Subgroups — C₄₃×#28548 #24948565

Order 11008.

954 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#442	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2566	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1972	C₂	1	1	yes	maximal, characteristic
12	C₄₃×#1970	C₂	1	1	yes	maximal, characteristic
13	C₄₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#1844	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×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	2	no	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#501	—	2	4	no	—
23	C₄₃×#478	—	2	4	no	—
24	C₄₃×#476	—	2	4	no	—
25	C₄₃×#442	—	2	4	no	—
26	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#399	—	2	2	no	—
46	C₄₃×#396	—	2	2	no	—
47	C₄₃×#390	C₂²	1	1	yes	characteristic
48	C₄₃×#390	C₂²	1	1	yes	characteristic
49	C₄₃×#390	C₂²	1	1	yes	characteristic
50	C₄₃×#390	C₂²	1	1	yes	characteristic
51	C₄₃×#385	—	2	2	no	—
52	C₄₃×#384	C₂²	1	1	yes	characteristic
53	C₄₃×#384	C₂²	1	1	yes	characteristic
54	C₄₃×#384	C₂²	1	1	yes	characteristic
55	C₄₃×#382	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₄₃	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	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	—	2	1	no	—
63	C₂³×C₄×C₄₃	—	2	1	no	—
64	C₂×D₈×C₄₃	—	2	2	no	—
65	C₂×D₈×C₄₃	—	2	2	no	—
66	C₂×D₈×C₄₃	Q₈	1	4	yes	complemented
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	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₄₃	—	2	2	no	—
72	C₄⋊Q₈×C₄₃	—	2	2	no	—
73	#125×C₄₃	—	2	2	no	—
74	#125×C₄₃	—	2	2	no	—
75	C₂²⋊Q₈×C₄₃	—	4	8	no	—
76	C₄×D₄×C₄₃	—	2	2	no	—
77	C₄×D₄×C₄₃	—	2	2	no	—
78	C₄×D₄×C₄₃	—	2	2	no	—
79	C₄×D₄×C₄₃	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	2	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	2	no	—
86	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
99	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	#107×C₄₃	—	2	2	no	—
103	#107×C₄₃	—	2	2	no	—
104	#107×C₄₃	—	2	2	no	—
105	#106×C₄₃	—	2	2	no	—
106	#106×C₄₃	—	2	2	no	—
107	#106×C₄₃	—	2	2	no	—
108	#106×C₄₃	—	2	2	no	—
109	#106×C₄₃	—	2	2	no	—
110	#106×C₄₃	—	2	2	no	—
111	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
112	#102×C₄₃	—	2	2	no	—
113	#102×C₄₃	—	2	2	no	—
114	#102×C₄₃	—	2	2	no	—
115	#102×C₄₃	—	2	2	no	—
116	#102×C₄₃	—	2	2	no	—
117	#102×C₄₃	—	2	2	no	—
118	#97×C₄₃	—	2	2	no	—
119	#97×C₄₃	D₄	1	4	yes	—
120	C₄×C₈×C₄₃	—	2	2	no	—
121	#95×C₄₃	—	2	2	no	—
122	#95×C₄₃	D₄	1	2	yes	—
123	C₂⁴×C₄₃	—	2	1	no	—
124	C₂⁴×C₄₃	—	2	1	no	—
125	C₂×Q₈×C₄₃	—	4	4	no	—
126	C₂×Q₈×C₄₃	—	4	2	no	—
127	C₂×D₄×C₄₃	—	2	1	no	—
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	—	2	1	no	—
130	C₂×D₄×C₄₃	—	2	1	no	—
131	C₂×D₄×C₄₃	—	2	1	no	—
132	C₂×D₄×C₄₃	—	2	1	no	—
133	C₂×D₄×C₄₃	—	2	1	no	—
134	C₂×D₄×C₄₃	—	2	1	no	—
135	C₂×D₄×C₄₃	—	2	1	no	—
136	C₂×D₄×C₄₃	—	2	1	no	—
137	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
138	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	—	2	1	no	—
142	C₂²×C₄×C₄₃	—	2	1	no	—
143	C₂²×C₄×C₄₃	—	2	1	no	—
144	C₂²×C₄×C₄₃	—	2	1	no	—
145	C₂²×C₄×C₄₃	—	4	4	no	—
146	C₂²×C₄×C₄₃	—	4	2	no	—
147	C₂²×C₄×C₄₃	—	4	2	no	—
148	C₂²×C₄×C₄₃	—	8	2	no	—
149	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
154	D₈×C₄₃	—	2	8	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	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
166	C₂×C₈×C₄₃	#41	1	2	yes	—
167	C₄⋊C₄×C₄₃	—	2	4	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	4	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	4	no	—
185	C₄⋊C₄×C₄₃	—	8	2	no	—
186	C₂²⋊C₄×C₄₃	—	4	4	no	—
187	C₂²⋊C₄×C₄₃	—	4	2	no	—
188	C₂²⋊C₄×C₄₃	—	4	2	no	—
189	C₂²⋊C₄×C₄₃	—	4	4	no	—
190	C₂²⋊C₄×C₄₃	—	4	4	no	—
191	C₂²⋊C₄×C₄₃	—	8	2	no	—
192	C₄²×C₄₃	—	2	1	no	—
193	C₄²×C₄₃	—	2	1	no	—
194	C₄²×C₄₃	—	2	1	no	—
195	C₄²×C₄₃	—	2	1	no	—
196	C₄²×C₄₃	C₂×D₄	1	2	yes	—
197	C₄²×C₄₃	C₂×D₄	1	2	yes	—
198	C₂³×C₄₃	—	2	2	no	—
199	C₂³×C₄₃	—	2	2	no	—
200	C₂³×C₄₃	—	4	1	no	—
201	C₂³×C₄₃	—	4	1	no	—
202	C₂³×C₄₃	—	4	1	no	—
203	C₂³×C₄₃	—	4	1	no	—
204	C₂³×C₄₃	—	4	2	no	—
205	C₂³×C₄₃	—	4	2	no	—
206	C₂³×C₄₃	—	4	2	no	—
207	C₂³×C₄₃	—	4	2	no	—
208	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₄₃	—	8	4	no	—
210	D₄×C₄₃	—	2	2	no	—
211	D₄×C₄₃	—	2	2	no	—
212	D₄×C₄₃	—	2	2	no	—
213	D₄×C₄₃	—	2	2	no	—
214	D₄×C₄₃	—	4	1	no	—
215	D₄×C₄₃	—	4	1	no	—
216	D₄×C₄₃	—	4	1	no	—
217	D₄×C₄₃	—	4	1	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	—	4	1	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	2	no	—
232	C₂×C₄×C₄₃	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	2	no	—
236	C₂×C₄×C₄₃	—	4	2	no	—
237	C₂×C₄×C₄₃	—	8	4	no	—
238	C₂×C₄×C₄₃	—	8	4	no	—
239	C₂×C₄×C₄₃	#127	1	2	yes	—
240	C₂×C₄×C₄₃	#127	1	2	yes	—
241	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
242	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
247	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
248	C₈×C₄₃	—	2	2	no	—
249	C₈×C₄₃	—	2	2	no	—
250	C₈×C₄₃	—	2	2	no	—
251	C₈×C₄₃	C₂²⋊Q₈	1	4	yes	complemented
252	#28548	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂²×C₄₃	—	4	4	no	—
254	C₂²×C₄₃	—	4	4	no	—
255	C₂²×C₄₃	—	4	2	no	—
256	C₂²×C₄₃	—	4	2	no	—
257	C₂²×C₄₃	—	8	2	no	—
258	C₂²×C₄₃	—	8	2	no	—
259	C₂²×C₄₃	—	8	1	no	—
260	C₂²×C₄₃	—	8	1	no	—
261	C₂²×C₄₃	—	8	1	no	—
262	C₂²×C₄₃	—	8	1	no	—
263	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
264	C₂²×C₄₃	#547	1	1	yes	characteristic
265	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
266	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
267	C₂²×C₄₃	#577	1	2	yes	—
268	C₄×C₄₃	—	2	4	no	—
269	C₄×C₄₃	—	2	2	no	—
270	C₄×C₄₃	—	2	2	no	—
271	C₄×C₄₃	—	4	2	no	—
272	C₄×C₄₃	—	8	1	no	—
273	C₄×C₄₃	—	8	1	no	—
274	C₄×C₄₃	—	8	1	no	—
275	C₄×C₄₃	—	8	1	no	—
276	C₄×C₄₃	—	8	1	no	—
277	C₄×C₄₃	—	8	1	no	—
278	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
279	C₄×C₄₃	#536	1	1	yes	characteristic
280	C₄×C₄₃	#547	1	1	yes	characteristic
281	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
282	C₂×#501	C₂×C₄₃	1	1	yes	characteristic, complemented
283	C₂×#478	C₂×C₄₃	1	1	yes	characteristic, complemented
284	C₂×#476	C₂×C₄₃	1	1	yes	characteristic, complemented
285	C₂×#442	C₂×C₄₃	1	1	yes	characteristic
286	#2566	C₂×C₄₃	1	1	yes	characteristic, complemented
287	#2542	C₂×C₄₃	1	1	yes	characteristic, complemented
288	#2094	C₂×C₄₃	1	1	yes	characteristic, complemented
289	#2094	C₂×C₄₃	1	1	yes	characteristic, complemented
290	#2093	C₂×C₄₃	1	1	yes	characteristic, complemented
291	#2092	C₂×C₄₃	1	1	yes	characteristic, complemented
292	#1972	C₂×C₄₃	1	1	yes	characteristic
293	#1970	C₂×C₄₃	1	1	yes	characteristic
294	#1847	C₂×C₄₃	1	1	yes	characteristic, complemented
295	#1844	C₂×C₄₃	1	1	yes	characteristic, complemented
296	#1771	C₂×C₄₃	1	1	yes	characteristic, complemented
297	C₂×C₄₃	—	8	2	no	—
298	C₂×C₄₃	—	8	2	no	—
299	C₂×C₄₃	#2542	1	1	yes	characteristic
300	C₂×C₄₃	#3151	1	1	yes	characteristic
301	C₂×C₄₃	#3154	1	1	yes	characteristic
302	C₂×C₄₃	#3345	1	2	yes	—
303	C₂×C₄₃	#3384	1	2	yes	—
304	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
305	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
306	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
307	C₂×C₂²⋊Q₈	—	2	2	no	—
308	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
310	#501	—	2	4	no	—
311	#478	—	2	4	no	—
312	#476	—	2	4	no	—
313	#442	—	2	4	no	—
314	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
315	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
316	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
317	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
318	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
319	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
320	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
321	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
322	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
324	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
325	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
326	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
327	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
328	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
329	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
330	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
331	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
333	#399	—	2	2	no	—
334	#396	—	2	2	no	—
335	#390	C₂²×C₄₃	1	1	yes	characteristic
336	#390	C₂²×C₄₃	1	1	yes	characteristic
337	#390	C₂²×C₄₃	1	1	yes	characteristic
338	#390	C₂²×C₄₃	1	1	yes	characteristic
339	#385	—	2	2	no	—
340	#384	C₂²×C₄₃	1	1	yes	characteristic
341	#384	C₂²×C₄₃	1	1	yes	characteristic
342	#384	C₂²×C₄₃	1	1	yes	characteristic
343	#382	C₂²×C₄₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
345	#336	C₂²×C₄₃	1	1	yes	characteristic
346	#336	C₂²×C₄₃	1	1	yes	characteristic
347	C₄₃	#28548	1	1	yes	characteristic, direct product factor, Sylow
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
350	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	—	2	1	no	—
353	C₂×D₈	—	2	2	no	—
354	C₂×D₈	—	2	2	no	—
355	C₂×D₈	Q₈×C₄₃	1	4	yes	complemented
356	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	—	2	2	no	—
362	#125	—	2	2	no	—
363	#125	—	2	2	no	—
364	C₂²⋊Q₈	—	4	8	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
391	#107	—	2	2	no	—
392	#107	—	2	2	no	—
393	#107	—	2	2	no	—
394	#106	—	2	2	no	—
395	#106	—	2	2	no	—
396	#106	—	2	2	no	—
397	#106	—	2	2	no	—
398	#106	—	2	2	no	—
399	#106	—	2	2	no	—
400	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	#102	—	2	2	no	—
407	#97	—	2	2	no	—
408	#97	D₄×C₄₃	1	4	yes	—
409	C₄×C₈	—	2	2	no	—
410	#95	—	2	2	no	—
411	#95	D₄×C₄₃	1	2	yes	—
412	C₂⁴	—	2	1	no	—
413	C₂⁴	—	2	1	no	—
414	C₂×Q₈	—	4	4	no	—
415	C₂×Q₈	—	4	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
427	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	8	2	no	—
438	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
443	D₈	—	2	8	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
451	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
452	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
453	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
454	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
455	C₂×C₈	#41×C₄₃	1	2	yes	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	4	4	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	4	no	—
474	C₄⋊C₄	—	8	2	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	4	no	—
480	C₂²⋊C₄	—	8	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	C₂×D₄×C₄₃	1	2	yes	—
486	C₄²	C₂×D₄×C₄₃	1	2	yes	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
498	Q₈	—	8	4	no	—
499	D₄	—	2	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	2	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	8	4	no	—
527	C₂×C₄	—	8	4	no	—
528	C₂×C₄	#127×C₄₃	1	2	yes	—
529	C₂×C₄	#127×C₄₃	1	2	yes	—
530	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
531	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
534	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
535	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
536	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
537	C₈	—	2	2	no	—
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₈	C₂²⋊Q₈×C₄₃	1	4	yes	complemented
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
552	C₂²	C₄₃×#547	1	1	yes	characteristic
553	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
554	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
555	C₂²	C₄₃×#577	1	2	yes	—
556	C₄	—	2	4	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
567	C₄	C₄₃×#536	1	1	yes	characteristic
568	C₄	C₄₃×#547	1	1	yes	characteristic
569	C₄	D₄×Q₈×C₄₃	1	1	yes	characteristic
570	C₂	—	8	2	no	—
571	C₂	—	8	2	no	—
572	C₂	C₄₃×#2542	1	1	yes	characteristic
573	C₂	C₄₃×#3151	1	1	yes	characteristic
574	C₂	C₄₃×#3154	1	1	yes	characteristic
575	C₂	C₄₃×#3345	1	2	yes	—
576	C₂	C₄₃×#3384	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₈×C₄₃	C₂²
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×#501	C₂	semidirect
2. C₂×C₄₃×#478	C₂	semidirect
3. C₂×C₄₃×#476	C₂	semidirect
5. C₄₃×#2566	C₂	semidirect
6. C₄₃×#2542	C₂	semidirect
7. C₄₃×#2094	C₂	semidirect
8. C₄₃×#2094	C₂	semidirect
9. C₄₃×#2093	C₂	semidirect
10. C₄₃×#2092	C₂	semidirect
13. C₄₃×#1847	C₂	semidirect
14. C₄₃×#1844	C₂	semidirect
15. C₄₃×#1771	C₂	semidirect
66. C₂×D₈×C₄₃	Q₈	semidirect
251. C₈×C₄₃	C₂²⋊Q₈	semidirect
252. #28548	C₄₃	direct (N × H)
282. C₂×#501	C₂×C₄₃	semidirect
283. C₂×#478	C₂×C₄₃	semidirect
284. C₂×#476	C₂×C₄₃	semidirect
286. #2566	C₂×C₄₃	semidirect
287. #2542	C₂×C₄₃	semidirect
288. #2094	C₂×C₄₃	semidirect
289. #2094	C₂×C₄₃	semidirect
290. #2093	C₂×C₄₃	semidirect
291. #2092	C₂×C₄₃	semidirect
294. #1847	C₂×C₄₃	semidirect
295. #1844	C₂×C₄₃	semidirect
296. #1771	C₂×C₄₃	semidirect
347. C₄₃	#28548	direct (N × H)
355. C₂×D₈	Q₈×C₄₃	semidirect
540. C₈	C₂²⋊Q₈×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×#501	2
C₂×C₄₃×#478	2
C₂×C₄₃×#476	2
C₂×C₄₃×#442	2
C₄₃×#2566	2
C₄₃×#2542	2
C₄₃×#2094	2
C₄₃×#2093	2
C₄₃×#2092	2
C₄₃×#1972	2
C₄₃×#1970	2
C₄₃×#1847	2
C₄₃×#1844	2
C₄₃×#1771	2
#28548	43

Subgroups — C43×#28548 #24948565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28548 #24948565