Subgroups — C₄₃×#29813 #24949830

Order 11008.

908 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2620	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2055	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2000	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1999	C₂	1	1	yes	maximal, characteristic
10	C₄₃×#1959	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×#121×C₄₃	C₂²	1	2	yes	—
18	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#495	—	2	4	no	—
20	C₄₃×#433	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#396	—	2	2	no	—
32	C₄₃×#396	—	2	2	no	—
33	C₄₃×#394	—	2	2	no	—
34	C₄₃×#394	—	2	2	no	—
35	C₄₃×#391	C₂²	1	2	yes	—
36	C₄₃×#390	C₂²	1	2	yes	—
37	C₄₃×#384	C₂²	1	2	yes	—
38	C₄₃×#340	C₂²	1	1	yes	characteristic
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₄₃	—	2	2	no	—
46	C₂×Q₁₆×C₄₃	—	4	2	no	—
47	C₂×SD₁₆×C₄₃	—	2	4	no	—
48	C₂×SD₁₆×C₄₃	—	4	2	no	—
49	C₂×SD₁₆×C₄₃	—	4	2	no	—
50	C₂×D₈×C₄₃	—	2	2	no	—
51	C₂×D₈×C₄₃	—	4	2	no	—
52	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	#124×C₄₃	—	2	4	no	—
57	#124×C₄₃	—	2	4	no	—
58	C₂²⋊Q₈×C₄₃	—	4	2	no	—
59	C₂²⋊Q₈×C₄₃	—	4	2	no	—
60	#121×C₄₃	—	4	2	no	—
61	#121×C₄₃	—	4	2	no	—
62	#117×C₄₃	—	2	2	no	—
63	#117×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
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	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₃	—	2	2	no	—
82	C₄⋊C₈×C₄₃	—	2	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	2	no	—
88	C₂²⋊C₈×C₄₃	—	2	2	no	—
89	#97×C₄₃	—	2	2	no	—
90	C₄×C₈×C₄₃	D₄	1	4	yes	complemented
91	#95×C₄₃	—	2	2	no	—
92	#95×C₄₃	—	2	2	no	—
93	C₂⁴×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	—	2	2	no	—
100	C₂×Q₈×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	4	no	—
108	C₂×D₄×C₄₃	—	8	2	no	—
109	C₂×D₄×C₄₃	—	8	2	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	1	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	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
123	Q₁₆×C₄₃	—	4	4	no	—
124	SD₁₆×C₄₃	—	4	8	no	—
125	D₈×C₄₃	—	4	4	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	4	4	no	—
141	C₄⋊C₄×C₄₃	—	8	2	no	—
142	C₄⋊C₄×C₄₃	—	8	2	no	—
143	C₂²⋊C₄×C₄₃	—	2	2	no	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₂²⋊C₄×C₄₃	—	4	4	no	—
146	C₂²⋊C₄×C₄₃	—	4	4	no	—
147	C₂²⋊C₄×C₄₃	—	4	4	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₂²⋊C₄×C₄₃	—	8	2	no	—
150	C₂²⋊C₄×C₄₃	—	8	2	no	—
151	C₄²×C₄₃	—	2	1	no	—
152	C₄²×C₄₃	—	2	1	no	—
153	C₄²×C₄₃	C₂×D₄	1	2	yes	—
154	C₄²×C₄₃	#41	1	2	yes	—
155	C₂³×C₄₃	—	2	1	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₄₃	—	4	2	no	—
169	Q₈×C₄₃	—	4	2	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	Q₈×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	4	2	no	—
173	D₄×C₄₃	—	4	2	no	—
174	D₄×C₄₃	—	4	2	no	—
175	D₄×C₄₃	—	4	2	no	—
176	D₄×C₄₃	—	8	8	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	2	1	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	—	4	1	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	2	no	—
196	C₂×C₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	#121	1	2	yes	—
200	C₂×C₄×C₄₃	#121	1	2	yes	—
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
204	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
205	C₈×C₄₃	—	2	2	no	—
206	C₈×C₄₃	—	2	2	no	—
207	C₈×C₄₃	—	4	1	no	—
208	C₈×C₄₃	—	4	1	no	—
209	#29813	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₄₃	—	4	1	no	—
211	C₂²×C₄₃	—	4	2	no	—
212	C₂²×C₄₃	—	4	2	no	—
213	C₂²×C₄₃	—	4	1	no	—
214	C₂²×C₄₃	—	4	1	no	—
215	C₂²×C₄₃	—	8	2	no	—
216	C₂²×C₄₃	—	8	2	no	—
217	C₂²×C₄₃	—	8	2	no	—
218	C₂²×C₄₃	—	8	2	no	—
219	C₂²×C₄₃	—	8	2	no	—
220	C₂²×C₄₃	—	8	2	no	—
221	C₂²×C₄₃	—	8	2	no	—
222	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
223	C₂²×C₄₃	#535	1	2	yes	—
224	C₂²×C₄₃	#576	1	1	yes	characteristic
225	C₂²×C₄₃	#577	1	2	yes	—
226	C₂²×C₄₃	#578	1	1	yes	characteristic
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	2	2	no	—
229	C₄×C₄₃	—	4	1	no	—
230	C₄×C₄₃	—	4	1	no	—
231	C₄×C₄₃	—	4	1	no	—
232	C₄×C₄₃	—	8	2	no	—
233	C₄×C₄₃	—	8	2	no	—
234	C₄×C₄₃	—	8	2	no	—
235	C₄×C₄₃	#535	1	1	yes	characteristic
236	C₄×C₄₃	#535	1	1	yes	characteristic
237	C₄×C₄₃	#540	1	2	yes	—
238	C₂×#495	C₂×C₄₃	1	1	yes	characteristic, complemented
239	C₂×#433	C₂×C₄₃	1	1	yes	characteristic, complemented
240	#2620	C₂×C₄₃	1	2	yes	complemented
241	#2056	C₂×C₄₃	1	1	yes	characteristic, complemented
242	#2055	C₂×C₄₃	1	2	yes	complemented
243	#2054	C₂×C₄₃	1	1	yes	characteristic, complemented
244	#2001	C₂×C₄₃	1	1	yes	characteristic, complemented
245	#2000	C₂×C₄₃	1	2	yes	complemented
246	#1999	C₂×C₄₃	1	1	yes	characteristic
247	#1959	C₂×C₄₃	1	2	yes	complemented
248	#1834	C₂×C₄₃	1	1	yes	characteristic, complemented
249	C₂×C₄₃	—	8	1	no	—
250	C₂×C₄₃	—	16	2	no	—
251	C₂×C₄₃	#2619	1	1	yes	characteristic
252	C₂×C₄₃	#3060	1	1	yes	characteristic
253	C₂×C₄₃	#3061	1	1	yes	characteristic
254	C₂×C₄₃	#3224	1	2	yes	—
255	C₂×C₄₃	#3225	1	2	yes	—
256	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
257	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
258	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
259	C₂×#124	C₂²×C₄₃	1	2	yes	—
260	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
261	C₂×#121	C₂²×C₄₃	1	2	yes	—
262	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
263	#495	—	2	4	no	—
264	#433	—	2	4	no	—
265	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×#103	C₂²×C₄₃	1	2	yes	—
268	C₂×#103	C₂²×C₄₃	1	2	yes	—
269	C₂×#102	C₂²×C₄₃	1	2	yes	—
270	C₂×#102	C₂²×C₄₃	1	2	yes	—
271	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
273	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
275	#396	—	2	2	no	—
276	#396	—	2	2	no	—
277	#394	—	2	2	no	—
278	#394	—	2	2	no	—
279	#391	C₂²×C₄₃	1	2	yes	—
280	#390	C₂²×C₄₃	1	2	yes	—
281	#384	C₂²×C₄₃	1	2	yes	—
282	#340	C₂²×C₄₃	1	1	yes	characteristic
283	#340	C₂²×C₄₃	1	2	yes	—
284	#340	C₂²×C₄₃	1	1	yes	characteristic
285	C₄₃	#29813	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
289	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
290	C₂×Q₁₆	—	2	2	no	—
291	C₂×Q₁₆	—	4	2	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	—	4	2	no	—
294	C₂×SD₁₆	—	4	2	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×D₈	—	4	2	no	—
297	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
301	#124	—	2	4	no	—
302	#124	—	2	4	no	—
303	C₂²⋊Q₈	—	4	2	no	—
304	C₂²⋊Q₈	—	4	2	no	—
305	#121	—	4	2	no	—
306	#121	—	4	2	no	—
307	#117	—	2	2	no	—
308	#117	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
326	C₄⋊C₈	—	2	2	no	—
327	C₄⋊C₈	—	2	2	no	—
328	#103	—	4	2	no	—
329	#103	—	4	2	no	—
330	#102	—	4	2	no	—
331	#102	—	4	2	no	—
332	C₂²⋊C₈	—	2	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	#97	—	2	2	no	—
335	C₄×C₈	D₄×C₄₃	1	4	yes	complemented
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	C₂⁴	—	2	2	no	—
339	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	8	2	no	—
354	C₂×D₄	—	8	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
368	Q₁₆	—	4	4	no	—
369	SD₁₆	—	4	8	no	—
370	D₈	—	4	4	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
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	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	—	8	2	no	—
387	C₄⋊C₄	—	8	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₂²⋊C₄	—	8	2	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	C₂×D₄×C₄₃	1	2	yes	—
399	C₄²	#41×C₄₃	1	2	yes	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	8	8	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	#121×C₄₃	1	2	yes	—
445	C₂×C₄	#121×C₄₃	1	2	yes	—
446	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
448	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
449	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	4	1	no	—
453	C₈	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
467	C₂²	C₄₃×#535	1	2	yes	—
468	C₂²	C₄₃×#576	1	1	yes	characteristic
469	C₂²	C₄₃×#577	1	2	yes	—
470	C₂²	C₄₃×#578	1	1	yes	characteristic
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	8	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	2	no	—
479	C₄	C₄₃×#535	1	1	yes	characteristic
480	C₄	C₄₃×#535	1	1	yes	characteristic
481	C₄	C₄₃×#540	1	2	yes	—
482	C₂	—	8	1	no	—
483	C₂	—	16	2	no	—
484	C₂	C₄₃×#2619	1	1	yes	characteristic
485	C₂	C₄₃×#3060	1	1	yes	characteristic
486	C₂	C₄₃×#3061	1	1	yes	characteristic
487	C₂	C₄₃×#3224	1	2	yes	—
488	C₂	C₄₃×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#1999	C₂
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×#495	C₂	semidirect
2. C₂×C₄₃×#433	C₂	semidirect
3. C₄₃×#2620	C₂	semidirect
4. C₄₃×#2056	C₂	semidirect
5. C₄₃×#2055	C₂	semidirect
6. C₄₃×#2054	C₂	semidirect
7. C₄₃×#2001	C₂	semidirect
8. C₄₃×#2000	C₂	semidirect
10. C₄₃×#1959	C₂	semidirect
11. C₄₃×#1834	C₂	semidirect
90. C₄×C₈×C₄₃	D₄	semidirect
209. #29813	C₄₃	direct (N × H)
238. C₂×#495	C₂×C₄₃	semidirect
239. C₂×#433	C₂×C₄₃	semidirect
240. #2620	C₂×C₄₃	semidirect
241. #2056	C₂×C₄₃	semidirect
242. #2055	C₂×C₄₃	semidirect
243. #2054	C₂×C₄₃	semidirect
244. #2001	C₂×C₄₃	semidirect
245. #2000	C₂×C₄₃	semidirect
247. #1959	C₂×C₄₃	semidirect
248. #1834	C₂×C₄₃	semidirect
285. C₄₃	#29813	direct (N × H)
335. C₄×C₈	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×#495	2
C₂×C₄₃×#433	2
C₄₃×#2620	2
C₄₃×#2056	2
C₄₃×#2055	2
C₄₃×#2054	2
C₄₃×#2001	2
C₄₃×#2000	2
C₄₃×#1999	2
C₄₃×#1959	2
C₄₃×#1834	2
#29813	43

Subgroups — C43×#29813 #24949830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29813 #24949830