Subgroups — C₄₃×#20976 #24940993

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 690 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×#537	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1895	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1894	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1893	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1892	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#131×C₄₃	—	2	4	no	—
15	C₂×#131×C₄₃	—	2	4	no	—
16	C₂×#131×C₄₃	—	2	4	no	—
17	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
18	C₂²×M₁₆×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×#537	—	2	4	no	—
22	C₄₃×#537	C₄	1	8	yes	complemented
23	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
25	C₂×#121×C₄₃	—	2	1	no	—
26	C₂×#121×C₄₃	—	2	2	no	—
27	C₂×#121×C₄₃	C₂²	1	2	yes	—
28	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#417	—	2	4	no	—
32	C₄₃×#416	—	2	4	no	—
33	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#103×C₄₃	C₂²	1	2	yes	—
36	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#102×C₄₃	C₂²	1	2	yes	—
39	C₄₃×#391	—	2	1	no	—
40	C₄₃×#390	—	2	1	no	—
41	C₄₃×#386	—	2	2	no	—
42	C₄₃×#380	C₂²	1	2	yes	—
43	C₄₃×#380	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₄₃×#340	C₂²	1	2	yes	—
46	C₄₃×#340	C₂²	1	2	yes	—
47	C₄₃×#340	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	—	2	2	no	—
54	C₂×#41×C₄₃	—	2	2	no	—
55	C₂×#41×C₄₃	—	2	2	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	—
59	C₂×#41×C₄₃	D₄	1	4	yes	—
60	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
61	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₄₃	—	2	1	no	—
63	C₂²×D₄×C₄₃	—	2	2	no	—
64	C₂²×D₄×C₄₃	D₄	1	2	yes	—
65	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₃	—	2	1	no	—
68	C₂³×C₄×C₄₃	—	2	1	no	—
69	C₂³×C₄×C₄₃	—	2	1	no	—
70	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
72	#131×C₄₃	—	2	32	no	—
73	C₂×M₁₆×C₄₃	—	2	4	no	—
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂×M₁₆×C₄₃	—	2	2	no	—
76	C₂×M₁₆×C₄₃	—	2	4	no	—
77	C₂×M₁₆×C₄₃	—	2	4	no	—
78	C₂×M₁₆×C₄₃	D₄	1	4	yes	complemented
79	C₂²×C₈×C₄₃	—	2	4	no	—
80	C₂²×C₈×C₄₃	—	2	2	no	—
81	C₂²×C₈×C₄₃	—	2	2	no	—
82	C₂²×C₈×C₄₃	—	2	4	no	—
83	C₂²×C₈×C₄₃	—	2	4	no	—
84	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
85	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²⋊Q₈×C₄₃	—	2	8	no	—
89	C₂²⋊Q₈×C₄₃	—	2	4	no	—
90	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
91	#121×C₄₃	—	2	16	no	—
92	#121×C₄₃	—	2	8	no	—
93	#121×C₄₃	—	2	4	no	—
94	#121×C₄₃	C₂×C₄	1	8	yes	complemented
95	#117×C₄₃	—	2	2	no	—
96	#117×C₄₃	—	2	2	no	—
97	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
99	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
100	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
101	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
102	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
104	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
109	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
113	C₂×C₄²×C₄₃	—	2	1	no	—
114	#103×C₄₃	—	2	2	no	—
115	#103×C₄₃	—	2	2	no	—
116	#103×C₄₃	—	2	4	no	—
117	#102×C₄₃	—	2	2	no	—
118	#102×C₄₃	—	2	2	no	—
119	#102×C₄₃	—	2	4	no	—
120	#95×C₄₃	—	2	2	no	—
121	#95×C₄₃	—	2	2	no	—
122	C₂⁴×C₄₃	—	2	1	no	—
123	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
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	#41×C₄₃	—	2	8	no	—
130	#41×C₄₃	—	2	8	no	—
131	#41×C₄₃	—	4	4	no	—
132	#41×C₄₃	—	4	4	no	—
133	C₂×Q₈×C₄₃	—	2	2	no	—
134	C₂×Q₈×C₄₃	—	2	2	no	—
135	C₂×Q₈×C₄₃	—	2	1	no	—
136	C₂×Q₈×C₄₃	—	2	1	no	—
137	C₂×Q₈×C₄₃	—	2	1	no	—
138	C₂×Q₈×C₄₃	—	2	1	no	—
139	C₂×Q₈×C₄₃	—	2	1	no	—
140	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
141	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₄₃	—	2	2	no	—
143	C₂×D₄×C₄₃	—	2	2	no	—
144	C₂×D₄×C₄₃	—	2	1	no	—
145	C₂×D₄×C₄₃	—	2	4	no	—
146	C₂×D₄×C₄₃	—	2	8	no	—
147	C₂×D₄×C₄₃	—	2	4	no	—
148	C₂×D₄×C₄₃	—	2	4	no	—
149	C₂×D₄×C₄₃	—	2	1	no	—
150	C₂×D₄×C₄₃	—	2	1	no	—
151	C₂×D₄×C₄₃	—	2	1	no	—
152	C₂×D₄×C₄₃	—	2	1	no	—
153	C₂×D₄×C₄₃	—	4	2	no	—
154	C₂×D₄×C₄₃	—	4	2	no	—
155	C₂×D₄×C₄₃	—	8	2	no	—
156	C₂×D₄×C₄₃	—	8	2	no	—
157	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
158	C₂×D₄×C₄₃	C₂²⋊C₄	1	8	yes	—
159	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₃	—	2	2	no	—
161	C₂²×C₄×C₄₃	—	2	2	no	—
162	C₂²×C₄×C₄₃	—	2	2	no	—
163	C₂²×C₄×C₄₃	—	2	2	no	—
164	C₂²×C₄×C₄₃	—	2	4	no	—
165	C₂²×C₄×C₄₃	—	2	4	no	—
166	C₂²×C₄×C₄₃	—	2	2	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	—	4	2	no	—
172	C₂²×C₄×C₄₃	—	4	2	no	—
173	C₂²×C₄×C₄₃	—	4	2	no	—
174	C₂²×C₄×C₄₃	—	8	1	no	—
175	C₂²×C₄×C₄₃	—	8	1	no	—
176	C₂²×C₄×C₄₃	—	8	1	no	—
177	C₂²×C₄×C₄₃	—	8	1	no	—
178	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
179	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
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	#41	1	2	yes	—
187	C₂²×C₄×C₄₃	#41	1	2	yes	—
188	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
189	M₁₆×C₄₃	—	2	16	no	—
190	M₁₆×C₄₃	—	2	8	no	—
191	C₂×C₈×C₄₃	—	2	16	no	—
192	C₂×C₈×C₄₃	—	2	8	no	—
193	C₂×C₈×C₄₃	—	2	1	no	—
194	C₂×C₈×C₄₃	—	2	1	no	—
195	C₂×C₈×C₄₃	—	2	1	no	—
196	C₂×C₈×C₄₃	—	2	2	no	—
197	C₂×C₈×C₄₃	—	2	2	no	—
198	C₂×C₈×C₄₃	—	2	1	no	—
199	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
200	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
201	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
202	C₄⋊C₄×C₄₃	—	2	4	no	—
203	C₄⋊C₄×C₄₃	—	2	8	no	—
204	C₄⋊C₄×C₄₃	—	2	2	no	—
205	C₄⋊C₄×C₄₃	—	2	2	no	—
206	C₄⋊C₄×C₄₃	—	2	1	no	—
207	C₄⋊C₄×C₄₃	—	2	1	no	—
208	C₄⋊C₄×C₄₃	—	2	2	no	—
209	C₄⋊C₄×C₄₃	—	2	1	no	—
210	C₄⋊C₄×C₄₃	—	2	1	no	—
211	C₄⋊C₄×C₄₃	—	4	2	no	—
212	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
213	C₂²⋊C₄×C₄₃	—	2	8	no	—
214	C₂²⋊C₄×C₄₃	—	2	8	no	—
215	C₂²⋊C₄×C₄₃	—	4	2	no	—
216	C₂²⋊C₄×C₄₃	—	8	2	no	—
217	C₂²⋊C₄×C₄₃	—	8	2	no	—
218	C₄²×C₄₃	—	4	2	no	—
219	C₂³×C₄₃	—	2	1	no	—
220	C₂³×C₄₃	—	2	1	no	—
221	C₂³×C₄₃	—	2	1	no	—
222	C₂³×C₄₃	—	2	1	no	—
223	C₂³×C₄₃	—	2	2	no	—
224	C₂³×C₄₃	—	2	2	no	—
225	C₂³×C₄₃	—	2	2	no	—
226	C₂³×C₄₃	—	2	2	no	—
227	C₂³×C₄₃	—	2	2	no	—
228	C₂³×C₄₃	—	2	2	no	—
229	C₂³×C₄₃	—	2	2	no	—
230	C₂³×C₄₃	—	4	1	no	—
231	C₂³×C₄₃	—	4	1	no	—
232	C₂³×C₄₃	—	4	1	no	—
233	C₂³×C₄₃	—	4	1	no	—
234	C₂³×C₄₃	—	4	1	no	—
235	C₂³×C₄₃	—	4	1	no	—
236	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
237	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂³×C₄₃	#121	1	2	yes	—
239	C₂³×C₄₃	#121	1	2	yes	—
240	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₄₃	—	2	8	no	—
242	Q₈×C₄₃	—	2	2	no	—
243	Q₈×C₄₃	—	2	2	no	—
244	Q₈×C₄₃	—	4	1	no	—
245	Q₈×C₄₃	—	4	1	no	—
246	D₄×C₄₃	—	2	16	no	—
247	D₄×C₄₃	—	2	2	no	—
248	D₄×C₄₃	—	2	2	no	—
249	D₄×C₄₃	—	2	8	no	—
250	D₄×C₄₃	—	4	8	no	—
251	D₄×C₄₃	—	4	1	no	—
252	D₄×C₄₃	—	4	1	no	—
253	D₄×C₄₃	—	8	8	no	—
254	C₂×C₄×C₄₃	—	2	2	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	2	4	no	—
257	C₂×C₄×C₄₃	—	2	4	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	2	no	—
262	C₂×C₄×C₄₃	—	4	1	no	—
263	C₂×C₄×C₄₃	—	4	1	no	—
264	C₂×C₄×C₄₃	—	4	2	no	—
265	C₂×C₄×C₄₃	—	4	2	no	—
266	C₂×C₄×C₄₃	—	4	8	no	—
267	C₂×C₄×C₄₃	—	4	1	no	—
268	C₂×C₄×C₄₃	—	4	1	no	—
269	C₂×C₄×C₄₃	—	4	2	no	—
270	C₂×C₄×C₄₃	—	4	1	no	—
271	C₂×C₄×C₄₃	—	4	2	no	—
272	C₂×C₄×C₄₃	—	4	1	no	—
273	C₂×C₄×C₄₃	—	4	2	no	—
274	C₂×C₄×C₄₃	—	4	1	no	—
275	C₂×C₄×C₄₃	—	4	1	no	—
276	C₂×C₄×C₄₃	—	8	4	no	—
277	C₂×C₄×C₄₃	—	8	4	no	—
278	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
279	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
281	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
282	C₂×C₄×C₄₃	#120	1	4	yes	—
283	C₂×C₄×C₄₃	#121	1	2	yes	—
284	C₂×C₄×C₄₃	#121	1	2	yes	—
285	C₂×C₄×C₄₃	#123	1	4	yes	—
286	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
292	C₈×C₄₃	—	2	2	no	—
293	C₈×C₄₃	—	2	4	no	—
294	C₈×C₄₃	—	2	2	no	—
295	#20976	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
301	C₂²×C₄₃	—	2	2	no	—
302	C₂²×C₄₃	—	2	4	no	—
303	C₂²×C₄₃	—	2	4	no	—
304	C₂²×C₄₃	—	2	4	no	—
305	C₂²×C₄₃	—	4	2	no	—
306	C₂²×C₄₃	—	4	2	no	—
307	C₂²×C₄₃	—	4	2	no	—
308	C₂²×C₄₃	—	4	2	no	—
309	C₂²×C₄₃	—	4	2	no	—
310	C₂²×C₄₃	—	4	2	no	—
311	C₂²×C₄₃	—	4	2	no	—
312	C₂²×C₄₃	—	8	1	no	—
313	C₂²×C₄₃	—	8	1	no	—
314	C₂²×C₄₃	—	8	1	no	—
315	C₂²×C₄₃	—	8	1	no	—
316	C₂²×C₄₃	#386	1	4	yes	—
317	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
319	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
320	C₂²×C₄₃	#576	1	1	yes	characteristic
321	C₂²×C₄₃	#577	1	1	yes	characteristic
322	C₂²×C₄₃	#577	1	1	yes	characteristic
323	C₂²×C₄₃	#578	1	1	yes	characteristic
324	C₄×C₄₃	—	2	4	no	—
325	C₄×C₄₃	—	4	4	no	—
326	C₄×C₄₃	—	4	2	no	—
327	C₄×C₄₃	—	8	1	no	—
328	C₄×C₄₃	—	8	1	no	—
329	C₄×C₄₃	—	8	2	no	—
330	C₄×C₄₃	#386	1	4	yes	—
331	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
332	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
333	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
334	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
335	C₂²×#131	C₂×C₄₃	1	1	yes	characteristic, complemented
336	C₂×#537	C₂×C₄₃	1	1	yes	characteristic
337	C₂×#417	C₂×C₄₃	1	1	yes	characteristic, complemented
338	C₂×#416	C₂×C₄₃	1	1	yes	characteristic, complemented
339	#2311	C₂×C₄₃	1	1	yes	characteristic, complemented
340	#1895	C₂×C₄₃	1	2	yes	complemented
341	#1894	C₂×C₄₃	1	2	yes	complemented
342	#1893	C₂×C₄₃	1	2	yes	complemented
343	#1892	C₂×C₄₃	1	2	yes	complemented
344	#1736	C₂×C₄₃	1	1	yes	characteristic, complemented
345	C₂×#340	C₂×C₄₃	1	1	yes	characteristic, complemented
346	C₂×C₄₃	—	2	4	no	—
347	C₂×C₄₃	—	4	4	no	—
348	C₂×C₄₃	—	8	2	no	—
349	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
350	C₂×C₄₃	#2897	1	1	yes	characteristic
351	C₂×C₄₃	#2898	1	1	yes	characteristic
352	C₂×C₄₃	#3060	1	1	yes	characteristic
353	C₂×C₄₃	#3061	1	1	yes	characteristic
354	C₂×C₄₃	#3062	1	1	yes	characteristic
355	C₂×C₄₃	#3063	1	1	yes	characteristic
356	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
357	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
358	C₂×#131	—	2	4	no	—
359	C₂×#131	—	2	4	no	—
360	C₂×#131	—	2	4	no	—
361	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
362	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
363	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
364	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
365	#537	—	2	4	no	—
366	#537	C₄×C₄₃	1	8	yes	complemented
367	C₂×C₂²⋊Q₈	—	2	1	no	—
368	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
369	C₂×#121	—	2	1	no	—
370	C₂×#121	—	2	2	no	—
371	C₂×#121	C₂²×C₄₃	1	2	yes	—
372	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
373	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
375	#417	—	2	4	no	—
376	#416	—	2	4	no	—
377	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
378	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
379	C₂×#103	C₂²×C₄₃	1	2	yes	—
380	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
381	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
382	C₂×#102	C₂²×C₄₃	1	2	yes	—
383	#391	—	2	1	no	—
384	#390	—	2	1	no	—
385	#386	—	2	2	no	—
386	#380	C₂²×C₄₃	1	2	yes	—
387	#380	C₂²×C₄₃	1	2	yes	—
388	#340	C₂²×C₄₃	1	2	yes	—
389	#340	C₂²×C₄₃	1	2	yes	—
390	#340	C₂²×C₄₃	1	2	yes	—
391	#340	C₂²×C₄₃	1	2	yes	—
392	C₄₃	#20976	1	1	yes	characteristic, direct product factor, Sylow
393	C₂×#41	—	2	2	no	—
394	C₂×#41	—	2	2	no	—
395	C₂×#41	—	2	2	no	—
396	C₂×#41	—	2	2	no	—
397	C₂×#41	—	2	2	no	—
398	C₂×#41	—	2	2	no	—
399	C₂×#41	—	2	2	no	—
400	C₂×#41	—	2	2	no	—
401	C₂×#41	—	2	2	no	—
402	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
403	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
404	C₂×#41	D₄×C₄₃	1	4	yes	—
405	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
406	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	—	2	2	no	—
409	C₂²×D₄	D₄×C₄₃	1	2	yes	—
410	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	—	2	1	no	—
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
416	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
417	#131	—	2	32	no	—
418	C₂×M₁₆	—	2	4	no	—
419	C₂×M₁₆	—	2	2	no	—
420	C₂×M₁₆	—	2	2	no	—
421	C₂×M₁₆	—	2	4	no	—
422	C₂×M₁₆	—	2	4	no	—
423	C₂×M₁₆	D₄×C₄₃	1	4	yes	complemented
424	C₂²×C₈	—	2	4	no	—
425	C₂²×C₈	—	2	2	no	—
426	C₂²×C₈	—	2	2	no	—
427	C₂²×C₈	—	2	4	no	—
428	C₂²×C₈	—	2	4	no	—
429	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
430	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
432	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
433	C₂²⋊Q₈	—	2	8	no	—
434	C₂²⋊Q₈	—	2	4	no	—
435	C₂²⋊Q₈	C₂×C₄×C₄₃	1	8	yes	complemented
436	#121	—	2	8	no	—
437	#121	—	2	16	no	—
438	#121	—	2	4	no	—
439	#121	C₂×C₄×C₄₃	1	8	yes	complemented
440	#117	—	2	2	no	—
441	#117	—	2	2	no	—
442	C₂×C₄⋊C₄	—	2	1	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	—	2	2	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
449	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
453	C₂×C₂²⋊C₄	—	2	2	no	—
454	C₂×C₂²⋊C₄	—	2	2	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	2	no	—
457	C₂×C₂²⋊C₄	—	2	2	no	—
458	C₂×C₄²	—	2	1	no	—
459	#103	—	2	2	no	—
460	#103	—	2	2	no	—
461	#103	—	2	4	no	—
462	#102	—	2	2	no	—
463	#102	—	2	2	no	—
464	#102	—	2	4	no	—
465	#95	—	2	2	no	—
466	#95	—	2	2	no	—
467	C₂⁴	—	2	1	no	—
468	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
469	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
470	#41	—	2	8	no	—
471	#41	—	2	8	no	—
472	#41	—	2	8	no	—
473	#41	—	2	8	no	—
474	#41	—	2	8	no	—
475	#41	—	2	8	no	—
476	#41	—	4	4	no	—
477	#41	—	4	4	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	C₂²⋊C₄×C₄₃	1	4	yes	—
486	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	8	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	4	2	no	—
499	C₂×D₄	—	4	2	no	—
500	C₂×D₄	—	8	2	no	—
501	C₂×D₄	—	8	2	no	—
502	C₂×D₄	C₂²⋊C₄×C₄₃	1	8	yes	—
503	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	—
504	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	8	1	no	—
520	C₂²×C₄	—	8	1	no	—
521	C₂²×C₄	—	8	1	no	—
522	C₂²×C₄	—	8	1	no	—
523	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
524	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
527	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
529	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
530	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
531	C₂²×C₄	#41×C₄₃	1	2	yes	—
532	C₂²×C₄	#41×C₄₃	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
534	M₁₆	—	2	16	no	—
535	M₁₆	—	2	8	no	—
536	C₂×C₈	—	2	16	no	—
537	C₂×C₈	—	2	8	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	2	no	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
545	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
546	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	8	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	8	2	no	—
562	C₂²⋊C₄	—	8	2	no	—
563	C₄²	—	4	2	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
582	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
583	C₂³	#121×C₄₃	1	2	yes	—
584	C₂³	#121×C₄₃	1	2	yes	—
585	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
586	Q₈	—	2	8	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	2	2	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	D₄	—	2	16	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	2	8	no	—
595	D₄	—	4	8	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	8	8	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	8	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	8	4	no	—
622	C₂×C₄	—	8	4	no	—
623	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
624	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
625	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
626	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
627	C₂×C₄	#120×C₄₃	1	4	yes	—
628	C₂×C₄	#121×C₄₃	1	2	yes	—
629	C₂×C₄	#121×C₄₃	1	2	yes	—
630	C₂×C₄	#123×C₄₃	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
633	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
635	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
636	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	4	no	—
639	C₈	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	C₄₃×#386	1	4	yes	—
661	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
662	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
663	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
664	C₂²	C₄₃×#576	1	1	yes	characteristic
665	C₂²	C₄₃×#577	1	1	yes	characteristic
666	C₂²	C₄₃×#577	1	1	yes	characteristic
667	C₂²	C₄₃×#578	1	1	yes	characteristic
668	C₄	—	2	4	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	2	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	—	8	2	no	—
674	C₄	C₄₃×#386	1	4	yes	—
675	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
676	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
677	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
678	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
679	C₂	—	2	4	no	—
680	C₂	—	4	4	no	—
681	C₂	—	8	2	no	—
682	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
683	C₂	C₄₃×#2897	1	1	yes	characteristic
684	C₂	C₄₃×#2898	1	1	yes	characteristic
685	C₂	C₄₃×#3060	1	1	yes	characteristic
686	C₂	C₄₃×#3061	1	1	yes	characteristic
687	C₂	C₄₃×#3062	1	1	yes	characteristic
688	C₂	C₄₃×#3063	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#537	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×#41×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×#417	C₂	semidirect
4. C₂×C₄₃×#416	C₂	semidirect
5. C₄₃×#2311	C₂	semidirect
6. C₄₃×#1895	C₂	semidirect
7. C₄₃×#1894	C₂	semidirect
8. C₄₃×#1893	C₂	semidirect
9. C₄₃×#1892	C₂	semidirect
10. C₄₃×#1736	C₂	semidirect
11. C₂×C₄₃×#340	C₂	semidirect
22. C₄₃×#537	C₄	semidirect
78. C₂×M₁₆×C₄₃	D₄	semidirect
84. C₂²×C₈×C₄₃	D₄	semidirect
90. C₂²⋊Q₈×C₄₃	C₂×C₄	semidirect
94. #121×C₄₃	C₂×C₄	semidirect
295. #20976	C₄₃	direct (N × H)
335. C₂²×#131	C₂×C₄₃	semidirect
337. C₂×#417	C₂×C₄₃	semidirect
338. C₂×#416	C₂×C₄₃	semidirect
339. #2311	C₂×C₄₃	semidirect
340. #1895	C₂×C₄₃	semidirect
341. #1894	C₂×C₄₃	semidirect
342. #1893	C₂×C₄₃	semidirect
343. #1892	C₂×C₄₃	semidirect
344. #1736	C₂×C₄₃	semidirect
345. C₂×#340	C₂×C₄₃	semidirect
366. #537	C₄×C₄₃	semidirect
392. C₄₃	#20976	direct (N × H)
423. C₂×M₁₆	D₄×C₄₃	semidirect
429. C₂²×C₈	D₄×C₄₃	semidirect
435. C₂²⋊Q₈	C₂×C₄×C₄₃	semidirect
439. #121	C₂×C₄×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×#537	2
C₂×C₄₃×#417	2
C₂×C₄₃×#416	2
C₄₃×#2311	2
C₄₃×#1895	2
C₄₃×#1894	2
C₄₃×#1893	2
C₄₃×#1892	2
C₄₃×#1736	2
C₂×C₄₃×#340	2
#20976	43

Subgroups — C43×#20976 #24940993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20976 #24940993