Subgroups — C₄₃×#29824 #24949841

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#474	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×#2067	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2054	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1988	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	1	no	—
14	C₂×#124×C₄₃	—	2	1	no	—
15	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₃	—	2	1	no	—
17	C₄₃×#474	—	2	4	no	—
18	C₄₃×#459	—	2	4	no	—
19	C₂×#107×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	4	yes	—
26	C₄₃×#390	—	2	2	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	4	no	—
50	#124×C₄₃	—	4	4	no	—
51	C₄×D₄×C₄₃	—	2	2	no	—
52	C₄×D₄×C₄₃	D₄	1	4	yes	—
53	#117×C₄₃	—	4	4	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₄²×C₄₃	—	2	1	no	—
65	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	D₄	1	2	yes	—
67	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	#107×C₄₃	—	2	4	no	—
71	C₄⋊C₈×C₄₃	—	2	2	no	—
72	C₄⋊C₈×C₄₃	—	2	2	no	—
73	C₄⋊C₈×C₄₃	—	4	4	no	—
74	#102×C₄₃	—	2	4	no	—
75	#102×C₄₃	—	2	4	no	—
76	#102×C₄₃	—	4	4	no	—
77	#95×C₄₃	—	2	2	no	—
78	#95×C₄₃	—	2	1	no	—
79	C₂⁴×C₄₃	—	2	1	no	—
80	C₂⁴×C₄₃	—	2	2	no	—
81	C₂×Q₈×C₄₃	—	4	2	no	—
82	C₂×Q₈×C₄₃	—	4	2	no	—
83	C₂×Q₈×C₄₃	—	4	2	no	—
84	C₂×D₄×C₄₃	—	2	1	no	—
85	C₂×D₄×C₄₃	—	2	2	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	2	no	—
90	C₂×D₄×C₄₃	—	2	4	no	—
91	C₂×D₄×C₄₃	—	4	4	no	—
92	C₂×D₄×C₄₃	—	4	2	no	—
93	C₂×D₄×C₄₃	—	4	2	no	—
94	C₂×D₄×C₄₃	—	4	2	no	—
95	C₂×D₄×C₄₃	—	4	2	no	—
96	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	4	2	no	—
102	C₂²×C₄×C₄₃	—	4	2	no	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	D₈×C₄₃	—	4	8	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	2	4	no	—
112	C₂×C₈×C₄₃	—	2	4	no	—
113	C₄⋊C₄×C₄₃	—	2	1	no	—
114	C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	4	2	no	—
119	C₄⋊C₄×C₄₃	—	4	4	no	—
120	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²⋊C₄×C₄₃	—	2	4	no	—
122	C₂²⋊C₄×C₄₃	—	4	4	no	—
123	C₂²⋊C₄×C₄₃	—	4	8	no	—
124	C₂²⋊C₄×C₄₃	—	4	4	no	—
125	C₂²⋊C₄×C₄₃	—	4	8	no	—
126	C₄²×C₄₃	—	2	2	no	—
127	C₄²×C₄₃	—	2	2	no	—
128	C₄²×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	—	4	2	no	—
130	C₄²×C₄₃	—	4	2	no	—
131	C₄²×C₄₃	D₈	1	4	yes	complemented
132	C₄²×C₄₃	C₂×D₄	1	2	yes	—
133	C₄²×C₄₃	#41	1	2	yes	—
134	C₂³×C₄₃	—	2	2	no	—
135	C₂³×C₄₃	—	4	2	no	—
136	C₂³×C₄₃	—	4	1	no	—
137	C₂³×C₄₃	—	4	1	no	—
138	C₂³×C₄₃	—	4	2	no	—
139	C₂³×C₄₃	—	4	2	no	—
140	C₂³×C₄₃	—	4	4	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	4	2	no	—
143	C₂³×C₄₃	—	4	4	no	—
144	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₄₃	—	8	4	no	—
146	D₄×C₄₃	—	2	2	no	—
147	D₄×C₄₃	—	2	2	no	—
148	D₄×C₄₃	—	4	2	no	—
149	D₄×C₄₃	—	4	2	no	—
150	D₄×C₄₃	—	4	2	no	—
151	D₄×C₄₃	—	4	4	no	—
152	D₄×C₄₃	—	8	4	no	—
153	D₄×C₄₃	—	8	4	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	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	8	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	#121	1	2	yes	—
171	C₂×C₄×C₄₃	#121	1	2	yes	—
172	C₂×C₄×C₄₃	C₂×D₈	1	4	yes	—
173	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
174	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
179	C₈×C₄₃	—	4	2	no	—
180	C₈×C₄₃	—	4	2	no	—
181	#29824	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₃	—	4	2	no	—
183	C₂²×C₄₃	—	4	2	no	—
184	C₂²×C₄₃	—	4	2	no	—
185	C₂²×C₄₃	—	8	2	no	—
186	C₂²×C₄₃	—	8	2	no	—
187	C₂²×C₄₃	—	8	2	no	—
188	C₂²×C₄₃	—	8	4	no	—
189	C₂²×C₄₃	—	8	4	no	—
190	C₂²×C₄₃	—	8	2	no	—
191	C₂²×C₄₃	—	8	2	no	—
192	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
193	C₂²×C₄₃	#537	1	2	yes	—
194	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
195	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₂²×C₄₃	#575	1	2	yes	—
197	C₄×C₄₃	—	2	4	no	—
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	4	2	no	—
201	C₄×C₄₃	—	8	2	no	—
202	C₄×C₄₃	—	8	2	no	—
203	C₄×C₄₃	#459	1	4	yes	—
204	C₄×C₄₃	#535	1	1	yes	characteristic
205	C₄×C₄₃	#536	1	1	yes	characteristic
206	C₄×C₄₃	#542	1	2	yes	—
207	C₂×#474	C₂×C₄₃	1	1	yes	characteristic, complemented
208	C₂×#459	C₂×C₄₃	1	1	yes	characteristic
209	#2858	C₂×C₄₃	1	1	yes	characteristic, complemented
210	#2293	C₂×C₄₃	1	1	yes	characteristic, complemented
211	#2067	C₂×C₄₃	1	4	yes	complemented
212	#2054	C₂×C₄₃	1	4	yes	complemented
213	#1988	C₂×C₄₃	1	1	yes	characteristic, complemented
214	#1982	C₂×C₄₃	1	1	yes	characteristic, complemented
215	#1842	C₂×C₄₃	1	1	yes	characteristic, complemented
216	C₂×C₄₃	—	8	2	no	—
217	C₂×C₄₃	—	16	2	no	—
218	C₂×C₄₃	#2620	1	1	yes	characteristic
219	C₂×C₄₃	C₂×#459	1	1	yes	characteristic
220	C₂×C₄₃	#3040	1	1	yes	characteristic
221	C₂×C₄₃	#3245	1	2	yes	—
222	C₂×C₄₃	#3251	1	2	yes	—
223	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
224	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
225	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
226	C₂×#124	—	2	1	no	—
227	C₂×#124	—	2	1	no	—
228	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
229	C₂×#117	—	2	1	no	—
230	#474	—	2	4	no	—
231	#459	—	2	4	no	—
232	C₂×#107	C₂²×C₄₃	1	2	yes	—
233	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	—
236	C₂×#102	C₂²×C₄₃	1	2	yes	—
237	C₂×#102	C₂²×C₄₃	1	2	yes	—
238	C₂×#102	C₂²×C₄₃	1	4	yes	—
239	#390	—	2	2	no	—
240	#390	C₂²×C₄₃	1	2	yes	—
241	#390	C₂²×C₄₃	1	4	yes	—
242	#389	C₂²×C₄₃	1	2	yes	—
243	#388	—	2	2	no	—
244	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
245	C₄×C₂²⋊C₄	—	2	1	no	—
246	C₄³	C₂²×C₄₃	1	1	yes	characteristic
247	#340	C₂²×C₄₃	1	4	yes	—
248	C₄₃	#29824	1	1	yes	characteristic, direct product factor, Sylow
249	C₂²×Q₈	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
253	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
254	C₂³×C₄	—	2	1	no	—
255	C₂×D₈	—	2	4	no	—
256	C₂×D₈	—	4	4	no	—
257	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
258	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	#127	—	2	2	no	—
262	#127	—	2	2	no	—
263	#124	—	4	4	no	—
264	#124	—	4	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	D₄×C₄₃	1	4	yes	—
267	#117	—	4	4	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
280	C₂×C₄²	D₄×C₄₃	1	2	yes	—
281	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
283	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
284	#107	—	2	4	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	4	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	4	no	—
290	#102	—	4	4	no	—
291	#95	—	2	2	no	—
292	#95	—	2	1	no	—
293	C₂⁴	—	2	1	no	—
294	C₂⁴	—	2	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
322	D₈	—	4	8	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	4	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	4	8	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₂²⋊C₄	—	4	4	no	—
339	C₂²⋊C₄	—	4	8	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	2	no	—
344	C₄²	—	4	2	no	—
345	C₄²	D₈×C₄₃	1	4	yes	complemented
346	C₄²	C₂×D₄×C₄₃	1	2	yes	—
347	C₄²	#41×C₄₃	1	2	yes	—
348	C₂³	—	2	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
359	Q₈	—	8	4	no	—
360	D₄	—	2	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	4	no	—
367	D₄	—	8	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	#121×C₄₃	1	2	yes	—
385	C₂×C₄	#121×C₄₃	1	2	yes	—
386	C₂×C₄	C₂×D₈×C₄₃	1	4	yes	—
387	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
388	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
389	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
391	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
392	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	4	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
406	C₂²	C₄₃×#537	1	2	yes	—
407	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
408	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
409	C₂²	C₄₃×#575	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	—	8	2	no	—
416	C₄	C₄₃×#459	1	4	yes	—
417	C₄	C₄₃×#535	1	1	yes	characteristic
418	C₄	C₄₃×#536	1	1	yes	characteristic
419	C₄	C₄₃×#542	1	2	yes	—
420	C₂	—	8	2	no	—
421	C₂	—	16	2	no	—
422	C₂	C₄₃×#2620	1	1	yes	characteristic
423	C₂	C₂×C₄₃×#459	1	1	yes	characteristic
424	C₂	C₄₃×#3040	1	1	yes	characteristic
425	C₂	C₄₃×#3245	1	2	yes	—
426	C₂	C₄₃×#3251	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×#474	C₂	semidirect
3. C₄₃×#2858	C₂	semidirect
4. C₄₃×#2293	C₂	semidirect
5. C₄₃×#2067	C₂	semidirect
6. C₄₃×#2054	C₂	semidirect
7. C₄₃×#1988	C₂	semidirect
8. C₄₃×#1982	C₂	semidirect
9. C₄₃×#1842	C₂	semidirect
131. C₄²×C₄₃	D₈	semidirect
181. #29824	C₄₃	direct (N × H)
207. C₂×#474	C₂×C₄₃	semidirect
209. #2858	C₂×C₄₃	semidirect
210. #2293	C₂×C₄₃	semidirect
211. #2067	C₂×C₄₃	semidirect
212. #2054	C₂×C₄₃	semidirect
213. #1988	C₂×C₄₃	semidirect
214. #1982	C₂×C₄₃	semidirect
215. #1842	C₂×C₄₃	semidirect
248. C₄₃	#29824	direct (N × H)
345. C₄²	D₈×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×#474	2
C₂×C₄₃×#459	2
C₄₃×#2858	2
C₄₃×#2293	2
C₄₃×#2067	2
C₄₃×#2054	2
C₄₃×#1988	2
C₄₃×#1982	2
C₄₃×#1842	2
#29824	43

Subgroups — C43×#29824 #24949841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29824 #24949841