Subgroups — C₄₃×#25720 #24945737

Order 11008.

1738 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#449	C₂	1	4	yes	maximal, complemented
5	C₄₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2012	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₄₃	C₂²	1	4	yes	—
12	C₂²×D₈×C₄₃	C₂²	1	4	yes	—
13	C₄₃×#532	—	2	4	no	—
14	C₄₃×#532	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	C₂²	1	2	yes	—
19	C₂×#121×C₄₃	—	2	2	no	—
20	C₂×#121×C₄₃	—	2	2	no	—
21	C₂×#121×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₄₃	—	2	2	no	—
23	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#493	—	2	4	no	—
25	C₄₃×#492	—	2	4	no	—
26	C₄₃×#449	—	2	16	no	—
27	C₂×#103×C₄₃	C₂²	1	4	yes	—
28	C₂×#102×C₄₃	C₂²	1	4	yes	—
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#390	—	2	2	no	—
33	C₄₃×#390	C₂²	1	2	yes	—
34	C₄₃×#384	C₂²	1	1	yes	characteristic
35	C₄₃×#336	C₂²	1	2	yes	—
36	C₂×#41×C₄₃	—	2	4	no	—
37	C₂×#41×C₄₃	—	2	4	no	—
38	C₂×#41×C₄₃	—	2	8	no	—
39	C₂×#41×C₄₃	—	4	4	no	—
40	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
41	C₂²×D₄×C₄₃	—	2	2	no	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	—	2	2	no	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₃	—	2	2	no	—
48	C₂³×C₄×C₄₃	D₄	1	2	yes	—
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂×SD₁₆×C₄₃	—	2	8	no	—
51	C₂×SD₁₆×C₄₃	—	2	8	no	—
52	C₂×SD₁₆×C₄₃	—	4	4	no	—
53	C₂×D₈×C₄₃	—	2	8	no	—
54	C₂×D₈×C₄₃	—	2	8	no	—
55	C₂×D₈×C₄₃	—	4	4	no	—
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	D₄	1	4	yes	complemented
60	#127×C₄₃	—	2	2	no	—
61	#127×C₄₃	—	2	2	no	—
62	#127×C₄₃	—	2	2	no	—
63	#127×C₄₃	D₄	1	4	yes	complemented
64	#124×C₄₃	—	2	4	no	—
65	#124×C₄₃	—	2	4	no	—
66	#121×C₄₃	—	2	16	no	—
67	#121×C₄₃	—	2	8	no	—
68	#121×C₄₃	—	4	8	no	—
69	C₄×D₄×C₄₃	—	2	16	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₄²×C₄₃	—	2	2	no	—
77	C₂×C₄²×C₄₃	—	2	2	no	—
78	C₂×C₄²×C₄₃	D₄	1	2	yes	—
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#103×C₄₃	—	2	8	no	—
82	#102×C₄₃	—	2	8	no	—
83	C₂²⋊C₈×C₄₃	D₄	1	8	yes	complemented
84	C₄×C₈×C₄₃	—	2	2	no	—
85	C₄×C₈×C₄₃	—	2	2	no	—
86	C₂⁴×C₄₃	—	2	2	no	—
87	C₂⁴×C₄₃	—	2	2	no	—
88	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
89	#41×C₄₃	—	4	16	no	—
90	#41×C₄₃	—	4	16	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	—	2	4	no	—
93	C₂×Q₈×C₄₃	—	2	4	no	—
94	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
95	C₂×D₄×C₄₃	—	2	8	no	—
96	C₂×D₄×C₄₃	—	2	8	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	4	no	—
99	C₂×D₄×C₄₃	—	2	4	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	2	4	no	—
103	C₂×D₄×C₄₃	—	2	4	no	—
104	C₂×D₄×C₄₃	—	4	4	no	—
105	C₂×D₄×C₄₃	—	4	8	no	—
106	C₂×D₄×C₄₃	—	4	4	no	—
107	C₂×D₄×C₄₃	—	4	4	no	—
108	C₂×D₄×C₄₃	—	4	4	no	—
109	C₂×D₄×C₄₃	—	4	4	no	—
110	C₂×D₄×C₄₃	—	4	4	no	—
111	C₂×D₄×C₄₃	—	4	4	no	—
112	C₂×D₄×C₄₃	—	4	4	no	—
113	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₄₃	—	2	1	no	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	8	no	—
118	C₂²×C₄×C₄₃	—	2	4	no	—
119	C₂²×C₄×C₄₃	—	2	4	no	—
120	C₂²×C₄×C₄₃	—	2	4	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	4	4	no	—
124	C₂²×C₄×C₄₃	—	4	4	no	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
130	SD₁₆×C₄₃	—	4	16	no	—
131	D₈×C₄₃	—	4	16	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
138	C₄⋊C₄×C₄₃	—	2	8	no	—
139	C₄⋊C₄×C₄₃	—	2	4	no	—
140	C₄⋊C₄×C₄₃	—	4	4	no	—
141	C₂²⋊C₄×C₄₃	—	2	16	no	—
142	C₂²⋊C₄×C₄₃	—	4	8	no	—
143	C₂²⋊C₄×C₄₃	—	4	4	no	—
144	C₄²×C₄₃	—	2	4	no	—
145	C₄²×C₄₃	—	2	1	no	—
146	C₄²×C₄₃	—	2	1	no	—
147	C₄²×C₄₃	C₂×D₄	1	2	yes	—
148	C₄²×C₄₃	C₂×D₄	1	2	yes	—
149	C₂³×C₄₃	—	2	1	no	—
150	C₂³×C₄₃	—	2	1	no	—
151	C₂³×C₄₃	—	2	2	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	2	4	no	—
154	C₂³×C₄₃	—	4	2	no	—
155	C₂³×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	—	4	4	no	—
157	C₂³×C₄₃	—	4	4	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	4	4	no	—
162	C₂³×C₄₃	—	4	4	no	—
163	C₂³×C₄₃	#127	1	2	yes	—
164	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₄₃	—	2	8	no	—
166	Q₈×C₄₃	—	4	4	no	—
167	D₄×C₄₃	—	2	8	no	—
168	D₄×C₄₃	—	4	16	no	—
169	D₄×C₄₃	—	4	4	no	—
170	D₄×C₄₃	—	4	4	no	—
171	D₄×C₄₃	—	4	4	no	—
172	D₄×C₄₃	—	4	16	no	—
173	D₄×C₄₃	—	8	8	no	—
174	D₄×C₄₃	—	8	8	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	4	16	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	8	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	4	no	—
189	C₂×C₄×C₄₃	#120	1	4	yes	—
190	C₂×C₄×C₄₃	#127	1	2	yes	—
191	C₂×C₄×C₄₃	#135	1	4	yes	—
192	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
193	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
197	C₈×C₄₃	—	2	4	no	—
198	C₈×C₄₃	—	2	4	no	—
199	#25720	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₃	—	2	2	no	—
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	4	no	—
206	C₂²×C₄₃	—	4	8	no	—
207	C₂²×C₄₃	—	8	2	no	—
208	C₂²×C₄₃	—	8	2	no	—
209	C₂²×C₄₃	—	8	4	no	—
210	C₂²×C₄₃	—	8	2	no	—
211	C₂²×C₄₃	—	8	2	no	—
212	C₂²×C₄₃	—	8	2	no	—
213	C₂²×C₄₃	—	8	4	no	—
214	C₂²×C₄₃	—	8	4	no	—
215	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
216	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
217	C₂²×C₄₃	#535	1	1	yes	characteristic
218	C₂²×C₄₃	C₂×#135	1	2	yes	—
219	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	4	4	no	—
222	C₄×C₄₃	—	4	2	no	—
223	C₄×C₄₃	—	8	2	no	—
224	C₄×C₄₃	#449	1	8	yes	complemented
225	C₄×C₄₃	D₄²	1	2	yes	—
226	C₄×C₄₃	D₄²	1	2	yes	—
227	C₂×#532	C₂×C₄₃	1	1	yes	characteristic, complemented
228	C₂×#493	C₂×C₄₃	1	1	yes	characteristic, complemented
229	C₂×#492	C₂×C₄₃	1	1	yes	characteristic, complemented
230	C₂×#449	C₂×C₄₃	1	4	yes	complemented
231	#2856	C₂×C₄₃	1	1	yes	characteristic, complemented
232	#2012	C₂×C₄₃	1	4	yes	complemented
233	#1957	C₂×C₄₃	1	1	yes	characteristic, complemented
234	#1956	C₂×C₄₃	1	1	yes	characteristic, complemented
235	C₄×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
236	C₂×C₄₃	—	4	2	no	—
237	C₂×C₄₃	—	8	4	no	—
238	C₂×C₄₃	—	16	2	no	—
239	C₂×C₄₃	#2433	1	1	yes	characteristic
240	C₂×C₄₃	C₂×#449	1	2	yes	—
241	C₂×C₄₃	#3147	1	1	yes	characteristic
242	C₂×C₄₃	#3151	1	1	yes	characteristic
243	C₂×C₄₃	#3207	1	2	yes	—
244	C₂²×#41	C₂²×C₄₃	1	2	yes	—
245	C₂²×SD₁₆	C₂²×C₄₃	1	4	yes	—
246	C₂²×D₈	C₂²×C₄₃	1	4	yes	—
247	#532	—	2	4	no	—
248	#532	—	2	4	no	—
249	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
251	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
252	C₂×#124	C₂²×C₄₃	1	2	yes	—
253	C₂×#121	—	2	2	no	—
254	C₂×#121	—	2	2	no	—
255	C₂×#121	C₂²×C₄₃	1	2	yes	—
256	C₂×C₄×D₄	—	2	2	no	—
257	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
258	#493	—	2	4	no	—
259	#492	—	2	4	no	—
260	#449	—	2	16	no	—
261	C₂×#103	C₂²×C₄₃	1	4	yes	—
262	C₂×#102	C₂²×C₄₃	1	4	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
266	#390	—	2	2	no	—
267	#390	C₂²×C₄₃	1	2	yes	—
268	#384	C₂²×C₄₃	1	1	yes	characteristic
269	#336	C₂²×C₄₃	1	2	yes	—
270	C₄₃	#25720	1	1	yes	characteristic, direct product factor, Sylow
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	4	no	—
273	C₂×#41	—	2	8	no	—
274	C₂×#41	—	4	4	no	—
275	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
281	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	D₄×C₄₃	1	2	yes	—
284	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
285	C₂×SD₁₆	—	2	8	no	—
286	C₂×SD₁₆	—	2	8	no	—
287	C₂×SD₁₆	—	4	4	no	—
288	C₂×D₈	—	2	8	no	—
289	C₂×D₈	—	2	8	no	—
290	C₂×D₈	—	4	4	no	—
291	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
292	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	D₄×C₄₃	1	4	yes	complemented
295	#127	—	2	2	no	—
296	#127	—	2	2	no	—
297	#127	—	2	2	no	—
298	#127	D₄×C₄₃	1	4	yes	complemented
299	#124	—	2	4	no	—
300	#124	—	2	4	no	—
301	#121	—	2	16	no	—
302	#121	—	2	8	no	—
303	#121	—	4	8	no	—
304	C₄×D₄	—	2	16	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	4	no	—
309	C₂×C₂²⋊C₄	—	2	4	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	D₄×C₄₃	1	2	yes	—
314	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
316	#103	—	2	8	no	—
317	#102	—	2	8	no	—
318	C₂²⋊C₈	D₄×C₄₃	1	8	yes	complemented
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
324	#41	—	4	16	no	—
325	#41	—	4	16	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
363	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
365	SD₁₆	—	4	16	no	—
366	D₈	—	4	16	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
372	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	2	16	no	—
377	C₂²⋊C₄	—	4	8	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	C₂×D₄×C₄₃	1	2	yes	—
383	C₄²	C₂×D₄×C₄₃	1	2	yes	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	#127×C₄₃	1	2	yes	—
399	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
400	Q₈	—	2	8	no	—
401	Q₈	—	4	4	no	—
402	D₄	—	2	8	no	—
403	D₄	—	4	16	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	16	no	—
408	D₄	—	8	8	no	—
409	D₄	—	8	8	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	16	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	#120×C₄₃	1	4	yes	—
425	C₂×C₄	#127×C₄₃	1	2	yes	—
426	C₂×C₄	#135×C₄₃	1	4	yes	—
427	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
431	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
432	C₈	—	2	4	no	—
433	C₈	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	4	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	4	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
450	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
451	C₂²	C₄₃×#535	1	1	yes	characteristic
452	C₂²	C₂×#135×C₄₃	1	2	yes	—
453	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
454	C₄	—	2	2	no	—
455	C₄	—	4	4	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	2	no	—
458	C₄	C₄₃×#449	1	8	yes	complemented
459	C₄	D₄²×C₄₃	1	2	yes	—
460	C₄	D₄²×C₄₃	1	2	yes	—
461	C₂	—	4	2	no	—
462	C₂	—	8	4	no	—
463	C₂	—	16	2	no	—
464	C₂	C₄₃×#2433	1	1	yes	characteristic
465	C₂	C₂×C₄₃×#449	1	2	yes	—
466	C₂	C₄₃×#3147	1	1	yes	characteristic
467	C₂	C₄₃×#3151	1	1	yes	characteristic
468	C₂	C₄₃×#3207	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#532	C₂	semidirect
2. C₂×C₄₃×#493	C₂	semidirect
3. C₂×C₄₃×#492	C₂	semidirect
4. C₂×C₄₃×#449	C₂	semidirect
5. C₄₃×#2856	C₂	semidirect
6. C₄₃×#2012	C₂	semidirect
7. C₄₃×#1957	C₂	semidirect
8. C₄₃×#1956	C₂	semidirect
9. C₄×C₂²⋊C₈×C₄₃	C₂	semidirect
59. C₄⋊Q₈×C₄₃	D₄	semidirect
63. #127×C₄₃	D₄	semidirect
83. C₂²⋊C₈×C₄₃	D₄	semidirect
199. #25720	C₄₃	direct (N × H)
224. C₄×C₄₃	#449	semidirect
227. C₂×#532	C₂×C₄₃	semidirect
228. C₂×#493	C₂×C₄₃	semidirect
229. C₂×#492	C₂×C₄₃	semidirect
230. C₂×#449	C₂×C₄₃	semidirect
231. #2856	C₂×C₄₃	semidirect
232. #2012	C₂×C₄₃	semidirect
233. #1957	C₂×C₄₃	semidirect
234. #1956	C₂×C₄₃	semidirect
235. C₄×C₂²⋊C₈	C₂×C₄₃	semidirect
270. C₄₃	#25720	direct (N × H)
294. C₄⋊Q₈	D₄×C₄₃	semidirect
298. #127	D₄×C₄₃	semidirect
318. C₂²⋊C₈	D₄×C₄₃	semidirect
458. C₄	C₄₃×#449	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#532	2
C₂×C₄₃×#493	2
C₂×C₄₃×#492	2
C₂×C₄₃×#449	2
C₄₃×#2856	2
C₄₃×#2012	2
C₄₃×#1957	2
C₄₃×#1956	2
C₄×C₂²⋊C₈×C₄₃	2
#25720	43

Subgroups — C43×#25720 #24945737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25720 #24945737