Subgroups — C₄₃×#25633 #24945650

Order 11008.

1282 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#493	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2012	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1879	C₂	1	4	yes	maximal, complemented
9	C₄×#103×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
11	C₂²×D₈×C₄₃	C₂²	1	4	yes	—
12	C₄₃×#559	—	2	4	no	—
13	C₄₃×#559	—	2	4	no	—
14	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₃	—	2	1	no	—
17	C₂×#124×C₄₃	—	2	1	no	—
18	C₂×#124×C₄₃	C₂²	1	2	yes	—
19	C₂×#123×C₄₃	—	2	2	no	—
20	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₃	—	2	1	no	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
24	C₄₃×#493	—	2	4	no	—
25	C₄₃×#460	—	2	4	no	—
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#103×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#394	—	2	2	no	—
32	C₄₃×#390	—	2	1	no	—
33	C₄₃×#390	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×#340	C₂²	1	2	yes	—
36	C₄₃×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	—	2	1	no	—
41	C₂²×D₄×C₄₃	—	2	1	no	—
42	C₂²×D₄×C₄₃	—	2	1	no	—
43	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	—	2	2	no	—
46	C₂×SD₁₆×C₄₃	—	2	4	no	—
47	C₂×SD₁₆×C₄₃	—	4	4	no	—
48	C₂×D₈×C₄₃	—	2	8	no	—
49	C₂×D₈×C₄₃	—	2	8	no	—
50	C₂×D₈×C₄₃	—	4	4	no	—
51	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
53	#127×C₄₃	—	2	2	no	—
54	#127×C₄₃	—	2	2	no	—
55	#127×C₄₃	—	2	2	no	—
56	#127×C₄₃	D₄	1	4	yes	—
57	#124×C₄₃	—	2	8	no	—
58	#124×C₄₃	—	2	4	no	—
59	#124×C₄₃	—	2	4	no	—
60	#124×C₄₃	—	4	4	no	—
61	#123×C₄₃	—	2	16	no	—
62	C₄×Q₈×C₄₃	—	2	2	no	—
63	C₄×Q₈×C₄₃	—	2	2	no	—
64	C₄×Q₈×C₄₃	—	2	2	no	—
65	C₄×Q₈×C₄₃	D₄	1	4	yes	—
66	C₄×D₄×C₄₃	—	2	8	no	—
67	C₄×D₄×C₄₃	—	2	4	no	—
68	C₄×D₄×C₄₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
79	C₂×C₄²×C₄₃	—	2	1	no	—
80	C₂×C₄²×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₃	—	2	2	no	—
84	#103×C₄₃	—	2	4	no	—
85	#102×C₄₃	—	2	4	no	—
86	#102×C₄₃	—	4	4	no	—
87	C₄×C₈×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	1	no	—
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	—	2	2	no	—
93	C₂×Q₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
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	2	no	—
103	C₂×D₄×C₄₃	—	2	4	no	—
104	C₂×D₄×C₄₃	—	2	4	no	—
105	C₂×D₄×C₄₃	—	2	4	no	—
106	C₂×D₄×C₄₃	—	2	4	no	—
107	C₂×D₄×C₄₃	—	4	2	no	—
108	C₂×D₄×C₄₃	—	4	2	no	—
109	C₂×D₄×C₄₃	—	4	2	no	—
110	C₂×D₄×C₄₃	—	4	2	no	—
111	C₂×D₄×C₄₃	—	4	2	no	—
112	C₂×D₄×C₄₃	—	4	2	no	—
113	C₂×D₄×C₄₃	—	8	2	no	—
114	C₂×D₄×C₄₃	—	8	2	no	—
115	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₄₃	—	2	8	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	8	4	no	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
126	SD₁₆×C₄₃	—	4	8	no	—
127	D₈×C₄₃	—	4	16	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	4	no	—
132	C₂×C₈×C₄₃	#41	1	4	yes	—
133	C₄⋊C₄×C₄₃	—	2	4	no	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	2	4	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₄₃	—	2	8	no	—
141	C₂²⋊C₄×C₄₃	—	2	8	no	—
142	C₂²⋊C₄×C₄₃	—	2	8	no	—
143	C₂²⋊C₄×C₄₃	—	4	8	no	—
144	C₂²⋊C₄×C₄₃	—	8	4	no	—
145	C₄²×C₄₃	—	2	4	no	—
146	C₄²×C₄₃	—	2	2	no	—
147	C₄²×C₄₃	—	2	2	no	—
148	C₄²×C₄₃	—	4	2	no	—
149	C₄²×C₄₃	C₂×D₄	1	2	yes	—
150	C₄²×C₄₃	C₂×D₄	1	2	yes	—
151	C₂³×C₄₃	—	2	4	no	—
152	C₂³×C₄₃	—	4	4	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	—	4	2	no	—
155	C₂³×C₄₃	—	4	4	no	—
156	C₂³×C₄₃	—	4	2	no	—
157	C₂³×C₄₃	—	4	4	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	4	no	—
161	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₄₃	—	2	2	no	—
163	Q₈×C₄₃	—	2	2	no	—
164	Q₈×C₄₃	—	4	2	no	—
165	Q₈×C₄₃	—	4	4	no	—
166	D₄×C₄₃	—	2	8	no	—
167	D₄×C₄₃	—	4	2	no	—
168	D₄×C₄₃	—	4	2	no	—
169	D₄×C₄₃	—	4	2	no	—
170	D₄×C₄₃	—	4	2	no	—
171	D₄×C₄₃	—	4	4	no	—
172	D₄×C₄₃	—	4	8	no	—
173	D₄×C₄₃	—	8	4	no	—
174	D₄×C₄₃	—	8	4	no	—
175	D₄×C₄₃	—	8	4	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	8	8	no	—
190	C₂×C₄×C₄₃	#120	1	2	yes	—
191	C₂×C₄×C₄₃	#120	1	2	yes	—
192	C₂×C₄×C₄₃	#135	1	2	yes	—
193	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
197	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
198	C₈×C₄₃	—	2	4	no	—
199	C₈×C₄₃	—	4	2	no	—
200	#25633	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₄₃	—	4	4	no	—
202	C₂²×C₄₃	—	4	4	no	—
203	C₂²×C₄₃	—	4	4	no	—
204	C₂²×C₄₃	—	8	4	no	—
205	C₂²×C₄₃	—	8	4	no	—
206	C₂²×C₄₃	—	8	4	no	—
207	C₂²×C₄₃	—	8	4	no	—
208	C₂²×C₄₃	—	8	2	no	—
209	C₂²×C₄₃	—	8	2	no	—
210	C₂²×C₄₃	—	8	2	no	—
211	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
212	C₂²×C₄₃	#550	1	2	yes	—
213	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
214	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂²×C₄₃	#576	1	2	yes	—
216	C₄×C₄₃	—	2	2	no	—
217	C₄×C₄₃	—	4	2	no	—
218	C₄×C₄₃	—	4	2	no	—
219	C₄×C₄₃	—	4	2	no	—
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	—	8	2	no	—
222	C₄×C₄₃	#449	1	4	yes	—
223	C₄×C₄₃	#532	1	1	yes	characteristic
224	C₄×C₄₃	#535	1	1	yes	characteristic
225	C₄×C₄₃	#546	1	2	yes	—
226	C₂×#559	C₂×C₄₃	1	1	yes	characteristic, complemented
227	C₂×#493	C₂×C₄₃	1	1	yes	characteristic
228	C₂×#460	C₂×C₄₃	1	1	yes	characteristic, complemented
229	#2548	C₂×C₄₃	1	1	yes	characteristic, complemented
230	#2012	C₂×C₄₃	1	4	yes	complemented
231	#1984	C₂×C₄₃	1	1	yes	characteristic, complemented
232	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
233	#1879	C₂×C₄₃	1	4	yes	complemented
234	C₄×#103	C₂×C₄₃	1	1	yes	characteristic, complemented
235	C₂×C₄₃	—	8	4	no	—
236	C₂×C₄₃	—	16	2	no	—
237	C₂×C₄₃	#2431	1	1	yes	characteristic
238	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
239	C₂×C₄₃	#3008	1	1	yes	characteristic
240	C₂×C₄₃	#3396	1	2	yes	—
241	C₂×C₄₃	#3399	1	2	yes	—
242	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
243	C₂²×D₈	C₂²×C₄₃	1	4	yes	—
244	#559	—	2	4	no	—
245	#559	—	2	4	no	—
246	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
247	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
248	C₂×#124	—	2	1	no	—
249	C₂×#124	—	2	1	no	—
250	C₂×#124	C₂²×C₄₃	1	2	yes	—
251	C₂×#123	—	2	2	no	—
252	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
254	C₂×C₄×D₄	—	2	1	no	—
255	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
256	#493	—	2	4	no	—
257	#460	—	2	4	no	—
258	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
259	C₂×#103	C₂²×C₄₃	1	2	yes	—
260	C₂×#102	C₂²×C₄₃	1	2	yes	—
261	C₂×#102	C₂²×C₄₃	1	4	yes	—
262	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
263	#394	—	2	2	no	—
264	#390	—	2	1	no	—
265	#390	C₂²×C₄₃	1	4	yes	—
266	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
267	#340	C₂²×C₄₃	1	2	yes	—
268	#336	C₂²×C₄₃	1	4	yes	—
269	C₄₃	#25633	1	1	yes	characteristic, direct product factor, Sylow
270	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
271	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
277	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
278	C₂³×C₄	—	2	2	no	—
279	C₂×SD₁₆	—	2	4	no	—
280	C₂×SD₁₆	—	4	4	no	—
281	C₂×D₈	—	2	8	no	—
282	C₂×D₈	—	2	8	no	—
283	C₂×D₈	—	4	4	no	—
284	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
285	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
286	#127	—	2	2	no	—
287	#127	—	2	2	no	—
288	#127	—	2	2	no	—
289	#127	D₄×C₄₃	1	4	yes	—
290	#124	—	2	8	no	—
291	#124	—	2	4	no	—
292	#124	—	2	4	no	—
293	#124	—	4	4	no	—
294	#123	—	2	16	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	D₄×C₄₃	1	4	yes	—
299	C₄×D₄	—	2	8	no	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
315	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
316	C₄⋊C₈	—	2	2	no	—
317	#103	—	2	4	no	—
318	#102	—	2	4	no	—
319	#102	—	4	4	no	—
320	C₄×C₈	—	2	2	no	—
321	#95	—	2	1	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	—	8	2	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	8	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	8	4	no	—
354	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
359	SD₁₆	—	4	8	no	—
360	D₈	—	4	16	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	#41×C₄₃	1	4	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	4	8	no	—
377	C₂²⋊C₄	—	8	4	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	2	no	—
382	C₄²	C₂×D₄×C₄₃	1	2	yes	—
383	C₄²	C₂×D₄×C₄₃	1	2	yes	—
384	C₂³	—	2	4	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	4	no	—
394	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	4	4	no	—
399	D₄	—	2	8	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	8	no	—
406	D₄	—	8	4	no	—
407	D₄	—	8	4	no	—
408	D₄	—	8	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	8	8	no	—
423	C₂×C₄	#120×C₄₃	1	2	yes	—
424	C₂×C₄	#120×C₄₃	1	2	yes	—
425	C₂×C₄	#135×C₄₃	1	2	yes	—
426	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
430	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
431	C₈	—	2	4	no	—
432	C₈	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	4	no	—
439	C₂²	—	8	4	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
444	C₂²	C₄₃×#550	1	2	yes	—
445	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
446	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
447	C₂²	C₄₃×#576	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	8	2	no	—
454	C₄	C₄₃×#449	1	4	yes	—
455	C₄	C₄₃×#532	1	1	yes	characteristic
456	C₄	C₄₃×#535	1	1	yes	characteristic
457	C₄	C₄₃×#546	1	2	yes	—
458	C₂	—	8	4	no	—
459	C₂	—	16	2	no	—
460	C₂	C₄₃×#2431	1	1	yes	characteristic
461	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
462	C₂	C₄₃×#3008	1	1	yes	characteristic
463	C₂	C₄₃×#3396	1	2	yes	—
464	C₂	C₄₃×#3399	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#493	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄×Q₈×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#559	C₂	semidirect
3. C₂×C₄₃×#460	C₂	semidirect
4. C₄₃×#2548	C₂	semidirect
5. C₄₃×#2012	C₂	semidirect
6. C₄₃×#1984	C₂	semidirect
7. C₄₃×#1982	C₂	semidirect
8. C₄₃×#1879	C₂	semidirect
9. C₄×#103×C₄₃	C₂	semidirect
200. #25633	C₄₃	direct (N × H)
226. C₂×#559	C₂×C₄₃	semidirect
228. C₂×#460	C₂×C₄₃	semidirect
229. #2548	C₂×C₄₃	semidirect
230. #2012	C₂×C₄₃	semidirect
231. #1984	C₂×C₄₃	semidirect
232. #1982	C₂×C₄₃	semidirect
233. #1879	C₂×C₄₃	semidirect
234. C₄×#103	C₂×C₄₃	semidirect
269. C₄₃	#25633	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#559	2
C₂×C₄₃×#493	2
C₂×C₄₃×#460	2
C₄₃×#2548	2
C₄₃×#2012	2
C₄₃×#1984	2
C₄₃×#1982	2
C₄₃×#1879	2
C₄×#103×C₄₃	2
#25633	43

Subgroups — C43×#25633 #24945650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25633 #24945650