Subgroups — C₄₃×#29802 #24949819

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2657	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2041	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2011	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₃	C₂²	1	2	yes	—
17	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#463	—	2	4	no	—
21	C₄₃×#459	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	2	yes	—
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#392	—	2	1	no	—
32	C₄₃×#392	—	2	1	no	—
33	C₄₃×#392	—	2	2	no	—
34	C₄₃×#390	C₂²	1	2	yes	—
35	C₄₃×#389	C₂²	1	2	yes	—
36	C₄₃×#388	—	2	2	no	—
37	C₄₃×#381	—	2	1	no	—
38	C₄₃×#380	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#376	C₂²	1	1	yes	characteristic
41	C₄₃×#336	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
50	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	—	2	1	no	—
52	C₂×SD₁₆×C₄₃	—	2	2	no	—
53	C₂×SD₁₆×C₄₃	—	4	2	no	—
54	C₂×D₈×C₄₃	—	2	4	no	—
55	C₂×D₈×C₄₃	—	2	2	no	—
56	C₂×D₈×C₄₃	—	4	2	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	1	yes	characteristic
61	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
62	#127×C₄₃	—	2	2	no	—
63	#127×C₄₃	—	2	2	no	—
64	#127×C₄₃	—	4	2	no	—
65	#127×C₄₃	—	4	2	no	—
66	#124×C₄₃	—	2	2	no	—
67	#124×C₄₃	—	2	2	no	—
68	#124×C₄₃	—	4	2	no	—
69	#124×C₄₃	—	4	2	no	—
70	C₄×D₄×C₄₃	—	2	2	no	—
71	C₄×D₄×C₄₃	D₄	1	4	yes	complemented
72	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₄²×C₄₃	—	2	1	no	—
83	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₄₃	—	2	2	no	—
86	C₄⋊C₈×C₄₃	—	2	2	no	—
87	#103×C₄₃	—	2	2	no	—
88	#103×C₄₃	—	4	2	no	—
89	#102×C₄₃	—	2	4	no	—
90	#102×C₄₃	—	2	2	no	—
91	#102×C₄₃	—	4	2	no	—
92	#102×C₄₃	—	4	2	no	—
93	#102×C₄₃	—	4	2	no	—
94	#95×C₄₃	—	2	1	no	—
95	#95×C₄₃	—	2	2	no	—
96	#95×C₄₃	D₄	1	1	yes	characteristic
97	#95×C₄₃	D₄	1	1	yes	characteristic
98	#95×C₄₃	D₄	1	2	yes	—
99	C₂⁴×C₄₃	—	2	1	no	—
100	C₂⁴×C₄₃	—	2	1	no	—
101	C₂⁴×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	4	4	no	—
120	C₂×D₄×C₄₃	—	4	4	no	—
121	C₂×D₄×C₄₃	—	4	2	no	—
122	C₂×D₄×C₄₃	—	4	2	no	—
123	C₂×D₄×C₄₃	—	8	1	no	—
124	C₂×D₄×C₄₃	—	8	2	no	—
125	C₂×D₄×C₄₃	—	8	2	no	—
126	C₂×D₄×C₄₃	—	8	2	no	—
127	C₂×D₄×C₄₃	—	8	2	no	—
128	C₂×D₄×C₄₃	—	8	1	no	—
129	C₂×D₄×C₄₃	—	8	2	no	—
130	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₃	—	2	4	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	2	no	—
134	C₂²×C₄×C₄₃	—	2	1	no	—
135	C₂²×C₄×C₄₃	—	8	2	no	—
136	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
141	SD₁₆×C₄₃	—	4	4	no	—
142	D₈×C₄₃	—	4	8	no	—
143	D₈×C₄₃	—	4	4	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	1	no	—
146	C₂×C₈×C₄₃	—	2	1	no	—
147	C₂×C₈×C₄₃	—	2	2	no	—
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₄⋊C₄×C₄₃	—	2	1	no	—
152	C₄⋊C₄×C₄₃	—	2	2	no	—
153	C₄⋊C₄×C₄₃	—	2	2	no	—
154	C₄⋊C₄×C₄₃	—	8	2	no	—
155	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₄₃	—	2	4	no	—
157	C₂²⋊C₄×C₄₃	—	4	4	no	—
158	C₂²⋊C₄×C₄₃	—	4	4	no	—
159	C₂²⋊C₄×C₄₃	—	4	2	no	—
160	C₂²⋊C₄×C₄₃	—	4	2	no	—
161	C₂²⋊C₄×C₄₃	—	8	2	no	—
162	C₂²⋊C₄×C₄₃	—	8	2	no	—
163	C₄²×C₄₃	—	2	2	no	—
164	C₄²×C₄₃	—	2	2	no	—
165	C₄²×C₄₃	—	8	1	no	—
166	C₄²×C₄₃	C₂×D₄	1	2	yes	—
167	C₄²×C₄₃	#41	1	2	yes	—
168	C₂³×C₄₃	—	2	2	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	4	1	no	—
171	C₂³×C₄₃	—	4	2	no	—
172	C₂³×C₄₃	—	4	1	no	—
173	C₂³×C₄₃	—	4	1	no	—
174	C₂³×C₄₃	—	4	2	no	—
175	C₂³×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	—	4	2	no	—
177	C₂³×C₄₃	—	4	2	no	—
178	C₂³×C₄₃	—	4	2	no	—
179	C₂³×C₄₃	—	4	2	no	—
180	C₂³×C₄₃	—	4	1	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	4	1	no	—
185	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₄₃	—	4	1	no	—
187	Q₈×C₄₃	—	4	1	no	—
188	Q₈×C₄₃	—	4	2	no	—
189	D₄×C₄₃	—	2	2	no	—
190	D₄×C₄₃	—	2	2	no	—
191	D₄×C₄₃	—	4	1	no	—
192	D₄×C₄₃	—	4	2	no	—
193	D₄×C₄₃	—	4	1	no	—
194	D₄×C₄₃	—	4	2	no	—
195	D₄×C₄₃	—	4	2	no	—
196	D₄×C₄₃	—	4	2	no	—
197	D₄×C₄₃	—	4	2	no	—
198	D₄×C₄₃	—	4	2	no	—
199	D₄×C₄₃	—	8	4	no	—
200	D₄×C₄₃	—	8	4	no	—
201	D₄×C₄₃	—	8	8	no	—
202	D₄×C₄₃	—	8	8	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	8	4	no	—
220	C₂×C₄×C₄₃	#121	1	2	yes	—
221	C₂×C₄×C₄₃	#121	1	2	yes	—
222	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
225	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
226	C₈×C₄₃	—	4	2	no	—
227	C₈×C₄₃	—	4	1	no	—
228	C₈×C₄₃	—	4	1	no	—
229	#29802	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂²×C₄₃	—	4	2	no	—
231	C₂²×C₄₃	—	4	2	no	—
232	C₂²×C₄₃	—	4	2	no	—
233	C₂²×C₄₃	—	8	2	no	—
234	C₂²×C₄₃	—	8	2	no	—
235	C₂²×C₄₃	—	8	1	no	—
236	C₂²×C₄₃	—	8	2	no	—
237	C₂²×C₄₃	—	8	2	no	—
238	C₂²×C₄₃	—	8	2	no	—
239	C₂²×C₄₃	—	8	2	no	—
240	C₂²×C₄₃	—	8	2	no	—
241	C₂²×C₄₃	—	8	2	no	—
242	C₂²×C₄₃	—	8	2	no	—
243	C₂²×C₄₃	—	8	1	no	—
244	C₂²×C₄₃	—	8	2	no	—
245	C₂²×C₄₃	—	8	1	no	—
246	C₂²×C₄₃	—	8	2	no	—
247	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
248	C₂²×C₄₃	#535	1	2	yes	—
249	C₂²×C₄₃	#576	1	1	yes	characteristic
250	C₂²×C₄₃	#576	1	2	yes	—
251	C₂²×C₄₃	#577	1	1	yes	characteristic
252	C₄×C₄₃	—	2	2	no	—
253	C₄×C₄₃	—	2	2	no	—
254	C₄×C₄₃	—	4	2	no	—
255	C₄×C₄₃	—	4	2	no	—
256	C₄×C₄₃	—	4	2	no	—
257	C₄×C₄₃	—	8	1	no	—
258	C₄×C₄₃	—	8	2	no	—
259	C₄×C₄₃	#535	1	1	yes	characteristic
260	C₄×C₄₃	#535	1	1	yes	characteristic
261	C₄×C₄₃	#540	1	2	yes	—
262	C₂×#463	C₂×C₄₃	1	1	yes	characteristic, complemented
263	C₂×#459	C₂×C₄₃	1	1	yes	characteristic, complemented
264	#2657	C₂×C₄₃	1	1	yes	characteristic, complemented
265	#2319	C₂×C₄₃	1	1	yes	characteristic, complemented
266	#2042	C₂×C₄₃	1	2	yes	complemented
267	#2041	C₂×C₄₃	1	2	yes	complemented
268	#2012	C₂×C₄₃	1	2	yes	complemented
269	#2011	C₂×C₄₃	1	2	yes	complemented
270	#1983	C₂×C₄₃	1	1	yes	characteristic, complemented
271	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
272	#1832	C₂×C₄₃	1	1	yes	characteristic, complemented
273	C₂×C₄₃	—	8	2	no	—
274	C₂×C₄₃	—	16	2	no	—
275	C₂×C₄₃	—	16	1	no	—
276	C₂×C₄₃	#2619	1	1	yes	characteristic
277	C₂×C₄₃	#3041	1	1	yes	characteristic
278	C₂×C₄₃	#3045	1	1	yes	characteristic
279	C₂×C₄₃	#3220	1	2	yes	—
280	C₂×C₄₃	#3224	1	2	yes	—
281	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
282	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
283	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
284	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
285	C₂×#127	C₂²×C₄₃	1	2	yes	—
286	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
287	C₂×#124	C₂²×C₄₃	1	2	yes	—
288	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
289	#463	—	2	4	no	—
290	#459	—	2	4	no	—
291	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
293	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
294	C₂×#103	C₂²×C₄₃	1	2	yes	—
295	C₂×#102	C₂²×C₄₃	1	2	yes	—
296	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×#102	C₂²×C₄₃	1	2	yes	—
298	C₂×#102	C₂²×C₄₃	1	2	yes	—
299	C₂×#102	C₂²×C₄₃	1	2	yes	—
300	#392	—	2	1	no	—
301	#392	—	2	1	no	—
302	#392	—	2	2	no	—
303	#390	C₂²×C₄₃	1	2	yes	—
304	#389	C₂²×C₄₃	1	2	yes	—
305	#388	—	2	2	no	—
306	#381	—	2	1	no	—
307	#380	—	2	1	no	—
308	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
309	#376	C₂²×C₄₃	1	1	yes	characteristic
310	#336	C₂²×C₄₃	1	2	yes	—
311	#336	C₂²×C₄₃	1	2	yes	—
312	C₄₃	#29802	1	1	yes	characteristic, direct product factor, Sylow
313	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
320	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
321	C₂³×C₄	—	2	1	no	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×SD₁₆	—	4	2	no	—
324	C₂×D₈	—	2	4	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	—	4	2	no	—
327	C₂×D₈	—	4	2	no	—
328	C₂×D₈	—	4	2	no	—
329	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
330	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
332	#127	—	2	2	no	—
333	#127	—	2	2	no	—
334	#127	—	4	2	no	—
335	#127	—	4	2	no	—
336	#124	—	2	2	no	—
337	#124	—	2	2	no	—
338	#124	—	4	2	no	—
339	#124	—	4	2	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	D₄×C₄₃	1	4	yes	complemented
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
354	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	2	2	no	—
357	#103	—	2	2	no	—
358	#103	—	4	2	no	—
359	#102	—	2	4	no	—
360	#102	—	2	2	no	—
361	#102	—	4	2	no	—
362	#102	—	4	2	no	—
363	#102	—	4	2	no	—
364	#95	—	2	1	no	—
365	#95	—	2	2	no	—
366	#95	D₄×C₄₃	1	1	yes	characteristic
367	#95	D₄×C₄₃	1	1	yes	characteristic
368	#95	D₄×C₄₃	1	2	yes	—
369	C₂⁴	—	2	1	no	—
370	C₂⁴	—	2	1	no	—
371	C₂⁴	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	8	1	no	—
394	C₂×D₄	—	8	2	no	—
395	C₂×D₄	—	8	1	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂×D₄	—	8	2	no	—
398	C₂×D₄	—	8	2	no	—
399	C₂×D₄	—	8	2	no	—
400	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	8	2	no	—
406	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
411	SD₁₆	—	4	4	no	—
412	D₈	—	4	8	no	—
413	D₈	—	4	4	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	8	2	no	—
425	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	—	4	2	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	8	2	no	—
432	C₂²⋊C₄	—	8	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	8	1	no	—
436	C₄²	C₂×D₄×C₄₃	1	2	yes	—
437	C₄²	#41×C₄₃	1	2	yes	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	2	no	—
455	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	4	1	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	8	4	no	—
470	D₄	—	8	4	no	—
471	D₄	—	8	8	no	—
472	D₄	—	8	8	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	8	4	no	—
490	C₂×C₄	#121×C₄₃	1	2	yes	—
491	C₂×C₄	#121×C₄₃	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
494	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
495	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
496	C₈	—	4	2	no	—
497	C₈	—	4	1	no	—
498	C₈	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	1	no	—
516	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
517	C₂²	C₄₃×#535	1	2	yes	—
518	C₂²	C₄₃×#576	1	1	yes	characteristic
519	C₂²	C₄₃×#576	1	2	yes	—
520	C₂²	C₄₃×#577	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	2	no	—
528	C₄	C₄₃×#535	1	1	yes	characteristic
529	C₄	C₄₃×#535	1	1	yes	characteristic
530	C₄	C₄₃×#540	1	2	yes	—
531	C₂	—	8	2	no	—
532	C₂	—	16	1	no	—
533	C₂	—	16	2	no	—
534	C₂	C₄₃×#2619	1	1	yes	characteristic
535	C₂	C₄₃×#3041	1	1	yes	characteristic
536	C₂	C₄₃×#3045	1	1	yes	characteristic
537	C₂	C₄₃×#3220	1	2	yes	—
538	C₂	C₄₃×#3224	1	2	yes	—

	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 ◁ C₄₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#463	C₂	semidirect
2. C₂×C₄₃×#459	C₂	semidirect
3. C₄₃×#2657	C₂	semidirect
4. C₄₃×#2319	C₂	semidirect
5. C₄₃×#2042	C₂	semidirect
6. C₄₃×#2041	C₂	semidirect
7. C₄₃×#2012	C₂	semidirect
8. C₄₃×#2011	C₂	semidirect
9. C₄₃×#1983	C₂	semidirect
10. C₄₃×#1982	C₂	semidirect
11. C₄₃×#1832	C₂	semidirect
71. C₄×D₄×C₄₃	D₄	semidirect
229. #29802	C₄₃	direct (N × H)
262. C₂×#463	C₂×C₄₃	semidirect
263. C₂×#459	C₂×C₄₃	semidirect
264. #2657	C₂×C₄₃	semidirect
265. #2319	C₂×C₄₃	semidirect
266. #2042	C₂×C₄₃	semidirect
267. #2041	C₂×C₄₃	semidirect
268. #2012	C₂×C₄₃	semidirect
269. #2011	C₂×C₄₃	semidirect
270. #1983	C₂×C₄₃	semidirect
271. #1982	C₂×C₄₃	semidirect
272. #1832	C₂×C₄₃	semidirect
312. C₄₃	#29802	direct (N × H)
341. C₄×D₄	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×#463	2
C₂×C₄₃×#459	2
C₄₃×#2657	2
C₄₃×#2319	2
C₄₃×#2042	2
C₄₃×#2041	2
C₄₃×#2012	2
C₄₃×#2011	2
C₄₃×#1983	2
C₄₃×#1982	2
C₄₃×#1832	2
#29802	43

Subgroups — C43×#29802 #24949819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29802 #24949819