Subgroups — C₄₃×#20943 #24940960

Order 11008.

1778 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1883	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1882	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₃×#343	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1733	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	C₄₃×#575	—	2	4	no	—
13	C₄₃×#575	C₄	1	8	yes	complemented
14	C₂×#137×C₄₃	—	2	1	no	—
15	C₂×#137×C₄₃	C₂²	1	2	yes	—
16	C₂×AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
17	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	2	yes	—
18	C₂×#135×C₄₃	—	2	2	no	—
19	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#520	—	2	2	no	—
22	C₄₃×#520	—	2	2	no	—
23	C₄₃×#520	—	2	2	no	—
24	C₄₃×#520	C₂²	1	4	yes	—
25	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
26	C₂×C₄×D₄×C₄₃	—	2	1	no	—
27	C₂×C₄×D₄×C₄₃	—	2	2	no	—
28	C₂×#117×C₄₃	—	2	1	no	—
29	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
32	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#421	—	2	4	no	—
34	C₂×#104×C₄₃	C₂²	1	4	yes	—
35	C₄₃×#419	C₂²	1	2	yes	complemented
36	C₄₃×#418	C₂²	1	2	yes	complemented
37	C₄₃×#417	—	2	1	no	—
38	C₄₃×#417	—	2	1	no	—
39	C₄₃×#416	—	2	2	no	—
40	C₄₃×#391	C₂²	1	2	yes	complemented
41	C₄₃×#390	C₂²	1	2	yes	complemented
42	C₄₃×#386	—	2	2	no	—
43	C₄₃×#380	—	2	2	no	—
44	C₄₃×#343	C₂²	1	4	yes	complemented
45	C₄₃×#339	C₂²	1	4	yes	complemented
46	C₂×#41×C₄₃	—	2	1	no	—
47	C₂×#41×C₄₃	—	2	1	no	—
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	1	no	—
52	C₂×#41×C₄₃	—	2	1	no	—
53	C₂×#41×C₄₃	—	2	2	no	—
54	C₂×#41×C₄₃	—	2	1	no	—
55	C₂×#41×C₄₃	—	2	1	no	—
56	C₂×#41×C₄₃	—	2	2	no	—
57	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
58	C₂×#41×C₄₃	C₂×C₄	1	4	yes	complemented
59	C₂×#41×C₄₃	D₄	1	4	yes	—
60	C₂×#41×C₄₃	D₄	1	2	yes	—
61	C₂×#41×C₄₃	C₂³	1	2	yes	—
62	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
63	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₄₃	—	2	1	no	—
65	C₂²×D₄×C₄₃	—	2	1	no	—
66	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₃	—	2	1	no	—
69	C₂³×C₄×C₄₃	—	2	2	no	—
70	C₂³×C₄×C₄₃	—	2	1	no	—
71	C₂³×C₄×C₄₃	D₄	1	2	yes	—
72	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
73	#137×C₄₃	—	2	4	no	—
74	#137×C₄₃	—	2	8	no	—
75	#137×C₄₃	C₂×C₄	1	8	yes	complemented
76	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
77	AGL(1,ℤ/8)×C₄₃	—	2	8	no	—
78	AGL(1,ℤ/8)×C₄₃	C₂×C₄	1	8	yes	complemented
79	#135×C₄₃	—	2	16	no	—
80	C₂×Q₁₆×C₄₃	—	2	2	no	—
81	C₂×SD₁₆×C₄₃	—	2	2	no	—
82	C₂×SD₁₆×C₄₃	—	2	2	no	—
83	C₂×D₈×C₄₃	—	2	2	no	—
84	C₂×M₁₆×C₄₃	—	2	1	no	—
85	C₂×M₁₆×C₄₃	—	2	2	no	—
86	C₂×M₁₆×C₄₃	—	2	1	no	—
87	C₂×M₁₆×C₄₃	—	2	2	no	—
88	C₂×M₁₆×C₄₃	—	2	2	no	—
89	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
90	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
91	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
92	C₂²×C₈×C₄₃	—	2	1	no	—
93	C₂²×C₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	—	2	4	no	—
95	C₄×Q₈×C₄₃	—	2	4	no	—
96	C₄×D₄×C₄₃	—	2	8	no	—
97	C₄×D₄×C₄₃	—	2	4	no	—
98	C₄×D₄×C₄₃	—	2	4	no	—
99	C₄×D₄×C₄₃	—	2	8	no	—
100	#117×C₄₃	—	2	4	no	—
101	#117×C₄₃	—	2	1	no	—
102	#117×C₄₃	—	2	1	no	—
103	#117×C₄₃	—	2	4	no	—
104	#117×C₄₃	—	2	2	no	—
105	#117×C₄₃	—	2	2	no	—
106	#117×C₄₃	D₄	1	2	yes	—
107	#117×C₄₃	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
109	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
110	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
112	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
114	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
115	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
116	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
117	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
121	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
124	C₂×C₄²×C₄₃	—	2	2	no	—
125	C₂×C₄²×C₄₃	—	2	1	no	—
126	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
127	#104×C₄₃	—	2	8	no	—
128	#103×C₄₃	—	2	2	no	—
129	#103×C₄₃	—	2	2	no	—
130	#102×C₄₃	—	2	2	no	—
131	#102×C₄₃	—	2	2	no	—
132	#95×C₄₃	—	2	4	no	—
133	C₂⁴×C₄₃	—	2	1	no	—
134	C₂⁴×C₄₃	—	2	1	no	—
135	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
136	#41×C₄₃	—	2	4	no	—
137	#41×C₄₃	—	2	4	no	—
138	#41×C₄₃	—	2	4	no	—
139	#41×C₄₃	—	2	4	no	—
140	#41×C₄₃	—	2	4	no	—
141	#41×C₄₃	—	2	2	no	—
142	#41×C₄₃	—	2	2	no	—
143	#41×C₄₃	—	2	4	no	—
144	#41×C₄₃	—	2	4	no	—
145	#41×C₄₃	—	2	4	no	—
146	#41×C₄₃	—	2	4	no	—
147	#41×C₄₃	—	4	2	no	—
148	#41×C₄₃	—	4	2	no	—
149	#41×C₄₃	—	4	2	no	—
150	#41×C₄₃	—	4	2	no	—
151	#41×C₄₃	C₂²⋊C₄	1	8	yes	complemented
152	#41×C₄₃	C₂²×C₄	1	4	yes	—
153	#41×C₄₃	C₂×D₄	1	4	yes	—
154	C₂×Q₈×C₄₃	—	2	1	no	—
155	C₂×Q₈×C₄₃	—	2	2	no	—
156	C₂×Q₈×C₄₃	—	2	1	no	—
157	C₂×Q₈×C₄₃	—	2	1	no	—
158	C₂×Q₈×C₄₃	—	2	1	no	—
159	C₂×Q₈×C₄₃	—	2	1	no	—
160	C₂×Q₈×C₄₃	—	2	1	no	—
161	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	complemented
162	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	complemented
163	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
164	C₂×D₄×C₄₃	—	2	1	no	—
165	C₂×D₄×C₄₃	—	2	2	no	—
166	C₂×D₄×C₄₃	—	2	1	no	—
167	C₂×D₄×C₄₃	—	2	4	no	—
168	C₂×D₄×C₄₃	—	2	4	no	—
169	C₂×D₄×C₄₃	—	2	2	no	—
170	C₂×D₄×C₄₃	—	2	4	no	—
171	C₂×D₄×C₄₃	—	2	2	no	—
172	C₂×D₄×C₄₃	—	2	1	no	—
173	C₂×D₄×C₄₃	—	2	1	no	—
174	C₂×D₄×C₄₃	—	2	1	no	—
175	C₂×D₄×C₄₃	—	2	1	no	—
176	C₂×D₄×C₄₃	—	4	1	no	—
177	C₂×D₄×C₄₃	—	4	1	no	—
178	C₂×D₄×C₄₃	—	4	2	no	—
179	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	complemented
180	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	complemented
181	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₄₃	—	2	4	no	—
183	C₂²×C₄×C₄₃	—	2	2	no	—
184	C₂²×C₄×C₄₃	—	2	4	no	—
185	C₂²×C₄×C₄₃	—	2	2	no	—
186	C₂²×C₄×C₄₃	—	2	8	no	—
187	C₂²×C₄×C₄₃	—	2	4	no	—
188	C₂²×C₄×C₄₃	—	2	1	no	—
189	C₂²×C₄×C₄₃	—	2	1	no	—
190	C₂²×C₄×C₄₃	—	2	2	no	—
191	C₂²×C₄×C₄₃	—	2	1	no	—
192	C₂²×C₄×C₄₃	—	2	2	no	—
193	C₂²×C₄×C₄₃	—	2	1	no	—
194	C₂²×C₄×C₄₃	—	2	2	no	—
195	C₂²×C₄×C₄₃	—	4	1	no	—
196	C₂²×C₄×C₄₃	—	4	1	no	—
197	C₂²×C₄×C₄₃	—	4	2	no	—
198	C₂²×C₄×C₄₃	—	8	2	no	—
199	C₂²×C₄×C₄₃	—	8	4	no	—
200	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₃	#41	1	2	yes	—
209	C₂²×C₄×C₄₃	#41	1	2	yes	—
210	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
211	Q₁₆×C₄₃	—	2	8	no	—
212	SD₁₆×C₄₃	—	2	8	no	—
213	SD₁₆×C₄₃	—	2	8	no	—
214	D₈×C₄₃	—	2	8	no	—
215	M₁₆×C₄₃	—	2	4	no	—
216	M₁₆×C₄₃	—	2	2	no	—
217	M₁₆×C₄₃	—	2	2	no	—
218	M₁₆×C₄₃	—	2	2	no	—
219	M₁₆×C₄₃	—	4	2	no	—
220	M₁₆×C₄₃	C₂²×C₄	1	4	yes	complemented
221	C₂×C₈×C₄₃	—	2	4	no	—
222	C₂×C₈×C₄₃	—	2	2	no	—
223	C₂×C₈×C₄₃	—	2	2	no	—
224	C₂×C₈×C₄₃	—	4	2	no	—
225	C₄⋊C₄×C₄₃	—	2	8	no	—
226	C₄⋊C₄×C₄₃	—	2	2	no	—
227	C₄⋊C₄×C₄₃	—	2	1	no	—
228	C₄⋊C₄×C₄₃	—	2	2	no	—
229	C₄⋊C₄×C₄₃	—	2	1	no	—
230	C₄⋊C₄×C₄₃	—	2	2	no	—
231	C₄⋊C₄×C₄₃	—	2	2	no	—
232	C₄⋊C₄×C₄₃	—	4	2	no	—
233	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
235	C₂²⋊C₄×C₄₃	—	2	8	no	—
236	C₂²⋊C₄×C₄₃	—	2	2	no	—
237	C₂²⋊C₄×C₄₃	—	2	2	no	—
238	C₂²⋊C₄×C₄₃	—	4	2	no	—
239	C₂²⋊C₄×C₄₃	—	8	4	no	—
240	C₄²×C₄₃	—	2	8	no	—
241	C₄²×C₄₃	—	2	2	no	—
242	C₄²×C₄₃	—	2	2	no	—
243	C₄²×C₄₃	—	2	2	no	—
244	C₄²×C₄₃	—	2	2	no	—
245	C₂³×C₄₃	—	2	2	no	—
246	C₂³×C₄₃	—	2	4	no	—
247	C₂³×C₄₃	—	2	2	no	—
248	C₂³×C₄₃	—	4	1	no	—
249	C₂³×C₄₃	—	4	1	no	—
250	C₂³×C₄₃	—	4	2	no	—
251	C₂³×C₄₃	—	4	2	no	—
252	C₂³×C₄₃	—	4	2	no	—
253	C₂³×C₄₃	—	4	2	no	—
254	C₂³×C₄₃	—	4	1	no	—
255	C₂³×C₄₃	—	4	1	no	—
256	C₂³×C₄₃	C₄×D₄	1	2	yes	—
257	C₂³×C₄₃	#120	1	1	yes	characteristic
258	C₂³×C₄₃	#120	1	1	yes	characteristic
259	C₂³×C₄₃	#121	1	2	yes	—
260	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
261	Q₈×C₄₃	—	2	2	no	—
262	Q₈×C₄₃	—	2	4	no	—
263	Q₈×C₄₃	—	2	2	no	—
264	Q₈×C₄₃	—	2	2	no	—
265	Q₈×C₄₃	—	4	1	no	—
266	Q₈×C₄₃	—	4	1	no	—
267	Q₈×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
268	D₄×C₄₃	—	2	4	no	—
269	D₄×C₄₃	—	2	4	no	—
270	D₄×C₄₃	—	2	8	no	—
271	D₄×C₄₃	—	2	2	no	—
272	D₄×C₄₃	—	2	2	no	—
273	D₄×C₄₃	—	2	2	no	—
274	D₄×C₄₃	—	2	4	no	—
275	D₄×C₄₃	—	4	4	no	—
276	D₄×C₄₃	—	4	4	no	—
277	D₄×C₄₃	—	4	1	no	—
278	D₄×C₄₃	—	4	1	no	—
279	D₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
280	C₂×C₄×C₄₃	—	2	2	no	—
281	C₂×C₄×C₄₃	—	2	4	no	—
282	C₂×C₄×C₄₃	—	2	4	no	—
283	C₂×C₄×C₄₃	—	2	4	no	—
284	C₂×C₄×C₄₃	—	2	8	no	—
285	C₂×C₄×C₄₃	—	2	2	no	—
286	C₂×C₄×C₄₃	—	2	2	no	—
287	C₂×C₄×C₄₃	—	2	4	no	—
288	C₂×C₄×C₄₃	—	2	2	no	—
289	C₂×C₄×C₄₃	—	4	2	no	—
290	C₂×C₄×C₄₃	—	4	4	no	—
291	C₂×C₄×C₄₃	—	4	2	no	—
292	C₂×C₄×C₄₃	—	4	1	no	—
293	C₂×C₄×C₄₃	—	4	1	no	—
294	C₂×C₄×C₄₃	—	4	4	no	—
295	C₂×C₄×C₄₃	—	4	4	no	—
296	C₂×C₄×C₄₃	—	4	4	no	—
297	C₂×C₄×C₄₃	—	4	2	no	—
298	C₂×C₄×C₄₃	—	4	2	no	—
299	C₂×C₄×C₄₃	—	4	2	no	—
300	C₂×C₄×C₄₃	—	8	2	no	—
301	C₂×C₄×C₄₃	—	8	8	no	—
302	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
305	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
306	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
307	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
308	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
309	C₂×C₄×C₄₃	#121	1	2	yes	—
310	C₂×C₄×C₄₃	#121	1	2	yes	—
311	C₂×C₄×C₄₃	#121	1	2	yes	—
312	C₂×C₄×C₄₃	#123	1	2	yes	—
313	C₂×C₄×C₄₃	#123	1	2	yes	—
314	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
315	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
320	C₈×C₄₃	—	2	4	no	—
321	C₈×C₄₃	—	4	2	no	—
322	#20943	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₂²×C₄₃	—	2	1	no	—
324	C₂²×C₄₃	—	2	1	no	—
325	C₂²×C₄₃	—	2	1	no	—
326	C₂²×C₄₃	—	2	1	no	—
327	C₂²×C₄₃	—	2	1	no	—
328	C₂²×C₄₃	—	2	1	no	—
329	C₂²×C₄₃	—	2	4	no	—
330	C₂²×C₄₃	—	4	2	no	—
331	C₂²×C₄₃	—	4	2	no	—
332	C₂²×C₄₃	—	4	8	no	—
333	C₂²×C₄₃	—	4	4	no	—
334	C₂²×C₄₃	—	4	2	no	—
335	C₂²×C₄₃	—	4	2	no	—
336	C₂²×C₄₃	—	4	2	no	—
337	C₂²×C₄₃	—	8	2	no	—
338	C₂²×C₄₃	—	8	1	no	—
339	C₂²×C₄₃	—	8	1	no	—
340	C₂²×C₄₃	#386	1	2	yes	—
341	C₂²×C₄₃	#386	1	2	yes	—
342	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
343	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
344	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
345	C₄×C₄₃	—	2	4	no	—
346	C₄×C₄₃	—	4	4	no	—
347	C₄×C₄₃	—	4	2	no	—
348	C₄×C₄₃	—	4	2	no	—
349	C₄×C₄₃	—	4	2	no	—
350	C₄×C₄₃	—	8	2	no	—
351	C₄×C₄₃	#386	1	2	yes	—
352	C₄×C₄₃	#386	1	2	yes	—
353	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
354	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
355	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
356	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
357	C₂×#575	C₂×C₄₃	1	1	yes	characteristic
358	C₂×#520	C₂×C₄₃	1	1	yes	characteristic, complemented
359	C₂×#421	C₂×C₄₃	1	1	yes	characteristic, complemented
360	#2896	C₂×C₄₃	1	1	yes	characteristic, complemented
361	#2311	C₂×C₄₃	1	1	yes	characteristic, complemented
362	#1883	C₂×C₄₃	1	4	yes	complemented
363	#1882	C₂×C₄₃	1	4	yes	complemented
364	C₂×#343	C₂×C₄₃	1	1	yes	characteristic, complemented
365	#1733	C₂×C₄₃	1	1	yes	characteristic, complemented
366	C₂×C₄₃	—	2	1	no	—
367	C₂×C₄₃	—	2	1	no	—
368	C₂×C₄₃	—	2	2	no	—
369	C₂×C₄₃	—	2	2	no	—
370	C₂×C₄₃	—	4	4	no	—
371	C₂×C₄₃	—	8	2	no	—
372	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
373	C₂×C₄₃	#3019	1	1	yes	characteristic
374	C₂×C₄₃	#3020	1	1	yes	characteristic
375	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
376	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
377	#575	—	2	4	no	—
378	#575	C₄×C₄₃	1	8	yes	complemented
379	C₂×#137	—	2	1	no	—
380	C₂×#137	C₂²×C₄₃	1	2	yes	—
381	C₂×AGL(1,ℤ/8)	—	2	1	no	—
382	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	2	yes	—
383	C₂×#135	—	2	2	no	—
384	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
385	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
386	#520	—	2	2	no	—
387	#520	—	2	2	no	—
388	#520	—	2	2	no	—
389	#520	C₂²×C₄₃	1	4	yes	—
390	C₂×C₄×Q₈	—	2	1	no	—
391	C₂×C₄×D₄	—	2	1	no	—
392	C₂×C₄×D₄	—	2	2	no	—
393	C₂×#117	—	2	1	no	—
394	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
395	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	—	2	1	no	—
397	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
398	#421	—	2	4	no	—
399	C₂×#104	C₂²×C₄₃	1	4	yes	—
400	#419	C₂²×C₄₃	1	2	yes	complemented
401	#418	C₂²×C₄₃	1	2	yes	complemented
402	#417	—	2	1	no	—
403	#417	—	2	1	no	—
404	#416	—	2	2	no	—
405	#391	C₂²×C₄₃	1	2	yes	complemented
406	#390	C₂²×C₄₃	1	2	yes	complemented
407	#386	—	2	2	no	—
408	#380	—	2	2	no	—
409	#343	C₂²×C₄₃	1	4	yes	complemented
410	#339	C₂²×C₄₃	1	4	yes	complemented
411	C₄₃	#20943	1	1	yes	characteristic, direct product factor, Sylow
412	C₂×#41	—	2	1	no	—
413	C₂×#41	—	2	1	no	—
414	C₂×#41	—	2	2	no	—
415	C₂×#41	—	2	2	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	2	no	—
420	C₂×#41	—	2	1	no	—
421	C₂×#41	—	2	1	no	—
422	C₂×#41	—	2	2	no	—
423	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
424	C₂×#41	C₂×C₄×C₄₃	1	4	yes	complemented
425	C₂×#41	D₄×C₄₃	1	4	yes	—
426	C₂×#41	D₄×C₄₃	1	2	yes	—
427	C₂×#41	C₂³×C₄₃	1	2	yes	—
428	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
433	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	—	2	2	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	D₄×C₄₃	1	2	yes	—
438	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
439	#137	—	2	4	no	—
440	#137	—	2	8	no	—
441	#137	C₂×C₄×C₄₃	1	8	yes	complemented
442	AGL(1,ℤ/8)	—	2	4	no	—
443	AGL(1,ℤ/8)	—	2	8	no	—
444	AGL(1,ℤ/8)	C₂×C₄×C₄₃	1	8	yes	complemented
445	#135	—	2	16	no	—
446	C₂×Q₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	2	2	no	—
449	C₂×D₈	—	2	2	no	—
450	C₂×M₁₆	—	2	1	no	—
451	C₂×M₁₆	—	2	2	no	—
452	C₂×M₁₆	—	2	1	no	—
453	C₂×M₁₆	—	2	2	no	—
454	C₂×M₁₆	—	2	2	no	—
455	C₂×M₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
456	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
457	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
458	C₂²×C₈	—	2	1	no	—
459	C₂²×C₈	—	2	1	no	—
460	C₄×Q₈	—	2	4	no	—
461	C₄×Q₈	—	2	4	no	—
462	C₄×D₄	—	2	8	no	—
463	C₄×D₄	—	2	4	no	—
464	C₄×D₄	—	2	4	no	—
465	C₄×D₄	—	2	8	no	—
466	#117	—	2	4	no	—
467	#117	—	2	1	no	—
468	#117	—	2	1	no	—
469	#117	—	2	4	no	—
470	#117	—	2	2	no	—
471	#117	—	2	2	no	—
472	#117	D₄×C₄₃	1	2	yes	—
473	#117	C₂³×C₄₃	1	2	yes	—
474	C₂×C₄⋊C₄	—	2	2	no	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
483	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
486	C₂×C₂²⋊C₄	—	2	2	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	4	no	—
490	C₂×C₄²	—	2	2	no	—
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
493	#104	—	2	8	no	—
494	#103	—	2	2	no	—
495	#103	—	2	2	no	—
496	#102	—	2	2	no	—
497	#102	—	2	2	no	—
498	#95	—	2	4	no	—
499	C₂⁴	—	2	1	no	—
500	C₂⁴	—	2	1	no	—
501	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
502	#41	—	2	4	no	—
503	#41	—	2	4	no	—
504	#41	—	2	4	no	—
505	#41	—	2	4	no	—
506	#41	—	2	4	no	—
507	#41	—	2	2	no	—
508	#41	—	2	2	no	—
509	#41	—	2	4	no	—
510	#41	—	2	4	no	—
511	#41	—	2	4	no	—
512	#41	—	2	4	no	—
513	#41	—	4	2	no	—
514	#41	—	4	2	no	—
515	#41	—	4	2	no	—
516	#41	—	4	2	no	—
517	#41	C₂²⋊C₄×C₄₃	1	8	yes	complemented
518	#41	C₂²×C₄×C₄₃	1	4	yes	—
519	#41	C₂×D₄×C₄₃	1	4	yes	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	C₂²⋊C₄×C₄₃	1	4	yes	complemented
528	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	complemented
529	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	4	1	no	—
543	C₂×D₄	—	4	1	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	complemented
546	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	complemented
547	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	8	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	4	1	no	—
562	C₂²×C₄	—	4	1	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	8	2	no	—
565	C₂²×C₄	—	8	4	no	—
566	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
567	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
568	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
571	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
574	C₂²×C₄	#41×C₄₃	1	2	yes	—
575	C₂²×C₄	#41×C₄₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
577	Q₁₆	—	2	8	no	—
578	SD₁₆	—	2	8	no	—
579	SD₁₆	—	2	8	no	—
580	D₈	—	2	8	no	—
581	M₁₆	—	2	4	no	—
582	M₁₆	—	2	2	no	—
583	M₁₆	—	2	2	no	—
584	M₁₆	—	2	2	no	—
585	M₁₆	—	4	2	no	—
586	M₁₆	C₂²×C₄×C₄₃	1	4	yes	complemented
587	C₂×C₈	—	2	4	no	—
588	C₂×C₈	—	2	2	no	—
589	C₂×C₈	—	2	2	no	—
590	C₂×C₈	—	4	2	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	4	2	no	—
599	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
600	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	8	4	no	—
606	C₄²	—	2	8	no	—
607	C₄²	—	2	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	2	no	—
617	C₂³	—	4	2	no	—
618	C₂³	—	4	2	no	—
619	C₂³	—	4	2	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	C₄×D₄×C₄₃	1	2	yes	—
623	C₂³	#120×C₄₃	1	1	yes	characteristic
624	C₂³	#120×C₄₃	1	1	yes	characteristic
625	C₂³	#121×C₄₃	1	2	yes	—
626	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
627	Q₈	—	2	2	no	—
628	Q₈	—	2	4	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	Q₈	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
634	D₄	—	2	4	no	—
635	D₄	—	2	4	no	—
636	D₄	—	2	8	no	—
637	D₄	—	2	2	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	2	no	—
640	D₄	—	2	4	no	—
641	D₄	—	4	4	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	1	no	—
645	D₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	8	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	4	4	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	4	2	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	8	2	no	—
667	C₂×C₄	—	8	8	no	—
668	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
669	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
670	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
671	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
672	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
673	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
674	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
675	C₂×C₄	#121×C₄₃	1	2	yes	—
676	C₂×C₄	#121×C₄₃	1	2	yes	—
677	C₂×C₄	#121×C₄₃	1	2	yes	—
678	C₂×C₄	#123×C₄₃	1	2	yes	—
679	C₂×C₄	#123×C₄₃	1	2	yes	—
680	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
681	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
684	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
685	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
686	C₈	—	2	4	no	—
687	C₈	—	4	2	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	8	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	8	2	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	C₄₃×#386	1	2	yes	—
706	C₂²	C₄₃×#386	1	2	yes	—
707	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
708	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
709	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
710	C₄	—	2	4	no	—
711	C₄	—	4	4	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	8	2	no	—
716	C₄	C₄₃×#386	1	2	yes	—
717	C₄	C₄₃×#386	1	2	yes	—
718	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
719	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
720	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
721	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
722	C₂	—	2	1	no	—
723	C₂	—	2	1	no	—
724	C₂	—	2	2	no	—
725	C₂	—	2	2	no	—
726	C₂	—	4	4	no	—
727	C₂	—	8	2	no	—
728	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
729	C₂	C₄₃×#3019	1	1	yes	characteristic
730	C₂	C₄₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#520	C₂	semidirect
3. C₂×C₄₃×#421	C₂	semidirect
4. C₄₃×#2896	C₂	semidirect
5. C₄₃×#2311	C₂	semidirect
6. C₄₃×#1883	C₂	semidirect
7. C₄₃×#1882	C₂	semidirect
8. C₂×C₄₃×#343	C₂	semidirect
9. C₄₃×#1733	C₂	semidirect
13. C₄₃×#575	C₄	semidirect
35. C₄₃×#419	C₂²	semidirect
36. C₄₃×#418	C₂²	semidirect
40. C₄₃×#391	C₂²	semidirect
41. C₄₃×#390	C₂²	semidirect
44. C₄₃×#343	C₂²	semidirect
45. C₄₃×#339	C₂²	semidirect
58. C₂×#41×C₄₃	C₂×C₄	semidirect
75. #137×C₄₃	C₂×C₄	semidirect
78. AGL(1,ℤ/8)×C₄₃	C₂×C₄	semidirect
89. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
151. #41×C₄₃	C₂²⋊C₄	semidirect
161. C₂×Q₈×C₄₃	C₂²⋊C₄	semidirect
162. C₂×Q₈×C₄₃	C₂²×C₄	semidirect
179. C₂×D₄×C₄₃	C₂²⋊C₄	semidirect
180. C₂×D₄×C₄₃	C₂²×C₄	semidirect
220. M₁₆×C₄₃	C₂²×C₄	semidirect
322. #20943	C₄₃	direct (N × H)
358. C₂×#520	C₂×C₄₃	semidirect
359. C₂×#421	C₂×C₄₃	semidirect
360. #2896	C₂×C₄₃	semidirect
361. #2311	C₂×C₄₃	semidirect
362. #1883	C₂×C₄₃	semidirect
363. #1882	C₂×C₄₃	semidirect
364. C₂×#343	C₂×C₄₃	semidirect
365. #1733	C₂×C₄₃	semidirect
378. #575	C₄×C₄₃	semidirect
400. #419	C₂²×C₄₃	semidirect
401. #418	C₂²×C₄₃	semidirect
405. #391	C₂²×C₄₃	semidirect
406. #390	C₂²×C₄₃	semidirect
409. #343	C₂²×C₄₃	semidirect
410. #339	C₂²×C₄₃	semidirect
411. C₄₃	#20943	direct (N × H)
424. C₂×#41	C₂×C₄×C₄₃	semidirect
441. #137	C₂×C₄×C₄₃	semidirect
444. AGL(1,ℤ/8)	C₂×C₄×C₄₃	semidirect
455. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
517. #41	C₂²⋊C₄×C₄₃	semidirect
527. C₂×Q₈	C₂²⋊C₄×C₄₃	semidirect
528. C₂×Q₈	C₂²×C₄×C₄₃	semidirect
545. C₂×D₄	C₂²⋊C₄×C₄₃	semidirect
546. C₂×D₄	C₂²×C₄×C₄₃	semidirect
586. M₁₆	C₂²×C₄×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×#575	2
C₂×C₄₃×#520	2
C₂×C₄₃×#421	2
C₄₃×#2896	2
C₄₃×#2311	2
C₄₃×#1883	2
C₄₃×#1882	2
C₂×C₄₃×#343	2
C₄₃×#1733	2
#20943	43

Subgroups — C43×#20943 #24940960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20943 #24940960