Subgroups — C₄₃×#29725 #24949742

Order 11008.

1070 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#449	C₂	1	2	yes	maximal, complemented
2	C₄₃×#2619	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2054	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1874	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#121×C₄₃	C₂²	1	2	yes	—
17	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#449	—	2	8	no	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
21	C₂×#103×C₄₃	C₂²	1	2	yes	—
22	C₂×#102×C₄₃	C₂²	1	2	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#394	—	2	2	no	—
27	C₄₃×#392	—	2	2	no	—
28	C₄₃×#391	C₂²	1	1	yes	characteristic
29	C₄₃×#391	C₂²	1	1	yes	characteristic
30	C₄₃×#390	C₂²	1	1	yes	characteristic
31	C₄₃×#390	C₂²	1	2	yes	—
32	C₄₃×#390	C₂²	1	1	yes	characteristic
33	C₄₃×#386	—	2	2	no	—
34	C₄₃×#382	C₂²	1	1	yes	characteristic
35	C₄₃×#380	—	2	2	no	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	2	yes	—
38	C₄₃×#336	C₂²	1	1	yes	characteristic
39	C₄₃×#336	C₂²	1	1	yes	characteristic
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	—	4	2	no	—
42	C₂×#41×C₄₃	—	4	2	no	—
43	C₂×#41×C₄₃	D₄	1	4	yes	complemented
44	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	—	2	2	no	—
47	C₂²×D₄×C₄₃	—	2	2	no	—
48	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	—	2	1	no	—
51	C₂³×C₄×C₄₃	—	2	1	no	—
52	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₄₃	—	2	4	no	—
54	C₂×SD₁₆×C₄₃	—	4	2	no	—
55	C₂×SD₁₆×C₄₃	—	4	2	no	—
56	C₂×D₈×C₄₃	—	2	4	no	—
57	C₂×D₈×C₄₃	—	4	2	no	—
58	C₂×D₈×C₄₃	—	4	2	no	—
59	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
61	#127×C₄₃	—	4	2	no	—
62	#121×C₄₃	—	2	4	no	—
63	#121×C₄₃	—	2	4	no	—
64	#117×C₄₃	—	4	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
67	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₃	—	4	2	no	—
80	#103×C₄₃	—	2	4	no	—
81	#102×C₄₃	—	2	4	no	—
82	#102×C₄₃	—	4	2	no	—
83	#102×C₄₃	—	4	2	no	—
84	C₂²⋊C₈×C₄₃	—	2	4	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	2	no	—
87	#95×C₄₃	—	2	2	no	—
88	C₂⁴×C₄₃	—	2	1	no	—
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
91	#41×C₄₃	—	4	8	no	—
92	#41×C₄₃	—	4	8	no	—
93	C₂×Q₈×C₄₃	—	2	1	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₄₃	—	2	1	no	—
98	C₂×D₄×C₄₃	—	2	4	no	—
99	C₂×D₄×C₄₃	—	2	2	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	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	4	2	no	—
108	C₂×D₄×C₄₃	—	4	2	no	—
109	C₂×D₄×C₄₃	—	4	4	no	—
110	C₂×D₄×C₄₃	—	4	4	no	—
111	C₂×D₄×C₄₃	—	8	2	no	—
112	C₂×D₄×C₄₃	—	8	2	no	—
113	C₂×D₄×C₄₃	—	8	2	no	—
114	C₂×D₄×C₄₃	—	8	2	no	—
115	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	4	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	1	no	—
123	C₂²×C₄×C₄₃	—	4	2	no	—
124	C₂²×C₄×C₄₃	—	4	2	no	—
125	C₂²×C₄×C₄₃	—	4	2	no	—
126	C₂²×C₄×C₄₃	—	8	2	no	—
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	#41	1	2	yes	—
132	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
133	SD₁₆×C₄₃	—	4	8	no	—
134	D₈×C₄₃	—	4	8	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	4	2	no	—
146	C₄⋊C₄×C₄₃	—	4	2	no	—
147	C₂²⋊C₄×C₄₃	—	4	2	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₂²⋊C₄×C₄₃	—	8	2	no	—
150	C₂²⋊C₄×C₄₃	—	8	2	no	—
151	C₂²⋊C₄×C₄₃	—	8	2	no	—
152	C₂²⋊C₄×C₄₃	—	8	2	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	1	no	—
156	C₂³×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	4	1	no	—
161	C₂³×C₄₃	—	4	1	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	4	2	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	#121	1	2	yes	—
172	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₄₃	—	2	4	no	—
174	Q₈×C₄₃	—	4	2	no	—
175	D₄×C₄₃	—	2	4	no	—
176	D₄×C₄₃	—	4	8	no	—
177	D₄×C₄₃	—	4	2	no	—
178	D₄×C₄₃	—	4	2	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	4	2	no	—
181	D₄×C₄₃	—	4	2	no	—
182	D₄×C₄₃	—	8	8	no	—
183	D₄×C₄₃	—	8	8	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	4	no	—
187	C₂×C₄×C₄₃	—	2	4	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	2	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	4	8	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	1	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	1	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	8	4	no	—
206	C₂×C₄×C₄₃	#121	1	2	yes	—
207	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
210	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
211	C₈×C₄₃	—	4	2	no	—
212	C₈×C₄₃	—	4	2	no	—
213	#29725	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	—	2	4	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	1	no	—
218	C₂²×C₄₃	—	4	1	no	—
219	C₂²×C₄₃	—	4	2	no	—
220	C₂²×C₄₃	—	4	4	no	—
221	C₂²×C₄₃	—	8	2	no	—
222	C₂²×C₄₃	—	8	1	no	—
223	C₂²×C₄₃	—	8	1	no	—
224	C₂²×C₄₃	—	8	2	no	—
225	C₂²×C₄₃	—	8	2	no	—
226	C₂²×C₄₃	—	8	2	no	—
227	C₂²×C₄₃	—	8	2	no	—
228	C₂²×C₄₃	—	8	2	no	—
229	C₂²×C₄₃	—	8	2	no	—
230	C₂²×C₄₃	—	8	2	no	—
231	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
232	C₂²×C₄₃	#534	1	1	yes	characteristic
233	C₂²×C₄₃	#535	1	1	yes	characteristic
234	C₂²×C₄₃	#576	1	2	yes	—
235	C₂²×C₄₃	#577	1	2	yes	—
236	C₄×C₄₃	—	2	2	no	—
237	C₄×C₄₃	—	4	2	no	—
238	C₄×C₄₃	—	4	2	no	—
239	C₄×C₄₃	—	4	2	no	—
240	C₄×C₄₃	—	8	1	no	—
241	C₄×C₄₃	—	8	1	no	—
242	C₄×C₄₃	—	8	2	no	—
243	C₄×C₄₃	#534	1	2	yes	—
244	C₄×C₄₃	#538	1	2	yes	—
245	C₂×#449	C₂×C₄₃	1	2	yes	complemented
246	#2619	C₂×C₄₃	1	1	yes	characteristic, complemented
247	#2311	C₂×C₄₃	1	1	yes	characteristic, complemented
248	#2074	C₂×C₄₃	1	1	yes	characteristic, complemented
249	#2073	C₂×C₄₃	1	1	yes	characteristic, complemented
250	#2055	C₂×C₄₃	1	2	yes	complemented
251	#2054	C₂×C₄₃	1	2	yes	complemented
252	#2014	C₂×C₄₃	1	1	yes	characteristic, complemented
253	#2011	C₂×C₄₃	1	1	yes	characteristic, complemented
254	#1874	C₂×C₄₃	1	2	yes	complemented
255	#1798	C₂×C₄₃	1	1	yes	characteristic, complemented
256	C₂×C₄₃	—	4	2	no	—
257	C₂×C₄₃	—	8	2	no	—
258	C₂×C₄₃	—	16	2	no	—
259	C₂×C₄₃	#2617	1	1	yes	characteristic
260	C₂×C₄₃	#3045	1	2	yes	—
261	C₂×C₄₃	#3198	1	2	yes	—
262	C₂×C₄₃	#3220	1	1	yes	characteristic
263	C₂×C₄₃	#3221	1	1	yes	characteristic
264	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
265	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
266	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
267	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
268	C₂×#121	C₂²×C₄₃	1	2	yes	—
269	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
271	#449	—	2	8	no	—
272	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
273	C₂×#103	C₂²×C₄₃	1	2	yes	—
274	C₂×#102	C₂²×C₄₃	1	2	yes	—
275	C₂×#102	C₂²×C₄₃	1	2	yes	—
276	C₂×#102	C₂²×C₄₃	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
278	#394	—	2	2	no	—
279	#392	—	2	2	no	—
280	#391	C₂²×C₄₃	1	1	yes	characteristic
281	#391	C₂²×C₄₃	1	1	yes	characteristic
282	#390	C₂²×C₄₃	1	1	yes	characteristic
283	#390	C₂²×C₄₃	1	2	yes	—
284	#390	C₂²×C₄₃	1	1	yes	characteristic
285	#386	—	2	2	no	—
286	#382	C₂²×C₄₃	1	1	yes	characteristic
287	#380	—	2	2	no	—
288	#340	C₂²×C₄₃	1	2	yes	—
289	#340	C₂²×C₄₃	1	2	yes	—
290	#336	C₂²×C₄₃	1	1	yes	characteristic
291	#336	C₂²×C₄₃	1	1	yes	characteristic
292	C₄₃	#29725	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#41	—	2	2	no	—
294	C₂×#41	—	4	2	no	—
295	C₂×#41	—	4	2	no	—
296	C₂×#41	D₄×C₄₃	1	4	yes	complemented
297	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
302	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
306	C₂×SD₁₆	—	2	4	no	—
307	C₂×SD₁₆	—	4	2	no	—
308	C₂×SD₁₆	—	4	2	no	—
309	C₂×D₈	—	2	4	no	—
310	C₂×D₈	—	4	2	no	—
311	C₂×D₈	—	4	2	no	—
312	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
313	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
314	#127	—	4	2	no	—
315	#121	—	2	4	no	—
316	#121	—	2	4	no	—
317	#117	—	4	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	4	2	no	—
320	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
330	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
332	C₄⋊C₈	—	4	2	no	—
333	#103	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	—	4	2	no	—
336	#102	—	4	2	no	—
337	C₂²⋊C₈	—	2	4	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	C₂⁴	—	2	1	no	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
344	#41	—	4	8	no	—
345	#41	—	4	8	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂×D₄	—	8	2	no	—
366	C₂×D₄	—	8	2	no	—
367	C₂×D₄	—	8	2	no	—
368	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	8	2	no	—
380	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
384	C₂²×C₄	#41×C₄₃	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
386	SD₁₆	—	4	8	no	—
387	D₈	—	4	8	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	8	2	no	—
403	C₂²⋊C₄	—	8	2	no	—
404	C₂²⋊C₄	—	8	2	no	—
405	C₂²⋊C₄	—	8	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	#121×C₄₃	1	2	yes	—
425	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
426	Q₈	—	2	4	no	—
427	Q₈	—	4	2	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	8	8	no	—
436	D₄	—	8	8	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	8	4	no	—
459	C₂×C₄	#121×C₄₃	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
462	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
463	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
484	C₂²	C₄₃×#534	1	1	yes	characteristic
485	C₂²	C₄₃×#535	1	1	yes	characteristic
486	C₂²	C₄₃×#576	1	2	yes	—
487	C₂²	C₄₃×#577	1	2	yes	—
488	C₄	—	2	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	1	no	—
493	C₄	—	8	1	no	—
494	C₄	—	8	2	no	—
495	C₄	C₄₃×#534	1	2	yes	—
496	C₄	C₄₃×#538	1	2	yes	—
497	C₂	—	4	2	no	—
498	C₂	—	8	2	no	—
499	C₂	—	16	2	no	—
500	C₂	C₄₃×#2617	1	1	yes	characteristic
501	C₂	C₄₃×#3045	1	2	yes	—
502	C₂	C₄₃×#3198	1	2	yes	—
503	C₂	C₄₃×#3220	1	1	yes	characteristic
504	C₂	C₄₃×#3221	1	1	yes	characteristic

	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 ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#449	C₂	semidirect
2. C₄₃×#2619	C₂	semidirect
3. C₄₃×#2311	C₂	semidirect
4. C₄₃×#2074	C₂	semidirect
5. C₄₃×#2073	C₂	semidirect
6. C₄₃×#2055	C₂	semidirect
7. C₄₃×#2054	C₂	semidirect
8. C₄₃×#2014	C₂	semidirect
9. C₄₃×#2011	C₂	semidirect
10. C₄₃×#1874	C₂	semidirect
11. C₄₃×#1798	C₂	semidirect
43. C₂×#41×C₄₃	D₄	semidirect
213. #29725	C₄₃	direct (N × H)
245. C₂×#449	C₂×C₄₃	semidirect
246. #2619	C₂×C₄₃	semidirect
247. #2311	C₂×C₄₃	semidirect
248. #2074	C₂×C₄₃	semidirect
249. #2073	C₂×C₄₃	semidirect
250. #2055	C₂×C₄₃	semidirect
251. #2054	C₂×C₄₃	semidirect
252. #2014	C₂×C₄₃	semidirect
253. #2011	C₂×C₄₃	semidirect
254. #1874	C₂×C₄₃	semidirect
255. #1798	C₂×C₄₃	semidirect
292. C₄₃	#29725	direct (N × H)
296. C₂×#41	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#449	2
C₄₃×#2619	2
C₄₃×#2311	2
C₄₃×#2074	2
C₄₃×#2073	2
C₄₃×#2055	2
C₄₃×#2054	2
C₄₃×#2014	2
C₄₃×#2011	2
C₄₃×#1874	2
C₄₃×#1798	2
#29725	43

Subgroups — C43×#29725 #24949742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29725 #24949742