Subgroups — C₄₃×#29825 #24949842

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2065	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2054	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₃	—	2	2	no	—
14	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₃	—	2	1	no	—
16	C₄₃×#476	—	2	4	no	—
17	C₄₃×#459	—	2	4	no	—
18	C₂×#106×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
22	C₂×#102×C₄₃	C₂²	1	2	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	4	yes	—
25	C₄₃×#390	—	2	1	no	—
26	C₄₃×#390	—	2	1	no	—
27	C₄₃×#390	C₂²	1	4	yes	—
28	C₄₃×#390	C₂²	1	2	yes	—
29	C₄₃×#389	C₂²	1	2	yes	—
30	C₄₃×#388	—	2	2	no	—
31	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
33	C₄³×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#340	C₂²	1	4	yes	—
35	C₂²×Q₈×C₄₃	—	2	1	no	—
36	C₂²×D₄×C₄₃	—	2	1	no	—
37	C₂²×D₄×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
39	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	—	2	1	no	—
41	C₂×D₈×C₄₃	—	2	4	no	—
42	C₂×D₈×C₄₃	—	4	4	no	—
43	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
45	C₄⋊Q₈×C₄₃	—	2	2	no	—
46	C₄⋊Q₈×C₄₃	—	2	2	no	—
47	#127×C₄₃	—	2	2	no	—
48	#127×C₄₃	—	2	2	no	—
49	#124×C₄₃	—	4	8	no	—
50	C₄×D₄×C₄₃	—	2	2	no	—
51	C₄×D₄×C₄₃	D₄	1	4	yes	—
52	#117×C₄₃	—	4	4	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄²×C₄₃	—	2	1	no	—
64	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	D₄	1	2	yes	—
66	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	#106×C₄₃	—	2	4	no	—
70	C₄⋊C₈×C₄₃	—	2	2	no	—
71	C₄⋊C₈×C₄₃	—	2	2	no	—
72	C₄⋊C₈×C₄₃	—	4	4	no	—
73	#102×C₄₃	—	2	4	no	—
74	#102×C₄₃	—	2	4	no	—
75	#102×C₄₃	—	4	4	no	—
76	#95×C₄₃	—	2	2	no	—
77	#95×C₄₃	—	2	1	no	—
78	C₂⁴×C₄₃	—	2	1	no	—
79	C₂⁴×C₄₃	—	2	2	no	—
80	C₂×Q₈×C₄₃	—	4	4	no	—
81	C₂×Q₈×C₄₃	—	4	2	no	—
82	C₂×D₄×C₄₃	—	2	1	no	—
83	C₂×D₄×C₄₃	—	2	2	no	—
84	C₂×D₄×C₄₃	—	2	2	no	—
85	C₂×D₄×C₄₃	—	2	2	no	—
86	C₂×D₄×C₄₃	—	2	4	no	—
87	C₂×D₄×C₄₃	—	2	2	no	—
88	C₂×D₄×C₄₃	—	2	4	no	—
89	C₂×D₄×C₄₃	—	4	4	no	—
90	C₂×D₄×C₄₃	—	4	2	no	—
91	C₂×D₄×C₄₃	—	4	2	no	—
92	C₂×D₄×C₄₃	—	4	2	no	—
93	C₂×D₄×C₄₃	—	4	2	no	—
94	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₃	—	2	4	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	4	2	no	—
100	C₂²×C₄×C₄₃	—	4	2	no	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
106	D₈×C₄₃	—	4	8	no	—
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	4	no	—
110	C₂×C₈×C₄₃	—	2	4	no	—
111	C₄⋊C₄×C₄₃	—	2	1	no	—
112	C₄⋊C₄×C₄₃	—	2	2	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	4	4	no	—
117	C₄⋊C₄×C₄₃	—	4	2	no	—
118	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
119	C₂²⋊C₄×C₄₃	—	2	4	no	—
120	C₂²⋊C₄×C₄₃	—	4	4	no	—
121	C₂²⋊C₄×C₄₃	—	4	8	no	—
122	C₂²⋊C₄×C₄₃	—	4	4	no	—
123	C₂²⋊C₄×C₄₃	—	4	8	no	—
124	C₄²×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	—	2	4	no	—
127	C₄²×C₄₃	—	2	2	no	—
128	C₄²×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	—	4	2	no	—
130	C₄²×C₄₃	C₂×D₄	1	2	yes	—
131	C₄²×C₄₃	#41	1	2	yes	—
132	C₂³×C₄₃	—	2	2	no	—
133	C₂³×C₄₃	—	4	2	no	—
134	C₂³×C₄₃	—	4	1	no	—
135	C₂³×C₄₃	—	4	1	no	—
136	C₂³×C₄₃	—	4	2	no	—
137	C₂³×C₄₃	—	4	2	no	—
138	C₂³×C₄₃	—	4	4	no	—
139	C₂³×C₄₃	—	4	2	no	—
140	C₂³×C₄₃	—	4	4	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₄₃	—	8	4	no	—
144	D₄×C₄₃	—	2	2	no	—
145	D₄×C₄₃	—	2	2	no	—
146	D₄×C₄₃	—	4	2	no	—
147	D₄×C₄₃	—	4	2	no	—
148	D₄×C₄₃	—	4	2	no	—
149	D₄×C₄₃	—	4	4	no	—
150	D₄×C₄₃	—	8	4	no	—
151	D₄×C₄₃	—	8	4	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	4	8	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	#121	1	2	yes	—
168	C₂×C₄×C₄₃	#121	1	2	yes	—
169	C₂×C₄×C₄₃	#135	1	2	yes	—
170	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
171	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
175	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
176	C₈×C₄₃	—	4	2	no	—
177	C₈×C₄₃	—	4	2	no	—
178	#29825	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₃	—	4	2	no	—
180	C₂²×C₄₃	—	4	2	no	—
181	C₂²×C₄₃	—	4	2	no	—
182	C₂²×C₄₃	—	8	2	no	—
183	C₂²×C₄₃	—	8	2	no	—
184	C₂²×C₄₃	—	8	2	no	—
185	C₂²×C₄₃	—	8	4	no	—
186	C₂²×C₄₃	—	8	4	no	—
187	C₂²×C₄₃	—	8	2	no	—
188	C₂²×C₄₃	—	8	2	no	—
189	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
190	C₂²×C₄₃	#537	1	2	yes	—
191	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
192	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
193	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₄×C₄₃	—	2	4	no	—
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	—	4	2	no	—
197	C₄×C₄₃	—	4	2	no	—
198	C₄×C₄₃	—	8	2	no	—
199	C₄×C₄₃	—	8	2	no	—
200	C₄×C₄₃	#463	1	4	yes	—
201	C₄×C₄₃	#535	1	1	yes	characteristic
202	C₄×C₄₃	#536	1	1	yes	characteristic
203	C₄×C₄₃	#542	1	2	yes	—
204	C₂×#476	C₂×C₄₃	1	1	yes	characteristic, complemented
205	C₂×#459	C₂×C₄₃	1	1	yes	characteristic
206	#2858	C₂×C₄₃	1	1	yes	characteristic, complemented
207	#2293	C₂×C₄₃	1	1	yes	characteristic, complemented
208	#2065	C₂×C₄₃	1	4	yes	complemented
209	#2054	C₂×C₄₃	1	4	yes	complemented
210	#1987	C₂×C₄₃	1	1	yes	characteristic, complemented
211	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
212	#1842	C₂×C₄₃	1	1	yes	characteristic, complemented
213	C₂×C₄₃	—	8	2	no	—
214	C₂×C₄₃	—	16	2	no	—
215	C₂×C₄₃	#2620	1	1	yes	characteristic
216	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
217	C₂×C₄₃	#3038	1	1	yes	characteristic
218	C₂×C₄₃	#3247	1	2	yes	—
219	C₂×C₄₃	#3253	1	2	yes	—
220	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
221	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
222	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
223	C₂×#124	—	2	2	no	—
224	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
225	C₂×#117	—	2	1	no	—
226	#476	—	2	4	no	—
227	#459	—	2	4	no	—
228	C₂×#106	C₂²×C₄₃	1	2	yes	—
229	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	—
232	C₂×#102	C₂²×C₄₃	1	2	yes	—
233	C₂×#102	C₂²×C₄₃	1	2	yes	—
234	C₂×#102	C₂²×C₄₃	1	4	yes	—
235	#390	—	2	1	no	—
236	#390	—	2	1	no	—
237	#390	C₂²×C₄₃	1	2	yes	—
238	#390	C₂²×C₄₃	1	4	yes	—
239	#389	C₂²×C₄₃	1	2	yes	—
240	#388	—	2	2	no	—
241	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	—	2	1	no	—
243	C₄³	C₂²×C₄₃	1	1	yes	characteristic
244	#340	C₂²×C₄₃	1	4	yes	—
245	C₄₃	#29825	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
250	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
251	C₂³×C₄	—	2	1	no	—
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	4	4	no	—
254	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
255	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	—	2	2	no	—
258	#127	—	2	2	no	—
259	#127	—	2	2	no	—
260	#124	—	4	8	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	D₄×C₄₃	1	4	yes	—
263	#117	—	4	4	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₄₃	1	2	yes	—
277	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
279	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
280	#106	—	2	4	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	4	4	no	—
284	#102	—	2	4	no	—
285	#102	—	2	4	no	—
286	#102	—	4	4	no	—
287	#95	—	2	2	no	—
288	#95	—	2	1	no	—
289	C₂⁴	—	2	1	no	—
290	C₂⁴	—	2	2	no	—
291	C₂×Q₈	—	4	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
317	D₈	—	4	8	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	8	no	—
333	C₂²⋊C₄	—	4	8	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	C₂×D₄×C₄₃	1	2	yes	—
342	C₄²	#41×C₄₃	1	2	yes	—
343	C₂³	—	2	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	4	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
354	Q₈	—	8	4	no	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	4	no	—
361	D₄	—	8	4	no	—
362	D₄	—	8	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	#121×C₄₃	1	2	yes	—
379	C₂×C₄	#121×C₄₃	1	2	yes	—
380	C₂×C₄	#135×C₄₃	1	2	yes	—
381	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
382	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
385	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
386	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	4	no	—
396	C₂²	—	8	4	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
400	C₂²	C₄₃×#537	1	2	yes	—
401	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
402	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
403	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	2	no	—
410	C₄	C₄₃×#463	1	4	yes	—
411	C₄	C₄₃×#535	1	1	yes	characteristic
412	C₄	C₄₃×#536	1	1	yes	characteristic
413	C₄	C₄₃×#542	1	2	yes	—
414	C₂	—	8	2	no	—
415	C₂	—	16	2	no	—
416	C₂	C₄₃×#2620	1	1	yes	characteristic
417	C₂	C₂×C₄₃×#463	1	1	yes	characteristic
418	C₂	C₄₃×#3038	1	1	yes	characteristic
419	C₂	C₄₃×#3247	1	2	yes	—
420	C₂	C₄₃×#3253	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#459	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×#476	C₂	semidirect
3. C₄₃×#2858	C₂	semidirect
4. C₄₃×#2293	C₂	semidirect
5. C₄₃×#2065	C₂	semidirect
6. C₄₃×#2054	C₂	semidirect
7. C₄₃×#1987	C₂	semidirect
8. C₄₃×#1982	C₂	semidirect
9. C₄₃×#1842	C₂	semidirect
178. #29825	C₄₃	direct (N × H)
204. C₂×#476	C₂×C₄₃	semidirect
206. #2858	C₂×C₄₃	semidirect
207. #2293	C₂×C₄₃	semidirect
208. #2065	C₂×C₄₃	semidirect
209. #2054	C₂×C₄₃	semidirect
210. #1987	C₂×C₄₃	semidirect
211. #1982	C₂×C₄₃	semidirect
212. #1842	C₂×C₄₃	semidirect
245. C₄₃	#29825	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×#476	2
C₂×C₄₃×#459	2
C₄₃×#2858	2
C₄₃×#2293	2
C₄₃×#2065	2
C₄₃×#2054	2
C₄₃×#1987	2
C₄₃×#1982	2
C₄₃×#1842	2
#29825	43

Subgroups — C43×#29825 #24949842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29825 #24949842