Subgroups — C₄₃×#29805 #24949822

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2658	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2043	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2042	C₂	1	2	yes	maximal
7	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2015	C₂	1	2	yes	maximal
9	C₄₃×#1983	C₂	1	1	yes	maximal, characteristic
10	C₄₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#464	—	2	4	no	—
21	C₄₃×#462	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₃	C₂²	1	2	yes	—
27	C₂×#103×C₄₃	C₂²	1	2	yes	—
28	C₂×#103×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#399	—	2	1	no	—
32	C₄₃×#399	—	2	1	no	—
33	C₄₃×#399	—	2	2	no	—
34	C₄₃×#391	C₂²	1	2	yes	—
35	C₄₃×#389	C₂²	1	2	yes	—
36	C₄₃×#387	—	2	2	no	—
37	C₄₃×#383	—	2	1	no	—
38	C₄₃×#382	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#376	C₂²	1	1	yes	characteristic
41	C₄₃×#336	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₄₃	—	2	4	no	—
48	C₂×Q₁₆×C₄₃	—	2	2	no	—
49	C₂×Q₁₆×C₄₃	—	4	2	no	—
50	C₂×Q₁₆×C₄₃	—	4	2	no	—
51	C₂×Q₁₆×C₄₃	—	4	2	no	—
52	C₂×SD₁₆×C₄₃	—	2	2	no	—
53	C₂×SD₁₆×C₄₃	—	4	2	no	—
54	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₄₃	—	2	2	no	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	—	4	2	no	—
60	C₄⋊Q₈×C₄₃	—	4	2	no	—
61	#124×C₄₃	—	2	2	no	—
62	#124×C₄₃	—	2	2	no	—
63	#124×C₄₃	—	4	2	no	—
64	#124×C₄₃	—	4	2	no	—
65	C₄×Q₈×C₄₃	—	2	2	no	—
66	C₄×Q₈×C₄₃	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄²×C₄₃	—	2	1	no	—
80	C₂×C₄²×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₃	—	2	2	no	—
84	C₄⋊C₈×C₄₃	—	2	2	no	—
85	#103×C₄₃	—	2	4	no	—
86	#103×C₄₃	—	2	2	no	—
87	#103×C₄₃	—	4	2	no	—
88	#103×C₄₃	—	4	2	no	—
89	#103×C₄₃	—	4	2	no	—
90	#102×C₄₃	—	2	2	no	—
91	#102×C₄₃	—	4	2	no	—
92	#95×C₄₃	—	2	1	no	—
93	#95×C₄₃	—	2	2	no	—
94	#95×C₄₃	—	2	2	no	—
95	#95×C₄₃	—	2	2	no	—
96	#95×C₄₃	D₄	1	1	yes	characteristic
97	#95×C₄₃	D₄	1	1	yes	characteristic
98	#95×C₄₃	D₄	1	2	yes	—
99	C₂⁴×C₄₃	—	2	1	no	—
100	C₂×Q₈×C₄₃	—	2	1	no	—
101	C₂×Q₈×C₄₃	—	2	1	no	—
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	—	2	2	no	—
112	C₂×Q₈×C₄₃	—	2	2	no	—
113	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₄₃	—	4	4	no	—
129	Q₁₆×C₄₃	—	4	8	no	—
130	SD₁₆×C₄₃	—	4	4	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	4	no	—
139	C₄⋊C₄×C₄₃	—	2	1	no	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	4	4	no	—
143	C₄⋊C₄×C₄₃	—	4	4	no	—
144	C₄⋊C₄×C₄₃	—	4	2	no	—
145	C₄⋊C₄×C₄₃	—	4	2	no	—
146	C₄⋊C₄×C₄₃	—	8	2	no	—
147	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₂²⋊C₄×C₄₃	—	4	4	no	—
150	C₂²⋊C₄×C₄₃	—	4	2	no	—
151	C₂²⋊C₄×C₄₃	—	4	2	no	—
152	C₄²×C₄₃	—	2	4	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	8	1	no	—
156	C₄²×C₄₃	C₂×D₄	1	2	yes	—
157	C₄²×C₄₃	#41	1	2	yes	—
158	C₂³×C₄₃	—	4	1	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	1	no	—
161	C₂³×C₄₃	—	4	1	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₄₃	—	2	2	no	—
165	Q₈×C₄₃	—	2	2	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	Q₈×C₄₃	—	4	1	no	—
168	Q₈×C₄₃	—	4	2	no	—
169	Q₈×C₄₃	—	4	1	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	Q₈×C₄₃	—	4	2	no	—
172	Q₈×C₄₃	—	4	2	no	—
173	Q₈×C₄₃	—	4	2	no	—
174	D₄×C₄₃	—	4	1	no	—
175	D₄×C₄₃	—	4	1	no	—
176	D₄×C₄₃	—	4	2	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	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	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	—	2	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	1	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	4	1	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	—	4	1	no	—
206	C₈×C₄₃	—	4	1	no	—
207	C₈×C₄₃	—	4	2	no	—
208	#29805	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂²×C₄₃	—	8	1	no	—
210	C₂²×C₄₃	—	8	2	no	—
211	C₂²×C₄₃	—	8	2	no	—
212	C₂²×C₄₃	—	8	1	no	—
213	C₂²×C₄₃	—	8	1	no	—
214	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
215	C₂²×C₄₃	#535	1	2	yes	—
216	C₂²×C₄₃	#577	1	1	yes	characteristic
217	C₂²×C₄₃	#578	1	1	yes	characteristic
218	C₂²×C₄₃	#578	1	2	yes	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	4	2	no	—
222	C₄×C₄₃	—	4	2	no	—
223	C₄×C₄₃	—	4	2	no	—
224	C₄×C₄₃	—	4	2	no	—
225	C₄×C₄₃	—	8	1	no	—
226	C₄×C₄₃	—	8	2	no	—
227	C₄×C₄₃	—	8	2	no	—
228	C₄×C₄₃	#535	1	1	yes	characteristic
229	C₄×C₄₃	#535	1	1	yes	characteristic
230	C₄×C₄₃	#540	1	2	yes	—
231	C₂×#464	C₂×C₄₃	1	1	yes	characteristic
232	C₂×#462	C₂×C₄₃	1	1	yes	characteristic, complemented
233	#2658	C₂×C₄₃	1	1	yes	characteristic
234	#2320	C₂×C₄₃	1	1	yes	characteristic, complemented
235	#2043	C₂×C₄₃	1	2	yes	complemented
236	#2042	C₂×C₄₃	1	2	yes	—
237	#2016	C₂×C₄₃	1	2	yes	complemented
238	#2015	C₂×C₄₃	1	2	yes	—
239	#1983	C₂×C₄₃	1	1	yes	characteristic
240	#1981	C₂×C₄₃	1	1	yes	characteristic, complemented
241	#1832	C₂×C₄₃	1	1	yes	characteristic, complemented
242	C₂×C₄₃	—	16	1	no	—
243	C₂×C₄₃	#2619	1	1	yes	characteristic
244	C₂×C₄₃	#3044	1	1	yes	characteristic
245	C₂×C₄₃	#3046	1	1	yes	characteristic
246	C₂×C₄₃	#3223	1	2	yes	—
247	C₂×C₄₃	#3225	1	2	yes	—
248	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
249	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
250	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
253	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
254	C₂×#124	C₂²×C₄₃	1	2	yes	—
255	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
256	#464	—	2	4	no	—
257	#462	—	2	4	no	—
258	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×#103	C₂²×C₄₃	1	2	yes	—
261	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
262	C₂×#103	C₂²×C₄₃	1	2	yes	—
263	C₂×#103	C₂²×C₄₃	1	2	yes	—
264	C₂×#103	C₂²×C₄₃	1	2	yes	—
265	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×#102	C₂²×C₄₃	1	2	yes	—
267	#399	—	2	1	no	—
268	#399	—	2	1	no	—
269	#399	—	2	2	no	—
270	#391	C₂²×C₄₃	1	2	yes	—
271	#389	C₂²×C₄₃	1	2	yes	—
272	#387	—	2	2	no	—
273	#383	—	2	1	no	—
274	#382	—	2	1	no	—
275	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
276	#376	C₂²×C₄₃	1	1	yes	characteristic
277	#336	C₂²×C₄₃	1	2	yes	—
278	#336	C₂²×C₄₃	1	2	yes	—
279	C₄₃	#29805	1	1	yes	characteristic, direct product factor, Sylow
280	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
282	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
283	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
284	C₂×Q₁₆	—	2	4	no	—
285	C₂×Q₁₆	—	2	2	no	—
286	C₂×Q₁₆	—	4	2	no	—
287	C₂×Q₁₆	—	4	2	no	—
288	C₂×Q₁₆	—	4	2	no	—
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	4	2	no	—
291	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	4	2	no	—
297	C₄⋊Q₈	—	4	2	no	—
298	#124	—	2	2	no	—
299	#124	—	2	2	no	—
300	#124	—	4	2	no	—
301	#124	—	4	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	D₄×C₄₃	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
319	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	2	no	—
322	#103	—	2	4	no	—
323	#103	—	2	2	no	—
324	#103	—	4	2	no	—
325	#103	—	4	2	no	—
326	#103	—	4	2	no	—
327	#102	—	2	2	no	—
328	#102	—	4	2	no	—
329	#95	—	2	1	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	D₄×C₄₃	1	1	yes	characteristic
334	#95	D₄×C₄₃	1	1	yes	characteristic
335	#95	D₄×C₄₃	1	2	yes	—
336	C₂⁴	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	1	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×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
365	Q₁₆	—	4	4	no	—
366	Q₁₆	—	4	8	no	—
367	SD₁₆	—	4	4	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	8	2	no	—
384	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	8	1	no	—
393	C₄²	C₂×D₄×C₄₃	1	2	yes	—
394	C₄²	#41×C₄₃	1	2	yes	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	2	no	—
400	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	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	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	#121×C₄₃	1	2	yes	—
437	C₂×C₄	#121×C₄₃	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
440	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
441	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
442	C₈	—	4	1	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	2	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
451	C₂²	C₄₃×#535	1	2	yes	—
452	C₂²	C₄₃×#577	1	1	yes	characteristic
453	C₂²	C₄₃×#578	1	1	yes	characteristic
454	C₂²	C₄₃×#578	1	2	yes	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	2	no	—
463	C₄	—	8	2	no	—
464	C₄	C₄₃×#535	1	1	yes	characteristic
465	C₄	C₄₃×#535	1	1	yes	characteristic
466	C₄	C₄₃×#540	1	2	yes	—
467	C₂	—	16	1	no	—
468	C₂	C₄₃×#2619	1	1	yes	characteristic
469	C₂	C₄₃×#3044	1	1	yes	characteristic
470	C₂	C₄₃×#3046	1	1	yes	characteristic
471	C₂	C₄₃×#3223	1	2	yes	—
472	C₂	C₄₃×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₄×C₄₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#462	C₂	semidirect
4. C₄₃×#2320	C₂	semidirect
5. C₄₃×#2043	C₂	semidirect
7. C₄₃×#2016	C₂	semidirect
10. C₄₃×#1981	C₂	semidirect
11. C₄₃×#1832	C₂	semidirect
208. #29805	C₄₃	direct (N × H)
232. C₂×#462	C₂×C₄₃	semidirect
234. #2320	C₂×C₄₃	semidirect
235. #2043	C₂×C₄₃	semidirect
237. #2016	C₂×C₄₃	semidirect
240. #1981	C₂×C₄₃	semidirect
241. #1832	C₂×C₄₃	semidirect
279. C₄₃	#29805	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×#464	2
C₂×C₄₃×#462	2
C₄₃×#2658	2
C₄₃×#2320	2
C₄₃×#2043	2
C₄₃×#2042	2
C₄₃×#2016	2
C₄₃×#2015	2
C₄₃×#1983	2
C₄₃×#1981	2
C₄₃×#1832	2
#29805	43

Subgroups — C43×#29805 #24949822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29805 #24949822