Subgroups — C₄₃×#29955 #24949972

Order 11008.

912 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2068	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1854	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1788	C₂	1	2	yes	maximal
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
15	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#107×C₄₃	C₂²	1	2	yes	—
18	C₂×#106×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
20	C₂×#103×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×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
25	C₄₃×#391	—	2	1	no	—
26	C₄₃×#391	C₂²	1	1	yes	characteristic
27	C₄₃×#391	C₂²	1	1	yes	characteristic
28	C₄₃×#390	C₂²	1	1	yes	characteristic
29	C₄₃×#390	C₂²	1	1	yes	characteristic
30	C₄₃×#389	—	2	1	no	—
31	C₄₃×#389	C₂²	1	2	yes	—
32	C₄₃×#386	—	2	1	no	—
33	C₄₃×#386	—	2	1	no	—
34	C₄₃×#384	C₂²	1	1	yes	characteristic
35	C₄₃×#380	—	2	1	no	—
36	C₄₃×#380	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#336	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	1	yes	characteristic
43	C₂×#41×C₄₃	—	2	2	no	—
44	C₂×#41×C₄₃	—	4	2	no	—
45	C₂×#41×C₄₃	—	4	2	no	—
46	C₂×#41×C₄₃	Q₈	1	4	yes	complemented
47	C₂²×Q₈×C₄₃	—	2	1	no	—
48	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₃	—	2	1	no	—
50	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	—	2	1	no	—
52	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₄₃	—	4	2	no	—
58	C₂²⋊Q₈×C₄₃	—	4	4	no	—
59	#117×C₄₃	—	4	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
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×C₄²×C₄₃	—	2	1	no	—
75	C₂×C₄²×C₄₃	—	4	2	no	—
76	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	#107×C₄₃	—	4	2	no	—
81	#106×C₄₃	—	4	2	no	—
82	C₄⋊C₈×C₄₃	—	4	2	no	—
83	#103×C₄₃	—	4	2	no	—
84	#103×C₄₃	—	4	2	no	—
85	#102×C₄₃	—	4	2	no	—
86	#102×C₄₃	—	4	2	no	—
87	C₂²⋊C₈×C₄₃	—	2	4	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	—	2	1	no	—
90	#95×C₄₃	—	2	1	no	—
91	#95×C₄₃	—	2	1	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	#41×C₄₃	—	4	8	no	—
97	#41×C₄₃	—	4	8	no	—
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	2	2	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	—	4	2	no	—
102	C₂×Q₈×C₄₃	—	4	2	no	—
103	C₂×Q₈×C₄₃	—	4	2	no	—
104	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
105	C₂×D₄×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	4	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	4	2	no	—
110	C₂×D₄×C₄₃	—	4	2	no	—
111	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
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	2	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	1	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	4	1	no	—
124	C₂²×C₄×C₄₃	—	4	1	no	—
125	C₂²×C₄×C₄₃	—	4	1	no	—
126	C₂²×C₄×C₄₃	—	4	2	no	—
127	C₂²×C₄×C₄₃	—	4	2	no	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
134	C₂²×C₄×C₄₃	#41	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×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	—	2	2	no	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	2	no	—
148	C₄⋊C₄×C₄₃	—	4	4	no	—
149	C₄⋊C₄×C₄₃	—	4	2	no	—
150	C₄⋊C₄×C₄₃	—	4	2	no	—
151	C₄⋊C₄×C₄₃	—	4	2	no	—
152	C₂²⋊C₄×C₄₃	—	4	2	no	—
153	C₂²⋊C₄×C₄₃	—	4	4	no	—
154	C₂²⋊C₄×C₄₃	—	4	2	no	—
155	C₂²⋊C₄×C₄₃	—	4	2	no	—
156	C₂²⋊C₄×C₄₃	—	4	2	no	—
157	C₂²⋊C₄×C₄₃	—	4	2	no	—
158	C₄²×C₄₃	—	2	2	no	—
159	C₄²×C₄₃	—	2	2	no	—
160	C₄²×C₄₃	—	4	1	no	—
161	C₄²×C₄₃	—	4	1	no	—
162	C₄²×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	—	2	1	no	—
164	C₂³×C₄₃	—	2	1	no	—
165	C₂³×C₄₃	—	2	1	no	—
166	C₂³×C₄₃	—	2	1	no	—
167	C₂³×C₄₃	—	2	1	no	—
168	C₂³×C₄₃	—	2	1	no	—
169	C₂³×C₄₃	—	2	2	no	—
170	C₂³×C₄₃	—	4	1	no	—
171	C₂³×C₄₃	—	4	1	no	—
172	C₂³×C₄₃	—	4	1	no	—
173	C₂³×C₄₃	—	4	1	no	—
174	C₂³×C₄₃	—	4	1	no	—
175	C₂³×C₄₃	—	4	1	no	—
176	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
177	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₄₃	—	2	4	no	—
179	Q₈×C₄₃	—	4	2	no	—
180	Q₈×C₄₃	—	8	4	no	—
181	D₄×C₄₃	—	2	4	no	—
182	D₄×C₄₃	—	4	8	no	—
183	D₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	4	no	—
193	C₂×C₄×C₄₃	—	2	4	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	4	4	no	—
199	C₂×C₄×C₄₃	—	4	4	no	—
200	C₂×C₄×C₄₃	—	4	8	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	—	4	1	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
216	C₂×C₄×C₄₃	#135	1	2	yes	—
217	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₄₃	#137	1	2	yes	—
219	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
222	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
223	C₈×C₄₃	—	4	2	no	—
224	C₈×C₄₃	—	4	2	no	—
225	#29955	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂²×C₄₃	—	2	2	no	—
227	C₂²×C₄₃	—	2	2	no	—
228	C₂²×C₄₃	—	2	2	no	—
229	C₂²×C₄₃	—	4	1	no	—
230	C₂²×C₄₃	—	4	1	no	—
231	C₂²×C₄₃	—	4	1	no	—
232	C₂²×C₄₃	—	4	1	no	—
233	C₂²×C₄₃	—	4	2	no	—
234	C₂²×C₄₃	—	4	2	no	—
235	C₂²×C₄₃	—	4	2	no	—
236	C₂²×C₄₃	—	8	1	no	—
237	C₂²×C₄₃	—	8	1	no	—
238	C₂²×C₄₃	—	8	1	no	—
239	C₂²×C₄₃	—	8	1	no	—
240	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
241	C₂²×C₄₃	#534	1	1	yes	characteristic
242	C₂²×C₄₃	#535	1	1	yes	characteristic
243	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
244	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
246	C₂²×C₄₃	#575	1	1	yes	characteristic
247	C₄×C₄₃	—	2	2	no	—
248	C₄×C₄₃	—	2	2	no	—
249	C₄×C₄₃	—	2	2	no	—
250	C₄×C₄₃	—	2	2	no	—
251	C₄×C₄₃	—	4	2	no	—
252	C₄×C₄₃	—	4	1	no	—
253	C₄×C₄₃	—	8	2	no	—
254	C₄×C₄₃	—	8	1	no	—
255	C₄×C₄₃	—	8	2	no	—
256	C₄×C₄₃	—	8	1	no	—
257	C₄×C₄₃	#538	1	2	yes	—
258	C₄×C₄₃	#543	1	2	yes	—
259	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
260	#2297	C₂×C₄₃	1	1	yes	characteristic
261	#2096	C₂×C₄₃	1	1	yes	characteristic, complemented
262	#2093	C₂×C₄₃	1	1	yes	characteristic, complemented
263	#2068	C₂×C₄₃	1	2	yes	complemented
264	#2065	C₂×C₄₃	1	2	yes	complemented
265	#2024	C₂×C₄₃	1	1	yes	characteristic, complemented
266	#2023	C₂×C₄₃	1	1	yes	characteristic, complemented
267	#1854	C₂×C₄₃	1	2	yes	complemented
268	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
269	#1788	C₂×C₄₃	1	2	yes	—
270	C₂×C₄₃	—	4	2	no	—
271	C₂×C₄₃	—	8	2	no	—
272	C₂×C₄₃	#2626	1	1	yes	characteristic
273	C₂×C₄₃	#3076	1	1	yes	characteristic
274	C₂×C₄₃	#3079	1	1	yes	characteristic
275	C₂×C₄₃	#3190	1	1	yes	characteristic
276	C₂×C₄₃	#3194	1	1	yes	characteristic
277	C₂×C₄₃	#3207	1	1	yes	characteristic
278	C₂×C₄₃	#3216	1	1	yes	characteristic
279	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
281	C₂×C₂²⋊Q₈	—	2	1	no	—
282	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
283	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
284	C₂×#107	C₂²×C₄₃	1	2	yes	—
285	C₂×#106	C₂²×C₄₃	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
287	C₂×#103	C₂²×C₄₃	1	2	yes	—
288	C₂×#103	C₂²×C₄₃	1	2	yes	—
289	C₂×#102	C₂²×C₄₃	1	2	yes	—
290	C₂×#102	C₂²×C₄₃	1	2	yes	—
291	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
292	#391	—	2	1	no	—
293	#391	C₂²×C₄₃	1	1	yes	characteristic
294	#391	C₂²×C₄₃	1	1	yes	characteristic
295	#390	C₂²×C₄₃	1	1	yes	characteristic
296	#390	C₂²×C₄₃	1	1	yes	characteristic
297	#389	—	2	1	no	—
298	#389	C₂²×C₄₃	1	2	yes	—
299	#386	—	2	1	no	—
300	#386	—	2	1	no	—
301	#384	C₂²×C₄₃	1	1	yes	characteristic
302	#380	—	2	1	no	—
303	#380	C₂²×C₄₃	1	2	yes	—
304	C₄×C₂²⋊C₄	—	2	1	no	—
305	C₄×C₂²⋊C₄	—	2	1	no	—
306	#340	C₂²×C₄₃	1	2	yes	—
307	#340	C₂²×C₄₃	1	2	yes	—
308	#336	C₂²×C₄₃	1	1	yes	characteristic
309	#336	C₂²×C₄₃	1	1	yes	characteristic
310	C₄₃	#29955	1	1	yes	characteristic, direct product factor, Sylow
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	4	2	no	—
313	C₂×#41	—	4	2	no	—
314	C₂×#41	Q₈×C₄₃	1	4	yes	complemented
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
321	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
324	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
325	C₄⋊Q₈	—	4	2	no	—
326	C₂²⋊Q₈	—	4	4	no	—
327	#117	—	4	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	4	2	no	—
344	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
345	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
348	#107	—	4	2	no	—
349	#106	—	4	2	no	—
350	C₄⋊C₈	—	4	2	no	—
351	#103	—	4	2	no	—
352	#103	—	4	2	no	—
353	#102	—	4	2	no	—
354	#102	—	4	2	no	—
355	C₂²⋊C₈	—	2	4	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	—	2	2	no	—
361	#95	—	2	2	no	—
362	C₂⁴	—	2	1	no	—
363	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
364	#41	—	4	8	no	—
365	#41	—	4	8	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	C₂×Q₈×C₄₃	1	2	yes	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
402	C₂²×C₄	#41×C₄₃	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	2	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	4	1	no	—
429	C₄²	—	4	1	no	—
430	C₄²	—	4	2	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	C₂²⋊Q₈×C₄₃	1	2	yes	—
445	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
446	Q₈	—	2	4	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	8	4	no	—
449	D₄	—	2	4	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
484	C₂×C₄	#135×C₄₃	1	2	yes	—
485	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
486	C₂×C₄	#137×C₄₃	1	2	yes	—
487	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
489	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
490	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
491	C₈	—	4	2	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
508	C₂²	C₄₃×#534	1	1	yes	characteristic
509	C₂²	C₄₃×#535	1	1	yes	characteristic
510	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
511	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
512	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
513	C₂²	C₄₃×#575	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	8	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	2	no	—
523	C₄	—	8	1	no	—
524	C₄	C₄₃×#538	1	2	yes	—
525	C₄	C₄₃×#543	1	2	yes	—
526	C₂	—	4	2	no	—
527	C₂	—	8	2	no	—
528	C₂	C₄₃×#2626	1	1	yes	characteristic
529	C₂	C₄₃×#3076	1	1	yes	characteristic
530	C₂	C₄₃×#3079	1	1	yes	characteristic
531	C₂	C₄₃×#3190	1	1	yes	characteristic
532	C₂	C₄₃×#3194	1	1	yes	characteristic
533	C₂	C₄₃×#3207	1	1	yes	characteristic
534	C₂	C₄₃×#3216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×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
1. C₄₃×#2857	C₂	semidirect
3. C₄₃×#2096	C₂	semidirect
4. C₄₃×#2093	C₂	semidirect
5. C₄₃×#2068	C₂	semidirect
6. C₄₃×#2065	C₂	semidirect
7. C₄₃×#2024	C₂	semidirect
8. C₄₃×#2023	C₂	semidirect
9. C₄₃×#1854	C₂	semidirect
10. C₄₃×#1797	C₂	semidirect
46. C₂×#41×C₄₃	Q₈	semidirect
225. #29955	C₄₃	direct (N × H)
259. #2857	C₂×C₄₃	semidirect
261. #2096	C₂×C₄₃	semidirect
262. #2093	C₂×C₄₃	semidirect
263. #2068	C₂×C₄₃	semidirect
264. #2065	C₂×C₄₃	semidirect
265. #2024	C₂×C₄₃	semidirect
266. #2023	C₂×C₄₃	semidirect
267. #1854	C₂×C₄₃	semidirect
268. #1797	C₂×C₄₃	semidirect
310. C₄₃	#29955	direct (N × H)
314. C₂×#41	Q₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#2857	2
C₄₃×#2297	2
C₄₃×#2096	2
C₄₃×#2093	2
C₄₃×#2068	2
C₄₃×#2065	2
C₄₃×#2024	2
C₄₃×#2023	2
C₄₃×#1854	2
C₄₃×#1797	2
C₄₃×#1788	2
#29955	43

Subgroups — C43×#29955 #24949972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29955 #24949972