Subgroups — C₂×C₄₃×#1789 #24940621

Order 11008.

4102 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#104×C₄₃	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1789	C₂	1	8	yes	maximal, direct product factor
6	C₂²×#41×C₄₃	—	2	16	no	—
7	C₂²×#41×C₄₃	—	2	1	no	—
8	C₂²×#41×C₄₃	—	2	2	no	—
9	C₂²×#41×C₄₃	—	2	2	no	—
10	C₂²×#41×C₄₃	—	2	1	no	—
11	C₂²×#41×C₄₃	C₄	1	2	yes	complemented
12	C₂²×#41×C₄₃	C₄	1	4	yes	complemented
13	C₂²×#41×C₄₃	C₂²	1	2	yes	—
14	C₂²×#41×C₄₃	C₂²	1	4	yes	—
15	C₂³×Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
16	C₂³×D₄×C₄₃	—	2	1	no	—
17	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic, complemented
18	C₂⁴×C₄×C₄₃	—	2	1	no	—
19	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
22	C₂²×C₄²×C₄₃	C₂²	1	2	yes	complemented
23	C₂×#104×C₄₃	—	2	16	no	—
24	C₂×#104×C₄₃	C₂²	1	16	yes	complemented
25	C₄₃×#407	—	2	2	no	—
26	C₄₃×#407	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
28	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
30	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	complemented
31	C₂×#95×C₄₃	—	2	1	no	—
32	C₂⁵×C₄₃	—	2	1	no	—
33	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
34	C₂×#41×C₄₃	—	2	32	no	—
35	C₂×#41×C₄₃	—	2	32	no	—
36	C₂×#41×C₄₃	—	2	16	no	—
37	C₂×#41×C₄₃	—	2	16	no	—
38	C₂×#41×C₄₃	—	2	32	no	—
39	C₂×#41×C₄₃	—	2	32	no	—
40	C₂×#41×C₄₃	—	2	8	no	—
41	C₂×#41×C₄₃	—	2	8	no	—
42	C₂×#41×C₄₃	—	2	4	no	—
43	C₂×#41×C₄₃	—	2	4	no	—
44	C₂×#41×C₄₃	—	2	4	no	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	2	4	no	—
47	C₂×#41×C₄₃	—	2	8	no	—
48	C₂×#41×C₄₃	—	2	4	no	—
49	C₂×#41×C₄₃	—	2	2	no	—
50	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
51	C₂×#41×C₄₃	C₂×C₄	1	8	yes	complemented
52	C₂×#41×C₄₃	D₄	1	16	yes	—
53	C₂×#41×C₄₃	C₂³	1	4	yes	—
54	C₂²×Q₈×C₄₃	—	2	8	no	—
55	C₂²×Q₈×C₄₃	—	2	1	no	—
56	C₂²×Q₈×C₄₃	—	2	2	no	—
57	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
58	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
59	C₂²×D₄×C₄₃	—	2	16	no	—
60	C₂²×D₄×C₄₃	—	2	2	no	—
61	C₂²×D₄×C₄₃	—	2	4	no	—
62	C₂²×D₄×C₄₃	—	2	2	no	—
63	C₂²×D₄×C₄₃	—	2	4	no	—
64	C₂²×D₄×C₄₃	—	2	8	no	—
65	C₂²×D₄×C₄₃	—	2	2	no	—
66	C₂²×D₄×C₄₃	—	2	1	no	—
67	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
68	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	complemented
69	C₂³×C₄×C₄₃	—	2	16	no	—
70	C₂³×C₄×C₄₃	—	2	1	no	—
71	C₂³×C₄×C₄₃	—	2	4	no	—
72	C₂³×C₄×C₄₃	—	2	2	no	—
73	C₂³×C₄×C₄₃	—	2	4	no	—
74	C₂³×C₄×C₄₃	—	2	8	no	—
75	C₂³×C₄×C₄₃	—	2	2	no	—
76	C₂³×C₄×C₄₃	—	2	2	no	—
77	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
79	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₄₃	D₄	1	2	yes	—
82	C₂³×C₄×C₄₃	D₄	1	2	yes	—
83	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₄₃	—	2	2	no	—
88	C₂×M₁₆×C₄₃	—	2	8	no	—
89	C₂×M₁₆×C₄₃	C₂³	1	4	yes	complemented
90	C₂²×C₈×C₄₃	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
93	C₂×C₄²×C₄₃	—	2	8	no	—
94	C₂×C₄²×C₄₃	—	2	2	no	—
95	C₂×C₄²×C₄₃	C₂³	1	4	yes	complemented
96	#104×C₄₃	—	2	32	no	—
97	C₂²⋊C₈×C₄₃	—	2	4	no	—
98	C₂²⋊C₈×C₄₃	—	2	4	no	—
99	#95×C₄₃	—	2	4	no	—
100	C₂⁴×C₄₃	—	2	8	no	—
101	C₂⁴×C₄₃	—	2	4	no	—
102	C₂⁴×C₄₃	—	2	2	no	—
103	C₂⁴×C₄₃	—	2	4	no	—
104	C₂⁴×C₄₃	—	2	4	no	—
105	C₂⁴×C₄₃	—	4	2	no	—
106	C₂⁴×C₄₃	—	4	4	no	—
107	C₂⁴×C₄₃	—	4	4	no	—
108	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×C₄₃	C₂²⋊C₄	1	2	yes	—
110	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
112	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
113	#41×C₄₃	—	2	32	no	—
114	#41×C₄₃	—	2	32	no	—
115	#41×C₄₃	—	2	32	no	—
116	#41×C₄₃	—	2	32	no	—
117	#41×C₄₃	—	2	32	no	—
118	#41×C₄₃	—	2	16	no	—
119	#41×C₄₃	—	2	16	no	—
120	#41×C₄₃	—	2	8	no	—
121	#41×C₄₃	—	2	16	no	—
122	#41×C₄₃	—	2	16	no	—
123	#41×C₄₃	—	2	8	no	—
124	#41×C₄₃	C₂²⋊C₄	1	16	yes	complemented
125	#41×C₄₃	C₂×D₄	1	16	yes	—
126	C₂×Q₈×C₄₃	—	2	16	no	—
127	C₂×Q₈×C₄₃	—	2	8	no	—
128	C₂×Q₈×C₄₃	—	2	16	no	—
129	C₂×Q₈×C₄₃	—	2	2	no	—
130	C₂×Q₈×C₄₃	—	2	4	no	—
131	C₂×Q₈×C₄₃	—	2	4	no	—
132	C₂×Q₈×C₄₃	C₂²⋊C₄	1	8	yes	complemented
133	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
134	C₂×D₄×C₄₃	—	2	16	no	—
135	C₂×D₄×C₄₃	—	2	32	no	—
136	C₂×D₄×C₄₃	—	2	32	no	—
137	C₂×D₄×C₄₃	—	2	16	no	—
138	C₂×D₄×C₄₃	—	2	8	no	—
139	C₂×D₄×C₄₃	—	2	16	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	4	no	—
142	C₂×D₄×C₄₃	—	2	4	no	—
143	C₂×D₄×C₄₃	—	2	4	no	—
144	C₂×D₄×C₄₃	—	2	8	no	—
145	C₂×D₄×C₄₃	—	2	16	no	—
146	C₂×D₄×C₄₃	—	2	4	no	—
147	C₂×D₄×C₄₃	C₂²⋊C₄	1	8	yes	complemented
148	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₄₃	—	2	8	no	—
150	C₂²×C₄×C₄₃	—	2	32	no	—
151	C₂²×C₄×C₄₃	—	2	32	no	—
152	C₂²×C₄×C₄₃	—	2	16	no	—
153	C₂²×C₄×C₄₃	—	2	4	no	—
154	C₂²×C₄×C₄₃	—	2	8	no	—
155	C₂²×C₄×C₄₃	—	2	4	no	—
156	C₂²×C₄×C₄₃	—	2	4	no	—
157	C₂²×C₄×C₄₃	—	2	8	no	—
158	C₂²×C₄×C₄₃	—	2	4	no	—
159	C₂²×C₄×C₄₃	—	2	16	no	—
160	C₂²×C₄×C₄₃	—	2	8	no	—
161	C₂²×C₄×C₄₃	—	2	4	no	—
162	C₂²×C₄×C₄₃	—	2	8	no	—
163	C₂²×C₄×C₄₃	—	2	4	no	—
164	C₂²×C₄×C₄₃	—	2	8	no	—
165	C₂²×C₄×C₄₃	—	2	8	no	—
166	C₂²×C₄×C₄₃	—	2	2	no	—
167	C₂²×C₄×C₄₃	—	2	4	no	—
168	C₂²×C₄×C₄₃	—	2	4	no	—
169	C₂²×C₄×C₄₃	—	2	4	no	—
170	C₂²×C₄×C₄₃	—	4	4	no	—
171	C₂²×C₄×C₄₃	—	4	4	no	—
172	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
173	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
175	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
177	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
178	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
179	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
181	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
187	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
191	M₁₆×C₄₃	—	2	8	no	—
192	M₁₆×C₄₃	—	4	4	no	—
193	C₂×C₈×C₄₃	—	2	4	no	—
194	C₂×C₈×C₄₃	—	4	4	no	—
195	C₂²⋊C₄×C₄₃	—	2	16	no	—
196	C₄²×C₄₃	—	2	8	no	—
197	C₄²×C₄₃	—	4	4	no	—
198	C₂³×C₄₃	—	2	2	no	—
199	C₂³×C₄₃	—	2	2	no	—
200	C₂³×C₄₃	—	2	2	no	—
201	C₂³×C₄₃	—	2	2	no	—
202	C₂³×C₄₃	—	2	16	no	—
203	C₂³×C₄₃	—	2	4	no	—
204	C₂³×C₄₃	—	2	4	no	—
205	C₂³×C₄₃	—	2	4	no	—
206	C₂³×C₄₃	—	2	2	no	—
207	C₂³×C₄₃	—	2	8	no	—
208	C₂³×C₄₃	—	2	2	no	—
209	C₂³×C₄₃	—	2	4	no	—
210	C₂³×C₄₃	—	2	4	no	—
211	C₂³×C₄₃	—	2	2	no	—
212	C₂³×C₄₃	—	4	2	no	—
213	C₂³×C₄₃	—	4	2	no	—
214	C₂³×C₄₃	—	4	16	no	—
215	C₂³×C₄₃	—	4	8	no	—
216	C₂³×C₄₃	—	4	32	no	—
217	C₂³×C₄₃	—	4	4	no	—
218	C₂³×C₄₃	—	4	8	no	—
219	C₂³×C₄₃	—	4	4	no	—
220	C₂³×C₄₃	#104	1	4	yes	complemented
221	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
222	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×C₄₃	#120	1	4	yes	—
226	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
227	Q₈×C₄₃	—	2	16	no	—
228	Q₈×C₄₃	—	2	4	no	—
229	Q₈×C₄₃	—	2	8	no	—
230	Q₈×C₄₃	C₂×C₂²⋊C₄	1	8	yes	complemented
231	D₄×C₄₃	—	2	32	no	—
232	D₄×C₄₃	—	2	16	no	—
233	D₄×C₄₃	—	2	16	no	—
234	D₄×C₄₃	—	2	16	no	—
235	D₄×C₄₃	—	2	4	no	—
236	D₄×C₄₃	—	2	8	no	—
237	D₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	complemented
238	C₂×C₄×C₄₃	—	2	16	no	—
239	C₂×C₄×C₄₃	—	2	32	no	—
240	C₂×C₄×C₄₃	—	2	4	no	—
241	C₂×C₄×C₄₃	—	2	4	no	—
242	C₂×C₄×C₄₃	—	2	2	no	—
243	C₂×C₄×C₄₃	—	2	8	no	—
244	C₂×C₄×C₄₃	—	2	2	no	—
245	C₂×C₄×C₄₃	—	2	4	no	—
246	C₂×C₄×C₄₃	—	2	4	no	—
247	C₂×C₄×C₄₃	—	2	4	no	—
248	C₂×C₄×C₄₃	—	2	4	no	—
249	C₂×C₄×C₄₃	—	2	16	no	—
250	C₂×C₄×C₄₃	—	2	4	no	—
251	C₂×C₄×C₄₃	—	2	4	no	—
252	C₂×C₄×C₄₃	—	2	16	no	—
253	C₂×C₄×C₄₃	—	2	4	no	—
254	C₂×C₄×C₄₃	—	2	4	no	—
255	C₂×C₄×C₄₃	—	2	4	no	—
256	C₂×C₄×C₄₃	—	2	8	no	—
257	C₂×C₄×C₄₃	—	4	4	no	—
258	C₂×C₄×C₄₃	—	4	16	no	—
259	C₂×C₄×C₄₃	—	4	4	no	—
260	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
263	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
264	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₄₃	#120	1	4	yes	—
267	C₂×C₄×C₄₃	#120	1	4	yes	—
268	C₂×C₄×C₄₃	#120	1	4	yes	—
269	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
272	C₈×C₄₃	—	4	4	no	—
273	C₂×#1789	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
274	C₂²×C₄₃	—	2	1	no	—
275	C₂²×C₄₃	—	2	1	no	—
276	C₂²×C₄₃	—	2	2	no	—
277	C₂²×C₄₃	—	2	1	no	—
278	C₂²×C₄₃	—	2	1	no	—
279	C₂²×C₄₃	—	2	2	no	—
280	C₂²×C₄₃	—	2	8	no	—
281	C₂²×C₄₃	—	2	8	no	—
282	C₂²×C₄₃	—	2	2	no	—
283	C₂²×C₄₃	—	2	2	no	—
284	C₂²×C₄₃	—	2	8	no	—
285	C₂²×C₄₃	—	2	2	no	—
286	C₂²×C₄₃	—	4	8	no	—
287	C₂²×C₄₃	—	4	8	no	—
288	C₂²×C₄₃	—	4	32	no	—
289	C₂²×C₄₃	—	4	4	no	—
290	C₂²×C₄₃	—	4	4	no	—
291	C₂²×C₄₃	—	4	4	no	—
292	C₂²×C₄₃	—	4	16	no	—
293	C₂²×C₄₃	#379	1	2	yes	—
294	C₂²×C₄₃	#379	1	2	yes	—
295	C₂²×C₄₃	C₂×#104	1	2	yes	—
296	C₂²×C₄₃	C₂×#104	1	4	yes	complemented
297	C₂²×C₄₃	#421	1	2	yes	—
298	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×C₄₃	C₂×#120	1	2	yes	—
300	C₄×C₄₃	—	2	2	no	—
301	C₄×C₄₃	—	2	8	no	—
302	C₄×C₄₃	—	2	2	no	—
303	C₄×C₄₃	—	4	8	no	—
304	C₄×C₄₃	#379	1	2	yes	—
305	C₄×C₄₃	#379	1	2	yes	—
306	C₄×C₄₃	C₂²×C₂²⋊C₄	1	2	yes	—
307	C₄×C₄₃	C₂×#120	1	2	yes	—
308	C₂³×#41	C₂×C₄₃	1	1	yes	characteristic
309	C₂²×#104	C₂×C₄₃	1	4	yes	complemented
310	C₂×#407	C₂×C₄₃	1	1	yes	characteristic, complemented
311	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
312	#1789	C₂×C₄₃	1	8	yes	direct product factor
313	C₂×C₄₃	—	2	2	no	—
314	C₂×C₄₃	—	2	4	no	—
315	C₂×C₄₃	—	2	2	no	—
316	C₂×C₄₃	—	4	2	no	—
317	C₂×C₄₃	—	4	8	no	—
318	C₂×C₄₃	#1789	1	4	yes	direct product factor
319	C₂×C₄₃	C₂×#379	1	1	yes	characteristic
320	C₂×C₄₃	C₂²×#104	1	1	yes	characteristic
321	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
322	C₂²×#41	—	2	16	no	—
323	C₂²×#41	—	2	1	no	—
324	C₂²×#41	—	2	2	no	—
325	C₂²×#41	—	2	1	no	—
326	C₂²×#41	—	2	2	no	—
327	C₂²×#41	C₄×C₄₃	1	2	yes	complemented
328	C₂²×#41	C₄×C₄₃	1	4	yes	complemented
329	C₂²×#41	C₂²×C₄₃	1	2	yes	—
330	C₂²×#41	C₂²×C₄₃	1	4	yes	—
331	C₂³×Q₈	C₄×C₄₃	1	1	yes	characteristic, complemented
332	C₂³×D₄	—	2	1	no	—
333	C₂³×D₄	C₄×C₄₃	1	1	yes	characteristic, complemented
334	C₂⁴×C₄	—	2	1	no	—
335	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
336	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	complemented
337	C₂²×C₂²⋊C₄	—	2	1	no	—
338	C₂²×C₄²	C₂²×C₄₃	1	2	yes	complemented
339	C₂×#104	—	2	16	no	—
340	C₂×#104	C₂²×C₄₃	1	16	yes	complemented
341	#407	—	2	2	no	—
342	#407	C₂²×C₄₃	1	4	yes	complemented
343	C₂×C₂²⋊C₈	—	2	1	no	—
344	C₂×C₂²⋊C₈	—	2	1	no	—
345	C₄×C₂²⋊C₄	—	2	2	no	—
346	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	complemented
347	C₂×#95	—	2	1	no	—
348	C₄₃	C₂×#1789	1	1	yes	characteristic, direct product factor, Sylow
349	C₂⁵	—	2	1	no	—
350	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
351	C₂×#41	—	2	16	no	—
352	C₂×#41	—	2	32	no	—
353	C₂×#41	—	2	32	no	—
354	C₂×#41	—	2	16	no	—
355	C₂×#41	—	2	32	no	—
356	C₂×#41	—	2	32	no	—
357	C₂×#41	—	2	8	no	—
358	C₂×#41	—	2	8	no	—
359	C₂×#41	—	2	4	no	—
360	C₂×#41	—	2	4	no	—
361	C₂×#41	—	2	4	no	—
362	C₂×#41	—	2	2	no	—
363	C₂×#41	—	2	4	no	—
364	C₂×#41	—	2	8	no	—
365	C₂×#41	—	2	4	no	—
366	C₂×#41	—	2	2	no	—
367	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
368	C₂×#41	C₂×C₄×C₄₃	1	8	yes	complemented
369	C₂×#41	D₄×C₄₃	1	16	yes	—
370	C₂×#41	C₂³×C₄₃	1	4	yes	—
371	C₂²×Q₈	—	2	8	no	—
372	C₂²×Q₈	—	2	1	no	—
373	C₂²×Q₈	—	2	2	no	—
374	C₂²×Q₈	C₂×C₄×C₄₃	1	2	yes	—
375	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
376	C₂²×D₄	—	2	16	no	—
377	C₂²×D₄	—	2	2	no	—
378	C₂²×D₄	—	2	4	no	—
379	C₂²×D₄	—	2	2	no	—
380	C₂²×D₄	—	2	4	no	—
381	C₂²×D₄	—	2	8	no	—
382	C₂²×D₄	—	2	2	no	—
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
385	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	complemented
386	C₂³×C₄	—	2	16	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	2	2	no	—
389	C₂³×C₄	—	2	4	no	—
390	C₂³×C₄	—	2	4	no	—
391	C₂³×C₄	—	2	2	no	—
392	C₂³×C₄	—	2	8	no	—
393	C₂³×C₄	—	2	2	no	—
394	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
395	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
396	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
397	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
398	C₂³×C₄	D₄×C₄₃	1	2	yes	—
399	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
400	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
401	C₂³×C₄	D₄×C₄₃	1	2	yes	—
402	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
403	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
404	C₂×M₁₆	—	2	2	no	—
405	C₂×M₁₆	—	2	8	no	—
406	C₂×M₁₆	C₂³×C₄₃	1	4	yes	complemented
407	C₂²×C₈	—	2	2	no	—
408	C₂×C₂²⋊C₄	—	2	8	no	—
409	C₂×C₂²⋊C₄	—	2	4	no	—
410	C₂×C₄²	—	2	8	no	—
411	C₂×C₄²	—	2	2	no	—
412	C₂×C₄²	C₂³×C₄₃	1	4	yes	complemented
413	#104	—	2	32	no	—
414	C₂²⋊C₈	—	2	4	no	—
415	C₂²⋊C₈	—	2	4	no	—
416	#95	—	2	4	no	—
417	C₂⁴	—	2	8	no	—
418	C₂⁴	—	2	4	no	—
419	C₂⁴	—	2	2	no	—
420	C₂⁴	—	2	4	no	—
421	C₂⁴	—	2	4	no	—
422	C₂⁴	—	4	2	no	—
423	C₂⁴	—	4	4	no	—
424	C₂⁴	—	4	4	no	—
425	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
426	C₂⁴	C₂²⋊C₄×C₄₃	1	2	yes	—
427	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
428	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
429	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
430	#41	—	2	32	no	—
431	#41	—	2	32	no	—
432	#41	—	2	32	no	—
433	#41	—	2	32	no	—
434	#41	—	2	32	no	—
435	#41	—	2	16	no	—
436	#41	—	2	16	no	—
437	#41	—	2	8	no	—
438	#41	—	2	16	no	—
439	#41	—	2	16	no	—
440	#41	—	2	8	no	—
441	#41	C₂²⋊C₄×C₄₃	1	16	yes	complemented
442	#41	C₂×D₄×C₄₃	1	16	yes	—
443	C₂×Q₈	—	2	16	no	—
444	C₂×Q₈	—	2	8	no	—
445	C₂×Q₈	—	2	16	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	C₂²⋊C₄×C₄₃	1	8	yes	complemented
450	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	—
451	C₂×D₄	—	2	32	no	—
452	C₂×D₄	—	2	32	no	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	16	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	8	no	—
458	C₂×D₄	—	2	16	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	16	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	C₂²⋊C₄×C₄₃	1	8	yes	complemented
465	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
466	C₂²×C₄	—	2	8	no	—
467	C₂²×C₄	—	2	32	no	—
468	C₂²×C₄	—	2	32	no	—
469	C₂²×C₄	—	2	16	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	16	no	—
480	C₂²×C₄	—	2	8	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	8	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	8	no	—
485	C₂²×C₄	—	2	8	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	4	4	no	—
488	C₂²×C₄	—	4	4	no	—
489	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
490	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
491	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
492	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
493	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
494	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
495	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
496	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
497	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
498	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
499	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
501	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
502	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
503	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
505	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
507	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
508	M₁₆	—	2	8	no	—
509	M₁₆	—	4	4	no	—
510	C₂×C₈	—	2	4	no	—
511	C₂×C₈	—	4	4	no	—
512	C₂²⋊C₄	—	2	16	no	—
513	C₄²	—	2	8	no	—
514	C₄²	—	4	4	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	16	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	16	no	—
532	C₂³	—	4	8	no	—
533	C₂³	—	4	32	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	4	8	no	—
536	C₂³	—	4	4	no	—
537	C₂³	#104×C₄₃	1	4	yes	complemented
538	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
539	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
540	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
541	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
542	C₂³	#120×C₄₃	1	4	yes	—
543	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
544	Q₈	—	2	16	no	—
545	Q₈	—	2	4	no	—
546	Q₈	—	2	8	no	—
547	Q₈	C₂×C₂²⋊C₄×C₄₃	1	8	yes	complemented
548	D₄	—	2	32	no	—
549	D₄	—	2	16	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	16	no	—
552	D₄	—	2	4	no	—
553	D₄	—	2	8	no	—
554	D₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	complemented
555	C₂×C₄	—	2	16	no	—
556	C₂×C₄	—	2	32	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	16	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	16	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	16	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
578	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
579	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
580	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
581	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
583	C₂×C₄	#120×C₄₃	1	4	yes	—
584	C₂×C₄	#120×C₄₃	1	4	yes	—
585	C₂×C₄	#120×C₄₃	1	4	yes	—
586	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
588	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
589	C₈	—	4	4	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	8	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	8	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	4	8	no	—
604	C₂²	—	4	32	no	—
605	C₂²	—	4	4	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	16	no	—
609	C₂²	C₄₃×#379	1	2	yes	—
610	C₂²	C₄₃×#379	1	2	yes	—
611	C₂²	C₂×#104×C₄₃	1	2	yes	—
612	C₂²	C₂×#104×C₄₃	1	4	yes	complemented
613	C₂²	C₄₃×#421	1	2	yes	—
614	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
615	C₂²	C₂×#120×C₄₃	1	2	yes	—
616	C₄	—	2	2	no	—
617	C₄	—	2	8	no	—
618	C₄	—	2	2	no	—
619	C₄	—	4	8	no	—
620	C₄	C₄₃×#379	1	2	yes	—
621	C₄	C₄₃×#379	1	2	yes	—
622	C₄	C₂²×C₂²⋊C₄×C₄₃	1	2	yes	—
623	C₄	C₂×#120×C₄₃	1	2	yes	—
624	C₂	—	2	2	no	—
625	C₂	—	2	4	no	—
626	C₂	—	2	2	no	—
627	C₂	—	4	2	no	—
628	C₂	—	4	8	no	—
629	C₂	C₄₃×#1789	1	4	yes	direct product factor
630	C₂	C₂×C₄₃×#379	1	1	yes	characteristic
631	C₂	C₂²×#104×C₄₃	1	1	yes	characteristic
632	C₂	C₂×C₄₃×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂³×#41×C₄₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#104×C₄₃	C₂	semidirect
3. C₂×C₄₃×#407	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₄₃	C₂	semidirect
5. C₄₃×#1789	C₂	direct (N × H)
11. C₂²×#41×C₄₃	C₄	semidirect
12. C₂²×#41×C₄₃	C₄	semidirect
15. C₂³×Q₈×C₄₃	C₄	semidirect
17. C₂³×D₄×C₄₃	C₄	semidirect
20. C₂²×M₁₆×C₄₃	C₂²	semidirect
22. C₂²×C₄²×C₄₃	C₂²	semidirect
24. C₂×#104×C₄₃	C₂²	semidirect
26. C₄₃×#407	C₂²	semidirect
30. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
51. C₂×#41×C₄₃	C₂×C₄	semidirect
58. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
68. C₂²×D₄×C₄₃	C₂×C₄	semidirect
89. C₂×M₁₆×C₄₃	C₂³	semidirect
95. C₂×C₄²×C₄₃	C₂³	semidirect
124. #41×C₄₃	C₂²⋊C₄	semidirect
132. C₂×Q₈×C₄₃	C₂²⋊C₄	semidirect
147. C₂×D₄×C₄₃	C₂²⋊C₄	semidirect
220. C₂³×C₄₃	#104	semidirect
230. Q₈×C₄₃	C₂×C₂²⋊C₄	semidirect
237. D₄×C₄₃	C₂×C₂²⋊C₄	semidirect
273. C₂×#1789	C₄₃	direct (N × H)
296. C₂²×C₄₃	C₂×#104	semidirect
309. C₂²×#104	C₂×C₄₃	semidirect
310. C₂×#407	C₂×C₄₃	semidirect
311. C₂×C₄×C₂²⋊C₄	C₂×C₄₃	semidirect
312. #1789	C₂×C₄₃	direct (N × H)
318. C₂×C₄₃	#1789	direct (N × H)
327. C₂²×#41	C₄×C₄₃	semidirect
328. C₂²×#41	C₄×C₄₃	semidirect
331. C₂³×Q₈	C₄×C₄₃	semidirect
333. C₂³×D₄	C₄×C₄₃	semidirect
336. C₂²×M₁₆	C₂²×C₄₃	semidirect
338. C₂²×C₄²	C₂²×C₄₃	semidirect
340. C₂×#104	C₂²×C₄₃	semidirect
342. #407	C₂²×C₄₃	semidirect
346. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
348. C₄₃	C₂×#1789	direct (N × H)
368. C₂×#41	C₂×C₄×C₄₃	semidirect
375. C₂²×Q₈	C₂×C₄×C₄₃	semidirect
385. C₂²×D₄	C₂×C₄×C₄₃	semidirect
406. C₂×M₁₆	C₂³×C₄₃	semidirect
412. C₂×C₄²	C₂³×C₄₃	semidirect
441. #41	C₂²⋊C₄×C₄₃	semidirect
449. C₂×Q₈	C₂²⋊C₄×C₄₃	semidirect
464. C₂×D₄	C₂²⋊C₄×C₄₃	semidirect
537. C₂³	#104×C₄₃	semidirect
547. Q₈	C₂×C₂²⋊C₄×C₄₃	semidirect
554. D₄	C₂×C₂²⋊C₄×C₄₃	semidirect
612. C₂²	C₂×#104×C₄₃	semidirect
629. C₂	C₄₃×#1789	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×#41×C₄₃	2
C₂²×#104×C₄₃	2
C₂×C₄₃×#407	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₄₃×#1789	2
C₂×#1789	43

Subgroups — C2×C43×#1789 #24940621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1789 #24940621