Subgroups — C₄₃×#20900 #24940917

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 586 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, complemented
2	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1870	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1869	C₂	1	4	yes	maximal, complemented
8	C₄₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×#131×C₄₃	—	2	4	no	—
13	C₂×#131×C₄₃	—	2	4	no	—
14	C₂×#131×C₄₃	—	2	4	no	—
15	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
20	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#532	—	2	4	no	—
22	C₄₃×#532	—	2	4	no	—
23	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
24	C₂×#127×C₄₃	C₄	1	1	yes	characteristic
25	C₂×#124×C₄₃	C₄	1	1	yes	characteristic
26	C₂×#124×C₄₃	C₄	1	1	yes	characteristic
27	C₂×#121×C₄₃	C₄	1	4	yes	—
28	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
29	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#408	—	2	4	no	—
31	C₄₃×#408	—	2	4	no	—
32	C₄₃×#408	—	2	4	no	—
33	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
35	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
37	C₄₃×#336	C₂²	1	2	yes	—
38	C₄₃×#336	C₂²	1	4	yes	—
39	C₄₃×#336	C₂²	1	2	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	—	2	2	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	—	2	2	no	—
48	C₂×#41×C₄₃	—	2	2	no	—
49	C₂×#41×C₄₃	—	2	2	no	—
50	C₂×#41×C₄₃	D₄	1	4	yes	—
51	C₂×#41×C₄₃	D₄	1	4	yes	—
52	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
55	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
57	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
58	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
60	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	#131×C₄₃	—	2	32	no	—
64	C₂×M₁₆×C₄₃	—	2	4	no	—
65	C₂×M₁₆×C₄₃	—	2	2	no	—
66	C₂×M₁₆×C₄₃	—	2	2	no	—
67	C₂×M₁₆×C₄₃	—	2	2	no	—
68	C₂×M₁₆×C₄₃	—	2	2	no	—
69	C₂×M₁₆×C₄₃	—	2	2	no	—
70	C₂×M₁₆×C₄₃	—	2	4	no	—
71	C₂×M₁₆×C₄₃	—	2	4	no	—
72	C₂×M₁₆×C₄₃	D₄	1	4	yes	complemented
73	C₂²×C₈×C₄₃	—	2	4	no	—
74	C₂²×C₈×C₄₃	—	2	2	no	—
75	C₂²×C₈×C₄₃	—	2	2	no	—
76	C₂²×C₈×C₄₃	—	2	4	no	—
77	C₂²×C₈×C₄₃	—	2	4	no	—
78	C₂²×C₈×C₄₃	—	2	2	no	—
79	C₂²×C₈×C₄₃	—	2	2	no	—
80	C₂²×C₈×C₄₃	—	2	2	no	—
81	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
82	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₃	—	2	4	no	—
88	#127×C₄₃	—	2	4	no	—
89	#124×C₄₃	—	2	4	no	—
90	#124×C₄₃	—	2	4	no	—
91	#121×C₄₃	—	2	16	no	—
92	C₄×D₄×C₄₃	—	2	8	no	—
93	C₄×D₄×C₄₃	—	2	8	no	—
94	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
95	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
96	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
97	C₂×C₄²×C₄₃	—	2	2	no	—
98	C₂×C₄²×C₄₃	—	2	2	no	—
99	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
102	C₂²⋊C₈×C₄₃	—	2	8	no	—
103	C₂²⋊C₈×C₄₃	—	2	8	no	—
104	C₂²⋊C₈×C₄₃	—	2	4	no	—
105	C₂²⋊C₈×C₄₃	—	2	4	no	—
106	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
107	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	#41×C₄₃	—	2	8	no	—
110	#41×C₄₃	—	2	8	no	—
111	#41×C₄₃	—	2	8	no	—
112	#41×C₄₃	—	2	8	no	—
113	#41×C₄₃	—	4	4	no	—
114	#41×C₄₃	—	4	4	no	—
115	#41×C₄₃	—	4	4	no	—
116	#41×C₄₃	—	4	4	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	2	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	8	no	—
129	C₂×D₄×C₄₃	—	2	8	no	—
130	C₂×D₄×C₄₃	—	2	4	no	—
131	C₂×D₄×C₄₃	—	2	4	no	—
132	C₂×D₄×C₄₃	—	2	4	no	—
133	C₂×D₄×C₄₃	—	2	4	no	—
134	C₂×D₄×C₄₃	—	2	4	no	—
135	C₂×D₄×C₄₃	—	4	4	no	—
136	C₂×D₄×C₄₃	C₂²⋊C₄	1	8	yes	—
137	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	2	no	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	—	2	4	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	2	no	—
149	C₂²×C₄×C₄₃	—	2	4	no	—
150	C₂²×C₄×C₄₃	—	4	2	no	—
151	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₄₃	C₂×D₄	1	4	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	2	yes	—
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	M₁₆×C₄₃	—	2	16	no	—
166	M₁₆×C₄₃	—	2	8	no	—
167	M₁₆×C₄₃	—	4	4	no	—
168	C₂×C₈×C₄₃	—	2	16	no	—
169	C₂×C₈×C₄₃	—	2	8	no	—
170	C₂×C₈×C₄₃	—	2	1	no	—
171	C₂×C₈×C₄₃	—	2	1	no	—
172	C₂×C₈×C₄₃	—	2	1	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	1	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₂×C₈×C₄₃	—	2	2	no	—
178	C₂×C₈×C₄₃	—	2	2	no	—
179	C₂×C₈×C₄₃	—	2	2	no	—
180	C₂×C₈×C₄₃	—	2	2	no	—
181	C₂×C₈×C₄₃	—	2	2	no	—
182	C₂×C₈×C₄₃	—	4	4	no	—
183	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
184	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
185	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₄₃	—	2	8	no	—
187	C₂²⋊C₄×C₄₃	—	2	8	no	—
188	C₂²⋊C₄×C₄₃	—	2	8	no	—
189	C₄²×C₄₃	—	2	2	no	—
190	C₄²×C₄₃	—	2	2	no	—
191	C₄²×C₄₃	—	2	2	no	—
192	C₄²×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	2	2	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	2	no	—
197	C₂³×C₄₃	—	2	4	no	—
198	C₂³×C₄₃	—	2	4	no	—
199	C₂³×C₄₃	—	2	2	no	—
200	C₂³×C₄₃	—	2	2	no	—
201	C₂³×C₄₃	—	2	2	no	—
202	C₂³×C₄₃	—	2	4	no	—
203	C₂³×C₄₃	—	2	4	no	—
204	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
205	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂³×C₄₃	C₄×D₄	1	2	yes	—
207	C₂³×C₄₃	C₄×D₄	1	2	yes	—
208	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
209	Q₈×C₄₃	—	2	8	no	—
210	Q₈×C₄₃	—	4	4	no	—
211	D₄×C₄₃	—	2	16	no	—
212	D₄×C₄₃	—	2	8	no	—
213	D₄×C₄₃	—	4	16	no	—
214	D₄×C₄₃	—	4	8	no	—
215	D₄×C₄₃	—	4	4	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	4	no	—
221	C₂×C₄×C₄₃	—	2	4	no	—
222	C₂×C₄×C₄₃	—	2	4	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	—	2	2	no	—
227	C₂×C₄×C₄₃	—	2	2	no	—
228	C₂×C₄×C₄₃	—	2	2	no	—
229	C₂×C₄×C₄₃	—	2	2	no	—
230	C₂×C₄×C₄₃	—	4	8	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	C₂×C₂²⋊C₄	1	4	yes	—
236	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
237	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
239	C₂×C₄×C₄₃	#120	1	4	yes	—
240	C₂×C₄×C₄₃	#121	1	4	yes	—
241	C₂×C₄×C₄₃	#121	1	4	yes	—
242	C₂×C₄×C₄₃	#123	1	4	yes	—
243	C₂×C₄×C₄₃	#131	1	4	yes	complemented
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	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
250	C₈×C₄₃	—	2	2	no	—
251	C₈×C₄₃	—	2	4	no	—
252	C₈×C₄₃	—	2	2	no	—
253	C₈×C₄₃	—	4	2	no	—
254	C₈×C₄₃	—	4	2	no	—
255	#20900	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₃	—	2	4	no	—
257	C₂²×C₄₃	—	2	2	no	—
258	C₂²×C₄₃	—	2	2	no	—
259	C₂²×C₄₃	—	2	4	no	—
260	C₂²×C₄₃	—	2	8	no	—
261	C₂²×C₄₃	—	2	4	no	—
262	C₂²×C₄₃	—	4	2	no	—
263	C₂²×C₄₃	—	4	2	no	—
264	C₂²×C₄₃	—	4	4	no	—
265	C₂²×C₄₃	—	4	4	no	—
266	C₂²×C₄₃	—	4	2	no	—
267	C₂²×C₄₃	—	4	2	no	—
268	C₂²×C₄₃	—	4	4	no	—
269	C₂²×C₄₃	—	4	2	no	—
270	C₂²×C₄₃	#386	1	4	yes	—
271	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂²×C₄₃	C₂×#131	1	2	yes	—
275	C₂²×C₄₃	#568	1	2	yes	—
276	C₄×C₄₃	—	2	4	no	—
277	C₄×C₄₃	—	2	4	no	—
278	C₄×C₄₃	—	4	2	no	—
279	C₄×C₄₃	—	4	2	no	—
280	C₄×C₄₃	#386	1	4	yes	—
281	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
282	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
283	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
284	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
285	C₂²×#131	C₂×C₄₃	1	1	yes	characteristic, complemented
286	C₂×#532	C₂×C₄₃	1	1	yes	characteristic
287	C₂×#408	C₂×C₄₃	1	1	yes	characteristic, complemented
288	C₂×#408	C₂×C₄₃	1	1	yes	characteristic, complemented
289	C₂×#408	C₂×C₄₃	1	1	yes	characteristic, complemented
290	#1870	C₂×C₄₃	1	4	yes	complemented
291	#1869	C₂×C₄₃	1	4	yes	complemented
292	#1728	C₂×C₄₃	1	1	yes	characteristic, complemented
293	C₂×#336	C₂×C₄₃	1	1	yes	characteristic, complemented
294	C₂×C₄₃	—	2	4	no	—
295	C₂×C₄₃	—	4	4	no	—
296	C₂×C₄₃	—	8	2	no	—
297	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
298	C₂×C₄₃	#2880	1	2	yes	—
299	C₂×C₄₃	#2931	1	1	yes	characteristic
300	C₂×C₄₃	#2932	1	1	yes	characteristic
301	C₂×C₄₃	#2935	1	2	yes	—
302	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
303	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
304	C₂×#131	—	2	4	no	—
305	C₂×#131	—	2	4	no	—
306	C₂×#131	—	2	4	no	—
307	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
308	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
309	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
310	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
311	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
312	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
313	#532	—	2	4	no	—
314	#532	—	2	4	no	—
315	C₂×C₄⋊Q₈	C₄×C₄₃	1	1	yes	characteristic
316	C₂×#127	C₄×C₄₃	1	1	yes	characteristic
317	C₂×#124	C₄×C₄₃	1	1	yes	characteristic
318	C₂×#124	C₄×C₄₃	1	1	yes	characteristic
319	C₂×#121	C₄×C₄₃	1	4	yes	—
320	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
321	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
322	#408	—	2	4	no	—
323	#408	—	2	4	no	—
324	#408	—	2	4	no	—
325	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
326	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
327	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
328	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
329	#336	C₂²×C₄₃	1	2	yes	—
330	#336	C₂²×C₄₃	1	4	yes	—
331	#336	C₂²×C₄₃	1	2	yes	—
332	C₄₃	#20900	1	1	yes	characteristic, direct product factor, Sylow
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	D₄×C₄₃	1	4	yes	—
344	C₂×#41	D₄×C₄₃	1	4	yes	—
345	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
346	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
347	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
348	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
349	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
350	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
351	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
352	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
353	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
354	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
355	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
356	#131	—	2	32	no	—
357	C₂×M₁₆	—	2	4	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	—	2	2	no	—
362	C₂×M₁₆	—	2	2	no	—
363	C₂×M₁₆	—	2	4	no	—
364	C₂×M₁₆	—	2	4	no	—
365	C₂×M₁₆	D₄×C₄₃	1	4	yes	complemented
366	C₂²×C₈	—	2	4	no	—
367	C₂²×C₈	—	2	2	no	—
368	C₂²×C₈	—	2	2	no	—
369	C₂²×C₈	—	2	4	no	—
370	C₂²×C₈	—	2	4	no	—
371	C₂²×C₈	—	2	2	no	—
372	C₂²×C₈	—	2	2	no	—
373	C₂²×C₈	—	2	2	no	—
374	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
375	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
376	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
377	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
379	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
380	C₄⋊Q₈	—	2	4	no	—
381	#127	—	2	4	no	—
382	#124	—	2	4	no	—
383	#124	—	2	4	no	—
384	#121	—	2	16	no	—
385	C₄×D₄	—	2	8	no	—
386	C₄×D₄	—	2	8	no	—
387	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
390	C₂×C₄²	—	2	2	no	—
391	C₂×C₄²	—	2	2	no	—
392	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
393	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
395	C₂²⋊C₈	—	2	8	no	—
396	C₂²⋊C₈	—	2	8	no	—
397	C₂²⋊C₈	—	2	4	no	—
398	C₂²⋊C₈	—	2	4	no	—
399	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
400	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
401	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
402	#41	—	2	8	no	—
403	#41	—	2	8	no	—
404	#41	—	2	8	no	—
405	#41	—	2	8	no	—
406	#41	—	4	4	no	—
407	#41	—	4	4	no	—
408	#41	—	4	4	no	—
409	#41	—	4	4	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	C₂²⋊C₄×C₄₃	1	4	yes	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	C₂²⋊C₄×C₄₃	1	8	yes	—
430	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
445	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
446	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
447	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
448	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
450	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
451	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
452	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
455	C₂²×C₄	#41×C₄₃	1	2	yes	—
456	C₂²×C₄	#41×C₄₃	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
458	M₁₆	—	2	16	no	—
459	M₁₆	—	2	8	no	—
460	M₁₆	—	4	4	no	—
461	C₂×C₈	—	2	16	no	—
462	C₂×C₈	—	2	8	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	4	4	no	—
476	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
477	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
478	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
479	C₄⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
498	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
499	C₂³	C₄×D₄×C₄₃	1	2	yes	—
500	C₂³	C₄×D₄×C₄₃	1	2	yes	—
501	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
502	Q₈	—	2	8	no	—
503	Q₈	—	4	4	no	—
504	D₄	—	2	16	no	—
505	D₄	—	2	8	no	—
506	D₄	—	4	16	no	—
507	D₄	—	4	8	no	—
508	D₄	—	4	4	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	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
529	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
530	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
531	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
532	C₂×C₄	#120×C₄₃	1	4	yes	—
533	C₂×C₄	#121×C₄₃	1	4	yes	—
534	C₂×C₄	#121×C₄₃	1	4	yes	—
535	C₂×C₄	#123×C₄₃	1	4	yes	—
536	C₂×C₄	#131×C₄₃	1	4	yes	complemented
537	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
541	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
542	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	2	4	no	—
545	C₈	—	2	2	no	—
546	C₈	—	4	2	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	2	no	—
562	C₂²	C₄₃×#386	1	4	yes	—
563	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
564	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
565	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
566	C₂²	C₂×#131×C₄₃	1	2	yes	—
567	C₂²	C₄₃×#568	1	2	yes	—
568	C₄	—	2	4	no	—
569	C₄	—	2	4	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	2	no	—
572	C₄	C₄₃×#386	1	4	yes	—
573	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
574	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
575	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
576	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
577	C₂	—	2	4	no	—
578	C₂	—	4	4	no	—
579	C₂	—	8	2	no	—
580	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
581	C₂	C₄₃×#2880	1	2	yes	—
582	C₂	C₄₃×#2931	1	1	yes	characteristic
583	C₂	C₄₃×#2932	1	1	yes	characteristic
584	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	C₂×C₄₃×#532	C₂
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
1. C₂²×#131×C₄₃	C₂	semidirect
3. C₂×C₄₃×#408	C₂	semidirect
4. C₂×C₄₃×#408	C₂	semidirect
5. C₂×C₄₃×#408	C₂	semidirect
6. C₄₃×#1870	C₂	semidirect
7. C₄₃×#1869	C₂	semidirect
8. C₄₃×#1728	C₂	semidirect
9. C₂×C₄₃×#336	C₂	semidirect
72. C₂×M₁₆×C₄₃	D₄	semidirect
81. C₂²×C₈×C₄₃	D₄	semidirect
243. C₂×C₄×C₄₃	#131	semidirect
255. #20900	C₄₃	direct (N × H)
285. C₂²×#131	C₂×C₄₃	semidirect
287. C₂×#408	C₂×C₄₃	semidirect
288. C₂×#408	C₂×C₄₃	semidirect
289. C₂×#408	C₂×C₄₃	semidirect
290. #1870	C₂×C₄₃	semidirect
291. #1869	C₂×C₄₃	semidirect
292. #1728	C₂×C₄₃	semidirect
293. C₂×#336	C₂×C₄₃	semidirect
332. C₄₃	#20900	direct (N × H)
365. C₂×M₁₆	D₄×C₄₃	semidirect
374. C₂²×C₈	D₄×C₄₃	semidirect
536. 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×#532	2
C₂×C₄₃×#408	2
C₄₃×#1870	2
C₄₃×#1869	2
C₄₃×#1728	2
C₂×C₄₃×#336	2
#20900	43

Subgroups — C43×#20900 #24940917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20900 #24940917