Subgroups — C₂×C₄₃×#1871 #24940918

Order 11008.

2050 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	C₂³×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#525	C₂	1	1	yes	maximal, characteristic
3	C₂²×#104×C₄₃	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1871	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₃×#339	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₃	—	2	2	no	—
10	C₂²×M₁₆×C₄₃	—	2	1	no	—
11	C₂²×M₁₆×C₄₃	—	2	8	no	—
12	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₄₃	C₂²	1	4	yes	complemented
14	C₂³×C₈×C₄₃	—	2	1	no	—
15	C₄₃×#525	—	2	2	no	—
16	C₄₃×#525	—	2	2	no	—
17	C₄₃×#525	C₄	1	4	yes	complemented
18	C₄₃×#525	C₂²	1	4	yes	—
19	C₂×#123×C₄₃	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
21	C₂×C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
22	C₂×#121×C₄₃	C₄	1	1	yes	characteristic, complemented
23	C₂×#121×C₄₃	C₄	1	1	yes	characteristic, complemented
24	C₂×#120×C₄₃	—	2	1	no	—
25	C₂×C₄×D₄×C₄₃	—	2	1	no	—
26	C₂×C₄×D₄×C₄₃	—	2	1	no	—
27	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
29	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
30	C₂×#104×C₄₃	—	2	8	no	—
31	C₂×#104×C₄₃	C₂²	1	8	yes	complemented
32	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
33	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	complemented
34	C₂×#95×C₄₃	—	2	1	no	—
35	C₄₃×#339	C₂²	1	8	yes	complemented
36	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
37	C₂×#41×C₄₃	—	2	1	no	—
38	C₂×#41×C₄₃	—	2	1	no	—
39	C₂×#41×C₄₃	—	2	4	no	—
40	C₂×#41×C₄₃	—	2	4	no	—
41	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
42	C₂×#41×C₄₃	C₂³	1	2	yes	—
43	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	—	2	4	no	—
49	C₂³×C₄×C₄₃	—	2	4	no	—
50	C₂³×C₄×C₄₃	—	2	2	no	—
51	C₂³×C₄×C₄₃	—	2	1	no	—
52	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	D₄	1	2	yes	—
57	C₂³×C₄×C₄₃	D₄	1	2	yes	—
58	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₄₃	—	2	16	no	—
63	C₂×M₁₆×C₄₃	—	2	8	no	—
64	C₂×M₁₆×C₄₃	—	2	4	no	—
65	C₂×M₁₆×C₄₃	—	2	2	no	—
66	C₂×M₁₆×C₄₃	—	2	4	no	—
67	C₂×M₁₆×C₄₃	—	2	16	no	—
68	C₂×M₁₆×C₄₃	D₄	1	8	yes	complemented
69	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
70	C₂²×C₈×C₄₃	—	2	8	no	—
71	C₂²×C₈×C₄₃	—	2	4	no	—
72	C₂²×C₈×C₄₃	—	2	2	no	—
73	#123×C₄₃	—	2	4	no	—
74	#123×C₄₃	—	2	4	no	—
75	C₂²⋊Q₈×C₄₃	—	2	2	no	—
76	C₂²⋊Q₈×C₄₃	—	2	2	no	—
77	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
78	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
79	#121×C₄₃	—	2	2	no	—
80	#121×C₄₃	—	2	2	no	—
81	#121×C₄₃	C₂×C₄	1	4	yes	complemented
82	#121×C₄₃	C₂×C₄	1	4	yes	complemented
83	#120×C₄₃	—	2	4	no	—
84	#120×C₄₃	—	2	4	no	—
85	C₄×D₄×C₄₃	—	2	4	no	—
86	C₄×D₄×C₄₃	—	2	4	no	—
87	C₄×D₄×C₄₃	—	2	4	no	—
88	C₄×D₄×C₄₃	—	2	4	no	—
89	#117×C₄₃	—	2	1	no	—
90	#117×C₄₃	—	2	1	no	—
91	#117×C₄₃	C₂×C₄	1	2	yes	—
92	#117×C₄₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
104	C₂×C₄²×C₄₃	—	2	1	no	—
105	C₂×C₄²×C₄₃	—	2	4	no	—
106	C₂×C₄²×C₄₃	—	2	4	no	—
107	C₂×C₄²×C₄₃	—	2	2	no	—
108	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
109	#104×C₄₃	—	2	16	no	—
110	#95×C₄₃	—	2	4	no	—
111	C₂⁴×C₄₃	—	2	4	no	—
112	C₂⁴×C₄₃	—	2	4	no	—
113	C₂⁴×C₄₃	—	2	1	no	—
114	C₂⁴×C₄₃	—	4	2	no	—
115	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂⁴×C₄₃	C₂²⋊C₄	1	2	yes	—
117	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
119	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
120	#41×C₄₃	—	2	8	no	—
121	#41×C₄₃	—	2	4	no	—
122	#41×C₄₃	—	2	4	no	—
123	#41×C₄₃	—	4	2	no	—
124	#41×C₄₃	—	4	4	no	—
125	#41×C₄₃	—	4	2	no	—
126	C₂×Q₈×C₄₃	—	2	1	no	—
127	C₂×Q₈×C₄₃	—	2	4	no	—
128	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
129	C₂×D₄×C₄₃	—	2	1	no	—
130	C₂×D₄×C₄₃	—	2	4	no	—
131	C₂×D₄×C₄₃	—	2	4	no	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	2	2	no	—
134	C₂×D₄×C₄₃	—	2	4	no	—
135	C₂×D₄×C₄₃	—	4	4	no	—
136	C₂×D₄×C₄₃	—	4	4	no	—
137	C₂×D₄×C₄₃	—	4	4	no	—
138	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₄₃	—	2	4	no	—
140	C₂²×C₄×C₄₃	—	2	4	no	—
141	C₂²×C₄×C₄₃	—	2	8	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	4	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	8	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	4	no	—
149	C₂²×C₄×C₄₃	—	2	4	no	—
150	C₂²×C₄×C₄₃	—	2	4	no	—
151	C₂²×C₄×C₄₃	—	2	8	no	—
152	C₂²×C₄×C₄₃	—	2	2	no	—
153	C₂²×C₄×C₄₃	—	2	2	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	2	1	no	—
156	C₂²×C₄×C₄₃	—	2	1	no	—
157	C₂²×C₄×C₄₃	—	2	4	no	—
158	C₂²×C₄×C₄₃	—	2	4	no	—
159	C₂²×C₄×C₄₃	—	4	4	no	—
160	C₂²×C₄×C₄₃	—	4	2	no	—
161	C₂²×C₄×C₄₃	—	4	2	no	—
162	C₂²×C₄×C₄₃	—	4	4	no	—
163	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
166	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
167	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
168	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
169	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
170	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₄₃	#41	1	4	yes	—
182	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
183	M₁₆×C₄₃	—	2	16	no	—
184	M₁₆×C₄₃	—	2	8	no	—
185	M₁₆×C₄₃	—	2	4	no	—
186	M₁₆×C₄₃	C₂×D₄	1	8	yes	complemented
187	C₂×C₈×C₄₃	—	2	16	no	—
188	C₂×C₈×C₄₃	—	2	8	no	—
189	C₂×C₈×C₄₃	—	2	4	no	—
190	C₄⋊C₄×C₄₃	—	2	4	no	—
191	C₄⋊C₄×C₄₃	—	2	4	no	—
192	C₄⋊C₄×C₄₃	—	2	1	no	—
193	C₄⋊C₄×C₄₃	—	2	1	no	—
194	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
195	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
196	C₂²⋊C₄×C₄₃	—	2	16	no	—
197	C₂²⋊C₄×C₄₃	—	2	4	no	—
198	C₂²⋊C₄×C₄₃	—	2	4	no	—
199	C₂²⋊C₄×C₄₃	—	2	2	no	—
200	C₂²⋊C₄×C₄₃	—	2	4	no	—
201	C₂²⋊C₄×C₄₃	—	2	4	no	—
202	C₂²⋊C₄×C₄₃	—	2	2	no	—
203	C₄²×C₄₃	—	2	2	no	—
204	C₄²×C₄₃	—	2	2	no	—
205	C₄²×C₄₃	—	2	4	no	—
206	C₄²×C₄₃	—	2	4	no	—
207	C₄²×C₄₃	—	4	4	no	—
208	C₂³×C₄₃	—	2	2	no	—
209	C₂³×C₄₃	—	2	2	no	—
210	C₂³×C₄₃	—	2	2	no	—
211	C₂³×C₄₃	—	2	2	no	—
212	C₂³×C₄₃	—	2	4	no	—
213	C₂³×C₄₃	—	2	4	no	—
214	C₂³×C₄₃	—	2	2	no	—
215	C₂³×C₄₃	—	2	2	no	—
216	C₂³×C₄₃	—	2	4	no	—
217	C₂³×C₄₃	—	2	4	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	2	2	no	—
220	C₂³×C₄₃	—	4	2	no	—
221	C₂³×C₄₃	—	4	2	no	—
222	C₂³×C₄₃	—	4	16	no	—
223	C₂³×C₄₃	—	4	2	no	—
224	C₂³×C₄₃	—	4	2	no	—
225	C₂³×C₄₃	—	4	2	no	—
226	C₂³×C₄₃	#104	1	4	yes	complemented
227	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×C₄₃	#121	1	4	yes	—
232	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₄₃	—	2	4	no	—
234	Q₈×C₄₃	—	4	2	no	—
235	D₄×C₄₃	—	2	4	no	—
236	D₄×C₄₃	—	4	8	no	—
237	D₄×C₄₃	—	4	4	no	—
238	D₄×C₄₃	—	4	4	no	—
239	D₄×C₄₃	—	4	8	no	—
240	D₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	—	2	4	no	—
242	C₂×C₄×C₄₃	—	2	4	no	—
243	C₂×C₄×C₄₃	—	2	2	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	2	no	—
248	C₂×C₄×C₄₃	—	2	2	no	—
249	C₂×C₄×C₄₃	—	2	2	no	—
250	C₂×C₄×C₄₃	—	2	2	no	—
251	C₂×C₄×C₄₃	—	2	4	no	—
252	C₂×C₄×C₄₃	—	2	4	no	—
253	C₂×C₄×C₄₃	—	2	4	no	—
254	C₂×C₄×C₄₃	—	2	4	no	—
255	C₂×C₄×C₄₃	—	2	8	no	—
256	C₂×C₄×C₄₃	—	2	2	no	—
257	C₂×C₄×C₄₃	—	2	2	no	—
258	C₂×C₄×C₄₃	—	2	2	no	—
259	C₂×C₄×C₄₃	—	4	16	no	—
260	C₂×C₄×C₄₃	—	4	4	no	—
261	C₂×C₄×C₄₃	—	4	4	no	—
262	C₂×C₄×C₄₃	—	4	2	no	—
263	C₂×C₄×C₄₃	—	4	2	no	—
264	C₂×C₄×C₄₃	—	4	2	no	—
265	C₂×C₄×C₄₃	—	4	2	no	—
266	C₂×C₄×C₄₃	—	4	2	no	—
267	C₂×C₄×C₄₃	—	4	4	no	—
268	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
273	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
274	C₂×C₄×C₄₃	#120	1	2	yes	—
275	C₂×C₄×C₄₃	#120	1	2	yes	—
276	C₂×C₄×C₄₃	#121	1	4	yes	—
277	C₂×C₄×C₄₃	#123	1	2	yes	—
278	C₂×C₄×C₄₃	#123	1	2	yes	—
279	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
283	C₈×C₄₃	—	2	8	no	—
284	C₂×#1871	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂²×C₄₃	—	2	8	no	—
286	C₂²×C₄₃	—	2	8	no	—
287	C₂²×C₄₃	—	2	1	no	—
288	C₂²×C₄₃	—	2	1	no	—
289	C₂²×C₄₃	—	2	1	no	—
290	C₂²×C₄₃	—	2	2	no	—
291	C₂²×C₄₃	—	2	1	no	—
292	C₂²×C₄₃	—	2	2	no	—
293	C₂²×C₄₃	—	2	2	no	—
294	C₂²×C₄₃	—	2	2	no	—
295	C₂²×C₄₃	—	2	2	no	—
296	C₂²×C₄₃	—	4	8	no	—
297	C₂²×C₄₃	—	4	8	no	—
298	C₂²×C₄₃	—	4	4	no	—
299	C₂²×C₄₃	—	4	2	no	—
300	C₂²×C₄₃	—	4	2	no	—
301	C₂²×C₄₃	—	4	2	no	—
302	C₂²×C₄₃	—	8	4	no	—
303	C₂²×C₄₃	#386	1	2	yes	—
304	C₂²×C₄₃	#386	1	2	yes	—
305	C₂²×C₄₃	C₂×#104	1	2	yes	—
306	C₂²×C₄₃	C₂×#104	1	4	yes	complemented
307	C₂²×C₄₃	#421	1	2	yes	—
308	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×C₄₃	C₂×#121	1	2	yes	—
310	C₄×C₄₃	—	2	2	no	—
311	C₄×C₄₃	—	2	2	no	—
312	C₄×C₄₃	—	4	8	no	—
313	C₄×C₄₃	—	4	2	no	—
314	C₄×C₄₃	—	4	2	no	—
315	C₄×C₄₃	—	4	2	no	—
316	C₄×C₄₃	#386	1	2	yes	—
317	C₄×C₄₃	#386	1	2	yes	—
318	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
319	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
320	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
321	C₂³×M₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
322	C₂×#525	C₂×C₄₃	1	1	yes	characteristic
323	C₂²×#104	C₂×C₄₃	1	2	yes	complemented
324	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
325	#1871	C₂×C₄₃	1	8	yes	direct product factor
326	C₂×#339	C₂×C₄₃	1	2	yes	complemented
327	C₂×C₄₃	—	2	2	no	—
328	C₂×C₄₃	—	2	2	no	—
329	C₂×C₄₃	—	2	4	no	—
330	C₂×C₄₃	—	4	2	no	—
331	C₂×C₄₃	—	8	2	no	—
332	C₂×C₄₃	#1871	1	4	yes	direct product factor
333	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
334	C₂×C₄₃	C₂²×#104	1	1	yes	characteristic
335	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
336	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
337	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
338	C₂²×M₁₆	—	2	1	no	—
339	C₂²×M₁₆	—	2	2	no	—
340	C₂²×M₁₆	—	2	8	no	—
341	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
342	C₂²×M₁₆	C₂²×C₄₃	1	4	yes	complemented
343	C₂³×C₈	—	2	1	no	—
344	#525	—	2	2	no	—
345	#525	—	2	2	no	—
346	#525	C₄×C₄₃	1	4	yes	complemented
347	#525	C₂²×C₄₃	1	4	yes	—
348	C₂×#123	—	2	1	no	—
349	C₂×C₂²⋊Q₈	C₄×C₄₃	1	1	yes	characteristic, complemented
350	C₂×C₂²⋊Q₈	C₄×C₄₃	1	1	yes	characteristic, complemented
351	C₂×#121	C₄×C₄₃	1	1	yes	characteristic, complemented
352	C₂×#121	C₄×C₄₃	1	1	yes	characteristic, complemented
353	C₂×#120	—	2	1	no	—
354	C₂×C₄×D₄	—	2	1	no	—
355	C₂×C₄×D₄	—	2	1	no	—
356	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	—	2	1	no	—
358	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
359	C₂×#104	—	2	8	no	—
360	C₂×#104	C₂²×C₄₃	1	8	yes	complemented
361	C₄×C₂²⋊C₄	—	2	2	no	—
362	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	complemented
363	C₂×#95	—	2	1	no	—
364	#339	C₂²×C₄₃	1	8	yes	complemented
365	C₄₃	C₂×#1871	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	4	no	—
370	C₂×#41	—	2	4	no	—
371	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
372	C₂×#41	C₂³×C₄₃	1	2	yes	—
373	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
374	C₂²×D₄	—	2	1	no	—
375	C₂²×D₄	—	2	1	no	—
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
378	C₂³×C₄	—	2	4	no	—
379	C₂³×C₄	—	2	4	no	—
380	C₂³×C₄	—	2	2	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
383	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
384	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
385	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
386	C₂³×C₄	D₄×C₄₃	1	2	yes	—
387	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
388	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
389	C₂³×C₄	D₄×C₄₃	1	2	yes	—
390	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
391	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
392	C₂×M₁₆	—	2	16	no	—
393	C₂×M₁₆	—	2	8	no	—
394	C₂×M₁₆	—	2	4	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	2	4	no	—
397	C₂×M₁₆	—	2	16	no	—
398	C₂×M₁₆	D₄×C₄₃	1	8	yes	complemented
399	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
400	C₂²×C₈	—	2	8	no	—
401	C₂²×C₈	—	2	2	no	—
402	C₂²×C₈	—	2	4	no	—
403	#123	—	2	4	no	—
404	#123	—	2	4	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	2	no	—
407	C₂²⋊Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
408	C₂²⋊Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
409	#121	—	2	2	no	—
410	#121	—	2	2	no	—
411	#121	C₂×C₄×C₄₃	1	4	yes	complemented
412	#121	C₂×C₄×C₄₃	1	4	yes	complemented
413	#120	—	2	4	no	—
414	#120	—	2	4	no	—
415	C₄×D₄	—	2	4	no	—
416	C₄×D₄	—	2	4	no	—
417	C₄×D₄	—	2	4	no	—
418	C₄×D₄	—	2	4	no	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	C₂×C₄×C₄₃	1	2	yes	—
422	#117	C₂³×C₄₃	1	2	yes	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	—	2	8	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	4	no	—
436	C₂×C₄²	—	2	4	no	—
437	C₂×C₄²	—	2	2	no	—
438	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
439	#104	—	2	16	no	—
440	#95	—	2	4	no	—
441	C₂⁴	—	2	4	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	1	no	—
444	C₂⁴	—	4	2	no	—
445	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
446	C₂⁴	C₂²⋊C₄×C₄₃	1	2	yes	—
447	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
448	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
449	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
450	#41	—	2	8	no	—
451	#41	—	2	4	no	—
452	#41	—	2	4	no	—
453	#41	—	4	2	no	—
454	#41	—	4	4	no	—
455	#41	—	4	2	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	8	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
494	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
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	2	yes	—
499	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
500	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
501	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
502	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
505	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
506	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
507	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
511	C₂²×C₄	#41×C₄₃	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
513	M₁₆	—	2	16	no	—
514	M₁₆	—	2	8	no	—
515	M₁₆	—	2	4	no	—
516	M₁₆	C₂×D₄×C₄₃	1	8	yes	complemented
517	C₂×C₈	—	2	16	no	—
518	C₂×C₈	—	2	8	no	—
519	C₂×C₈	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
525	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
526	C₂²⋊C₄	—	2	16	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	4	no	—
536	C₄²	—	2	4	no	—
537	C₄²	—	4	4	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	16	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	#104×C₄₃	1	4	yes	complemented
557	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
558	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
559	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
560	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
561	C₂³	#121×C₄₃	1	4	yes	—
562	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
563	Q₈	—	2	4	no	—
564	Q₈	—	4	2	no	—
565	D₄	—	2	4	no	—
566	D₄	—	4	8	no	—
567	D₄	—	4	4	no	—
568	D₄	—	4	4	no	—
569	D₄	—	4	8	no	—
570	D₄	—	4	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	8	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	4	16	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
599	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
600	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
601	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
602	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
603	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
604	C₂×C₄	#120×C₄₃	1	2	yes	—
605	C₂×C₄	#120×C₄₃	1	2	yes	—
606	C₂×C₄	#121×C₄₃	1	4	yes	—
607	C₂×C₄	#123×C₄₃	1	2	yes	—
608	C₂×C₄	#123×C₄₃	1	2	yes	—
609	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
611	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
612	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
613	C₈	—	2	8	no	—
614	C₂²	—	2	8	no	—
615	C₂²	—	2	8	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	4	8	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	8	4	no	—
632	C₂²	C₄₃×#386	1	2	yes	—
633	C₂²	C₄₃×#386	1	2	yes	—
634	C₂²	C₂×#104×C₄₃	1	2	yes	—
635	C₂²	C₂×#104×C₄₃	1	4	yes	complemented
636	C₂²	C₄₃×#421	1	2	yes	—
637	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
638	C₂²	C₂×#121×C₄₃	1	2	yes	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	4	8	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	2	no	—
645	C₄	C₄₃×#386	1	2	yes	—
646	C₄	C₄₃×#386	1	2	yes	—
647	C₄	C₂×C₄×D₄×C₄₃	1	2	yes	—
648	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
649	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
650	C₂	—	2	2	no	—
651	C₂	—	2	2	no	—
652	C₂	—	2	4	no	—
653	C₂	—	4	2	no	—
654	C₂	—	8	2	no	—
655	C₂	C₄₃×#1871	1	4	yes	direct product factor
656	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
657	C₂	C₂²×#104×C₄₃	1	1	yes	characteristic
658	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	C₂×C₄₃×#525	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
1. C₂³×M₁₆×C₄₃	C₂	semidirect
3. C₂²×#104×C₄₃	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₄₃	C₂	semidirect
5. C₄₃×#1871	C₂	direct (N × H)
6. C₂×C₄₃×#339	C₂	semidirect
13. C₂²×M₁₆×C₄₃	C₂²	semidirect
17. C₄₃×#525	C₄	semidirect
20. C₂×C₂²⋊Q₈×C₄₃	C₄	semidirect
21. C₂×C₂²⋊Q₈×C₄₃	C₄	semidirect
22. C₂×#121×C₄₃	C₄	semidirect
23. C₂×#121×C₄₃	C₄	semidirect
31. C₂×#104×C₄₃	C₂²	semidirect
33. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
35. C₄₃×#339	C₂²	semidirect
68. C₂×M₁₆×C₄₃	D₄	semidirect
77. C₂²⋊Q₈×C₄₃	C₂×C₄	semidirect
78. C₂²⋊Q₈×C₄₃	C₂×C₄	semidirect
81. #121×C₄₃	C₂×C₄	semidirect
82. #121×C₄₃	C₂×C₄	semidirect
186. M₁₆×C₄₃	C₂×D₄	semidirect
226. C₂³×C₄₃	#104	semidirect
284. C₂×#1871	C₄₃	direct (N × H)
306. C₂²×C₄₃	C₂×#104	semidirect
321. C₂³×M₁₆	C₂×C₄₃	semidirect
323. C₂²×#104	C₂×C₄₃	semidirect
324. C₂×C₄×C₂²⋊C₄	C₂×C₄₃	semidirect
325. #1871	C₂×C₄₃	direct (N × H)
326. C₂×#339	C₂×C₄₃	semidirect
332. C₂×C₄₃	#1871	direct (N × H)
342. C₂²×M₁₆	C₂²×C₄₃	semidirect
346. #525	C₄×C₄₃	semidirect
349. C₂×C₂²⋊Q₈	C₄×C₄₃	semidirect
350. C₂×C₂²⋊Q₈	C₄×C₄₃	semidirect
351. C₂×#121	C₄×C₄₃	semidirect
352. C₂×#121	C₄×C₄₃	semidirect
360. C₂×#104	C₂²×C₄₃	semidirect
362. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
364. #339	C₂²×C₄₃	semidirect
365. C₄₃	C₂×#1871	direct (N × H)
398. C₂×M₁₆	D₄×C₄₃	semidirect
407. C₂²⋊Q₈	C₂×C₄×C₄₃	semidirect
408. C₂²⋊Q₈	C₂×C₄×C₄₃	semidirect
411. #121	C₂×C₄×C₄₃	semidirect
412. #121	C₂×C₄×C₄₃	semidirect
516. M₁₆	C₂×D₄×C₄₃	semidirect
556. C₂³	#104×C₄₃	semidirect
635. C₂²	C₂×#104×C₄₃	semidirect
655. C₂	C₄₃×#1871	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×M₁₆×C₄₃	2
C₂×C₄₃×#525	2
C₂²×#104×C₄₃	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₄₃×#1871	2
C₂×C₄₃×#339	2
C₂×#1871	43

Subgroups — C2×C43×#1871 #24940918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1871 #24940918