Subgroups — C₄₃×#9231 #24929248

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3101	C₂	1	1	yes	maximal, characteristic
2	C₄²×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1503	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1486	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1276	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#533	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄×C₄₃	—	2	1	no	—
10	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₄₃	—	2	1	no	—
12	C₄₃×#483	—	2	1	no	—
13	C₄₃×#476	C₄	1	2	yes	complemented
14	C₄₃×#461	C₄	1	2	yes	complemented
15	C₄₃×#450	—	2	1	no	—
16	C₄×SD₁₆×C₄₃	—	2	2	no	—
17	C₄₃×#431	C₂²	1	1	yes	characteristic
18	C₄₃×#431	C₂²	1	1	yes	characteristic
19	C₄₃×#423	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
21	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
23	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
24	C₄³×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#339	—	2	1	no	—
26	C₄₃×#339	—	2	1	no	—
27	C₄₃×#328	—	2	2	no	—
28	C₄₃×D₄⋊C₈	—	2	2	no	—
29	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₃	—	2	2	no	—
31	C₂³×C₄×C₄₃	—	2	1	no	—
32	C₂×SD₁₆×C₄₃	—	2	2	no	—
33	C₂×M₁₆×C₄₃	—	2	1	no	—
34	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic, complemented
35	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic, complemented
36	#125×C₄₃	—	2	1	no	—
37	C₂²⋊Q₈×C₄₃	—	2	1	no	—
38	C₂²⋊Q₈×C₄₃	—	2	1	no	—
39	C₄×Q₈×C₄₃	—	2	1	no	—
40	C₄×Q₈×C₄₃	—	2	1	no	—
41	C₄×D₄×C₄₃	—	2	8	no	—
42	C₄×D₄×C₄₃	—	2	1	no	—
43	C₄×D₄×C₄₃	—	2	1	no	—
44	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
45	C₄×D₄×C₄₃	D₄	1	2	yes	—
46	#117×C₄₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
51	C₂×C₄²×C₄₃	—	2	1	no	—
52	C₂×C₄²×C₄₃	—	2	2	no	—
53	C₂×C₄²×C₄₃	—	2	1	no	—
54	C₂×C₄²×C₄₃	—	2	1	no	—
55	C₂×C₄²×C₄₃	—	4	2	no	—
56	C₂×C₄²×C₄₃	—	4	2	no	—
57	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
60	#106×C₄₃	—	2	2	no	—
61	C₄⋊C₈×C₄₃	—	2	1	no	—
62	C₄⋊C₈×C₄₃	—	2	1	no	—
63	C₄⋊C₈×C₄₃	—	2	1	no	—
64	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	complemented
65	#103×C₄₃	—	2	2	no	—
66	#102×C₄₃	—	2	2	no	—
67	C₂²⋊C₈×C₄₃	—	2	1	no	—
68	C₂²⋊C₈×C₄₃	—	2	1	no	—
69	C₄×C₈×C₄₃	—	2	1	no	—
70	C₄×C₈×C₄₃	—	2	1	no	—
71	#95×C₄₃	—	2	2	no	—
72	#95×C₄₃	D₄	1	2	yes	—
73	C₂⁴×C₄₃	—	2	1	no	—
74	C₂×Q₈×C₄₃	—	2	1	no	—
75	C₂×Q₈×C₄₃	—	2	1	no	—
76	C₂×D₄×C₄₃	—	2	4	no	—
77	C₂×D₄×C₄₃	—	2	1	no	—
78	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₄₃	—	2	8	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	—	4	4	no	—
87	C₂²×C₄×C₄₃	—	4	4	no	—
88	C₂²×C₄×C₄₃	—	4	1	no	—
89	C₂²×C₄×C₄₃	—	4	1	no	—
90	C₂²×C₄×C₄₃	—	4	1	no	—
91	C₂²×C₄×C₄₃	—	4	1	no	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	SD₁₆×C₄₃	—	4	4	no	—
96	M₁₆×C₄₃	—	4	1	no	—
97	M₁₆×C₄₃	—	4	1	no	—
98	C₂×C₈×C₄₃	—	2	2	no	—
99	C₂×C₈×C₄₃	—	4	1	no	—
100	C₂×C₈×C₄₃	—	4	1	no	—
101	C₄⋊C₄×C₄₃	—	2	4	no	—
102	C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₄⋊C₄×C₄₃	—	2	1	no	—
104	C₄⋊C₄×C₄₃	—	2	1	no	—
105	C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₄⋊C₄×C₄₃	—	2	1	no	—
107	C₄⋊C₄×C₄₃	—	4	1	no	—
108	C₄⋊C₄×C₄₃	—	4	1	no	—
109	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
110	C₂²⋊C₄×C₄₃	—	2	8	no	—
111	C₂²⋊C₄×C₄₃	—	2	2	no	—
112	C₂²⋊C₄×C₄₃	—	2	2	no	—
113	C₂²⋊C₄×C₄₃	—	4	1	no	—
114	C₄²×C₄₃	—	2	4	no	—
115	C₄²×C₄₃	—	2	1	no	—
116	C₄²×C₄₃	—	2	1	no	—
117	C₄²×C₄₃	—	2	1	no	—
118	C₄²×C₄₃	—	4	2	no	—
119	C₄²×C₄₃	—	4	4	no	—
120	C₄²×C₄₃	—	4	1	no	—
121	C₄²×C₄₃	—	4	1	no	—
122	C₄²×C₄₃	—	4	1	no	—
123	C₄²×C₄₃	SD₁₆	1	2	yes	complemented
124	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₃	#41	1	1	yes	characteristic
127	C₄²×C₄₃	#41	1	1	yes	characteristic
128	C₂³×C₄₃	—	2	4	no	—
129	C₂³×C₄₃	—	2	2	no	—
130	C₂³×C₄₃	—	4	2	no	—
131	C₂³×C₄₃	—	4	1	no	—
132	C₂³×C₄₃	—	4	1	no	—
133	C₂³×C₄₃	#120	1	1	yes	characteristic
134	Q₈×C₄₃	—	4	2	no	—
135	Q₈×C₄₃	—	8	1	no	—
136	D₄×C₄₃	—	2	4	no	—
137	D₄×C₄₃	—	2	2	no	—
138	D₄×C₄₃	#104	1	4	yes	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	2	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	2	no	—
144	C₂×C₄×C₄₃	—	2	4	no	—
145	C₂×C₄×C₄₃	—	2	2	no	—
146	C₂×C₄×C₄₃	—	4	1	no	—
147	C₂×C₄×C₄₃	—	4	16	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	1	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
168	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
170	C₈×C₄₃	—	4	2	no	—
171	C₈×C₄₃	—	8	1	no	—
172	C₈×C₄₃	—	8	1	no	—
173	#9231	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₃	—	2	1	no	—
175	C₂²×C₄₃	—	2	1	no	—
176	C₂²×C₄₃	—	2	4	no	—
177	C₂²×C₄₃	—	4	4	no	—
178	C₂²×C₄₃	—	4	4	no	—
179	C₂²×C₄₃	—	4	2	no	—
180	C₂²×C₄₃	—	4	2	no	—
181	C₂²×C₄₃	#386	1	1	yes	characteristic
182	C₂²×C₄₃	#450	1	1	yes	characteristic
183	C₂²×C₄₃	#452	1	1	yes	characteristic
184	C₄×C₄₃	—	2	4	no	—
185	C₄×C₄₃	—	2	1	no	—
186	C₄×C₄₃	—	2	1	no	—
187	C₄×C₄₃	—	2	1	no	—
188	C₄×C₄₃	—	4	2	no	—
189	C₄×C₄₃	—	4	4	no	—
190	C₄×C₄₃	—	4	2	no	—
191	C₄×C₄₃	—	8	1	no	—
192	C₄×C₄₃	—	8	1	no	—
193	C₄×C₄₃	C₂×#104	1	2	yes	—
194	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
195	C₄×C₄₃	#440	1	1	yes	characteristic
196	C₄×C₄₃	#461	1	1	yes	characteristic
197	C₄×C₄₃	#463	1	1	yes	characteristic
198	#3101	C₂×C₄₃	1	1	yes	characteristic
199	C₄²×D₄	C₂×C₄₃	1	1	yes	characteristic
200	#1994	C₂×C₄₃	1	1	yes	characteristic, complemented
201	#1503	C₂×C₄₃	1	1	yes	characteristic, complemented
202	#1486	C₂×C₄₃	1	1	yes	characteristic
203	#1303	C₂×C₄₃	1	1	yes	characteristic, complemented
204	#1276	C₂×C₄₃	1	1	yes	characteristic, complemented
205	C₂×C₄₃	—	2	1	no	—
206	C₂×C₄₃	—	2	1	no	—
207	C₂×C₄₃	—	4	4	no	—
208	C₂×C₄₃	#1877	1	1	yes	characteristic
209	C₂×C₄₃	#1896	1	1	yes	characteristic
210	C₂×C₄₃	#1906	1	1	yes	characteristic
211	#533	C₂²×C₄₃	1	1	yes	characteristic
212	C₂×C₄×D₄	—	2	1	no	—
213	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
214	C₂²×C₄²	—	2	1	no	—
215	#483	—	2	1	no	—
216	#476	C₄×C₄₃	1	2	yes	complemented
217	#461	C₄×C₄₃	1	2	yes	complemented
218	#450	—	2	1	no	—
219	C₄×SD₁₆	—	2	2	no	—
220	#431	C₂²×C₄₃	1	1	yes	characteristic
221	#431	C₂²×C₄₃	1	1	yes	characteristic
222	#423	C₂²×C₄₃	1	1	yes	characteristic
223	C₄×C₄⋊C₄	—	2	1	no	—
224	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
225	C₄×C₂²⋊C₄	—	2	1	no	—
226	C₄×C₂²⋊C₄	—	2	2	no	—
227	C₄³	C₂²×C₄₃	1	1	yes	characteristic
228	#339	—	2	1	no	—
229	#339	—	2	1	no	—
230	#328	—	2	2	no	—
231	D₄⋊C₈	—	2	2	no	—
232	C₄₃	#9231	1	1	yes	characteristic, direct product factor, Sylow
233	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	—	2	1	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₄⋊Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic, complemented
239	C₄⋊Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic, complemented
240	#125	—	2	1	no	—
241	C₂²⋊Q₈	—	2	1	no	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×D₄	—	2	8	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
249	C₄×D₄	D₄×C₄₃	1	2	yes	—
250	#117	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	4	2	no	—
260	C₂×C₄²	—	4	2	no	—
261	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
264	#106	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	C₂×C₄×C₄₃	1	2	yes	complemented
269	#103	—	2	2	no	—
270	#102	—	2	2	no	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₄×C₈	—	2	1	no	—
274	C₄×C₈	—	2	1	no	—
275	#95	—	2	2	no	—
276	#95	D₄×C₄₃	1	2	yes	—
277	C₂⁴	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	C₂²⋊C₄×C₄₃	1	2	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
299	SD₁₆	—	4	4	no	—
300	M₁₆	—	4	1	no	—
301	M₁₆	—	4	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	4	4	no	—
323	C₄²	—	4	2	no	—
324	C₄²	—	4	1	no	—
325	C₄²	—	4	1	no	—
326	C₄²	—	4	1	no	—
327	C₄²	SD₁₆×C₄₃	1	2	yes	complemented
328	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
330	C₄²	#41×C₄₃	1	1	yes	characteristic
331	C₄²	#41×C₄₃	1	1	yes	characteristic
332	C₂³	—	2	4	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	1	no	—
337	C₂³	#120×C₄₃	1	1	yes	characteristic
338	Q₈	—	4	2	no	—
339	Q₈	—	8	1	no	—
340	D₄	—	2	4	no	—
341	D₄	—	2	2	no	—
342	D₄	#104×C₄₃	1	4	yes	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	16	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
365	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
366	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
367	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
368	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
369	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
370	C₂×C₄	C₂×SD₁₆×C₄₃	1	1	yes	characteristic
371	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
372	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
373	C₂×C₄	#137×C₄₃	1	1	yes	characteristic
374	C₈	—	4	2	no	—
375	C₈	—	8	1	no	—
376	C₈	—	8	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	C₄₃×#386	1	1	yes	characteristic
385	C₂²	C₄₃×#450	1	1	yes	characteristic
386	C₂²	C₄₃×#452	1	1	yes	characteristic
387	C₄	—	2	4	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	1	no	—
396	C₄	C₂×#104×C₄₃	1	2	yes	—
397	C₄	C₄×SD₁₆×C₄₃	1	1	yes	characteristic
398	C₄	C₄₃×#440	1	1	yes	characteristic
399	C₄	C₄₃×#461	1	1	yes	characteristic
400	C₄	C₄₃×#463	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	4	no	—
404	C₂	C₄₃×#1877	1	1	yes	characteristic
405	C₂	C₄₃×#1896	1	1	yes	characteristic
406	C₂	C₄₃×#1906	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	#121
commutator	C₄²	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
socle	C₂²×C₄₃	#386
prime radical	C₂²×D₄×C₄₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₃×#1994	C₂	semidirect
4. C₄₃×#1503	C₂	semidirect
6. C₄₃×#1303	C₂	semidirect
7. C₄₃×#1276	C₂	semidirect
13. C₄₃×#476	C₄	semidirect
14. C₄₃×#461	C₄	semidirect
34. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
35. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
64. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
123. C₄²×C₄₃	SD₁₆	semidirect
173. #9231	C₄₃	direct (N × H)
200. #1994	C₂×C₄₃	semidirect
201. #1503	C₂×C₄₃	semidirect
203. #1303	C₂×C₄₃	semidirect
204. #1276	C₂×C₄₃	semidirect
216. #476	C₄×C₄₃	semidirect
217. #461	C₄×C₄₃	semidirect
232. C₄₃	#9231	direct (N × H)
238. C₄⋊Q₈	C₂×C₄×C₄₃	semidirect
239. C₄⋊Q₈	C₂×C₄×C₄₃	semidirect
268. C₄⋊C₈	C₂×C₄×C₄₃	semidirect
327. C₄²	SD₁₆×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3101	2
C₄²×D₄×C₄₃	2
C₄₃×#1994	2
C₄₃×#1503	2
C₄₃×#1486	2
C₄₃×#1303	2
C₄₃×#1276	2
#9231	43

Subgroups — C43×#9231 #24929248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#9231 #24929248