Subgroups — C₄₃×#29775 #24949792

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#465	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2854	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2088	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2068	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2055	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1893	C₂	1	1	yes	maximal, characteristic
10	C₄₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#123×C₄₃	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#465	—	2	4	no	—
20	C₂×#107×C₄₃	C₂²	1	2	yes	—
21	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	—	2	4	no	—
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
25	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₃	C₂²	1	2	yes	—
27	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#391	C₂²	1	2	yes	—
30	C₄₃×#390	C₂²	1	2	yes	—
31	C₄₃×#389	C₂²	1	2	yes	—
32	C₄₃×#389	C₂²	1	2	yes	—
33	C₄₃×#388	—	2	2	no	—
34	C₄₃×#387	—	2	2	no	—
35	C₄₃×#386	—	2	1	no	—
36	C₄₃×#385	—	2	1	no	—
37	C₄₃×#381	—	2	1	no	—
38	C₄₃×#380	C₂²	1	1	yes	characteristic
39	C₄₃×#380	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₄₃	—	2	2	no	—
50	C₂×SD₁₆×C₄₃	—	4	2	no	—
51	C₂²×C₈×C₄₃	—	2	2	no	—
52	C₂²×C₈×C₄₃	—	4	2	no	—
53	C₂²×C₈×C₄₃	—	4	2	no	—
54	C₂²×C₈×C₄₃	D₄	1	4	yes	—
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
58	#123×C₄₃	—	4	4	no	—
59	C₂²⋊Q₈×C₄₃	—	2	2	no	—
60	C₂²⋊Q₈×C₄₃	—	2	2	no	—
61	#121×C₄₃	—	2	2	no	—
62	#121×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	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	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	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	2	yes	—
80	#107×C₄₃	—	4	2	no	—
81	#106×C₄₃	—	2	2	no	—
82	C₄⋊C₈×C₄₃	—	2	4	no	—
83	C₄⋊C₈×C₄₃	—	2	4	no	—
84	#103×C₄₃	—	2	2	no	—
85	#103×C₄₃	—	4	2	no	—
86	#102×C₄₃	—	2	2	no	—
87	#102×C₄₃	—	4	2	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	—	2	1	no	—
90	#95×C₄₃	—	2	2	no	—
91	#95×C₄₃	—	2	2	no	—
92	#95×C₄₃	—	2	2	no	—
93	#95×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	—	2	1	no	—
95	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	2	1	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	1	no	—
101	C₂×D₄×C₄₃	—	2	1	no	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	2	2	no	—
104	C₂×D₄×C₄₃	—	4	2	no	—
105	C₂×D₄×C₄₃	—	4	2	no	—
106	C₂×D₄×C₄₃	—	4	2	no	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	#41	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	SD₁₆×C₄₃	—	4	4	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	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	—	4	4	no	—
132	C₂×C₈×C₄₃	—	4	4	no	—
133	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	4	4	no	—
144	C₄⋊C₄×C₄₃	—	4	2	no	—
145	C₄⋊C₄×C₄₃	—	4	4	no	—
146	C₂²⋊C₄×C₄₃	—	4	4	no	—
147	C₂²⋊C₄×C₄₃	—	4	2	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₂²⋊C₄×C₄₃	—	4	2	no	—
150	C₂²⋊C₄×C₄₃	—	4	2	no	—
151	C₂²⋊C₄×C₄₃	—	4	2	no	—
152	C₄²×C₄₃	—	2	4	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	4	1	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	1	no	—
161	C₂³×C₄₃	—	4	1	no	—
162	C₂³×C₄₃	#121	1	2	yes	—
163	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
164	C₂³×C₄₃	#137	1	2	yes	—
165	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₄₃	—	4	1	no	—
167	Q₈×C₄₃	—	4	1	no	—
168	Q₈×C₄₃	—	4	2	no	—
169	D₄×C₄₃	—	4	1	no	—
170	D₄×C₄₃	—	4	1	no	—
171	D₄×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	8	4	no	—
173	C₂×C₄×C₄₃	—	2	8	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	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	4	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	—	4	4	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	4	1	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	2	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	1	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	#121	1	2	yes	—
198	C₂×C₄×C₄₃	#135	1	4	yes	—
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
202	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
203	C₈×C₄₃	—	2	2	no	—
204	C₈×C₄₃	—	2	2	no	—
205	C₈×C₄₃	—	4	2	no	—
206	#29775	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	2	4	no	—
209	C₂²×C₄₃	—	2	4	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	8	1	no	—
212	C₂²×C₄₃	—	8	2	no	—
213	C₂²×C₄₃	—	8	2	no	—
214	C₂²×C₄₃	—	8	1	no	—
215	C₂²×C₄₃	—	8	1	no	—
216	C₂²×C₄₃	#468	1	4	yes	—
217	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
218	C₂²×C₄₃	#537	1	2	yes	—
219	C₂²×C₄₃	C₂×#135	1	2	yes	—
220	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	2	4	no	—
224	C₄×C₄₃	—	4	2	no	—
225	C₄×C₄₃	—	8	1	no	—
226	C₄×C₄₃	—	8	2	no	—
227	C₄×C₄₃	—	8	2	no	—
228	C₄×C₄₃	—	8	1	no	—
229	C₄×C₄₃	—	8	1	no	—
230	C₄×C₄₃	#534	1	1	yes	characteristic
231	C₄×C₄₃	#536	1	1	yes	characteristic
232	C₄×C₄₃	#539	1	2	yes	—
233	C₂×#465	C₂×C₄₃	1	1	yes	characteristic
234	C₂²×C₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
235	#2855	C₂×C₄₃	1	1	yes	characteristic, complemented
236	#2854	C₂×C₄₃	1	1	yes	characteristic
237	#2088	C₂×C₄₃	1	2	yes	complemented
238	#2068	C₂×C₄₃	1	2	yes	complemented
239	#2067	C₂×C₄₃	1	2	yes	complemented
240	#2055	C₂×C₄₃	1	2	yes	complemented
241	#1893	C₂×C₄₃	1	1	yes	characteristic
242	#1892	C₂×C₄₃	1	1	yes	characteristic, complemented
243	#1808	C₂×C₄₃	1	1	yes	characteristic, complemented
244	C₂×C₄₃	—	2	4	no	—
245	C₂×C₄₃	—	16	1	no	—
246	C₂×C₄₃	#2618	1	1	yes	characteristic
247	C₂×C₄₃	#3050	1	1	yes	characteristic
248	C₂×C₄₃	C₂×#468	1	1	yes	characteristic
249	C₂×C₄₃	#3247	1	2	yes	—
250	C₂×C₄₃	#3248	1	2	yes	—
251	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
254	C₂×#123	—	2	1	no	—
255	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
256	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
257	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
258	#465	—	2	4	no	—
259	C₂×#107	C₂²×C₄₃	1	2	yes	—
260	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
261	C₂×C₄⋊C₈	—	2	4	no	—
262	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
263	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
264	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
265	C₂×#103	C₂²×C₄₃	1	2	yes	—
266	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×#102	C₂²×C₄₃	1	2	yes	—
268	#391	C₂²×C₄₃	1	2	yes	—
269	#390	C₂²×C₄₃	1	2	yes	—
270	#389	C₂²×C₄₃	1	2	yes	—
271	#389	C₂²×C₄₃	1	2	yes	—
272	#388	—	2	2	no	—
273	#387	—	2	2	no	—
274	#386	—	2	1	no	—
275	#385	—	2	1	no	—
276	#381	—	2	1	no	—
277	#380	C₂²×C₄₃	1	1	yes	characteristic
278	#380	C₂²×C₄₃	1	1	yes	characteristic
279	#340	C₂²×C₄₃	1	2	yes	—
280	#340	C₂²×C₄₃	1	2	yes	—
281	#340	C₂²×C₄₃	1	2	yes	—
282	C₄₃	#29775	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
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×SD₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	4	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	4	2	no	—
293	C₂²×C₈	—	4	2	no	—
294	C₂²×C₈	D₄×C₄₃	1	4	yes	—
295	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
296	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
298	#123	—	4	4	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	D₄×C₄₃	1	2	yes	—
319	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
320	#107	—	4	2	no	—
321	#106	—	2	2	no	—
322	C₄⋊C₈	—	2	4	no	—
323	C₄⋊C₈	—	2	4	no	—
324	#103	—	2	2	no	—
325	#103	—	4	2	no	—
326	#102	—	2	2	no	—
327	#102	—	4	2	no	—
328	#95	—	2	1	no	—
329	#95	—	2	1	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	C₂⁴	—	2	1	no	—
335	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
363	C₂²×C₄	#41×C₄₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
365	SD₁₆	—	4	4	no	—
366	C₂×C₈	—	2	2	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	—	4	4	no	—
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	#121×C₄₃	1	2	yes	—
403	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
404	C₂³	#137×C₄₃	1	2	yes	—
405	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
406	Q₈	—	4	1	no	—
407	Q₈	—	4	1	no	—
408	Q₈	—	4	2	no	—
409	D₄	—	4	1	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	2	no	—
412	D₄	—	8	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	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	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	#121×C₄₃	1	2	yes	—
438	C₂×C₄	#135×C₄₃	1	4	yes	—
439	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
441	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
442	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	4	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	C₄₃×#468	1	4	yes	—
456	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
457	C₂²	C₄₃×#537	1	2	yes	—
458	C₂²	C₂×#135×C₄₃	1	2	yes	—
459	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
460	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	4	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	1	no	—
469	C₄	C₄₃×#534	1	1	yes	characteristic
470	C₄	C₄₃×#536	1	1	yes	characteristic
471	C₄	C₄₃×#539	1	2	yes	—
472	C₂	—	2	4	no	—
473	C₂	—	16	1	no	—
474	C₂	C₄₃×#2618	1	1	yes	characteristic
475	C₂	C₄₃×#3050	1	1	yes	characteristic
476	C₂	C₂×C₄₃×#468	1	1	yes	characteristic
477	C₂	C₄₃×#3247	1	2	yes	—
478	C₂	C₄₃×#3248	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×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. C₂²×C₄⋊C₈×C₄₃	C₂	semidirect
3. C₄₃×#2855	C₂	semidirect
5. C₄₃×#2088	C₂	semidirect
6. C₄₃×#2068	C₂	semidirect
7. C₄₃×#2067	C₂	semidirect
8. C₄₃×#2055	C₂	semidirect
10. C₄₃×#1892	C₂	semidirect
11. C₄₃×#1808	C₂	semidirect
206. #29775	C₄₃	direct (N × H)
234. C₂²×C₄⋊C₈	C₂×C₄₃	semidirect
235. #2855	C₂×C₄₃	semidirect
237. #2088	C₂×C₄₃	semidirect
238. #2068	C₂×C₄₃	semidirect
239. #2067	C₂×C₄₃	semidirect
240. #2055	C₂×C₄₃	semidirect
242. #1892	C₂×C₄₃	semidirect
243. #1808	C₂×C₄₃	semidirect
282. C₄₃	#29775	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×#465	2
C₂²×C₄⋊C₈×C₄₃	2
C₄₃×#2855	2
C₄₃×#2854	2
C₄₃×#2088	2
C₄₃×#2068	2
C₄₃×#2067	2
C₄₃×#2055	2
C₄₃×#1893	2
C₄₃×#1892	2
C₄₃×#1808	2
#29775	43

Subgroups — C43×#29775 #24949792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29775 #24949792