Subgroups — C₄₃×#24822 #24944839

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#478	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2349	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1877	C₂	1	1	yes	maximal, characteristic
12	C₄₃×#1877	C₂	1	1	yes	maximal, characteristic
13	C₄₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#1804	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1802	C₂	1	1	yes	maximal, characteristic
16	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#478	—	2	4	no	—
23	C₄×SD₁₆×C₄₃	—	2	4	no	—
24	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#398	—	2	1	no	—
38	C₄₃×#398	—	2	1	no	—
39	C₄₃×#391	C₂²	1	1	yes	characteristic
40	C₄₃×#391	C₂²	1	1	yes	characteristic
41	C₄₃×#389	C₂²	1	1	yes	characteristic
42	C₄₃×#389	C₂²	1	1	yes	characteristic
43	C₄₃×#387	—	2	1	no	—
44	C₄₃×#387	—	2	1	no	—
45	C₄₃×#385	—	2	1	no	—
46	C₄₃×#385	—	2	1	no	—
47	C₄₃×#384	C₂²	1	1	yes	characteristic
48	C₄₃×#382	C₂²	1	1	yes	characteristic
49	C₄₃×#382	C₂²	1	1	yes	characteristic
50	C₄₃×#380	—	2	1	no	—
51	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×#95×C₄₃	—	2	1	no	—
53	C₄₃×#340	C₂²	1	1	yes	characteristic
54	C₄₃×#340	C₂²	1	1	yes	characteristic
55	C₄₃×#340	C₂²	1	1	yes	characteristic
56	C₄₃×#340	C₂²	1	1	yes	characteristic
57	C₄₃×#340	C₂²	1	1	yes	characteristic
58	C₄₃×#340	C₂²	1	1	yes	characteristic
59	C₄₃×#336	C₂²	1	1	yes	characteristic
60	C₄₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₃	—	2	1	no	—
64	C₂³×C₄×C₄₃	—	2	1	no	—
65	C₂³×C₄×C₄₃	—	2	1	no	—
66	C₂×SD₁₆×C₄₃	—	2	2	no	—
67	C₂×SD₁₆×C₄₃	—	2	2	no	—
68	C₂×SD₁₆×C₄₃	Q₈	1	4	yes	—
69	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
73	#125×C₄₃	—	2	2	no	—
74	#125×C₄₃	—	2	2	no	—
75	C₄×Q₈×C₄₃	—	2	2	no	—
76	C₄×Q₈×C₄₃	—	2	2	no	—
77	C₄×D₄×C₄₃	—	2	2	no	—
78	C₄×D₄×C₄₃	—	2	2	no	—
79	C₄×D₄×C₄₃	—	2	2	no	—
80	C₄×D₄×C₄₃	—	4	1	no	—
81	C₄×D₄×C₄₃	—	4	1	no	—
82	C₄×D₄×C₄₃	D₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
101	C₂×C₄²×C₄₃	—	2	1	no	—
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	#107×C₄₃	—	2	2	no	—
106	#106×C₄₃	—	2	2	no	—
107	#106×C₄₃	—	2	2	no	—
108	C₄⋊C₈×C₄₃	—	2	2	no	—
109	C₄⋊C₈×C₄₃	—	4	1	no	—
110	C₄⋊C₈×C₄₃	—	4	1	no	—
111	#103×C₄₃	—	2	2	no	—
112	#103×C₄₃	—	4	1	no	—
113	#103×C₄₃	—	4	1	no	—
114	#102×C₄₃	—	2	2	no	—
115	#102×C₄₃	—	2	2	no	—
116	#102×C₄₃	—	2	2	no	—
117	C₄×C₈×C₄₃	—	2	2	no	—
118	#95×C₄₃	—	2	1	no	—
119	#95×C₄₃	—	2	1	no	—
120	#95×C₄₃	—	2	1	no	—
121	#95×C₄₃	—	2	1	no	—
122	#95×C₄₃	—	2	1	no	—
123	#95×C₄₃	—	2	1	no	—
124	#95×C₄₃	—	2	1	no	—
125	#95×C₄₃	—	2	1	no	—
126	#95×C₄₃	—	2	1	no	—
127	#95×C₄₃	—	2	1	no	—
128	#95×C₄₃	D₄	1	1	yes	characteristic
129	#95×C₄₃	D₄	1	1	yes	characteristic
130	C₂⁴×C₄₃	—	2	1	no	—
131	C₂×Q₈×C₄₃	—	2	1	no	—
132	C₂×Q₈×C₄₃	—	2	1	no	—
133	C₂×Q₈×C₄₃	—	2	1	no	—
134	C₂×Q₈×C₄₃	—	2	1	no	—
135	C₂×Q₈×C₄₃	—	2	1	no	—
136	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
137	C₂×D₄×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	1	no	—
139	C₂×D₄×C₄₃	—	2	1	no	—
140	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
142	C₂×D₄×C₄₃	#41	1	2	yes	—
143	C₂²×C₄×C₄₃	—	2	4	no	—
144	C₂²×C₄×C₄₃	—	2	1	no	—
145	C₂²×C₄×C₄₃	—	2	1	no	—
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	4	2	no	—
152	C₂²×C₄×C₄₃	—	4	2	no	—
153	C₂²×C₄×C₄₃	—	4	2	no	—
154	C₂²×C₄×C₄₃	—	4	2	no	—
155	C₂²×C₄×C₄₃	—	8	1	no	—
156	C₂²×C₄×C₄₃	—	8	1	no	—
157	C₂²×C₄×C₄₃	—	8	1	no	—
158	C₂²×C₄×C₄₃	—	8	1	no	—
159	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	SD₁₆×C₄₃	—	2	8	no	—
167	C₂×C₈×C₄₃	—	2	1	no	—
168	C₂×C₈×C₄₃	—	2	1	no	—
169	C₂×C₈×C₄₃	—	2	1	no	—
170	C₂×C₈×C₄₃	—	2	1	no	—
171	C₂×C₈×C₄₃	—	2	1	no	—
172	C₂×C₈×C₄₃	—	2	1	no	—
173	C₂×C₈×C₄₃	—	2	1	no	—
174	C₂×C₈×C₄₃	—	2	1	no	—
175	C₂×C₈×C₄₃	—	2	1	no	—
176	C₂×C₈×C₄₃	—	2	1	no	—
177	C₂×C₈×C₄₃	—	2	1	no	—
178	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
179	C₄⋊C₄×C₄₃	—	2	2	no	—
180	C₄⋊C₄×C₄₃	—	2	1	no	—
181	C₄⋊C₄×C₄₃	—	2	1	no	—
182	C₄⋊C₄×C₄₃	—	2	1	no	—
183	C₄⋊C₄×C₄₃	—	2	1	no	—
184	C₄⋊C₄×C₄₃	—	2	1	no	—
185	C₄⋊C₄×C₄₃	—	2	1	no	—
186	C₄⋊C₄×C₄₃	—	2	1	no	—
187	C₄⋊C₄×C₄₃	—	2	1	no	—
188	C₄⋊C₄×C₄₃	—	2	1	no	—
189	C₄⋊C₄×C₄₃	—	2	1	no	—
190	C₄⋊C₄×C₄₃	—	2	1	no	—
191	C₄⋊C₄×C₄₃	—	4	1	no	—
192	C₄⋊C₄×C₄₃	—	4	2	no	—
193	C₄⋊C₄×C₄₃	—	4	2	no	—
194	C₄⋊C₄×C₄₃	—	4	2	no	—
195	C₄⋊C₄×C₄₃	—	4	2	no	—
196	C₄⋊C₄×C₄₃	—	4	2	no	—
197	C₄⋊C₄×C₄₃	—	8	1	no	—
198	C₄⋊C₄×C₄₃	—	8	1	no	—
199	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
200	C₂²⋊C₄×C₄₃	—	2	4	no	—
201	C₂²⋊C₄×C₄₃	—	4	2	no	—
202	C₂²⋊C₄×C₄₃	—	4	2	no	—
203	C₄²×C₄₃	—	2	1	no	—
204	C₄²×C₄₃	—	2	1	no	—
205	C₄²×C₄₃	—	2	1	no	—
206	C₄²×C₄₃	—	2	1	no	—
207	C₄²×C₄₃	—	4	2	no	—
208	C₄²×C₄₃	C₂×D₄	1	2	yes	—
209	C₄²×C₄₃	#41	1	2	yes	—
210	C₂³×C₄₃	—	2	2	no	—
211	C₂³×C₄₃	—	2	2	no	—
212	C₂³×C₄₃	—	2	2	no	—
213	C₂³×C₄₃	—	4	1	no	—
214	C₂³×C₄₃	—	4	1	no	—
215	C₂³×C₄₃	—	4	1	no	—
216	C₂³×C₄₃	—	4	1	no	—
217	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₄₃	—	2	2	no	—
219	Q₈×C₄₃	—	2	2	no	—
220	Q₈×C₄₃	—	4	1	no	—
221	Q₈×C₄₃	—	4	1	no	—
222	D₄×C₄₃	—	2	2	no	—
223	D₄×C₄₃	—	2	2	no	—
224	D₄×C₄₃	—	2	2	no	—
225	D₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
226	C₂×C₄×C₄₃	—	2	1	no	—
227	C₂×C₄×C₄₃	—	2	1	no	—
228	C₂×C₄×C₄₃	—	2	1	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	1	no	—
231	C₂×C₄×C₄₃	—	2	1	no	—
232	C₂×C₄×C₄₃	—	2	2	no	—
233	C₂×C₄×C₄₃	—	2	1	no	—
234	C₂×C₄×C₄₃	—	2	1	no	—
235	C₂×C₄×C₄₃	—	2	1	no	—
236	C₂×C₄×C₄₃	—	2	2	no	—
237	C₂×C₄×C₄₃	—	2	1	no	—
238	C₂×C₄×C₄₃	—	2	1	no	—
239	C₂×C₄×C₄₃	—	2	1	no	—
240	C₂×C₄×C₄₃	—	2	1	no	—
241	C₂×C₄×C₄₃	—	2	1	no	—
242	C₂×C₄×C₄₃	—	2	1	no	—
243	C₂×C₄×C₄₃	—	4	1	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	—	4	1	no	—
249	C₂×C₄×C₄₃	—	4	1	no	—
250	C₂×C₄×C₄₃	—	4	1	no	—
251	C₂×C₄×C₄₃	—	4	1	no	—
252	C₂×C₄×C₄₃	—	4	1	no	—
253	C₂×C₄×C₄₃	—	4	1	no	—
254	C₂×C₄×C₄₃	—	4	1	no	—
255	C₂×C₄×C₄₃	—	4	1	no	—
256	C₂×C₄×C₄₃	—	4	1	no	—
257	C₂×C₄×C₄₃	—	4	1	no	—
258	C₂×C₄×C₄₃	—	4	1	no	—
259	C₂×C₄×C₄₃	—	4	1	no	—
260	C₂×C₄×C₄₃	—	4	1	no	—
261	C₂×C₄×C₄₃	—	4	1	no	—
262	C₂×C₄×C₄₃	—	8	4	no	—
263	C₂×C₄×C₄₃	—	8	4	no	—
264	C₂×C₄×C₄₃	—	8	4	no	—
265	C₂×C₄×C₄₃	#121	1	2	yes	—
266	C₂×C₄×C₄₃	#121	1	2	yes	—
267	C₂×C₄×C₄₃	#135	1	2	yes	—
268	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
270	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
274	C₈×C₄₃	—	2	2	no	—
275	C₈×C₄₃	—	4	1	no	—
276	C₈×C₄₃	—	4	1	no	—
277	C₈×C₄₃	—	4	1	no	—
278	#24822	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂²×C₄₃	—	2	4	no	—
280	C₂²×C₄₃	—	4	2	no	—
281	C₂²×C₄₃	—	4	2	no	—
282	C₂²×C₄₃	—	4	2	no	—
283	C₂²×C₄₃	—	4	2	no	—
284	C₂²×C₄₃	—	4	2	no	—
285	C₂²×C₄₃	—	4	2	no	—
286	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
287	C₂²×C₄₃	#546	1	1	yes	characteristic
288	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
289	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
290	C₂²×C₄₃	#575	1	1	yes	characteristic
291	C₂²×C₄₃	#577	1	1	yes	characteristic
292	C₂²×C₄₃	#577	1	1	yes	characteristic
293	C₄×C₄₃	—	2	2	no	—
294	C₄×C₄₃	—	2	2	no	—
295	C₄×C₄₃	—	2	2	no	—
296	C₄×C₄₃	—	4	2	no	—
297	C₄×C₄₃	—	4	1	no	—
298	C₄×C₄₃	—	4	2	no	—
299	C₄×C₄₃	—	4	1	no	—
300	C₄×C₄₃	—	4	1	no	—
301	C₄×C₄₃	—	8	1	no	—
302	C₄×C₄₃	—	8	1	no	—
303	C₄×C₄₃	—	8	1	no	—
304	C₄×C₄₃	—	8	1	no	—
305	C₄×C₄₃	—	8	1	no	—
306	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
307	C₄×C₄₃	#537	1	1	yes	characteristic
308	C₄×C₄₃	#552	1	1	yes	characteristic
309	C₄×C₄₃	#554	1	1	yes	characteristic
310	C₂×#478	C₂×C₄₃	1	1	yes	characteristic
311	C₂×C₄×SD₁₆	C₂×C₄₃	1	1	yes	characteristic
312	#2565	C₂×C₄₃	1	1	yes	characteristic, complemented
313	#2349	C₂×C₄₃	1	1	yes	characteristic
314	#2085	C₂×C₄₃	1	1	yes	characteristic, complemented
315	#2084	C₂×C₄₃	1	1	yes	characteristic, complemented
316	#2068	C₂×C₄₃	1	1	yes	characteristic, complemented
317	#2066	C₂×C₄₃	1	1	yes	characteristic, complemented
318	#1991	C₂×C₄₃	1	1	yes	characteristic, complemented
319	#1939	C₂×C₄₃	1	1	yes	characteristic, complemented
320	#1877	C₂×C₄₃	1	1	yes	characteristic
321	#1877	C₂×C₄₃	1	1	yes	characteristic
322	#1805	C₂×C₄₃	1	1	yes	characteristic, complemented
323	#1804	C₂×C₄₃	1	1	yes	characteristic
324	#1802	C₂×C₄₃	1	1	yes	characteristic
325	C₂×C₄₃	—	4	4	no	—
326	C₂×C₄₃	#2417	1	1	yes	characteristic
327	C₂×C₄₃	#3035	1	1	yes	characteristic
328	C₂×C₄₃	#3042	1	1	yes	characteristic
329	C₂×C₄₃	#3296	1	1	yes	characteristic
330	C₂×C₄₃	#3323	1	1	yes	characteristic
331	C₂×C₄₃	#3381	1	1	yes	characteristic
332	C₂×C₄₃	#3388	1	1	yes	characteristic
333	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
334	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
335	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
336	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
337	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
339	#478	—	2	4	no	—
340	C₄×SD₁₆	—	2	4	no	—
341	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
342	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
343	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
344	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
345	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
346	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
347	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
348	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
349	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
350	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
351	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
352	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
353	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
354	#398	—	2	1	no	—
355	#398	—	2	1	no	—
356	#391	C₂²×C₄₃	1	1	yes	characteristic
357	#391	C₂²×C₄₃	1	1	yes	characteristic
358	#389	C₂²×C₄₃	1	1	yes	characteristic
359	#389	C₂²×C₄₃	1	1	yes	characteristic
360	#387	—	2	1	no	—
361	#387	—	2	1	no	—
362	#385	—	2	1	no	—
363	#385	—	2	1	no	—
364	#384	C₂²×C₄₃	1	1	yes	characteristic
365	#382	C₂²×C₄₃	1	1	yes	characteristic
366	#382	C₂²×C₄₃	1	1	yes	characteristic
367	#380	—	2	1	no	—
368	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
369	C₂×#95	—	2	1	no	—
370	#340	C₂²×C₄₃	1	1	yes	characteristic
371	#340	C₂²×C₄₃	1	1	yes	characteristic
372	#340	C₂²×C₄₃	1	1	yes	characteristic
373	#340	C₂²×C₄₃	1	1	yes	characteristic
374	#340	C₂²×C₄₃	1	1	yes	characteristic
375	#340	C₂²×C₄₃	1	1	yes	characteristic
376	#336	C₂²×C₄₃	1	1	yes	characteristic
377	#336	C₂²×C₄₃	1	1	yes	characteristic
378	C₄₃	#24822	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	—	2	1	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×SD₁₆	Q₈×C₄₃	1	4	yes	—
387	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
391	#125	—	2	2	no	—
392	#125	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	4	1	no	—
399	C₄×D₄	—	4	1	no	—
400	C₄×D₄	D₄×C₄₃	1	4	yes	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
423	#107	—	2	2	no	—
424	#106	—	2	2	no	—
425	#106	—	2	2	no	—
426	C₄⋊C₈	—	2	2	no	—
427	C₄⋊C₈	—	4	1	no	—
428	C₄⋊C₈	—	4	1	no	—
429	#103	—	2	2	no	—
430	#103	—	4	1	no	—
431	#103	—	4	1	no	—
432	#102	—	2	2	no	—
433	#102	—	2	2	no	—
434	#102	—	2	2	no	—
435	C₄×C₈	—	2	2	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	D₄×C₄₃	1	1	yes	characteristic
447	#95	D₄×C₄₃	1	1	yes	characteristic
448	C₂⁴	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	C₂×Q₈×C₄₃	1	2	yes	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
459	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
460	C₂×D₄	#41×C₄₃	1	2	yes	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	8	1	no	—
474	C₂²×C₄	—	8	1	no	—
475	C₂²×C₄	—	8	1	no	—
476	C₂²×C₄	—	8	1	no	—
477	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
484	SD₁₆	—	2	8	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	8	1	no	—
516	C₄⋊C₄	—	8	1	no	—
517	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	4	2	no	—
526	C₄²	C₂×D₄×C₄₃	1	2	yes	—
527	C₄²	#41×C₄₃	1	2	yes	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
536	Q₈	—	2	2	no	—
537	Q₈	—	2	2	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	4	no	—
581	C₂×C₄	—	8	4	no	—
582	C₂×C₄	—	8	4	no	—
583	C₂×C₄	#121×C₄₃	1	2	yes	—
584	C₂×C₄	#121×C₄₃	1	2	yes	—
585	C₂×C₄	#135×C₄₃	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
587	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
588	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
590	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
591	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
592	C₈	—	2	2	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	4	1	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
604	C₂²	C₄₃×#546	1	1	yes	characteristic
605	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
606	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
607	C₂²	C₄₃×#575	1	1	yes	characteristic
608	C₂²	C₄₃×#577	1	1	yes	characteristic
609	C₂²	C₄₃×#577	1	1	yes	characteristic
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	8	1	no	—
619	C₄	—	8	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
624	C₄	C₄₃×#537	1	1	yes	characteristic
625	C₄	C₄₃×#552	1	1	yes	characteristic
626	C₄	C₄₃×#554	1	1	yes	characteristic
627	C₂	—	4	4	no	—
628	C₂	C₄₃×#2417	1	1	yes	characteristic
629	C₂	C₄₃×#3035	1	1	yes	characteristic
630	C₂	C₄₃×#3042	1	1	yes	characteristic
631	C₂	C₄₃×#3296	1	1	yes	characteristic
632	C₂	C₄₃×#3323	1	1	yes	characteristic
633	C₂	C₄₃×#3381	1	1	yes	characteristic
634	C₂	C₄₃×#3388	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄₃×#2565	C₂	semidirect
5. C₄₃×#2085	C₂	semidirect
6. C₄₃×#2084	C₂	semidirect
7. C₄₃×#2068	C₂	semidirect
8. C₄₃×#2066	C₂	semidirect
9. C₄₃×#1991	C₂	semidirect
10. C₄₃×#1939	C₂	semidirect
13. C₄₃×#1805	C₂	semidirect
278. #24822	C₄₃	direct (N × H)
312. #2565	C₂×C₄₃	semidirect
314. #2085	C₂×C₄₃	semidirect
315. #2084	C₂×C₄₃	semidirect
316. #2068	C₂×C₄₃	semidirect
317. #2066	C₂×C₄₃	semidirect
318. #1991	C₂×C₄₃	semidirect
319. #1939	C₂×C₄₃	semidirect
322. #1805	C₂×C₄₃	semidirect
378. C₄₃	#24822	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×#478	2
C₂×C₄×SD₁₆×C₄₃	2
C₄₃×#2565	2
C₄₃×#2349	2
C₄₃×#2085	2
C₄₃×#2084	2
C₄₃×#2068	2
C₄₃×#2066	2
C₄₃×#1991	2
C₄₃×#1939	2
C₄₃×#1877	2
C₄₃×#1805	2
C₄₃×#1804	2
C₄₃×#1802	2
#24822	43

Subgroups — C43×#24822 #24944839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#24822 #24944839