Subgroups — D₄₃×#1581 #25066089

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#436×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133427	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133426	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133425	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133424	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133423	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133422	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133421	C₂	1	1	yes	maximal, characteristic, complemented
11	#335×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄⋊C₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄⋊C₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#322×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₈×D₄₃	C₄	1	1	yes	characteristic
17	C₂×M₁₆×D₄₃	—	2	1	no	—
18	C₂²×C₈×D₄₃	—	2	1	no	—
19	C₄×D₄×D₄₃	C₂²	1	1	yes	characteristic
20	C₄×D₄×D₄₃	C₂²	1	1	yes	characteristic
21	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
22	D₈×Dic₄₃	C₄	1	1	yes	characteristic
23	#14582981	C₄	1	1	yes	characteristic
24	C₄×#10621882	C₂²	1	1	yes	characteristic
25	C₄×#10621882	C₂²	1	1	yes	characteristic
26	#14582979	C₄	1	1	yes	characteristic
27	#14582979	C₄	1	1	yes	characteristic
28	#14582978	C₂²	1	1	yes	characteristic, complemented
29	#14582977	C₂²	1	1	yes	characteristic, complemented
30	#14582976	C₂²	1	1	yes	characteristic, complemented
31	#14582975	—	2	1	no	—
32	#14582974	—	2	1	no	—
33	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
34	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	#14582964	C₂²	1	1	yes	characteristic, complemented
36	C₈×C₂²⋊D₄₃	—	2	1	no	—
37	(C₂²⋊D₄₃)⋊C₈	—	2	1	no	—
38	#107×D₄₃	C₄	1	1	yes	characteristic
39	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
41	#102×D₄₃	C₄	1	1	yes	characteristic
42	#102×D₄₃	C₄	1	1	yes	characteristic
43	C₂²⋊C₈×D₄₃	—	2	1	no	—
44	C₂²⋊C₈×D₄₃	—	2	1	no	—
45	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
48	#14582652	C₂²	1	1	yes	characteristic, complemented
49	#14582651	C₂²	1	1	yes	characteristic, complemented
50	#14582651	C₂²	1	1	yes	characteristic, complemented
51	#14582628	C₂²	1	1	yes	characteristic, complemented
52	#14582628	C₂²	1	1	yes	characteristic, complemented
53	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
54	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#14582626	C₂²	1	1	yes	characteristic, complemented
56	#14582626	C₂²	1	1	yes	characteristic, complemented
57	#14582621	C₂²	1	1	yes	characteristic, complemented
58	#14582621	C₂²	1	1	yes	characteristic, complemented
59	#14582620	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
61	C₄₃×#436	C₂²	1	1	yes	characteristic, complemented
62	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
63	C₄₃×#335	C₂²	1	1	yes	characteristic, complemented
64	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₄₃×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×D₄×D₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₄₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₄₃	—	2	1	no	—
70	C₂²×C₄×D₄₃	—	2	1	no	—
71	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
72	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
73	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
74	D₈×D₄₃	—	2	4	no	—
75	C₂×#10621877	—	2	1	no	—
76	C₂×#10621872	—	2	1	no	—
77	C₂×#10621872	—	2	1	no	—
78	M₁₆×D₄₃	—	4	4	no	—
79	C₂²×C₄₃⋊C₈	—	2	1	no	—
80	C₂×C₈×D₄₃	—	2	1	no	—
81	C₂×C₈×D₄₃	—	2	1	no	—
82	C₂×C₈×D₄₃	—	2	1	no	—
83	C₂×C₈×D₄₃	—	2	1	no	—
84	C₂×C₈×D₄₃	—	2	1	no	—
85	C₂×C₈×D₄₃	—	4	4	no	—
86	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
89	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
90	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
91	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
92	D₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
93	D₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
94	#13063287	C₂×C₄	1	1	yes	characteristic
95	#13063287	C₂×C₄	1	1	yes	characteristic
96	C₄×C₂²⋊D₄₃	—	2	1	no	—
97	C₄×C₂²⋊D₄₃	—	2	1	no	—
98	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
99	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
100	C₄⋊C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊C₄×D₄₃	—	2	1	no	—
103	C₂²⋊C₄×D₄₃	—	2	1	no	—
104	C₄²×D₄₃	C₂³	1	1	yes	characteristic
105	#13063259	C₂×C₄	1	1	yes	characteristic
106	#13063258	C₂×C₄	1	1	yes	characteristic
107	#13063258	C₂×C₄	1	1	yes	characteristic
108	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
109	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
110	Dic₄₃⋊C₈	—	2	1	no	—
111	Dic₄₃⋊C₈	—	2	1	no	—
112	#13063247	C₂×C₄	1	1	yes	characteristic
113	#13063247	C₂×C₄	1	1	yes	characteristic
114	#13063246	C₂×C₄	1	1	yes	characteristic
115	#13063246	C₂×C₄	1	1	yes	characteristic
116	#13063245	C₂×C₄	1	1	yes	characteristic
117	#13063245	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
119	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
120	(C₂×D₄₃)⋊C₈	—	2	1	no	—
121	(C₂×D₄₃)⋊C₈	—	2	1	no	—
122	(C₂×D₄₃)⋊C₈	—	2	1	no	—
123	(C₂×D₄₃)⋊C₈	—	2	1	no	—
124	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₈×Dic₄₃	—	2	1	no	—
128	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₄₃	D₄	1	1	yes	characteristic
131	C₈×Dic₄₃	D₄	1	1	yes	characteristic
132	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
133	C₂×M₁₆×C₄₃	—	2	1	no	—
134	C₂²×C₈×C₄₃	—	2	1	no	—
135	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
137	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
138	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
140	#102×C₄₃	C₂×C₄	1	1	yes	characteristic
141	#102×C₄₃	C₂×C₄	1	1	yes	characteristic
142	C₂²⋊C₈×C₄₃	—	2	1	no	—
143	C₂²⋊C₈×C₄₃	—	2	1	no	—
144	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
147	C₂³×D₄₃	—	2	1	no	—
148	C₂³×D₄₃	—	2	1	no	—
149	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂×C₂²⋊D₄₃	—	2	1	no	—
154	C₂×C₂²⋊D₄₃	—	2	1	no	—
155	C₂²×Dic₄₃	—	2	1	no	—
156	C₂²×Dic₄₃	—	2	1	no	—
157	D₄×D₄₃	—	2	2	no	—
158	D₄×D₄₃	—	2	2	no	—
159	D₄×D₄₃	—	2	2	no	—
160	D₄×D₄₃	M₁₆	1	4	yes	complemented
161	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₄₃	—	2	1	no	—
164	C₂×C₄×D₄₃	—	2	1	no	—
165	C₂×C₄×D₄₃	—	2	1	no	—
166	C₂×C₄×D₄₃	—	2	1	no	—
167	C₂×C₄×D₄₃	—	2	1	no	—
168	C₂×C₄×D₄₃	—	2	1	no	—
169	C₂×C₄×D₄₃	—	4	2	no	—
170	C₂×C₄×D₄₃	—	4	2	no	—
171	C₂×C₄×D₄₃	—	4	2	no	—
172	C₂×C₄×D₄₃	—	4	2	no	—
173	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
176	D₈×C₄₃	—	2	2	no	—
177	M₁₆×C₄₃	—	4	2	no	—
178	C₂×C₈×C₄₃	—	2	1	no	—
179	C₂×C₈×C₄₃	—	2	1	no	—
180	C₂×C₈×C₄₃	—	2	1	no	—
181	C₂×C₈×C₄₃	—	4	2	no	—
182	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
186	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
187	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₄₃	—	2	1	no	—
189	C₂²⋊C₄×C₄₃	—	2	1	no	—
190	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
191	C₂²⋊Dic₄₃	—	2	1	no	—
192	C₂²⋊Dic₄₃	—	2	1	no	—
193	#10621882	—	2	2	no	—
194	#10621882	—	2	2	no	—
195	(C₂×D₄₃)⋊C₄	—	2	1	no	—
196	(C₂×D₄₃)⋊C₄	—	2	1	no	—
197	(C₂×D₄₃)⋊C₄	—	2	1	no	—
198	(C₂×D₄₃)⋊C₄	—	2	1	no	—
199	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
201	Dic₄₃⋊C₄	—	2	1	no	—
202	Dic₄₃⋊C₄	—	2	1	no	—
203	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
204	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
205	C₄×Dic₄₃	#41	1	1	yes	characteristic
206	#10621877	—	4	2	no	—
207	C₂×C₄₃⋊C₈	—	2	1	no	—
208	C₂×C₄₃⋊C₈	—	2	1	no	—
209	C₂×C₄₃⋊C₈	—	2	1	no	—
210	C₂×C₄₃⋊C₈	—	4	2	no	—
211	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
214	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
215	D₃₄₄	—	2	2	no	—
216	#10621872	—	4	2	no	—
217	#10621872	—	4	2	no	—
218	C₈×D₄₃	—	2	2	no	—
219	C₈×D₄₃	—	2	2	no	—
220	C₈×D₄₃	—	2	2	no	—
221	C₈×D₄₃	—	4	2	no	—
222	C₈×D₄₃	—	4	2	no	—
223	C₈×D₄₃	—	4	2	no	—
224	C₈×D₄₃	—	4	2	no	—
225	C₈×D₄₃	—	4	2	no	—
226	C₈×D₄₃	D₈	1	4	yes	complemented
227	C₂³×C₄₃	—	2	1	no	—
228	C₂³×C₄₃	—	2	1	no	—
229	C₂²×D₄₃	—	2	1	no	—
230	C₂²×D₄₃	—	2	4	no	—
231	C₂²×D₄₃	—	2	1	no	—
232	C₂²×D₄₃	—	4	2	no	—
233	C₂²×D₄₃	—	4	2	no	—
234	C₂²×D₄₃	—	4	2	no	—
235	C₂²×D₄₃	—	4	2	no	—
236	C₂²×D₄₃	—	4	2	no	—
237	C₂²×D₄₃	C₄×D₄	1	1	yes	characteristic
238	D₄×C₄₃	—	2	1	no	—
239	D₄×C₄₃	—	2	1	no	—
240	D₄×C₄₃	—	2	1	no	—
241	D₄×C₄₃	C₂×M₁₆	1	2	yes	complemented
242	C₂×C₄×C₄₃	—	2	1	no	—
243	C₂×C₄×C₄₃	—	2	1	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
251	C₂²⋊D₄₃	—	2	4	no	—
252	C₂²⋊D₄₃	—	4	2	no	—
253	C₂×Dic₄₃	—	2	1	no	—
254	C₂×Dic₄₃	—	2	1	no	—
255	C₂×Dic₄₃	—	4	2	no	—
256	C₂×Dic₄₃	—	4	2	no	—
257	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
258	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
259	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
260	D₁₇₂	—	2	1	no	—
261	D₁₇₂	—	2	1	no	—
262	D₁₇₂	—	2	1	no	—
263	D₁₇₂	C₂×M₁₆	1	2	yes	complemented
264	C₄×D₄₃	—	2	2	no	—
265	C₄×D₄₃	—	4	2	no	—
266	C₄×D₄₃	—	4	2	no	—
267	C₄×D₄₃	—	4	1	no	—
268	C₄×D₄₃	—	4	1	no	—
269	C₄×D₄₃	—	4	1	no	—
270	C₄×D₄₃	—	4	1	no	—
271	C₄×D₄₃	—	4	2	no	—
272	C₄×D₄₃	—	4	2	no	—
273	C₄×D₄₃	C₂×M₁₆	1	2	yes	—
274	C₄×D₄₃	#131	1	2	yes	—
275	C₄×D₄₃	C₂×D₈	1	2	yes	—
276	C₄×D₄₃	#135	1	2	yes	—
277	C₈×C₄₃	—	2	1	no	—
278	C₈×C₄₃	—	2	1	no	—
279	C₈×C₄₃	—	2	1	no	—
280	C₈×C₄₃	—	4	1	no	—
281	C₈×C₄₃	—	4	1	no	—
282	C₈×C₄₃	—	4	1	no	—
283	C₈×C₄₃	C₂×D₈	1	2	yes	complemented
284	C₄₃⋊C₈	—	2	1	no	—
285	C₄₃⋊C₈	—	2	1	no	—
286	C₄₃⋊C₈	—	2	1	no	—
287	C₄₃⋊C₈	—	4	1	no	—
288	C₄₃⋊C₈	—	4	1	no	—
289	C₄₃⋊C₈	—	4	1	no	—
290	C₄₃⋊C₈	C₂×D₈	1	2	yes	complemented
291	C₂×#1581	—	43	1	no	maximal, Sylow
292	C₂²×C₄₃	—	2	2	no	—
293	C₂²×C₄₃	—	4	1	no	—
294	C₂²×C₄₃	—	4	1	no	—
295	C₂²×C₄₃	—	4	1	no	—
296	C₂²×C₄₃	—	4	1	no	—
297	C₂²×C₄₃	—	4	1	no	—
298	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂×D₄₃	—	2	2	no	—
300	C₂×D₄₃	—	4	1	no	—
301	C₂×D₄₃	—	4	1	no	—
302	C₂×D₄₃	—	4	8	no	—
303	C₂×D₄₃	—	4	1	no	—
304	C₂×D₄₃	—	4	1	no	—
305	C₂×D₄₃	—	4	1	no	—
306	C₂×D₄₃	—	8	4	no	—
307	C₂×D₄₃	#435	1	2	yes	—
308	C₂×D₄₃	C₄×D₈	1	2	yes	—
309	C₂×D₄₃	#444	1	2	yes	—
310	C₄×C₄₃	—	2	1	no	—
311	C₄×C₄₃	—	4	1	no	—
312	C₄×C₄₃	—	4	1	no	—
313	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
314	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
315	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
316	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
317	Dic₄₃	—	2	1	no	—
318	Dic₄₃	—	4	1	no	—
319	Dic₄₃	—	4	1	no	—
320	Dic₄₃	#435	1	2	yes	—
321	Dic₄₃	C₄×D₈	1	2	yes	—
322	C₂×C₄×D₈	—	43	1	no	—
323	C₂×#436	—	43	1	no	—
324	C₂×C₈×D₄	—	43	1	no	—
325	#1581	—	43	1	no	—
326	#1581	—	43	1	no	—
327	#1581	—	43	1	no	—
328	#1581	—	43	1	no	—
329	#1581	—	43	1	no	—
330	#1581	—	43	1	no	—
331	#1581	—	43	1	no	—
332	#1581	D₄₃	1	1	yes	characteristic, direct product factor
333	C₂×#335	—	43	1	no	—
334	C₂×D₄⋊C₈	—	43	1	no	—
335	C₂×D₄⋊C₈	—	43	1	no	—
336	C₂×#322	—	43	1	no	—
337	C₂×C₄₃	—	4	2	no	—
338	C₂×C₄₃	—	8	1	no	—
339	C₂×C₄₃	C₂×#435	1	1	yes	characteristic
340	C₂×C₄₃	C₂×C₄×D₈	1	1	yes	characteristic
341	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
342	D₄₃	—	4	2	no	—
343	D₄₃	—	8	1	no	—
344	D₄₃	#1581	1	4	yes	direct product factor
345	C₂²×D₈	—	43	1	no	—
346	C₂²×M₁₆	—	86	1	no	—
347	C₂³×C₈	—	86	1	no	—
348	C₂×C₄×D₄	—	43	1	no	—
349	C₂×C₄×D₄	—	43	1	no	—
350	C₄×D₈	—	43	1	no	—
351	C₄×D₈	—	43	1	no	—
352	C₄×D₈	—	43	1	no	—
353	C₄×D₈	—	43	1	no	—
354	C₄×D₈	—	43	1	no	—
355	C₄×D₈	—	43	1	no	—
356	C₄×D₈	—	43	1	no	—
357	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
358	#436	—	43	1	no	—
359	#436	—	43	1	no	—
360	#436	—	43	1	no	—
361	#436	—	86	1	no	—
362	#436	—	86	1	no	—
363	#436	C₂×D₄₃	1	1	yes	characteristic, complemented
364	C₈×D₄	—	43	1	no	—
365	C₈×D₄	—	43	1	no	—
366	C₈×D₄	—	43	1	no	—
367	C₈×D₄	—	86	1	no	—
368	C₈×D₄	—	86	1	no	—
369	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
370	C₂×#107	—	43	1	no	—
371	C₂×C₄⋊C₈	—	43	1	no	—
372	C₂×C₄⋊C₈	—	43	1	no	—
373	C₂×#102	—	43	1	no	—
374	C₂×#102	—	43	1	no	—
375	C₂×C₂²⋊C₈	—	86	1	no	—
376	C₂×C₂²⋊C₈	—	86	1	no	—
377	C₂×C₄×C₈	—	43	1	no	—
378	C₂×C₄×C₈	—	43	1	no	—
379	C₂×C₄×C₈	—	43	1	no	—
380	#335	—	43	1	no	—
381	#335	—	43	1	no	—
382	#335	—	43	1	no	—
383	#335	C₂×D₄₃	1	1	yes	characteristic, complemented
384	D₄⋊C₈	—	43	1	no	—
385	D₄⋊C₈	—	43	1	no	—
386	D₄⋊C₈	—	43	1	no	—
387	D₄⋊C₈	—	43	1	no	—
388	D₄⋊C₈	—	43	1	no	—
389	D₄⋊C₈	—	43	1	no	—
390	D₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
391	D₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
392	#322	—	43	1	no	—
393	#322	—	43	1	no	—
394	#322	—	43	1	no	—
395	#322	C₂×D₄₃	1	1	yes	characteristic, complemented
396	C₄₃	C₂×#1581	1	1	yes	characteristic, complemented, Sylow
397	C₂²×D₄	—	43	1	no	—
398	C₂²×D₄	—	43	1	no	—
399	C₂³×C₄	—	86	1	no	—
400	C₂³×C₄	—	86	1	no	—
401	C₂×D₈	—	43	1	no	—
402	C₂×D₈	—	43	1	no	—
403	C₂×D₈	—	43	1	no	—
404	C₂×D₈	—	86	4	no	—
405	C₂×D₈	C₄×D₄₃	1	1	yes	characteristic
406	C₂×M₁₆	—	2	1	no	—
407	C₂×M₁₆	—	86	1	no	—
408	C₂×M₁₆	—	86	1	no	—
409	C₂×M₁₆	—	86	1	no	—
410	C₂×M₁₆	—	172	4	no	—
411	C₂²×C₈	—	2	1	no	—
412	C₂²×C₈	—	43	1	no	—
413	C₂²×C₈	—	43	1	no	—
414	C₂²×C₈	—	43	1	no	—
415	C₂²×C₈	—	43	1	no	—
416	C₂²×C₈	—	86	1	no	—
417	C₂²×C₈	—	86	1	no	—
418	C₂²×C₈	—	86	1	no	—
419	C₂²×C₈	—	86	1	no	—
420	C₂²×C₈	—	86	1	no	—
421	C₂²×C₈	—	86	1	no	—
422	C₂²×C₈	—	172	4	no	—
423	C₄×D₄	—	43	1	no	—
424	C₄×D₄	—	43	1	no	—
425	C₄×D₄	—	43	1	no	—
426	C₄×D₄	—	43	1	no	—
427	C₄×D₄	—	43	1	no	—
428	C₄×D₄	—	43	1	no	—
429	C₄×D₄	—	86	1	no	—
430	C₄×D₄	—	86	1	no	—
431	C₄×D₄	—	86	1	no	—
432	C₄×D₄	—	86	1	no	—
433	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
434	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	—	43	1	no	—
436	C₂×C₄⋊C₄	—	43	1	no	—
437	C₂×C₂²⋊C₄	—	86	1	no	—
438	C₂×C₂²⋊C₄	—	86	1	no	—
439	C₂×C₄²	—	43	1	no	—
440	#107	—	43	1	no	—
441	#107	—	43	1	no	—
442	#107	—	43	1	no	—
443	#107	C₄×D₄₃	1	1	yes	characteristic
444	C₄⋊C₈	—	43	1	no	—
445	C₄⋊C₈	—	43	1	no	—
446	C₄⋊C₈	—	86	1	no	—
447	C₄⋊C₈	—	86	1	no	—
448	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
449	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
450	#102	—	43	1	no	—
451	#102	—	43	1	no	—
452	#102	—	43	1	no	—
453	#102	—	43	1	no	—
454	#102	—	43	1	no	—
455	#102	—	43	1	no	—
456	#102	C₄×D₄₃	1	1	yes	characteristic
457	#102	C₄×D₄₃	1	1	yes	characteristic
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	86	1	no	—
461	C₂²⋊C₈	—	86	1	no	—
462	C₂²⋊C₈	—	86	1	no	—
463	C₂²⋊C₈	—	86	1	no	—
464	C₂²⋊C₈	—	86	1	no	—
465	C₂²⋊C₈	—	86	1	no	—
466	C₄×C₈	—	43	1	no	—
467	C₄×C₈	—	43	1	no	—
468	C₄×C₈	—	43	1	no	—
469	C₄×C₈	—	43	1	no	—
470	C₄×C₈	—	43	1	no	—
471	C₄×C₈	—	43	1	no	—
472	C₄×C₈	—	43	1	no	—
473	C₄×C₈	—	86	1	no	—
474	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
475	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
476	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
477	C₂⁴	—	86	1	no	—
478	C₂⁴	—	86	1	no	—
479	C₂×D₄	—	43	4	no	—
480	C₂×D₄	—	43	1	no	—
481	C₂×D₄	—	43	1	no	—
482	C₂×D₄	—	86	2	no	—
483	C₂×D₄	—	86	2	no	—
484	C₂×D₄	—	86	2	no	—
485	C₂×D₄	—	86	1	no	—
486	C₂×D₄	—	86	1	no	—
487	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
488	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	43	1	no	—
492	C₂²×C₄	—	43	1	no	—
493	C₂²×C₄	—	43	1	no	—
494	C₂²×C₄	—	86	1	no	—
495	C₂²×C₄	—	86	1	no	—
496	C₂²×C₄	—	86	1	no	—
497	C₂²×C₄	—	86	1	no	—
498	C₂²×C₄	—	86	1	no	—
499	C₂²×C₄	—	86	1	no	—
500	C₂²×C₄	—	86	1	no	—
501	C₂²×C₄	—	86	1	no	—
502	C₂²×C₄	—	172	2	no	—
503	C₂²×C₄	—	172	2	no	—
504	C₂²×C₄	—	172	2	no	—
505	C₂²×C₄	—	172	2	no	—
506	D₈	—	2	2	no	—
507	D₈	—	86	2	no	—
508	D₈	—	86	2	no	—
509	D₈	—	86	2	no	—
510	M₁₆	—	4	2	no	—
511	M₁₆	—	172	2	no	—
512	M₁₆	—	172	2	no	—
513	M₁₆	—	172	2	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	4	2	no	—
518	C₂×C₈	—	43	1	no	—
519	C₂×C₈	—	43	4	no	—
520	C₂×C₈	—	43	1	no	—
521	C₂×C₈	—	43	1	no	—
522	C₂×C₈	—	43	1	no	—
523	C₂×C₈	—	86	2	no	—
524	C₂×C₈	—	86	2	no	—
525	C₂×C₈	—	86	2	no	—
526	C₂×C₈	—	86	1	no	—
527	C₂×C₈	—	86	1	no	—
528	C₂×C₈	—	86	1	no	—
529	C₂×C₈	—	172	2	no	—
530	C₂×C₈	—	172	2	no	—
531	C₂×C₈	—	172	2	no	—
532	C₂×C₈	—	172	2	no	—
533	C₂×C₈	—	172	2	no	—
534	C₂×C₈	—	172	2	no	—
535	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
536	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
537	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
538	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
539	C₄⋊C₄	—	43	1	no	—
540	C₄⋊C₄	—	43	1	no	—
541	C₄⋊C₄	—	86	1	no	—
542	C₄⋊C₄	—	86	1	no	—
543	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	86	1	no	—
548	C₂²⋊C₄	—	86	1	no	—
549	C₂²⋊C₄	—	86	1	no	—
550	C₂²⋊C₄	—	86	1	no	—
551	C₂²⋊C₄	—	86	1	no	—
552	C₂²⋊C₄	—	86	1	no	—
553	C₄²	—	43	1	no	—
554	C₄²	—	43	1	no	—
555	C₄²	—	43	1	no	—
556	C₄²	C₂³×D₄₃	1	1	yes	characteristic
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	43	1	no	—
560	C₂³	—	86	4	no	—
561	C₂³	—	86	1	no	—
562	C₂³	—	86	1	no	—
563	C₂³	—	172	2	no	—
564	C₂³	—	172	2	no	—
565	C₂³	—	172	2	no	—
566	C₂³	—	172	2	no	—
567	C₂³	—	172	2	no	—
568	D₄	—	2	1	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	1	no	—
571	D₄	—	43	2	no	—
572	D₄	—	86	4	no	—
573	D₄	—	86	1	no	—
574	D₄	—	86	1	no	—
575	D₄	—	86	1	no	—
576	D₄	—	172	2	no	—
577	D₄	M₁₆×D₄₃	1	2	yes	complemented
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	43	1	no	—
585	C₂×C₄	—	43	1	no	—
586	C₂×C₄	—	43	2	no	—
587	C₂×C₄	—	43	2	no	—
588	C₂×C₄	—	43	2	no	—
589	C₂×C₄	—	43	2	no	—
590	C₂×C₄	—	43	1	no	—
591	C₂×C₄	—	86	2	no	—
592	C₂×C₄	—	86	1	no	—
593	C₂×C₄	—	86	1	no	—
594	C₂×C₄	—	172	2	no	—
595	C₂×C₄	—	172	2	no	—
596	C₂×C₄	—	172	2	no	—
597	C₂×C₄	—	172	2	no	—
598	C₂×C₄	—	172	2	no	—
599	C₂×C₄	—	172	2	no	—
600	C₂×C₄	—	172	1	no	—
601	C₂×C₄	—	172	1	no	—
602	C₂×C₄	—	172	1	no	—
603	C₂×C₄	—	172	1	no	—
604	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
605	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
606	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
607	C₈	—	2	1	no	—
608	C₈	—	2	1	no	—
609	C₈	—	2	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	4	1	no	—
612	C₈	—	4	1	no	—
613	C₈	—	43	2	no	—
614	C₈	—	86	1	no	—
615	C₈	—	86	1	no	—
616	C₈	—	86	1	no	—
617	C₈	—	172	1	no	—
618	C₈	—	172	1	no	—
619	C₈	—	172	1	no	—
620	C₈	D₈×D₄₃	1	2	yes	complemented
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	43	2	no	—
628	C₂²	—	43	2	no	—
629	C₂²	—	43	2	no	—
630	C₂²	—	86	2	no	—
631	C₂²	—	344	4	no	—
632	C₂²	—	172	8	no	—
633	C₂²	—	172	1	no	—
634	C₂²	—	172	1	no	—
635	C₂²	—	172	1	no	—
636	C₂²	—	172	1	no	—
637	C₂²	—	172	1	no	—
638	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
639	C₄	—	2	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	43	2	no	—
643	C₄	—	43	2	no	—
644	C₄	—	86	1	no	—
645	C₄	—	172	1	no	—
646	C₄	—	172	1	no	—
647	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
648	C₄	#131×D₄₃	1	1	yes	characteristic
649	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
650	C₄	#135×D₄₃	1	1	yes	characteristic
651	C₂	—	4	2	no	—
652	C₂	—	8	1	no	—
653	C₂	—	43	4	no	—
654	C₂	—	344	1	no	—
655	C₂	—	172	2	no	—
656	C₂	#435×D₄₃	1	1	yes	characteristic
657	C₂	C₄×D₈×D₄₃	1	1	yes	characteristic
658	C₂	#444×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1581	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₄₃	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1581	D₄₃
hypocenter	C₄₃	C₂×#1581
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
2. #436×D₄₃	C₂	semidirect
3. C₈×D₄×D₄₃	C₂	semidirect
4. #19133427	C₂	semidirect
5. #19133426	C₂	semidirect
6. #19133425	C₂	semidirect
7. #19133424	C₂	semidirect
8. #19133423	C₂	semidirect
9. #19133422	C₂	semidirect
10. #19133421	C₂	semidirect
11. #335×D₄₃	C₂	semidirect
12. D₄⋊C₈×D₄₃	C₂	semidirect
13. D₄⋊C₈×D₄₃	C₂	semidirect
14. #322×D₄₃	C₂	semidirect
15. C₄₃×#1581	C₂	semidirect
28. #14582978	C₂²	semidirect
29. #14582977	C₂²	semidirect
30. #14582976	C₂²	semidirect
33. C₈×D₁₇₂	C₂²	semidirect
34. D₄×C₄₃⋊C₈	C₂²	semidirect
35. #14582964	C₂²	semidirect
48. #14582652	C₂²	semidirect
49. #14582651	C₂²	semidirect
50. #14582651	C₂²	semidirect
51. #14582628	C₂²	semidirect
52. #14582628	C₂²	semidirect
53. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
54. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
55. #14582626	C₂²	semidirect
56. #14582626	C₂²	semidirect
57. #14582621	C₂²	semidirect
58. #14582621	C₂²	semidirect
59. #14582620	C₂²	semidirect
61. C₄₃×#436	C₂²	semidirect
62. C₈×D₄×C₄₃	C₂²	semidirect
63. C₄₃×#335	C₂²	semidirect
64. C₄₃×D₄⋊C₈	C₂²	semidirect
65. C₄₃×D₄⋊C₈	C₂²	semidirect
66. C₄₃×#322	C₂²	semidirect
160. D₄×D₄₃	M₁₆	semidirect
226. C₈×D₄₃	D₈	semidirect
241. D₄×C₄₃	C₂×M₁₆	semidirect
263. D₁₇₂	C₂×M₁₆	semidirect
283. C₈×C₄₃	C₂×D₈	semidirect
290. C₄₃⋊C₈	C₂×D₈	semidirect
332. #1581	D₄₃	direct (N × H)
344. D₄₃	#1581	direct (N × H)
363. #436	C₂×D₄₃	semidirect
369. C₈×D₄	C₂×D₄₃	semidirect
383. #335	C₂×D₄₃	semidirect
390. D₄⋊C₈	C₂×D₄₃	semidirect
391. D₄⋊C₈	C₂×D₄₃	semidirect
395. #322	C₂×D₄₃	semidirect
396. C₄₃	C₂×#1581	semidirect
577. D₄	M₁₆×D₄₃	semidirect
620. C₈	D₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₄₃	2
#436×D₄₃	2
C₈×D₄×D₄₃	2
#19133427	2
#19133426	2
#19133425	2
#19133424	2
#19133423	2
#19133422	2
#19133421	2
#335×D₄₃	2
D₄⋊C₈×D₄₃	2
#322×D₄₃	2
C₄₃×#1581	2
C₂×#1581	43

Subgroups — D43×#1581 #25066089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1581 #25066089