Subgroups — C₄₃×#28443 #24948460

Order 11008.

1310 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#463	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#127×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2012	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₃	C₂²	1	4	yes	—
11	C₂²×D₈×C₄₃	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₃	C₂²	1	2	yes	—
16	C₂×#124×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₃	—	2	2	no	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#493	—	2	4	no	—
20	C₄₃×#492	—	2	4	no	—
21	C₄₃×#463	—	2	16	no	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	4	yes	—
24	C₂×#102×C₄₃	C₂²	1	4	yes	—
25	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#390	—	2	2	no	—
28	C₄₃×#390	—	2	2	no	—
29	C₄₃×#390	—	2	2	no	—
30	C₄₃×#390	C₂²	1	2	yes	—
31	C₄₃×#384	C₂²	1	1	yes	characteristic
32	C₄³×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
35	C₂²×D₄×C₄₃	—	2	2	no	—
36	C₂²×D₄×C₄₃	—	2	2	no	—
37	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
38	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₃	—	2	2	no	—
40	C₂×SD₁₆×C₄₃	—	2	8	no	—
41	C₂×SD₁₆×C₄₃	—	2	8	no	—
42	C₂×SD₁₆×C₄₃	—	4	4	no	—
43	C₂×D₈×C₄₃	—	2	8	no	—
44	C₂×D₈×C₄₃	—	2	8	no	—
45	C₂×D₈×C₄₃	—	4	4	no	—
46	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₄₃	—	2	2	no	—
49	C₄⋊Q₈×C₄₃	—	2	2	no	—
50	#127×C₄₃	—	2	2	no	—
51	#127×C₄₃	—	2	2	no	—
52	#127×C₄₃	—	2	2	no	—
53	#127×C₄₃	D₄	1	4	yes	—
54	#124×C₄₃	—	2	8	no	—
55	#124×C₄₃	—	4	4	no	—
56	C₄×D₄×C₄₃	—	2	8	no	—
57	C₄×D₄×C₄₃	—	4	8	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄²×C₄₃	D₄	1	2	yes	—
67	C₂×C₄²×C₄₃	D₄	1	2	yes	—
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₃	D₄	1	8	yes	complemented
72	#103×C₄₃	—	2	8	no	—
73	#102×C₄₃	—	2	8	no	—
74	C₄×C₈×C₄₃	—	2	2	no	—
75	C₄×C₈×C₄₃	—	2	2	no	—
76	C₂⁴×C₄₃	—	2	2	no	—
77	C₂⁴×C₄₃	—	2	2	no	—
78	C₂×Q₈×C₄₃	—	2	4	no	—
79	C₂×Q₈×C₄₃	—	2	2	no	—
80	C₂×Q₈×C₄₃	—	2	2	no	—
81	C₂×Q₈×C₄₃	—	2	4	no	—
82	C₂×D₄×C₄₃	—	2	8	no	—
83	C₂×D₄×C₄₃	—	2	2	no	—
84	C₂×D₄×C₄₃	—	2	4	no	—
85	C₂×D₄×C₄₃	—	2	4	no	—
86	C₂×D₄×C₄₃	—	2	2	no	—
87	C₂×D₄×C₄₃	—	2	2	no	—
88	C₂×D₄×C₄₃	—	2	4	no	—
89	C₂×D₄×C₄₃	—	2	4	no	—
90	C₂×D₄×C₄₃	—	4	4	no	—
91	C₂×D₄×C₄₃	—	4	4	no	—
92	C₂×D₄×C₄₃	—	4	4	no	—
93	C₂×D₄×C₄₃	—	4	4	no	—
94	C₂×D₄×C₄₃	—	4	4	no	—
95	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	4	8	no	—
99	C₂²×C₄×C₄₃	—	4	4	no	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
105	SD₁₆×C₄₃	—	4	16	no	—
106	D₈×C₄₃	—	4	16	no	—
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
112	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
113	C₄⋊C₄×C₄₃	—	2	4	no	—
114	C₄⋊C₄×C₄₃	—	4	4	no	—
115	C₄⋊C₄×C₄₃	—	4	4	no	—
116	C₂²⋊C₄×C₄₃	—	4	8	no	—
117	C₂²⋊C₄×C₄₃	—	4	8	no	—
118	C₂²⋊C₄×C₄₃	—	4	4	no	—
119	C₂²⋊C₄×C₄₃	—	4	4	no	—
120	C₂²⋊C₄×C₄₃	—	4	4	no	—
121	C₄²×C₄₃	—	2	4	no	—
122	C₄²×C₄₃	—	2	4	no	—
123	C₄²×C₄₃	—	2	2	no	—
124	C₄²×C₄₃	C₂×D₄	1	2	yes	—
125	C₄²×C₄₃	C₂×D₄	1	4	yes	—
126	C₄²×C₄₃	#41	1	2	yes	—
127	C₂³×C₄₃	—	2	4	no	—
128	C₂³×C₄₃	—	4	2	no	—
129	C₂³×C₄₃	—	4	2	no	—
130	C₂³×C₄₃	—	4	4	no	—
131	C₂³×C₄₃	—	4	4	no	—
132	C₂³×C₄₃	—	4	2	no	—
133	C₂³×C₄₃	—	4	2	no	—
134	C₂³×C₄₃	—	4	2	no	—
135	C₂³×C₄₃	—	4	4	no	—
136	C₂³×C₄₃	—	4	4	no	—
137	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₄₃	—	4	4	no	—
139	Q₈×C₄₃	—	4	4	no	—
140	D₄×C₄₃	—	2	8	no	—
141	D₄×C₄₃	—	4	4	no	—
142	D₄×C₄₃	—	4	4	no	—
143	D₄×C₄₃	—	4	4	no	—
144	D₄×C₄₃	—	4	16	no	—
145	D₄×C₄₃	—	8	8	no	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	4	no	—
156	C₂×C₄×C₄₃	—	8	8	no	—
157	C₂×C₄×C₄₃	#121	1	4	yes	—
158	C₂×C₄×C₄₃	#127	1	2	yes	—
159	C₂×C₄×C₄₃	#127	1	2	yes	—
160	C₂×C₄×C₄₃	#135	1	4	yes	—
161	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
166	C₈×C₄₃	—	2	4	no	—
167	C₈×C₄₃	—	2	4	no	—
168	#28443	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₄₃	—	4	8	no	—
170	C₂²×C₄₃	—	4	4	no	—
171	C₂²×C₄₃	—	8	2	no	—
172	C₂²×C₄₃	—	8	2	no	—
173	C₂²×C₄₃	—	8	4	no	—
174	C₂²×C₄₃	—	8	2	no	—
175	C₂²×C₄₃	—	8	2	no	—
176	C₂²×C₄₃	—	8	4	no	—
177	C₂²×C₄₃	—	8	4	no	—
178	C₂²×C₄₃	—	8	2	no	—
179	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
180	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
181	C₂²×C₄₃	#535	1	1	yes	characteristic
182	C₂²×C₄₃	C₂×#135	1	2	yes	—
183	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
184	C₄×C₄₃	—	2	2	no	—
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	4	2	no	—
187	C₄×C₄₃	—	8	2	no	—
188	C₄×C₄₃	—	8	2	no	—
189	C₄×C₄₃	#463	1	8	yes	complemented
190	C₄×C₄₃	D₄²	1	2	yes	—
191	C₄×C₄₃	#550	1	2	yes	—
192	C₂×#493	C₂×C₄₃	1	1	yes	characteristic
193	C₂×#492	C₂×C₄₃	1	1	yes	characteristic, complemented
194	C₂×#463	C₂×C₄₃	1	4	yes	complemented
195	#2858	C₂×C₄₃	1	1	yes	characteristic, complemented
196	C₄×#127	C₂×C₄₃	1	1	yes	characteristic, complemented
197	#2012	C₂×C₄₃	1	4	yes	complemented
198	#1957	C₂×C₄₃	1	1	yes	characteristic, complemented
199	#1956	C₂×C₄₃	1	1	yes	characteristic, complemented
200	C₄×C₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
201	C₂×C₄₃	—	8	4	no	—
202	C₂×C₄₃	—	16	2	no	—
203	C₂×C₄₃	#2541	1	1	yes	characteristic
204	C₂×C₄₃	C₂×#463	1	2	yes	—
205	C₂×C₄₃	#3147	1	1	yes	characteristic
206	C₂×C₄₃	#3151	1	1	yes	characteristic
207	C₂×C₄₃	#3207	1	2	yes	—
208	C₂²×SD₁₆	C₂²×C₄₃	1	4	yes	—
209	C₂²×D₈	C₂²×C₄₃	1	4	yes	—
210	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
211	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
212	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
213	C₂×#124	C₂²×C₄₃	1	2	yes	—
214	C₂×#124	C₂²×C₄₃	1	2	yes	—
215	C₂×C₄×D₄	—	2	2	no	—
216	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
217	#493	—	2	4	no	—
218	#492	—	2	4	no	—
219	#463	—	2	16	no	—
220	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
221	C₂×#103	C₂²×C₄₃	1	4	yes	—
222	C₂×#102	C₂²×C₄₃	1	4	yes	—
223	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
225	#390	—	2	2	no	—
226	#390	—	2	2	no	—
227	#390	—	2	2	no	—
228	#390	C₂²×C₄₃	1	2	yes	—
229	#384	C₂²×C₄₃	1	1	yes	characteristic
230	C₄³	C₂²×C₄₃	1	1	yes	characteristic
231	#336	C₂²×C₄₃	1	2	yes	—
232	C₄₃	#28443	1	1	yes	characteristic, direct product factor, Sylow
233	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
237	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
238	C₂³×C₄	—	2	2	no	—
239	C₂×SD₁₆	—	2	8	no	—
240	C₂×SD₁₆	—	2	8	no	—
241	C₂×SD₁₆	—	4	4	no	—
242	C₂×D₈	—	2	8	no	—
243	C₂×D₈	—	2	8	no	—
244	C₂×D₈	—	4	4	no	—
245	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
246	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	—	2	2	no	—
249	#127	—	2	2	no	—
250	#127	—	2	2	no	—
251	#127	—	2	2	no	—
252	#127	D₄×C₄₃	1	4	yes	—
253	#124	—	2	8	no	—
254	#124	—	4	4	no	—
255	C₄×D₄	—	2	8	no	—
256	C₄×D₄	—	4	8	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	D₄×C₄₃	1	2	yes	—
266	C₂×C₄²	D₄×C₄₃	1	2	yes	—
267	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
270	C₄⋊C₈	D₄×C₄₃	1	8	yes	complemented
271	#103	—	2	8	no	—
272	#102	—	2	8	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	2	2	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	—	2	2	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	4	no	—
292	C₂×D₄	—	4	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	8	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
304	SD₁₆	—	4	16	no	—
305	D₈	—	4	16	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
311	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₂²⋊C₄	—	4	8	no	—
316	C₂²⋊C₄	—	4	8	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₄²	—	2	4	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	2	no	—
323	C₄²	C₂×D₄×C₄₃	1	2	yes	—
324	C₄²	C₂×D₄×C₄₃	1	4	yes	—
325	C₄²	#41×C₄₃	1	2	yes	—
326	C₂³	—	2	4	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	4	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	4	4	no	—
336	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	Q₈	—	4	4	no	—
339	D₄	—	2	8	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	16	no	—
344	D₄	—	8	8	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	8	8	no	—
356	C₂×C₄	#121×C₄₃	1	4	yes	—
357	C₂×C₄	#127×C₄₃	1	2	yes	—
358	C₂×C₄	#127×C₄₃	1	2	yes	—
359	C₂×C₄	#135×C₄₃	1	4	yes	—
360	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
361	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
363	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
364	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
365	C₈	—	2	4	no	—
366	C₈	—	2	4	no	—
367	C₂²	—	4	8	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	4	no	—
375	C₂²	—	8	4	no	—
376	C₂²	—	8	2	no	—
377	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
378	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
379	C₂²	C₄₃×#535	1	1	yes	characteristic
380	C₂²	C₂×#135×C₄₃	1	2	yes	—
381	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₄₃×#463	1	8	yes	complemented
388	C₄	D₄²×C₄₃	1	2	yes	—
389	C₄	C₄₃×#550	1	2	yes	—
390	C₂	—	8	4	no	—
391	C₂	—	16	2	no	—
392	C₂	C₄₃×#2541	1	1	yes	characteristic
393	C₂	C₂×C₄₃×#463	1	2	yes	—
394	C₂	C₄₃×#3147	1	1	yes	characteristic
395	C₂	C₄₃×#3151	1	1	yes	characteristic
396	C₂	C₄₃×#3207	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#493	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
2. C₂×C₄₃×#492	C₂	semidirect
3. C₂×C₄₃×#463	C₂	semidirect
4. C₄₃×#2858	C₂	semidirect
5. C₄×#127×C₄₃	C₂	semidirect
6. C₄₃×#2012	C₂	semidirect
7. C₄₃×#1957	C₂	semidirect
8. C₄₃×#1956	C₂	semidirect
9. C₄×C₄⋊C₈×C₄₃	C₂	semidirect
71. C₄⋊C₈×C₄₃	D₄	semidirect
168. #28443	C₄₃	direct (N × H)
189. C₄×C₄₃	#463	semidirect
193. C₂×#492	C₂×C₄₃	semidirect
194. C₂×#463	C₂×C₄₃	semidirect
195. #2858	C₂×C₄₃	semidirect
196. C₄×#127	C₂×C₄₃	semidirect
197. #2012	C₂×C₄₃	semidirect
198. #1957	C₂×C₄₃	semidirect
199. #1956	C₂×C₄₃	semidirect
200. C₄×C₄⋊C₈	C₂×C₄₃	semidirect
232. C₄₃	#28443	direct (N × H)
270. C₄⋊C₈	D₄×C₄₃	semidirect
387. C₄	C₄₃×#463	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#493	2
C₂×C₄₃×#492	2
C₂×C₄₃×#463	2
C₄₃×#2858	2
C₄×#127×C₄₃	2
C₄₃×#2012	2
C₄₃×#1957	2
C₄₃×#1956	2
C₄×C₄⋊C₈×C₄₃	2
#28443	43

Subgroups — C43×#28443 #24948460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28443 #24948460