Subgroups — C₄₃×#28775 #24948792

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2442	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2440	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1992	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1853	C₂	1	1	yes	maximal, characteristic
12	C₄₃×#1852	C₂	1	1	yes	maximal, characteristic
13	C₄₃×#1808	C₂	1	1	yes	maximal, characteristic
14	C₄₃×#1752	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄₃×#340	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#400	—	2	1	no	—
32	C₄₃×#398	—	2	1	no	—
33	C₄₃×#398	—	2	1	no	—
34	C₄₃×#395	—	2	1	no	—
35	C₄₃×#389	C₂²	1	1	yes	characteristic
36	C₄₃×#389	C₂²	1	1	yes	characteristic
37	C₄₃×#389	C₂²	1	1	yes	characteristic
38	C₄₃×#389	C₂²	1	1	yes	characteristic
39	C₄₃×#385	—	2	1	no	—
40	C₄₃×#385	—	2	1	no	—
41	C₄₃×#384	C₂²	1	1	yes	characteristic
42	C₄₃×#382	C₂²	1	1	yes	characteristic
43	C₄₃×#380	—	2	1	no	—
44	C₄₃×#380	C₂²	1	1	yes	characteristic
45	C₄₃×#380	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#340	C₂²	1	1	yes	characteristic
48	C₄₃×#340	C₂²	1	1	yes	characteristic
49	C₄₃×#340	C₂²	1	1	yes	characteristic
50	C₄₃×#340	C₂²	1	1	yes	characteristic
51	C₄₃×#340	C₂²	1	1	yes	characteristic
52	C₄₃×#340	C₂²	1	1	yes	characteristic
53	C₄₃×#340	C₂²	1	1	yes	characteristic
54	C₄₃×#340	C₂²	1	1	yes	characteristic
55	C₄₃×#340	C₂²	1	1	yes	characteristic
56	C₄₃×#340	C₂²	1	1	yes	characteristic
57	C₄₃×#336	C₂²	1	1	yes	characteristic
58	C₄₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	—	2	1	no	—
61	C₂³×C₄×C₄₃	—	2	1	no	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₃	—	4	1	no	—
64	C₂²×C₈×C₄₃	—	4	1	no	—
65	C₂²×C₈×C₄₃	Q₈	1	4	yes	complemented
66	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₃	—	2	2	no	—
71	C₄⋊Q₈×C₄₃	—	4	1	no	—
72	#125×C₄₃	—	2	2	no	—
73	#125×C₄₃	—	4	1	no	—
74	C₂²⋊Q₈×C₄₃	—	4	4	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	1	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	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
89	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#107×C₄₃	—	2	2	no	—
105	#107×C₄₃	—	4	1	no	—
106	#107×C₄₃	—	4	1	no	—
107	#107×C₄₃	—	4	1	no	—
108	#106×C₄₃	—	2	2	no	—
109	#106×C₄₃	—	4	1	no	—
110	C₂²⋊C₈×C₄₃	Q₈	1	4	yes	complemented
111	#97×C₄₃	—	4	1	no	—
112	#97×C₄₃	—	4	1	no	—
113	#95×C₄₃	—	2	1	no	—
114	#95×C₄₃	—	2	1	no	—
115	#95×C₄₃	—	2	1	no	—
116	#95×C₄₃	—	2	1	no	—
117	#95×C₄₃	—	2	1	no	—
118	#95×C₄₃	—	2	1	no	—
119	#95×C₄₃	—	2	1	no	—
120	#95×C₄₃	—	2	1	no	—
121	#95×C₄₃	D₄	1	1	yes	characteristic
122	#95×C₄₃	D₄	1	1	yes	characteristic
123	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×Q₈×C₄₃	—	4	2	no	—
125	C₂×Q₈×C₄₃	—	4	2	no	—
126	C₂×Q₈×C₄₃	—	8	1	no	—
127	C₂²×C₄×C₄₃	—	2	1	no	—
128	C₂²×C₄×C₄₃	—	2	1	no	—
129	C₂²×C₄×C₄₃	—	2	1	no	—
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	—	2	1	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	1	no	—
139	C₂²×C₄×C₄₃	—	4	2	no	—
140	C₂²×C₄×C₄₃	—	4	2	no	—
141	C₂²×C₄×C₄₃	—	4	2	no	—
142	C₂²×C₄×C₄₃	—	4	2	no	—
143	C₂²×C₄×C₄₃	—	8	1	no	—
144	C₂²×C₄×C₄₃	—	8	1	no	—
145	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
151	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
152	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
153	C₂×C₈×C₄₃	—	2	1	no	—
154	C₂×C₈×C₄₃	—	2	1	no	—
155	C₂×C₈×C₄₃	—	2	1	no	—
156	C₂×C₈×C₄₃	—	2	1	no	—
157	C₂×C₈×C₄₃	—	2	1	no	—
158	C₂×C₈×C₄₃	—	2	1	no	—
159	C₂×C₈×C₄₃	—	2	1	no	—
160	C₂×C₈×C₄₃	—	2	1	no	—
161	C₂×C₈×C₄₃	—	4	4	no	—
162	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
163	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
164	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
165	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
166	C₄⋊C₄×C₄₃	—	2	1	no	—
167	C₄⋊C₄×C₄₃	—	2	1	no	—
168	C₄⋊C₄×C₄₃	—	2	1	no	—
169	C₄⋊C₄×C₄₃	—	2	1	no	—
170	C₄⋊C₄×C₄₃	—	2	1	no	—
171	C₄⋊C₄×C₄₃	—	2	1	no	—
172	C₄⋊C₄×C₄₃	—	2	1	no	—
173	C₄⋊C₄×C₄₃	—	2	1	no	—
174	C₄⋊C₄×C₄₃	—	2	1	no	—
175	C₄⋊C₄×C₄₃	—	2	1	no	—
176	C₄⋊C₄×C₄₃	—	2	1	no	—
177	C₄⋊C₄×C₄₃	—	2	1	no	—
178	C₄⋊C₄×C₄₃	—	2	1	no	—
179	C₄⋊C₄×C₄₃	—	2	1	no	—
180	C₄⋊C₄×C₄₃	—	4	2	no	—
181	C₄⋊C₄×C₄₃	—	4	2	no	—
182	C₄⋊C₄×C₄₃	—	4	2	no	—
183	C₄⋊C₄×C₄₃	—	4	2	no	—
184	C₄⋊C₄×C₄₃	—	4	2	no	—
185	C₄⋊C₄×C₄₃	—	4	2	no	—
186	C₄⋊C₄×C₄₃	—	4	2	no	—
187	C₄⋊C₄×C₄₃	—	4	2	no	—
188	C₄⋊C₄×C₄₃	—	8	1	no	—
189	C₄⋊C₄×C₄₃	—	8	1	no	—
190	C₄⋊C₄×C₄₃	—	8	1	no	—
191	C₄⋊C₄×C₄₃	#41	1	2	yes	—
192	C₄⋊C₄×C₄₃	#41	1	2	yes	—
193	C₂²⋊C₄×C₄₃	—	2	2	no	—
194	C₂²⋊C₄×C₄₃	—	2	2	no	—
195	C₂²⋊C₄×C₄₃	—	4	2	no	—
196	C₂²⋊C₄×C₄₃	—	4	2	no	—
197	C₄²×C₄₃	—	2	1	no	—
198	C₄²×C₄₃	—	2	1	no	—
199	C₄²×C₄₃	—	2	1	no	—
200	C₄²×C₄₃	—	2	1	no	—
201	C₂³×C₄₃	—	2	1	no	—
202	C₂³×C₄₃	—	2	1	no	—
203	C₂³×C₄₃	—	2	1	no	—
204	C₂³×C₄₃	—	2	1	no	—
205	C₂³×C₄₃	C₄⋊Q₈	1	2	yes	—
206	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
207	C₂³×C₄₃	#137	1	2	yes	—
208	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₄₃	—	8	4	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	2	no	—
216	C₂×C₄×C₄₃	—	2	1	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	1	no	—
224	C₂×C₄×C₄₃	—	2	1	no	—
225	C₂×C₄×C₄₃	—	2	1	no	—
226	C₂×C₄×C₄₃	—	2	1	no	—
227	C₂×C₄×C₄₃	—	2	1	no	—
228	C₂×C₄×C₄₃	—	2	1	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	1	no	—
232	C₂×C₄×C₄₃	—	4	1	no	—
233	C₂×C₄×C₄₃	—	4	1	no	—
234	C₂×C₄×C₄₃	—	4	1	no	—
235	C₂×C₄×C₄₃	—	4	1	no	—
236	C₂×C₄×C₄₃	—	4	1	no	—
237	C₂×C₄×C₄₃	—	4	1	no	—
238	C₂×C₄×C₄₃	—	4	1	no	—
239	C₂×C₄×C₄₃	—	4	1	no	—
240	C₂×C₄×C₄₃	—	4	1	no	—
241	C₂×C₄×C₄₃	—	4	1	no	—
242	C₂×C₄×C₄₃	—	4	1	no	—
243	C₂×C₄×C₄₃	—	4	1	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	—	4	1	no	—
249	C₂×C₄×C₄₃	—	4	1	no	—
250	C₂×C₄×C₄₃	—	4	1	no	—
251	C₂×C₄×C₄₃	—	4	1	no	—
252	C₂×C₄×C₄₃	—	8	4	no	—
253	C₂×C₄×C₄₃	—	8	4	no	—
254	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
255	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
256	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
257	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
261	C₈×C₄₃	—	2	2	no	—
262	C₈×C₄₃	—	2	2	no	—
263	C₈×C₄₃	—	2	2	no	—
264	C₈×C₄₃	—	2	2	no	—
265	#28775	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂²×C₄₃	—	2	2	no	—
267	C₂²×C₄₃	—	2	2	no	—
268	C₂²×C₄₃	—	2	2	no	—
269	C₂²×C₄₃	—	2	2	no	—
270	C₂²×C₄₃	—	2	2	no	—
271	C₂²×C₄₃	—	2	2	no	—
272	C₂²×C₄₃	#501	1	4	yes	—
273	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
274	C₂²×C₄₃	#546	1	1	yes	characteristic
275	C₂²×C₄₃	#546	1	1	yes	characteristic
276	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
278	C₂²×C₄₃	#576	1	1	yes	characteristic
279	C₂²×C₄₃	#578	1	1	yes	characteristic
280	C₄×C₄₃	—	2	2	no	—
281	C₄×C₄₃	—	4	1	no	—
282	C₄×C₄₃	—	4	1	no	—
283	C₄×C₄₃	—	4	1	no	—
284	C₄×C₄₃	—	4	2	no	—
285	C₄×C₄₃	—	4	1	no	—
286	C₄×C₄₃	—	4	2	no	—
287	C₄×C₄₃	—	8	1	no	—
288	C₄×C₄₃	—	8	1	no	—
289	C₄×C₄₃	—	8	1	no	—
290	C₄×C₄₃	—	8	1	no	—
291	C₄×C₄₃	—	8	1	no	—
292	C₄×C₄₃	—	8	1	no	—
293	C₄×C₄₃	#533	1	1	yes	characteristic
294	C₄×C₄₃	#543	1	1	yes	characteristic
295	C₄×C₄₃	#554	1	1	yes	characteristic
296	C₄×C₄₃	#554	1	1	yes	characteristic
297	#2442	C₂×C₄₃	1	1	yes	characteristic
298	#2440	C₂×C₄₃	1	1	yes	characteristic
299	#2085	C₂×C₄₃	1	1	yes	characteristic, complemented
300	#2083	C₂×C₄₃	1	1	yes	characteristic, complemented
301	#2059	C₂×C₄₃	1	1	yes	characteristic, complemented
302	#2057	C₂×C₄₃	1	1	yes	characteristic, complemented
303	#1993	C₂×C₄₃	1	1	yes	characteristic, complemented
304	#1992	C₂×C₄₃	1	1	yes	characteristic, complemented
305	#1944	C₂×C₄₃	1	1	yes	characteristic, complemented
306	#1943	C₂×C₄₃	1	1	yes	characteristic, complemented
307	#1853	C₂×C₄₃	1	1	yes	characteristic
308	#1852	C₂×C₄₃	1	1	yes	characteristic
309	#1808	C₂×C₄₃	1	1	yes	characteristic
310	#1752	C₂×C₄₃	1	1	yes	characteristic
311	C₂×#340	C₂×C₄₃	1	1	yes	characteristic
312	C₂×C₄₃	—	2	4	no	—
313	C₂×C₄₃	#2549	1	1	yes	characteristic
314	C₂×C₄₃	C₂×#501	1	1	yes	characteristic
315	C₂×C₄₃	#3164	1	1	yes	characteristic
316	C₂×C₄₃	#3308	1	1	yes	characteristic
317	C₂×C₄₃	#3312	1	1	yes	characteristic
318	C₂×C₄₃	#3314	1	1	yes	characteristic
319	C₂×C₄₃	#3318	1	1	yes	characteristic
320	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
321	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
322	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
323	C₂×C₂²⋊Q₈	—	2	1	no	—
324	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
326	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
327	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
328	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
329	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
330	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
331	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
332	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
333	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
334	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
335	#400	—	2	1	no	—
336	#398	—	2	1	no	—
337	#398	—	2	1	no	—
338	#395	—	2	1	no	—
339	#389	C₂²×C₄₃	1	1	yes	characteristic
340	#389	C₂²×C₄₃	1	1	yes	characteristic
341	#389	C₂²×C₄₃	1	1	yes	characteristic
342	#389	C₂²×C₄₃	1	1	yes	characteristic
343	#385	—	2	1	no	—
344	#385	—	2	1	no	—
345	#384	C₂²×C₄₃	1	1	yes	characteristic
346	#382	C₂²×C₄₃	1	1	yes	characteristic
347	#380	—	2	1	no	—
348	#380	C₂²×C₄₃	1	1	yes	characteristic
349	#380	C₂²×C₄₃	1	1	yes	characteristic
350	C₄×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
351	#340	C₂²×C₄₃	1	1	yes	characteristic
352	#340	C₂²×C₄₃	1	1	yes	characteristic
353	#340	C₂²×C₄₃	1	1	yes	characteristic
354	#340	C₂²×C₄₃	1	1	yes	characteristic
355	#340	C₂²×C₄₃	1	1	yes	characteristic
356	#340	C₂²×C₄₃	1	1	yes	characteristic
357	#340	C₂²×C₄₃	1	1	yes	characteristic
358	#340	C₂²×C₄₃	1	1	yes	characteristic
359	#340	C₂²×C₄₃	1	1	yes	characteristic
360	#340	C₂²×C₄₃	1	1	yes	characteristic
361	#336	C₂²×C₄₃	1	1	yes	characteristic
362	#336	C₂²×C₄₃	1	1	yes	characteristic
363	C₄₃	#28775	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²×Q₈	—	2	1	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
368	C₂²×C₈	—	4	1	no	—
369	C₂²×C₈	—	4	1	no	—
370	C₂²×C₈	Q₈×C₄₃	1	4	yes	complemented
371	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
375	C₄⋊Q₈	—	2	2	no	—
376	C₄⋊Q₈	—	4	1	no	—
377	#125	—	2	2	no	—
378	#125	—	4	1	no	—
379	C₂²⋊Q₈	—	4	4	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	4	1	no	—
394	C₂×C₄⋊C₄	—	4	1	no	—
395	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
409	#107	—	2	2	no	—
410	#107	—	4	1	no	—
411	#107	—	4	1	no	—
412	#107	—	4	1	no	—
413	#106	—	2	2	no	—
414	#106	—	4	1	no	—
415	C₂²⋊C₈	Q₈×C₄₃	1	4	yes	complemented
416	#97	—	4	1	no	—
417	#97	—	4	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	D₄×C₄₃	1	1	yes	characteristic
427	#95	D₄×C₄₃	1	1	yes	characteristic
428	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	2	no	—
431	C₂×Q₈	—	8	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	8	1	no	—
449	C₂²×C₄	—	8	1	no	—
450	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
456	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	4	4	no	—
467	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
468	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
469	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
470	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	8	1	no	—
494	C₄⋊C₄	—	8	1	no	—
495	C₄⋊C₄	—	8	1	no	—
496	C₄⋊C₄	#41×C₄₃	1	2	yes	—
497	C₄⋊C₄	#41×C₄₃	1	2	yes	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	C₄⋊Q₈×C₄₃	1	2	yes	—
511	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
512	C₂³	#137×C₄₃	1	2	yes	—
513	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
514	Q₈	—	8	4	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	8	4	no	—
558	C₂×C₄	—	8	4	no	—
559	C₂×C₄	C₄⋊Q₈×C₄₃	1	2	yes	—
560	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
561	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
562	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
564	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
565	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	C₄₃×#501	1	4	yes	—
577	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
578	C₂²	C₄₃×#546	1	1	yes	characteristic
579	C₂²	C₄₃×#546	1	1	yes	characteristic
580	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
581	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
582	C₂²	C₄₃×#576	1	1	yes	characteristic
583	C₂²	C₄₃×#578	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₄₃×#533	1	1	yes	characteristic
598	C₄	C₄₃×#543	1	1	yes	characteristic
599	C₄	C₄₃×#554	1	1	yes	characteristic
600	C₄	C₄₃×#554	1	1	yes	characteristic
601	C₂	—	2	4	no	—
602	C₂	C₄₃×#2549	1	1	yes	characteristic
603	C₂	C₂×C₄₃×#501	1	1	yes	characteristic
604	C₂	C₄₃×#3164	1	1	yes	characteristic
605	C₂	C₄₃×#3308	1	1	yes	characteristic
606	C₂	C₄₃×#3312	1	1	yes	characteristic
607	C₂	C₄₃×#3314	1	1	yes	characteristic
608	C₂	C₄₃×#3318	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄₃×#2085	C₂	semidirect
4. C₄₃×#2083	C₂	semidirect
5. C₄₃×#2059	C₂	semidirect
6. C₄₃×#2057	C₂	semidirect
7. C₄₃×#1993	C₂	semidirect
8. C₄₃×#1992	C₂	semidirect
9. C₄₃×#1944	C₂	semidirect
10. C₄₃×#1943	C₂	semidirect
65. C₂²×C₈×C₄₃	Q₈	semidirect
110. C₂²⋊C₈×C₄₃	Q₈	semidirect
265. #28775	C₄₃	direct (N × H)
299. #2085	C₂×C₄₃	semidirect
300. #2083	C₂×C₄₃	semidirect
301. #2059	C₂×C₄₃	semidirect
302. #2057	C₂×C₄₃	semidirect
303. #1993	C₂×C₄₃	semidirect
304. #1992	C₂×C₄₃	semidirect
305. #1944	C₂×C₄₃	semidirect
306. #1943	C₂×C₄₃	semidirect
363. C₄₃	#28775	direct (N × H)
370. C₂²×C₈	Q₈×C₄₃	semidirect
415. C₂²⋊C₈	Q₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#2442	2
C₄₃×#2440	2
C₄₃×#2085	2
C₄₃×#2083	2
C₄₃×#2059	2
C₄₃×#2057	2
C₄₃×#1993	2
C₄₃×#1992	2
C₄₃×#1944	2
C₄₃×#1943	2
C₄₃×#1853	2
C₄₃×#1852	2
C₄₃×#1808	2
C₄₃×#1752	2
C₂×C₄₃×#340	2
#28775	43

Subgroups — C43×#28775 #24948792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28775 #24948792