Subgroups — C₄₃×#29626 #24949643

Order 11008.

1454 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#450	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2042	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2015	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1786	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	complemented
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂×#124×C₄₃	—	2	4	no	—
15	C₂×#124×C₄₃	—	2	4	no	—
16	C₂×#124×C₄₃	—	2	2	no	—
17	C₂×#124×C₄₃	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
20	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#451	—	2	4	no	—
23	C₄₃×#450	—	2	4	no	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
25	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×#102×C₄₃	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#391	C₂²	1	2	yes	complemented
31	C₄₃×#389	C₂²	1	2	yes	complemented
32	C₄₃×#387	—	2	2	no	—
33	C₄₃×#385	—	2	1	no	—
34	C₄₃×#381	—	2	1	no	—
35	C₄₃×#380	C₂²	1	1	yes	characteristic
36	C₄₃×#336	C₂²	1	4	yes	complemented
37	C₂⁵×C₄₃	—	2	1	no	—
38	C₂²×Q₈×C₄₃	—	2	2	no	—
39	C₂²×Q₈×C₄₃	—	2	1	no	—
40	C₂²×Q₈×C₄₃	—	4	4	no	—
41	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
42	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	—	4	4	no	—
47	C₂²×D₄×C₄₃	D₄	1	4	yes	—
48	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₃	—	2	1	no	—
50	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
53	C₂×Q₁₆×C₄₃	—	2	4	no	—
54	C₂×Q₁₆×C₄₃	—	4	4	no	—
55	C₂×SD₁₆×C₄₃	—	2	4	no	—
56	C₂×SD₁₆×C₄₃	—	4	4	no	—
57	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
59	#124×C₄₃	—	2	16	no	—
60	#124×C₄₃	—	2	8	no	—
61	#124×C₄₃	—	2	8	no	—
62	C₂²⋊Q₈×C₄₃	—	2	2	no	—
63	C₂²⋊Q₈×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄²×C₄₃	—	2	2	no	—
75	C₂×C₄²×C₄₃	—	2	2	no	—
76	C₂×C₄²×C₄₃	D₄	1	2	yes	—
77	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
78	#103×C₄₃	—	2	4	no	—
79	#103×C₄₃	—	4	4	no	—
80	#102×C₄₃	—	2	4	no	—
81	#102×C₄₃	—	4	4	no	—
82	C₂²⋊C₈×C₄₃	—	2	2	no	—
83	C₂²⋊C₈×C₄₃	—	2	2	no	—
84	#95×C₄₃	—	2	1	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	2	no	—
87	#95×C₄₃	—	2	2	no	—
88	C₂⁴×C₄₃	—	2	4	no	—
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	—	4	4	no	—
91	C₂⁴×C₄₃	—	4	4	no	—
92	C₂⁴×C₄₃	—	4	2	no	—
93	C₂⁴×C₄₃	—	4	2	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₃	—	2	4	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	1	no	—
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	2	4	no	—
100	C₂×Q₈×C₄₃	—	2	4	no	—
101	C₂×Q₈×C₄₃	—	2	4	no	—
102	C₂×Q₈×C₄₃	—	4	8	no	—
103	C₂×Q₈×C₄₃	—	4	4	no	—
104	C₂×Q₈×C₄₃	—	4	8	no	—
105	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
106	C₂×D₄×C₄₃	—	2	4	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	4	no	—
109	C₂×D₄×C₄₃	—	2	4	no	—
110	C₂×D₄×C₄₃	—	4	8	no	—
111	C₂×D₄×C₄₃	—	4	8	no	—
112	C₂×D₄×C₄₃	—	4	4	no	—
113	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	4	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	1	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	4	2	no	—
125	C₂²×C₄×C₄₃	—	4	4	no	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₄₃	—	4	8	no	—
133	SD₁₆×C₄₃	—	4	8	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	4	no	—
137	C₂×C₈×C₄₃	—	2	4	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	—	2	1	no	—
140	C₄⋊C₄×C₄₃	—	2	4	no	—
141	C₄⋊C₄×C₄₃	—	4	4	no	—
142	C₄⋊C₄×C₄₃	—	4	2	no	—
143	C₂²⋊C₄×C₄₃	—	2	16	no	—
144	C₂²⋊C₄×C₄₃	—	2	16	no	—
145	C₂²⋊C₄×C₄₃	—	4	2	no	—
146	C₂²⋊C₄×C₄₃	—	4	2	no	—
147	C₄²×C₄₃	—	2	4	no	—
148	C₄²×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₂³×C₄₃	—	2	2	no	—
151	C₂³×C₄₃	—	2	2	no	—
152	C₂³×C₄₃	—	2	4	no	—
153	C₂³×C₄₃	—	4	8	no	—
154	C₂³×C₄₃	—	4	8	no	—
155	C₂³×C₄₃	—	4	4	no	—
156	C₂³×C₄₃	—	4	2	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	—	4	4	no	—
159	C₂³×C₄₃	—	4	8	no	—
160	C₂³×C₄₃	—	8	8	no	—
161	C₂³×C₄₃	—	8	8	no	—
162	C₂³×C₄₃	#120	1	2	yes	—
163	C₂³×C₄₃	#135	1	2	yes	—
164	C₂³×C₄₃	#137	1	2	yes	—
165	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₄₃	—	2	4	no	—
167	Q₈×C₄₃	—	2	4	no	—
168	Q₈×C₄₃	—	4	8	no	—
169	Q₈×C₄₃	—	4	4	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	Q₈×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	2	4	no	—
173	D₄×C₄₃	—	2	4	no	—
174	D₄×C₄₃	—	4	8	no	—
175	D₄×C₄₃	—	4	4	no	—
176	C₂×C₄×C₄₃	—	2	2	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	2	no	—
181	C₂×C₄×C₄₃	—	2	4	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	4	4	no	—
187	C₂×C₄×C₄₃	—	4	8	no	—
188	C₂×C₄×C₄₃	—	4	4	no	—
189	C₂×C₄×C₄₃	—	4	4	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	4	1	no	—
192	C₂×C₄×C₄₃	—	4	2	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	#120	1	2	yes	—
198	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
201	C₈×C₄₃	—	4	2	no	—
202	C₈×C₄₃	—	4	2	no	—
203	#29626	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	4	no	—
206	C₂²×C₄₃	—	2	4	no	—
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	4	4	no	—
209	C₂²×C₄₃	—	4	4	no	—
210	C₂²×C₄₃	—	4	4	no	—
211	C₂²×C₄₃	—	8	16	no	—
212	C₂²×C₄₃	—	8	4	no	—
213	C₂²×C₄₃	—	8	4	no	—
214	C₂²×C₄₃	#452	1	4	yes	—
215	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
216	C₂²×C₄₃	#535	1	2	yes	—
217	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
218	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
219	C₂²×C₄₃	#575	1	2	yes	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	4	4	no	—
222	C₄×C₄₃	—	4	2	no	—
223	C₄×C₄₃	—	4	2	no	—
224	C₄×C₄₃	—	8	1	no	—
225	C₄×C₄₃	—	8	2	no	—
226	C₄×C₄₃	—	8	1	no	—
227	C₄×C₄₃	#534	1	2	yes	—
228	C₄×C₄₃	#534	1	2	yes	—
229	C₂²×#124	C₂×C₄₃	1	1	yes	characteristic
230	C₂×#451	C₂×C₄₃	1	1	yes	characteristic, complemented
231	C₂×#450	C₂×C₄₃	1	1	yes	characteristic
232	#2855	C₂×C₄₃	1	1	yes	characteristic, complemented
233	#2042	C₂×C₄₃	1	4	yes	complemented
234	#2015	C₂×C₄₃	1	4	yes	complemented
235	#1817	C₂×C₄₃	1	1	yes	characteristic, complemented
236	#1787	C₂×C₄₃	1	1	yes	characteristic, complemented
237	#1786	C₂×C₄₃	1	1	yes	characteristic
238	C₂×C₄₃	—	2	4	no	—
239	C₂×C₄₃	—	8	4	no	—
240	C₂×C₄₃	#2613	1	1	yes	characteristic
241	C₂×C₄₃	C₂×#452	1	1	yes	characteristic
242	C₂×C₄₃	#3005	1	1	yes	characteristic
243	C₂×C₄₃	#3211	1	2	yes	—
244	C₂×C₄₃	#3215	1	2	yes	—
245	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
246	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
247	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	complemented
248	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
249	C₂×#124	—	2	4	no	—
250	C₂×#124	—	2	4	no	—
251	C₂×#124	—	2	2	no	—
252	C₂×#124	C₂²×C₄₃	1	4	yes	—
253	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	—	2	1	no	—
255	C₂²×C₂²⋊C₄	—	2	1	no	—
256	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
257	#451	—	2	4	no	—
258	#450	—	2	4	no	—
259	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
260	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
261	C₂×#102	C₂²×C₄₃	1	2	yes	—
262	C₂×#102	C₂²×C₄₃	1	4	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
264	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
265	#391	C₂²×C₄₃	1	2	yes	complemented
266	#389	C₂²×C₄₃	1	2	yes	complemented
267	#387	—	2	2	no	—
268	#385	—	2	1	no	—
269	#381	—	2	1	no	—
270	#380	C₂²×C₄₃	1	1	yes	characteristic
271	#336	C₂²×C₄₃	1	4	yes	complemented
272	C₄₃	#29626	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁵	—	2	1	no	—
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	—	4	4	no	—
277	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
278	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
279	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	4	4	no	—
283	C₂²×D₄	D₄×C₄₃	1	4	yes	—
284	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
285	C₂³×C₄	—	2	1	no	—
286	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
287	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
289	C₂×Q₁₆	—	2	4	no	—
290	C₂×Q₁₆	—	4	4	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	4	4	no	—
293	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
294	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
295	#124	—	2	16	no	—
296	#124	—	2	8	no	—
297	#124	—	2	8	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	8	no	—
305	C₂×C₂²⋊C₄	—	2	8	no	—
306	C₂×C₂²⋊C₄	—	2	4	no	—
307	C₂×C₂²⋊C₄	—	2	4	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	D₄×C₄₃	1	2	yes	—
313	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
314	#103	—	2	4	no	—
315	#103	—	4	4	no	—
316	#102	—	2	4	no	—
317	#102	—	4	4	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	#95	—	2	1	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	2	no	—
326	C₂⁴	—	4	4	no	—
327	C₂⁴	—	4	4	no	—
328	C₂⁴	—	4	2	no	—
329	C₂⁴	—	4	2	no	—
330	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	4	8	no	—
339	C₂×Q₈	—	4	4	no	—
340	C₂×Q₈	—	4	8	no	—
341	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	4	8	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	4	8	no	—
349	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
368	Q₁₆	—	4	8	no	—
369	SD₁₆	—	4	8	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	4	no	—
373	C₂×C₈	—	2	4	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	2	16	no	—
380	C₂²⋊C₄	—	2	16	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₄²	—	2	4	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	4	8	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	8	8	no	—
397	C₂³	—	8	8	no	—
398	C₂³	#120×C₄₃	1	2	yes	—
399	C₂³	#135×C₄₃	1	2	yes	—
400	C₂³	#137×C₄₃	1	2	yes	—
401	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	8	no	—
405	Q₈	—	4	4	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	4	8	no	—
411	D₄	—	4	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	#120×C₄₃	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
436	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	16	no	—
447	C₂²	—	8	4	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₄₃×#452	1	4	yes	—
450	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
451	C₂²	C₄₃×#535	1	2	yes	—
452	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
453	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
454	C₂²	C₄₃×#575	1	2	yes	—
455	C₄	—	2	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	1	no	—
462	C₄	C₄₃×#534	1	2	yes	—
463	C₄	C₄₃×#534	1	2	yes	—
464	C₂	—	2	4	no	—
465	C₂	—	8	4	no	—
466	C₂	C₄₃×#2613	1	1	yes	characteristic
467	C₂	C₂×C₄₃×#452	1	1	yes	characteristic
468	C₂	C₄₃×#3005	1	1	yes	characteristic
469	C₂	C₄₃×#3211	1	2	yes	—
470	C₂	C₄₃×#3215	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
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
2. C₂×C₄₃×#451	C₂	semidirect
4. C₄₃×#2855	C₂	semidirect
5. C₄₃×#2042	C₂	semidirect
6. C₄₃×#2015	C₂	semidirect
7. C₄₃×#1817	C₂	semidirect
8. C₄₃×#1787	C₂	semidirect
12. C₂²×Q₁₆×C₄₃	C₂²	semidirect
24. C₂×#103×C₄₃	C₂²	semidirect
25. C₂×#103×C₄₃	C₂²	semidirect
30. C₄₃×#391	C₂²	semidirect
31. C₄₃×#389	C₂²	semidirect
36. C₄₃×#336	C₂²	semidirect
203. #29626	C₄₃	direct (N × H)
230. C₂×#451	C₂×C₄₃	semidirect
232. #2855	C₂×C₄₃	semidirect
233. #2042	C₂×C₄₃	semidirect
234. #2015	C₂×C₄₃	semidirect
235. #1817	C₂×C₄₃	semidirect
236. #1787	C₂×C₄₃	semidirect
247. C₂²×Q₁₆	C₂²×C₄₃	semidirect
259. C₂×#103	C₂²×C₄₃	semidirect
260. C₂×#103	C₂²×C₄₃	semidirect
265. #391	C₂²×C₄₃	semidirect
266. #389	C₂²×C₄₃	semidirect
271. #336	C₂²×C₄₃	semidirect
272. C₄₃	#29626	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₄₃	2
C₂×C₄₃×#451	2
C₂×C₄₃×#450	2
C₄₃×#2855	2
C₄₃×#2042	2
C₄₃×#2015	2
C₄₃×#1817	2
C₄₃×#1787	2
C₄₃×#1786	2
#29626	43

Subgroups — C43×#29626 #24949643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29626 #24949643