Subgroups — D₄₃×#3531 #26003494

Order 11008.

6554 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148743	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148742	C₂	1	5	yes	maximal, complemented
3	#19148741	C₂	1	10	yes	maximal, complemented
4	#19148740	C₂	1	10	yes	maximal, complemented
5	#19148739	C₂	1	5	yes	maximal, complemented
6	#564×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#563×D₄₃	C₂	1	10	yes	maximal, complemented
8	#562×D₄₃	C₂	1	5	yes	maximal, complemented
9	#533×D₄₃	C₂	1	5	yes	maximal, complemented
10	#529×D₄₃	C₂	1	10	yes	maximal, complemented
11	C₄₃×#3531	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃⋊#564	C₂²	1	5	yes	complemented
13	C₄₃⋊#564	C₂²	1	10	yes	complemented
14	#14583653	C₂²	1	10	yes	complemented
15	#14583653	C₂²	1	10	yes	complemented
16	#14583652	C₂²	1	20	yes	complemented
17	#14583651	C₂²	1	20	yes	complemented
18	#14583651	C₂²	1	20	yes	complemented
19	#14583650	C₂²	1	20	yes	complemented
20	#14583650	C₂²	1	20	yes	complemented
21	#14583649	C₂²	1	10	yes	complemented
22	#14583648	C₂²	1	20	yes	complemented
23	#14583647	C₂²	1	5	yes	complemented
24	#14583646	C₂²	1	20	yes	complemented
25	#14583645	C₂²	1	20	yes	complemented
26	#14583644	C₂²	1	20	yes	complemented
27	#14583643	C₂²	1	10	yes	complemented
28	#14583456	C₂²	1	5	yes	complemented
29	#14583455	C₂²	1	5	yes	complemented
30	#14583455	C₂²	1	5	yes	complemented
31	#14583454	C₂²	1	10	yes	complemented
32	#14583453	C₂²	1	20	yes	complemented
33	#14583452	C₂²	1	10	yes	complemented
34	#14583451	C₂²	1	20	yes	complemented
35	C₄⋊Q₈×D₄₃	C₂²	1	10	yes	—
36	#14583436	C₂²	1	10	yes	complemented
37	#14583435	C₂²	1	10	yes	complemented
38	#14583434	C₂²	1	10	yes	complemented
39	#14583433	C₂²	1	10	yes	complemented
40	#14583432	C₂²	1	20	yes	complemented
41	#14583431	C₂²	1	10	yes	complemented
42	#14583430	C₂²	1	10	yes	complemented
43	#14583429	C₂²	1	20	yes	complemented
44	#14583428	C₂²	1	10	yes	complemented
45	#14583427	C₂²	1	20	yes	complemented
46	#14583426	C₂²	1	20	yes	complemented
47	#126×D₄₃	C₂²	1	20	yes	—
48	#125×D₄₃	C₂²	1	10	yes	—
49	#125×D₄₃	C₂²	1	5	yes	—
50	#125×D₄₃	C₂²	1	5	yes	—
51	#124×D₄₃	C₂²	1	10	yes	—
52	#123×D₄₃	C₂²	1	20	yes	—
53	C₂²⋊Q₈×D₄₃	C₂²	1	10	yes	—
54	C₂²⋊Q₈×D₄₃	C₂²	1	20	yes	—
55	#121×D₄₃	C₂²	1	10	yes	—
56	C₄×Q₈×D₄₃	C₂²	1	10	yes	—
57	C₄×D₄×D₄₃	C₂²	1	10	yes	—
58	#117×D₄₃	C₂²	1	10	yes	—
59	C₂×C₄²×D₄₃	C₂²	1	5	yes	—
60	C₄₃×#564	C₂²	1	1	yes	characteristic, complemented
61	C₄₃×#563	C₂²	1	10	yes	complemented
62	C₄₃×#562	C₂²	1	5	yes	complemented
63	C₄₃×#533	C₂²	1	5	yes	complemented
64	C₄₃×#529	C₂²	1	10	yes	complemented
65	C₂×Q₈×D₄₃	C₂³	1	10	yes	—
66	C₂×D₄×D₄₃	C₂³	1	10	yes	—
67	C₂²×C₄×D₄₃	C₂³	1	5	yes	—
68	C₂²×C₄×D₄₃	C₂³	1	10	yes	—
69	#13063325	C₂³	1	10	yes	—
70	#13063324	C₂³	1	10	yes	—
71	#13063324	C₂³	1	20	yes	—
72	#13063324	C₂³	1	10	yes	—
73	#13063323	C₂³	1	20	yes	—
74	#13063320	C₂³	1	20	yes	—
75	#13063320	C₂³	1	20	yes	—
76	#13063320	C₂³	1	20	yes	—
77	#13063319	C₂³	1	20	yes	—
78	#13063318	C₂³	1	20	yes	—
79	#13063318	C₂³	1	20	yes	—
80	#13063318	C₂³	1	20	yes	—
81	#13063317	C₂³	1	5	yes	—
82	#13063317	C₂³	1	5	yes	—
83	#13063317	C₂³	1	10	yes	—
84	#13063316	C₂³	1	10	yes	—
85	#13063316	C₂³	1	10	yes	—
86	#13063316	C₂³	1	10	yes	—
87	#13063316	C₂³	1	10	yes	—
88	#13063315	C₂³	1	20	yes	—
89	#13063315	C₂³	1	20	yes	—
90	#13063315	C₂³	1	20	yes	—
91	#13063315	C₂³	1	20	yes	—
92	#13063314	C₂³	1	10	yes	—
93	#13063313	C₂³	1	10	yes	—
94	#13063312	C₂³	1	10	yes	—
95	#13063311	C₂³	1	20	yes	—
96	#13063311	C₂³	1	20	yes	—
97	#13063310	C₂³	1	20	yes	—
98	#13063310	C₂³	1	20	yes	—
99	#13063309	C₂³	1	20	yes	—
100	#13063308	C₂³	1	20	yes	—
101	#13063307	C₂³	1	20	yes	—
102	#13063307	C₂³	1	20	yes	—
103	#13063306	C₂³	1	20	yes	—
104	#13063305	C₂³	1	20	yes	—
105	#13063305	C₂³	1	10	yes	—
106	#13063304	C₂³	1	20	yes	—
107	#13063304	C₂³	1	10	yes	—
108	#13063303	C₂³	1	20	yes	—
109	#13063303	C₂³	1	20	yes	—
110	#13063303	C₂³	1	20	yes	—
111	#13063302	C₂³	1	20	yes	—
112	#13063302	C₂³	1	20	yes	—
113	#13063302	C₂³	1	20	yes	—
114	#13063301	C₂³	1	20	yes	—
115	#13063301	C₂³	1	10	yes	—
116	#13063300	C₂³	1	10	yes	—
117	#13063299	C₂³	1	10	yes	—
118	#13063298	C₂³	1	20	yes	—
119	#13063297	C₂³	1	20	yes	—
120	#13063296	C₂³	1	10	yes	—
121	Q₈×Dic₄₃	C₂³	1	10	yes	—
122	C₄×Dic₈₆	C₂³	1	20	yes	—
123	C₄×Dic₈₆	C₂³	1	10	yes	—
124	#13063290	C₂³	1	20	yes	—
125	#13063290	C₂³	1	10	yes	—
126	C₄×D₁₇₂	C₂³	1	10	yes	—
127	D₄×Dic₄₃	C₂³	1	10	yes	—
128	#13063287	C₂³	1	10	yes	—
129	C₄×C₂²⋊D₄₃	C₂³	1	20	yes	—
130	(C₂²⋊D₄₃)⋊C₄	C₂³	1	20	yes	—
131	#13063284	C₂³	1	10	yes	—
132	#13063283	C₂³	1	10	yes	—
133	#13063283	C₂³	1	10	yes	—
134	#13063282	C₂³	1	20	yes	—
135	#13063281	C₂³	1	20	yes	—
136	C₄⋊C₄×D₄₃	C₂³	1	10	yes	—
137	C₄⋊C₄×D₄₃	C₂³	1	10	yes	—
138	C₄⋊C₄×D₄₃	C₂³	1	10	yes	—
139	C₄⋊C₄×D₄₃	C₂³	1	10	yes	—
140	C₄⋊C₄×D₄₃	C₂³	1	20	yes	—
141	C₂²⋊C₄×D₄₃	C₂³	1	20	yes	—
142	C₂²⋊C₄×D₄₃	C₂³	1	20	yes	—
143	C₂×C₄×Dic₄₃	C₂³	1	10	yes	—
144	C₂×C₄×Dic₄₃	C₂³	1	5	yes	—
145	C₄²×D₄₃	C₂³	1	10	yes	—
146	C₄²×D₄₃	C₂³	1	5	yes	—
147	C₄²×D₄₃	C₂³	1	5	yes	—
148	C₄²×D₄₃	C₂³	1	10	yes	—
149	C₄²×D₄₃	C₂³	1	5	yes	—
150	C₄²×D₄₃	C₂³	1	5	yes	—
151	C₄⋊Q₈×C₄₃	C₂³	1	10	yes	—
152	#126×C₄₃	C₂³	1	20	yes	—
153	#125×C₄₃	C₂³	1	10	yes	—
154	#125×C₄₃	C₂³	1	5	yes	—
155	#125×C₄₃	C₂³	1	5	yes	—
156	#124×C₄₃	C₂³	1	10	yes	—
157	#123×C₄₃	C₂³	1	20	yes	—
158	C₂²⋊Q₈×C₄₃	C₂³	1	10	yes	—
159	C₂²⋊Q₈×C₄₃	C₂³	1	20	yes	—
160	#121×C₄₃	C₂³	1	10	yes	—
161	C₄×Q₈×C₄₃	C₂³	1	10	yes	—
162	C₄×D₄×C₄₃	C₂³	1	10	yes	—
163	#117×C₄₃	C₂³	1	10	yes	—
164	C₂×C₄²×C₄₃	C₂³	1	5	yes	—
165	C₂³×D₄₃	C₂⁴	1	5	yes	—
166	C₂×Q₈×C₄₃	C₂⁴	1	10	yes	—
167	C₂×D₄×C₄₃	C₂⁴	1	10	yes	—
168	C₂²×C₄×C₄₃	C₂⁴	1	5	yes	—
169	C₂²×C₄×C₄₃	C₂⁴	1	10	yes	—
170	C₂×C₂²⋊D₄₃	C₂⁴	1	20	yes	—
171	C₂²×Dic₄₃	C₂⁴	1	5	yes	—
172	C₂²×Dic₄₃	C₂⁴	1	10	yes	—
173	Q₈×D₄₃	—	4	20	no	—
174	D₄×D₄₃	—	4	20	no	—
175	C₂×D₁₇₂	C₂⁴	1	10	yes	—
176	C₂×C₄×D₄₃	—	2	20	no	—
177	C₂×C₄×D₄₃	—	4	20	no	—
178	C₂×C₄×D₄₃	C₂⁴	1	5	yes	—
179	C₂×C₄×D₄₃	C₂⁴	1	10	yes	—
180	C₂×C₄×D₄₃	C₂⁴	1	10	yes	—
181	C₂×C₄×D₄₃	C₂⁴	1	5	yes	—
182	C₂×C₄×D₄₃	C₂⁴	1	5	yes	—
183	C₂×C₄×D₄₃	C₂⁴	1	10	yes	—
184	C₂×C₄×D₄₃	C₂⁴	1	10	yes	—
185	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₈₆	C₂⁴	1	20	yes	—
187	C₂×Dic₈₆	C₂⁴	1	10	yes	—
188	C₄⋊C₄×C₄₃	C₂⁴	1	10	yes	—
189	C₄⋊C₄×C₄₃	C₂⁴	1	10	yes	—
190	C₄⋊C₄×C₄₃	C₂⁴	1	10	yes	—
191	C₄⋊C₄×C₄₃	C₂⁴	1	10	yes	—
192	C₄⋊C₄×C₄₃	C₂⁴	1	20	yes	—
193	C₂²⋊C₄×C₄₃	C₂⁴	1	20	yes	—
194	C₂²⋊C₄×C₄₃	C₂⁴	1	20	yes	—
195	C₄²×C₄₃	C₂⁴	1	10	yes	—
196	C₄²×C₄₃	C₂⁴	1	5	yes	—
197	C₄²×C₄₃	C₂⁴	1	5	yes	—
198	C₂²⋊Dic₄₃	C₂⁴	1	20	yes	—
199	C₂²⋊Dic₄₃	C₂⁴	1	20	yes	—
200	(C₂×D₄₃)⋊C₄	C₂⁴	1	20	yes	—
201	(C₂×D₄₃)⋊C₄	C₂⁴	1	20	yes	—
202	(C₂×D₄₃)⋊C₄	C₂⁴	1	20	yes	—
203	(C₂×D₄₃)⋊C₄	C₂⁴	1	20	yes	—
204	C₄⋊Dic₄₃	C₂⁴	1	10	yes	—
205	C₄⋊Dic₄₃	C₂⁴	1	10	yes	—
206	C₄⋊Dic₄₃	C₂⁴	1	10	yes	—
207	C₄⋊Dic₄₃	C₂⁴	1	10	yes	—
208	C₄⋊Dic₄₃	C₂⁴	1	20	yes	—
209	Dic₄₃⋊C₄	C₂⁴	1	20	yes	—
210	Dic₄₃⋊C₄	C₂⁴	1	20	yes	—
211	Dic₄₃⋊C₄	C₂⁴	1	20	yes	—
212	Dic₄₃⋊C₄	C₂⁴	1	20	yes	—
213	Dic₄₃⋊C₄	C₂⁴	1	20	yes	—
214	Dic₄₃⋊C₄	C₂⁴	1	20	yes	—
215	C₄×Dic₄₃	C₂⁴	1	10	yes	—
216	C₄×Dic₄₃	C₂⁴	1	10	yes	—
217	C₄×Dic₄₃	C₂⁴	1	10	yes	—
218	C₄×Dic₄₃	C₂⁴	1	5	yes	—
219	C₄×Dic₄₃	C₂⁴	1	10	yes	—
220	C₄×Dic₄₃	C₂⁴	1	10	yes	—
221	C₄×Dic₄₃	C₂⁴	1	5	yes	—
222	C₂³×C₄₃	C₂⁵	1	5	yes	—
223	C₂²×D₄₃	—	2	10	no	—
224	C₂²×D₄₃	—	2	20	no	—
225	C₂²×D₄₃	C₂⁵	1	5	yes	—
226	C₂²×D₄₃	C₂⁵	1	1	yes	characteristic
227	Q₈×C₄₃	—	4	10	no	—
228	D₄×C₄₃	—	4	10	no	—
229	C₂×C₄×C₄₃	—	2	10	no	—
230	C₂×C₄×C₄₃	—	4	10	no	—
231	C₂×C₄×C₄₃	C₂⁵	1	10	yes	—
232	C₂×C₄×C₄₃	C₂⁵	1	5	yes	—
233	C₂×C₄×C₄₃	C₂⁵	1	10	yes	—
234	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
235	C₂²⋊D₄₃	—	4	20	no	—
236	C₂×Dic₄₃	—	2	10	no	—
237	C₂×Dic₄₃	—	4	10	no	—
238	C₂×Dic₄₃	C₂⁵	1	5	yes	—
239	C₂×Dic₄₃	C₂⁵	1	10	yes	—
240	C₂×Dic₄₃	C₂⁵	1	10	yes	—
241	C₂×Dic₄₃	C₂⁵	1	1	yes	characteristic
242	D₁₇₂	—	4	10	no	—
243	C₄×D₄₃	—	2	10	no	—
244	C₄×D₄₃	—	2	20	no	—
245	C₄×D₄₃	—	2	20	no	—
246	C₄×D₄₃	—	2	10	no	—
247	C₄×D₄₃	—	2	10	no	—
248	C₄×D₄₃	—	4	10	no	—
249	C₄×D₄₃	—	4	10	no	—
250	C₄×D₄₃	2₋¹⁺⁴	1	4	yes	—
251	Dic₈₆	—	4	10	no	—
252	Dic₈₆	—	4	20	no	—
253	C₂×#3531	—	43	1	no	maximal, Sylow
254	C₂²×C₄₃	—	2	5	no	—
255	C₂²×C₄₃	—	2	10	no	—
256	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
257	C₂×D₄₃	—	2	5	no	—
258	C₂×D₄₃	—	2	10	no	—
259	C₂×D₄₃	—	4	20	no	—
260	C₂×D₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
261	C₂×D₄₃	#585	1	4	yes	—
262	C₄×C₄₃	—	2	5	no	—
263	C₄×C₄₃	—	2	10	no	—
264	C₄×C₄₃	—	2	10	no	—
265	C₄×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
266	Dic₄₃	—	2	5	no	—
267	Dic₄₃	—	2	10	no	—
268	Dic₄₃	—	2	10	no	—
269	Dic₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
270	#3531	—	43	1	no	—
271	#3531	—	43	10	no	—
272	#3531	—	43	5	no	—
273	#3531	—	43	5	no	—
274	#3531	—	43	10	no	—
275	#3531	D₄₃	1	1	yes	characteristic, direct product factor
276	C₂×#564	—	43	1	no	—
277	C₂×#563	—	43	10	no	—
278	C₂×#562	—	43	5	no	—
279	C₂×#533	—	43	5	no	—
280	C₂×#529	—	43	10	no	—
281	C₂×C₄₃	—	4	5	no	—
282	C₂×C₄₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
283	C₂×C₄₃	C₂×#585	1	2	yes	—
284	D₄₃	—	4	5	no	—
285	D₄₃	#3531	1	4	yes	direct product factor
286	#564	—	43	10	no	—
287	#564	—	43	5	no	—
288	#564	C₂×D₄₃	1	1	yes	characteristic, complemented
289	#563	—	43	20	no	—
290	#563	—	43	20	no	—
291	#563	—	43	20	no	—
292	#563	—	43	10	no	—
293	#563	—	43	10	no	—
294	#563	—	43	10	no	—
295	#563	—	43	20	no	—
296	#563	—	43	20	no	—
297	#563	—	43	20	no	—
298	#563	C₂×D₄₃	1	10	yes	complemented
299	#562	—	43	5	no	—
300	#562	—	43	10	no	—
301	#562	—	43	20	no	—
302	#562	—	43	20	no	—
303	#562	—	43	20	no	—
304	#562	C₂×D₄₃	1	5	yes	complemented
305	#533	—	43	10	no	—
306	#533	—	43	5	no	—
307	#533	—	43	5	no	—
308	#533	—	43	20	no	—
309	#533	—	43	20	no	—
310	#533	—	43	10	no	—
311	#533	—	43	5	no	—
312	#533	C₂×D₄₃	1	5	yes	complemented
313	C₂×C₄⋊Q₈	—	43	10	no	—
314	#529	—	43	20	no	—
315	#529	—	43	10	no	—
316	#529	—	43	10	no	—
317	#529	—	43	20	no	—
318	#529	—	43	10	no	—
319	#529	—	43	10	no	—
320	#529	—	43	10	no	—
321	#529	—	43	20	no	—
322	#529	—	43	10	no	—
323	#529	—	43	20	no	—
324	#529	—	43	10	no	—
325	#529	C₂×D₄₃	1	10	yes	complemented
326	C₂×#126	—	43	20	no	—
327	C₂×#125	—	43	10	no	—
328	C₂×#125	—	43	5	no	—
329	C₂×#125	—	43	5	no	—
330	C₂×#124	—	43	10	no	—
331	C₂×#123	—	43	20	no	—
332	C₂×C₂²⋊Q₈	—	43	10	no	—
333	C₂×C₂²⋊Q₈	—	43	20	no	—
334	C₂×#121	—	43	10	no	—
335	C₂×C₄×Q₈	—	43	10	no	—
336	C₂×C₄×D₄	—	43	10	no	—
337	C₂×#117	—	43	10	no	—
338	C₂²×C₄²	—	43	5	no	—
339	C₄₃	C₂×#3531	1	1	yes	characteristic, complemented, Sylow
340	C₂²×Q₈	—	43	10	no	—
341	C₂²×D₄	—	43	10	no	—
342	C₂³×C₄	—	43	5	no	—
343	C₂³×C₄	—	43	10	no	—
344	C₄⋊Q₈	—	43	20	no	—
345	C₄⋊Q₈	—	43	20	no	—
346	C₄⋊Q₈	—	43	10	no	—
347	C₄⋊Q₈	—	43	10	no	—
348	C₄⋊Q₈	—	43	10	no	—
349	C₄⋊Q₈	C₂²×D₄₃	1	10	yes	—
350	#126	—	43	20	no	—
351	#126	—	43	20	no	—
352	#126	—	43	20	no	—
353	#126	—	43	20	no	—
354	#126	—	43	20	no	—
355	#126	—	43	20	no	—
356	#126	—	43	20	no	—
357	#126	C₂²×D₄₃	1	20	yes	—
358	#125	—	43	20	no	—
359	#125	—	43	20	no	—
360	#125	—	43	10	no	—
361	#125	—	43	10	no	—
362	#125	—	43	20	no	—
363	#125	—	43	10	no	—
364	#125	—	43	20	no	—
365	#125	—	43	10	no	—
366	#125	—	43	10	no	—
367	#125	—	43	5	no	—
368	#125	—	43	5	no	—
369	#125	C₂²×D₄₃	1	10	yes	—
370	#125	C₂²×D₄₃	1	5	yes	—
371	#125	C₂²×D₄₃	1	5	yes	—
372	#124	—	43	10	no	—
373	#124	—	43	10	no	—
374	#124	—	43	20	no	—
375	#124	—	43	20	no	—
376	#124	—	43	10	no	—
377	#124	C₂²×D₄₃	1	10	yes	—
378	#123	—	43	20	no	—
379	#123	—	43	20	no	—
380	#123	—	43	20	no	—
381	#123	—	43	20	no	—
382	#123	—	43	20	no	—
383	#123	—	43	20	no	—
384	#123	—	43	20	no	—
385	#123	C₂²×D₄₃	1	20	yes	—
386	C₂²⋊Q₈	—	43	10	no	—
387	C₂²⋊Q₈	—	43	20	no	—
388	C₂²⋊Q₈	—	43	10	no	—
389	C₂²⋊Q₈	—	43	20	no	—
390	C₂²⋊Q₈	—	43	20	no	—
391	C₂²⋊Q₈	—	43	10	no	—
392	C₂²⋊Q₈	—	43	20	no	—
393	C₂²⋊Q₈	—	43	20	no	—
394	C₂²⋊Q₈	—	43	20	no	—
395	C₂²⋊Q₈	—	43	20	no	—
396	C₂²⋊Q₈	—	43	20	no	—
397	C₂²⋊Q₈	—	43	20	no	—
398	C₂²⋊Q₈	C₂²×D₄₃	1	10	yes	—
399	C₂²⋊Q₈	C₂²×D₄₃	1	20	yes	—
400	#121	—	43	10	no	—
401	#121	—	43	20	no	—
402	#121	—	43	10	no	—
403	#121	—	43	10	no	—
404	#121	—	43	20	no	—
405	#121	C₂²×D₄₃	1	10	yes	—
406	C₄×Q₈	—	43	10	no	—
407	C₄×Q₈	—	43	20	no	—
408	C₄×Q₈	—	43	10	no	—
409	C₄×Q₈	—	43	20	no	—
410	C₄×Q₈	—	43	10	no	—
411	C₄×Q₈	C₂²×D₄₃	1	10	yes	—
412	C₄×D₄	—	43	10	no	—
413	C₄×D₄	—	43	20	no	—
414	C₄×D₄	—	43	10	no	—
415	C₄×D₄	—	43	20	no	—
416	C₄×D₄	—	43	10	no	—
417	C₄×D₄	C₂²×D₄₃	1	10	yes	—
418	#117	—	43	10	no	—
419	#117	—	43	10	no	—
420	#117	—	43	10	no	—
421	#117	—	43	20	no	—
422	#117	—	43	20	no	—
423	#117	C₂²×D₄₃	1	10	yes	—
424	C₂×C₄⋊C₄	—	43	10	no	—
425	C₂×C₄⋊C₄	—	43	10	no	—
426	C₂×C₄⋊C₄	—	43	10	no	—
427	C₂×C₄⋊C₄	—	43	10	no	—
428	C₂×C₄⋊C₄	—	43	20	no	—
429	C₂×C₂²⋊C₄	—	43	20	no	—
430	C₂×C₂²⋊C₄	—	43	20	no	—
431	C₂×C₄²	—	43	10	no	—
432	C₂×C₄²	—	43	5	no	—
433	C₂×C₄²	—	43	10	no	—
434	C₂×C₄²	—	43	5	no	—
435	C₂×C₄²	—	43	5	no	—
436	C₂×C₄²	—	43	5	no	—
437	C₂×C₄²	—	43	5	no	—
438	C₂×C₄²	—	43	10	no	—
439	C₂×C₄²	C₂²×D₄₃	1	5	yes	—
440	C₂⁴	—	43	5	no	—
441	C₂×Q₈	—	43	10	no	—
442	C₂×Q₈	—	43	20	no	—
443	C₂×Q₈	—	172	20	no	—
444	C₂×Q₈	C₂³×D₄₃	1	10	yes	—
445	C₂×D₄	—	43	20	no	—
446	C₂×D₄	—	43	10	no	—
447	C₂×D₄	—	172	20	no	—
448	C₂×D₄	C₂³×D₄₃	1	10	yes	—
449	C₂²×C₄	—	43	1	no	—
450	C₂²×C₄	—	43	5	no	—
451	C₂²×C₄	—	43	10	no	—
452	C₂²×C₄	—	43	5	no	—
453	C₂²×C₄	—	43	10	no	—
454	C₂²×C₄	—	43	10	no	—
455	C₂²×C₄	—	43	5	no	—
456	C₂²×C₄	—	43	5	no	—
457	C₂²×C₄	—	43	10	no	—
458	C₂²×C₄	—	43	10	no	—
459	C₂²×C₄	—	86	20	no	—
460	C₂²×C₄	—	172	20	no	—
461	C₂²×C₄	C₂³×D₄₃	1	5	yes	—
462	C₂²×C₄	C₂³×D₄₃	1	10	yes	—
463	C₄⋊C₄	—	43	20	no	—
464	C₄⋊C₄	—	43	10	no	—
465	C₄⋊C₄	—	43	20	no	—
466	C₄⋊C₄	—	43	10	no	—
467	C₄⋊C₄	—	43	20	no	—
468	C₄⋊C₄	—	43	10	no	—
469	C₄⋊C₄	—	43	20	no	—
470	C₄⋊C₄	—	43	10	no	—
471	C₄⋊C₄	—	43	20	no	—
472	C₄⋊C₄	—	43	20	no	—
473	C₄⋊C₄	—	43	20	no	—
474	C₄⋊C₄	C₂³×D₄₃	1	10	yes	—
475	C₄⋊C₄	C₂³×D₄₃	1	10	yes	—
476	C₄⋊C₄	C₂³×D₄₃	1	10	yes	—
477	C₄⋊C₄	C₂³×D₄₃	1	10	yes	—
478	C₄⋊C₄	C₂³×D₄₃	1	20	yes	—
479	C₂²⋊C₄	—	43	20	no	—
480	C₂²⋊C₄	—	43	20	no	—
481	C₂²⋊C₄	—	43	20	no	—
482	C₂²⋊C₄	—	43	20	no	—
483	C₂²⋊C₄	—	43	20	no	—
484	C₂²⋊C₄	—	43	20	no	—
485	C₂²⋊C₄	C₂³×D₄₃	1	20	yes	—
486	C₂²⋊C₄	C₂³×D₄₃	1	20	yes	—
487	C₄²	—	43	10	no	—
488	C₄²	—	43	10	no	—
489	C₄²	—	43	10	no	—
490	C₄²	—	43	5	no	—
491	C₄²	—	43	10	no	—
492	C₄²	—	43	5	no	—
493	C₄²	—	43	10	no	—
494	C₄²	C₂³×D₄₃	1	5	yes	—
495	C₄²	C₂³×D₄₃	1	5	yes	—
496	C₄²	C₂³×D₄₃	1	10	yes	—
497	C₂³	—	43	1	no	—
498	C₂³	—	43	5	no	—
499	C₂³	—	86	10	no	—
500	C₂³	—	86	20	no	—
501	C₂³	C₂⁴×D₄₃	1	5	yes	—
502	Q₈	—	4	10	no	—
503	Q₈	—	172	10	no	—
504	Q₈	—	172	20	no	—
505	D₄	—	4	10	no	—
506	D₄	—	172	10	no	—
507	D₄	—	172	20	no	—
508	C₂×C₄	—	2	10	no	—
509	C₂×C₄	—	4	10	no	—
510	C₂×C₄	—	43	1	no	—
511	C₂×C₄	—	43	4	no	—
512	C₂×C₄	—	43	5	no	—
513	C₂×C₄	—	43	10	no	—
514	C₂×C₄	—	43	10	no	—
515	C₂×C₄	—	86	10	no	—
516	C₂×C₄	—	86	10	no	—
517	C₂×C₄	—	86	20	no	—
518	C₂×C₄	—	86	20	no	—
519	C₂×C₄	—	86	10	no	—
520	C₂×C₄	—	86	10	no	—
521	C₂×C₄	—	172	10	no	—
522	C₂×C₄	—	172	10	no	—
523	C₂×C₄	—	172	10	no	—
524	C₂×C₄	C₂⁴×D₄₃	1	5	yes	—
525	C₂×C₄	C₂⁴×D₄₃	1	10	yes	—
526	C₂×C₄	C₂⁴×D₄₃	1	10	yes	—
527	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
528	C₂²	—	2	5	no	—
529	C₂²	—	2	10	no	—
530	C₂²	—	43	2	no	—
531	C₂²	—	43	4	no	—
532	C₂²	—	86	5	no	—
533	C₂²	—	86	10	no	—
534	C₂²	—	172	20	no	—
535	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
536	C₄	—	2	5	no	—
537	C₄	—	2	10	no	—
538	C₄	—	2	10	no	—
539	C₄	—	43	2	no	—
540	C₄	—	86	5	no	—
541	C₄	—	86	10	no	—
542	C₄	—	86	10	no	—
543	C₄	2₋¹⁺⁴×D₄₃	1	2	yes	—
544	C₂	—	4	5	no	—
545	C₂	—	43	4	no	—
546	C₂	—	172	5	no	—
547	C₂	C₂×2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
548	C₂	#585×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₄₃×#3531	C₂
hypercenter	#3531	D₄₃
hypocenter	C₄₃	C₂×#3531
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #3531

Complements

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

N	H ≅ G/N	type
1. #19148743	C₂	semidirect
2. #19148742	C₂	semidirect
3. #19148741	C₂	semidirect
4. #19148740	C₂	semidirect
5. #19148739	C₂	semidirect
6. #564×D₄₃	C₂	semidirect
7. #563×D₄₃	C₂	semidirect
8. #562×D₄₃	C₂	semidirect
9. #533×D₄₃	C₂	semidirect
10. #529×D₄₃	C₂	semidirect
11. C₄₃×#3531	C₂	semidirect
12. C₄₃⋊#564	C₂²	semidirect
13. C₄₃⋊#564	C₂²	semidirect
14. #14583653	C₂²	semidirect
15. #14583653	C₂²	semidirect
16. #14583652	C₂²	semidirect
17. #14583651	C₂²	semidirect
18. #14583651	C₂²	semidirect
19. #14583650	C₂²	semidirect
20. #14583650	C₂²	semidirect
21. #14583649	C₂²	semidirect
22. #14583648	C₂²	semidirect
23. #14583647	C₂²	semidirect
24. #14583646	C₂²	semidirect
25. #14583645	C₂²	semidirect
26. #14583644	C₂²	semidirect
27. #14583643	C₂²	semidirect
28. #14583456	C₂²	semidirect
29. #14583455	C₂²	semidirect
30. #14583455	C₂²	semidirect
31. #14583454	C₂²	semidirect
32. #14583453	C₂²	semidirect
33. #14583452	C₂²	semidirect
34. #14583451	C₂²	semidirect
36. #14583436	C₂²	semidirect
37. #14583435	C₂²	semidirect
38. #14583434	C₂²	semidirect
39. #14583433	C₂²	semidirect
40. #14583432	C₂²	semidirect
41. #14583431	C₂²	semidirect
42. #14583430	C₂²	semidirect
43. #14583429	C₂²	semidirect
44. #14583428	C₂²	semidirect
45. #14583427	C₂²	semidirect
46. #14583426	C₂²	semidirect
60. C₄₃×#564	C₂²	semidirect
61. C₄₃×#563	C₂²	semidirect
62. C₄₃×#562	C₂²	semidirect
63. C₄₃×#533	C₂²	semidirect
64. C₄₃×#529	C₂²	semidirect
275. #3531	D₄₃	direct (N × H)
285. D₄₃	#3531	direct (N × H)
288. #564	C₂×D₄₃	semidirect
298. #563	C₂×D₄₃	semidirect
304. #562	C₂×D₄₃	semidirect
312. #533	C₂×D₄₃	semidirect
325. #529	C₂×D₄₃	semidirect
339. C₄₃	C₂×#3531	semidirect

Maximal subgroups

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

subgroup	index
#19148743	2
#19148742	2
#19148741	2
#19148740	2
#19148739	2
#564×D₄₃	2
#563×D₄₃	2
#562×D₄₃	2
#533×D₄₃	2
#529×D₄₃	2
C₄₃×#3531	2
C₂×#3531	43

Subgroups — D43×#3531 #26003494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#3531 #26003494