Subgroups — C₄₃×#32913 #24952930

Order 11008.

1506 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×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#449	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2619	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1880	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1879	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1874	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#121×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#520	—	2	4	no	—
18	C₄₃×#520	—	2	4	no	—
19	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₃	—	2	1	no	—
22	C₂×C₄×D₄×C₄₃	—	2	1	no	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₃	—	2	1	no	—
26	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
28	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#460	—	2	4	no	—
30	C₄₃×#459	—	2	4	no	—
31	C₄₃×#449	—	2	8	no	—
32	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#103×C₄₃	C₂²	1	2	yes	—
35	C₂×#102×C₄₃	C₂²	1	2	yes	—
36	C₂×#102×C₄₃	C₂²	1	2	yes	—
37	C₂×#102×C₄₃	C₂²	1	2	yes	—
38	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
39	C₄₃×#394	—	2	1	no	—
40	C₄₃×#394	—	2	1	no	—
41	C₄₃×#392	—	2	1	no	—
42	C₄₃×#392	—	2	1	no	—
43	C₄₃×#390	C₂²	1	2	yes	—
44	C₄₃×#382	C₂²	1	1	yes	characteristic
45	C₄₃×#340	C₂²	1	2	yes	—
46	C₄₃×#340	C₂²	1	2	yes	—
47	C₄₃×#336	C₂²	1	2	yes	—
48	C₂×#41×C₄₃	—	2	2	no	—
49	C₂×#41×C₄₃	—	2	2	no	—
50	C₂×#41×C₄₃	—	2	2	no	—
51	C₂×#41×C₄₃	—	2	2	no	—
52	C₂×#41×C₄₃	—	2	2	no	—
53	C₂×#41×C₄₃	D₄	1	4	yes	complemented
54	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₄₃	—	2	1	no	—
56	C₂²×D₄×C₄₃	—	2	2	no	—
57	C₂²×D₄×C₄₃	—	2	1	no	—
58	C₂²×D₄×C₄₃	—	2	1	no	—
59	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	—	2	1	no	—
62	C₂³×C₄×C₄₃	—	2	1	no	—
63	C₂³×C₄×C₄₃	—	2	1	no	—
64	C₂³×C₄×C₄₃	—	2	1	no	—
65	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₄₃	—	2	4	no	—
67	C₂×SD₁₆×C₄₃	—	2	4	no	—
68	C₂×SD₁₆×C₄₃	—	2	4	no	—
69	C₂×D₈×C₄₃	—	2	4	no	—
70	C₂×D₈×C₄₃	—	2	4	no	—
71	C₂×D₈×C₄₃	—	2	4	no	—
72	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
74	#127×C₄₃	—	2	2	no	—
75	#127×C₄₃	—	2	2	no	—
76	#121×C₄₃	—	2	4	no	—
77	#121×C₄₃	—	2	4	no	—
78	C₄×Q₈×C₄₃	—	2	2	no	—
79	C₄×Q₈×C₄₃	—	2	2	no	—
80	C₄×Q₈×C₄₃	—	2	2	no	—
81	C₄×Q₈×C₄₃	D₄	1	4	yes	complemented
82	C₄×D₄×C₄₃	—	2	8	no	—
83	C₄×D₄×C₄₃	—	2	8	no	—
84	C₄×D₄×C₄₃	—	2	2	no	—
85	C₄×D₄×C₄₃	—	2	2	no	—
86	C₄×D₄×C₄₃	—	2	2	no	—
87	C₄×D₄×C₄₃	D₄	1	4	yes	complemented
88	#117×C₄₃	—	2	8	no	—
89	#117×C₄₃	—	2	2	no	—
90	#117×C₄₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
92	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
97	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₃	—	2	1	no	—
110	C₂×C₄²×C₄₃	—	2	1	no	—
111	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₃	—	2	2	no	—
114	C₄⋊C₈×C₄₃	—	2	2	no	—
115	#103×C₄₃	—	2	4	no	—
116	#102×C₄₃	—	2	4	no	—
117	#102×C₄₃	—	2	4	no	—
118	#102×C₄₃	—	2	4	no	—
119	C₂²⋊C₈×C₄₃	—	2	4	no	—
120	#95×C₄₃	—	2	1	no	—
121	#95×C₄₃	—	2	1	no	—
122	C₂⁴×C₄₃	—	2	1	no	—
123	C₂⁴×C₄₃	—	2	2	no	—
124	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
125	#41×C₄₃	—	2	8	no	—
126	#41×C₄₃	—	2	8	no	—
127	#41×C₄₃	—	2	8	no	—
128	#41×C₄₃	—	2	8	no	—
129	C₂×Q₈×C₄₃	—	2	1	no	—
130	C₂×Q₈×C₄₃	—	2	1	no	—
131	C₂×Q₈×C₄₃	—	2	1	no	—
132	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₄₃	#41	1	2	yes	—
135	C₂×D₄×C₄₃	—	2	4	no	—
136	C₂×D₄×C₄₃	—	2	4	no	—
137	C₂×D₄×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	1	no	—
139	C₂×D₄×C₄₃	—	2	1	no	—
140	C₂×D₄×C₄₃	—	2	4	no	—
141	C₂×D₄×C₄₃	—	2	2	no	—
142	C₂×D₄×C₄₃	—	2	2	no	—
143	C₂×D₄×C₄₃	—	2	2	no	—
144	C₂×D₄×C₄₃	—	2	2	no	—
145	C₂×D₄×C₄₃	—	2	2	no	—
146	C₂×D₄×C₄₃	—	2	2	no	—
147	C₂×D₄×C₄₃	—	4	2	no	—
148	C₂×D₄×C₄₃	—	4	2	no	—
149	C₂×D₄×C₄₃	—	4	4	no	—
150	C₂×D₄×C₄₃	—	8	2	no	—
151	C₂×D₄×C₄₃	—	8	2	no	—
152	C₂×D₄×C₄₃	—	8	2	no	—
153	C₂×D₄×C₄₃	—	8	2	no	—
154	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₄₃	#41	1	2	yes	—
157	C₂²×C₄×C₄₃	—	2	4	no	—
158	C₂²×C₄×C₄₃	—	2	4	no	—
159	C₂²×C₄×C₄₃	—	2	4	no	—
160	C₂²×C₄×C₄₃	—	2	1	no	—
161	C₂²×C₄×C₄₃	—	2	1	no	—
162	C₂²×C₄×C₄₃	—	2	1	no	—
163	C₂²×C₄×C₄₃	—	2	1	no	—
164	C₂²×C₄×C₄₃	—	2	4	no	—
165	C₂²×C₄×C₄₃	—	2	4	no	—
166	C₂²×C₄×C₄₃	—	2	4	no	—
167	C₂²×C₄×C₄₃	—	2	1	no	—
168	C₂²×C₄×C₄₃	—	2	1	no	—
169	C₂²×C₄×C₄₃	—	2	1	no	—
170	C₂²×C₄×C₄₃	—	2	2	no	—
171	C₂²×C₄×C₄₃	—	8	2	no	—
172	C₂²×C₄×C₄₃	—	8	2	no	—
173	C₂²×C₄×C₄₃	—	8	2	no	—
174	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₄₃	#41	1	2	yes	—
181	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
182	SD₁₆×C₄₃	—	4	8	no	—
183	D₈×C₄₃	—	4	8	no	—
184	C₂×C₈×C₄₃	—	2	2	no	—
185	C₂×C₈×C₄₃	—	2	2	no	—
186	C₂×C₈×C₄₃	—	2	2	no	—
187	C₂×C₈×C₄₃	—	2	2	no	—
188	C₂×C₈×C₄₃	—	2	2	no	—
189	C₂×C₈×C₄₃	—	2	2	no	—
190	C₄⋊C₄×C₄₃	—	2	4	no	—
191	C₄⋊C₄×C₄₃	—	2	4	no	—
192	C₄⋊C₄×C₄₃	—	2	2	no	—
193	C₄⋊C₄×C₄₃	—	2	4	no	—
194	C₄⋊C₄×C₄₃	—	2	2	no	—
195	C₄⋊C₄×C₄₃	—	2	1	no	—
196	C₄⋊C₄×C₄₃	—	2	1	no	—
197	C₄⋊C₄×C₄₃	—	2	2	no	—
198	C₄⋊C₄×C₄₃	—	2	2	no	—
199	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
201	C₂²⋊C₄×C₄₃	—	2	4	no	—
202	C₂²⋊C₄×C₄₃	—	2	4	no	—
203	C₂²⋊C₄×C₄₃	—	2	2	no	—
204	C₂²⋊C₄×C₄₃	—	2	2	no	—
205	C₂²⋊C₄×C₄₃	—	4	4	no	—
206	C₂²⋊C₄×C₄₃	—	8	2	no	—
207	C₂²⋊C₄×C₄₃	—	8	2	no	—
208	C₄²×C₄₃	—	2	4	no	—
209	C₄²×C₄₃	—	2	4	no	—
210	C₄²×C₄₃	—	2	1	no	—
211	C₄²×C₄₃	—	2	1	no	—
212	C₄²×C₄₃	C₂×D₄	1	2	yes	—
213	C₄²×C₄₃	C₂×D₄	1	2	yes	—
214	C₂³×C₄₃	—	2	1	no	—
215	C₂³×C₄₃	—	2	2	no	—
216	C₂³×C₄₃	—	2	2	no	—
217	C₂³×C₄₃	—	2	1	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	2	2	no	—
220	C₂³×C₄₃	—	2	2	no	—
221	C₂³×C₄₃	—	4	2	no	—
222	C₂³×C₄₃	—	4	2	no	—
223	C₂³×C₄₃	—	4	2	no	—
224	C₂³×C₄₃	—	4	2	no	—
225	C₂³×C₄₃	—	4	2	no	—
226	C₂³×C₄₃	—	4	2	no	—
227	C₂³×C₄₃	—	4	2	no	—
228	C₂³×C₄₃	—	4	2	no	—
229	C₂³×C₄₃	—	4	2	no	—
230	C₂³×C₄₃	#121	1	2	yes	—
231	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₄₃	—	2	2	no	—
233	Q₈×C₄₃	—	2	2	no	—
234	Q₈×C₄₃	—	2	2	no	—
235	Q₈×C₄₃	#121	1	4	yes	—
236	D₄×C₄₃	—	2	16	no	—
237	D₄×C₄₃	—	2	2	no	—
238	D₄×C₄₃	—	2	2	no	—
239	D₄×C₄₃	—	2	2	no	—
240	D₄×C₄₃	—	4	2	no	—
241	D₄×C₄₃	—	4	2	no	—
242	D₄×C₄₃	—	4	2	no	—
243	D₄×C₄₃	—	4	2	no	—
244	D₄×C₄₃	—	8	4	no	—
245	D₄×C₄₃	—	8	4	no	—
246	D₄×C₄₃	—	8	8	no	—
247	D₄×C₄₃	#121	1	4	yes	—
248	C₂×C₄×C₄₃	—	2	16	no	—
249	C₂×C₄×C₄₃	—	2	2	no	—
250	C₂×C₄×C₄₃	—	2	1	no	—
251	C₂×C₄×C₄₃	—	2	2	no	—
252	C₂×C₄×C₄₃	—	2	1	no	—
253	C₂×C₄×C₄₃	—	2	2	no	—
254	C₂×C₄×C₄₃	—	2	2	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	2	2	no	—
257	C₂×C₄×C₄₃	—	2	2	no	—
258	C₂×C₄×C₄₃	—	2	2	no	—
259	C₂×C₄×C₄₃	—	2	2	no	—
260	C₂×C₄×C₄₃	—	2	1	no	—
261	C₂×C₄×C₄₃	—	2	1	no	—
262	C₂×C₄×C₄₃	—	2	2	no	—
263	C₂×C₄×C₄₃	—	2	2	no	—
264	C₂×C₄×C₄₃	—	2	2	no	—
265	C₂×C₄×C₄₃	—	2	2	no	—
266	C₂×C₄×C₄₃	—	4	2	no	—
267	C₂×C₄×C₄₃	—	4	2	no	—
268	C₂×C₄×C₄₃	—	4	2	no	—
269	C₂×C₄×C₄₃	—	4	2	no	—
270	C₂×C₄×C₄₃	—	4	2	no	—
271	C₂×C₄×C₄₃	—	8	4	no	—
272	C₂×C₄×C₄₃	—	8	4	no	—
273	C₂×C₄×C₄₃	—	8	4	no	—
274	C₂×C₄×C₄₃	#120	1	2	yes	—
275	C₂×C₄×C₄₃	#120	1	2	yes	—
276	C₂×C₄×C₄₃	#121	1	2	yes	—
277	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
283	C₈×C₄₃	—	4	2	no	—
284	C₈×C₄₃	—	4	2	no	—
285	#32913	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂²×C₄₃	—	2	4	no	—
287	C₂²×C₄₃	—	2	2	no	—
288	C₂²×C₄₃	—	2	4	no	—
289	C₂²×C₄₃	—	4	2	no	—
290	C₂²×C₄₃	—	4	4	no	—
291	C₂²×C₄₃	—	4	1	no	—
292	C₂²×C₄₃	—	4	2	no	—
293	C₂²×C₄₃	—	4	1	no	—
294	C₂²×C₄₃	—	4	2	no	—
295	C₂²×C₄₃	—	4	4	no	—
296	C₂²×C₄₃	—	8	2	no	—
297	C₂²×C₄₃	—	8	2	no	—
298	C₂²×C₄₃	—	8	2	no	—
299	C₂²×C₄₃	—	8	2	no	—
300	C₂²×C₄₃	—	8	2	no	—
301	C₂²×C₄₃	—	8	2	no	—
302	C₂²×C₄₃	—	8	2	no	—
303	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
304	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
305	C₂²×C₄₃	#525	1	1	yes	characteristic
306	C₂²×C₄₃	#576	1	2	yes	—
307	C₂²×C₄₃	#577	1	2	yes	—
308	C₄×C₄₃	—	2	2	no	—
309	C₄×C₄₃	—	2	4	no	—
310	C₄×C₄₃	—	2	2	no	—
311	C₄×C₄₃	—	2	2	no	—
312	C₄×C₄₃	—	4	1	no	—
313	C₄×C₄₃	—	4	2	no	—
314	C₄×C₄₃	—	4	2	no	—
315	C₄×C₄₃	—	4	1	no	—
316	C₄×C₄₃	—	8	2	no	—
317	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
318	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
319	C₄×C₄₃	#525	1	1	yes	characteristic
320	C₄×C₄₃	#525	1	1	yes	characteristic
321	C₂×#520	C₂×C₄₃	1	1	yes	characteristic, complemented
322	C₂×#460	C₂×C₄₃	1	1	yes	characteristic, complemented
323	C₂×#459	C₂×C₄₃	1	1	yes	characteristic, complemented
324	C₂×#449	C₂×C₄₃	1	2	yes	complemented
325	#2619	C₂×C₄₃	1	1	yes	characteristic, complemented
326	#1880	C₂×C₄₃	1	2	yes	complemented
327	#1879	C₂×C₄₃	1	2	yes	complemented
328	#1874	C₂×C₄₃	1	2	yes	complemented
329	#1805	C₂×C₄₃	1	1	yes	characteristic, complemented
330	#1804	C₂×C₄₃	1	1	yes	characteristic, complemented
331	#1798	C₂×C₄₃	1	1	yes	characteristic, complemented
332	C₂×C₄₃	—	4	2	no	—
333	C₂×C₄₃	—	4	4	no	—
334	C₂×C₄₃	—	16	2	no	—
335	C₂×C₄₃	#2847	1	1	yes	characteristic
336	C₂×C₄₃	#3008	1	1	yes	characteristic
337	C₂×C₄₃	#3010	1	1	yes	characteristic
338	C₂×C₄₃	#3045	1	2	yes	—
339	C₂×C₄₃	#3119	1	2	yes	—
340	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
341	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
342	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
343	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
344	C₂×#121	C₂²×C₄₃	1	2	yes	—
345	#520	—	2	4	no	—
346	#520	—	2	4	no	—
347	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
348	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
349	C₂×C₄×D₄	—	2	1	no	—
350	C₂×C₄×D₄	—	2	1	no	—
351	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
352	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
353	C₂×#117	—	2	1	no	—
354	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
355	C₂²×C₄⋊C₄	—	2	1	no	—
356	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
357	#460	—	2	4	no	—
358	#459	—	2	4	no	—
359	#449	—	2	8	no	—
360	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
361	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
362	C₂×#103	C₂²×C₄₃	1	2	yes	—
363	C₂×#102	C₂²×C₄₃	1	2	yes	—
364	C₂×#102	C₂²×C₄₃	1	2	yes	—
365	C₂×#102	C₂²×C₄₃	1	2	yes	—
366	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
367	#394	—	2	1	no	—
368	#394	—	2	1	no	—
369	#392	—	2	1	no	—
370	#392	—	2	1	no	—
371	#390	C₂²×C₄₃	1	2	yes	—
372	#382	C₂²×C₄₃	1	1	yes	characteristic
373	#340	C₂²×C₄₃	1	2	yes	—
374	#340	C₂²×C₄₃	1	2	yes	—
375	#336	C₂²×C₄₃	1	2	yes	—
376	C₄₃	#32913	1	1	yes	characteristic, direct product factor, Sylow
377	C₂×#41	—	2	2	no	—
378	C₂×#41	—	2	2	no	—
379	C₂×#41	—	2	2	no	—
380	C₂×#41	—	2	2	no	—
381	C₂×#41	—	2	2	no	—
382	C₂×#41	D₄×C₄₃	1	4	yes	complemented
383	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
384	C₂²×D₄	—	2	1	no	—
385	C₂²×D₄	—	2	2	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
389	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
395	C₂×SD₁₆	—	2	4	no	—
396	C₂×SD₁₆	—	2	4	no	—
397	C₂×SD₁₆	—	2	4	no	—
398	C₂×D₈	—	2	4	no	—
399	C₂×D₈	—	2	4	no	—
400	C₂×D₈	—	2	4	no	—
401	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
402	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
403	#127	—	2	2	no	—
404	#127	—	2	2	no	—
405	#121	—	2	4	no	—
406	#121	—	2	4	no	—
407	C₄×Q₈	—	2	2	no	—
408	C₄×Q₈	—	2	2	no	—
409	C₄×Q₈	—	2	2	no	—
410	C₄×Q₈	D₄×C₄₃	1	4	yes	complemented
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	8	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	D₄×C₄₃	1	4	yes	complemented
417	#117	—	2	8	no	—
418	#117	—	2	2	no	—
419	#117	—	2	2	no	—
420	C₂×C₄⋊C₄	—	2	8	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	2	no	—
425	C₂×C₄⋊C₄	—	2	2	no	—
426	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	2	no	—
434	C₂×C₂²⋊C₄	—	2	2	no	—
435	C₂×C₂²⋊C₄	—	2	2	no	—
436	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
442	C₄⋊C₈	—	2	2	no	—
443	C₄⋊C₈	—	2	2	no	—
444	#103	—	2	4	no	—
445	#102	—	2	4	no	—
446	#102	—	2	4	no	—
447	#102	—	2	4	no	—
448	C₂²⋊C₈	—	2	4	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	C₂⁴	—	2	1	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
454	#41	—	2	8	no	—
455	#41	—	2	8	no	—
456	#41	—	2	8	no	—
457	#41	—	2	8	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
462	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
463	C₂×Q₈	#41×C₄₃	1	2	yes	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	4	4	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	8	2	no	—
480	C₂×D₄	—	8	2	no	—
481	C₂×D₄	—	8	2	no	—
482	C₂×D₄	—	8	2	no	—
483	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
484	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
485	C₂×D₄	#41×C₄₃	1	2	yes	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	8	2	no	—
501	C₂²×C₄	—	8	2	no	—
502	C₂²×C₄	—	8	2	no	—
503	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
509	C₂²×C₄	#41×C₄₃	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
511	SD₁₆	—	4	8	no	—
512	D₈	—	4	8	no	—
513	C₂×C₈	—	2	2	no	—
514	C₂×C₈	—	2	2	no	—
515	C₂×C₈	—	2	2	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	2	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
529	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	4	4	no	—
535	C₂²⋊C₄	—	8	2	no	—
536	C₂²⋊C₄	—	8	2	no	—
537	C₄²	—	2	4	no	—
538	C₄²	—	2	4	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	C₂×D₄×C₄₃	1	2	yes	—
542	C₄²	C₂×D₄×C₄₃	1	2	yes	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	#121×C₄₃	1	2	yes	—
560	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	#121×C₄₃	1	4	yes	—
565	D₄	—	2	16	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	8	4	no	—
574	D₄	—	8	4	no	—
575	D₄	—	8	8	no	—
576	D₄	#121×C₄₃	1	4	yes	—
577	C₂×C₄	—	2	16	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	8	4	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	#120×C₄₃	1	2	yes	—
604	C₂×C₄	#120×C₄₃	1	2	yes	—
605	C₂×C₄	#121×C₄₃	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
610	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
611	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
612	C₈	—	4	2	no	—
613	C₈	—	4	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	4	no	—
624	C₂²	—	8	2	no	—
625	C₂²	—	8	2	no	—
626	C₂²	—	8	2	no	—
627	C₂²	—	8	2	no	—
628	C₂²	—	8	2	no	—
629	C₂²	—	8	2	no	—
630	C₂²	—	8	2	no	—
631	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
632	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
633	C₂²	C₄₃×#525	1	1	yes	characteristic
634	C₂²	C₄₃×#576	1	2	yes	—
635	C₂²	C₄₃×#577	1	2	yes	—
636	C₄	—	2	2	no	—
637	C₄	—	2	4	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	1	no	—
644	C₄	—	8	2	no	—
645	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
646	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
647	C₄	C₄₃×#525	1	1	yes	characteristic
648	C₄	C₄₃×#525	1	1	yes	characteristic
649	C₂	—	4	2	no	—
650	C₂	—	4	4	no	—
651	C₂	—	16	2	no	—
652	C₂	C₄₃×#2847	1	1	yes	characteristic
653	C₂	C₄₃×#3008	1	1	yes	characteristic
654	C₂	C₄₃×#3010	1	1	yes	characteristic
655	C₂	C₄₃×#3045	1	2	yes	—
656	C₂	C₄₃×#3119	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#520	C₂	semidirect
2. C₂×C₄₃×#460	C₂	semidirect
3. C₂×C₄₃×#459	C₂	semidirect
4. C₂×C₄₃×#449	C₂	semidirect
5. C₄₃×#2619	C₂	semidirect
6. C₄₃×#1880	C₂	semidirect
7. C₄₃×#1879	C₂	semidirect
8. C₄₃×#1874	C₂	semidirect
9. C₄₃×#1805	C₂	semidirect
10. C₄₃×#1804	C₂	semidirect
11. C₄₃×#1798	C₂	semidirect
53. C₂×#41×C₄₃	D₄	semidirect
81. C₄×Q₈×C₄₃	D₄	semidirect
87. C₄×D₄×C₄₃	D₄	semidirect
285. #32913	C₄₃	direct (N × H)
321. C₂×#520	C₂×C₄₃	semidirect
322. C₂×#460	C₂×C₄₃	semidirect
323. C₂×#459	C₂×C₄₃	semidirect
324. C₂×#449	C₂×C₄₃	semidirect
325. #2619	C₂×C₄₃	semidirect
326. #1880	C₂×C₄₃	semidirect
327. #1879	C₂×C₄₃	semidirect
328. #1874	C₂×C₄₃	semidirect
329. #1805	C₂×C₄₃	semidirect
330. #1804	C₂×C₄₃	semidirect
331. #1798	C₂×C₄₃	semidirect
376. C₄₃	#32913	direct (N × H)
382. C₂×#41	D₄×C₄₃	semidirect
410. C₄×Q₈	D₄×C₄₃	semidirect
416. C₄×D₄	D₄×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×#520	2
C₂×C₄₃×#460	2
C₂×C₄₃×#459	2
C₂×C₄₃×#449	2
C₄₃×#2619	2
C₄₃×#1880	2
C₄₃×#1879	2
C₄₃×#1874	2
C₄₃×#1805	2
C₄₃×#1804	2
C₄₃×#1798	2
#32913	43

Subgroups — C43×#32913 #24952930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#32913 #24952930