Subgroups — C₄₃×#20926 #24940943

Order 11008.

1802 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#417	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1880	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1878	C₂	1	4	yes	maximal, complemented
8	C₄₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×#137×C₄₃	—	2	4	no	—
13	C₂×#137×C₄₃	—	2	4	no	—
14	C₂×#137×C₄₃	C₄	1	8	yes	complemented
15	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₃	—	2	4	no	—
20	C₂×C₄×Q₈×C₄₃	—	2	4	no	—
21	C₂×C₄×Q₈×C₄₃	—	2	2	no	—
22	C₂×C₄×Q₈×C₄₃	C₂²	1	4	yes	—
23	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
25	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₄₃	—	2	1	no	—
27	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#419	—	2	4	no	—
29	C₄₃×#417	—	2	4	no	—
30	C₂×#103×C₄₃	C₂²	1	4	yes	—
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#102×C₄₃	C₂²	1	2	yes	—
33	C₄₃×#391	C₂²	1	2	yes	—
34	C₄₃×#390	C₂²	1	2	yes	—
35	C₄₃×#386	—	2	1	no	—
36	C₄₃×#386	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
38	C₄₃×#340	C₂²	1	4	yes	—
39	C₄₃×#336	C₂²	1	4	yes	—
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	—	2	2	no	—
42	C₂×#41×C₄₃	—	2	2	no	—
43	C₂×#41×C₄₃	—	2	2	no	—
44	C₂×#41×C₄₃	—	2	2	no	—
45	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
46	C₂²×Q₈×C₄₃	—	2	2	no	—
47	C₂²×Q₈×C₄₃	—	2	1	no	—
48	C₂²×Q₈×C₄₃	—	2	2	no	—
49	C₂²×Q₈×C₄₃	—	2	2	no	—
50	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
51	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
52	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
53	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₄₃	—	2	1	no	—
56	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	—	2	1	no	—
58	C₂³×C₄×C₄₃	—	2	1	no	—
59	C₂³×C₄×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	#137×C₄₃	—	2	32	no	—
64	C₂×Q₁₆×C₄₃	—	2	4	no	—
65	C₂×Q₁₆×C₄₃	—	2	4	no	—
66	C₂×Q₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
67	C₂×SD₁₆×C₄₃	—	2	4	no	—
68	C₂×SD₁₆×C₄₃	—	2	4	no	—
69	C₂×SD₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
70	C₂×M₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	—	2	2	no	—
73	C₂×M₁₆×C₄₃	—	2	2	no	—
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
76	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
78	C₄×Q₈×C₄₃	—	2	16	no	—
79	C₄×Q₈×C₄₃	—	2	8	no	—
80	C₄×Q₈×C₄₃	—	2	8	no	—
81	#117×C₄₃	—	2	2	no	—
82	#117×C₄₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
88	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₄²×C₄₃	—	2	8	no	—
94	C₂×C₄²×C₄₃	—	2	4	no	—
95	C₂×C₄²×C₄₃	—	2	2	no	—
96	C₂×C₄²×C₄₃	—	2	2	no	—
97	C₂×C₄²×C₄₃	—	2	1	no	—
98	C₂×C₄²×C₄₃	D₄	1	2	yes	—
99	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
100	#103×C₄₃	—	2	8	no	—
101	#103×C₄₃	—	2	4	no	—
102	#102×C₄₃	—	2	4	no	—
103	#95×C₄₃	—	2	2	no	—
104	#95×C₄₃	—	2	2	no	—
105	C₂⁴×C₄₃	—	2	1	no	—
106	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
107	#41×C₄₃	—	2	8	no	—
108	#41×C₄₃	—	2	8	no	—
109	#41×C₄₃	—	4	4	no	—
110	#41×C₄₃	—	4	4	no	—
111	C₂×Q₈×C₄₃	—	2	4	no	—
112	C₂×Q₈×C₄₃	—	2	8	no	—
113	C₂×Q₈×C₄₃	—	2	4	no	—
114	C₂×Q₈×C₄₃	—	2	4	no	—
115	C₂×Q₈×C₄₃	—	2	8	no	—
116	C₂×Q₈×C₄₃	—	2	8	no	—
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	2	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	—	2	1	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	2	1	no	—
125	C₂×Q₈×C₄₃	C₂²⋊C₄	1	16	yes	complemented
126	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
127	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
128	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
129	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₄₃	—	2	1	no	—
131	C₂×D₄×C₄₃	—	2	4	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	—	4	2	no	—
137	C₂×D₄×C₄₃	—	4	2	no	—
138	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₄₃	—	2	4	no	—
140	C₂²×C₄×C₄₃	—	2	4	no	—
141	C₂²×C₄×C₄₃	—	2	4	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	4	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	4	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	2	2	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	4	2	no	—
152	C₂²×C₄×C₄₃	—	4	4	no	—
153	C₂²×C₄×C₄₃	—	4	2	no	—
154	C₂²×C₄×C₄₃	—	4	2	no	—
155	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	#41	1	2	yes	—
163	C₂²×C₄×C₄₃	#41	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
165	Q₁₆×C₄₃	—	2	16	no	—
166	SD₁₆×C₄₃	—	2	16	no	—
167	M₁₆×C₄₃	—	2	8	no	—
168	M₁₆×C₄₃	—	4	4	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	2	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
175	C₄⋊C₄×C₄₃	—	2	16	no	—
176	C₄⋊C₄×C₄₃	—	2	4	no	—
177	C₄⋊C₄×C₄₃	—	2	2	no	—
178	C₄⋊C₄×C₄₃	—	2	2	no	—
179	C₄⋊C₄×C₄₃	—	2	2	no	—
180	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
181	C₂²⋊C₄×C₄₃	—	4	4	no	—
182	C₂²⋊C₄×C₄₃	—	4	4	no	—
183	C₂²⋊C₄×C₄₃	—	4	2	no	—
184	C₄²×C₄₃	—	2	16	no	—
185	C₄²×C₄₃	—	2	4	no	—
186	C₄²×C₄₃	—	2	2	no	—
187	C₄²×C₄₃	—	2	2	no	—
188	C₄²×C₄₃	—	4	2	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	2	no	—
191	C₂³×C₄₃	—	2	2	no	—
192	C₂³×C₄₃	—	4	1	no	—
193	C₂³×C₄₃	—	4	1	no	—
194	C₂³×C₄₃	—	4	2	no	—
195	C₂³×C₄₃	—	4	2	no	—
196	C₂³×C₄₃	C₄×D₄	1	2	yes	—
197	C₂³×C₄₃	#120	1	2	yes	—
198	C₂³×C₄₃	#121	1	2	yes	—
199	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₄₃	—	2	4	no	—
201	Q₈×C₄₃	—	2	4	no	—
202	Q₈×C₄₃	—	2	4	no	—
203	Q₈×C₄₃	—	2	16	no	—
204	Q₈×C₄₃	—	2	2	no	—
205	Q₈×C₄₃	—	2	2	no	—
206	Q₈×C₄₃	—	4	1	no	—
207	Q₈×C₄₃	—	4	1	no	—
208	Q₈×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
209	D₄×C₄₃	—	2	2	no	—
210	D₄×C₄₃	—	2	2	no	—
211	D₄×C₄₃	—	4	8	no	—
212	D₄×C₄₃	—	4	1	no	—
213	D₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	2	8	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	16	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	4	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	2	2	no	—
226	C₂×C₄×C₄₃	—	4	4	no	—
227	C₂×C₄×C₄₃	—	4	8	no	—
228	C₂×C₄×C₄₃	—	4	1	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	4	no	—
231	C₂×C₄×C₄₃	—	4	8	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	C₂×C₂²⋊C₄	1	4	yes	—
236	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
237	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₄₃	#120	1	2	yes	—
239	C₂×C₄×C₄₃	#121	1	4	yes	—
240	C₂×C₄×C₄₃	#121	1	2	yes	—
241	C₂×C₄×C₄₃	#123	1	4	yes	—
242	C₂×C₄×C₄₃	#137	1	4	yes	complemented
243	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
249	C₈×C₄₃	—	2	4	no	—
250	C₈×C₄₃	—	4	2	no	—
251	#20926	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂²×C₄₃	—	2	4	no	—
253	C₂²×C₄₃	—	2	2	no	—
254	C₂²×C₄₃	—	2	2	no	—
255	C₂²×C₄₃	—	2	4	no	—
256	C₂²×C₄₃	—	4	4	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	—	8	1	no	—
259	C₂²×C₄₃	—	8	1	no	—
260	C₂²×C₄₃	—	8	2	no	—
261	C₂²×C₄₃	#386	1	4	yes	—
262	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
264	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
265	C₂²×C₄₃	C₂×#137	1	2	yes	—
266	C₂²×C₄₃	#575	1	2	yes	—
267	C₄×C₄₃	—	2	4	no	—
268	C₄×C₄₃	—	2	8	no	—
269	C₄×C₄₃	—	4	2	no	—
270	C₄×C₄₃	—	4	4	no	—
271	C₄×C₄₃	—	4	2	no	—
272	C₄×C₄₃	—	8	2	no	—
273	C₄×C₄₃	#386	1	4	yes	—
274	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
275	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
276	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
277	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
278	C₂²×#137	C₂×C₄₃	1	1	yes	characteristic
279	C₂²×C₄×Q₈	C₂×C₄₃	1	1	yes	characteristic, complemented
280	C₂×#417	C₂×C₄₃	1	1	yes	characteristic
281	C₂×#419	C₂×C₄₃	1	1	yes	characteristic, complemented
282	#2297	C₂×C₄₃	1	1	yes	characteristic
283	#1880	C₂×C₄₃	1	4	yes	complemented
284	#1878	C₂×C₄₃	1	4	yes	complemented
285	#1736	C₂×C₄₃	1	1	yes	characteristic, complemented
286	#1728	C₂×C₄₃	1	1	yes	characteristic, complemented
287	C₂×C₄₃	—	2	4	no	—
288	C₂×C₄₃	—	8	2	no	—
289	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
290	C₂×C₄₃	C₄×#137	1	2	yes	—
291	C₂×C₄₃	#3004	1	1	yes	characteristic
292	C₂×C₄₃	#3005	1	1	yes	characteristic
293	C₂×C₄₃	#3037	1	2	yes	—
294	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
295	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×#137	—	2	4	no	—
297	C₂×#137	—	2	4	no	—
298	C₂×#137	C₄×C₄₃	1	8	yes	complemented
299	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
300	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
301	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
302	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
303	C₂×C₄×Q₈	—	2	4	no	—
304	C₂×C₄×Q₈	—	2	4	no	—
305	C₂×C₄×Q₈	—	2	2	no	—
306	C₂×C₄×Q₈	C₂²×C₄₃	1	4	yes	—
307	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
308	C₂²×C₄⋊C₄	—	2	1	no	—
309	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
310	C₂²×C₄²	—	2	1	no	—
311	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
312	#419	—	2	4	no	—
313	#417	—	2	4	no	—
314	C₂×#103	C₂²×C₄₃	1	4	yes	—
315	C₂×#103	C₂²×C₄₃	1	2	yes	—
316	C₂×#102	C₂²×C₄₃	1	2	yes	—
317	#391	C₂²×C₄₃	1	2	yes	—
318	#390	C₂²×C₄₃	1	2	yes	—
319	#386	—	2	1	no	—
320	#386	—	2	1	no	—
321	C₄×C₂²⋊C₄	—	2	2	no	—
322	#340	C₂²×C₄₃	1	4	yes	—
323	#336	C₂²×C₄₃	1	4	yes	—
324	C₄₃	#20926	1	1	yes	characteristic, direct product factor, Sylow
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
331	C₂²×Q₈	—	2	2	no	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	—	2	2	no	—
334	C₂²×Q₈	—	2	2	no	—
335	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
336	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
337	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
338	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
339	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
346	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
348	#137	—	2	32	no	—
349	C₂×Q₁₆	—	2	4	no	—
350	C₂×Q₁₆	—	2	4	no	—
351	C₂×Q₁₆	C₂×C₄×C₄₃	1	8	yes	complemented
352	C₂×SD₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	2	4	no	—
354	C₂×SD₁₆	C₂×C₄×C₄₃	1	8	yes	complemented
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	C₂×C₄×C₄₃	1	4	yes	—
361	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
362	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
363	C₄×Q₈	—	2	16	no	—
364	C₄×Q₈	—	2	8	no	—
365	C₄×Q₈	—	2	8	no	—
366	#117	—	2	2	no	—
367	#117	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	8	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₄²	—	2	8	no	—
379	C₂×C₄²	—	2	2	no	—
380	C₂×C₄²	—	2	2	no	—
381	C₂×C₄²	—	2	4	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	D₄×C₄₃	1	2	yes	—
384	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
385	#103	—	2	8	no	—
386	#103	—	2	4	no	—
387	#102	—	2	4	no	—
388	#95	—	2	2	no	—
389	#95	—	2	2	no	—
390	C₂⁴	—	2	1	no	—
391	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
392	#41	—	2	8	no	—
393	#41	—	2	8	no	—
394	#41	—	4	4	no	—
395	#41	—	4	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	8	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	8	no	—
401	C₂×Q₈	—	2	8	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	C₂²⋊C₄×C₄₃	1	16	yes	complemented
411	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
412	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	—
413	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
414	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
415	C₂×D₄	—	2	4	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	—	4	2	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
447	C₂²×C₄	#41×C₄₃	1	2	yes	—
448	C₂²×C₄	#41×C₄₃	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
450	Q₁₆	—	2	16	no	—
451	SD₁₆	—	2	16	no	—
452	M₁₆	—	2	8	no	—
453	M₁₆	—	4	4	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
460	C₄⋊C₄	—	2	16	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
466	C₂²⋊C₄	—	4	4	no	—
467	C₂²⋊C₄	—	4	2	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₄²	—	2	16	no	—
470	C₄²	—	2	4	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	4	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	C₄×D₄×C₄₃	1	2	yes	—
482	C₂³	#120×C₄₃	1	2	yes	—
483	C₂³	#121×C₄₃	1	2	yes	—
484	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
485	Q₈	—	2	4	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	4	no	—
488	Q₈	—	2	16	no	—
489	Q₈	—	2	2	no	—
490	Q₈	—	2	2	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	C₂×C₂²⋊C₄×C₄₃	1	8	yes	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	4	8	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	1	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	16	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	8	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
521	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
522	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
523	C₂×C₄	#120×C₄₃	1	2	yes	—
524	C₂×C₄	#121×C₄₃	1	4	yes	—
525	C₂×C₄	#121×C₄₃	1	2	yes	—
526	C₂×C₄	#123×C₄₃	1	4	yes	—
527	C₂×C₄	#137×C₄₃	1	4	yes	complemented
528	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
532	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
533	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
534	C₈	—	2	4	no	—
535	C₈	—	4	2	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	2	no	—
545	C₂²	C₄₃×#386	1	4	yes	—
546	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
547	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
548	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
549	C₂²	C₂×#137×C₄₃	1	2	yes	—
550	C₂²	C₄₃×#575	1	2	yes	—
551	C₄	—	2	4	no	—
552	C₄	—	2	8	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	2	no	—
556	C₄	—	8	2	no	—
557	C₄	C₄₃×#386	1	4	yes	—
558	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
559	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
560	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
561	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
562	C₂	—	2	4	no	—
563	C₂	—	8	2	no	—
564	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
565	C₂	C₄×#137×C₄₃	1	2	yes	—
566	C₂	C₄₃×#3004	1	1	yes	characteristic
567	C₂	C₄₃×#3005	1	1	yes	characteristic
568	C₂	C₄₃×#3037	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂×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. C₂²×C₄×Q₈×C₄₃	C₂	semidirect
4. C₂×C₄₃×#419	C₂	semidirect
6. C₄₃×#1880	C₂	semidirect
7. C₄₃×#1878	C₂	semidirect
8. C₄₃×#1736	C₂	semidirect
9. C₄₃×#1728	C₂	semidirect
14. C₂×#137×C₄₃	C₄	semidirect
66. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
69. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
125. C₂×Q₈×C₄₃	C₂²⋊C₄	semidirect
242. C₂×C₄×C₄₃	#137	semidirect
251. #20926	C₄₃	direct (N × H)
279. C₂²×C₄×Q₈	C₂×C₄₃	semidirect
281. C₂×#419	C₂×C₄₃	semidirect
283. #1880	C₂×C₄₃	semidirect
284. #1878	C₂×C₄₃	semidirect
285. #1736	C₂×C₄₃	semidirect
286. #1728	C₂×C₄₃	semidirect
298. C₂×#137	C₄×C₄₃	semidirect
324. C₄₃	#20926	direct (N × H)
351. C₂×Q₁₆	C₂×C₄×C₄₃	semidirect
354. C₂×SD₁₆	C₂×C₄×C₄₃	semidirect
410. C₂×Q₈	C₂²⋊C₄×C₄₃	semidirect
527. C₂×C₄	#137×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₃	2
C₂²×C₄×Q₈×C₄₃	2
C₂×C₄₃×#417	2
C₂×C₄₃×#419	2
C₄₃×#2297	2
C₄₃×#1880	2
C₄₃×#1878	2
C₄₃×#1736	2
C₄₃×#1728	2
#20926	43

Subgroups — C43×#20926 #24940943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20926 #24940943