Subgroups — C₄₃×#20914 #24940931

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1875	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1874	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	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#535	—	2	4	no	—
15	C₄₃×#535	C₄	1	8	yes	complemented
16	C₂×#127×C₄₃	—	2	1	no	—
17	C₂×#124×C₄₃	—	2	1	no	—
18	C₂×#121×C₄₃	C₂²	1	4	yes	—
19	C₂×#120×C₄₃	—	2	2	no	—
20	C₄₃×#520	—	2	4	no	—
21	C₄₃×#520	—	2	4	no	—
22	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
23	C₂×C₄×D₄×C₄₃	—	2	1	no	—
24	C₂×C₄×D₄×C₄₃	—	2	2	no	—
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₃	C₂²	1	2	yes	complemented
28	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
30	C₄₃×#418	—	2	4	no	—
31	C₂×#102×C₄₃	—	2	4	no	—
32	C₂×#102×C₄₃	C₂²	1	4	yes	—
33	C₂×#102×C₄₃	C₂²	1	2	yes	—
34	C₂×#102×C₄₃	C₂²	1	2	yes	—
35	C₄₃×#408	—	2	4	no	—
36	C₂×C₂²⋊C₈×C₄₃	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	complemented
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	—	2	2	no	—
61	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₄₃	—	2	2	no	—
64	C₂×M₁₆×C₄₃	—	2	2	no	—
65	C₂×M₁₆×C₄₃	—	2	2	no	—
66	C₂²×C₈×C₄₃	—	2	2	no	—
67	C₂²×C₈×C₄₃	—	2	2	no	—
68	C₂²×C₈×C₄₃	—	2	2	no	—
69	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
70	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
71	#127×C₄₃	—	2	8	no	—
72	#124×C₄₃	—	2	8	no	—
73	#121×C₄₃	—	2	8	no	—
74	#121×C₄₃	C₂×C₄	1	16	yes	complemented
75	#120×C₄₃	—	2	16	no	—
76	C₄×Q₈×C₄₃	—	2	8	no	—
77	C₄×D₄×C₄₃	—	2	16	no	—
78	C₄×D₄×C₄₃	—	2	8	no	—
79	#117×C₄₃	—	2	2	no	—
80	#117×C₄₃	—	2	2	no	—
81	#117×C₄₃	—	2	4	no	—
82	#117×C₄₃	—	2	4	no	—
83	#117×C₄₃	C₂×C₄	1	4	yes	complemented
84	#117×C₄₃	D₄	1	4	yes	complemented
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
90	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	complemented
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
99	C₂×C₄²×C₄₃	—	2	1	no	—
100	C₂×C₄²×C₄₃	—	2	1	no	—
101	C₂×C₄²×C₄₃	—	2	2	no	—
102	#102×C₄₃	—	2	8	no	—
103	#102×C₄₃	—	2	4	no	—
104	#102×C₄₃	—	2	4	no	—
105	C₂²⋊C₈×C₄₃	—	2	8	no	—
106	C₂⁴×C₄₃	—	2	2	no	—
107	C₂⁴×C₄₃	—	2	4	no	—
108	C₂⁴×C₄₃	—	4	2	no	—
109	C₂⁴×C₄₃	—	4	2	no	—
110	C₂⁴×C₄₃	—	8	2	no	—
111	C₂⁴×C₄₃	—	8	2	no	—
112	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
113	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
114	#41×C₄₃	—	2	8	no	—
115	#41×C₄₃	—	2	8	no	—
116	#41×C₄₃	—	2	8	no	—
117	#41×C₄₃	—	2	8	no	—
118	C₂×Q₈×C₄₃	—	2	2	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
121	C₂×D₄×C₄₃	—	2	4	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	16	no	—
126	C₂×D₄×C₄₃	—	2	4	no	—
127	C₂×D₄×C₄₃	—	2	4	no	—
128	C₂×D₄×C₄₃	—	2	8	no	—
129	C₂×D₄×C₄₃	—	2	8	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	2	2	no	—
134	C₂×D₄×C₄₃	—	4	2	no	—
135	C₂×D₄×C₄₃	—	4	4	no	—
136	C₂×D₄×C₄₃	—	4	4	no	—
137	C₂×D₄×C₄₃	—	4	2	no	—
138	C₂×D₄×C₄₃	—	8	4	no	—
139	C₂×D₄×C₄₃	—	8	4	no	—
140	C₂×D₄×C₄₃	C₂²⋊C₄	1	8	yes	—
141	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
142	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
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	—	2	8	no	—
148	C₂²×C₄×C₄₃	—	2	4	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	2	2	no	—
153	C₂²×C₄×C₄₃	—	8	2	no	—
154	C₂²×C₄×C₄₃	—	8	4	no	—
155	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	#41	1	2	yes	—
164	C₂²×C₄×C₄₃	#41	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	M₁₆×C₄₃	—	4	4	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	2	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	—	4	4	no	—
174	C₄⋊C₄×C₄₃	—	2	8	no	—
175	C₄⋊C₄×C₄₃	—	2	4	no	—
176	C₄⋊C₄×C₄₃	—	2	2	no	—
177	C₄⋊C₄×C₄₃	—	2	1	no	—
178	C₄⋊C₄×C₄₃	—	2	1	no	—
179	C₄⋊C₄×C₄₃	—	2	2	no	—
180	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
181	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
182	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
183	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
184	C₂²⋊C₄×C₄₃	—	2	8	no	—
185	C₂²⋊C₄×C₄₃	—	2	16	no	—
186	C₂²⋊C₄×C₄₃	—	2	4	no	—
187	C₂²⋊C₄×C₄₃	—	2	4	no	—
188	C₄²×C₄₃	—	2	8	no	—
189	C₄²×C₄₃	—	2	4	no	—
190	C₄²×C₄₃	—	2	4	no	—
191	C₂³×C₄₃	—	2	2	no	—
192	C₂³×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	2	2	no	—
195	C₂³×C₄₃	—	2	4	no	—
196	C₂³×C₄₃	—	2	4	no	—
197	C₂³×C₄₃	—	2	4	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	4	no	—
201	C₂³×C₄₃	—	4	4	no	—
202	C₂³×C₄₃	—	4	8	no	—
203	C₂³×C₄₃	—	8	8	no	—
204	C₂³×C₄₃	—	8	8	no	—
205	C₂³×C₄₃	—	8	4	no	—
206	C₂³×C₄₃	—	8	4	no	—
207	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
208	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂³×C₄₃	#120	1	2	yes	—
210	C₂³×C₄₃	#123	1	2	yes	—
211	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₄₃	—	2	8	no	—
213	D₄×C₄₃	—	2	16	no	—
214	D₄×C₄₃	—	2	4	no	—
215	D₄×C₄₃	—	2	4	no	—
216	D₄×C₄₃	—	2	8	no	—
217	D₄×C₄₃	—	4	2	no	—
218	D₄×C₄₃	—	4	2	no	—
219	D₄×C₄₃	—	4	8	no	—
220	D₄×C₄₃	—	8	16	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	4	no	—
224	C₂×C₄×C₄₃	—	2	4	no	—
225	C₂×C₄×C₄₃	—	2	4	no	—
226	C₂×C₄×C₄₃	—	2	4	no	—
227	C₂×C₄×C₄₃	—	2	4	no	—
228	C₂×C₄×C₄₃	—	2	2	no	—
229	C₂×C₄×C₄₃	—	2	4	no	—
230	C₂×C₄×C₄₃	—	2	2	no	—
231	C₂×C₄×C₄₃	—	4	4	no	—
232	C₂×C₄×C₄₃	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	2	no	—
236	C₂×C₄×C₄₃	—	8	4	no	—
237	C₂×C₄×C₄₃	—	8	8	no	—
238	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
239	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
240	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
241	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
242	C₂×C₄×C₄₃	#120	1	2	yes	—
243	C₂×C₄×C₄₃	#121	1	4	yes	—
244	C₂×C₄×C₄₃	#121	1	4	yes	—
245	C₂×C₄×C₄₃	#123	1	2	yes	—
246	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
252	C₈×C₄₃	—	4	2	no	—
253	C₈×C₄₃	—	4	2	no	—
254	#20914	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂²×C₄₃	—	2	4	no	—
256	C₂²×C₄₃	—	2	4	no	—
257	C₂²×C₄₃	—	2	2	no	—
258	C₂²×C₄₃	—	2	2	no	—
259	C₂²×C₄₃	—	2	8	no	—
260	C₂²×C₄₃	—	2	4	no	—
261	C₂²×C₄₃	—	4	4	no	—
262	C₂²×C₄₃	—	4	2	no	—
263	C₂²×C₄₃	—	4	2	no	—
264	C₂²×C₄₃	—	4	8	no	—
265	C₂²×C₄₃	—	4	4	no	—
266	C₂²×C₄₃	—	8	16	no	—
267	C₂²×C₄₃	—	8	4	no	—
268	C₂²×C₄₃	—	8	2	no	—
269	C₂²×C₄₃	—	8	2	no	—
270	C₂²×C₄₃	#386	1	4	yes	—
271	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
273	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
274	C₂²×C₄₃	#576	1	2	yes	—
275	C₂²×C₄₃	#577	1	2	yes	—
276	C₄×C₄₃	—	2	4	no	—
277	C₄×C₄₃	—	4	4	no	—
278	C₄×C₄₃	—	4	4	no	—
279	C₄×C₄₃	—	4	2	no	—
280	C₄×C₄₃	—	4	2	no	—
281	C₄×C₄₃	#386	1	4	yes	—
282	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
284	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
285	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
286	C₂×#535	C₂×C₄₃	1	1	yes	characteristic
287	C₂×#520	C₂×C₄₃	1	1	yes	characteristic, complemented
288	C₂×#418	C₂×C₄₃	1	1	yes	characteristic, complemented
289	C₂²×#102	C₂×C₄₃	1	1	yes	characteristic, complemented
290	C₂×#408	C₂×C₄₃	1	1	yes	characteristic, complemented
291	#1875	C₂×C₄₃	1	4	yes	complemented
292	#1874	C₂×C₄₃	1	4	yes	complemented
293	#1736	C₂×C₄₃	1	1	yes	characteristic, complemented
294	#1735	C₂×C₄₃	1	1	yes	characteristic, complemented
295	C₂×C₄₃	—	2	4	no	—
296	C₂×C₄₃	—	4	4	no	—
297	C₂×C₄₃	—	8	4	no	—
298	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
299	C₂×C₄₃	#2897	1	2	yes	—
300	C₂×C₄₃	#3008	1	1	yes	characteristic
301	C₂×C₄₃	#3010	1	1	yes	characteristic
302	C₂×C₄₃	#3096	1	2	yes	—
303	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
304	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
305	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
306	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
307	#535	—	2	4	no	—
308	#535	C₄×C₄₃	1	8	yes	complemented
309	C₂×#127	—	2	1	no	—
310	C₂×#124	—	2	1	no	—
311	C₂×#121	C₂²×C₄₃	1	4	yes	—
312	C₂×#120	—	2	2	no	—
313	#520	—	2	4	no	—
314	#520	—	2	4	no	—
315	C₂×C₄×Q₈	—	2	1	no	—
316	C₂×C₄×D₄	—	2	1	no	—
317	C₂×C₄×D₄	—	2	2	no	—
318	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
319	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
320	C₂×#117	C₂²×C₄₃	1	2	yes	complemented
321	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	complemented
323	#418	—	2	4	no	—
324	C₂×#102	—	2	4	no	—
325	C₂×#102	C₂²×C₄₃	1	4	yes	—
326	C₂×#102	C₂²×C₄₃	1	2	yes	—
327	C₂×#102	C₂²×C₄₃	1	2	yes	—
328	#408	—	2	4	no	—
329	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	complemented
330	#340	C₂²×C₄₃	1	2	yes	complemented
331	#340	C₂²×C₄₃	1	4	yes	complemented
332	#340	C₂²×C₄₃	1	2	yes	complemented
333	C₄₃	#20914	1	1	yes	characteristic, direct product factor, Sylow
334	C₂⁵	—	2	1	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
340	C₂×#41	D₄×C₄₃	1	4	yes	—
341	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
342	C₂²×D₄	—	2	4	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	—	2	2	no	—
349	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	complemented
350	C₂²×D₄	D₄×C₄₃	1	2	yes	—
351	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
352	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	2	2	no	—
355	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
356	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	2	no	—
360	C₂²×C₈	—	2	2	no	—
361	C₂²×C₈	—	2	2	no	—
362	C₂²×C₈	—	2	2	no	—
363	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
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	C₄×Q₈	—	2	8	no	—
371	C₄×D₄	—	2	16	no	—
372	C₄×D₄	—	2	8	no	—
373	#117	—	2	2	no	—
374	#117	—	2	2	no	—
375	#117	—	2	4	no	—
376	#117	—	2	4	no	—
377	#117	C₂×C₄×C₄₃	1	4	yes	complemented
378	#117	D₄×C₄₃	1	4	yes	complemented
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	4	no	—
383	C₂×C₄⋊C₄	—	2	4	no	—
384	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	complemented
385	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	4	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	2	no	—
396	#102	—	2	8	no	—
397	#102	—	2	4	no	—
398	#102	—	2	4	no	—
399	C₂²⋊C₈	—	2	8	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	4	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	—	4	2	no	—
404	C₂⁴	—	8	2	no	—
405	C₂⁴	—	8	2	no	—
406	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
407	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
408	#41	—	2	8	no	—
409	#41	—	2	8	no	—
410	#41	—	2	8	no	—
411	#41	—	2	8	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	C₂²⋊C₄×C₄₃	1	4	yes	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	16	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	8	4	no	—
433	C₂×D₄	—	8	4	no	—
434	C₂×D₄	C₂²⋊C₄×C₄₃	1	8	yes	—
435	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	—
436	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	8	2	no	—
448	C₂²×C₄	—	8	4	no	—
449	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
450	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
451	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
452	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
453	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
455	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
457	C₂²×C₄	#41×C₄₃	1	2	yes	—
458	C₂²×C₄	#41×C₄₃	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
460	M₁₆	—	4	4	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	4	4	no	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
475	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
476	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
477	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
478	C₂²⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	16	no	—
482	C₄²	—	2	8	no	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	4	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	8	no	—
497	C₂³	—	8	8	no	—
498	C₂³	—	8	8	no	—
499	C₂³	—	8	4	no	—
500	C₂³	—	8	4	no	—
501	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
502	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
503	C₂³	#120×C₄₃	1	2	yes	—
504	C₂³	#123×C₄₃	1	2	yes	—
505	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
506	Q₈	—	2	8	no	—
507	D₄	—	2	16	no	—
508	D₄	—	2	4	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	8	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	8	no	—
514	D₄	—	8	16	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	8	4	no	—
531	C₂×C₄	—	8	8	no	—
532	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
533	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
534	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
535	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
536	C₂×C₄	#120×C₄₃	1	2	yes	—
537	C₂×C₄	#121×C₄₃	1	4	yes	—
538	C₂×C₄	#121×C₄₃	1	4	yes	—
539	C₂×C₄	#123×C₄₃	1	2	yes	—
540	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
544	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
545	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
546	C₈	—	4	2	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	8	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	8	16	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	C₄₃×#386	1	4	yes	—
564	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
565	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
566	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
567	C₂²	C₄₃×#576	1	2	yes	—
568	C₂²	C₄₃×#577	1	2	yes	—
569	C₄	—	2	4	no	—
570	C₄	—	4	4	no	—
571	C₄	—	4	4	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	C₄₃×#386	1	4	yes	—
575	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
576	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
577	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
578	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
579	C₂	—	2	4	no	—
580	C₂	—	4	4	no	—
581	C₂	—	8	4	no	—
582	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
583	C₂	C₄₃×#2897	1	2	yes	—
584	C₂	C₄₃×#3008	1	1	yes	characteristic
585	C₂	C₄₃×#3010	1	1	yes	characteristic
586	C₂	C₄₃×#3096	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
2. C₂×C₄₃×#520	C₂	semidirect
3. C₂×C₄₃×#418	C₂	semidirect
4. C₂²×#102×C₄₃	C₂	semidirect
5. C₂×C₄₃×#408	C₂	semidirect
6. C₄₃×#1875	C₂	semidirect
7. C₄₃×#1874	C₂	semidirect
8. C₄₃×#1736	C₂	semidirect
9. C₄₃×#1735	C₂	semidirect
15. C₄₃×#535	C₄	semidirect
27. C₂×#117×C₄₃	C₂²	semidirect
29. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
36. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
37. C₄₃×#340	C₂²	semidirect
38. C₄₃×#340	C₂²	semidirect
39. C₄₃×#340	C₂²	semidirect
55. C₂²×D₄×C₄₃	C₂×C₄	semidirect
74. #121×C₄₃	C₂×C₄	semidirect
83. #117×C₄₃	C₂×C₄	semidirect
84. #117×C₄₃	D₄	semidirect
90. C₂×C₄⋊C₄×C₄₃	D₄	semidirect
254. #20914	C₄₃	direct (N × H)
287. C₂×#520	C₂×C₄₃	semidirect
288. C₂×#418	C₂×C₄₃	semidirect
289. C₂²×#102	C₂×C₄₃	semidirect
290. C₂×#408	C₂×C₄₃	semidirect
291. #1875	C₂×C₄₃	semidirect
292. #1874	C₂×C₄₃	semidirect
293. #1736	C₂×C₄₃	semidirect
294. #1735	C₂×C₄₃	semidirect
308. #535	C₄×C₄₃	semidirect
320. C₂×#117	C₂²×C₄₃	semidirect
322. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
329. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
330. #340	C₂²×C₄₃	semidirect
331. #340	C₂²×C₄₃	semidirect
332. #340	C₂²×C₄₃	semidirect
333. C₄₃	#20914	direct (N × H)
349. C₂²×D₄	C₂×C₄×C₄₃	semidirect
368. #121	C₂×C₄×C₄₃	semidirect
377. #117	C₂×C₄×C₄₃	semidirect
378. #117	D₄×C₄₃	semidirect
384. C₂×C₄⋊C₄	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×#535	2
C₂×C₄₃×#520	2
C₂×C₄₃×#418	2
C₂²×#102×C₄₃	2
C₂×C₄₃×#408	2
C₄₃×#1875	2
C₄₃×#1874	2
C₄₃×#1736	2
C₄₃×#1735	2
#20914	43

Subgroups — C43×#20914 #24940931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20914 #24940931