Subgroups — C₄₃×#18574 #24938591

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3498	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1642	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1641	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1639	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1639	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₄₃	—	2	1	no	—
13	C₄₃×#550	—	2	1	no	—
14	C₄₃×#550	C₂²	1	2	yes	—
15	D₄²×C₄₃	—	2	2	no	—
16	D₄²×C₄₃	—	2	2	no	—
17	D₄²×C₄₃	—	2	1	no	—
18	D₄²×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#535	—	2	2	no	—
20	C₄₃×#535	—	2	1	no	—
21	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
22	C₄₃×#532	—	2	1	no	—
23	C₄₃×#532	C₂²	1	1	yes	characteristic
24	C₂×#127×C₄₃	—	2	1	no	—
25	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
26	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#490	—	2	2	no	—
28	C₄₃×#486	C₂²	1	2	yes	complemented
29	C₄₃×#486	C₂²	1	2	yes	complemented
30	C₄₃×#485	—	2	1	no	—
31	C₄₃×#477	—	2	1	no	—
32	C₄₃×#475	C₂²	1	1	yes	characteristic, complemented
33	C₄₃×#474	C₂²	1	1	yes	characteristic, complemented
34	C₄₃×#474	C₂²	1	2	yes	complemented
35	C₄₃×#468	—	2	2	no	—
36	C₄₃×#462	C₂²	1	1	yes	characteristic, complemented
37	C₄₃×#461	C₂²	1	1	yes	characteristic, complemented
38	C₄₃×#461	C₂²	1	2	yes	complemented
39	C₄₃×#460	—	2	1	no	—
40	C₄₃×#452	—	2	1	no	—
41	C₄×Q₁₆×C₄₃	—	2	1	no	—
42	C₄×SD₁₆×C₄₃	—	2	1	no	—
43	C₄₃×#431	C₂²	1	1	yes	characteristic, complemented
44	C₄₃×#423	C₂²	1	1	yes	characteristic, complemented
45	C₄₃×#418	—	2	2	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
47	C₄₃×#331	C₂²	1	2	yes	complemented
48	C₄₃×#331	C₂²	1	2	yes	complemented
49	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
50	C₄₃×D₄⋊C₈	C₂²	1	2	yes	complemented
51	C₄₃×D₄⋊C₈	C₂²	1	2	yes	complemented
52	C₄₃×D₄⋊C₈	C₂²	1	2	yes	complemented
53	H(5,𝔽₂)×C₄₃	—	4	4	no	—
54	H(5,𝔽₂)×C₄₃	—	4	4	no	—
55	C₂×#41×C₄₃	—	2	2	no	—
56	C₂×#41×C₄₃	—	2	2	no	—
57	C₂×#41×C₄₃	—	2	1	no	—
58	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₄₃	—	2	2	no	—
60	C₂²×D₄×C₄₃	—	2	4	no	—
61	C₂²×D₄×C₄₃	—	2	2	no	—
62	C₂²×D₄×C₄₃	—	2	2	no	—
63	C₂²×D₄×C₄₃	—	2	2	no	—
64	C₂²×D₄×C₄₃	—	2	1	no	—
65	C₂²×D₄×C₄₃	—	2	1	no	—
66	C₂²×D₄×C₄₃	D₄	1	2	yes	—
67	C₂×Q₁₆×C₄₃	—	2	1	no	—
68	C₂×SD₁₆×C₄₃	—	2	1	no	—
69	C₂×SD₁₆×C₄₃	—	2	2	no	—
70	C₂×M₁₆×C₄₃	—	2	1	no	—
71	C₂×M₁₆×C₄₃	—	2	1	no	—
72	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
75	#127×C₄₃	—	2	2	no	—
76	#127×C₄₃	—	2	2	no	—
77	#127×C₄₃	—	2	2	no	—
78	#127×C₄₃	—	2	1	no	—
79	#127×C₄₃	—	2	1	no	—
80	#127×C₄₃	D₄	1	1	yes	characteristic
81	#127×C₄₃	D₄	1	2	yes	—
82	#127×C₄₃	C₂³	1	2	yes	—
83	#125×C₄₃	—	2	1	no	—
84	#124×C₄₃	—	2	2	no	—
85	#124×C₄₃	—	2	1	no	—
86	C₂²⋊Q₈×C₄₃	—	2	1	no	—
87	C₂²⋊Q₈×C₄₃	—	2	1	no	—
88	#121×C₄₃	—	2	2	no	—
89	#121×C₄₃	—	2	4	no	—
90	#121×C₄₃	—	2	4	no	—
91	#121×C₄₃	—	2	1	no	—
92	#121×C₄₃	—	2	2	no	—
93	#121×C₄₃	—	2	2	no	—
94	#121×C₄₃	—	2	2	no	—
95	#121×C₄₃	D₄	1	2	yes	—
96	#120×C₄₃	—	2	4	no	—
97	#120×C₄₃	—	2	4	no	—
98	#120×C₄₃	—	2	4	no	—
99	C₄×Q₈×C₄₃	—	2	1	no	—
100	C₄×Q₈×C₄₃	—	2	1	no	—
101	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
102	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₄₃	—	2	2	no	—
104	C₄×D₄×C₄₃	—	2	1	no	—
105	C₄×D₄×C₄₃	—	2	1	no	—
106	C₄×D₄×C₄₃	—	2	2	no	—
107	C₄×D₄×C₄₃	—	2	1	no	—
108	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
109	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
110	C₄×D₄×C₄₃	C₂³	1	2	yes	—
111	#117×C₄₃	—	2	1	no	—
112	#117×C₄₃	—	2	1	no	—
113	#117×C₄₃	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₄₃	—	2	1	no	—
115	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	#107×C₄₃	—	2	1	no	—
117	#107×C₄₃	—	2	2	no	—
118	#106×C₄₃	—	2	1	no	—
119	C₄⋊C₈×C₄₃	—	2	1	no	—
120	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
123	#103×C₄₃	—	2	1	no	—
124	#103×C₄₃	—	2	1	no	—
125	#103×C₄₃	—	2	1	no	—
126	#103×C₄₃	—	2	2	no	—
127	#102×C₄₃	—	2	4	no	—
128	#102×C₄₃	—	2	4	no	—
129	#102×C₄₃	—	2	1	no	—
130	#102×C₄₃	—	2	2	no	—
131	C₂²⋊C₈×C₄₃	—	2	1	no	—
132	#97×C₄₃	—	2	1	no	—
133	C₄×C₈×C₄₃	—	2	1	no	—
134	C₄×C₈×C₄₃	C₂³	1	2	yes	—
135	C₂⁴×C₄₃	—	2	4	no	—
136	C₂⁴×C₄₃	—	2	2	no	—
137	#41×C₄₃	—	2	2	no	—
138	#41×C₄₃	—	2	2	no	—
139	#41×C₄₃	—	4	8	no	—
140	#41×C₄₃	—	4	2	no	—
141	#41×C₄₃	—	4	2	no	—
142	#41×C₄₃	—	4	4	no	—
143	#41×C₄₃	—	4	4	no	—
144	C₂×Q₈×C₄₃	—	2	1	no	—
145	C₂×Q₈×C₄₃	—	2	1	no	—
146	C₂×Q₈×C₄₃	—	2	1	no	—
147	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₄₃	—	2	4	no	—
149	C₂×D₄×C₄₃	—	2	4	no	—
150	C₂×D₄×C₄₃	—	2	4	no	—
151	C₂×D₄×C₄₃	—	2	4	no	—
152	C₂×D₄×C₄₃	—	2	2	no	—
153	C₂×D₄×C₄₃	—	2	1	no	—
154	C₂×D₄×C₄₃	—	2	2	no	—
155	C₂×D₄×C₄₃	—	2	1	no	—
156	C₂×D₄×C₄₃	—	2	2	no	—
157	C₂×D₄×C₄₃	—	2	2	no	—
158	C₂×D₄×C₄₃	—	2	2	no	—
159	C₂×D₄×C₄₃	—	2	1	no	—
160	C₂×D₄×C₄₃	—	2	2	no	—
161	C₂×D₄×C₄₃	—	4	8	no	—
162	C₂×D₄×C₄₃	—	4	2	no	—
163	C₂×D₄×C₄₃	—	4	2	no	—
164	C₂×D₄×C₄₃	—	4	16	no	—
165	C₂×D₄×C₄₃	—	4	4	no	—
166	C₂×D₄×C₄₃	—	4	4	no	—
167	C₂×D₄×C₄₃	—	4	4	no	—
168	C₂×D₄×C₄₃	—	8	1	no	—
169	C₂×D₄×C₄₃	—	8	1	no	—
170	C₂×D₄×C₄₃	—	8	2	no	—
171	C₂×D₄×C₄₃	—	8	2	no	—
172	C₂×D₄×C₄₃	—	8	4	no	—
173	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
174	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₄₃	—	2	1	no	—
177	C₂²×C₄×C₄₃	—	2	4	no	—
178	C₂²×C₄×C₄₃	—	2	1	no	—
179	C₂²×C₄×C₄₃	—	2	1	no	—
180	C₂²×C₄×C₄₃	—	2	2	no	—
181	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
184	Q₁₆×C₄₃	—	4	2	no	—
185	SD₁₆×C₄₃	—	4	2	no	—
186	SD₁₆×C₄₃	—	8	2	no	—
187	M₁₆×C₄₃	—	4	2	no	—
188	M₁₆×C₄₃	—	8	1	no	—
189	C₂×C₈×C₄₃	—	2	1	no	—
190	C₂×C₈×C₄₃	—	2	1	no	—
191	C₂×C₈×C₄₃	—	2	2	no	—
192	C₂×C₈×C₄₃	—	2	2	no	—
193	C₄⋊C₄×C₄₃	—	2	1	no	—
194	C₄⋊C₄×C₄₃	—	2	1	no	—
195	C₄⋊C₄×C₄₃	—	2	1	no	—
196	C₄⋊C₄×C₄₃	—	2	1	no	—
197	C₄⋊C₄×C₄₃	—	2	1	no	—
198	C₄⋊C₄×C₄₃	—	2	1	no	—
199	C₄⋊C₄×C₄₃	—	2	1	no	—
200	C₄⋊C₄×C₄₃	—	4	1	no	—
201	C₄⋊C₄×C₄₃	—	4	1	no	—
202	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
205	C₂²⋊C₄×C₄₃	—	2	4	no	—
206	C₂²⋊C₄×C₄₃	—	2	4	no	—
207	C₂²⋊C₄×C₄₃	—	2	1	no	—
208	C₂²⋊C₄×C₄₃	—	2	2	no	—
209	C₂²⋊C₄×C₄₃	—	2	1	no	—
210	C₂²⋊C₄×C₄₃	—	2	2	no	—
211	C₂²⋊C₄×C₄₃	—	2	1	no	—
212	C₂²⋊C₄×C₄₃	—	4	1	no	—
213	C₄²×C₄₃	—	2	1	no	—
214	C₄²×C₄₃	—	2	1	no	—
215	C₄²×C₄₃	—	2	1	no	—
216	C₄²×C₄₃	—	4	1	no	—
217	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
221	C₂³×C₄₃	—	2	1	no	—
222	C₂³×C₄₃	—	2	2	no	—
223	C₂³×C₄₃	—	2	4	no	—
224	C₂³×C₄₃	—	4	8	no	—
225	C₂³×C₄₃	—	4	4	no	—
226	C₂³×C₄₃	—	8	2	no	—
227	C₂³×C₄₃	—	8	2	no	—
228	C₂³×C₄₃	—	8	4	no	—
229	C₂³×C₄₃	—	8	4	no	—
230	C₂³×C₄₃	#120	1	1	yes	characteristic
231	Q₈×C₄₃	—	2	1	no	—
232	Q₈×C₄₃	—	4	2	no	—
233	Q₈×C₄₃	—	4	1	no	—
234	Q₈×C₄₃	—	4	1	no	—
235	Q₈×C₄₃	—	4	1	no	—
236	Q₈×C₄₃	—	4	1	no	—
237	Q₈×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
238	D₄×C₄₃	—	2	4	no	—
239	D₄×C₄₃	—	2	1	no	—
240	D₄×C₄₃	—	2	2	no	—
241	D₄×C₄₃	—	2	2	no	—
242	D₄×C₄₃	—	4	4	no	—
243	D₄×C₄₃	—	4	4	no	—
244	D₄×C₄₃	—	4	2	no	—
245	D₄×C₄₃	—	4	8	no	—
246	D₄×C₄₃	—	4	8	no	—
247	D₄×C₄₃	—	4	4	no	—
248	D₄×C₄₃	—	4	2	no	—
249	D₄×C₄₃	—	4	2	no	—
250	D₄×C₄₃	—	4	2	no	—
251	D₄×C₄₃	—	4	2	no	—
252	D₄×C₄₃	—	4	4	no	—
253	D₄×C₄₃	—	4	2	no	—
254	D₄×C₄₃	—	8	2	no	—
255	D₄×C₄₃	—	8	4	no	—
256	D₄×C₄₃	—	8	4	no	—
257	D₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
258	C₂×C₄×C₄₃	—	2	4	no	—
259	C₂×C₄×C₄₃	—	2	1	no	—
260	C₂×C₄×C₄₃	—	2	1	no	—
261	C₂×C₄×C₄₃	—	2	1	no	—
262	C₂×C₄×C₄₃	—	2	1	no	—
263	C₂×C₄×C₄₃	—	2	1	no	—
264	C₂×C₄×C₄₃	—	2	2	no	—
265	C₂×C₄×C₄₃	—	2	1	no	—
266	C₂×C₄×C₄₃	—	2	1	no	—
267	C₂×C₄×C₄₃	—	2	2	no	—
268	C₂×C₄×C₄₃	—	4	8	no	—
269	C₂×C₄×C₄₃	—	4	2	no	—
270	C₂×C₄×C₄₃	—	4	2	no	—
271	C₂×C₄×C₄₃	—	4	1	no	—
272	C₂×C₄×C₄₃	—	4	1	no	—
273	C₂×C₄×C₄₃	—	4	2	no	—
274	C₂×C₄×C₄₃	—	4	1	no	—
275	C₂×C₄×C₄₃	—	4	1	no	—
276	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
277	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
278	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
279	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
282	C₈×C₄₃	—	4	2	no	—
283	C₈×C₄₃	—	4	1	no	—
284	C₈×C₄₃	—	4	1	no	—
285	C₈×C₄₃	—	4	2	no	—
286	#18574	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂²×C₄₃	—	2	2	no	—
288	C₂²×C₄₃	—	2	1	no	—
289	C₂²×C₄₃	—	2	1	no	—
290	C₂²×C₄₃	—	2	1	no	—
291	C₂²×C₄₃	—	4	1	no	—
292	C₂²×C₄₃	—	4	1	no	—
293	C₂²×C₄₃	—	4	4	no	—
294	C₂²×C₄₃	—	4	2	no	—
295	C₂²×C₄₃	—	4	2	no	—
296	C₂²×C₄₃	—	4	4	no	—
297	C₂²×C₄₃	—	4	4	no	—
298	C₂²×C₄₃	—	4	2	no	—
299	C₂²×C₄₃	—	16	4	no	—
300	C₂²×C₄₃	—	16	8	no	—
301	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
302	C₄×C₄₃	—	2	1	no	—
303	C₄×C₄₃	—	2	2	no	—
304	C₄×C₄₃	—	2	1	no	—
305	C₄×C₄₃	—	2	1	no	—
306	C₄×C₄₃	—	4	2	no	—
307	C₄×C₄₃	—	4	1	no	—
308	C₄×C₄₃	—	4	1	no	—
309	C₄×C₄₃	—	8	1	no	—
310	C₄×C₄₃	—	8	1	no	—
311	C₄×C₄₃	#455	1	2	yes	—
312	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
313	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
314	C₄×C₄₃	#576	1	1	yes	characteristic
315	C₄×C₄₃	#577	1	1	yes	characteristic
316	#3498	C₂×C₄₃	1	1	yes	characteristic
317	#3254	C₂×C₄₃	1	1	yes	characteristic, complemented
318	#3138	C₂×C₄₃	1	1	yes	characteristic, complemented
319	#3107	C₂×C₄₃	1	1	yes	characteristic, complemented
320	#1642	C₂×C₄₃	1	2	yes	complemented
321	#1641	C₂×C₄₃	1	2	yes	complemented
322	#1639	C₂×C₄₃	1	2	yes	complemented
323	#1639	C₂×C₄₃	1	2	yes	complemented
324	#1545	C₂×C₄₃	1	1	yes	characteristic, complemented
325	#1489	C₂×C₄₃	1	1	yes	characteristic, complemented
326	#1484	C₂×C₄₃	1	1	yes	characteristic, complemented
327	C₂×C₄₃	—	4	1	no	—
328	C₂×C₄₃	—	4	2	no	—
329	C₂×C₄₃	—	8	2	no	—
330	C₂×C₄₃	—	8	4	no	—
331	C₂×C₄₃	#3003	1	1	yes	characteristic
332	C₂×C₄₃	#3012	1	1	yes	characteristic
333	C₂×C₄₃	C₂×#455	1	1	yes	characteristic
334	C₂×H(5,𝔽₂)	—	2	1	no	—
335	#550	—	2	1	no	—
336	#550	C₂²×C₄₃	1	2	yes	—
337	D₄²	—	2	2	no	—
338	D₄²	—	2	2	no	—
339	D₄²	—	2	1	no	—
340	D₄²	C₂²×C₄₃	1	2	yes	—
341	#535	—	2	2	no	—
342	#535	—	2	1	no	—
343	#533	C₂²×C₄₃	1	1	yes	characteristic, complemented
344	#532	—	2	1	no	—
345	#532	C₂²×C₄₃	1	1	yes	characteristic
346	C₂×#127	—	2	1	no	—
347	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
348	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
349	#490	—	2	2	no	—
350	#486	C₂²×C₄₃	1	2	yes	complemented
351	#486	C₂²×C₄₃	1	2	yes	complemented
352	#485	—	2	1	no	—
353	#477	—	2	1	no	—
354	#475	C₂²×C₄₃	1	1	yes	characteristic, complemented
355	#474	C₂²×C₄₃	1	1	yes	characteristic, complemented
356	#474	C₂²×C₄₃	1	2	yes	complemented
357	#468	—	2	2	no	—
358	#462	C₂²×C₄₃	1	1	yes	characteristic, complemented
359	#461	C₂²×C₄₃	1	1	yes	characteristic, complemented
360	#461	C₂²×C₄₃	1	2	yes	complemented
361	#460	—	2	1	no	—
362	#452	—	2	1	no	—
363	C₄×Q₁₆	—	2	1	no	—
364	C₄×SD₁₆	—	2	1	no	—
365	#431	C₂²×C₄₃	1	1	yes	characteristic, complemented
366	#423	C₂²×C₄₃	1	1	yes	characteristic, complemented
367	#418	—	2	2	no	—
368	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
369	#331	C₂²×C₄₃	1	2	yes	complemented
370	#331	C₂²×C₄₃	1	2	yes	complemented
371	Q₈⋊C₈	C₂²×C₄₃	1	2	yes	complemented
372	D₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
373	D₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
374	D₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
375	C₄₃	#18574	1	1	yes	characteristic, direct product factor, Sylow
376	H(5,𝔽₂)	—	4	4	no	—
377	H(5,𝔽₂)	—	4	4	no	—
378	C₂×#41	—	2	2	no	—
379	C₂×#41	—	2	2	no	—
380	C₂×#41	—	2	1	no	—
381	C₂×#41	D₄×C₄₃	1	1	yes	characteristic
382	C₂²×D₄	—	2	2	no	—
383	C₂²×D₄	—	2	4	no	—
384	C₂²×D₄	—	2	2	no	—
385	C₂²×D₄	—	2	2	no	—
386	C₂²×D₄	—	2	2	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	D₄×C₄₃	1	2	yes	—
390	C₂×Q₁₆	—	2	1	no	—
391	C₂×SD₁₆	—	2	1	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
396	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
397	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
398	#127	—	2	2	no	—
399	#127	—	2	2	no	—
400	#127	—	2	2	no	—
401	#127	—	2	1	no	—
402	#127	—	2	1	no	—
403	#127	D₄×C₄₃	1	1	yes	characteristic
404	#127	D₄×C₄₃	1	2	yes	—
405	#127	C₂³×C₄₃	1	2	yes	—
406	#125	—	2	1	no	—
407	#124	—	2	2	no	—
408	#124	—	2	1	no	—
409	C₂²⋊Q₈	—	2	1	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	#121	—	2	2	no	—
412	#121	—	2	4	no	—
413	#121	—	2	4	no	—
414	#121	—	2	1	no	—
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	2	no	—
418	#121	D₄×C₄₃	1	2	yes	—
419	#120	—	2	4	no	—
420	#120	—	2	4	no	—
421	#120	—	2	4	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	—	2	1	no	—
424	C₄×Q₈	D₄×C₄₃	1	1	yes	characteristic
425	C₄×Q₈	C₂³×C₄₃	1	1	yes	characteristic
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	D₄×C₄₃	1	1	yes	characteristic
432	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
433	C₄×D₄	C₂³×C₄₃	1	2	yes	—
434	#117	—	2	1	no	—
435	#117	—	2	1	no	—
436	#117	D₄×C₄₃	1	1	yes	characteristic
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
439	#107	—	2	1	no	—
440	#107	—	2	2	no	—
441	#106	—	2	1	no	—
442	C₄⋊C₈	—	2	1	no	—
443	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
444	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
445	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
446	#103	—	2	1	no	—
447	#103	—	2	1	no	—
448	#103	—	2	1	no	—
449	#103	—	2	2	no	—
450	#102	—	2	4	no	—
451	#102	—	2	4	no	—
452	#102	—	2	1	no	—
453	#102	—	2	2	no	—
454	C₂²⋊C₈	—	2	1	no	—
455	#97	—	2	1	no	—
456	C₄×C₈	—	2	1	no	—
457	C₄×C₈	C₂³×C₄₃	1	2	yes	—
458	C₂⁴	—	2	4	no	—
459	C₂⁴	—	2	2	no	—
460	#41	—	2	2	no	—
461	#41	—	2	2	no	—
462	#41	—	4	8	no	—
463	#41	—	4	2	no	—
464	#41	—	4	2	no	—
465	#41	—	4	4	no	—
466	#41	—	4	4	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	C₂×D₄×C₄₃	1	1	yes	characteristic
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	4	8	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	4	4	no	—
488	C₂×D₄	—	4	16	no	—
489	C₂×D₄	—	4	4	no	—
490	C₂×D₄	—	4	4	no	—
491	C₂×D₄	—	8	1	no	—
492	C₂×D₄	—	8	1	no	—
493	C₂×D₄	—	8	2	no	—
494	C₂×D₄	—	8	2	no	—
495	C₂×D₄	—	8	4	no	—
496	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
497	C₂×D₄	C₂×D₄×C₄₃	1	1	yes	characteristic
498	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
507	Q₁₆	—	4	2	no	—
508	SD₁₆	—	4	2	no	—
509	SD₁₆	—	8	2	no	—
510	M₁₆	—	4	2	no	—
511	M₁₆	—	8	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	2	no	—
515	C₂×C₈	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	4	1	no	—
540	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
541	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
542	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
543	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
544	C₂³	—	2	1	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	8	2	no	—
550	C₂³	—	8	2	no	—
551	C₂³	—	8	4	no	—
552	C₂³	—	8	4	no	—
553	C₂³	#120×C₄₃	1	1	yes	characteristic
554	Q₈	—	2	1	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	4	1	no	—
560	Q₈	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
561	D₄	—	2	4	no	—
562	D₄	—	2	1	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	4	4	no	—
566	D₄	—	4	4	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	8	no	—
569	D₄	—	4	4	no	—
570	D₄	—	4	8	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	4	no	—
576	D₄	—	4	2	no	—
577	D₄	—	8	2	no	—
578	D₄	—	8	4	no	—
579	D₄	—	8	4	no	—
580	D₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	8	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
600	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
601	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
605	C₈	—	4	2	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	4	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	16	4	no	—
622	C₂²	—	16	8	no	—
623	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	C₄₃×#455	1	2	yes	—
634	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
635	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
636	C₄	C₄₃×#576	1	1	yes	characteristic
637	C₄	C₄₃×#577	1	1	yes	characteristic
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	8	2	no	—
641	C₂	—	8	4	no	—
642	C₂	C₄₃×#3003	1	1	yes	characteristic
643	C₂	C₄₃×#3012	1	1	yes	characteristic
644	C₂	C₂×C₄₃×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
prime radical	C₄₃×#3498	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3254	C₂	semidirect
3. C₄₃×#3138	C₂	semidirect
4. C₄₃×#3107	C₂	semidirect
5. C₄₃×#1642	C₂	semidirect
6. C₄₃×#1641	C₂	semidirect
7. C₄₃×#1639	C₂	semidirect
8. C₄₃×#1639	C₂	semidirect
9. C₄₃×#1545	C₂	semidirect
10. C₄₃×#1489	C₂	semidirect
11. C₄₃×#1484	C₂	semidirect
21. C₄₃×#533	C₂²	semidirect
28. C₄₃×#486	C₂²	semidirect
29. C₄₃×#486	C₂²	semidirect
32. C₄₃×#475	C₂²	semidirect
33. C₄₃×#474	C₂²	semidirect
34. C₄₃×#474	C₂²	semidirect
36. C₄₃×#462	C₂²	semidirect
37. C₄₃×#461	C₂²	semidirect
38. C₄₃×#461	C₂²	semidirect
43. C₄₃×#431	C₂²	semidirect
44. C₄₃×#423	C₂²	semidirect
46. C₄×M₁₆×C₄₃	C₂²	semidirect
47. C₄₃×#331	C₂²	semidirect
48. C₄₃×#331	C₂²	semidirect
49. C₄₃×Q₈⋊C₈	C₂²	semidirect
50. C₄₃×D₄⋊C₈	C₂²	semidirect
51. C₄₃×D₄⋊C₈	C₂²	semidirect
52. C₄₃×D₄⋊C₈	C₂²	semidirect
286. #18574	C₄₃	direct (N × H)
317. #3254	C₂×C₄₃	semidirect
318. #3138	C₂×C₄₃	semidirect
319. #3107	C₂×C₄₃	semidirect
320. #1642	C₂×C₄₃	semidirect
321. #1641	C₂×C₄₃	semidirect
322. #1639	C₂×C₄₃	semidirect
323. #1639	C₂×C₄₃	semidirect
324. #1545	C₂×C₄₃	semidirect
325. #1489	C₂×C₄₃	semidirect
326. #1484	C₂×C₄₃	semidirect
343. #533	C₂²×C₄₃	semidirect
350. #486	C₂²×C₄₃	semidirect
351. #486	C₂²×C₄₃	semidirect
354. #475	C₂²×C₄₃	semidirect
355. #474	C₂²×C₄₃	semidirect
356. #474	C₂²×C₄₃	semidirect
358. #462	C₂²×C₄₃	semidirect
359. #461	C₂²×C₄₃	semidirect
360. #461	C₂²×C₄₃	semidirect
365. #431	C₂²×C₄₃	semidirect
366. #423	C₂²×C₄₃	semidirect
368. C₄×M₁₆	C₂²×C₄₃	semidirect
369. #331	C₂²×C₄₃	semidirect
370. #331	C₂²×C₄₃	semidirect
371. Q₈⋊C₈	C₂²×C₄₃	semidirect
372. D₄⋊C₈	C₂²×C₄₃	semidirect
373. D₄⋊C₈	C₂²×C₄₃	semidirect
374. D₄⋊C₈	C₂²×C₄₃	semidirect
375. C₄₃	#18574	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3498	2
C₄₃×#3254	2
C₄₃×#3138	2
C₄₃×#3107	2
C₄₃×#1642	2
C₄₃×#1641	2
C₄₃×#1639	2
C₄₃×#1545	2
C₄₃×#1489	2
C₄₃×#1484	2
#18574	43

Subgroups — C43×#18574 #24938591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18574 #24938591