Subgroups — C₄₃×#25886 #24945903

Order 11008.

1314 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2035	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1788	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	2	yes	—
11	C₄₃×#547	—	2	4	no	—
12	C₄₃×#547	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#123×C₄₃	—	2	2	no	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×#121×C₄₃	—	2	1	no	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
21	C₄₃×#487	—	2	4	no	—
22	C₄₃×#476	—	2	4	no	—
23	C₂×#106×C₄₃	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₃	C₂²	1	4	yes	—
26	C₂×#103×C₄₃	C₂²	1	4	yes	—
27	C₂×#102×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₄₃×#393	—	2	2	no	—
32	C₄₃×#390	—	2	1	no	—
33	C₄₃×#382	—	2	1	no	—
34	C₄₃×#380	C₂²	1	4	yes	—
35	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₂×#41×C₄₃	—	2	4	no	—
38	C₂×#41×C₄₃	—	2	4	no	—
39	C₂×#41×C₄₃	—	2	8	no	—
40	C₂×#41×C₄₃	—	4	4	no	—
41	C₂²×Q₈×C₄₃	—	2	1	no	—
42	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₃	—	2	2	no	—
44	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂³×C₄×C₄₃	—	2	2	no	—
48	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₄₃	—	2	2	no	—
52	C₄⋊Q₈×C₄₃	—	2	2	no	—
53	C₄⋊Q₈×C₄₃	—	2	2	no	—
54	C₄⋊Q₈×C₄₃	D₄	1	4	yes	—
55	#123×C₄₃	—	2	16	no	—
56	C₂²⋊Q₈×C₄₃	—	2	4	no	—
57	C₂²⋊Q₈×C₄₃	—	2	4	no	—
58	#121×C₄₃	—	2	8	no	—
59	C₄×D₄×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	C₄×D₄×C₄₃	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
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×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
76	C₂×C₄²×C₄₃	—	2	1	no	—
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#106×C₄₃	—	2	4	no	—
79	C₄⋊C₈×C₄₃	—	2	2	no	—
80	#103×C₄₃	—	2	8	no	—
81	#103×C₄₃	—	4	4	no	—
82	#102×C₄₃	—	2	4	no	—
83	#102×C₄₃	—	2	4	no	—
84	C₂²⋊C₈×C₄₃	—	4	4	no	—
85	C₄×C₈×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	1	no	—
87	#95×C₄₃	—	2	4	no	—
88	C₂⁴×C₄₃	—	2	1	no	—
89	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
90	#41×C₄₃	—	4	16	no	—
91	#41×C₄₃	—	4	8	no	—
92	#41×C₄₃	—	4	8	no	—
93	C₂×Q₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	—	2	4	no	—
95	C₂×Q₈×C₄₃	—	2	4	no	—
96	C₂×Q₈×C₄₃	—	4	2	no	—
97	C₂×Q₈×C₄₃	—	8	2	no	—
98	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
99	C₂×D₄×C₄₃	—	2	8	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	4	8	no	—
106	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₄₃	#41	1	4	yes	—
108	C₂²×C₄×C₄₃	—	2	8	no	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	2	1	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	—	4	8	no	—
119	C₂²×C₄×C₄₃	—	4	2	no	—
120	C₂²×C₄×C₄₃	—	4	2	no	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
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	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	2	8	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	4	no	—
133	C₄⋊C₄×C₄₃	—	2	4	no	—
134	C₄⋊C₄×C₄₃	—	2	1	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	—	4	2	no	—
140	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₄₃	—	2	8	no	—
142	C₂²⋊C₄×C₄₃	—	2	4	no	—
143	C₂²⋊C₄×C₄₃	—	2	4	no	—
144	C₂²⋊C₄×C₄₃	—	8	4	no	—
145	C₄²×C₄₃	—	4	2	no	—
146	C₄²×C₄₃	C₂×D₄	1	2	yes	—
147	C₄²×C₄₃	C₂×D₄	1	2	yes	—
148	C₂³×C₄₃	—	2	2	no	—
149	C₂³×C₄₃	—	2	4	no	—
150	C₂³×C₄₃	—	2	2	no	—
151	C₂³×C₄₃	—	2	4	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	2	4	no	—
155	C₂³×C₄₃	—	4	1	no	—
156	C₂³×C₄₃	—	4	1	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₃	—	2	8	no	—
160	Q₈×C₄₃	—	4	2	no	—
161	Q₈×C₄₃	—	4	2	no	—
162	Q₈×C₄₃	—	8	4	no	—
163	D₄×C₄₃	—	2	2	no	—
164	D₄×C₄₃	—	2	4	no	—
165	D₄×C₄₃	—	4	16	no	—
166	D₄×C₄₃	—	4	4	no	—
167	D₄×C₄₃	#124	1	4	yes	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	4	no	—
172	C₂×C₄×C₄₃	—	2	4	no	—
173	C₂×C₄×C₄₃	—	4	16	no	—
174	C₂×C₄×C₄₃	—	4	4	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	1	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	4	no	—
180	C₂×C₄×C₄₃	—	4	8	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	—	4	4	no	—
186	C₂×C₄×C₄₃	#120	1	2	yes	—
187	C₂×C₄×C₄₃	#120	1	2	yes	—
188	C₂×C₄×C₄₃	#135	1	2	yes	—
189	C₂×C₄×C₄₃	#137	1	2	yes	—
190	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
193	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
194	C₈×C₄₃	—	4	2	no	—
195	C₈×C₄₃	—	4	2	no	—
196	#25886	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₃	—	2	4	no	—
198	C₂²×C₄₃	—	4	4	no	—
199	C₂²×C₄₃	—	4	2	no	—
200	C₂²×C₄₃	—	4	2	no	—
201	C₂²×C₄₃	—	4	4	no	—
202	C₂²×C₄₃	—	4	4	no	—
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	4	no	—
207	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
208	C₂²×C₄₃	#546	1	2	yes	—
209	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
210	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
211	C₂²×C₄₃	#577	1	2	yes	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	—	4	2	no	—
214	C₄×C₄₃	—	4	4	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	8	2	no	—
217	C₄×C₄₃	—	8	2	no	—
218	C₄×C₄₃	#452	1	4	yes	—
219	C₄×C₄₃	C₂×#124	1	1	yes	characteristic
220	C₄×C₄₃	#535	1	1	yes	characteristic
221	C₄×C₄₃	#546	1	2	yes	—
222	C₂×#547	C₂×C₄₃	1	1	yes	characteristic
223	C₂×#487	C₂×C₄₃	1	1	yes	characteristic, complemented
224	C₂×#476	C₂×C₄₃	1	1	yes	characteristic, complemented
225	#2563	C₂×C₄₃	1	1	yes	characteristic, complemented
226	#2035	C₂×C₄₃	1	4	yes	complemented
227	#1981	C₂×C₄₃	1	1	yes	characteristic, complemented
228	#1954	C₂×C₄₃	1	1	yes	characteristic, complemented
229	#1788	C₂×C₄₃	1	4	yes	complemented
230	C₄×#102	C₂×C₄₃	1	1	yes	characteristic, complemented
231	C₂×C₄₃	—	4	4	no	—
232	C₂×C₄₃	—	8	2	no	—
233	C₂×C₄₃	#2435	1	1	yes	characteristic
234	C₂×C₄₃	C₂×#452	1	1	yes	characteristic
235	C₂×C₄₃	#3010	1	1	yes	characteristic
236	C₂×C₄₃	#3303	1	2	yes	—
237	C₂×C₄₃	#3331	1	2	yes	—
238	C₂²×#41	C₂²×C₄₃	1	2	yes	—
239	#547	—	2	4	no	—
240	#547	—	2	4	no	—
241	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
243	C₂×#123	—	2	2	no	—
244	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
245	C₂×#121	—	2	1	no	—
246	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	—	2	1	no	—
249	#487	—	2	4	no	—
250	#476	—	2	4	no	—
251	C₂×#106	C₂²×C₄₃	1	2	yes	—
252	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
253	C₂×#103	C₂²×C₄₃	1	4	yes	—
254	C₂×#103	C₂²×C₄₃	1	4	yes	—
255	C₂×#102	C₂²×C₄₃	1	2	yes	—
256	C₂×#102	C₂²×C₄₃	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
258	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
259	#393	—	2	2	no	—
260	#390	—	2	1	no	—
261	#382	—	2	1	no	—
262	#380	C₂²×C₄₃	1	4	yes	—
263	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
264	#340	C₂²×C₄₃	1	2	yes	—
265	C₄₃	#25886	1	1	yes	characteristic, direct product factor, Sylow
266	C₂×#41	—	2	4	no	—
267	C₂×#41	—	2	4	no	—
268	C₂×#41	—	2	8	no	—
269	C₂×#41	—	4	4	no	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
274	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
279	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	D₄×C₄₃	1	4	yes	—
284	#123	—	2	16	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	2	4	no	—
287	#121	—	2	8	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	D₄×C₄₃	1	4	yes	—
292	C₂×C₄⋊C₄	—	2	8	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	4	no	—
304	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
307	#106	—	2	4	no	—
308	C₄⋊C₈	—	2	2	no	—
309	#103	—	2	8	no	—
310	#103	—	4	4	no	—
311	#102	—	2	4	no	—
312	#102	—	2	4	no	—
313	C₂²⋊C₈	—	4	4	no	—
314	C₄×C₈	—	2	2	no	—
315	#95	—	2	1	no	—
316	#95	—	2	4	no	—
317	C₂⁴	—	2	1	no	—
318	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
319	#41	—	4	16	no	—
320	#41	—	4	8	no	—
321	#41	—	4	8	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	8	2	no	—
327	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	8	no	—
335	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
336	C₂×D₄	#41×C₄₃	1	4	yes	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	8	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	4	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
370	C₂²⋊C₄	—	2	8	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	8	4	no	—
374	C₄²	—	4	2	no	—
375	C₄²	C₂×D₄×C₄₃	1	2	yes	—
376	C₄²	C₂×D₄×C₄₃	1	2	yes	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	2	no	—
387	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	8	4	no	—
392	D₄	—	2	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	4	16	no	—
395	D₄	—	4	4	no	—
396	D₄	#124×C₄₃	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	16	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	8	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	4	no	—
415	C₂×C₄	#120×C₄₃	1	2	yes	—
416	C₂×C₄	#120×C₄₃	1	2	yes	—
417	C₂×C₄	#135×C₄₃	1	2	yes	—
418	C₂×C₄	#137×C₄₃	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
422	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
436	C₂²	C₄₃×#546	1	2	yes	—
437	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
438	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
439	C₂²	C₄₃×#577	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	2	no	—
446	C₄	C₄₃×#452	1	4	yes	—
447	C₄	C₂×#124×C₄₃	1	1	yes	characteristic
448	C₄	C₄₃×#535	1	1	yes	characteristic
449	C₄	C₄₃×#546	1	2	yes	—
450	C₂	—	4	4	no	—
451	C₂	—	8	2	no	—
452	C₂	C₄₃×#2435	1	1	yes	characteristic
453	C₂	C₂×C₄₃×#452	1	1	yes	characteristic
454	C₂	C₄₃×#3010	1	1	yes	characteristic
455	C₂	C₄₃×#3303	1	2	yes	—
456	C₂	C₄₃×#3331	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#547	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄×D₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#487	C₂	semidirect
3. C₂×C₄₃×#476	C₂	semidirect
4. C₄₃×#2563	C₂	semidirect
5. C₄₃×#2035	C₂	semidirect
6. C₄₃×#1981	C₂	semidirect
7. C₄₃×#1954	C₂	semidirect
8. C₄₃×#1788	C₂	semidirect
9. C₄×#102×C₄₃	C₂	semidirect
196. #25886	C₄₃	direct (N × H)
223. C₂×#487	C₂×C₄₃	semidirect
224. C₂×#476	C₂×C₄₃	semidirect
225. #2563	C₂×C₄₃	semidirect
226. #2035	C₂×C₄₃	semidirect
227. #1981	C₂×C₄₃	semidirect
228. #1954	C₂×C₄₃	semidirect
229. #1788	C₂×C₄₃	semidirect
230. C₄×#102	C₂×C₄₃	semidirect
265. C₄₃	#25886	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×#547	2
C₂×C₄₃×#487	2
C₂×C₄₃×#476	2
C₄₃×#2563	2
C₄₃×#2035	2
C₄₃×#1981	2
C₄₃×#1954	2
C₄₃×#1788	2
C₄×#102×C₄₃	2
#25886	43

Subgroups — C43×#25886 #24945903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25886 #24945903