Subgroups — C₄₃×#20838 #24940855

Order 11008.

1466 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1851	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1850	C₂	1	4	yes	maximal, complemented
8	C₄₃×#1729	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	C₂×#131×C₄₃	—	2	4	no	—
12	C₂×#131×C₄₃	—	2	4	no	—
13	C₂×#131×C₄₃	—	2	4	no	—
14	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
18	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#424	—	2	4	no	—
23	C₂×C₄⋊C₈×C₄₃	—	2	4	no	—
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#408	—	2	4	no	—
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
29	C₄₃×#391	C₄	1	2	yes	—
30	C₄₃×#390	C₄	1	2	yes	—
31	C₄₃×#386	C₄	1	2	yes	—
32	C₄₃×#386	C₄	1	2	yes	—
33	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
34	C₄₃×#336	C₂²	1	2	yes	—
35	C₄₃×#336	C₂²	1	4	yes	—
36	C₄₃×#336	C₂²	1	2	yes	—
37	C₂×#41×C₄₃	—	2	2	no	—
38	C₂×#41×C₄₃	—	2	2	no	—
39	C₂×#41×C₄₃	—	2	2	no	—
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	D₄	1	4	yes	—
42	C₂×#41×C₄₃	Q₈	1	4	yes	—
43	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	#131×C₄₃	—	2	32	no	—
51	C₂×M₁₆×C₄₃	—	2	4	no	—
52	C₂×M₁₆×C₄₃	—	2	2	no	—
53	C₂×M₁₆×C₄₃	—	2	2	no	—
54	C₂×M₁₆×C₄₃	—	2	2	no	—
55	C₂×M₁₆×C₄₃	—	2	2	no	—
56	C₂×M₁₆×C₄₃	—	2	2	no	—
57	C₂×M₁₆×C₄₃	—	2	4	no	—
58	C₂×M₁₆×C₄₃	—	2	4	no	—
59	C₂×M₁₆×C₄₃	D₄	1	4	yes	—
60	C₂²×C₈×C₄₃	—	2	4	no	—
61	C₂²×C₈×C₄₃	—	2	2	no	—
62	C₂²×C₈×C₄₃	—	2	2	no	—
63	C₂²×C₈×C₄₃	—	2	4	no	—
64	C₂²×C₈×C₄₃	—	2	4	no	—
65	C₂²×C₈×C₄₃	—	2	2	no	—
66	C₂²×C₈×C₄₃	—	2	2	no	—
67	C₂²×C₈×C₄₃	—	2	2	no	—
68	C₂²×C₈×C₄₃	D₄	1	4	yes	—
69	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
70	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
71	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	#117×C₄₃	—	2	2	no	—
75	#117×C₄₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
79	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
80	C₂×C₄²×C₄₃	—	2	2	no	—
81	C₂×C₄²×C₄₃	—	2	2	no	—
82	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
85	C₄⋊C₈×C₄₃	—	2	4	no	—
86	C₄⋊C₈×C₄₃	—	2	4	no	—
87	C₄⋊C₈×C₄₃	—	2	8	no	—
88	C₂²⋊C₈×C₄₃	—	2	8	no	—
89	#95×C₄₃	C₂×C₄	1	4	yes	—
90	#95×C₄₃	C₂×C₄	1	4	yes	—
91	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
92	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
93	#41×C₄₃	—	2	8	no	—
94	#41×C₄₃	—	2	8	no	—
95	#41×C₄₃	—	2	8	no	—
96	#41×C₄₃	—	2	8	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	C₄⋊C₄	1	4	yes	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	2	4	no	—
103	C₂×D₄×C₄₃	—	2	4	no	—
104	C₂×D₄×C₄₃	C₄⋊C₄	1	4	yes	—
105	C₂×D₄×C₄₃	C₄⋊C₄	1	8	yes	—
106	C₂²×C₄×C₄₃	—	2	4	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
124	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₄₃	#41	1	2	yes	—
126	C₂²×C₄×C₄₃	#41	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₄₃	—	2	16	no	—
129	M₁₆×C₄₃	—	2	8	no	—
130	M₁₆×C₄₃	—	4	4	no	—
131	C₂×C₈×C₄₃	—	2	16	no	—
132	C₂×C₈×C₄₃	—	2	8	no	—
133	C₂×C₈×C₄₃	—	2	1	no	—
134	C₂×C₈×C₄₃	—	2	1	no	—
135	C₂×C₈×C₄₃	—	2	1	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	—	2	1	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	—	2	2	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	4	4	no	—
146	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₄₃	—	2	4	no	—
150	C₂²⋊C₄×C₄₃	—	2	8	no	—
151	C₂²⋊C₄×C₄₃	—	2	4	no	—
152	C₂²⋊C₄×C₄₃	—	4	4	no	—
153	C₄²×C₄₃	—	2	4	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	2	2	no	—
156	C₄²×C₄₃	—	2	2	no	—
157	C₄²×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	2	2	no	—
162	C₂³×C₄₃	—	2	4	no	—
163	C₂³×C₄₃	—	2	4	no	—
164	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
165	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
166	C₂³×C₄₃	C₄×D₄	1	2	yes	—
167	C₂³×C₄₃	C₄×D₄	1	2	yes	—
168	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
169	Q₈×C₄₃	—	2	8	no	—
170	D₄×C₄₃	—	2	16	no	—
171	D₄×C₄₃	—	2	8	no	—
172	C₂×C₄×C₄₃	—	2	8	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	4	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	4	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	2	4	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
189	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₄₃	#120	1	4	yes	—
193	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
194	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
195	C₂×C₄×C₄₃	#123	1	4	yes	—
196	C₂×C₄×C₄₃	#131	1	4	yes	complemented
197	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
203	C₈×C₄₃	—	2	2	no	—
204	C₈×C₄₃	—	2	4	no	—
205	C₈×C₄₃	—	2	2	no	—
206	C₈×C₄₃	—	4	2	no	—
207	C₈×C₄₃	—	4	2	no	—
208	#20838	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂²×C₄₃	—	2	4	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	2	2	no	—
212	C₂²×C₄₃	—	2	4	no	—
213	C₂²×C₄₃	—	2	8	no	—
214	C₂²×C₄₃	—	2	4	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	4	no	—
218	C₂²×C₄₃	#385	1	4	yes	—
219	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂²×C₄₃	C₂×#131	1	2	yes	—
223	C₂²×C₄₃	#568	1	2	yes	—
224	C₄×C₄₃	—	2	4	no	—
225	C₄×C₄₃	—	2	4	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	—	4	4	no	—
228	C₄×C₄₃	#385	1	4	yes	—
229	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
230	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
231	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
232	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
233	C₂²×#131	C₂×C₄₃	1	1	yes	characteristic
234	C₂×#424	C₂×C₄₃	1	1	yes	characteristic, complemented
235	C₂²×C₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
236	C₂×#408	C₂×C₄₃	1	1	yes	characteristic
237	#2297	C₂×C₄₃	1	1	yes	characteristic
238	#1851	C₂×C₄₃	1	4	yes	complemented
239	#1850	C₂×C₄₃	1	4	yes	complemented
240	#1729	C₂×C₄₃	1	1	yes	characteristic, complemented
241	#1728	C₂×C₄₃	1	1	yes	characteristic, complemented
242	C₂×C₄₃	—	2	4	no	—
243	C₂×C₄₃	—	4	4	no	—
244	C₂×C₄₃	C₂×#385	1	1	yes	characteristic
245	C₂×C₄₃	#2906	1	2	yes	—
246	C₂×C₄₃	#2929	1	1	yes	characteristic
247	C₂×C₄₃	#2930	1	1	yes	characteristic
248	C₂×C₄₃	#2935	1	2	yes	—
249	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×#131	—	2	4	no	—
251	C₂×#131	—	2	4	no	—
252	C₂×#131	—	2	4	no	—
253	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
254	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
256	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
257	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
258	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
259	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
260	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
261	#424	—	2	4	no	—
262	C₂×C₄⋊C₈	—	2	4	no	—
263	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
264	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	—
265	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
266	#408	—	2	4	no	—
267	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
268	#391	C₄×C₄₃	1	2	yes	—
269	#390	C₄×C₄₃	1	2	yes	—
270	#386	C₄×C₄₃	1	2	yes	—
271	#386	C₄×C₄₃	1	2	yes	—
272	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
273	#336	C₂²×C₄₃	1	2	yes	—
274	#336	C₂²×C₄₃	1	4	yes	—
275	#336	C₂²×C₄₃	1	2	yes	—
276	C₄₃	#20838	1	1	yes	characteristic, direct product factor, Sylow
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	D₄×C₄₃	1	4	yes	—
282	C₂×#41	Q₈×C₄₃	1	4	yes	—
283	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
284	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
285	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
286	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
287	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
289	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
290	#131	—	2	32	no	—
291	C₂×M₁₆	—	2	4	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	4	no	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	D₄×C₄₃	1	4	yes	—
300	C₂²×C₈	—	2	4	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	4	no	—
304	C₂²×C₈	—	2	4	no	—
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	D₄×C₄₃	1	4	yes	—
309	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
310	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
313	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
319	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
323	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
324	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
325	C₄⋊C₈	—	2	4	no	—
326	C₄⋊C₈	—	2	4	no	—
327	C₄⋊C₈	—	2	8	no	—
328	C₂²⋊C₈	—	2	8	no	—
329	#95	C₂×C₄×C₄₃	1	4	yes	—
330	#95	C₂×C₄×C₄₃	1	4	yes	—
331	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
332	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
333	#41	—	2	8	no	—
334	#41	—	2	8	no	—
335	#41	—	2	8	no	—
336	#41	—	2	8	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	C₄⋊C₄×C₄₃	1	4	yes	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₄⋊C₄×C₄₃	1	8	yes	—
345	C₂×D₄	C₄⋊C₄×C₄₃	1	4	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
355	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
356	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
358	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
363	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
364	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
365	C₂²×C₄	#41×C₄₃	1	2	yes	—
366	C₂²×C₄	#41×C₄₃	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
368	M₁₆	—	2	16	no	—
369	M₁₆	—	2	8	no	—
370	M₁₆	—	4	4	no	—
371	C₂×C₈	—	2	16	no	—
372	C₂×C₈	—	2	8	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	4	4	no	—
386	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
387	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
388	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
389	C₄⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
405	C₂³	C₂×C₄⋊C₄×C₄₃	1	2	yes	—
406	C₂³	C₄×D₄×C₄₃	1	2	yes	—
407	C₂³	C₄×D₄×C₄₃	1	2	yes	—
408	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
409	Q₈	—	2	8	no	—
410	D₄	—	2	16	no	—
411	D₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
429	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	2	yes	—
430	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
431	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
432	C₂×C₄	#120×C₄₃	1	4	yes	—
433	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
434	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
435	C₂×C₄	#123×C₄₃	1	4	yes	—
436	C₂×C₄	#131×C₄₃	1	4	yes	complemented
437	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
443	C₈	—	2	2	no	—
444	C₈	—	2	4	no	—
445	C₈	—	2	2	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	C₄₃×#385	1	4	yes	—
458	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
459	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
460	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
461	C₂²	C₂×#131×C₄₃	1	2	yes	—
462	C₂²	C₄₃×#568	1	2	yes	—
463	C₄	—	2	4	no	—
464	C₄	—	2	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	C₄₃×#385	1	4	yes	—
468	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
469	C₄	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
470	C₄	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
471	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
472	C₂	—	2	4	no	—
473	C₂	—	4	4	no	—
474	C₂	C₂×C₄₃×#385	1	1	yes	characteristic
475	C₂	C₄₃×#2906	1	2	yes	—
476	C₂	C₄₃×#2929	1	1	yes	characteristic
477	C₂	C₄₃×#2930	1	1	yes	characteristic
478	C₂	C₄₃×#2935	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#424	C₂	semidirect
3. C₂²×C₄⋊C₈×C₄₃	C₂	semidirect
6. C₄₃×#1851	C₂	semidirect
7. C₄₃×#1850	C₂	semidirect
8. C₄₃×#1729	C₂	semidirect
9. C₄₃×#1728	C₂	semidirect
196. C₂×C₄×C₄₃	#131	semidirect
208. #20838	C₄₃	direct (N × H)
234. C₂×#424	C₂×C₄₃	semidirect
235. C₂²×C₄⋊C₈	C₂×C₄₃	semidirect
238. #1851	C₂×C₄₃	semidirect
239. #1850	C₂×C₄₃	semidirect
240. #1729	C₂×C₄₃	semidirect
241. #1728	C₂×C₄₃	semidirect
276. C₄₃	#20838	direct (N × H)
436. C₂×C₄	#131×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#131×C₄₃	2
C₂×C₄₃×#424	2
C₂²×C₄⋊C₈×C₄₃	2
C₂×C₄₃×#408	2
C₄₃×#2297	2
C₄₃×#1851	2
C₄₃×#1850	2
C₄₃×#1729	2
C₄₃×#1728	2
#20838	43

Subgroups — C43×#20838 #24940855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20838 #24940855