Subgroups — C₄₃×#23487 #24943504

Order 11008.

1418 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#103×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2311	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#2036	C₂	1	4	yes	maximal, complemented
8	C₄₃×#2035	C₂	1	4	yes	maximal, complemented
9	C₄₃×#1736	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	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#536	—	2	4	no	—
15	C₄₃×#536	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
17	C₂×#124×C₄₃	—	2	1	no	—
18	C₂×#123×C₄₃	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	—
20	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#427	—	2	4	no	—
24	C₂×#107×C₄₃	C₂²	1	2	yes	—
25	C₂×#106×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#419	—	2	4	no	—
27	C₂×#103×C₄₃	—	2	4	no	—
28	C₂×#103×C₄₃	C₂²	1	2	yes	—
29	C₂×#103×C₄₃	C₂²	1	2	yes	—
30	C₂×#103×C₄₃	C₂²	1	4	yes	—
31	C₄₃×#408	—	2	4	no	—
32	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
34	C₄₃×#391	—	2	1	no	—
35	C₄₃×#390	—	2	1	no	—
36	C₄₃×#386	—	2	2	no	—
37	C₄₃×#380	C₂²	1	4	yes	—
38	C₄₃×#340	C₂²	1	4	yes	—
39	C₂×#41×C₄₃	—	2	2	no	—
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	C₂²×Q₈×C₄₃	—	2	1	no	—
46	C₂²×Q₈×C₄₃	—	2	2	no	—
47	C₂²×Q₈×C₄₃	—	2	2	no	—
48	C₂²×Q₈×C₄₃	—	2	2	no	—
49	C₂²×Q₈×C₄₃	—	2	2	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
52	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
53	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₄₃	D₄	1	2	yes	—
55	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	—	2	1	no	—
57	C₂³×C₄×C₄₃	—	2	1	no	—
58	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₄₃	—	2	2	no	—
61	C₂×M₁₆×C₄₃	—	2	2	no	—
62	C₂×M₁₆×C₄₃	—	2	2	no	—
63	C₂²×C₈×C₄₃	—	2	2	no	—
64	C₂²×C₈×C₄₃	—	2	2	no	—
65	C₂²×C₈×C₄₃	D₄	1	4	yes	—
66	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₃	—	2	8	no	—
70	#124×C₄₃	—	2	8	no	—
71	#123×C₄₃	—	2	16	no	—
72	C₂²⋊Q₈×C₄₃	—	2	8	no	—
73	C₂²⋊Q₈×C₄₃	—	2	8	no	—
74	#117×C₄₃	—	2	2	no	—
75	#117×C₄₃	—	2	2	no	—
76	#117×C₄₃	—	2	2	no	—
77	#117×C₄₃	D₄	1	4	yes	—
78	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
89	C₂×C₄²×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	—	2	1	no	—
91	#107×C₄₃	—	2	4	no	—
92	#106×C₄₃	—	2	4	no	—
93	#103×C₄₃	—	2	8	no	—
94	#103×C₄₃	—	2	4	no	—
95	#103×C₄₃	—	2	4	no	—
96	C₂²⋊C₈×C₄₃	—	2	4	no	—
97	C₂²⋊C₈×C₄₃	—	2	4	no	—
98	#95×C₄₃	—	2	4	no	—
99	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
100	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
101	#41×C₄₃	—	4	4	no	—
102	#41×C₄₃	—	4	4	no	—
103	#41×C₄₃	—	4	4	no	—
104	#41×C₄₃	—	4	4	no	—
105	C₂×Q₈×C₄₃	—	2	4	no	—
106	C₂×Q₈×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	8	no	—
111	C₂×Q₈×C₄₃	—	2	8	no	—
112	C₂×Q₈×C₄₃	—	2	2	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	4	2	no	—
117	C₂×Q₈×C₄₃	—	4	4	no	—
118	C₂×Q₈×C₄₃	—	4	2	no	—
119	C₂×Q₈×C₄₃	—	4	4	no	—
120	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	4	no	—
125	C₂×D₄×C₄₃	—	2	4	no	—
126	C₂×D₄×C₄₃	—	2	4	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	4	2	no	—
139	C₂²×C₄×C₄₃	—	4	2	no	—
140	C₂²×C₄×C₄₃	—	4	2	no	—
141	C₂²×C₄×C₄₃	—	8	2	no	—
142	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	#41	1	2	yes	—
148	C₂²×C₄×C₄₃	#41	1	2	yes	—
149	C₂²×C₄×C₄₃	#41	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
151	M₁₆×C₄₃	—	4	4	no	—
152	C₂×C₈×C₄₃	—	2	8	no	—
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	2	no	—
158	C₂×C₈×C₄₃	—	2	2	no	—
159	C₂×C₈×C₄₃	—	2	2	no	—
160	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₄₃	—	2	16	no	—
163	C₄⋊C₄×C₄₃	—	2	2	no	—
164	C₄⋊C₄×C₄₃	—	2	2	no	—
165	C₄⋊C₄×C₄₃	—	2	2	no	—
166	C₄⋊C₄×C₄₃	—	2	2	no	—
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	—	4	2	no	—
169	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
170	C₂²⋊C₄×C₄₃	—	2	16	no	—
171	C₂²⋊C₄×C₄₃	—	2	4	no	—
172	C₂²⋊C₄×C₄₃	—	4	2	no	—
173	C₂²⋊C₄×C₄₃	—	8	4	no	—
174	C₄²×C₄₃	—	2	4	no	—
175	C₄²×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	—	2	2	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	2	2	no	—
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	—	2	4	no	—
182	C₂³×C₄₃	—	2	4	no	—
183	C₂³×C₄₃	#120	1	2	yes	—
184	C₂³×C₄₃	#121	1	2	yes	—
185	C₂³×C₄₃	#123	1	2	yes	—
186	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₄₃	—	2	4	no	—
188	Q₈×C₄₃	—	2	4	no	—
189	Q₈×C₄₃	—	4	2	no	—
190	Q₈×C₄₃	—	4	2	no	—
191	Q₈×C₄₃	—	4	8	no	—
192	Q₈×C₄₃	—	4	4	no	—
193	D₄×C₄₃	—	4	8	no	—
194	D₄×C₄₃	—	4	4	no	—
195	C₂×C₄×C₄₃	—	2	4	no	—
196	C₂×C₄×C₄₃	—	2	4	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	8	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	—	4	2	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	4	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	8	4	no	—
215	C₂×C₄×C₄₃	#120	1	2	yes	—
216	C₂×C₄×C₄₃	#121	1	4	yes	—
217	C₂×C₄×C₄₃	#121	1	4	yes	—
218	C₂×C₄×C₄₃	#121	1	2	yes	—
219	C₂×C₄×C₄₃	#123	1	4	yes	—
220	C₂×C₄×C₄₃	#123	1	2	yes	—
221	C₂×C₄×C₄₃	#124	1	4	yes	—
222	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
228	C₈×C₄₃	—	2	2	no	—
229	C₈×C₄₃	—	2	2	no	—
230	C₈×C₄₃	—	4	2	no	—
231	#23487	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₄₃	—	2	4	no	—
233	C₂²×C₄₃	—	2	4	no	—
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	4	4	no	—
237	C₂²×C₄₃	—	4	2	no	—
238	C₂²×C₄₃	—	4	4	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	4	2	no	—
241	C₂²×C₄₃	#394	1	4	yes	—
242	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
243	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
244	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
245	C₂²×C₄₃	#577	1	2	yes	—
246	C₂²×C₄₃	#578	1	2	yes	—
247	C₄×C₄₃	—	4	2	no	—
248	C₄×C₄₃	—	4	4	no	—
249	C₄×C₄₃	—	4	4	no	—
250	C₄×C₄₃	—	8	2	no	—
251	C₄×C₄₃	—	8	2	no	—
252	C₄×C₄₃	#394	1	4	yes	—
253	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
254	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
255	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
256	C₄×C₄₃	C₂×#124	1	1	yes	characteristic
257	C₂×#536	C₂×C₄₃	1	1	yes	characteristic
258	C₂×#427	C₂×C₄₃	1	1	yes	characteristic, complemented
259	C₂×#419	C₂×C₄₃	1	1	yes	characteristic, complemented
260	C₂²×#103	C₂×C₄₃	1	1	yes	characteristic, complemented
261	C₂×#408	C₂×C₄₃	1	1	yes	characteristic
262	#2311	C₂×C₄₃	1	1	yes	characteristic
263	#2036	C₂×C₄₃	1	4	yes	complemented
264	#2035	C₂×C₄₃	1	4	yes	complemented
265	#1736	C₂×C₄₃	1	1	yes	characteristic, complemented
266	C₂×C₄₃	—	2	4	no	—
267	C₂×C₄₃	—	8	2	no	—
268	C₂×C₄₃	C₂×#394	1	1	yes	characteristic
269	C₂×C₄₃	#3013	1	2	yes	—
270	C₂×C₄₃	#3057	1	1	yes	characteristic
271	C₂×C₄₃	#3059	1	1	yes	characteristic
272	C₂×C₄₃	#3097	1	2	yes	—
273	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
274	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
275	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
276	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
277	#536	—	2	4	no	—
278	#536	—	2	4	no	—
279	C₂×C₄⋊Q₈	—	2	1	no	—
280	C₂×#124	—	2	1	no	—
281	C₂×#123	—	2	2	no	—
282	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	—
283	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
284	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
286	#427	—	2	4	no	—
287	C₂×#107	C₂²×C₄₃	1	2	yes	—
288	C₂×#106	C₂²×C₄₃	1	2	yes	—
289	#419	—	2	4	no	—
290	C₂×#103	—	2	4	no	—
291	C₂×#103	C₂²×C₄₃	1	2	yes	—
292	C₂×#103	C₂²×C₄₃	1	2	yes	—
293	C₂×#103	C₂²×C₄₃	1	4	yes	—
294	#408	—	2	4	no	—
295	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
296	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
297	#391	—	2	1	no	—
298	#390	—	2	1	no	—
299	#386	—	2	2	no	—
300	#380	C₂²×C₄₃	1	4	yes	—
301	#340	C₂²×C₄₃	1	4	yes	—
302	C₄₃	#23487	1	1	yes	characteristic, direct product factor, Sylow
303	C₂×#41	—	2	2	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	—	2	2	no	—
312	C₂²×Q₈	—	2	2	no	—
313	C₂²×Q₈	—	2	2	no	—
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
316	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
318	C₂²×D₄	D₄×C₄₃	1	2	yes	—
319	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	1	no	—
322	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
323	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
324	C₂×M₁₆	—	2	2	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	D₄×C₄₃	1	4	yes	—
330	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
331	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
333	C₄⋊Q₈	—	2	8	no	—
334	#124	—	2	8	no	—
335	#123	—	2	16	no	—
336	C₂²⋊Q₈	—	2	8	no	—
337	C₂²⋊Q₈	—	2	8	no	—
338	#117	—	2	2	no	—
339	#117	—	2	2	no	—
340	#117	—	2	2	no	—
341	#117	D₄×C₄₃	1	4	yes	—
342	C₂×C₄⋊C₄	—	2	4	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	4	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	4	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	#107	—	2	4	no	—
356	#106	—	2	4	no	—
357	#103	—	2	8	no	—
358	#103	—	2	4	no	—
359	#103	—	2	4	no	—
360	C₂²⋊C₈	—	2	4	no	—
361	C₂²⋊C₈	—	2	4	no	—
362	#95	—	2	4	no	—
363	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
364	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
365	#41	—	4	4	no	—
366	#41	—	4	4	no	—
367	#41	—	4	4	no	—
368	#41	—	4	4	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	8	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	4	2	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂×Q₈	—	4	2	no	—
383	C₂×Q₈	—	4	4	no	—
384	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	8	2	no	—
406	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
411	C₂²×C₄	#41×C₄₃	1	2	yes	—
412	C₂²×C₄	#41×C₄₃	1	2	yes	—
413	C₂²×C₄	#41×C₄₃	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
415	M₁₆	—	4	4	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
425	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
426	C₄⋊C₄	—	2	16	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
434	C₂²⋊C₄	—	2	16	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	4	2	no	—
437	C₂²⋊C₄	—	8	4	no	—
438	C₄²	—	2	4	no	—
439	C₄²	—	4	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	#120×C₄₃	1	2	yes	—
448	C₂³	#121×C₄₃	1	2	yes	—
449	C₂³	#123×C₄₃	1	2	yes	—
450	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
451	Q₈	—	2	4	no	—
452	Q₈	—	2	4	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	4	8	no	—
456	Q₈	—	4	4	no	—
457	D₄	—	4	8	no	—
458	D₄	—	4	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	#120×C₄₃	1	2	yes	—
480	C₂×C₄	#121×C₄₃	1	4	yes	—
481	C₂×C₄	#121×C₄₃	1	4	yes	—
482	C₂×C₄	#121×C₄₃	1	2	yes	—
483	C₂×C₄	#123×C₄₃	1	4	yes	—
484	C₂×C₄	#123×C₄₃	1	2	yes	—
485	C₂×C₄	#124×C₄₃	1	4	yes	—
486	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₈	—	4	2	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	C₄₃×#394	1	4	yes	—
505	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
506	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
507	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
508	C₂²	C₄₃×#577	1	2	yes	—
509	C₂²	C₄₃×#578	1	2	yes	—
510	C₄	—	4	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	—	8	2	no	—
514	C₄	—	8	2	no	—
515	C₄	C₄₃×#394	1	4	yes	—
516	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
517	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
518	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
519	C₄	C₂×#124×C₄₃	1	1	yes	characteristic
520	C₂	—	2	4	no	—
521	C₂	—	8	2	no	—
522	C₂	C₂×C₄₃×#394	1	1	yes	characteristic
523	C₂	C₄₃×#3013	1	2	yes	—
524	C₂	C₄₃×#3057	1	1	yes	characteristic
525	C₂	C₄₃×#3059	1	1	yes	characteristic
526	C₂	C₄₃×#3097	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×#41×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#427	C₂	semidirect
3. C₂×C₄₃×#419	C₂	semidirect
4. C₂²×#103×C₄₃	C₂	semidirect
7. C₄₃×#2036	C₂	semidirect
8. C₄₃×#2035	C₂	semidirect
9. C₄₃×#1736	C₂	semidirect
231. #23487	C₄₃	direct (N × H)
258. C₂×#427	C₂×C₄₃	semidirect
259. C₂×#419	C₂×C₄₃	semidirect
260. C₂²×#103	C₂×C₄₃	semidirect
263. #2036	C₂×C₄₃	semidirect
264. #2035	C₂×C₄₃	semidirect
265. #1736	C₂×C₄₃	semidirect
302. C₄₃	#23487	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#536	2
C₂×C₄₃×#427	2
C₂×C₄₃×#419	2
C₂²×#103×C₄₃	2
C₂×C₄₃×#408	2
C₄₃×#2311	2
C₄₃×#2036	2
C₄₃×#2035	2
C₄₃×#1736	2
#23487	43

Subgroups — C43×#23487 #24943504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#23487 #24943504