Subgroups — C₄₃×#20601 #24940618

Order 11008.

4038 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#417	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1788	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1787	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1786	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₃	—	2	16	no	—
9	C₂²×#41×C₄₃	—	2	4	no	—
10	C₂²×#41×C₄₃	—	2	1	no	—
11	C₂²×#41×C₄₃	—	2	1	no	—
12	C₂²×#41×C₄₃	C₄	1	8	yes	complemented
13	C₂²×#41×C₄₃	C₂²	1	2	yes	—
14	C₂²×#41×C₄₃	C₂²	1	2	yes	—
15	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₄₃	—	2	1	no	—
17	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₄₃	—	2	1	no	—
19	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	complemented
21	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
23	C₄₃×#417	—	2	16	no	—
24	C₂×#103×C₄₃	C₂²	1	8	yes	complemented
25	C₂×#102×C₄₃	C₂²	1	8	yes	complemented
26	C₄₃×#407	—	2	4	no	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	complemented
29	C₄₃×#380	—	2	1	no	—
30	C₄₃×#380	—	2	1	no	—
31	C₄₃×#380	C₂²	1	2	yes	—
32	C₄₃×#380	C₂²	1	2	yes	complemented
33	C₂×#95×C₄₃	—	2	1	no	—
34	C₂⁵×C₄₃	—	2	1	no	—
35	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
36	C₂×#41×C₄₃	—	2	64	no	—
37	C₂×#41×C₄₃	—	2	16	no	—
38	C₂×#41×C₄₃	—	2	16	no	—
39	C₂×#41×C₄₃	—	2	64	no	—
40	C₂×#41×C₄₃	—	2	8	no	—
41	C₂×#41×C₄₃	—	2	8	no	—
42	C₂×#41×C₄₃	—	2	8	no	—
43	C₂×#41×C₄₃	—	2	8	no	—
44	C₂×#41×C₄₃	—	2	4	no	—
45	C₂×#41×C₄₃	—	2	4	no	—
46	C₂×#41×C₄₃	—	2	8	no	—
47	C₂×#41×C₄₃	C₂×C₄	1	8	yes	—
48	C₂×#41×C₄₃	C₂×C₄	1	8	yes	complemented
49	C₂×#41×C₄₃	D₄	1	16	yes	—
50	C₂²×Q₈×C₄₃	—	2	8	no	—
51	C₂²×Q₈×C₄₃	—	2	2	no	—
52	C₂²×Q₈×C₄₃	—	2	1	no	—
53	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
54	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₄₃	—	2	16	no	—
56	C₂²×D₄×C₄₃	—	2	8	no	—
57	C₂²×D₄×C₄₃	—	2	2	no	—
58	C₂²×D₄×C₄₃	—	2	2	no	—
59	C₂²×D₄×C₄₃	—	2	8	no	—
60	C₂²×D₄×C₄₃	—	2	2	no	—
61	C₂²×D₄×C₄₃	—	2	1	no	—
62	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	complemented
63	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₄₃	—	2	16	no	—
65	C₂³×C₄×C₄₃	—	2	1	no	—
66	C₂³×C₄×C₄₃	—	2	8	no	—
67	C₂³×C₄×C₄₃	—	2	2	no	—
68	C₂³×C₄×C₄₃	—	2	2	no	—
69	C₂³×C₄×C₄₃	—	2	8	no	—
70	C₂³×C₄×C₄₃	—	2	2	no	—
71	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
72	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₄₃	D₄	1	4	yes	—
76	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₄₃	—	2	4	no	—
80	C₂×M₁₆×C₄₃	—	2	8	no	—
81	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
88	#103×C₄₃	—	2	16	no	—
89	#102×C₄₃	—	2	16	no	—
90	C₂²⋊C₈×C₄₃	—	2	4	no	—
91	C₂²⋊C₈×C₄₃	—	2	4	no	—
92	#95×C₄₃	—	2	2	no	—
93	#95×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	—	2	8	no	—
95	C₂⁴×C₄₃	—	2	4	no	—
96	C₂⁴×C₄₃	—	2	4	no	—
97	C₂⁴×C₄₃	—	2	2	no	—
98	C₂⁴×C₄₃	—	2	2	no	—
99	C₂⁴×C₄₃	—	2	2	no	—
100	C₂⁴×C₄₃	—	4	2	no	—
101	C₂⁴×C₄₃	—	4	4	no	—
102	C₂⁴×C₄₃	—	4	2	no	—
103	C₂⁴×C₄₃	—	4	2	no	—
104	C₂⁴×C₄₃	C₂²⋊C₄	1	4	yes	—
105	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
108	#41×C₄₃	—	2	64	no	—
109	#41×C₄₃	—	2	32	no	—
110	#41×C₄₃	—	2	64	no	—
111	#41×C₄₃	—	2	16	no	—
112	#41×C₄₃	—	2	16	no	—
113	#41×C₄₃	—	2	16	no	—
114	#41×C₄₃	—	2	32	no	—
115	#41×C₄₃	C₂²⋊C₄	1	32	yes	complemented
116	C₂×Q₈×C₄₃	—	2	16	no	—
117	C₂×Q₈×C₄₃	—	2	8	no	—
118	C₂×Q₈×C₄₃	—	2	16	no	—
119	C₂×Q₈×C₄₃	—	2	4	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	4	no	—
122	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
123	C₂×Q₈×C₄₃	C₂×D₄	1	8	yes	—
124	C₂×D₄×C₄₃	—	2	16	no	—
125	C₂×D₄×C₄₃	—	2	64	no	—
126	C₂×D₄×C₄₃	—	2	16	no	—
127	C₂×D₄×C₄₃	—	2	8	no	—
128	C₂×D₄×C₄₃	—	2	16	no	—
129	C₂×D₄×C₄₃	—	2	4	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	4	no	—
132	C₂×D₄×C₄₃	—	2	8	no	—
133	C₂×D₄×C₄₃	—	2	8	no	—
134	C₂×D₄×C₄₃	—	2	16	no	—
135	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
136	C₂×D₄×C₄₃	C₂×D₄	1	8	yes	—
137	C₂²×C₄×C₄₃	—	2	8	no	—
138	C₂²×C₄×C₄₃	—	2	64	no	—
139	C₂²×C₄×C₄₃	—	2	16	no	—
140	C₂²×C₄×C₄₃	—	2	8	no	—
141	C₂²×C₄×C₄₃	—	2	8	no	—
142	C₂²×C₄×C₄₃	—	2	16	no	—
143	C₂²×C₄×C₄₃	—	2	4	no	—
144	C₂²×C₄×C₄₃	—	2	16	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	16	no	—
147	C₂²×C₄×C₄₃	—	2	4	no	—
148	C₂²×C₄×C₄₃	—	2	4	no	—
149	C₂²×C₄×C₄₃	—	2	4	no	—
150	C₂²×C₄×C₄₃	—	2	4	no	—
151	C₂²×C₄×C₄₃	—	2	2	no	—
152	C₂²×C₄×C₄₃	—	2	4	no	—
153	C₂²×C₄×C₄₃	—	4	4	no	—
154	C₂²×C₄×C₄₃	—	4	4	no	—
155	C₂²×C₄×C₄₃	—	4	4	no	—
156	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
157	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
158	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
159	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
166	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
170	M₁₆×C₄₃	—	4	8	no	—
171	C₂×C₈×C₄₃	—	2	4	no	—
172	C₂×C₈×C₄₃	—	2	8	no	—
173	C₄⋊C₄×C₄₃	—	2	8	no	—
174	C₄⋊C₄×C₄₃	—	4	4	no	—
175	C₂²⋊C₄×C₄₃	—	4	4	no	—
176	C₂²⋊C₄×C₄₃	—	4	4	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	2	1	no	—
179	C₂³×C₄₃	—	2	1	no	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	—	2	2	no	—
182	C₂³×C₄₃	—	2	16	no	—
183	C₂³×C₄₃	—	2	4	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	2	8	no	—
186	C₂³×C₄₃	—	2	1	no	—
187	C₂³×C₄₃	—	2	1	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	8	no	—
190	C₂³×C₄₃	—	2	8	no	—
191	C₂³×C₄₃	—	4	4	no	—
192	C₂³×C₄₃	—	4	8	no	—
193	C₂³×C₄₃	—	4	8	no	—
194	C₂³×C₄₃	—	4	8	no	—
195	C₂³×C₄₃	—	4	16	no	—
196	C₂³×C₄₃	—	4	16	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	4	no	—
200	C₂³×C₄₃	—	4	8	no	—
201	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂³×C₄₃	#120	1	4	yes	—
205	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
206	C₂³×C₄₃	#137	1	2	yes	—
207	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₄₃	—	2	16	no	—
209	Q₈×C₄₃	—	2	4	no	—
210	Q₈×C₄₃	—	2	8	no	—
211	Q₈×C₄₃	C₂×C₂²⋊C₄	1	8	yes	complemented
212	D₄×C₄₃	—	2	32	no	—
213	D₄×C₄₃	—	2	16	no	—
214	D₄×C₄₃	—	2	32	no	—
215	D₄×C₄₃	—	2	4	no	—
216	D₄×C₄₃	—	2	8	no	—
217	D₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	complemented
218	C₂×C₄×C₄₃	—	2	16	no	—
219	C₂×C₄×C₄₃	—	2	32	no	—
220	C₂×C₄×C₄₃	—	2	4	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	8	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	8	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	4	no	—
229	C₂×C₄×C₄₃	—	2	8	no	—
230	C₂×C₄×C₄₃	—	2	32	no	—
231	C₂×C₄×C₄₃	—	2	8	no	—
232	C₂×C₄×C₄₃	—	4	4	no	—
233	C₂×C₄×C₄₃	—	4	4	no	—
234	C₂×C₄×C₄₃	—	4	4	no	—
235	C₂×C₄×C₄₃	—	8	8	no	—
236	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
237	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
239	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
240	C₂×C₄×C₄₃	#120	1	8	yes	—
241	C₂×C₄×C₄₃	#120	1	4	yes	—
242	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
245	C₈×C₄₃	—	4	4	no	—
246	#20601	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₄₃	—	2	2	no	—
248	C₂²×C₄₃	—	2	2	no	—
249	C₂²×C₄₃	—	2	2	no	—
250	C₂²×C₄₃	—	2	4	no	—
251	C₂²×C₄₃	—	2	4	no	—
252	C₂²×C₄₃	—	2	4	no	—
253	C₂²×C₄₃	—	2	4	no	—
254	C₂²×C₄₃	—	2	2	no	—
255	C₂²×C₄₃	—	2	2	no	—
256	C₂²×C₄₃	—	2	2	no	—
257	C₂²×C₄₃	—	2	8	no	—
258	C₂²×C₄₃	—	2	2	no	—
259	C₂²×C₄₃	—	4	16	no	—
260	C₂²×C₄₃	—	4	32	no	—
261	C₂²×C₄₃	—	4	4	no	—
262	C₂²×C₄₃	—	4	4	no	—
263	C₂²×C₄₃	—	4	2	no	—
264	C₂²×C₄₃	—	4	8	no	—
265	C₂²×C₄₃	—	4	2	no	—
266	C₂²×C₄₃	—	4	8	no	—
267	C₂²×C₄₃	#379	1	4	yes	—
268	C₂²×C₄₃	#417	1	4	yes	complemented
269	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
270	C₂²×C₄₃	C₂×#120	1	2	yes	—
271	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
273	C₂²×C₄₃	#575	1	2	yes	—
274	C₄×C₄₃	—	2	2	no	—
275	C₄×C₄₃	—	2	8	no	—
276	C₄×C₄₃	—	2	2	no	—
277	C₄×C₄₃	—	8	4	no	—
278	C₄×C₄₃	#379	1	4	yes	—
279	C₄×C₄₃	C₂²×C₂²⋊C₄	1	2	yes	—
280	C₄×C₄₃	C₂×#120	1	2	yes	—
281	C₂³×#41	C₂×C₄₃	1	1	yes	characteristic
282	C₂×#417	C₂×C₄₃	1	4	yes	complemented
283	C₂×#407	C₂×C₄₃	1	1	yes	characteristic, complemented
284	C₂×#380	C₂×C₄₃	1	1	yes	characteristic, complemented
285	#1788	C₂×C₄₃	1	4	yes	complemented
286	#1787	C₂×C₄₃	1	2	yes	complemented
287	#1786	C₂×C₄₃	1	2	yes	complemented
288	C₂×C₄₃	—	2	4	no	—
289	C₂×C₄₃	—	2	4	no	—
290	C₂×C₄₃	—	4	2	no	—
291	C₂×C₄₃	—	4	8	no	—
292	C₂×C₄₃	C₂×#379	1	1	yes	characteristic
293	C₂×C₄₃	C₂×#417	1	1	yes	characteristic
294	C₂×C₄₃	#2896	1	1	yes	characteristic
295	C₂×C₄₃	#3006	1	2	yes	—
296	C₂×C₄₃	#3007	1	2	yes	—
297	C₂²×#41	—	2	16	no	—
298	C₂²×#41	—	2	4	no	—
299	C₂²×#41	—	2	1	no	—
300	C₂²×#41	—	2	1	no	—
301	C₂²×#41	C₄×C₄₃	1	8	yes	complemented
302	C₂²×#41	C₂²×C₄₃	1	2	yes	—
303	C₂²×#41	C₂²×C₄₃	1	2	yes	—
304	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
305	C₂³×D₄	—	2	1	no	—
306	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
307	C₂⁴×C₄	—	2	1	no	—
308	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
309	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	complemented
310	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	complemented
311	C₂²×C₂²⋊C₄	—	2	1	no	—
312	#417	—	2	16	no	—
313	C₂×#103	C₂²×C₄₃	1	8	yes	complemented
314	C₂×#102	C₂²×C₄₃	1	8	yes	complemented
315	#407	—	2	4	no	—
316	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	complemented
318	#380	—	2	1	no	—
319	#380	—	2	1	no	—
320	#380	C₂²×C₄₃	1	2	yes	—
321	#380	C₂²×C₄₃	1	2	yes	complemented
322	C₂×#95	—	2	1	no	—
323	C₄₃	#20601	1	1	yes	characteristic, direct product factor, Sylow
324	C₂⁵	—	2	1	no	—
325	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
326	C₂×#41	—	2	16	no	—
327	C₂×#41	—	2	64	no	—
328	C₂×#41	—	2	16	no	—
329	C₂×#41	—	2	64	no	—
330	C₂×#41	—	2	8	no	—
331	C₂×#41	—	2	8	no	—
332	C₂×#41	—	2	8	no	—
333	C₂×#41	—	2	8	no	—
334	C₂×#41	—	2	4	no	—
335	C₂×#41	—	2	4	no	—
336	C₂×#41	—	2	8	no	—
337	C₂×#41	C₂×C₄×C₄₃	1	8	yes	—
338	C₂×#41	C₂×C₄×C₄₃	1	8	yes	complemented
339	C₂×#41	D₄×C₄₃	1	16	yes	—
340	C₂²×Q₈	—	2	8	no	—
341	C₂²×Q₈	—	2	2	no	—
342	C₂²×Q₈	—	2	1	no	—
343	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
344	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
345	C₂²×D₄	—	2	16	no	—
346	C₂²×D₄	—	2	8	no	—
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	—	2	2	no	—
349	C₂²×D₄	—	2	8	no	—
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	complemented
353	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
354	C₂³×C₄	—	2	16	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	—	2	8	no	—
357	C₂³×C₄	—	2	2	no	—
358	C₂³×C₄	—	2	2	no	—
359	C₂³×C₄	—	2	8	no	—
360	C₂³×C₄	—	2	2	no	—
361	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
362	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
363	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
364	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
365	C₂³×C₄	D₄×C₄₃	1	4	yes	—
366	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
369	C₂×M₁₆	—	2	4	no	—
370	C₂×M₁₆	—	2	8	no	—
371	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
372	C₂×C₄⋊C₄	—	2	8	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	4	4	no	—
378	#103	—	2	16	no	—
379	#102	—	2	16	no	—
380	C₂²⋊C₈	—	2	4	no	—
381	C₂²⋊C₈	—	2	4	no	—
382	#95	—	2	2	no	—
383	#95	—	2	2	no	—
384	C₂⁴	—	2	8	no	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	4	2	no	—
391	C₂⁴	—	4	4	no	—
392	C₂⁴	—	4	2	no	—
393	C₂⁴	—	4	2	no	—
394	C₂⁴	C₂²⋊C₄×C₄₃	1	4	yes	—
395	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
396	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
397	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
398	#41	—	2	64	no	—
399	#41	—	2	32	no	—
400	#41	—	2	64	no	—
401	#41	—	2	16	no	—
402	#41	—	2	16	no	—
403	#41	—	2	16	no	—
404	#41	—	2	32	no	—
405	#41	C₂²⋊C₄×C₄₃	1	32	yes	complemented
406	C₂×Q₈	—	2	16	no	—
407	C₂×Q₈	—	2	8	no	—
408	C₂×Q₈	—	2	16	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	—
413	C₂×Q₈	C₂×D₄×C₄₃	1	8	yes	—
414	C₂×D₄	—	2	64	no	—
415	C₂×D₄	—	2	16	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	16	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	16	no	—
421	C₂×D₄	—	2	16	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
426	C₂×D₄	C₂×D₄×C₄₃	1	8	yes	—
427	C₂²×C₄	—	2	8	no	—
428	C₂²×C₄	—	2	64	no	—
429	C₂²×C₄	—	2	16	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	8	no	—
434	C₂²×C₄	—	2	8	no	—
435	C₂²×C₄	—	2	16	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	16	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	16	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
447	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
448	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
449	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
450	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
451	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
452	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
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	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
458	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
460	M₁₆	—	4	8	no	—
461	C₂×C₈	—	2	4	no	—
462	C₂×C₈	—	2	8	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	4	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	16	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	2	8	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	8	no	—
484	C₂³	—	4	8	no	—
485	C₂³	—	4	16	no	—
486	C₂³	—	4	16	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	8	no	—
491	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
492	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
493	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
494	C₂³	#120×C₄₃	1	4	yes	—
495	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
496	C₂³	#137×C₄₃	1	2	yes	—
497	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
498	Q₈	—	2	16	no	—
499	Q₈	—	2	4	no	—
500	Q₈	—	2	8	no	—
501	Q₈	C₂×C₂²⋊C₄×C₄₃	1	8	yes	complemented
502	D₄	—	2	32	no	—
503	D₄	—	2	16	no	—
504	D₄	—	2	32	no	—
505	D₄	—	2	4	no	—
506	D₄	—	2	8	no	—
507	D₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	complemented
508	C₂×C₄	—	2	16	no	—
509	C₂×C₄	—	2	32	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	8	no	—
520	C₂×C₄	—	2	32	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	8	8	no	—
526	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
527	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
528	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	—
529	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
530	C₂×C₄	#120×C₄₃	1	8	yes	—
531	C₂×C₄	#120×C₄₃	1	4	yes	—
532	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
534	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
535	C₈	—	4	4	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	2	4	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	8	no	—
548	C₂²	—	4	16	no	—
549	C₂²	—	4	32	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	8	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	8	no	—
556	C₂²	C₄₃×#379	1	4	yes	—
557	C₂²	C₄₃×#417	1	4	yes	complemented
558	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
559	C₂²	C₂×#120×C₄₃	1	2	yes	—
560	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
561	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
562	C₂²	C₄₃×#575	1	2	yes	—
563	C₄	—	2	2	no	—
564	C₄	—	2	8	no	—
565	C₄	—	2	2	no	—
566	C₄	—	8	4	no	—
567	C₄	C₄₃×#379	1	4	yes	—
568	C₄	C₂²×C₂²⋊C₄×C₄₃	1	2	yes	—
569	C₄	C₂×#120×C₄₃	1	2	yes	—
570	C₂	—	2	4	no	—
571	C₂	—	2	4	no	—
572	C₂	—	4	2	no	—
573	C₂	—	4	8	no	—
574	C₂	C₂×C₄₃×#379	1	1	yes	characteristic
575	C₂	C₂×C₄₃×#417	1	1	yes	characteristic
576	C₂	C₄₃×#2896	1	1	yes	characteristic
577	C₂	C₄₃×#3006	1	2	yes	—
578	C₂	C₄₃×#3007	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	C₂³×#41×C₄₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#417	C₂	semidirect
3. C₂×C₄₃×#407	C₂	semidirect
4. C₂×C₄₃×#380	C₂	semidirect
5. C₄₃×#1788	C₂	semidirect
6. C₄₃×#1787	C₂	semidirect
7. C₄₃×#1786	C₂	semidirect
12. C₂²×#41×C₄₃	C₄	semidirect
20. C₂²×M₁₆×C₄₃	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
24. C₂×#103×C₄₃	C₂²	semidirect
25. C₂×#102×C₄₃	C₂²	semidirect
28. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
32. C₄₃×#380	C₂²	semidirect
48. C₂×#41×C₄₃	C₂×C₄	semidirect
53. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
62. C₂²×D₄×C₄₃	C₂×C₄	semidirect
115. #41×C₄₃	C₂²⋊C₄	semidirect
211. Q₈×C₄₃	C₂×C₂²⋊C₄	semidirect
217. D₄×C₄₃	C₂×C₂²⋊C₄	semidirect
246. #20601	C₄₃	direct (N × H)
268. C₂²×C₄₃	#417	semidirect
282. C₂×#417	C₂×C₄₃	semidirect
283. C₂×#407	C₂×C₄₃	semidirect
284. C₂×#380	C₂×C₄₃	semidirect
285. #1788	C₂×C₄₃	semidirect
286. #1787	C₂×C₄₃	semidirect
287. #1786	C₂×C₄₃	semidirect
301. C₂²×#41	C₄×C₄₃	semidirect
309. C₂²×M₁₆	C₂²×C₄₃	semidirect
310. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
313. C₂×#103	C₂²×C₄₃	semidirect
314. C₂×#102	C₂²×C₄₃	semidirect
317. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
321. #380	C₂²×C₄₃	semidirect
323. C₄₃	#20601	direct (N × H)
338. C₂×#41	C₂×C₄×C₄₃	semidirect
343. C₂²×Q₈	C₂×C₄×C₄₃	semidirect
352. C₂²×D₄	C₂×C₄×C₄₃	semidirect
405. #41	C₂²⋊C₄×C₄₃	semidirect
501. Q₈	C₂×C₂²⋊C₄×C₄₃	semidirect
507. D₄	C₂×C₂²⋊C₄×C₄₃	semidirect
557. C₂²	C₄₃×#417	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×#41×C₄₃	2
C₂×C₄₃×#417	2
C₂×C₄₃×#407	2
C₂×C₄₃×#380	2
C₄₃×#1788	2
C₄₃×#1787	2
C₄₃×#1786	2
#20601	43

Subgroups — C43×#20601 #24940618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20601 #24940618