Subgroups — C₄₃×#20975 #24940992

Order 11008.

1946 conjugacy classes of subgroups.

The subgroup lattice has 574 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×#535	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1895	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1893	C₂	1	4	yes	maximal, complemented
8	C₄₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×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	complemented
17	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₄₃	C₂²	1	2	yes	complemented
19	C₄₃×#535	—	2	4	no	—
20	C₄₃×#535	C₄	1	8	yes	complemented
21	C₂×#127×C₄₃	—	2	1	no	—
22	C₂×#124×C₄₃	—	2	1	no	—
23	C₂×#121×C₄₃	C₂²	1	4	yes	—
24	C₂×#120×C₄₃	—	2	2	no	—
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#418	—	2	4	no	—
29	C₂×#102×C₄₃	—	2	4	no	—
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×#102×C₄₃	C₂²	1	2	yes	—
32	C₂×#102×C₄₃	C₂²	1	4	yes	—
33	C₄₃×#391	—	2	1	no	—
34	C₄₃×#390	—	2	1	no	—
35	C₄₃×#386	—	2	2	no	—
36	C₄₃×#380	C₂²	1	4	yes	complemented
37	C₄₃×#340	C₂²	1	2	yes	complemented
38	C₄₃×#340	C₂²	1	4	yes	complemented
39	C₄₃×#340	C₂²	1	2	yes	complemented
40	C₂⁵×C₄₃	—	2	1	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	C₂×C₄	1	4	yes	—
46	C₂×#41×C₄₃	D₄	1	4	yes	—
47	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₄₃	—	2	4	no	—
49	C₂²×D₄×C₄₃	—	2	2	no	—
50	C₂²×D₄×C₄₃	—	2	2	no	—
51	C₂²×D₄×C₄₃	—	2	1	no	—
52	C₂²×D₄×C₄₃	—	2	2	no	—
53	C₂²×D₄×C₄₃	—	2	2	no	—
54	C₂²×D₄×C₄₃	—	2	2	no	—
55	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
56	C₂²×D₄×C₄₃	D₄	1	2	yes	—
57	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	#131×C₄₃	—	2	32	no	—
63	C₂×M₁₆×C₄₃	—	2	2	no	—
64	C₂×M₁₆×C₄₃	—	2	2	no	—
65	C₂×M₁₆×C₄₃	—	2	4	no	—
66	C₂×M₁₆×C₄₃	—	2	4	no	—
67	C₂×M₁₆×C₄₃	—	2	4	no	—
68	C₂×M₁₆×C₄₃	D₄	1	4	yes	complemented
69	C₂²×C₈×C₄₃	—	2	2	no	—
70	C₂²×C₈×C₄₃	—	2	2	no	—
71	C₂²×C₈×C₄₃	—	2	4	no	—
72	C₂²×C₈×C₄₃	—	2	4	no	—
73	C₂²×C₈×C₄₃	—	2	4	no	—
74	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
78	#127×C₄₃	—	2	8	no	—
79	#124×C₄₃	—	2	8	no	—
80	#121×C₄₃	—	2	8	no	—
81	#121×C₄₃	C₂×C₄	1	16	yes	complemented
82	#120×C₄₃	—	2	16	no	—
83	#117×C₄₃	—	2	2	no	—
84	#117×C₄₃	—	2	2	no	—
85	#117×C₄₃	—	2	2	no	—
86	#117×C₄₃	C₂×C₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
97	C₂×C₄²×C₄₃	—	2	1	no	—
98	C₂×C₄²×C₄₃	—	2	1	no	—
99	#102×C₄₃	—	2	4	no	—
100	#102×C₄₃	—	2	4	no	—
101	#102×C₄₃	—	2	8	no	—
102	#95×C₄₃	—	2	4	no	—
103	C₂⁴×C₄₃	—	2	2	no	—
104	C₂⁴×C₄₃	—	2	4	no	—
105	C₂⁴×C₄₃	—	4	2	no	—
106	C₂⁴×C₄₃	—	4	2	no	—
107	C₂⁴×C₄₃	—	8	2	no	—
108	C₂⁴×C₄₃	—	8	2	no	—
109	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
110	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
111	#41×C₄₃	—	2	8	no	—
112	#41×C₄₃	—	2	8	no	—
113	#41×C₄₃	—	2	8	no	—
114	#41×C₄₃	—	2	8	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
118	C₂×D₄×C₄₃	—	2	4	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	16	no	—
123	C₂×D₄×C₄₃	—	2	4	no	—
124	C₂×D₄×C₄₃	—	2	4	no	—
125	C₂×D₄×C₄₃	—	2	8	no	—
126	C₂×D₄×C₄₃	—	2	8	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	4	4	no	—
132	C₂×D₄×C₄₃	—	4	2	no	—
133	C₂×D₄×C₄₃	—	4	2	no	—
134	C₂×D₄×C₄₃	—	4	4	no	—
135	C₂×D₄×C₄₃	—	8	4	no	—
136	C₂×D₄×C₄₃	—	8	4	no	—
137	C₂×D₄×C₄₃	C₂²⋊C₄	1	8	yes	—
138	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
139	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	—	2	2	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	—	4	2	no	—
148	C₂²×C₄×C₄₃	—	8	2	no	—
149	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	#41	1	2	yes	—
158	C₂²×C₄×C₄₃	#41	1	2	yes	—
159	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
160	M₁₆×C₄₃	—	2	16	no	—
161	M₁₆×C₄₃	—	2	8	no	—
162	C₂×C₈×C₄₃	—	2	16	no	—
163	C₂×C₈×C₄₃	—	2	8	no	—
164	C₂×C₈×C₄₃	—	2	1	no	—
165	C₂×C₈×C₄₃	—	2	1	no	—
166	C₂×C₈×C₄₃	—	2	1	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	1	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
172	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
173	C₄⋊C₄×C₄₃	—	2	2	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	2	2	no	—
176	C₄⋊C₄×C₄₃	—	2	2	no	—
177	C₄⋊C₄×C₄₃	—	2	2	no	—
178	C₄⋊C₄×C₄₃	—	4	2	no	—
179	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
180	C₂²⋊C₄×C₄₃	—	2	16	no	—
181	C₂²⋊C₄×C₄₃	—	2	4	no	—
182	C₂²⋊C₄×C₄₃	—	4	2	no	—
183	C₂²⋊C₄×C₄₃	—	8	4	no	—
184	C₄²×C₄₃	—	2	4	no	—
185	C₄²×C₄₃	—	4	2	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	2	2	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	4	no	—
191	C₂³×C₄₃	—	2	4	no	—
192	C₂³×C₄₃	—	2	4	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	—	4	2	no	—
195	C₂³×C₄₃	—	4	4	no	—
196	C₂³×C₄₃	—	4	4	no	—
197	C₂³×C₄₃	—	4	8	no	—
198	C₂³×C₄₃	—	8	8	no	—
199	C₂³×C₄₃	—	8	4	no	—
200	C₂³×C₄₃	—	8	4	no	—
201	C₂³×C₄₃	—	8	8	no	—
202	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
203	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂³×C₄₃	#121	1	2	yes	—
205	C₂³×C₄₃	#121	1	2	yes	—
206	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₄₃	—	2	8	no	—
208	D₄×C₄₃	—	2	16	no	—
209	D₄×C₄₃	—	2	4	no	—
210	D₄×C₄₃	—	2	4	no	—
211	D₄×C₄₃	—	2	8	no	—
212	D₄×C₄₃	—	4	2	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	4	8	no	—
215	D₄×C₄₃	—	8	16	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	2	4	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	—	4	2	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	2	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	4	4	no	—
229	C₂×C₄×C₄₃	—	4	2	no	—
230	C₂×C₄×C₄₃	—	8	4	no	—
231	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
232	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
233	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
234	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
235	C₂×C₄×C₄₃	#120	1	4	yes	—
236	C₂×C₄×C₄₃	#121	1	2	yes	—
237	C₂×C₄×C₄₃	#121	1	2	yes	—
238	C₂×C₄×C₄₃	#123	1	4	yes	—
239	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
245	C₈×C₄₃	—	2	2	no	—
246	C₈×C₄₃	—	2	4	no	—
247	C₈×C₄₃	—	2	2	no	—
248	#20975	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂²×C₄₃	—	2	4	no	—
250	C₂²×C₄₃	—	2	2	no	—
251	C₂²×C₄₃	—	2	2	no	—
252	C₂²×C₄₃	—	2	4	no	—
253	C₂²×C₄₃	—	2	8	no	—
254	C₂²×C₄₃	—	2	4	no	—
255	C₂²×C₄₃	—	4	2	no	—
256	C₂²×C₄₃	—	4	2	no	—
257	C₂²×C₄₃	—	4	4	no	—
258	C₂²×C₄₃	—	4	8	no	—
259	C₂²×C₄₃	—	4	4	no	—
260	C₂²×C₄₃	—	8	16	no	—
261	C₂²×C₄₃	—	8	2	no	—
262	C₂²×C₄₃	—	8	2	no	—
263	C₂²×C₄₃	—	8	4	no	—
264	C₂²×C₄₃	#386	1	4	yes	—
265	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
267	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
268	C₂²×C₄₃	#576	1	2	yes	—
269	C₂²×C₄₃	#577	1	2	yes	—
270	C₄×C₄₃	—	2	4	no	—
271	C₄×C₄₃	—	4	4	no	—
272	C₄×C₄₃	—	8	2	no	—
273	C₄×C₄₃	—	8	2	no	—
274	C₄×C₄₃	#386	1	4	yes	—
275	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
276	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
277	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
278	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
279	C₂²×#131	C₂×C₄₃	1	1	yes	characteristic, complemented
280	C₂×#535	C₂×C₄₃	1	1	yes	characteristic
281	C₂×#418	C₂×C₄₃	1	1	yes	characteristic, complemented
282	C₂²×#102	C₂×C₄₃	1	1	yes	characteristic, complemented
283	#2311	C₂×C₄₃	1	1	yes	characteristic, complemented
284	#1895	C₂×C₄₃	1	4	yes	complemented
285	#1893	C₂×C₄₃	1	4	yes	complemented
286	#1736	C₂×C₄₃	1	1	yes	characteristic, complemented
287	#1735	C₂×C₄₃	1	1	yes	characteristic, complemented
288	C₂×C₄₃	—	2	4	no	—
289	C₂×C₄₃	—	4	4	no	—
290	C₂×C₄₃	—	8	4	no	—
291	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
292	C₂×C₄₃	#2897	1	2	yes	—
293	C₂×C₄₃	#3057	1	1	yes	characteristic
294	C₂×C₄₃	#3058	1	1	yes	characteristic
295	C₂×C₄₃	#3062	1	2	yes	—
296	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
297	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×#131	—	2	4	no	—
299	C₂×#131	—	2	4	no	—
300	C₂×#131	—	2	4	no	—
301	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
302	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	complemented
303	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
304	C₂³×C₈	C₂²×C₄₃	1	2	yes	complemented
305	#535	—	2	4	no	—
306	#535	C₄×C₄₃	1	8	yes	complemented
307	C₂×#127	—	2	1	no	—
308	C₂×#124	—	2	1	no	—
309	C₂×#121	C₂²×C₄₃	1	4	yes	—
310	C₂×#120	—	2	2	no	—
311	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
313	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
314	#418	—	2	4	no	—
315	C₂×#102	—	2	4	no	—
316	C₂×#102	C₂²×C₄₃	1	2	yes	—
317	C₂×#102	C₂²×C₄₃	1	2	yes	—
318	C₂×#102	C₂²×C₄₃	1	4	yes	—
319	#391	—	2	1	no	—
320	#390	—	2	1	no	—
321	#386	—	2	2	no	—
322	#380	C₂²×C₄₃	1	4	yes	complemented
323	#340	C₂²×C₄₃	1	2	yes	complemented
324	#340	C₂²×C₄₃	1	4	yes	complemented
325	#340	C₂²×C₄₃	1	2	yes	complemented
326	C₄₃	#20975	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁵	—	2	1	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
333	C₂×#41	D₄×C₄₃	1	4	yes	—
334	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
335	C₂²×D₄	—	2	4	no	—
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	2	2	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
343	C₂²×D₄	D₄×C₄₃	1	2	yes	—
344	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
345	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
348	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
349	#131	—	2	32	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	—	2	2	no	—
352	C₂×M₁₆	—	2	4	no	—
353	C₂×M₁₆	—	2	4	no	—
354	C₂×M₁₆	—	2	4	no	—
355	C₂×M₁₆	D₄×C₄₃	1	4	yes	complemented
356	C₂²×C₈	—	2	2	no	—
357	C₂²×C₈	—	2	2	no	—
358	C₂²×C₈	—	2	4	no	—
359	C₂²×C₈	—	2	4	no	—
360	C₂²×C₈	—	2	4	no	—
361	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
362	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
365	#127	—	2	8	no	—
366	#124	—	2	8	no	—
367	#121	—	2	8	no	—
368	#121	C₂×C₄×C₄₃	1	16	yes	complemented
369	#120	—	2	16	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	#117	C₂×C₄×C₄₃	1	4	yes	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	4	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	4	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	#102	—	2	4	no	—
387	#102	—	2	4	no	—
388	#102	—	2	8	no	—
389	#95	—	2	4	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	4	no	—
392	C₂⁴	—	4	2	no	—
393	C₂⁴	—	4	2	no	—
394	C₂⁴	—	8	2	no	—
395	C₂⁴	—	8	2	no	—
396	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
397	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
398	#41	—	2	8	no	—
399	#41	—	2	8	no	—
400	#41	—	2	8	no	—
401	#41	—	2	8	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	C₂²⋊C₄×C₄₃	1	4	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	16	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	8	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	4	no	—
422	C₂×D₄	—	8	4	no	—
423	C₂×D₄	—	8	4	no	—
424	C₂×D₄	C₂²⋊C₄×C₄₃	1	8	yes	—
425	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	—
426	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	8	2	no	—
436	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
437	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
440	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
444	C₂²×C₄	#41×C₄₃	1	2	yes	—
445	C₂²×C₄	#41×C₄₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
447	M₁₆	—	2	16	no	—
448	M₁₆	—	2	8	no	—
449	C₂×C₈	—	2	16	no	—
450	C₂×C₈	—	2	8	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
458	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
459	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	16	no	—
469	C₂²⋊C₄	—	4	2	no	—
470	C₂²⋊C₄	—	8	4	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	4	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	4	8	no	—
485	C₂³	—	8	8	no	—
486	C₂³	—	8	4	no	—
487	C₂³	—	8	4	no	—
488	C₂³	—	8	8	no	—
489	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
490	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
491	C₂³	#121×C₄₃	1	2	yes	—
492	C₂³	#121×C₄₃	1	2	yes	—
493	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
494	Q₈	—	2	8	no	—
495	D₄	—	2	16	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	4	no	—
498	D₄	—	2	8	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	8	no	—
502	D₄	—	8	16	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	8	4	no	—
518	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
519	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
520	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
521	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
522	C₂×C₄	#120×C₄₃	1	4	yes	—
523	C₂×C₄	#121×C₄₃	1	2	yes	—
524	C₂×C₄	#121×C₄₃	1	2	yes	—
525	C₂×C₄	#123×C₄₃	1	4	yes	—
526	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
530	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
531	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	2	4	no	—
534	C₈	—	2	2	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	8	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	8	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	8	16	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	4	no	—
550	C₂²	C₄₃×#386	1	4	yes	—
551	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
552	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
553	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
554	C₂²	C₄₃×#576	1	2	yes	—
555	C₂²	C₄₃×#577	1	2	yes	—
556	C₄	—	2	4	no	—
557	C₄	—	4	4	no	—
558	C₄	—	8	2	no	—
559	C₄	—	8	2	no	—
560	C₄	C₄₃×#386	1	4	yes	—
561	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
562	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
563	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
564	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
565	C₂	—	2	4	no	—
566	C₂	—	4	4	no	—
567	C₂	—	8	4	no	—
568	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
569	C₂	C₄₃×#2897	1	2	yes	—
570	C₂	C₄₃×#3057	1	1	yes	characteristic
571	C₂	C₄₃×#3058	1	1	yes	characteristic
572	C₂	C₄₃×#3062	1	2	yes	—

	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×#535	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×#418	C₂	semidirect
4. C₂²×#102×C₄₃	C₂	semidirect
5. C₄₃×#2311	C₂	semidirect
6. C₄₃×#1895	C₂	semidirect
7. C₄₃×#1893	C₂	semidirect
8. C₄₃×#1736	C₂	semidirect
9. C₄₃×#1735	C₂	semidirect
16. C₂²×M₁₆×C₄₃	C₂²	semidirect
18. C₂³×C₈×C₄₃	C₂²	semidirect
20. C₄₃×#535	C₄	semidirect
36. C₄₃×#380	C₂²	semidirect
37. C₄₃×#340	C₂²	semidirect
38. C₄₃×#340	C₂²	semidirect
39. C₄₃×#340	C₂²	semidirect
68. C₂×M₁₆×C₄₃	D₄	semidirect
74. C₂²×C₈×C₄₃	D₄	semidirect
81. #121×C₄₃	C₂×C₄	semidirect
248. #20975	C₄₃	direct (N × H)
279. C₂²×#131	C₂×C₄₃	semidirect
281. C₂×#418	C₂×C₄₃	semidirect
282. C₂²×#102	C₂×C₄₃	semidirect
283. #2311	C₂×C₄₃	semidirect
284. #1895	C₂×C₄₃	semidirect
285. #1893	C₂×C₄₃	semidirect
286. #1736	C₂×C₄₃	semidirect
287. #1735	C₂×C₄₃	semidirect
302. C₂²×M₁₆	C₂²×C₄₃	semidirect
304. C₂³×C₈	C₂²×C₄₃	semidirect
306. #535	C₄×C₄₃	semidirect
322. #380	C₂²×C₄₃	semidirect
323. #340	C₂²×C₄₃	semidirect
324. #340	C₂²×C₄₃	semidirect
325. #340	C₂²×C₄₃	semidirect
326. C₄₃	#20975	direct (N × H)
355. C₂×M₁₆	D₄×C₄₃	semidirect
361. C₂²×C₈	D₄×C₄₃	semidirect
368. #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×#535	2
C₂×C₄₃×#418	2
C₂²×#102×C₄₃	2
C₄₃×#2311	2
C₄₃×#1895	2
C₄₃×#1893	2
C₄₃×#1736	2
C₄₃×#1735	2
#20975	43

Subgroups — C43×#20975 #24940992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20975 #24940992