Subgroups — C₄₃×#29647 #24949664

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#481	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#482	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2624	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2059	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2058	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2025	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2023	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃×#544	—	2	4	no	—
13	C₄₃×#544	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
16	C₂×#125×C₄₃	—	2	1	no	—
17	C₂×#125×C₄₃	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₄₃	—	2	2	no	—
19	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#482	—	2	4	no	—
24	C₄₃×#481	—	2	4	no	—
25	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#106×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#399	—	2	1	no	—
34	C₄₃×#397	—	2	1	no	—
35	C₄₃×#394	—	2	2	no	—
36	C₄₃×#390	C₂²	1	2	yes	—
37	C₄₃×#389	C₂²	1	2	yes	—
38	C₄₃×#380	C₂²	1	1	yes	characteristic
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₄₃×#336	C₂²	1	2	yes	—
44	C₄₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	—	2	1	no	—
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₃	—	2	8	no	—
54	C₄⋊Q₈×C₄₃	—	2	4	no	—
55	C₄⋊Q₈×C₄₃	—	2	4	no	—
56	#125×C₄₃	—	2	8	no	—
57	#125×C₄₃	—	2	4	no	—
58	#125×C₄₃	—	2	4	no	—
59	C₂²⋊Q₈×C₄₃	—	2	16	no	—
60	#121×C₄₃	—	2	2	no	—
61	#121×C₄₃	—	2	2	no	—
62	#117×C₄₃	—	2	2	no	—
63	#117×C₄₃	—	2	2	no	—
64	#117×C₄₃	—	2	2	no	—
65	#117×C₄₃	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
86	C₂×C₄²×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
88	#107×C₄₃	—	2	2	no	—
89	#106×C₄₃	—	2	4	no	—
90	#106×C₄₃	—	2	2	no	—
91	#102×C₄₃	—	2	4	no	—
92	#102×C₄₃	—	2	2	no	—
93	#102×C₄₃	—	2	2	no	—
94	C₂²⋊C₈×C₄₃	—	2	2	no	—
95	C₂²⋊C₈×C₄₃	—	2	2	no	—
96	#95×C₄₃	—	2	1	no	—
97	#95×C₄₃	—	2	2	no	—
98	C₂⁴×C₄₃	—	2	1	no	—
99	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₄₃	—	2	8	no	—
101	C₂×Q₈×C₄₃	—	8	2	no	—
102	C₂×Q₈×C₄₃	—	8	2	no	—
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	1	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	—	8	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	4	no	—
112	C₂²×C₄×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	8	1	no	—
118	C₂²×C₄×C₄₃	—	8	1	no	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	8	no	—
133	C₄⋊C₄×C₄₃	—	2	8	no	—
134	C₄⋊C₄×C₄₃	—	2	8	no	—
135	C₄⋊C₄×C₄₃	—	2	4	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	1	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	8	2	no	—
146	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
147	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₄₃	—	2	4	no	—
150	C₂²⋊C₄×C₄₃	—	2	4	no	—
151	C₂²⋊C₄×C₄₃	—	4	2	no	—
152	C₂²⋊C₄×C₄₃	—	8	1	no	—
153	C₂²⋊C₄×C₄₃	—	8	2	no	—
154	C₂²⋊C₄×C₄₃	—	8	2	no	—
155	C₄²×C₄₃	—	2	4	no	—
156	C₄²×C₄₃	—	2	2	no	—
157	C₄²×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	—	2	2	no	—
162	C₂³×C₄₃	—	4	1	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	1	no	—
165	C₂³×C₄₃	—	4	2	no	—
166	C₂³×C₄₃	—	4	1	no	—
167	C₂³×C₄₃	#120	1	2	yes	—
168	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₄₃	—	8	8	no	—
170	D₄×C₄₃	—	4	2	no	—
171	D₄×C₄₃	—	4	1	no	—
172	D₄×C₄₃	—	4	1	no	—
173	D₄×C₄₃	—	8	4	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	4	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	4	2	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	1	no	—
192	C₂×C₄×C₄₃	—	4	1	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	—	8	4	no	—
198	C₂×C₄×C₄₃	#120	1	2	yes	—
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
202	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
203	C₈×C₄₃	—	4	2	no	—
204	C₈×C₄₃	—	4	1	no	—
205	C₈×C₄₃	—	4	1	no	—
206	#29647	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	—	2	2	no	—
210	C₂²×C₄₃	—	4	2	no	—
211	C₂²×C₄₃	—	4	2	no	—
212	C₂²×C₄₃	—	8	1	no	—
213	C₂²×C₄₃	—	8	2	no	—
214	C₂²×C₄₃	—	8	2	no	—
215	C₂²×C₄₃	—	8	1	no	—
216	C₂²×C₄₃	—	8	1	no	—
217	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
218	C₂²×C₄₃	#536	1	2	yes	—
219	C₂²×C₄₃	#576	1	1	yes	characteristic
220	C₂²×C₄₃	#577	1	2	yes	—
221	C₂²×C₄₃	#577	1	1	yes	characteristic
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	4	2	no	—
224	C₄×C₄₃	—	4	2	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	4	4	no	—
227	C₄×C₄₃	—	4	2	no	—
228	C₄×C₄₃	—	8	2	no	—
229	C₄×C₄₃	—	8	1	no	—
230	C₄×C₄₃	#536	1	1	yes	characteristic
231	C₄×C₄₃	#536	1	2	yes	—
232	C₄×C₄₃	#536	1	1	yes	characteristic
233	C₂×#544	C₂×C₄₃	1	1	yes	characteristic, complemented
234	C₂×#481	C₂×C₄₃	1	1	yes	characteristic
235	C₂×#482	C₂×C₄₃	1	1	yes	characteristic
236	#2624	C₂×C₄₃	1	1	yes	characteristic
237	#2059	C₂×C₄₃	1	2	yes	complemented
238	#2058	C₂×C₄₃	1	2	yes	complemented
239	#2025	C₂×C₄₃	1	2	yes	complemented
240	#2023	C₂×C₄₃	1	2	yes	complemented
241	#1825	C₂×C₄₃	1	1	yes	characteristic, complemented
242	#1823	C₂×C₄₃	1	1	yes	characteristic, complemented
243	#1818	C₂×C₄₃	1	1	yes	characteristic, complemented
244	C₂×C₄₃	—	4	2	no	—
245	C₂×C₄₃	—	16	1	no	—
246	C₂×C₄₃	#2614	1	1	yes	characteristic
247	C₂×C₄₃	#3010	1	1	yes	characteristic
248	C₂×C₄₃	#3012	1	1	yes	characteristic
249	C₂×C₄₃	#3241	1	2	yes	—
250	C₂×C₄₃	#3244	1	2	yes	—
251	#544	—	2	4	no	—
252	#544	—	2	4	no	—
253	C₂×C₄⋊Q₈	—	2	1	no	—
254	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
255	C₂×#125	—	2	1	no	—
256	C₂×#125	C₂²×C₄₃	1	2	yes	—
257	C₂×C₂²⋊Q₈	—	2	2	no	—
258	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
259	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
262	#482	—	2	4	no	—
263	#481	—	2	4	no	—
264	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
265	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×#106	C₂²×C₄₃	1	2	yes	—
267	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
268	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
269	C₂×#102	C₂²×C₄₃	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
272	#399	—	2	1	no	—
273	#397	—	2	1	no	—
274	#394	—	2	2	no	—
275	#390	C₂²×C₄₃	1	2	yes	—
276	#389	C₂²×C₄₃	1	2	yes	—
277	#380	C₂²×C₄₃	1	1	yes	characteristic
278	#340	C₂²×C₄₃	1	2	yes	—
279	#340	C₂²×C₄₃	1	2	yes	—
280	#340	C₂²×C₄₃	1	2	yes	—
281	#340	C₂²×C₄₃	1	2	yes	—
282	#336	C₂²×C₄₃	1	2	yes	—
283	#336	C₂²×C₄₃	1	2	yes	—
284	C₄₃	#29647	1	1	yes	characteristic, direct product factor, Sylow
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
292	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
293	C₄⋊Q₈	—	2	8	no	—
294	C₄⋊Q₈	—	2	4	no	—
295	C₄⋊Q₈	—	2	4	no	—
296	#125	—	2	8	no	—
297	#125	—	2	4	no	—
298	#125	—	2	4	no	—
299	C₂²⋊Q₈	—	2	16	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	D₄×C₄₃	1	4	yes	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	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	D₄×C₄₃	1	4	yes	—
315	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
328	#107	—	2	2	no	—
329	#106	—	2	4	no	—
330	#106	—	2	2	no	—
331	#102	—	2	4	no	—
332	#102	—	2	2	no	—
333	#102	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	#95	—	2	1	no	—
337	#95	—	2	2	no	—
338	C₂⁴	—	2	1	no	—
339	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	—	8	2	no	—
342	C₂×Q₈	—	8	2	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	8	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	8	1	no	—
358	C₂²×C₄	—	8	1	no	—
359	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	8	2	no	—
386	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
387	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
388	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	8	2	no	—
393	C₂²⋊C₄	—	8	2	no	—
394	C₂²⋊C₄	—	8	1	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	1	no	—
407	C₂³	#120×C₄₃	1	2	yes	—
408	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
409	Q₈	—	8	8	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	8	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	8	4	no	—
438	C₂×C₄	#120×C₄₃	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
441	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
442	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
443	C₈	—	4	2	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
457	C₂²	C₄₃×#536	1	2	yes	—
458	C₂²	C₄₃×#576	1	1	yes	characteristic
459	C₂²	C₄₃×#577	1	2	yes	—
460	C₂²	C₄₃×#577	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	1	no	—
469	C₄	C₄₃×#536	1	1	yes	characteristic
470	C₄	C₄₃×#536	1	2	yes	—
471	C₄	C₄₃×#536	1	1	yes	characteristic
472	C₂	—	4	2	no	—
473	C₂	—	16	1	no	—
474	C₂	C₄₃×#2614	1	1	yes	characteristic
475	C₂	C₄₃×#3010	1	1	yes	characteristic
476	C₂	C₄₃×#3012	1	1	yes	characteristic
477	C₂	C₄₃×#3241	1	2	yes	—
478	C₂	C₄₃×#3244	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
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×#544	C₂	semidirect
5. C₄₃×#2059	C₂	semidirect
6. C₄₃×#2058	C₂	semidirect
7. C₄₃×#2025	C₂	semidirect
8. C₄₃×#2023	C₂	semidirect
9. C₄₃×#1825	C₂	semidirect
10. C₄₃×#1823	C₂	semidirect
11. C₄₃×#1818	C₂	semidirect
206. #29647	C₄₃	direct (N × H)
233. C₂×#544	C₂×C₄₃	semidirect
237. #2059	C₂×C₄₃	semidirect
238. #2058	C₂×C₄₃	semidirect
239. #2025	C₂×C₄₃	semidirect
240. #2023	C₂×C₄₃	semidirect
241. #1825	C₂×C₄₃	semidirect
242. #1823	C₂×C₄₃	semidirect
243. #1818	C₂×C₄₃	semidirect
284. C₄₃	#29647	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#544	2
C₂×C₄₃×#481	2
C₂×C₄₃×#482	2
C₄₃×#2624	2
C₄₃×#2059	2
C₄₃×#2058	2
C₄₃×#2025	2
C₄₃×#2023	2
C₄₃×#1825	2
C₄₃×#1823	2
C₄₃×#1818	2
#29647	43

Subgroups — C43×#29647 #24949664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29647 #24949664