Subgroups — C₄₃×#18622 #24938639

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#3038	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1623	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1622	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1548	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
11	C₂²×SD₁₆×C₄₃	—	2	2	no	—
12	Q₈²×C₄₃	C₂²	1	2	yes	complemented
13	C₄₃×#557	—	2	1	no	—
14	C₄₃×#554	—	2	2	no	—
15	C₄₃×#554	C₂²	1	2	yes	complemented
16	D₄×Q₈×C₄₃	—	2	2	no	—
17	D₄×Q₈×C₄₃	—	2	1	no	—
18	C₄₃×#544	—	2	2	no	—
19	C₄₃×#544	—	2	1	no	—
20	C₄₃×#533	—	2	1	no	—
21	C₄₃×#533	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
23	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#520	—	2	1	no	—
26	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#492	—	2	2	no	—
28	C₄₃×#492	—	2	1	no	—
29	C₄₃×#492	C₂²	1	4	yes	—
30	C₄₃×#486	—	2	1	no	—
31	C₄₃×#460	—	2	1	no	—
32	C₄₃×#460	C₂²	1	4	yes	—
33	C₄₃×#460	C₂²	1	2	yes	—
34	C₄₃×#459	—	2	1	no	—
35	C₄₃×#459	C₂²	1	2	yes	—
36	C₄₃×#450	—	2	2	no	—
37	C₄₃×#431	C₂²	1	1	yes	characteristic
38	C₄₃×#423	C₂²	1	1	yes	characteristic
39	C₄₃×#418	—	2	1	no	—
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#333	C₂²	1	4	yes	complemented
42	C₄₃×Q₈⋊C₈	C₂²	1	4	yes	complemented
43	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₄₃×D₄⋊C₈	C₂²	1	2	yes	complemented
45	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₄₃	—	2	2	no	—
47	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
48	C₂²×D₄×C₄₃	—	2	1	no	—
49	C₂²×D₄×C₄₃	—	2	1	no	—
50	C₂²×D₄×C₄₃	—	2	1	no	—
51	AGL(1,ℤ/8)×C₄₃	—	4	4	no	—
52	C₂×SD₁₆×C₄₃	—	2	8	no	—
53	C₂×SD₁₆×C₄₃	—	2	2	no	—
54	C₂×SD₁₆×C₄₃	—	2	4	no	—
55	C₂×SD₁₆×C₄₃	—	4	8	no	—
56	C₂×D₈×C₄₃	—	2	2	no	—
57	C₂×M₁₆×C₄₃	—	2	1	no	—
58	C₂²×C₈×C₄₃	—	2	1	no	—
59	C₄⋊Q₈×C₄₃	—	2	2	no	—
60	C₄⋊Q₈×C₄₃	—	2	2	no	—
61	C₄⋊Q₈×C₄₃	—	2	4	no	—
62	C₄⋊Q₈×C₄₃	—	2	2	no	—
63	C₄⋊Q₈×C₄₃	—	2	2	no	—
64	C₄⋊Q₈×C₄₃	—	2	1	no	—
65	C₄⋊Q₈×C₄₃	—	2	1	no	—
66	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
67	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
70	#127×C₄₃	—	2	1	no	—
71	#127×C₄₃	—	2	1	no	—
72	#127×C₄₃	—	2	1	no	—
73	#127×C₄₃	C₂³	1	2	yes	—
74	#125×C₄₃	—	2	2	no	—
75	#125×C₄₃	—	2	4	no	—
76	#125×C₄₃	—	2	2	no	—
77	#125×C₄₃	—	2	1	no	—
78	C₂²⋊Q₈×C₄₃	—	2	2	no	—
79	C₂²⋊Q₈×C₄₃	—	2	4	no	—
80	C₂²⋊Q₈×C₄₃	—	2	4	no	—
81	C₂²⋊Q₈×C₄₃	—	2	2	no	—
82	C₂²⋊Q₈×C₄₃	—	2	4	no	—
83	C₂²⋊Q₈×C₄₃	—	2	1	no	—
84	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
85	C₄×Q₈×C₄₃	—	2	2	no	—
86	C₄×Q₈×C₄₃	—	2	2	no	—
87	C₄×Q₈×C₄₃	—	2	2	no	—
88	C₄×Q₈×C₄₃	—	2	1	no	—
89	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
92	C₄×D₄×C₄₃	—	2	4	no	—
93	C₄×D₄×C₄₃	—	2	2	no	—
94	C₄×D₄×C₄₃	—	2	1	no	—
95	C₄×D₄×C₄₃	—	2	1	no	—
96	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
97	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
98	#117×C₄₃	—	2	2	no	—
99	#117×C₄₃	—	2	1	no	—
100	#117×C₄₃	—	2	1	no	—
101	#117×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
103	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
104	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
105	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
106	C₂×C₄²×C₄₃	—	2	1	no	—
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₄₃	—	2	1	no	—
109	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
110	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
111	#102×C₄₃	—	2	2	no	—
112	#102×C₄₃	—	2	2	no	—
113	#102×C₄₃	—	2	4	no	—
114	C₂²⋊C₈×C₄₃	—	2	1	no	—
115	C₄×C₈×C₄₃	—	2	1	no	—
116	C₄×C₈×C₄₃	—	2	1	no	—
117	C₄×C₈×C₄₃	C₂³	1	2	yes	—
118	C₂⁴×C₄₃	—	4	1	no	—
119	#41×C₄₃	—	2	2	no	—
120	#41×C₄₃	SD₁₆	1	4	yes	complemented
121	C₂×Q₈×C₄₃	—	2	4	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	4	4	no	—
125	C₂×Q₈×C₄₃	—	8	4	no	—
126	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
127	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₄₃	—	2	1	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	4	1	no	—
134	C₂×D₄×C₄₃	—	4	1	no	—
135	C₂×D₄×C₄₃	—	4	1	no	—
136	C₂×D₄×C₄₃	—	4	4	no	—
137	C₂×D₄×C₄₃	—	4	2	no	—
138	C₂×D₄×C₄₃	—	4	2	no	—
139	C₂×D₄×C₄₃	—	8	2	no	—
140	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	—	2	1	no	—
142	C₂²×C₄×C₄₃	—	2	4	no	—
143	C₂²×C₄×C₄₃	—	2	1	no	—
144	C₂²×C₄×C₄₃	—	2	1	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
149	SD₁₆×C₄₃	—	4	16	no	—
150	SD₁₆×C₄₃	—	4	4	no	—
151	SD₁₆×C₄₃	—	8	4	no	—
152	D₈×C₄₃	—	4	4	no	—
153	M₁₆×C₄₃	—	4	2	no	—
154	C₂×C₈×C₄₃	—	2	4	no	—
155	C₂×C₈×C₄₃	—	2	2	no	—
156	C₂×C₈×C₄₃	—	2	2	no	—
157	C₂×C₈×C₄₃	—	2	2	no	—
158	C₄⋊C₄×C₄₃	—	2	4	no	—
159	C₄⋊C₄×C₄₃	—	2	4	no	—
160	C₄⋊C₄×C₄₃	—	2	4	no	—
161	C₄⋊C₄×C₄₃	—	2	4	no	—
162	C₄⋊C₄×C₄₃	—	2	2	no	—
163	C₄⋊C₄×C₄₃	—	2	1	no	—
164	C₄⋊C₄×C₄₃	—	2	2	no	—
165	C₄⋊C₄×C₄₃	—	2	1	no	—
166	C₄⋊C₄×C₄₃	—	2	1	no	—
167	C₄⋊C₄×C₄₃	—	2	1	no	—
168	C₄⋊C₄×C₄₃	—	2	2	no	—
169	C₄⋊C₄×C₄₃	—	2	2	no	—
170	C₄⋊C₄×C₄₃	—	2	2	no	—
171	C₄⋊C₄×C₄₃	—	2	1	no	—
172	C₄⋊C₄×C₄₃	—	2	2	no	—
173	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₂²⋊C₄×C₄₃	—	2	4	no	—
177	C₂²⋊C₄×C₄₃	—	2	1	no	—
178	C₂²⋊C₄×C₄₃	—	2	1	no	—
179	C₂²⋊C₄×C₄₃	—	2	2	no	—
180	C₂²⋊C₄×C₄₃	—	2	1	no	—
181	C₄²×C₄₃	—	2	4	no	—
182	C₄²×C₄₃	—	2	1	no	—
183	C₄²×C₄₃	—	2	1	no	—
184	C₄²×C₄₃	—	2	1	no	—
185	C₄²×C₄₃	—	2	2	no	—
186	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
190	C₂³×C₄₃	—	2	1	no	—
191	C₂³×C₄₃	—	4	2	no	—
192	C₂³×C₄₃	—	8	2	no	—
193	C₂³×C₄₃	—	8	2	no	—
194	C₂³×C₄₃	—	8	2	no	—
195	C₂³×C₄₃	#120	1	1	yes	characteristic
196	Q₈×C₄₃	—	2	1	no	—
197	Q₈×C₄₃	—	2	4	no	—
198	Q₈×C₄₃	—	4	4	no	—
199	Q₈×C₄₃	—	4	4	no	—
200	Q₈×C₄₃	—	4	2	no	—
201	Q₈×C₄₃	—	8	4	no	—
202	Q₈×C₄₃	C₂×SD₁₆	1	2	yes	complemented
203	D₄×C₄₃	—	2	4	no	—
204	D₄×C₄₃	—	2	1	no	—
205	D₄×C₄₃	—	4	4	no	—
206	D₄×C₄₃	—	4	2	no	—
207	D₄×C₄₃	—	4	2	no	—
208	D₄×C₄₃	—	4	4	no	—
209	D₄×C₄₃	—	8	2	no	—
210	D₄×C₄₃	—	8	2	no	—
211	D₄×C₄₃	—	8	2	no	—
212	D₄×C₄₃	C₂×SD₁₆	1	2	yes	complemented
213	C₂×C₄×C₄₃	—	2	1	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	4	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	2	no	—
224	C₂×C₄×C₄₃	—	8	2	no	—
225	C₂×C₄×C₄₃	—	8	4	no	—
226	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
227	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
230	C₂×C₄×C₄₃	#137	1	2	yes	—
231	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
234	C₈×C₄₃	—	2	4	no	—
235	C₈×C₄₃	—	4	2	no	—
236	C₈×C₄₃	—	4	2	no	—
237	#18622	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂²×C₄₃	—	2	1	no	—
239	C₂²×C₄₃	—	2	1	no	—
240	C₂²×C₄₃	—	2	2	no	—
241	C₂²×C₄₃	—	4	1	no	—
242	C₂²×C₄₃	—	4	1	no	—
243	C₂²×C₄₃	—	8	2	no	—
244	C₂²×C₄₃	—	8	2	no	—
245	C₂²×C₄₃	—	8	2	no	—
246	C₂²×C₄₃	—	16	4	no	—
247	C₂²×C₄₃	#448	1	2	yes	—
248	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
249	C₄×C₄₃	—	2	2	no	—
250	C₄×C₄₃	—	2	1	no	—
251	C₄×C₄₃	—	2	1	no	—
252	C₄×C₄₃	—	4	1	no	—
253	C₄×C₄₃	—	4	2	no	—
254	C₄×C₄₃	—	4	1	no	—
255	C₄×C₄₃	—	4	4	no	—
256	C₄×C₄₃	—	4	2	no	—
257	C₄×C₄₃	#448	1	2	yes	—
258	C₄×C₄₃	#453	1	2	yes	—
259	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
260	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
261	C₄×C₄₃	#577	1	2	yes	—
262	#3503	C₂×C₄₃	1	1	yes	characteristic, complemented
263	#3208	C₂×C₄₃	1	1	yes	characteristic, complemented
264	C₂×#492	C₂×C₄₃	1	1	yes	characteristic, complemented
265	#3038	C₂×C₄₃	1	1	yes	characteristic
266	#1623	C₂×C₄₃	1	4	yes	complemented
267	#1622	C₂×C₄₃	1	4	yes	complemented
268	#1548	C₂×C₄₃	1	1	yes	characteristic, complemented
269	#1493	C₂×C₄₃	1	1	yes	characteristic, complemented
270	#1476	C₂×C₄₃	1	1	yes	characteristic, complemented
271	C₂×C₄₃	—	2	2	no	—
272	C₂×C₄₃	—	4	2	no	—
273	C₂×C₄₃	—	16	2	no	—
274	C₂×C₄₃	C₂×#448	1	1	yes	characteristic
275	C₂×C₄₃	#3010	1	1	yes	characteristic
276	C₂×C₄₃	C₂×#453	1	1	yes	characteristic
277	C₂×AGL(1,ℤ/8)	—	2	1	no	—
278	C₂²×SD₁₆	—	2	2	no	—
279	Q₈²	C₂²×C₄₃	1	2	yes	complemented
280	#557	—	2	1	no	—
281	#554	—	2	2	no	—
282	#554	C₂²×C₄₃	1	2	yes	complemented
283	D₄×Q₈	—	2	2	no	—
284	D₄×Q₈	—	2	1	no	—
285	#544	—	2	2	no	—
286	#544	—	2	1	no	—
287	#533	—	2	1	no	—
288	#533	C₂²×C₄₃	1	1	yes	characteristic
289	C₂×C₄⋊Q₈	—	2	1	no	—
290	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
291	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
292	#520	—	2	1	no	—
293	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
294	#492	—	2	2	no	—
295	#492	—	2	1	no	—
296	#492	C₂²×C₄₃	1	4	yes	—
297	#486	—	2	1	no	—
298	#460	—	2	1	no	—
299	#460	C₂²×C₄₃	1	4	yes	—
300	#460	C₂²×C₄₃	1	2	yes	—
301	#459	—	2	1	no	—
302	#459	C₂²×C₄₃	1	2	yes	—
303	#450	—	2	2	no	—
304	#431	C₂²×C₄₃	1	1	yes	characteristic
305	#423	C₂²×C₄₃	1	1	yes	characteristic
306	#418	—	2	1	no	—
307	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
308	#333	C₂²×C₄₃	1	4	yes	complemented
309	Q₈⋊C₈	C₂²×C₄₃	1	4	yes	complemented
310	Q₈⋊C₈	C₂²×C₄₃	1	2	yes	complemented
311	D₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
312	C₄₃	#18622	1	1	yes	characteristic, direct product factor, Sylow
313	C₂×#41	D₄×C₄₃	1	1	yes	characteristic
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	D₄×C₄₃	1	2	yes	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	2	1	no	—
319	AGL(1,ℤ/8)	—	4	4	no	—
320	C₂×SD₁₆	—	2	8	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×SD₁₆	—	4	8	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂²×C₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	—	2	4	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	—	2	1	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
335	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
336	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
337	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
338	#127	—	2	1	no	—
339	#127	—	2	1	no	—
340	#127	—	2	1	no	—
341	#127	C₂³×C₄₃	1	2	yes	—
342	#125	—	2	2	no	—
343	#125	—	2	4	no	—
344	#125	—	2	2	no	—
345	#125	—	2	1	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	D₄×C₄₃	1	2	yes	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	2	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	D₄×C₄₃	1	1	yes	characteristic
358	C₄×Q₈	C₂³×C₄₃	1	1	yes	characteristic
359	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
360	C₄×D₄	—	2	4	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	D₄×C₄₃	1	1	yes	characteristic
365	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
366	#117	—	2	2	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	D₄×C₄₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
376	C₄⋊C₈	—	2	1	no	—
377	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
378	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
379	#102	—	2	2	no	—
380	#102	—	2	2	no	—
381	#102	—	2	4	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	C₄×C₈	—	2	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	C₂³×C₄₃	1	2	yes	—
386	C₂⁴	—	4	1	no	—
387	#41	—	2	2	no	—
388	#41	SD₁₆×C₄₃	1	4	yes	complemented
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	—	8	4	no	—
394	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
395	C₂×Q₈	C₂×D₄×C₄₃	1	1	yes	characteristic
396	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	8	2	no	—
408	C₂×D₄	C₂×D₄×C₄₃	1	1	yes	characteristic
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
417	SD₁₆	—	4	16	no	—
418	SD₁₆	—	4	4	no	—
419	SD₁₆	—	8	4	no	—
420	D₈	—	4	4	no	—
421	M₁₆	—	4	2	no	—
422	C₂×C₈	—	2	4	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
442	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
443	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	2	no	—
454	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
455	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
457	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
458	C₂³	—	2	1	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	8	2	no	—
461	C₂³	—	8	2	no	—
462	C₂³	—	8	2	no	—
463	C₂³	#120×C₄₃	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	4	no	—
466	Q₈	—	4	4	no	—
467	Q₈	—	4	4	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	8	4	no	—
470	Q₈	C₂×SD₁₆×C₄₃	1	2	yes	complemented
471	D₄	—	2	4	no	—
472	D₄	—	2	1	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	4	no	—
477	D₄	—	8	2	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	2	no	—
480	D₄	C₂×SD₁₆×C₄₃	1	2	yes	complemented
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	—	8	4	no	—
494	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
495	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
496	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
497	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
498	C₂×C₄	#137×C₄₃	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
502	C₈	—	2	4	no	—
503	C₈	—	4	2	no	—
504	C₈	—	4	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	16	4	no	—
514	C₂²	C₄₃×#448	1	2	yes	—
515	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	2	no	—
524	C₄	C₄₃×#448	1	2	yes	—
525	C₄	C₄₃×#453	1	2	yes	—
526	C₄	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
527	C₄	C₂×#137×C₄₃	1	1	yes	characteristic
528	C₄	C₄₃×#577	1	2	yes	—
529	C₂	—	2	2	no	—
530	C₂	—	4	2	no	—
531	C₂	—	16	2	no	—
532	C₂	C₂×C₄₃×#448	1	1	yes	characteristic
533	C₂	C₄₃×#3010	1	1	yes	characteristic
534	C₂	C₂×C₄₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
prime radical	C₄₃×#3038	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
1. C₄₃×#3503	C₂	semidirect
2. C₄₃×#3208	C₂	semidirect
3. C₂×C₄₃×#492	C₂	semidirect
5. C₄₃×#1623	C₂	semidirect
6. C₄₃×#1622	C₂	semidirect
7. C₄₃×#1548	C₂	semidirect
8. C₄₃×#1493	C₂	semidirect
9. C₄₃×#1476	C₂	semidirect
12. Q₈²×C₄₃	C₂²	semidirect
15. C₄₃×#554	C₂²	semidirect
41. C₄₃×#333	C₂²	semidirect
42. C₄₃×Q₈⋊C₈	C₂²	semidirect
43. C₄₃×Q₈⋊C₈	C₂²	semidirect
44. C₄₃×D₄⋊C₈	C₂²	semidirect
120. #41×C₄₃	SD₁₆	semidirect
202. Q₈×C₄₃	C₂×SD₁₆	semidirect
212. D₄×C₄₃	C₂×SD₁₆	semidirect
237. #18622	C₄₃	direct (N × H)
262. #3503	C₂×C₄₃	semidirect
263. #3208	C₂×C₄₃	semidirect
264. C₂×#492	C₂×C₄₃	semidirect
266. #1623	C₂×C₄₃	semidirect
267. #1622	C₂×C₄₃	semidirect
268. #1548	C₂×C₄₃	semidirect
269. #1493	C₂×C₄₃	semidirect
270. #1476	C₂×C₄₃	semidirect
279. Q₈²	C₂²×C₄₃	semidirect
282. #554	C₂²×C₄₃	semidirect
308. #333	C₂²×C₄₃	semidirect
309. Q₈⋊C₈	C₂²×C₄₃	semidirect
310. Q₈⋊C₈	C₂²×C₄₃	semidirect
311. D₄⋊C₈	C₂²×C₄₃	semidirect
312. C₄₃	#18622	direct (N × H)
388. #41	SD₁₆×C₄₃	semidirect
470. Q₈	C₂×SD₁₆×C₄₃	semidirect
480. D₄	C₂×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×#3503	2
C₄₃×#3208	2
C₂×C₄₃×#492	2
C₄₃×#3038	2
C₄₃×#1623	2
C₄₃×#1622	2
C₄₃×#1548	2
C₄₃×#1493	2
C₄₃×#1476	2
#18622	43

Subgroups — C43×#18622 #24938639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18622 #24938639