Subgroups — C₄₃×#32935 #24952952

Order 11008.

1580 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#468	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2847	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1895	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1894	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1809	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
14	C₂²×M₁₆×C₄₃	—	2	8	no	—
15	C₂²×M₁₆×C₄₃	—	2	4	no	—
16	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
18	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
22	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#121×C₄₃	C₂²	1	2	yes	—
24	C₂×#120×C₄₃	—	2	1	no	—
25	C₄₃×#468	—	2	8	no	—
26	C₄₃×#465	—	2	4	no	—
27	C₂×#107×C₄₃	C₂²	1	2	yes	complemented
28	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
30	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
32	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic, complemented
33	C₄₃×#386	—	2	2	no	—
34	C₄₃×#386	—	2	1	no	—
35	C₄₃×#385	—	2	2	no	—
36	C₄₃×#385	—	2	1	no	—
37	C₄₃×#380	C₂²	1	1	yes	characteristic
38	C₄₃×#380	C₂²	1	1	yes	characteristic
39	C₄₃×#380	C₂²	1	2	yes	—
40	C₄₃×#380	C₂²	1	2	yes	—
41	C₄₃×#379	—	2	1	no	—
42	C₄₃×#340	C₂²	1	2	yes	complemented
43	C₄₃×#340	C₂²	1	2	yes	complemented
44	C₄₃×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₄₃	—	2	2	no	—
48	C₂²×D₄×C₄₃	—	2	1	no	—
49	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	—	2	4	no	—
51	C₂³×C₄×C₄₃	—	2	2	no	—
52	C₂³×C₄×C₄₃	—	2	4	no	—
53	C₂³×C₄×C₄₃	—	2	2	no	—
54	C₂³×C₄×C₄₃	D₄	1	2	yes	—
55	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
58	C₂×SD₁₆×C₄₃	—	2	2	no	—
59	C₂×SD₁₆×C₄₃	—	2	4	no	—
60	C₂×M₁₆×C₄₃	—	2	32	no	—
61	C₂×M₁₆×C₄₃	—	2	4	no	—
62	C₂×M₁₆×C₄₃	—	2	4	no	—
63	C₂×M₁₆×C₄₃	—	2	4	no	—
64	C₂×M₁₆×C₄₃	—	2	4	no	—
65	C₂×M₁₆×C₄₃	—	2	4	no	—
66	C₂×M₁₆×C₄₃	D₄	1	8	yes	complemented
67	C₂²×C₈×C₄₃	—	2	2	no	—
68	C₂²×C₈×C₄₃	—	2	4	no	—
69	C₂²×C₈×C₄₃	—	2	4	no	—
70	C₂²×C₈×C₄₃	D₄	1	4	yes	complemented
71	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₂²⋊Q₈×C₄₃	—	2	2	no	—
75	C₂²⋊Q₈×C₄₃	—	2	4	no	—
76	C₂²⋊Q₈×C₄₃	—	2	2	no	—
77	C₂²⋊Q₈×C₄₃	—	2	4	no	—
78	#121×C₄₃	—	2	2	no	—
79	#121×C₄₃	—	2	4	no	—
80	#121×C₄₃	—	2	2	no	—
81	#121×C₄₃	—	2	4	no	—
82	#120×C₄₃	—	4	4	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
97	#107×C₄₃	—	2	4	no	—
98	#106×C₄₃	—	2	2	no	—
99	#103×C₄₃	—	2	2	no	—
100	#103×C₄₃	—	2	4	no	—
101	#102×C₄₃	—	2	2	no	—
102	#102×C₄₃	—	2	4	no	—
103	#95×C₄₃	—	2	1	no	—
104	#95×C₄₃	—	2	2	no	—
105	#95×C₄₃	—	2	1	no	—
106	#95×C₄₃	—	2	2	no	—
107	C₂⁴×C₄₃	—	2	4	no	—
108	C₂⁴×C₄₃	—	2	2	no	—
109	C₂⁴×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	C₂⁴×C₄₃	—	4	2	no	—
113	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
114	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₄₃	—	2	1	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	—	2	1	no	—
118	C₂×Q₈×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	1	no	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	—	2	1	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	4	4	no	—
124	C₂×D₄×C₄₃	—	4	4	no	—
125	C₂×D₄×C₄₃	—	4	4	no	—
126	C₂×D₄×C₄₃	—	4	2	no	—
127	C₂×D₄×C₄₃	—	4	2	no	—
128	C₂×D₄×C₄₃	—	4	2	no	—
129	C₂²×C₄×C₄₃	—	2	8	no	—
130	C₂²×C₄×C₄₃	—	2	8	no	—
131	C₂²×C₄×C₄₃	—	2	16	no	—
132	C₂²×C₄×C₄₃	—	2	4	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	2	4	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	2	no	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	2	4	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	1	no	—
145	C₂²×C₄×C₄₃	—	2	1	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₃	#41	1	4	yes	—
153	C₂²×C₄×C₄₃	#41	1	2	yes	—
154	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
155	SD₁₆×C₄₃	—	4	4	no	—
156	M₁₆×C₄₃	—	2	16	no	—
157	M₁₆×C₄₃	—	2	16	no	—
158	C₂×C₈×C₄₃	—	2	8	no	—
159	C₂×C₈×C₄₃	—	2	2	no	—
160	C₂×C₈×C₄₃	—	2	2	no	—
161	C₂×C₈×C₄₃	—	2	2	no	—
162	C₂×C₈×C₄₃	—	2	8	no	—
163	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
164	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₄₃	—	2	1	no	—
168	C₄⋊C₄×C₄₃	—	2	2	no	—
169	C₄⋊C₄×C₄₃	—	2	1	no	—
170	C₄⋊C₄×C₄₃	—	2	2	no	—
171	C₄⋊C₄×C₄₃	—	2	1	no	—
172	C₄⋊C₄×C₄₃	—	2	2	no	—
173	C₄⋊C₄×C₄₃	—	2	1	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	4	2	no	—
176	C₄⋊C₄×C₄₃	—	4	4	no	—
177	C₂²⋊C₄×C₄₃	—	4	4	no	—
178	C₂²⋊C₄×C₄₃	—	4	4	no	—
179	C₂²⋊C₄×C₄₃	—	4	2	no	—
180	C₂²⋊C₄×C₄₃	—	4	4	no	—
181	C₂²⋊C₄×C₄₃	—	4	4	no	—
182	C₂²⋊C₄×C₄₃	—	4	2	no	—
183	C₂²⋊C₄×C₄₃	—	4	2	no	—
184	C₂²⋊C₄×C₄₃	—	4	2	no	—
185	C₂³×C₄₃	—	2	2	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	2	8	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	2	no	—
191	C₂³×C₄₃	—	2	2	no	—
192	C₂³×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	4	8	no	—
195	C₂³×C₄₃	—	4	8	no	—
196	C₂³×C₄₃	—	4	4	no	—
197	C₂³×C₄₃	—	4	4	no	—
198	C₂³×C₄₃	—	4	1	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	1	no	—
201	C₂³×C₄₃	—	4	1	no	—
202	C₂³×C₄₃	—	4	2	no	—
203	C₂³×C₄₃	#121	1	4	yes	—
204	C₂³×C₄₃	#121	1	2	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	—	4	1	no	—
209	Q₈×C₄₃	—	4	1	no	—
210	Q₈×C₄₃	—	4	2	no	—
211	D₄×C₄₃	—	4	1	no	—
212	D₄×C₄₃	—	4	1	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	8	8	no	—
215	D₄×C₄₃	—	8	4	no	—
216	C₂×C₄×C₄₃	—	2	8	no	—
217	C₂×C₄×C₄₃	—	2	16	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	4	no	—
223	C₂×C₄×C₄₃	—	2	2	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	—	4	1	no	—
229	C₂×C₄×C₄₃	—	4	2	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	2	no	—
232	C₂×C₄×C₄₃	—	4	1	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	1	no	—
235	C₂×C₄×C₄₃	—	4	2	no	—
236	C₂×C₄×C₄₃	—	4	2	no	—
237	C₂×C₄×C₄₃	—	4	1	no	—
238	C₂×C₄×C₄₃	—	4	2	no	—
239	C₂×C₄×C₄₃	—	4	2	no	—
240	C₂×C₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	#121	1	2	yes	—
242	C₂×C₄×C₄₃	#121	1	4	yes	—
243	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
247	C₈×C₄₃	—	2	4	no	—
248	C₈×C₄₃	—	2	2	no	—
249	C₈×C₄₃	#120	1	4	yes	complemented
250	#32935	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂²×C₄₃	—	2	2	no	—
252	C₂²×C₄₃	—	2	2	no	—
253	C₂²×C₄₃	—	2	4	no	—
254	C₂²×C₄₃	—	2	4	no	—
255	C₂²×C₄₃	—	2	4	no	—
256	C₂²×C₄₃	—	2	4	no	—
257	C₂²×C₄₃	—	2	4	no	—
258	C₂²×C₄₃	—	4	16	no	—
259	C₂²×C₄₃	—	4	2	no	—
260	C₂²×C₄₃	—	4	2	no	—
261	C₂²×C₄₃	—	4	2	no	—
262	C₂²×C₄₃	—	4	2	no	—
263	C₂²×C₄₃	—	8	1	no	—
264	C₂²×C₄₃	—	8	1	no	—
265	C₂²×C₄₃	—	8	1	no	—
266	C₂²×C₄₃	—	8	2	no	—
267	C₂²×C₄₃	—	8	2	no	—
268	C₂²×C₄₃	#468	1	4	yes	complemented
269	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
270	C₂²×C₄₃	C₂×#121	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	4	no	—
276	C₄×C₄₃	—	8	1	no	—
277	C₄×C₄₃	—	8	1	no	—
278	C₄×C₄₃	—	8	1	no	—
279	C₄×C₄₃	—	8	2	no	—
280	C₄×C₄₃	—	8	2	no	—
281	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
282	C₄×C₄₃	#525	1	1	yes	characteristic
283	C₄×C₄₃	#525	1	2	yes	—
284	C₂³×M₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
285	C₂×#468	C₂×C₄₃	1	2	yes	complemented
286	C₂×#465	C₂×C₄₃	1	1	yes	characteristic, complemented
287	#2848	C₂×C₄₃	1	1	yes	characteristic, complemented
288	#2847	C₂×C₄₃	1	1	yes	characteristic
289	#1895	C₂×C₄₃	1	2	yes	complemented
290	#1894	C₂×C₄₃	1	2	yes	complemented
291	#1893	C₂×C₄₃	1	1	yes	characteristic, complemented
292	#1892	C₂×C₄₃	1	1	yes	characteristic, complemented
293	#1809	C₂×C₄₃	1	2	yes	complemented
294	#1808	C₂×C₄₃	1	1	yes	characteristic, complemented
295	C₂×C₄₃	—	2	4	no	—
296	C₂×C₄₃	—	4	4	no	—
297	C₂×C₄₃	—	16	1	no	—
298	C₂×C₄₃	#2847	1	1	yes	characteristic
299	C₂×C₄₃	C₂×#468	1	1	yes	characteristic
300	C₂×C₄₃	#3054	1	1	yes	characteristic
301	C₂×C₄₃	#3055	1	2	yes	—
302	C₂×C₄₃	#3056	1	2	yes	—
303	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
304	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
305	C₂²×M₁₆	—	2	8	no	—
306	C₂²×M₁₆	—	2	4	no	—
307	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
308	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
309	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
310	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
311	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
313	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
314	C₂×#121	C₂²×C₄₃	1	2	yes	—
315	C₂×#120	—	2	1	no	—
316	#468	—	2	8	no	—
317	#465	—	2	4	no	—
318	C₂×#107	C₂²×C₄₃	1	2	yes	complemented
319	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic, complemented
320	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
321	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic, complemented
322	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
323	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic, complemented
324	#386	—	2	2	no	—
325	#386	—	2	1	no	—
326	#385	—	2	2	no	—
327	#385	—	2	1	no	—
328	#380	C₂²×C₄₃	1	1	yes	characteristic
329	#380	C₂²×C₄₃	1	1	yes	characteristic
330	#380	C₂²×C₄₃	1	2	yes	—
331	#380	C₂²×C₄₃	1	2	yes	—
332	#379	—	2	1	no	—
333	#340	C₂²×C₄₃	1	2	yes	complemented
334	#340	C₂²×C₄₃	1	2	yes	complemented
335	#340	C₂²×C₄₃	1	2	yes	complemented
336	C₄₃	#32935	1	1	yes	characteristic, direct product factor, Sylow
337	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	4	no	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	—	2	4	no	—
345	C₂³×C₄	—	2	2	no	—
346	C₂³×C₄	D₄×C₄₃	1	2	yes	—
347	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
350	C₂×SD₁₆	—	2	2	no	—
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×M₁₆	—	2	32	no	—
353	C₂×M₁₆	—	2	4	no	—
354	C₂×M₁₆	—	2	4	no	—
355	C₂×M₁₆	—	2	4	no	—
356	C₂×M₁₆	—	2	4	no	—
357	C₂×M₁₆	—	2	4	no	—
358	C₂×M₁₆	D₄×C₄₃	1	8	yes	complemented
359	C₂²×C₈	—	2	2	no	—
360	C₂²×C₈	—	2	4	no	—
361	C₂²×C₈	—	2	4	no	—
362	C₂²×C₈	D₄×C₄₃	1	4	yes	complemented
363	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
364	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	4	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	#121	—	2	2	no	—
371	#121	—	2	4	no	—
372	#121	—	2	2	no	—
373	#121	—	2	4	no	—
374	#120	—	4	4	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	#107	—	2	4	no	—
390	#106	—	2	2	no	—
391	#103	—	2	2	no	—
392	#103	—	2	4	no	—
393	#102	—	2	2	no	—
394	#102	—	2	4	no	—
395	#95	—	2	1	no	—
396	#95	—	2	2	no	—
397	#95	—	2	1	no	—
398	#95	—	2	2	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	—	4	2	no	—
405	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
406	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	2	16	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	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	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
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	4	yes	—
444	C₂²×C₄	#41×C₄₃	1	4	yes	—
445	C₂²×C₄	#41×C₄₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
447	SD₁₆	—	4	4	no	—
448	M₁₆	—	2	16	no	—
449	M₁₆	—	2	16	no	—
450	C₂×C₈	—	2	8	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	8	no	—
455	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
456	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
457	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
458	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	4	4	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	4	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	2	no	—
495	C₂³	#121×C₄₃	1	4	yes	—
496	C₂³	#121×C₄₃	1	2	yes	—
497	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
498	C₂³	#137×C₄₃	1	2	yes	—
499	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	2	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	8	no	—
507	D₄	—	8	4	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	16	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	#121×C₄₃	1	2	yes	—
534	C₂×C₄	#121×C₄₃	1	4	yes	—
535	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
537	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
539	C₈	—	2	4	no	—
540	C₈	—	2	2	no	—
541	C₈	#120×C₄₃	1	4	yes	complemented
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	4	16	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	2	no	—
558	C₂²	—	8	2	no	—
559	C₂²	C₄₃×#468	1	4	yes	complemented
560	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
561	C₂²	C₂×#121×C₄₃	1	2	yes	—
562	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
563	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
564	C₂²	C₄₃×#575	1	2	yes	—
565	C₄	—	2	2	no	—
566	C₄	—	2	4	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	1	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	2	no	—
571	C₄	—	8	2	no	—
572	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
573	C₄	C₄₃×#525	1	1	yes	characteristic
574	C₄	C₄₃×#525	1	2	yes	—
575	C₂	—	2	4	no	—
576	C₂	—	4	4	no	—
577	C₂	—	16	1	no	—
578	C₂	C₄₃×#2847	1	1	yes	characteristic
579	C₂	C₂×C₄₃×#468	1	1	yes	characteristic
580	C₂	C₄₃×#3054	1	1	yes	characteristic
581	C₂	C₄₃×#3055	1	2	yes	—
582	C₂	C₄₃×#3056	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2847	C₂
LCS	G ▷ C₂²×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
1. C₂³×M₁₆×C₄₃	C₂	semidirect
2. C₂×C₄₃×#468	C₂	semidirect
3. C₂×C₄₃×#465	C₂	semidirect
4. C₄₃×#2848	C₂	semidirect
6. C₄₃×#1895	C₂	semidirect
7. C₄₃×#1894	C₂	semidirect
8. C₄₃×#1893	C₂	semidirect
9. C₄₃×#1892	C₂	semidirect
10. C₄₃×#1809	C₂	semidirect
11. C₄₃×#1808	C₂	semidirect
13. C₂²×SD₁₆×C₄₃	C₂²	semidirect
27. C₂×#107×C₄₃	C₂²	semidirect
28. C₂×#106×C₄₃	C₂²	semidirect
29. C₂×#103×C₄₃	C₂²	semidirect
30. C₂×#103×C₄₃	C₂²	semidirect
31. C₂×#102×C₄₃	C₂²	semidirect
32. C₂×#102×C₄₃	C₂²	semidirect
42. C₄₃×#340	C₂²	semidirect
43. C₄₃×#340	C₂²	semidirect
44. C₄₃×#340	C₂²	semidirect
66. C₂×M₁₆×C₄₃	D₄	semidirect
70. C₂²×C₈×C₄₃	D₄	semidirect
249. C₈×C₄₃	#120	semidirect
250. #32935	C₄₃	direct (N × H)
268. C₂²×C₄₃	#468	semidirect
284. C₂³×M₁₆	C₂×C₄₃	semidirect
285. C₂×#468	C₂×C₄₃	semidirect
286. C₂×#465	C₂×C₄₃	semidirect
287. #2848	C₂×C₄₃	semidirect
289. #1895	C₂×C₄₃	semidirect
290. #1894	C₂×C₄₃	semidirect
291. #1893	C₂×C₄₃	semidirect
292. #1892	C₂×C₄₃	semidirect
293. #1809	C₂×C₄₃	semidirect
294. #1808	C₂×C₄₃	semidirect
304. C₂²×SD₁₆	C₂²×C₄₃	semidirect
318. C₂×#107	C₂²×C₄₃	semidirect
319. C₂×#106	C₂²×C₄₃	semidirect
320. C₂×#103	C₂²×C₄₃	semidirect
321. C₂×#103	C₂²×C₄₃	semidirect
322. C₂×#102	C₂²×C₄₃	semidirect
323. C₂×#102	C₂²×C₄₃	semidirect
333. #340	C₂²×C₄₃	semidirect
334. #340	C₂²×C₄₃	semidirect
335. #340	C₂²×C₄₃	semidirect
336. C₄₃	#32935	direct (N × H)
358. C₂×M₁₆	D₄×C₄₃	semidirect
362. C₂²×C₈	D₄×C₄₃	semidirect
541. C₈	#120×C₄₃	semidirect
559. C₂²	C₄₃×#468	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₄₃	2
C₂×C₄₃×#468	2
C₂×C₄₃×#465	2
C₄₃×#2848	2
C₄₃×#2847	2
C₄₃×#1895	2
C₄₃×#1894	2
C₄₃×#1893	2
C₄₃×#1892	2
C₄₃×#1809	2
C₄₃×#1808	2
#32935	43

Subgroups — C43×#32935 #24952952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#32935 #24952952