Subgroups — C₄₃×#29928 #24949945

Order 11008.

798 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2035	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2033	C₂	1	2	yes	maximal
9	C₄₃×#1983	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1949	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₃	—	2	1	no	—
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#107×C₄₃	C₂²	1	2	yes	—
18	C₂×#106×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
20	C₂×#103×C₄₃	C₂²	1	2	yes	—
21	C₂×#103×C₄₃	C₂²	1	2	yes	—
22	C₂×#102×C₄₃	C₂²	1	2	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
25	C₄₃×#391	C₂²	1	1	yes	characteristic
26	C₄₃×#390	C₂²	1	1	yes	characteristic
27	C₄₃×#388	—	2	1	no	—
28	C₄₃×#388	—	2	1	no	—
29	C₄₃×#386	—	2	1	no	—
30	C₄₃×#386	—	2	1	no	—
31	C₄₃×#384	C₂²	1	1	yes	characteristic
32	C₄₃×#384	C₂²	1	1	yes	characteristic
33	C₄₃×#382	—	2	1	no	—
34	C₄₃×#382	C₂²	1	1	yes	characteristic
35	C₄₃×#380	—	2	1	no	—
36	C₄₃×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
38	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#336	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
51	#124×C₄₃	—	2	4	no	—
52	C₂²⋊Q₈×C₄₃	—	4	2	no	—
53	#121×C₄₃	—	4	2	no	—
54	#117×C₄₃	—	4	4	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄²×C₄₃	—	2	4	no	—
72	C₂×C₄²×C₄₃	—	2	2	no	—
73	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#107×C₄₃	—	4	2	no	—
78	#106×C₄₃	—	4	2	no	—
79	C₄⋊C₈×C₄₃	—	2	4	no	—
80	#103×C₄₃	—	4	2	no	—
81	#103×C₄₃	—	4	2	no	—
82	#102×C₄₃	—	4	2	no	—
83	#102×C₄₃	—	4	2	no	—
84	C₂²⋊C₈×C₄₃	—	4	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	2	no	—
87	#95×C₄₃	—	2	1	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	—	2	1	no	—
90	#95×C₄₃	—	2	1	no	—
91	C₂⁴×C₄₃	—	2	1	no	—
92	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	1	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	1	no	—
101	C₂×D₄×C₄₃	—	4	2	no	—
102	C₂×D₄×C₄₃	—	4	2	no	—
103	C₂×D₄×C₄₃	—	4	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	4	1	no	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	4	2	no	—
138	C₄⋊C₄×C₄₃	—	4	2	no	—
139	C₄⋊C₄×C₄₃	—	4	2	no	—
140	C₄⋊C₄×C₄₃	—	4	2	no	—
141	C₄⋊C₄×C₄₃	—	4	2	no	—
142	C₂²⋊C₄×C₄₃	—	4	2	no	—
143	C₂²⋊C₄×C₄₃	—	4	2	no	—
144	C₂²⋊C₄×C₄₃	—	4	2	no	—
145	C₂²⋊C₄×C₄₃	—	4	2	no	—
146	C₂²⋊C₄×C₄₃	—	4	2	no	—
147	C₂²⋊C₄×C₄₃	—	4	2	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₄²×C₄₃	—	2	2	no	—
151	C₄²×C₄₃	—	2	2	no	—
152	C₄²×C₄₃	—	4	4	no	—
153	C₄²×C₄₃	#41	1	4	yes	—
154	C₂³×C₄₃	—	2	1	no	—
155	C₂³×C₄₃	—	2	1	no	—
156	C₂³×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	4	1	no	—
161	C₂³×C₄₃	—	4	1	no	—
162	C₂³×C₄₃	—	4	1	no	—
163	C₂³×C₄₃	—	4	1	no	—
164	C₂³×C₄₃	—	4	1	no	—
165	C₂³×C₄₃	—	4	1	no	—
166	C₂³×C₄₃	—	4	1	no	—
167	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
168	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₄₃	—	4	2	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	D₄×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	4	2	no	—
173	D₄×C₄₃	—	8	4	no	—
174	C₂×C₄×C₄₃	—	2	8	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	2	1	no	—
183	C₂×C₄×C₄₃	—	2	1	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	4	4	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	1	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	4	1	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	1	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	#123	1	2	yes	—
205	C₂×C₄×C₄₃	#123	1	2	yes	—
206	C₂×C₄×C₄₃	#135	1	2	yes	—
207	C₂×C₄×C₄₃	#137	1	2	yes	—
208	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
209	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
211	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₄₃	—	4	2	no	—
213	C₈×C₄₃	—	4	2	no	—
214	#29928	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₃	—	2	2	no	—
216	C₂²×C₄₃	—	2	2	no	—
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	4	1	no	—
219	C₂²×C₄₃	—	4	1	no	—
220	C₂²×C₄₃	—	4	1	no	—
221	C₂²×C₄₃	—	4	1	no	—
222	C₂²×C₄₃	—	8	1	no	—
223	C₂²×C₄₃	—	8	1	no	—
224	C₂²×C₄₃	—	8	1	no	—
225	C₂²×C₄₃	—	8	1	no	—
226	C₂²×C₄₃	—	8	1	no	—
227	C₂²×C₄₃	—	8	1	no	—
228	C₂²×C₄₃	—	8	1	no	—
229	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
230	C₂²×C₄₃	#535	1	1	yes	characteristic
231	C₂²×C₄₃	#537	1	1	yes	characteristic
232	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
233	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
235	C₂²×C₄₃	#575	1	1	yes	characteristic
236	C₄×C₄₃	—	2	2	no	—
237	C₄×C₄₃	—	2	2	no	—
238	C₄×C₄₃	—	2	2	no	—
239	C₄×C₄₃	—	2	2	no	—
240	C₄×C₄₃	—	4	1	no	—
241	C₄×C₄₃	—	8	1	no	—
242	C₄×C₄₃	—	8	1	no	—
243	C₄×C₄₃	—	8	2	no	—
244	C₄×C₄₃	—	8	1	no	—
245	C₄×C₄₃	—	8	2	no	—
246	C₄×C₄₃	#540	1	2	yes	—
247	C₄×C₄₃	#542	1	2	yes	—
248	#2850	C₂×C₄₃	1	1	yes	characteristic
249	#2285	C₂×C₄₃	1	1	yes	characteristic, complemented
250	#2095	C₂×C₄₃	1	1	yes	characteristic, complemented
251	#2094	C₂×C₄₃	1	1	yes	characteristic, complemented
252	#2072	C₂×C₄₃	1	1	yes	characteristic, complemented
253	#2071	C₂×C₄₃	1	1	yes	characteristic, complemented
254	#2035	C₂×C₄₃	1	2	yes	complemented
255	#2033	C₂×C₄₃	1	2	yes	—
256	#1983	C₂×C₄₃	1	2	yes	complemented
257	#1949	C₂×C₄₃	1	2	yes	complemented
258	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
259	C₂×C₄₃	—	4	2	no	—
260	C₂×C₄₃	—	16	1	no	—
261	C₂×C₄₃	#2624	1	1	yes	characteristic
262	C₂×C₄₃	#3091	1	1	yes	characteristic
263	C₂×C₄₃	#3092	1	1	yes	characteristic
264	C₂×C₄₃	#3210	1	1	yes	characteristic
265	C₂×C₄₃	#3213	1	1	yes	characteristic
266	C₂×C₄₃	#3247	1	1	yes	characteristic
267	C₂×C₄₃	#3252	1	1	yes	characteristic
268	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
269	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
270	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
271	C₂×#117	—	2	1	no	—
272	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
273	C₂×#107	C₂²×C₄₃	1	2	yes	—
274	C₂×#106	C₂²×C₄₃	1	2	yes	—
275	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
276	C₂×#103	C₂²×C₄₃	1	2	yes	—
277	C₂×#103	C₂²×C₄₃	1	2	yes	—
278	C₂×#102	C₂²×C₄₃	1	2	yes	—
279	C₂×#102	C₂²×C₄₃	1	2	yes	—
280	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
281	#391	C₂²×C₄₃	1	1	yes	characteristic
282	#390	C₂²×C₄₃	1	1	yes	characteristic
283	#388	—	2	1	no	—
284	#388	—	2	1	no	—
285	#386	—	2	1	no	—
286	#386	—	2	1	no	—
287	#384	C₂²×C₄₃	1	1	yes	characteristic
288	#384	C₂²×C₄₃	1	1	yes	characteristic
289	#382	—	2	1	no	—
290	#382	C₂²×C₄₃	1	1	yes	characteristic
291	#380	—	2	1	no	—
292	#380	C₂²×C₄₃	1	2	yes	—
293	C₄×C₄⋊C₄	—	2	1	no	—
294	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
295	#340	C₂²×C₄₃	1	2	yes	—
296	#340	C₂²×C₄₃	1	2	yes	—
297	#336	C₂²×C₄₃	1	1	yes	characteristic
298	#336	C₂²×C₄₃	1	1	yes	characteristic
299	C₄₃	#29928	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
303	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
304	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
307	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
308	#124	—	2	4	no	—
309	C₂²⋊Q₈	—	4	2	no	—
310	#121	—	4	2	no	—
311	#117	—	4	4	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₄²	—	2	4	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
331	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
334	#107	—	4	2	no	—
335	#106	—	4	2	no	—
336	C₄⋊C₈	—	2	4	no	—
337	#103	—	4	2	no	—
338	#103	—	4	2	no	—
339	#102	—	4	2	no	—
340	#102	—	4	2	no	—
341	C₂²⋊C₈	—	4	2	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	#95	—	2	1	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	4	2	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	4	4	no	—
410	C₄²	#41×C₄₃	1	4	yes	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
425	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	8	4	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	#123×C₄₃	1	2	yes	—
462	C₂×C₄	#123×C₄₃	1	2	yes	—
463	C₂×C₄	#135×C₄₃	1	2	yes	—
464	C₂×C₄	#137×C₄₃	1	2	yes	—
465	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
466	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
467	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
468	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
469	C₈	—	4	2	no	—
470	C₈	—	4	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	—	8	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	—	8	1	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
486	C₂²	C₄₃×#535	1	1	yes	characteristic
487	C₂²	C₄₃×#537	1	1	yes	characteristic
488	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
489	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
490	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
491	C₂²	C₄₃×#575	1	1	yes	characteristic
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	2	no	—
501	C₄	—	8	2	no	—
502	C₄	C₄₃×#540	1	2	yes	—
503	C₄	C₄₃×#542	1	2	yes	—
504	C₂	—	4	2	no	—
505	C₂	—	16	1	no	—
506	C₂	C₄₃×#2624	1	1	yes	characteristic
507	C₂	C₄₃×#3091	1	1	yes	characteristic
508	C₂	C₄₃×#3092	1	1	yes	characteristic
509	C₂	C₄₃×#3210	1	1	yes	characteristic
510	C₂	C₄₃×#3213	1	1	yes	characteristic
511	C₂	C₄₃×#3247	1	1	yes	characteristic
512	C₂	C₄₃×#3252	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
2. C₄₃×#2285	C₂	semidirect
3. C₄₃×#2095	C₂	semidirect
4. C₄₃×#2094	C₂	semidirect
5. C₄₃×#2072	C₂	semidirect
6. C₄₃×#2071	C₂	semidirect
7. C₄₃×#2035	C₂	semidirect
9. C₄₃×#1983	C₂	semidirect
10. C₄₃×#1949	C₂	semidirect
11. C₄₃×#1797	C₂	semidirect
214. #29928	C₄₃	direct (N × H)
249. #2285	C₂×C₄₃	semidirect
250. #2095	C₂×C₄₃	semidirect
251. #2094	C₂×C₄₃	semidirect
252. #2072	C₂×C₄₃	semidirect
253. #2071	C₂×C₄₃	semidirect
254. #2035	C₂×C₄₃	semidirect
256. #1983	C₂×C₄₃	semidirect
257. #1949	C₂×C₄₃	semidirect
258. #1797	C₂×C₄₃	semidirect
299. C₄₃	#29928	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#2850	2
C₄₃×#2285	2
C₄₃×#2095	2
C₄₃×#2094	2
C₄₃×#2072	2
C₄₃×#2071	2
C₄₃×#2035	2
C₄₃×#2033	2
C₄₃×#1983	2
C₄₃×#1949	2
C₄₃×#1797	2
#29928	43

Subgroups — C43×#29928 #24949945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29928 #24949945