Subgroups — C₄₃×#28378 #24948395

Order 11008.

1080 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#478	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₃×#463	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2861	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#127×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2011	C₂	1	1	yes	maximal, characteristic
9	C₄₃×#1973	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1972	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₃	—	2	2	no	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#478	—	2	8	no	—
20	C₄₃×#463	—	2	8	no	—
21	C₂×#107×C₄₃	C₂²	1	2	yes	—
22	C₂×#106×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×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×#102×C₄₃	C₂²	1	2	yes	—
28	C₂×#97×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#391	C₂²	1	1	yes	characteristic
30	C₄₃×#391	C₂²	1	1	yes	characteristic
31	C₄₃×#390	—	2	2	no	—
32	C₄₃×#390	C₂²	1	1	yes	characteristic
33	C₄₃×#390	C₂²	1	1	yes	characteristic
34	C₄₃×#390	C₂²	1	2	yes	—
35	C₄₃×#388	—	2	2	no	—
36	C₄₃×#388	—	2	2	no	—
37	C₄₃×#384	C₂²	1	1	yes	characteristic
38	C₄³×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#336	C₂²	1	1	yes	characteristic
40	C₄₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	—	2	2	no	—
46	C₂×SD₁₆×C₄₃	—	2	4	no	—
47	C₂×SD₁₆×C₄₃	—	2	4	no	—
48	C₂×SD₁₆×C₄₃	—	4	2	no	—
49	C₂×D₈×C₄₃	—	2	4	no	—
50	C₂×D₈×C₄₃	—	2	4	no	—
51	C₂×D₈×C₄₃	—	4	2	no	—
52	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
54	#127×C₄₃	—	2	4	no	—
55	#125×C₄₃	—	2	4	no	—
56	#124×C₄₃	—	2	4	no	—
57	C₄×D₄×C₄₃	—	2	4	no	—
58	C₄×D₄×C₄₃	—	2	4	no	—
59	C₄×D₄×C₄₃	—	4	8	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₄²×C₄₃	D₄	1	2	yes	—
73	C₂×C₄²×C₄₃	D₄	1	2	yes	—
74	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#107×C₄₃	—	2	4	no	—
78	#106×C₄₃	—	2	4	no	—
79	C₄⋊C₈×C₄₃	D₄	1	8	yes	complemented
80	#103×C₄₃	—	2	4	no	—
81	#102×C₄₃	—	2	4	no	—
82	#102×C₄₃	—	2	4	no	—
83	#102×C₄₃	—	2	4	no	—
84	#97×C₄₃	—	4	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	2	no	—
87	C₂⁴×C₄₃	—	2	2	no	—
88	C₂⁴×C₄₃	—	2	1	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	2	1	no	—
92	C₂×Q₈×C₄₃	—	2	1	no	—
93	C₂×D₄×C₄₃	—	2	8	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	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	1	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	2	1	no	—
103	C₂×D₄×C₄₃	—	4	4	no	—
104	C₂×D₄×C₄₃	—	4	4	no	—
105	C₂×D₄×C₄₃	#41	1	4	yes	—
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	4	8	no	—
111	C₂²×C₄×C₄₃	—	4	4	no	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	SD₁₆×C₄₃	—	4	8	no	—
118	D₈×C₄₃	—	4	8	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
124	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
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	2	no	—
130	C₄⋊C₄×C₄₃	—	4	2	no	—
131	C₄⋊C₄×C₄₃	—	4	4	no	—
132	C₂²⋊C₄×C₄₃	—	4	4	no	—
133	C₂²⋊C₄×C₄₃	—	4	8	no	—
134	C₂²⋊C₄×C₄₃	—	4	4	no	—
135	C₂²⋊C₄×C₄₃	—	4	2	no	—
136	C₂²⋊C₄×C₄₃	—	4	2	no	—
137	C₂²⋊C₄×C₄₃	—	4	4	no	—
138	C₄²×C₄₃	—	2	4	no	—
139	C₄²×C₄₃	—	2	2	no	—
140	C₄²×C₄₃	—	2	1	no	—
141	C₄²×C₄₃	—	2	1	no	—
142	C₄²×C₄₃	—	4	2	no	—
143	C₄²×C₄₃	C₂×D₄	1	4	yes	—
144	C₂³×C₄₃	—	2	4	no	—
145	C₂³×C₄₃	—	4	2	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	4	no	—
148	C₂³×C₄₃	—	4	4	no	—
149	C₂³×C₄₃	—	4	1	no	—
150	C₂³×C₄₃	—	4	1	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	—	4	2	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₃	—	4	2	no	—
156	Q₈×C₄₃	—	4	2	no	—
157	D₄×C₄₃	—	2	4	no	—
158	D₄×C₄₃	—	2	4	no	—
159	D₄×C₄₃	—	4	16	no	—
160	D₄×C₄₃	—	4	2	no	—
161	D₄×C₄₃	—	4	2	no	—
162	D₄×C₄₃	—	4	2	no	—
163	D₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	2	2	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	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	1	no	—
177	C₂×C₄×C₄₃	—	4	4	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	8	8	no	—
181	C₂×C₄×C₄₃	#127	1	2	yes	—
182	C₂×C₄×C₄₃	#127	1	2	yes	—
183	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
184	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
186	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
188	C₈×C₄₃	—	2	4	no	—
189	C₈×C₄₃	—	2	4	no	—
190	#28378	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₃	—	4	8	no	—
192	C₂²×C₄₃	—	4	4	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	2	no	—
195	C₂²×C₄₃	—	8	4	no	—
196	C₂²×C₄₃	—	8	2	no	—
197	C₂²×C₄₃	—	8	1	no	—
198	C₂²×C₄₃	—	8	1	no	—
199	C₂²×C₄₃	—	8	2	no	—
200	C₂²×C₄₃	—	8	1	no	—
201	C₂²×C₄₃	#525	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
203	C₂²×C₄₃	#537	1	1	yes	characteristic
204	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
205	C₂²×C₄₃	#575	1	2	yes	—
206	C₄×C₄₃	—	2	4	no	—
207	C₄×C₄₃	—	2	2	no	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	4	2	no	—
210	C₄×C₄₃	—	8	1	no	—
211	C₄×C₄₃	—	8	1	no	—
212	C₄×C₄₃	—	8	2	no	—
213	C₄×C₄₃	—	8	1	no	—
214	C₄×C₄₃	#546	1	2	yes	—
215	C₄×C₄₃	#548	1	2	yes	—
216	C₂×#478	C₂×C₄₃	1	2	yes	complemented
217	C₂×#463	C₂×C₄₃	1	2	yes	complemented
218	#2861	C₂×C₄₃	1	1	yes	characteristic, complemented
219	C₄×#127	C₂×C₄₃	1	1	yes	characteristic, complemented
220	#2096	C₂×C₄₃	1	1	yes	characteristic, complemented
221	#2093	C₂×C₄₃	1	1	yes	characteristic, complemented
222	#2014	C₂×C₄₃	1	1	yes	characteristic, complemented
223	#2011	C₂×C₄₃	1	1	yes	characteristic
224	#1973	C₂×C₄₃	1	2	yes	complemented
225	#1972	C₂×C₄₃	1	2	yes	complemented
226	#1767	C₂×C₄₃	1	1	yes	characteristic, complemented
227	C₂×C₄₃	—	8	4	no	—
228	C₂×C₄₃	—	16	1	no	—
229	C₂×C₄₃	#2540	1	1	yes	characteristic
230	C₂×C₄₃	#3114	1	2	yes	—
231	C₂×C₄₃	#3150	1	1	yes	characteristic
232	C₂×C₄₃	#3151	1	1	yes	characteristic
233	C₂×C₄₃	#3251	1	2	yes	—
234	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
235	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
236	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
238	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
239	C₂×C₄×D₄	—	2	2	no	—
240	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
241	#478	—	2	8	no	—
242	#463	—	2	8	no	—
243	C₂×#107	C₂²×C₄₃	1	2	yes	—
244	C₂×#106	C₂²×C₄₃	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
246	C₂×#103	C₂²×C₄₃	1	2	yes	—
247	C₂×#102	C₂²×C₄₃	1	2	yes	—
248	C₂×#102	C₂²×C₄₃	1	2	yes	—
249	C₂×#102	C₂²×C₄₃	1	2	yes	—
250	C₂×#97	C₂²×C₄₃	1	2	yes	—
251	#391	C₂²×C₄₃	1	1	yes	characteristic
252	#391	C₂²×C₄₃	1	1	yes	characteristic
253	#390	—	2	2	no	—
254	#390	C₂²×C₄₃	1	2	yes	—
255	#390	C₂²×C₄₃	1	1	yes	characteristic
256	#390	C₂²×C₄₃	1	1	yes	characteristic
257	#388	—	2	2	no	—
258	#388	—	2	2	no	—
259	#384	C₂²×C₄₃	1	1	yes	characteristic
260	C₄³	C₂²×C₄₃	1	1	yes	characteristic
261	#336	C₂²×C₄₃	1	1	yes	characteristic
262	#336	C₂²×C₄₃	1	1	yes	characteristic
263	C₄₃	#28378	1	1	yes	characteristic, direct product factor, Sylow
264	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
267	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
268	C₂³×C₄	—	2	2	no	—
269	C₂×SD₁₆	—	2	4	no	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	4	2	no	—
272	C₂×D₈	—	2	4	no	—
273	C₂×D₈	—	2	4	no	—
274	C₂×D₈	—	4	2	no	—
275	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
276	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
277	#127	—	2	4	no	—
278	#125	—	2	4	no	—
279	#124	—	2	4	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	4	8	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	D₄×C₄₃	1	2	yes	—
296	C₂×C₄²	D₄×C₄₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
300	#107	—	2	4	no	—
301	#106	—	2	4	no	—
302	C₄⋊C₈	D₄×C₄₃	1	8	yes	complemented
303	#103	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	2	4	no	—
307	#97	—	4	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	#41×C₄₃	1	4	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	8	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
339	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
340	SD₁₆	—	4	8	no	—
341	D₈	—	4	8	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
347	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	8	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₄²	—	2	4	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	4	2	no	—
366	C₄²	C₂×D₄×C₄₃	1	4	yes	—
367	C₂³	—	2	4	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	D₄	—	2	4	no	—
381	D₄	—	2	4	no	—
382	D₄	—	4	16	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	8	no	—
404	C₂×C₄	#127×C₄₃	1	2	yes	—
405	C₂×C₄	#127×C₄₃	1	2	yes	—
406	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
408	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
409	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
410	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
411	C₈	—	2	4	no	—
412	C₈	—	2	4	no	—
413	C₂²	—	4	8	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	4	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	1	no	—
423	C₂²	C₄₃×#525	1	1	yes	characteristic
424	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
425	C₂²	C₄₃×#537	1	1	yes	characteristic
426	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
427	C₂²	C₄₃×#575	1	2	yes	—
428	C₄	—	2	4	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	1	no	—
436	C₄	C₄₃×#546	1	2	yes	—
437	C₄	C₄₃×#548	1	2	yes	—
438	C₂	—	8	4	no	—
439	C₂	—	16	1	no	—
440	C₂	C₄₃×#2540	1	1	yes	characteristic
441	C₂	C₄₃×#3114	1	2	yes	—
442	C₂	C₄₃×#3150	1	1	yes	characteristic
443	C₂	C₄₃×#3151	1	1	yes	characteristic
444	C₂	C₄₃×#3251	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#478	C₂	semidirect
2. C₂×C₄₃×#463	C₂	semidirect
3. C₄₃×#2861	C₂	semidirect
4. C₄×#127×C₄₃	C₂	semidirect
5. C₄₃×#2096	C₂	semidirect
6. C₄₃×#2093	C₂	semidirect
7. C₄₃×#2014	C₂	semidirect
9. C₄₃×#1973	C₂	semidirect
10. C₄₃×#1972	C₂	semidirect
11. C₄₃×#1767	C₂	semidirect
79. C₄⋊C₈×C₄₃	D₄	semidirect
190. #28378	C₄₃	direct (N × H)
216. C₂×#478	C₂×C₄₃	semidirect
217. C₂×#463	C₂×C₄₃	semidirect
218. #2861	C₂×C₄₃	semidirect
219. C₄×#127	C₂×C₄₃	semidirect
220. #2096	C₂×C₄₃	semidirect
221. #2093	C₂×C₄₃	semidirect
222. #2014	C₂×C₄₃	semidirect
224. #1973	C₂×C₄₃	semidirect
225. #1972	C₂×C₄₃	semidirect
226. #1767	C₂×C₄₃	semidirect
263. C₄₃	#28378	direct (N × H)
302. 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×#478	2
C₂×C₄₃×#463	2
C₄₃×#2861	2
C₄×#127×C₄₃	2
C₄₃×#2096	2
C₄₃×#2093	2
C₄₃×#2014	2
C₄₃×#2011	2
C₄₃×#1973	2
C₄₃×#1972	2
C₄₃×#1767	2
#28378	43

Subgroups — C43×#28378 #24948395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28378 #24948395