Subgroups — C₄₃×#60511 #24980528

Order 11008.

2346 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3095	C₂	1	4	yes	maximal, complemented
4	C₄₃×#3094	C₂	1	4	yes	maximal, complemented
5	C₄₃×#3093	C₂	1	4	yes	maximal, complemented
6	C₄₃×#3092	C₂	1	4	yes	maximal, complemented
7	C₄₃×#3091	C₂	1	8	yes	maximal, complemented
8	C₄₃×#2911	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2896	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
14	C₄₃×#525	—	2	1	no	—
15	C₄₃×#525	—	2	2	no	—
16	C₄₃×#525	—	2	1	no	—
17	C₄₃×#525	C₂²	1	4	yes	—
18	C₄₃×#525	C₂²	1	2	yes	—
19	C₄₃×#525	C₂²	1	2	yes	—
20	C₂×#123×C₄₃	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
22	C₂×#121×C₄₃	C₂²	1	2	yes	—
23	C₂×#120×C₄₃	—	2	1	no	—
24	C₂×C₄×D₄×C₄₃	—	2	2	no	—
25	C₂×#117×C₄₃	—	2	2	no	—
26	C₂×#117×C₄₃	—	2	1	no	—
27	C₂×#117×C₄₃	—	2	2	no	—
28	C₂×#117×C₄₃	—	2	1	no	—
29	C₂×#117×C₄₃	C₂²	1	4	yes	—
30	C₂×#117×C₄₃	C₂²	1	2	yes	—
31	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₃	C₂²	1	4	yes	complemented
33	C₂×#117×C₄₃	C₂²	1	2	yes	complemented
34	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
36	C₂²×C₄²×C₄₃	—	2	1	no	—
37	C₄₃×#485	C₂²	1	16	yes	complemented
38	C₄₃×#484	C₂²	1	8	yes	complemented
39	C₄₃×#483	C₂²	1	8	yes	complemented
40	C₄₃×#482	C₂²	1	16	yes	complemented
41	C₄₃×#481	C₂²	1	8	yes	complemented
42	C₄₃×#480	C₂²	1	8	yes	complemented
43	C₄₃×#428	C₂²	1	8	yes	complemented
44	C₄₃×#428	C₂²	1	8	yes	complemented
45	C₄₃×#427	C₂²	1	8	yes	complemented
46	C₄₃×#419	C₂²	1	4	yes	complemented
47	C₄₃×#418	C₂²	1	4	yes	complemented
48	C₄₃×#417	C₂²	1	8	yes	complemented
49	C₄₃×#416	C₂²	1	8	yes	complemented
50	C₄₃×#407	C₂²	1	4	yes	—
51	C₄₃×#407	C₂²	1	2	yes	complemented
52	C₄₃×#407	C₂²	1	2	yes	complemented
53	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	complemented
54	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
55	C₂×#41×C₄₃	—	2	1	no	—
56	C₂×#41×C₄₃	—	2	1	no	—
57	C₂×#41×C₄₃	—	2	8	no	—
58	C₂×#41×C₄₃	C₂³	1	2	yes	—
59	C₂×#41×C₄₃	C₂³	1	2	yes	—
60	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₄₃	—	2	2	no	—
62	C₂²×D₄×C₄₃	—	2	1	no	—
63	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₃	—	2	8	no	—
65	C₂³×C₄×C₄₃	—	2	2	no	—
66	C₂³×C₄×C₄₃	—	2	1	no	—
67	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₃	D₄	1	2	yes	—
69	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₃	D₄	1	2	yes	—
71	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₄₃	—	2	8	no	—
78	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
79	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
80	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
81	#123×C₄₃	—	2	2	no	—
82	#123×C₄₃	—	2	2	no	—
83	#123×C₄₃	—	2	4	no	—
84	C₂²⋊Q₈×C₄₃	—	2	2	no	—
85	C₂²⋊Q₈×C₄₃	—	2	2	no	—
86	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
87	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
88	#121×C₄₃	—	2	2	no	—
89	#121×C₄₃	—	2	2	no	—
90	#121×C₄₃	C₂³	1	4	yes	—
91	#121×C₄₃	C₂³	1	4	yes	—
92	#120×C₄₃	—	2	2	no	—
93	#120×C₄₃	—	2	4	no	—
94	#120×C₄₃	—	2	2	no	—
95	C₄×D₄×C₄₃	—	2	4	no	—
96	C₄×D₄×C₄₃	—	2	4	no	—
97	C₄×D₄×C₄₃	—	2	4	no	—
98	C₄×D₄×C₄₃	—	2	4	no	—
99	#117×C₄₃	—	2	4	no	—
100	#117×C₄₃	—	2	4	no	—
101	#117×C₄₃	—	2	2	no	—
102	#117×C₄₃	—	2	2	no	—
103	#117×C₄₃	—	2	4	no	—
104	#117×C₄₃	—	2	4	no	—
105	#117×C₄₃	—	2	4	no	—
106	#117×C₄₃	—	2	1	no	—
107	#117×C₄₃	—	2	1	no	—
108	#117×C₄₃	C₂³	1	4	yes	—
109	#117×C₄₃	C₂³	1	4	yes	—
110	#117×C₄₃	C₂³	1	8	yes	—
111	#117×C₄₃	C₂³	1	2	yes	—
112	#117×C₄₃	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
127	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
128	C₂×C₄²×C₄₃	—	2	4	no	—
129	C₂×C₄²×C₄₃	—	2	2	no	—
130	C₂×C₄²×C₄₃	—	2	2	no	—
131	C₂×C₄²×C₄₃	—	2	4	no	—
132	C₂×C₄²×C₄₃	—	2	1	no	—
133	#107×C₄₃	C₂³	1	16	yes	complemented
134	#106×C₄₃	C₂³	1	16	yes	complemented
135	#103×C₄₃	C₂³	1	16	yes	complemented
136	#102×C₄₃	C₂³	1	16	yes	complemented
137	C₂²⋊C₈×C₄₃	C₂³	1	8	yes	—
138	C₂²⋊C₈×C₄₃	C₂³	1	8	yes	—
139	C₂⁴×C₄₃	—	2	4	no	—
140	C₂⁴×C₄₃	—	2	1	no	—
141	C₂⁴×C₄₃	—	4	4	no	—
142	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
144	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
145	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
147	#41×C₄₃	—	2	8	no	—
148	#41×C₄₃	—	2	8	no	—
149	#41×C₄₃	—	4	4	no	—
150	#41×C₄₃	—	4	4	no	—
151	C₂×Q₈×C₄₃	—	2	1	no	—
152	C₂×Q₈×C₄₃	—	2	4	no	—
153	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
154	C₂×D₄×C₄₃	—	2	1	no	—
155	C₂×D₄×C₄₃	—	2	4	no	—
156	C₂×D₄×C₄₃	—	2	4	no	—
157	C₂×D₄×C₄₃	—	2	2	no	—
158	C₂×D₄×C₄₃	—	2	2	no	—
159	C₂×D₄×C₄₃	—	2	4	no	—
160	C₂×D₄×C₄₃	—	4	8	no	—
161	C₂×D₄×C₄₃	—	4	4	no	—
162	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₄₃	—	2	4	no	—
164	C₂²×C₄×C₄₃	—	2	8	no	—
165	C₂²×C₄×C₄₃	—	2	8	no	—
166	C₂²×C₄×C₄₃	—	2	4	no	—
167	C₂²×C₄×C₄₃	—	2	4	no	—
168	C₂²×C₄×C₄₃	—	2	8	no	—
169	C₂²×C₄×C₄₃	—	2	8	no	—
170	C₂²×C₄×C₄₃	—	2	4	no	—
171	C₂²×C₄×C₄₃	—	2	2	no	—
172	C₂²×C₄×C₄₃	—	2	2	no	—
173	C₂²×C₄×C₄₃	—	2	4	no	—
174	C₂²×C₄×C₄₃	—	2	4	no	—
175	C₂²×C₄×C₄₃	—	2	4	no	—
176	C₂²×C₄×C₄₃	—	2	4	no	—
177	C₂²×C₄×C₄₃	—	2	2	no	—
178	C₂²×C₄×C₄₃	—	2	1	no	—
179	C₂²×C₄×C₄₃	—	4	8	no	—
180	C₂²×C₄×C₄₃	—	4	4	no	—
181	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₃	#41	1	8	yes	—
195	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
200	M₁₆×C₄₃	—	2	8	no	—
201	M₁₆×C₄₃	—	2	8	no	—
202	C₂×C₈×C₄₃	—	2	8	no	—
203	C₂×C₈×C₄₃	C₂⁴	1	8	yes	—
204	C₄⋊C₄×C₄₃	—	2	4	no	—
205	C₄⋊C₄×C₄₃	—	2	4	no	—
206	C₄⋊C₄×C₄₃	—	2	4	no	—
207	C₄⋊C₄×C₄₃	—	2	4	no	—
208	C₄⋊C₄×C₄₃	—	2	4	no	—
209	C₄⋊C₄×C₄₃	—	2	2	no	—
210	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
211	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
212	C₂²⋊C₄×C₄₃	—	2	4	no	—
213	C₂²⋊C₄×C₄₃	—	2	4	no	—
214	C₂²⋊C₄×C₄₃	—	2	8	no	—
215	C₂²⋊C₄×C₄₃	—	2	4	no	—
216	C₂²⋊C₄×C₄₃	—	2	4	no	—
217	C₂²⋊C₄×C₄₃	—	2	2	no	—
218	C₂²⋊C₄×C₄₃	—	2	2	no	—
219	C₂²⋊C₄×C₄₃	—	2	4	no	—
220	C₂²⋊C₄×C₄₃	—	2	4	no	—
221	C₄²×C₄₃	—	2	8	no	—
222	C₄²×C₄₃	—	2	4	no	—
223	C₄²×C₄₃	—	2	2	no	—
224	C₄²×C₄₃	—	2	4	no	—
225	C₄²×C₄₃	—	2	2	no	—
226	C₂³×C₄₃	—	2	2	no	—
227	C₂³×C₄₃	—	2	4	no	—
228	C₂³×C₄₃	—	2	4	no	—
229	C₂³×C₄₃	—	2	4	no	—
230	C₂³×C₄₃	—	2	2	no	—
231	C₂³×C₄₃	—	2	4	no	—
232	C₂³×C₄₃	—	2	4	no	—
233	C₂³×C₄₃	—	2	2	no	—
234	C₂³×C₄₃	—	4	2	no	—
235	C₂³×C₄₃	—	4	2	no	—
236	C₂³×C₄₃	—	4	2	no	—
237	C₂³×C₄₃	—	4	2	no	—
238	C₂³×C₄₃	—	4	16	no	—
239	C₂³×C₄₃	—	4	4	no	—
240	C₂³×C₄₃	—	4	2	no	—
241	C₂³×C₄₃	#123	1	4	yes	—
242	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
243	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
244	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
245	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
246	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
247	Q₈×C₄₃	—	2	4	no	—
248	Q₈×C₄₃	—	4	2	no	—
249	D₄×C₄₃	—	2	4	no	—
250	D₄×C₄₃	—	4	8	no	—
251	D₄×C₄₃	—	4	4	no	—
252	D₄×C₄₃	—	4	4	no	—
253	D₄×C₄₃	—	4	8	no	—
254	D₄×C₄₃	—	4	2	no	—
255	C₂×C₄×C₄₃	—	2	4	no	—
256	C₂×C₄×C₄₃	—	2	2	no	—
257	C₂×C₄×C₄₃	—	2	2	no	—
258	C₂×C₄×C₄₃	—	2	4	no	—
259	C₂×C₄×C₄₃	—	2	4	no	—
260	C₂×C₄×C₄₃	—	2	4	no	—
261	C₂×C₄×C₄₃	—	2	4	no	—
262	C₂×C₄×C₄₃	—	2	4	no	—
263	C₂×C₄×C₄₃	—	2	4	no	—
264	C₂×C₄×C₄₃	—	2	4	no	—
265	C₂×C₄×C₄₃	—	2	4	no	—
266	C₂×C₄×C₄₃	—	2	4	no	—
267	C₂×C₄×C₄₃	—	2	8	no	—
268	C₂×C₄×C₄₃	—	2	4	no	—
269	C₂×C₄×C₄₃	—	2	2	no	—
270	C₂×C₄×C₄₃	—	4	8	no	—
271	C₂×C₄×C₄₃	—	4	8	no	—
272	C₂×C₄×C₄₃	—	4	4	no	—
273	C₂×C₄×C₄₃	—	4	2	no	—
274	C₂×C₄×C₄₃	—	4	8	no	—
275	C₂×C₄×C₄₃	—	4	4	no	—
276	C₂×C₄×C₄₃	—	4	4	no	—
277	C₂×C₄×C₄₃	#123	1	4	yes	—
278	C₂×C₄×C₄₃	#123	1	4	yes	—
279	C₂×C₄×C₄₃	#123	1	4	yes	—
280	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
286	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
287	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
288	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
289	C₈×C₄₃	—	2	8	no	—
290	#60511	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂²×C₄₃	—	2	8	no	—
292	C₂²×C₄₃	—	2	2	no	—
293	C₂²×C₄₃	—	2	2	no	—
294	C₂²×C₄₃	—	2	2	no	—
295	C₂²×C₄₃	—	2	2	no	—
296	C₂²×C₄₃	—	2	2	no	—
297	C₂²×C₄₃	—	2	2	no	—
298	C₂²×C₄₃	—	2	2	no	—
299	C₂²×C₄₃	—	2	2	no	—
300	C₂²×C₄₃	—	4	4	no	—
301	C₂²×C₄₃	—	4	8	no	—
302	C₂²×C₄₃	—	4	8	no	—
303	C₂²×C₄₃	—	4	4	no	—
304	C₂²×C₄₃	—	4	2	no	—
305	C₂²×C₄₃	—	4	4	no	—
306	C₂²×C₄₃	—	8	4	no	—
307	C₂²×C₄₃	C₂×#123	1	2	yes	—
308	C₂²×C₄₃	C₂×#123	1	2	yes	—
309	C₂²×C₄₃	C₂×#123	1	2	yes	—
310	C₂²×C₄₃	#575	1	4	yes	—
311	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
312	C₄×C₄₃	—	2	2	no	—
313	C₄×C₄₃	—	2	2	no	—
314	C₄×C₄₃	—	4	2	no	—
315	C₄×C₄₃	—	4	8	no	—
316	C₄×C₄₃	—	4	4	no	—
317	C₄×C₄₃	C₂×#123	1	2	yes	—
318	C₄×C₄₃	C₂×#123	1	2	yes	—
319	C₄×C₄₃	C₂×#123	1	2	yes	—
320	C₄×C₄₃	C₂²×#41	1	2	yes	—
321	C₂×#525	C₂×C₄₃	1	1	yes	characteristic
322	C₂²×#117	C₂×C₄₃	1	1	yes	characteristic, complemented
323	#3095	C₂×C₄₃	1	4	yes	complemented
324	#3094	C₂×C₄₃	1	4	yes	complemented
325	#3093	C₂×C₄₃	1	4	yes	complemented
326	#3092	C₂×C₄₃	1	4	yes	complemented
327	#3091	C₂×C₄₃	1	8	yes	complemented
328	#2911	C₂×C₄₃	1	2	yes	complemented
329	#2896	C₂×C₄₃	1	2	yes	complemented
330	C₂×#407	C₂×C₄₃	1	1	yes	characteristic, complemented
331	C₂×C₄₃	—	2	2	no	—
332	C₂×C₄₃	—	2	4	no	—
333	C₂×C₄₃	—	2	2	no	—
334	C₂×C₄₃	—	2	2	no	—
335	C₂×C₄₃	—	4	2	no	—
336	C₂×C₄₃	—	8	2	no	—
337	C₂×C₄₃	C₂²×#123	1	1	yes	characteristic
338	C₂×C₄₃	C₂×#575	1	2	yes	—
339	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
340	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
341	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
342	#525	—	2	1	no	—
343	#525	—	2	2	no	—
344	#525	—	2	1	no	—
345	#525	C₂²×C₄₃	1	4	yes	—
346	#525	C₂²×C₄₃	1	2	yes	—
347	#525	C₂²×C₄₃	1	2	yes	—
348	C₂×#123	—	2	1	no	—
349	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
350	C₂×#121	C₂²×C₄₃	1	2	yes	—
351	C₂×#120	—	2	1	no	—
352	C₂×C₄×D₄	—	2	2	no	—
353	C₂×#117	—	2	2	no	—
354	C₂×#117	—	2	1	no	—
355	C₂×#117	—	2	2	no	—
356	C₂×#117	—	2	1	no	—
357	C₂×#117	C₂²×C₄₃	1	4	yes	—
358	C₂×#117	C₂²×C₄₃	1	2	yes	—
359	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
360	C₂×#117	C₂²×C₄₃	1	4	yes	complemented
361	C₂×#117	C₂²×C₄₃	1	2	yes	complemented
362	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	complemented
363	C₂²×C₂²⋊C₄	—	2	1	no	—
364	C₂²×C₄²	—	2	1	no	—
365	#485	C₂²×C₄₃	1	16	yes	complemented
366	#484	C₂²×C₄₃	1	8	yes	complemented
367	#483	C₂²×C₄₃	1	8	yes	complemented
368	#482	C₂²×C₄₃	1	16	yes	complemented
369	#481	C₂²×C₄₃	1	8	yes	complemented
370	#480	C₂²×C₄₃	1	8	yes	complemented
371	#428	C₂²×C₄₃	1	8	yes	complemented
372	#428	C₂²×C₄₃	1	8	yes	complemented
373	#427	C₂²×C₄₃	1	8	yes	complemented
374	#419	C₂²×C₄₃	1	4	yes	complemented
375	#418	C₂²×C₄₃	1	4	yes	complemented
376	#417	C₂²×C₄₃	1	8	yes	complemented
377	#416	C₂²×C₄₃	1	8	yes	complemented
378	#407	C₂²×C₄₃	1	4	yes	—
379	#407	C₂²×C₄₃	1	2	yes	complemented
380	#407	C₂²×C₄₃	1	2	yes	complemented
381	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	complemented
382	C₄₃	#60511	1	1	yes	characteristic, direct product factor, Sylow
383	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
384	C₂×#41	—	2	1	no	—
385	C₂×#41	—	2	1	no	—
386	C₂×#41	—	2	8	no	—
387	C₂×#41	C₂³×C₄₃	1	2	yes	—
388	C₂×#41	C₂³×C₄₃	1	2	yes	—
389	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
390	C₂²×D₄	—	2	2	no	—
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
393	C₂³×C₄	—	2	8	no	—
394	C₂³×C₄	—	2	2	no	—
395	C₂³×C₄	—	2	1	no	—
396	C₂³×C₄	D₄×C₄₃	1	2	yes	—
397	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
398	C₂³×C₄	D₄×C₄₃	1	2	yes	—
399	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
400	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
403	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
404	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
406	C₂×M₁₆	—	2	8	no	—
407	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
408	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
409	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
410	#123	—	2	2	no	—
411	#123	—	2	2	no	—
412	#123	—	2	4	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	—	2	2	no	—
415	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
416	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
417	#121	—	2	2	no	—
418	#121	—	2	2	no	—
419	#121	C₂³×C₄₃	1	4	yes	—
420	#121	C₂³×C₄₃	1	4	yes	—
421	#120	—	2	2	no	—
422	#120	—	2	4	no	—
423	#120	—	2	2	no	—
424	C₄×D₄	—	2	4	no	—
425	C₄×D₄	—	2	4	no	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	—	2	4	no	—
428	#117	—	2	4	no	—
429	#117	—	2	4	no	—
430	#117	—	2	2	no	—
431	#117	—	2	2	no	—
432	#117	—	2	4	no	—
433	#117	—	2	4	no	—
434	#117	—	2	4	no	—
435	#117	—	2	1	no	—
436	#117	—	2	1	no	—
437	#117	C₂³×C₄₃	1	4	yes	—
438	#117	C₂³×C₄₃	1	4	yes	—
439	#117	C₂³×C₄₃	1	8	yes	—
440	#117	C₂³×C₄₃	1	2	yes	—
441	#117	C₂³×C₄₃	1	2	yes	—
442	C₂×C₄⋊C₄	—	2	2	no	—
443	C₂×C₄⋊C₄	—	2	2	no	—
444	C₂×C₄⋊C₄	—	2	2	no	—
445	C₂×C₄⋊C₄	—	2	2	no	—
446	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
448	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
449	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
450	C₂×C₂²⋊C₄	—	2	4	no	—
451	C₂×C₂²⋊C₄	—	2	2	no	—
452	C₂×C₂²⋊C₄	—	2	4	no	—
453	C₂×C₂²⋊C₄	—	2	2	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	2	no	—
456	C₂×C₂²⋊C₄	—	2	2	no	—
457	C₂×C₄²	—	2	4	no	—
458	C₂×C₄²	—	2	2	no	—
459	C₂×C₄²	—	2	4	no	—
460	C₂×C₄²	—	2	2	no	—
461	C₂×C₄²	—	2	1	no	—
462	#107	C₂³×C₄₃	1	16	yes	complemented
463	#106	C₂³×C₄₃	1	16	yes	complemented
464	#103	C₂³×C₄₃	1	16	yes	complemented
465	#102	C₂³×C₄₃	1	16	yes	complemented
466	C₂²⋊C₈	C₂³×C₄₃	1	8	yes	—
467	C₂²⋊C₈	C₂³×C₄₃	1	8	yes	—
468	C₂⁴	—	2	4	no	—
469	C₂⁴	—	2	1	no	—
470	C₂⁴	—	4	4	no	—
471	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
472	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
473	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
474	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
475	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
476	#41	—	2	8	no	—
477	#41	—	2	8	no	—
478	#41	—	4	4	no	—
479	#41	—	4	4	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	4	no	—
482	C₂×Q₈	C₂⁴×C₄₃	1	2	yes	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	4	8	no	—
490	C₂×D₄	—	4	4	no	—
491	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	8	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	8	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	2	8	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	4	8	no	—
509	C₂²×C₄	—	4	4	no	—
510	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
511	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
512	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
514	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
515	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
517	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
518	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
519	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
520	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
523	C₂²×C₄	#41×C₄₃	1	8	yes	—
524	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
529	M₁₆	—	2	8	no	—
530	M₁₆	—	2	8	no	—
531	C₂×C₈	—	2	8	no	—
532	C₂×C₈	C₂⁴×C₄₃	1	8	yes	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	C₂⁴×C₄₃	1	8	yes	—
540	C₄⋊C₄	C₂⁴×C₄₃	1	4	yes	—
541	C₂²⋊C₄	—	2	8	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₄²	—	2	8	no	—
551	C₄²	—	2	4	no	—
552	C₄²	—	2	4	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	4	2	no	—
564	C₂³	—	4	2	no	—
565	C₂³	—	4	2	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	4	16	no	—
568	C₂³	—	4	4	no	—
569	C₂³	—	4	2	no	—
570	C₂³	#123×C₄₃	1	4	yes	—
571	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
572	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
573	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
574	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
575	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
576	Q₈	—	2	4	no	—
577	Q₈	—	4	2	no	—
578	D₄	—	2	4	no	—
579	D₄	—	4	8	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	4	no	—
582	D₄	—	4	8	no	—
583	D₄	—	4	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	8	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	4	4	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	8	no	—
604	C₂×C₄	—	4	4	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	#123×C₄₃	1	4	yes	—
607	C₂×C₄	#123×C₄₃	1	4	yes	—
608	C₂×C₄	#123×C₄₃	1	4	yes	—
609	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
610	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
611	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
612	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
613	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
614	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
615	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
616	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
617	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
618	C₈	—	2	8	no	—
619	C₂²	—	2	8	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	4	8	no	—
630	C₂²	—	4	8	no	—
631	C₂²	—	4	4	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	8	4	no	—
635	C₂²	C₂×#123×C₄₃	1	2	yes	—
636	C₂²	C₂×#123×C₄₃	1	2	yes	—
637	C₂²	C₂×#123×C₄₃	1	2	yes	—
638	C₂²	C₄₃×#575	1	4	yes	—
639	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	8	no	—
644	C₄	—	4	4	no	—
645	C₄	C₂×#123×C₄₃	1	2	yes	—
646	C₄	C₂×#123×C₄₃	1	2	yes	—
647	C₄	C₂×#123×C₄₃	1	2	yes	—
648	C₄	C₂²×#41×C₄₃	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	2	4	no	—
651	C₂	—	2	2	no	—
652	C₂	—	2	2	no	—
653	C₂	—	4	2	no	—
654	C₂	—	8	2	no	—
655	C₂	C₂²×#123×C₄₃	1	1	yes	characteristic
656	C₂	C₂×C₄₃×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×C₄₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₄₃	C₂	semidirect
3. C₄₃×#3095	C₂	semidirect
4. C₄₃×#3094	C₂	semidirect
5. C₄₃×#3093	C₂	semidirect
6. C₄₃×#3092	C₂	semidirect
7. C₄₃×#3091	C₂	semidirect
8. C₄₃×#2911	C₂	semidirect
9. C₄₃×#2896	C₂	semidirect
10. C₂×C₄₃×#407	C₂	semidirect
32. C₂×#117×C₄₃	C₂²	semidirect
33. C₂×#117×C₄₃	C₂²	semidirect
34. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
37. C₄₃×#485	C₂²	semidirect
38. C₄₃×#484	C₂²	semidirect
39. C₄₃×#483	C₂²	semidirect
40. C₄₃×#482	C₂²	semidirect
41. C₄₃×#481	C₂²	semidirect
42. C₄₃×#480	C₂²	semidirect
43. C₄₃×#428	C₂²	semidirect
44. C₄₃×#428	C₂²	semidirect
45. C₄₃×#427	C₂²	semidirect
46. C₄₃×#419	C₂²	semidirect
47. C₄₃×#418	C₂²	semidirect
48. C₄₃×#417	C₂²	semidirect
49. C₄₃×#416	C₂²	semidirect
51. C₄₃×#407	C₂²	semidirect
52. C₄₃×#407	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
133. #107×C₄₃	C₂³	semidirect
134. #106×C₄₃	C₂³	semidirect
135. #103×C₄₃	C₂³	semidirect
136. #102×C₄₃	C₂³	semidirect
290. #60511	C₄₃	direct (N × H)
322. C₂²×#117	C₂×C₄₃	semidirect
323. #3095	C₂×C₄₃	semidirect
324. #3094	C₂×C₄₃	semidirect
325. #3093	C₂×C₄₃	semidirect
326. #3092	C₂×C₄₃	semidirect
327. #3091	C₂×C₄₃	semidirect
328. #2911	C₂×C₄₃	semidirect
329. #2896	C₂×C₄₃	semidirect
330. C₂×#407	C₂×C₄₃	semidirect
360. C₂×#117	C₂²×C₄₃	semidirect
361. C₂×#117	C₂²×C₄₃	semidirect
362. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
365. #485	C₂²×C₄₃	semidirect
366. #484	C₂²×C₄₃	semidirect
367. #483	C₂²×C₄₃	semidirect
368. #482	C₂²×C₄₃	semidirect
369. #481	C₂²×C₄₃	semidirect
370. #480	C₂²×C₄₃	semidirect
371. #428	C₂²×C₄₃	semidirect
372. #428	C₂²×C₄₃	semidirect
373. #427	C₂²×C₄₃	semidirect
374. #419	C₂²×C₄₃	semidirect
375. #418	C₂²×C₄₃	semidirect
376. #417	C₂²×C₄₃	semidirect
377. #416	C₂²×C₄₃	semidirect
379. #407	C₂²×C₄₃	semidirect
380. #407	C₂²×C₄₃	semidirect
381. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
382. C₄₃	#60511	direct (N × H)
462. #107	C₂³×C₄₃	semidirect
463. #106	C₂³×C₄₃	semidirect
464. #103	C₂³×C₄₃	semidirect
465. #102	C₂³×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×#525	2
C₂²×#117×C₄₃	2
C₄₃×#3095	2
C₄₃×#3094	2
C₄₃×#3093	2
C₄₃×#3092	2
C₄₃×#3091	2
C₄₃×#2911	2
C₄₃×#2896	2
C₂×C₄₃×#407	2
#60511	43

Subgroups — C43×#60511 #24980528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#60511 #24980528