Subgroups — C₄₃×#28544 #24948561

Order 11008.

898 conjugacy classes of subgroups.

The subgroup lattice has 572 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×#474	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×#2563	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2092	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×#1846	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×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#501	—	2	4	no	—
22	C₄₃×#478	—	2	4	no	—
23	C₄₃×#474	—	2	4	no	—
24	C₄₃×#442	—	2	4	no	—
25	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
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×#107×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×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#102×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×#97×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#396	—	2	2	no	—
45	C₄₃×#393	—	2	2	no	—
46	C₄₃×#390	C₂²	1	1	yes	characteristic
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×#385	—	2	2	no	—
51	C₄₃×#384	C₂²	1	1	yes	characteristic
52	C₄₃×#382	C₂²	1	1	yes	characteristic
53	C₄₃×#382	C₂²	1	1	yes	characteristic
54	C₄₃×#382	C₂²	1	1	yes	characteristic
55	C₄₃×#380	—	2	2	no	—
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	C₄×D₄×C₄₃	—	2	2	no	—
76	C₄×D₄×C₄₃	—	2	2	no	—
77	C₄×D₄×C₄₃	—	2	2	no	—
78	C₄×D₄×C₄₃	—	2	2	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	2	no	—
83	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
99	#107×C₄₃	—	2	2	no	—
100	#107×C₄₃	—	2	2	no	—
101	#107×C₄₃	—	2	2	no	—
102	#107×C₄₃	—	2	2	no	—
103	#107×C₄₃	—	2	2	no	—
104	#106×C₄₃	—	2	2	no	—
105	#106×C₄₃	—	2	2	no	—
106	#106×C₄₃	—	2	2	no	—
107	#106×C₄₃	—	2	2	no	—
108	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
109	#102×C₄₃	—	2	2	no	—
110	#102×C₄₃	—	2	2	no	—
111	#102×C₄₃	—	2	2	no	—
112	#102×C₄₃	—	2	2	no	—
113	#102×C₄₃	—	2	2	no	—
114	#102×C₄₃	—	2	2	no	—
115	#97×C₄₃	—	2	2	no	—
116	#97×C₄₃	D₄	1	4	yes	—
117	C₄×C₈×C₄₃	—	2	2	no	—
118	#95×C₄₃	—	2	2	no	—
119	#95×C₄₃	—	2	2	no	—
120	#95×C₄₃	—	2	2	no	—
121	#95×C₄₃	D₄	1	2	yes	—
122	C₂⁴×C₄₃	—	2	1	no	—
123	C₂⁴×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	4	2	no	—
125	C₂×Q₈×C₄₃	—	8	2	no	—
126	C₂×D₄×C₄₃	—	2	1	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	C₂×Q₈	1	2	yes	—
137	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₄₃	—	2	1	no	—
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	—	4	4	no	—
145	C₂²×C₄×C₄₃	—	4	2	no	—
146	C₂²×C₄×C₄₃	—	4	2	no	—
147	C₂²×C₄×C₄₃	—	8	2	no	—
148	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
153	D₈×C₄₃	—	2	8	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	C₂×D₄	1	2	yes	—
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×Q₈	1	2	yes	—
165	C₂×C₈×C₄₃	#41	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	—	4	2	no	—
179	C₄⋊C₄×C₄₃	—	4	2	no	—
180	C₄⋊C₄×C₄₃	—	4	2	no	—
181	C₄⋊C₄×C₄₃	—	4	2	no	—
182	C₄⋊C₄×C₄₃	—	8	2	no	—
183	C₂²⋊C₄×C₄₃	—	4	4	no	—
184	C₂²⋊C₄×C₄₃	—	4	2	no	—
185	C₂²⋊C₄×C₄₃	—	4	2	no	—
186	C₂²⋊C₄×C₄₃	—	8	2	no	—
187	C₂²⋊C₄×C₄₃	—	8	2	no	—
188	C₂²⋊C₄×C₄₃	—	8	2	no	—
189	C₄²×C₄₃	—	2	1	no	—
190	C₄²×C₄₃	—	2	1	no	—
191	C₄²×C₄₃	—	2	1	no	—
192	C₄²×C₄₃	—	2	1	no	—
193	C₄²×C₄₃	C₂×D₄	1	2	yes	—
194	C₄²×C₄₃	C₂×D₄	1	2	yes	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	2	no	—
197	C₂³×C₄₃	—	4	1	no	—
198	C₂³×C₄₃	—	4	1	no	—
199	C₂³×C₄₃	—	4	1	no	—
200	C₂³×C₄₃	—	4	1	no	—
201	C₂³×C₄₃	—	4	2	no	—
202	C₂³×C₄₃	—	4	2	no	—
203	C₂³×C₄₃	—	4	2	no	—
204	C₂³×C₄₃	—	4	2	no	—
205	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₄₃	—	8	4	no	—
207	D₄×C₄₃	—	2	2	no	—
208	D₄×C₄₃	—	2	2	no	—
209	D₄×C₄₃	—	2	2	no	—
210	D₄×C₄₃	—	2	2	no	—
211	D₄×C₄₃	—	4	1	no	—
212	D₄×C₄₃	—	4	1	no	—
213	D₄×C₄₃	—	4	1	no	—
214	D₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	2	2	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	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	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	1	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	2	no	—
230	C₂×C₄×C₄₃	—	4	2	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	—	8	4	no	—
236	C₂×C₄×C₄₃	—	8	4	no	—
237	C₂×C₄×C₄₃	#127	1	2	yes	—
238	C₂×C₄×C₄₃	#127	1	2	yes	—
239	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
244	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
245	C₈×C₄₃	—	2	2	no	—
246	C₈×C₄₃	—	2	2	no	—
247	C₈×C₄₃	—	2	2	no	—
248	C₈×C₄₃	C₂²⋊Q₈	1	4	yes	—
249	#28544	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂²×C₄₃	—	4	4	no	—
251	C₂²×C₄₃	—	4	4	no	—
252	C₂²×C₄₃	—	4	2	no	—
253	C₂²×C₄₃	—	4	2	no	—
254	C₂²×C₄₃	—	8	2	no	—
255	C₂²×C₄₃	—	8	2	no	—
256	C₂²×C₄₃	—	8	1	no	—
257	C₂²×C₄₃	—	8	1	no	—
258	C₂²×C₄₃	—	8	1	no	—
259	C₂²×C₄₃	—	8	1	no	—
260	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
261	C₂²×C₄₃	#547	1	1	yes	characteristic
262	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
263	C₂²×C₄₃	#575	1	2	yes	—
264	C₂²×C₄₃	#576	1	2	yes	—
265	C₄×C₄₃	—	2	2	no	—
266	C₄×C₄₃	—	2	2	no	—
267	C₄×C₄₃	—	4	2	no	—
268	C₄×C₄₃	—	4	2	no	—
269	C₄×C₄₃	—	8	1	no	—
270	C₄×C₄₃	—	8	1	no	—
271	C₄×C₄₃	—	8	1	no	—
272	C₄×C₄₃	—	8	1	no	—
273	C₄×C₄₃	—	8	1	no	—
274	C₄×C₄₃	—	8	1	no	—
275	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
276	C₄×C₄₃	#536	1	1	yes	characteristic
277	C₄×C₄₃	#547	1	1	yes	characteristic
278	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
279	C₂×#501	C₂×C₄₃	1	1	yes	characteristic, complemented
280	C₂×#478	C₂×C₄₃	1	1	yes	characteristic, complemented
281	C₂×#474	C₂×C₄₃	1	1	yes	characteristic, complemented
282	C₂×#442	C₂×C₄₃	1	1	yes	characteristic
283	#2566	C₂×C₄₃	1	1	yes	characteristic, complemented
284	#2563	C₂×C₄₃	1	1	yes	characteristic, complemented
285	#2093	C₂×C₄₃	1	1	yes	characteristic, complemented
286	#2092	C₂×C₄₃	1	1	yes	characteristic, complemented
287	#2092	C₂×C₄₃	1	1	yes	characteristic, complemented
288	#2092	C₂×C₄₃	1	1	yes	characteristic, complemented
289	#1972	C₂×C₄₃	1	1	yes	characteristic
290	#1970	C₂×C₄₃	1	1	yes	characteristic
291	#1847	C₂×C₄₃	1	1	yes	characteristic, complemented
292	#1846	C₂×C₄₃	1	1	yes	characteristic, complemented
293	#1771	C₂×C₄₃	1	1	yes	characteristic, complemented
294	C₂×C₄₃	—	8	2	no	—
295	C₂×C₄₃	—	8	2	no	—
296	C₂×C₄₃	#2542	1	1	yes	characteristic
297	C₂×C₄₃	#3153	1	1	yes	characteristic
298	C₂×C₄₃	#3155	1	1	yes	characteristic
299	C₂×C₄₃	#3347	1	2	yes	—
300	C₂×C₄₃	#3389	1	2	yes	—
301	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
302	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
303	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
306	#501	—	2	4	no	—
307	#478	—	2	4	no	—
308	#474	—	2	4	no	—
309	#442	—	2	4	no	—
310	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
311	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
313	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
314	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
315	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
316	C₂×#106	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×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
320	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
321	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
322	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
323	C₂×#102	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×#97	C₂²×C₄₃	1	1	yes	characteristic
327	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
328	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
329	#396	—	2	2	no	—
330	#393	—	2	2	no	—
331	#390	C₂²×C₄₃	1	1	yes	characteristic
332	#390	C₂²×C₄₃	1	1	yes	characteristic
333	#390	C₂²×C₄₃	1	1	yes	characteristic
334	#390	C₂²×C₄₃	1	1	yes	characteristic
335	#385	—	2	2	no	—
336	#384	C₂²×C₄₃	1	1	yes	characteristic
337	#382	C₂²×C₄₃	1	1	yes	characteristic
338	#382	C₂²×C₄₃	1	1	yes	characteristic
339	#382	C₂²×C₄₃	1	1	yes	characteristic
340	#380	—	2	2	no	—
341	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
342	#336	C₂²×C₄₃	1	1	yes	characteristic
343	#336	C₂²×C₄₃	1	1	yes	characteristic
344	C₄₃	#28544	1	1	yes	characteristic, direct product factor, Sylow
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
347	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂×D₈	—	2	2	no	—
351	C₂×D₈	—	2	2	no	—
352	C₂×D₈	Q₈×C₄₃	1	4	yes	complemented
353	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
357	C₄⋊Q₈	—	2	2	no	—
358	C₄⋊Q₈	—	2	2	no	—
359	#125	—	2	2	no	—
360	#125	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
385	#107	—	2	2	no	—
386	#107	—	2	2	no	—
387	#107	—	2	2	no	—
388	#107	—	2	2	no	—
389	#107	—	2	2	no	—
390	#106	—	2	2	no	—
391	#106	—	2	2	no	—
392	#106	—	2	2	no	—
393	#106	—	2	2	no	—
394	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	2	no	—
398	#102	—	2	2	no	—
399	#102	—	2	2	no	—
400	#102	—	2	2	no	—
401	#97	—	2	2	no	—
402	#97	D₄×C₄₃	1	4	yes	—
403	C₄×C₈	—	2	2	no	—
404	#95	—	2	2	no	—
405	#95	—	2	2	no	—
406	#95	—	2	2	no	—
407	#95	D₄×C₄₃	1	2	yes	—
408	C₂⁴	—	2	1	no	—
409	C₂⁴	—	2	1	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	8	2	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	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	C₂×Q₈×C₄₃	1	2	yes	—
423	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	4	4	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	8	2	no	—
434	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
436	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
439	D₈	—	2	8	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
447	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
448	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
449	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
450	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
451	C₂×C₈	#41×C₄₃	1	2	yes	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	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	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	8	2	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	4	2	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	8	2	no	—
473	C₂²⋊C₄	—	8	2	no	—
474	C₂²⋊C₄	—	8	2	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	C₂×D₄×C₄₃	1	2	yes	—
480	C₄²	C₂×D₄×C₄₃	1	2	yes	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
492	Q₈	—	8	4	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	2	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	8	4	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	#127×C₄₃	1	2	yes	—
524	C₂×C₄	#127×C₄₃	1	2	yes	—
525	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
528	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
529	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
530	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
531	C₈	—	2	2	no	—
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	C₂²⋊Q₈×C₄₃	1	4	yes	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	8	2	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
546	C₂²	C₄₃×#547	1	1	yes	characteristic
547	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
548	C₂²	C₄₃×#575	1	2	yes	—
549	C₂²	C₄₃×#576	1	2	yes	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	1	no	—
560	C₄	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
561	C₄	C₄₃×#536	1	1	yes	characteristic
562	C₄	C₄₃×#547	1	1	yes	characteristic
563	C₄	D₄×Q₈×C₄₃	1	1	yes	characteristic
564	C₂	—	8	2	no	—
565	C₂	—	8	2	no	—
566	C₂	C₄₃×#2542	1	1	yes	characteristic
567	C₂	C₄₃×#3153	1	1	yes	characteristic
568	C₂	C₄₃×#3155	1	1	yes	characteristic
569	C₂	C₄₃×#3347	1	2	yes	—
570	C₂	C₄₃×#3389	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×#474	C₂	semidirect
5. C₄₃×#2566	C₂	semidirect
6. C₄₃×#2563	C₂	semidirect
7. C₄₃×#2093	C₂	semidirect
8. C₄₃×#2092	C₂	semidirect
9. C₄₃×#2092	C₂	semidirect
10. C₄₃×#2092	C₂	semidirect
13. C₄₃×#1847	C₂	semidirect
14. C₄₃×#1846	C₂	semidirect
15. C₄₃×#1771	C₂	semidirect
66. C₂×D₈×C₄₃	Q₈	semidirect
249. #28544	C₄₃	direct (N × H)
279. C₂×#501	C₂×C₄₃	semidirect
280. C₂×#478	C₂×C₄₃	semidirect
281. C₂×#474	C₂×C₄₃	semidirect
283. #2566	C₂×C₄₃	semidirect
284. #2563	C₂×C₄₃	semidirect
285. #2093	C₂×C₄₃	semidirect
286. #2092	C₂×C₄₃	semidirect
287. #2092	C₂×C₄₃	semidirect
288. #2092	C₂×C₄₃	semidirect
291. #1847	C₂×C₄₃	semidirect
292. #1846	C₂×C₄₃	semidirect
293. #1771	C₂×C₄₃	semidirect
344. C₄₃	#28544	direct (N × H)
352. C₂×D₈	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×#474	2
C₂×C₄₃×#442	2
C₄₃×#2566	2
C₄₃×#2563	2
C₄₃×#2093	2
C₄₃×#2092	2
C₄₃×#1972	2
C₄₃×#1970	2
C₄₃×#1847	2
C₄₃×#1846	2
C₄₃×#1771	2
#28544	43

Subgroups — C43×#28544 #24948561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28544 #24948561