Subgroups — C₂×C₄₃×#1879 #24940938

Order 11008.

2470 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1879	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₃	—	2	1	no	—
12	C₂²×D₈×C₄₃	—	2	4	no	—
13	C₂²×D₈×C₄₃	—	2	4	no	—
14	C₂²×D₈×C₄₃	C₄	1	8	yes	complemented
15	C₂²×D₈×C₄₃	C₂²	1	4	yes	—
16	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₃	—	2	4	no	—
19	C₂×C₄×D₄×C₄₃	—	2	4	no	—
20	C₂×C₄×D₄×C₄₃	—	2	2	no	—
21	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	complemented
22	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
25	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
26	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
27	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₃	—	2	4	no	—
29	C₂×#102×C₄₃	—	2	4	no	—
30	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
31	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
32	C₄₃×#390	—	2	2	no	—
33	C₄₃×#390	C₂²	1	4	yes	complemented
34	C₄₃×#340	C₂²	1	4	yes	complemented
35	C₄₃×#336	C₂²	1	4	yes	complemented
36	C₂⁵×C₄₃	—	2	1	no	—
37	C₂⁵×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	—	2	2	no	—
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	—	2	2	no	—
41	C₂²×D₄×C₄₃	—	2	2	no	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	2	2	no	—
47	C₂²×D₄×C₄₃	—	2	2	no	—
48	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
49	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	complemented
50	C₂²×D₄×C₄₃	D₄	1	4	yes	—
51	C₂²×D₄×C₄₃	D₄	1	4	yes	—
52	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₃	—	2	8	no	—
55	C₂³×C₄×C₄₃	—	2	1	no	—
56	C₂³×C₄×C₄₃	—	2	4	no	—
57	C₂³×C₄×C₄₃	—	2	1	no	—
58	C₂³×C₄×C₄₃	—	4	4	no	—
59	C₂³×C₄×C₄₃	—	4	4	no	—
60	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×D₈×C₄₃	—	2	32	no	—
64	C₂×D₈×C₄₃	—	2	8	no	—
65	C₂×D₈×C₄₃	—	2	8	no	—
66	C₂×D₈×C₄₃	C₂×C₄	1	16	yes	complemented
67	C₂²×C₈×C₄₃	—	2	2	no	—
68	C₂²×C₈×C₄₃	—	2	2	no	—
69	C₂²×C₈×C₄₃	—	2	2	no	—
70	C₂²×C₈×C₄₃	—	2	2	no	—
71	C₂²×C₈×C₄₃	—	2	2	no	—
72	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
73	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
74	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
75	C₄×D₄×C₄₃	—	2	16	no	—
76	C₄×D₄×C₄₃	—	2	8	no	—
77	C₄×D₄×C₄₃	—	2	8	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
92	C₂×C₄²×C₄₃	—	2	2	no	—
93	C₂×C₄²×C₄₃	—	2	2	no	—
94	C₂×C₄²×C₄₃	D₄	1	2	yes	—
95	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
96	#102×C₄₃	—	2	8	no	—
97	#102×C₄₃	—	2	8	no	—
98	C₂⁴×C₄₃	—	2	4	no	—
99	C₂⁴×C₄₃	—	2	4	no	—
100	C₂⁴×C₄₃	—	2	4	no	—
101	C₂⁴×C₄₃	—	2	2	no	—
102	C₂⁴×C₄₃	—	2	4	no	—
103	C₂⁴×C₄₃	—	2	2	no	—
104	C₂⁴×C₄₃	—	4	2	no	—
105	C₂⁴×C₄₃	—	4	2	no	—
106	C₂⁴×C₄₃	—	4	2	no	—
107	C₂⁴×C₄₃	—	4	2	no	—
108	C₂⁴×C₄₃	—	4	2	no	—
109	C₂⁴×C₄₃	—	4	2	no	—
110	C₂⁴×C₄₃	—	4	2	no	—
111	C₂⁴×C₄₃	—	4	2	no	—
112	C₂⁴×C₄₃	—	4	2	no	—
113	C₂⁴×C₄₃	—	4	2	no	—
114	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₄₃	—	2	4	no	—
116	C₂×D₄×C₄₃	—	2	8	no	—
117	C₂×D₄×C₄₃	—	2	4	no	—
118	C₂×D₄×C₄₃	—	2	4	no	—
119	C₂×D₄×C₄₃	—	2	4	no	—
120	C₂×D₄×C₄₃	—	2	8	no	—
121	C₂×D₄×C₄₃	—	2	8	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	2	8	no	—
127	C₂×D₄×C₄₃	—	2	8	no	—
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	—	4	2	no	—
133	C₂×D₄×C₄₃	—	4	2	no	—
134	C₂×D₄×C₄₃	—	4	4	no	—
135	C₂×D₄×C₄₃	—	4	4	no	—
136	C₂×D₄×C₄₃	C₂²⋊C₄	1	16	yes	complemented
137	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
138	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	complemented
139	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
140	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₄₃	—	2	16	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	4	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	2	no	—
149	C₂²×C₄×C₄₃	—	2	2	no	—
150	C₂²×C₄×C₄₃	—	4	8	no	—
151	C₂²×C₄×C₄₃	—	4	32	no	—
152	C₂²×C₄×C₄₃	—	4	8	no	—
153	C₂²×C₄×C₄₃	—	4	2	no	—
154	C₂²×C₄×C₄₃	—	4	2	no	—
155	C₂²×C₄×C₄₃	—	4	2	no	—
156	C₂²×C₄×C₄₃	—	4	2	no	—
157	C₂²×C₄×C₄₃	—	4	2	no	—
158	C₂²×C₄×C₄₃	D₈	1	4	yes	complemented
159	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₃	#41	1	2	yes	—
167	C₂²×C₄×C₄₃	#41	1	2	yes	—
168	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	D₈×C₄₃	—	2	32	no	—
170	C₂×C₈×C₄₃	—	2	8	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	4	4	no	—
177	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	complemented
178	C₄⋊C₄×C₄₃	—	2	4	no	—
179	C₄⋊C₄×C₄₃	—	2	2	no	—
180	C₄⋊C₄×C₄₃	—	2	2	no	—
181	C₄⋊C₄×C₄₃	—	2	2	no	—
182	C₄⋊C₄×C₄₃	—	4	2	no	—
183	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
184	C₂²⋊C₄×C₄₃	—	2	16	no	—
185	C₂²⋊C₄×C₄₃	—	4	8	no	—
186	C₂²⋊C₄×C₄₃	—	4	8	no	—
187	C₄²×C₄₃	—	2	4	no	—
188	C₄²×C₄₃	—	2	2	no	—
189	C₄²×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	4	no	—
191	C₂³×C₄₃	—	2	4	no	—
192	C₂³×C₄₃	—	2	4	no	—
193	C₂³×C₄₃	—	2	16	no	—
194	C₂³×C₄₃	—	2	4	no	—
195	C₂³×C₄₃	—	4	2	no	—
196	C₂³×C₄₃	—	4	2	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	8	no	—
200	C₂³×C₄₃	—	4	8	no	—
201	C₂³×C₄₃	—	4	8	no	—
202	C₂³×C₄₃	—	4	8	no	—
203	C₂³×C₄₃	—	4	8	no	—
204	C₂³×C₄₃	—	4	8	no	—
205	C₂³×C₄₃	—	4	2	no	—
206	C₂³×C₄₃	—	4	2	no	—
207	C₂³×C₄₃	—	4	2	no	—
208	C₂³×C₄₃	—	4	2	no	—
209	C₂³×C₄₃	—	4	2	no	—
210	C₂³×C₄₃	—	4	2	no	—
211	C₂³×C₄₃	—	4	8	no	—
212	C₂³×C₄₃	—	4	8	no	—
213	C₂³×C₄₃	—	4	8	no	—
214	C₂³×C₄₃	—	8	4	no	—
215	C₂³×C₄₃	—	8	4	no	—
216	C₂³×C₄₃	—	8	4	no	—
217	C₂³×C₄₃	—	8	4	no	—
218	C₂³×C₄₃	C₄×D₄	1	2	yes	—
219	C₂³×C₄₃	#120	1	2	yes	—
220	C₂³×C₄₃	#121	1	2	yes	—
221	C₂³×C₄₃	C₂×D₈	1	2	yes	—
222	C₂³×C₄₃	#135	1	2	yes	—
223	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
224	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
225	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
226	D₄×C₄₃	—	2	4	no	—
227	D₄×C₄₃	—	2	4	no	—
228	D₄×C₄₃	—	2	4	no	—
229	D₄×C₄₃	—	2	4	no	—
230	D₄×C₄₃	—	2	4	no	—
231	D₄×C₄₃	—	2	16	no	—
232	D₄×C₄₃	—	4	2	no	—
233	D₄×C₄₃	—	4	2	no	—
234	D₄×C₄₃	—	4	8	no	—
235	D₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	complemented
236	C₂×C₄×C₄₃	—	2	2	no	—
237	C₂×C₄×C₄₃	—	2	2	no	—
238	C₂×C₄×C₄₃	—	2	8	no	—
239	C₂×C₄×C₄₃	—	2	2	no	—
240	C₂×C₄×C₄₃	—	2	4	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	2	2	no	—
243	C₂×C₄×C₄₃	—	4	32	no	—
244	C₂×C₄×C₄₃	—	4	2	no	—
245	C₂×C₄×C₄₃	—	4	2	no	—
246	C₂×C₄×C₄₃	—	4	8	no	—
247	C₂×C₄×C₄₃	—	4	4	no	—
248	C₂×C₄×C₄₃	—	4	2	no	—
249	C₂×C₄×C₄₃	—	4	2	no	—
250	C₂×C₄×C₄₃	—	4	2	no	—
251	C₂×C₄×C₄₃	—	8	4	no	—
252	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
253	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
254	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
255	C₂×C₄×C₄₃	#120	1	2	yes	—
256	C₂×C₄×C₄₃	#121	1	4	yes	—
257	C₂×C₄×C₄₃	#121	1	2	yes	—
258	C₂×C₄×C₄₃	#123	1	4	yes	—
259	C₂×C₄×C₄₃	C₂×D₈	1	4	yes	complemented
260	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
266	C₈×C₄₃	—	2	4	no	—
267	C₈×C₄₃	—	4	2	no	—
268	C₂×#1879	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂²×C₄₃	—	2	8	no	—
270	C₂²×C₄₃	—	4	32	no	—
271	C₂²×C₄₃	—	4	4	no	—
272	C₂²×C₄₃	—	4	4	no	—
273	C₂²×C₄₃	—	4	4	no	—
274	C₂²×C₄₃	—	4	4	no	—
275	C₂²×C₄₃	—	4	4	no	—
276	C₂²×C₄₃	—	4	4	no	—
277	C₂²×C₄₃	—	4	4	no	—
278	C₂²×C₄₃	—	4	4	no	—
279	C₂²×C₄₃	—	4	4	no	—
280	C₂²×C₄₃	—	8	16	no	—
281	C₂²×C₄₃	—	8	2	no	—
282	C₂²×C₄₃	—	8	2	no	—
283	C₂²×C₄₃	—	8	2	no	—
284	C₂²×C₄₃	—	8	2	no	—
285	C₂²×C₄₃	#386	1	4	yes	—
286	C₂²×C₄₃	C₄×D₈	1	4	yes	—
287	C₂²×C₄₃	#442	1	4	yes	—
288	C₂²×C₄₃	#447	1	4	yes	—
289	C₂²×C₄₃	#449	1	4	yes	—
290	C₂²×C₄₃	#459	1	4	yes	—
291	C₂²×C₄₃	#463	1	4	yes	—
292	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
294	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
295	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
296	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
297	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
298	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₄×C₄₃	—	2	4	no	—
300	C₄×C₄₃	—	4	4	no	—
301	C₄×C₄₃	—	4	2	no	—
302	C₄×C₄₃	—	8	2	no	—
303	C₄×C₄₃	#386	1	4	yes	—
304	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
305	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
306	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
307	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
308	C₂³×D₈	C₂×C₄₃	1	1	yes	characteristic
309	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic, complemented
310	C₂²×#102	C₂×C₄₃	1	1	yes	characteristic, complemented
311	C₂²×#102	C₂×C₄₃	1	1	yes	characteristic, complemented
312	C₂×#390	C₂×C₄₃	1	1	yes	characteristic, complemented
313	#1879	C₂×C₄₃	1	8	yes	direct product factor
314	C₂×#340	C₂×C₄₃	1	1	yes	characteristic, complemented
315	C₂×#336	C₂×C₄₃	1	1	yes	characteristic, complemented
316	C₂×C₄₃	—	4	8	no	—
317	C₂×C₄₃	—	8	4	no	—
318	C₂×C₄₃	#1879	1	8	yes	direct product factor
319	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
320	C₂×C₄₃	C₂×C₄×D₈	1	1	yes	characteristic
321	C₂×C₄₃	C₂×#442	1	1	yes	characteristic
322	C₂×C₄₃	C₂×#447	1	1	yes	characteristic
323	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
324	C₂×C₄₃	C₂×#459	1	1	yes	characteristic
325	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
326	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
327	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
328	C₂⁴×C₄	—	2	1	no	—
329	C₂²×D₈	—	2	4	no	—
330	C₂²×D₈	—	2	4	no	—
331	C₂²×D₈	C₄×C₄₃	1	8	yes	complemented
332	C₂²×D₈	C₂²×C₄₃	1	4	yes	—
333	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
334	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
335	C₂×C₄×D₄	—	2	4	no	—
336	C₂×C₄×D₄	—	2	4	no	—
337	C₂×C₄×D₄	—	2	2	no	—
338	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	complemented
339	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
341	C₂²×C₂²⋊C₄	—	2	1	no	—
342	C₂²×C₂²⋊C₄	—	2	1	no	—
343	C₂²×C₂²⋊C₄	—	2	1	no	—
344	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
345	C₂×#102	—	2	4	no	—
346	C₂×#102	—	2	4	no	—
347	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
348	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
349	#390	—	2	2	no	—
350	#390	C₂²×C₄₃	1	4	yes	complemented
351	#340	C₂²×C₄₃	1	4	yes	complemented
352	#336	C₂²×C₄₃	1	4	yes	complemented
353	C₄₃	C₂×#1879	1	1	yes	characteristic, direct product factor, Sylow
354	C₂⁵	—	2	1	no	—
355	C₂⁵	—	2	1	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	—	2	2	no	—
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
367	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	complemented
368	C₂²×D₄	D₄×C₄₃	1	4	yes	—
369	C₂²×D₄	D₄×C₄₃	1	4	yes	—
370	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
371	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
372	C₂³×C₄	—	2	8	no	—
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	—	2	4	no	—
375	C₂³×C₄	—	2	1	no	—
376	C₂³×C₄	—	4	4	no	—
377	C₂³×C₄	—	4	4	no	—
378	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
379	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
381	C₂×D₈	—	2	32	no	—
382	C₂×D₈	—	2	8	no	—
383	C₂×D₈	—	2	8	no	—
384	C₂×D₈	C₂×C₄×C₄₃	1	16	yes	complemented
385	C₂²×C₈	—	2	2	no	—
386	C₂²×C₈	—	2	2	no	—
387	C₂²×C₈	—	2	2	no	—
388	C₂²×C₈	—	2	2	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	C₂×C₄×C₄₃	1	4	yes	complemented
391	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
392	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
393	C₄×D₄	—	2	16	no	—
394	C₄×D₄	—	2	8	no	—
395	C₄×D₄	—	2	8	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
404	C₂×C₂²⋊C₄	—	2	8	no	—
405	C₂×C₂²⋊C₄	—	2	4	no	—
406	C₂×C₂²⋊C₄	—	2	4	no	—
407	C₂×C₂²⋊C₄	—	2	4	no	—
408	C₂×C₂²⋊C₄	—	4	4	no	—
409	C₂×C₂²⋊C₄	—	4	4	no	—
410	C₂×C₄²	—	2	2	no	—
411	C₂×C₄²	—	2	2	no	—
412	C₂×C₄²	D₄×C₄₃	1	2	yes	—
413	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
414	#102	—	2	8	no	—
415	#102	—	2	8	no	—
416	C₂⁴	—	2	4	no	—
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	2	4	no	—
419	C₂⁴	—	2	2	no	—
420	C₂⁴	—	2	4	no	—
421	C₂⁴	—	2	2	no	—
422	C₂⁴	—	4	2	no	—
423	C₂⁴	—	4	2	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	—	4	2	no	—
426	C₂⁴	—	4	2	no	—
427	C₂⁴	—	4	2	no	—
428	C₂⁴	—	4	2	no	—
429	C₂⁴	—	4	2	no	—
430	C₂⁴	—	4	2	no	—
431	C₂⁴	—	4	2	no	—
432	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	4	no	—
454	C₂×D₄	C₂²⋊C₄×C₄₃	1	16	yes	complemented
455	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
456	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	complemented
457	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
458	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	16	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	4	8	no	—
469	C₂²×C₄	—	4	32	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	8	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	D₈×C₄₃	1	4	yes	complemented
477	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
479	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
480	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
481	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
482	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
484	C₂²×C₄	#41×C₄₃	1	2	yes	—
485	C₂²×C₄	#41×C₄₃	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
487	D₈	—	2	32	no	—
488	C₂×C₈	—	2	8	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	4	4	no	—
495	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	complemented
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
502	C₂²⋊C₄	—	2	16	no	—
503	C₂²⋊C₄	—	4	8	no	—
504	C₂²⋊C₄	—	4	8	no	—
505	C₄²	—	2	4	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	2	16	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	8	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	8	no	—
520	C₂³	—	4	8	no	—
521	C₂³	—	4	8	no	—
522	C₂³	—	4	8	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	8	no	—
530	C₂³	—	4	8	no	—
531	C₂³	—	4	8	no	—
532	C₂³	—	8	4	no	—
533	C₂³	—	8	4	no	—
534	C₂³	—	8	4	no	—
535	C₂³	—	8	4	no	—
536	C₂³	C₄×D₄×C₄₃	1	2	yes	—
537	C₂³	#120×C₄₃	1	2	yes	—
538	C₂³	#121×C₄₃	1	2	yes	—
539	C₂³	C₂×D₈×C₄₃	1	2	yes	—
540	C₂³	#135×C₄₃	1	2	yes	—
541	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
542	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
543	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
544	D₄	—	2	4	no	—
545	D₄	—	2	4	no	—
546	D₄	—	2	4	no	—
547	D₄	—	2	4	no	—
548	D₄	—	2	4	no	—
549	D₄	—	2	16	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	8	no	—
553	D₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	complemented
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	32	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	8	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	8	4	no	—
570	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
571	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
572	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
573	C₂×C₄	#120×C₄₃	1	2	yes	—
574	C₂×C₄	#121×C₄₃	1	4	yes	—
575	C₂×C₄	#121×C₄₃	1	2	yes	—
576	C₂×C₄	#123×C₄₃	1	4	yes	—
577	C₂×C₄	C₂×D₈×C₄₃	1	4	yes	complemented
578	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
582	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
583	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
584	C₈	—	2	4	no	—
585	C₈	—	4	2	no	—
586	C₂²	—	2	8	no	—
587	C₂²	—	4	32	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	8	16	no	—
598	C₂²	—	8	2	no	—
599	C₂²	—	8	2	no	—
600	C₂²	—	8	2	no	—
601	C₂²	—	8	2	no	—
602	C₂²	C₄₃×#386	1	4	yes	—
603	C₂²	C₄×D₈×C₄₃	1	4	yes	—
604	C₂²	C₄₃×#442	1	4	yes	—
605	C₂²	C₄₃×#447	1	4	yes	—
606	C₂²	C₄₃×#449	1	4	yes	—
607	C₂²	C₄₃×#459	1	4	yes	—
608	C₂²	C₄₃×#463	1	4	yes	—
609	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
610	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
611	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
612	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
613	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
614	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
615	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
616	C₄	—	2	4	no	—
617	C₄	—	4	4	no	—
618	C₄	—	4	2	no	—
619	C₄	—	8	2	no	—
620	C₄	C₄₃×#386	1	4	yes	—
621	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
622	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
623	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
624	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
625	C₂	—	4	8	no	—
626	C₂	—	8	4	no	—
627	C₂	C₄₃×#1879	1	8	yes	direct product factor
628	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
629	C₂	C₂×C₄×D₈×C₄₃	1	1	yes	characteristic
630	C₂	C₂×C₄₃×#442	1	1	yes	characteristic
631	C₂	C₂×C₄₃×#447	1	1	yes	characteristic
632	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
633	C₂	C₂×C₄₃×#459	1	1	yes	characteristic
634	C₂	C₂×C₄₃×#463	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂³×D₈×C₄₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₄₃	C₂	semidirect
3. C₂²×#102×C₄₃	C₂	semidirect
4. C₂²×#102×C₄₃	C₂	semidirect
5. C₂×C₄₃×#390	C₂	semidirect
6. C₄₃×#1879	C₂	direct (N × H)
7. C₂×C₄₃×#340	C₂	semidirect
8. C₂×C₄₃×#336	C₂	semidirect
14. C₂²×D₈×C₄₃	C₄	semidirect
21. C₂×C₄×D₄×C₄₃	C₂²	semidirect
30. C₂×#102×C₄₃	C₂²	semidirect
31. C₂×#102×C₄₃	C₂²	semidirect
33. C₄₃×#390	C₂²	semidirect
34. C₄₃×#340	C₂²	semidirect
35. C₄₃×#336	C₂²	semidirect
49. C₂²×D₄×C₄₃	C₂×C₄	semidirect
66. C₂×D₈×C₄₃	C₂×C₄	semidirect
72. C₂²×C₈×C₄₃	C₂×C₄	semidirect
136. C₂×D₄×C₄₃	C₂²⋊C₄	semidirect
138. C₂×D₄×C₄₃	C₂²×C₄	semidirect
158. C₂²×C₄×C₄₃	D₈	semidirect
177. C₂×C₈×C₄₃	C₂²×C₄	semidirect
235. D₄×C₄₃	C₂×C₂²⋊C₄	semidirect
259. C₂×C₄×C₄₃	C₂×D₈	semidirect
268. C₂×#1879	C₄₃	direct (N × H)
309. C₂²×C₄×D₄	C₂×C₄₃	semidirect
310. C₂²×#102	C₂×C₄₃	semidirect
311. C₂²×#102	C₂×C₄₃	semidirect
312. C₂×#390	C₂×C₄₃	semidirect
313. #1879	C₂×C₄₃	direct (N × H)
314. C₂×#340	C₂×C₄₃	semidirect
315. C₂×#336	C₂×C₄₃	semidirect
318. C₂×C₄₃	#1879	direct (N × H)
331. C₂²×D₈	C₄×C₄₃	semidirect
338. C₂×C₄×D₄	C₂²×C₄₃	semidirect
347. C₂×#102	C₂²×C₄₃	semidirect
348. C₂×#102	C₂²×C₄₃	semidirect
350. #390	C₂²×C₄₃	semidirect
351. #340	C₂²×C₄₃	semidirect
352. #336	C₂²×C₄₃	semidirect
353. C₄₃	C₂×#1879	direct (N × H)
367. C₂²×D₄	C₂×C₄×C₄₃	semidirect
384. C₂×D₈	C₂×C₄×C₄₃	semidirect
390. C₂²×C₈	C₂×C₄×C₄₃	semidirect
454. C₂×D₄	C₂²⋊C₄×C₄₃	semidirect
456. C₂×D₄	C₂²×C₄×C₄₃	semidirect
476. C₂²×C₄	D₈×C₄₃	semidirect
495. C₂×C₈	C₂²×C₄×C₄₃	semidirect
553. D₄	C₂×C₂²⋊C₄×C₄₃	semidirect
577. C₂×C₄	C₂×D₈×C₄₃	semidirect
627. C₂	C₄₃×#1879	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₄₃	2
C₂²×C₄×D₄×C₄₃	2
C₂²×#102×C₄₃	2
C₂×C₄₃×#390	2
C₄₃×#1879	2
C₂×C₄₃×#340	2
C₂×C₄₃×#336	2
C₂×#1879	43

Subgroups — C2×C43×#1879 #24940938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1879 #24940938