Subgroups — C₂×C₄₃×#1625 #24938503

Order 11008.

1322 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	C₂×C₄₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1625	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	—	2	1	no	—
10	C₂²×D₈×C₄₃	—	2	1	no	—
11	C₂²×D₈×C₄₃	—	2	1	no	—
12	C₄₃×#547	—	2	2	no	—
13	C₄₃×#547	—	2	2	no	—
14	C₄₃×#547	—	2	2	no	—
15	C₄₃×#547	C₂²	1	4	yes	complemented
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#123×C₄₃	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
20	C₂×#121×C₄₃	—	2	1	no	—
21	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
24	C₄₃×#486	—	2	2	no	—
25	C₄₃×#486	C₂²	1	4	yes	complemented
26	C₄₃×#459	—	2	2	no	—
27	C₄₃×#459	—	2	2	no	—
28	C₄₃×#459	C₂²	1	4	yes	complemented
29	C₄₃×#459	C₂²	1	4	yes	complemented
30	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#102×C₄₃	—	2	2	no	—
33	C₂×#102×C₄₃	—	2	1	no	—
34	C₂×#102×C₄₃	—	2	1	no	—
35	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#332	C₂²	1	4	yes	complemented
37	C₄₃×D₄⋊C₈	C₂²	1	4	yes	complemented
38	C₄₃×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂×#41×C₄₃	—	2	4	no	—
40	C₂×#41×C₄₃	—	2	4	no	—
41	C₂×#41×C₄₃	—	4	4	no	—
42	C₂×#41×C₄₃	—	4	4	no	—
43	C₂²×Q₈×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	—	2	2	no	—
51	C₂³×C₄×C₄₃	—	2	1	no	—
52	C₂³×C₄×C₄₃	—	2	1	no	—
53	C₂×D₈×C₄₃	—	2	4	no	—
54	C₂×D₈×C₄₃	—	2	4	no	—
55	C₂×D₈×C₄₃	—	4	4	no	—
56	C₂×D₈×C₄₃	—	4	4	no	—
57	C₂²×C₈×C₄₃	—	2	1	no	—
58	C₂²×C₈×C₄₃	—	2	1	no	—
59	C₂²×C₈×C₄₃	—	2	1	no	—
60	C₄⋊Q₈×C₄₃	—	2	1	no	—
61	C₄⋊Q₈×C₄₃	—	2	1	no	—
62	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
63	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
64	#127×C₄₃	—	2	1	no	—
65	#127×C₄₃	—	2	1	no	—
66	#127×C₄₃	—	2	1	no	—
67	#127×C₄₃	C₂³	1	2	yes	—
68	#123×C₄₃	—	2	8	no	—
69	#123×C₄₃	—	2	8	no	—
70	C₂²⋊Q₈×C₄₃	—	2	4	no	—
71	C₂²⋊Q₈×C₄₃	—	2	4	no	—
72	#121×C₄₃	—	2	4	no	—
73	#121×C₄₃	—	2	4	no	—
74	C₄×D₄×C₄₃	—	2	1	no	—
75	C₄×D₄×C₄₃	—	2	1	no	—
76	C₄×D₄×C₄₃	—	2	1	no	—
77	C₄×D₄×C₄₃	—	2	1	no	—
78	C₄×D₄×C₄₃	D₄	1	2	yes	—
79	C₄×D₄×C₄₃	D₄	1	2	yes	—
80	C₄×D₄×C₄₃	C₂³	1	2	yes	—
81	C₄×D₄×C₄₃	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
86	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	—	2	1	no	—
94	C₄⋊C₈×C₄₃	—	2	1	no	—
95	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
96	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
97	#102×C₄₃	—	2	4	no	—
98	#102×C₄₃	—	2	4	no	—
99	#102×C₄₃	—	2	8	no	—
100	C₄×C₈×C₄₃	—	2	1	no	—
101	C₄×C₈×C₄₃	C₂³	1	2	yes	—
102	C₂⁴×C₄₃	—	2	1	no	—
103	C₂⁴×C₄₃	—	2	1	no	—
104	C₂⁴×C₄₃	—	4	1	no	—
105	#41×C₄₃	—	4	8	no	—
106	#41×C₄₃	—	4	16	no	—
107	#41×C₄₃	—	4	8	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	4	2	no	—
111	C₂×Q₈×C₄₃	—	4	2	no	—
112	C₂×D₄×C₄₃	—	2	8	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	—	4	8	no	—
122	C₂×D₄×C₄₃	—	4	1	no	—
123	C₂×D₄×C₄₃	—	4	1	no	—
124	C₂×D₄×C₄₃	—	4	1	no	—
125	C₂×D₄×C₄₃	—	4	4	no	—
126	C₂×D₄×C₄₃	—	4	2	no	—
127	C₂×D₄×C₄₃	—	4	2	no	—
128	C₂×D₄×C₄₃	—	4	2	no	—
129	C₂×D₄×C₄₃	—	4	2	no	—
130	C₂×D₄×C₄₃	D₈	1	4	yes	complemented
131	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₃	—	2	8	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	1	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	4	8	no	—
142	C₂²×C₄×C₄₃	—	4	2	no	—
143	C₂²×C₄×C₄₃	—	4	2	no	—
144	C₂²×C₄×C₄₃	—	4	2	no	—
145	C₂²×C₄×C₄₃	—	4	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	D₈×C₄₃	—	4	8	no	—
150	D₈×C₄₃	—	4	8	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	2	2	no	—
153	C₂×C₈×C₄₃	—	2	2	no	—
154	C₂×C₈×C₄₃	—	4	2	no	—
155	C₂×C₈×C₄₃	—	4	2	no	—
156	C₂×C₈×C₄₃	—	4	2	no	—
157	C₄⋊C₄×C₄₃	—	2	8	no	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	2	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	2	2	no	—
162	C₄⋊C₄×C₄₃	—	2	2	no	—
163	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
166	C₂²⋊C₄×C₄₃	—	2	8	no	—
167	C₂²⋊C₄×C₄₃	—	2	2	no	—
168	C₂²⋊C₄×C₄₃	—	2	2	no	—
169	C₂²⋊C₄×C₄₃	—	2	2	no	—
170	C₂²⋊C₄×C₄₃	—	2	2	no	—
171	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
175	C₂³×C₄₃	—	2	2	no	—
176	C₂³×C₄₃	—	2	4	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	4	2	no	—
179	C₂³×C₄₃	—	4	2	no	—
180	C₂³×C₄₃	—	4	2	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	8	2	no	—
185	C₂³×C₄₃	—	8	2	no	—
186	C₂³×C₄₃	—	8	2	no	—
187	C₂³×C₄₃	#120	1	1	yes	characteristic
188	Q₈×C₄₃	—	4	2	no	—
189	Q₈×C₄₃	—	4	2	no	—
190	Q₈×C₄₃	—	4	4	no	—
191	D₄×C₄₃	—	2	2	no	—
192	D₄×C₄₃	—	2	2	no	—
193	D₄×C₄₃	—	2	2	no	—
194	D₄×C₄₃	—	2	4	no	—
195	D₄×C₄₃	—	4	4	no	—
196	D₄×C₄₃	—	4	16	no	—
197	D₄×C₄₃	—	4	2	no	—
198	D₄×C₄₃	—	4	2	no	—
199	D₄×C₄₃	—	4	2	no	—
200	D₄×C₄₃	—	4	2	no	—
201	D₄×C₄₃	—	4	2	no	—
202	D₄×C₄₃	—	8	2	no	—
203	D₄×C₄₃	—	8	2	no	—
204	D₄×C₄₃	—	8	2	no	—
205	D₄×C₄₃	C₂×D₈	1	4	yes	complemented
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	4	no	—
210	C₂×C₄×C₄₃	—	4	16	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	4	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	4	4	no	—
219	C₂×C₄×C₄₃	—	4	4	no	—
220	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
221	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
222	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
224	C₂×C₄×C₄₃	#135	1	2	yes	—
225	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
227	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
230	C₈×C₄₃	—	4	2	no	—
231	C₈×C₄₃	—	4	2	no	—
232	C₈×C₄₃	—	4	2	no	—
233	C₂×#1625	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂²×C₄₃	—	2	4	no	—
235	C₂²×C₄₃	—	4	8	no	—
236	C₂²×C₄₃	—	4	2	no	—
237	C₂²×C₄₃	—	4	2	no	—
238	C₂²×C₄₃	—	4	2	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	4	2	no	—
241	C₂²×C₄₃	—	8	4	no	—
242	C₂²×C₄₃	—	8	2	no	—
243	C₂²×C₄₃	—	8	2	no	—
244	C₂²×C₄₃	—	8	2	no	—
245	C₂²×C₄₃	—	16	4	no	—
246	C₂²×C₄₃	#447	1	2	yes	—
247	C₂²×C₄₃	#449	1	2	yes	—
248	C₂²×C₄₃	#454	1	2	yes	—
249	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
250	C₄×C₄₃	—	2	1	no	—
251	C₄×C₄₃	—	2	1	no	—
252	C₄×C₄₃	—	4	2	no	—
253	C₄×C₄₃	—	4	4	no	—
254	C₄×C₄₃	—	4	2	no	—
255	C₄×C₄₃	#447	1	2	yes	—
256	C₄×C₄₃	#449	1	2	yes	—
257	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
258	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
259	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
260	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂×#547	C₂×C₄₃	1	1	yes	characteristic, complemented
262	C₂×#486	C₂×C₄₃	1	1	yes	characteristic, complemented
263	C₂×#459	C₂×C₄₃	1	1	yes	characteristic, complemented
264	C₂×#459	C₂×C₄₃	1	1	yes	characteristic, complemented
265	#1625	C₂×C₄₃	1	8	yes	direct product factor
266	C₂×#332	C₂×C₄₃	1	1	yes	characteristic, complemented
267	C₂×D₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
268	C₂×D₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
269	C₂×C₄₃	—	4	4	no	—
270	C₂×C₄₃	—	8	2	no	—
271	C₂×C₄₃	—	16	2	no	—
272	C₂×C₄₃	#1625	1	4	yes	direct product factor
273	C₂×C₄₃	C₂×#447	1	1	yes	characteristic
274	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
275	C₂×C₄₃	C₂×#454	1	1	yes	characteristic
276	C₂²×#41	—	2	1	no	—
277	C₂²×D₈	—	2	1	no	—
278	C₂²×D₈	—	2	1	no	—
279	#547	—	2	2	no	—
280	#547	—	2	2	no	—
281	#547	—	2	2	no	—
282	#547	C₂²×C₄₃	1	4	yes	complemented
283	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
284	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
285	C₂×#123	—	2	2	no	—
286	C₂×C₂²⋊Q₈	—	2	1	no	—
287	C₂×#121	—	2	1	no	—
288	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
290	C₂²×C₄⋊C₄	—	2	1	no	—
291	#486	—	2	2	no	—
292	#486	C₂²×C₄₃	1	4	yes	complemented
293	#459	—	2	2	no	—
294	#459	—	2	2	no	—
295	#459	C₂²×C₄₃	1	4	yes	complemented
296	#459	C₂²×C₄₃	1	4	yes	complemented
297	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
299	C₂×#102	—	2	2	no	—
300	C₂×#102	—	2	1	no	—
301	C₂×#102	—	2	1	no	—
302	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
303	#332	C₂²×C₄₃	1	4	yes	complemented
304	D₄⋊C₈	C₂²×C₄₃	1	4	yes	complemented
305	D₄⋊C₈	C₂²×C₄₃	1	4	yes	complemented
306	C₄₃	C₂×#1625	1	1	yes	characteristic, direct product factor, Sylow
307	C₂×#41	—	2	4	no	—
308	C₂×#41	—	2	4	no	—
309	C₂×#41	—	4	4	no	—
310	C₂×#41	—	4	4	no	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
317	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
318	C₂³×C₄	—	2	2	no	—
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	—	2	1	no	—
321	C₂×D₈	—	2	4	no	—
322	C₂×D₈	—	2	4	no	—
323	C₂×D₈	—	4	4	no	—
324	C₂×D₈	—	4	4	no	—
325	C₂²×C₈	—	2	1	no	—
326	C₂²×C₈	—	2	1	no	—
327	C₂²×C₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	1	no	—
330	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
331	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
332	#127	—	2	1	no	—
333	#127	—	2	1	no	—
334	#127	—	2	1	no	—
335	#127	C₂³×C₄₃	1	2	yes	—
336	#123	—	2	8	no	—
337	#123	—	2	8	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	#121	—	2	4	no	—
341	#121	—	2	4	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	D₄×C₄₃	1	2	yes	—
347	C₄×D₄	D₄×C₄₃	1	2	yes	—
348	C₄×D₄	C₂³×C₄₃	1	2	yes	—
349	C₄×D₄	C₂³×C₄₃	1	2	yes	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	2	1	no	—
363	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
364	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
365	#102	—	2	4	no	—
366	#102	—	2	4	no	—
367	#102	—	2	8	no	—
368	C₄×C₈	—	2	1	no	—
369	C₄×C₈	C₂³×C₄₃	1	2	yes	—
370	C₂⁴	—	2	1	no	—
371	C₂⁴	—	2	1	no	—
372	C₂⁴	—	4	1	no	—
373	#41	—	4	8	no	—
374	#41	—	4	16	no	—
375	#41	—	4	8	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	—	4	2	no	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	D₈×C₄₃	1	4	yes	complemented
399	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
400	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	2	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	D₈	—	4	8	no	—
418	D₈	—	4	8	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	4	2	no	—
423	C₂×C₈	—	4	2	no	—
424	C₂×C₈	—	4	2	no	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
433	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
442	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	8	2	no	—
453	C₂³	—	8	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	#120×C₄₃	1	1	yes	characteristic
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	4	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	4	no	—
463	D₄	—	4	4	no	—
464	D₄	—	4	16	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	8	2	no	—
471	D₄	—	8	2	no	—
472	D₄	—	8	2	no	—
473	D₄	C₂×D₈×C₄₃	1	4	yes	complemented
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	4	16	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
489	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
490	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
491	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
492	C₂×C₄	#135×C₄₃	1	2	yes	—
493	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
494	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
498	C₈	—	4	2	no	—
499	C₈	—	4	2	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	4	8	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	4	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	16	4	no	—
513	C₂²	C₄₃×#447	1	2	yes	—
514	C₂²	C₄₃×#449	1	2	yes	—
515	C₂²	C₄₃×#454	1	2	yes	—
516	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	C₄₃×#447	1	2	yes	—
523	C₄	C₄₃×#449	1	2	yes	—
524	C₄	C₂²×D₈×C₄₃	1	1	yes	characteristic
525	C₄	C₂×#135×C₄₃	1	1	yes	characteristic
526	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
527	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
528	C₂	—	4	4	no	—
529	C₂	—	8	2	no	—
530	C₂	—	16	2	no	—
531	C₂	C₄₃×#1625	1	4	yes	direct product factor
532	C₂	C₂×C₄₃×#447	1	1	yes	characteristic
533	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
534	C₂	C₂×C₄₃×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#547	C₂	semidirect
2. C₂×C₄₃×#486	C₂	semidirect
3. C₂×C₄₃×#459	C₂	semidirect
4. C₂×C₄₃×#459	C₂	semidirect
5. C₄₃×#1625	C₂	direct (N × H)
6. C₂×C₄₃×#332	C₂	semidirect
7. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
8. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
15. C₄₃×#547	C₂²	semidirect
25. C₄₃×#486	C₂²	semidirect
28. C₄₃×#459	C₂²	semidirect
29. C₄₃×#459	C₂²	semidirect
36. C₄₃×#332	C₂²	semidirect
37. C₄₃×D₄⋊C₈	C₂²	semidirect
38. C₄₃×D₄⋊C₈	C₂²	semidirect
130. C₂×D₄×C₄₃	D₈	semidirect
205. D₄×C₄₃	C₂×D₈	semidirect
233. C₂×#1625	C₄₃	direct (N × H)
261. C₂×#547	C₂×C₄₃	semidirect
262. C₂×#486	C₂×C₄₃	semidirect
263. C₂×#459	C₂×C₄₃	semidirect
264. C₂×#459	C₂×C₄₃	semidirect
265. #1625	C₂×C₄₃	direct (N × H)
266. C₂×#332	C₂×C₄₃	semidirect
267. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
268. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
272. C₂×C₄₃	#1625	direct (N × H)
282. #547	C₂²×C₄₃	semidirect
292. #486	C₂²×C₄₃	semidirect
295. #459	C₂²×C₄₃	semidirect
296. #459	C₂²×C₄₃	semidirect
303. #332	C₂²×C₄₃	semidirect
304. D₄⋊C₈	C₂²×C₄₃	semidirect
305. D₄⋊C₈	C₂²×C₄₃	semidirect
306. C₄₃	C₂×#1625	direct (N × H)
398. C₂×D₄	D₈×C₄₃	semidirect
473. D₄	C₂×D₈×C₄₃	semidirect
531. C₂	C₄₃×#1625	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#547	2
C₂×C₄₃×#486	2
C₂×C₄₃×#459	2
C₄₃×#1625	2
C₂×C₄₃×#332	2
C₂×C₄₃×D₄⋊C₈	2
C₂×#1625	43

Subgroups — C2×C43×#1625 #24938503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1625 #24938503