×#489	C₂×C₄₃	semidirect
262. C₂×#432	C₂×C₄₃	semidirect
263. #2857	C₂×C₄₃	semidirect
265. #2067	C₂×C₄₃	semidirect
266. #2066	C₂×C₄₃	semidirect
267. #2036	C₂×C₄₃	semidirect
269. #1993	C₂×C₄₃	semidirect
270. #1959	C₂×C₄₃	semidirect
271. #1847	C₂×C₄₃	semidirect
314. C₄₃	#29854	direct (N × H)
362. #97	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×#489	2
C₂×C₄₃×#432	2
C₄₃×#2857	2
C₄₃×#2850	2
C₄₃×#2067	2
C₄₃×#2066	2
C₄₃×#2036	2
C₄₃×#2034	2
C₄₃×#1993	2
C₄₃×#1959	2
C₄₃×#1847	2
#29854	43

Subgroups — C43×#29854 #24949871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29854 #24949871