Subgroups — C₄₃×#29855 #24949872

Order 11008.

832 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2629	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2619	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2034	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2033	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#490	—	2	4	no	—
18	C₄₃×#433	—	2	4	no	—
19	C₂×#107×C₄₃	C₂²	1	2	yes	—
20	C₂×#106×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×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×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#398	—	2	2	no	—
30	C₄₃×#396	—	2	2	no	—
31	C₄₃×#394	—	2	2	no	—
32	C₄₃×#392	—	2	2	no	—
33	C₄₃×#390	C₂²	1	1	yes	characteristic
34	C₄₃×#390	C₂²	1	1	yes	characteristic
35	C₄₃×#389	C₂²	1	2	yes	—
36	C₄₃×#384	C₂²	1	1	yes	characteristic
37	C₄₃×#382	C₂²	1	1	yes	characteristic
38	C₄₃×#380	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₂²×D₄×C₄₃	—	2	1	no	—
42	C₂²×D₄×C₄₃	—	2	1	no	—
43	C₂²×D₄×C₄₃	—	2	2	no	—
44	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
49	#127×C₄₃	—	2	2	no	—
50	#127×C₄₃	—	2	2	no	—
51	#125×C₄₃	—	2	2	no	—
52	#125×C₄₃	—	2	2	no	—
53	#121×C₄₃	—	4	2	no	—
54	#121×C₄₃	—	4	2	no	—
55	#117×C₄₃	—	2	2	no	—
56	#117×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
71	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	#107×C₄₃	—	4	2	no	—
74	#106×C₄₃	—	4	2	no	—
75	C₄⋊C₈×C₄₃	—	2	4	no	—
76	#102×C₄₃	—	2	4	no	—
77	#102×C₄₃	—	2	4	no	—
78	#102×C₄₃	—	4	2	no	—
79	#102×C₄₃	—	4	2	no	—
80	C₂²⋊C₈×C₄₃	—	2	4	no	—
81	#97×C₄₃	D₄	1	4	yes	complemented
82	C₄×C₈×C₄₃	—	2	2	no	—
83	#95×C₄₃	—	2	2	no	—
84	#95×C₄₃	—	2	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	C₂⁴×C₄₃	—	2	1	no	—
87	C₂⁴×C₄₃	—	2	1	no	—
88	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₄₃	—	2	1	no	—
90	C₂×D₄×C₄₃	—	2	1	no	—
91	C₂×D₄×C₄₃	—	2	1	no	—
92	C₂×D₄×C₄₃	—	2	1	no	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	2	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	4	2	no	—
98	C₂×D₄×C₄₃	—	4	2	no	—
99	C₂×D₄×C₄₃	—	4	4	no	—
100	C₂×D₄×C₄₃	—	8	2	no	—
101	C₂×D₄×C₄₃	—	8	2	no	—
102	C₂×D₄×C₄₃	—	8	2	no	—
103	C₂×D₄×C₄₃	—	8	2	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	—	2	1	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
122	C₄⋊C₄×C₄₃	—	2	4	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	4	4	no	—
130	C₄⋊C₄×C₄₃	—	8	2	no	—
131	C₄⋊C₄×C₄₃	—	8	2	no	—
132	C₂²⋊C₄×C₄₃	—	2	4	no	—
133	C₂²⋊C₄×C₄₃	—	4	2	no	—
134	C₂²⋊C₄×C₄₃	—	4	2	no	—
135	C₂²⋊C₄×C₄₃	—	8	2	no	—
136	C₂²⋊C₄×C₄₃	—	8	2	no	—
137	C₂²⋊C₄×C₄₃	—	8	2	no	—
138	C₄²×C₄₃	—	2	1	no	—
139	C₄²×C₄₃	—	2	1	no	—
140	C₄²×C₄₃	C₂×D₄	1	2	yes	—
141	C₄²×C₄₃	#41	1	2	yes	—
142	C₂³×C₄₃	—	2	1	no	—
143	C₂³×C₄₃	—	2	1	no	—
144	C₂³×C₄₃	—	2	1	no	—
145	C₂³×C₄₃	—	2	2	no	—
146	C₂³×C₄₃	—	2	2	no	—
147	C₂³×C₄₃	—	4	1	no	—
148	C₂³×C₄₃	—	4	1	no	—
149	C₂³×C₄₃	—	4	1	no	—
150	C₂³×C₄₃	—	4	1	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	—	4	1	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	—	4	2	no	—
155	C₂³×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	—	4	2	no	—
157	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
158	D₄×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	4	2	no	—
160	D₄×C₄₃	—	4	2	no	—
161	D₄×C₄₃	—	4	2	no	—
162	D₄×C₄₃	—	8	8	no	—
163	D₄×C₄₃	—	8	4	no	—
164	D₄×C₄₃	—	8	4	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	1	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	#121	1	4	yes	—
186	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
189	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
190	C₈×C₄₃	—	2	4	no	—
191	C₈×C₄₃	—	4	2	no	—
192	#29855	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₄₃	—	4	1	no	—
194	C₂²×C₄₃	—	4	1	no	—
195	C₂²×C₄₃	—	4	1	no	—
196	C₂²×C₄₃	—	4	2	no	—
197	C₂²×C₄₃	—	4	2	no	—
198	C₂²×C₄₃	—	8	1	no	—
199	C₂²×C₄₃	—	8	1	no	—
200	C₂²×C₄₃	—	8	1	no	—
201	C₂²×C₄₃	—	8	1	no	—
202	C₂²×C₄₃	—	8	1	no	—
203	C₂²×C₄₃	—	8	1	no	—
204	C₂²×C₄₃	—	8	2	no	—
205	C₂²×C₄₃	—	8	2	no	—
206	C₂²×C₄₃	—	8	2	no	—
207	C₂²×C₄₃	—	8	2	no	—
208	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
209	C₂²×C₄₃	#535	1	1	yes	characteristic
210	C₂²×C₄₃	#536	1	1	yes	characteristic
211	C₂²×C₄₃	#576	1	2	yes	—
212	C₂²×C₄₃	#577	1	2	yes	—
213	C₄×C₄₃	—	2	4	no	—
214	C₄×C₄₃	—	4	1	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	8	2	no	—
217	C₄×C₄₃	—	8	1	no	—
218	C₄×C₄₃	—	8	1	no	—
219	C₄×C₄₃	—	8	2	no	—
220	C₄×C₄₃	#537	1	2	yes	—
221	C₄×C₄₃	#542	1	2	yes	—
222	C₂×#490	C₂×C₄₃	1	1	yes	characteristic, complemented
223	C₂×#433	C₂×C₄₃	1	1	yes	characteristic, complemented
224	#2629	C₂×C₄₃	1	1	yes	characteristic, complemented
225	#2619	C₂×C₄₃	1	1	yes	characteristic
226	#2067	C₂×C₄₃	1	2	yes	complemented
227	#2065	C₂×C₄₃	1	2	yes	complemented
228	#2034	C₂×C₄₃	1	2	yes	complemented
229	#2033	C₂×C₄₃	1	2	yes	complemented
230	#1991	C₂×C₄₃	1	1	yes	characteristic, complemented
231	#1957	C₂×C₄₃	1	1	yes	characteristic, complemented
232	#1847	C₂×C₄₃	1	1	yes	characteristic, complemented
233	C₂×C₄₃	—	8	1	no	—
234	C₂×C₄₃	—	16	1	no	—
235	C₂×C₄₃	—	16	1	no	—
236	C₂×C₄₃	#2620	1	1	yes	characteristic
237	C₂×C₄₃	#3062	1	2	yes	—
238	C₂×C₄₃	#3220	1	1	yes	characteristic
239	C₂×C₄₃	#3222	1	1	yes	characteristic
240	C₂×C₄₃	#3241	1	2	yes	—
241	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
242	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
243	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
244	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
245	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
246	#490	—	2	4	no	—
247	#433	—	2	4	no	—
248	C₂×#107	C₂²×C₄₃	1	2	yes	—
249	C₂×#106	C₂²×C₄₃	1	2	yes	—
250	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
251	C₂×#102	C₂²×C₄₃	1	2	yes	—
252	C₂×#102	C₂²×C₄₃	1	2	yes	—
253	C₂×#102	C₂²×C₄₃	1	2	yes	—
254	C₂×#102	C₂²×C₄₃	1	2	yes	—
255	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
256	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
258	#398	—	2	2	no	—
259	#396	—	2	2	no	—
260	#394	—	2	2	no	—
261	#392	—	2	2	no	—
262	#390	C₂²×C₄₃	1	1	yes	characteristic
263	#390	C₂²×C₄₃	1	1	yes	characteristic
264	#389	C₂²×C₄₃	1	2	yes	—
265	#384	C₂²×C₄₃	1	1	yes	characteristic
266	#382	C₂²×C₄₃	1	1	yes	characteristic
267	#380	C₂²×C₄₃	1	2	yes	—
268	#340	C₂²×C₄₃	1	2	yes	—
269	#340	C₂²×C₄₃	1	2	yes	—
270	C₄₃	#29855	1	1	yes	characteristic, direct product factor, Sylow
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
275	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
279	#127	—	2	2	no	—
280	#127	—	2	2	no	—
281	#125	—	2	2	no	—
282	#125	—	2	2	no	—
283	#121	—	4	2	no	—
284	#121	—	4	2	no	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
301	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
303	#107	—	4	2	no	—
304	#106	—	4	2	no	—
305	C₄⋊C₈	—	2	4	no	—
306	#102	—	2	4	no	—
307	#102	—	2	4	no	—
308	#102	—	4	2	no	—
309	#102	—	4	2	no	—
310	C₂²⋊C₈	—	2	4	no	—
311	#97	D₄×C₄₃	1	4	yes	complemented
312	C₄×C₈	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	C₂⁴	—	2	1	no	—
317	C₂⁴	—	2	1	no	—
318	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	8	2	no	—
331	C₂×D₄	—	8	2	no	—
332	C₂×D₄	—	8	2	no	—
333	C₂×D₄	—	8	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	8	2	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂×D₄×C₄₃	1	2	yes	—
371	C₄²	#41×C₄₃	1	2	yes	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	8	no	—
393	D₄	—	8	4	no	—
394	D₄	—	8	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	#121×C₄₃	1	4	yes	—
416	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
418	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
419	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
420	C₈	—	2	4	no	—
421	C₈	—	4	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
438	C₂²	C₄₃×#535	1	1	yes	characteristic
439	C₂²	C₄₃×#536	1	1	yes	characteristic
440	C₂²	C₄₃×#576	1	2	yes	—
441	C₂²	C₄₃×#577	1	2	yes	—
442	C₄	—	2	4	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	2	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	2	no	—
449	C₄	C₄₃×#537	1	2	yes	—
450	C₄	C₄₃×#542	1	2	yes	—
451	C₂	—	8	1	no	—
452	C₂	—	16	1	no	—
453	C₂	—	16	1	no	—
454	C₂	C₄₃×#2620	1	1	yes	characteristic
455	C₂	C₄₃×#3062	1	2	yes	—
456	C₂	C₄₃×#3220	1	1	yes	characteristic
457	C₂	C₄₃×#3222	1	1	yes	characteristic
458	C₂	C₄₃×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2619	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×#490	C₂	semidirect
2. C₂×C₄₃×#433	C₂	semidirect
3. C₄₃×#2629	C₂	semidirect
5. C₄₃×#2067	C₂	semidirect
6. C₄₃×#2065	C₂	semidirect
7. C₄₃×#2034	C₂	semidirect
8. C₄₃×#2033	C₂	semidirect
9. C₄₃×#1991	C₂	semidirect
10. C₄₃×#1957	C₂	semidirect
11. C₄₃×#1847	C₂	semidirect
81. #97×C₄₃	D₄	semidirect
192. #29855	C₄₃	direct (N × H)
222. C₂×#490	C₂×C₄₃	semidirect
223. C₂×#433	C₂×C₄₃	semidirect
224. #2629	C₂×C₄₃	semidirect
226. #2067	C₂×C₄₃	semidirect
227. #2065	C₂×C₄₃	semidirect
228. #2034	C₂×C₄₃	semidirect
229. #2033	C₂×C₄₃	semidirect
230. #1991	C₂×C₄₃	semidirect
231. #1957	C₂×C₄₃	semidirect
232. #1847	C₂×C₄₃	semidirect
270. C₄₃	#29855	direct (N × H)
311. #97	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×#490	2
C₂×C₄₃×#433	2
C₄₃×#2629	2
C₄₃×#2619	2
C₄₃×#2067	2
C₄₃×#2065	2
C₄₃×#2034	2
C₄₃×#2033	2
C₄₃×#1991	2
C₄₃×#1957	2
C₄₃×#1847	2
#29855	43

Subgroups — C43×#29855 #24949872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29855 #24949872