Subgroups — C₂×C₄₃×#2543 #24954835

Order 11008.

4326 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₄₃	C₂	1	2	yes	maximal, complemented
2	C₂²×#121×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2543	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₄₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#388	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₃×#386	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#386	C₂	1	2	yes	maximal, complemented
12	C₂²×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₄₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₄₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#121×C₄₃	—	2	16	no	—
21	C₂×#121×C₄₃	—	2	8	no	—
22	C₂×#121×C₄₃	C₂²	1	8	yes	complemented
23	C₂×#121×C₄₃	C₂²	1	16	yes	complemented
24	C₂×C₄×D₄×C₄₃	—	2	8	no	—
25	C₂×C₄×D₄×C₄₃	C₂²	1	8	yes	complemented
26	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
36	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#398	C₂²	1	8	yes	complemented
38	C₄₃×#397	C₂²	1	8	yes	complemented
39	C₄₃×#394	C₂²	1	8	yes	complemented
40	C₄₃×#392	C₂²	1	8	yes	complemented
41	C₄₃×#388	C₂²	1	16	yes	complemented
42	C₄₃×#386	C₂²	1	16	yes	complemented
43	C₄₃×#386	C₂²	1	16	yes	complemented
44	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#95×C₄₃	C₂²	1	2	yes	—
47	C₂×#95×C₄₃	C₂²	1	2	yes	—
48	C₂×#95×C₄₃	C₂²	1	2	yes	—
49	C₂×#95×C₄₃	C₂²	1	8	yes	complemented
50	C₂⁵×C₄₃	C₂³	1	2	yes	—
51	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
52	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₄₃	—	2	4	no	—
54	C₂²×D₄×C₄₃	—	2	4	no	—
55	C₂²×D₄×C₄₃	—	2	8	no	—
56	C₂²×D₄×C₄₃	—	2	8	no	—
57	C₂²×D₄×C₄₃	—	2	8	no	—
58	C₂²×D₄×C₄₃	—	2	8	no	—
59	C₂²×D₄×C₄₃	—	2	4	no	—
60	C₂²×D₄×C₄₃	—	2	8	no	—
61	C₂²×D₄×C₄₃	—	4	4	no	—
62	C₂²×D₄×C₄₃	—	4	4	no	—
63	C₂²×D₄×C₄₃	D₄	1	8	yes	complemented
64	C₂²×D₄×C₄₃	C₂³	1	8	yes	—
65	C₂²×D₄×C₄₃	C₂³	1	8	yes	—
66	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₄₃	—	2	8	no	—
69	C₂³×C₄×C₄₃	—	2	4	no	—
70	C₂³×C₄×C₄₃	—	2	8	no	—
71	C₂³×C₄×C₄₃	—	4	4	no	—
72	C₂³×C₄×C₄₃	—	4	4	no	—
73	C₂³×C₄×C₄₃	—	4	4	no	—
74	C₂³×C₄×C₄₃	D₄	1	8	yes	complemented
75	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₄₃	C₂³	1	8	yes	—
80	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
86	#121×C₄₃	—	2	64	no	—
87	#121×C₄₃	—	2	32	no	—
88	C₄×D₄×C₄₃	—	2	32	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
90	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
91	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
101	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
102	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
108	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
109	C₂×C₄²×C₄₃	—	2	4	no	—
110	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
111	#95×C₄₃	C₂³	1	8	yes	—
112	#95×C₄₃	C₂³	1	4	yes	—
113	#95×C₄₃	C₂³	1	4	yes	—
114	#95×C₄₃	C₂³	1	8	yes	—
115	#95×C₄₃	C₂³	1	8	yes	—
116	C₂⁴×C₄₃	—	2	4	no	—
117	C₂⁴×C₄₃	—	2	4	no	—
118	C₂⁴×C₄₃	—	2	2	no	—
119	C₂⁴×C₄₃	—	2	2	no	—
120	C₂⁴×C₄₃	—	2	4	no	—
121	C₂⁴×C₄₃	—	2	4	no	—
122	C₂⁴×C₄₃	—	2	4	no	—
123	C₂⁴×C₄₃	—	2	4	no	—
124	C₂⁴×C₄₃	—	2	4	no	—
125	C₂⁴×C₄₃	—	2	4	no	—
126	C₂⁴×C₄₃	—	2	4	no	—
127	C₂⁴×C₄₃	—	2	4	no	—
128	C₂⁴×C₄₃	—	2	4	no	—
129	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
130	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
131	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
132	C₂⁴×C₄₃	#41	1	4	yes	—
133	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
134	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
135	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
136	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
137	C₂×D₄×C₄₃	—	2	8	no	—
138	C₂×D₄×C₄₃	—	2	16	no	—
139	C₂×D₄×C₄₃	—	2	32	no	—
140	C₂×D₄×C₄₃	—	2	8	no	—
141	C₂×D₄×C₄₃	—	2	16	no	—
142	C₂×D₄×C₄₃	—	2	16	no	—
143	C₂×D₄×C₄₃	—	2	16	no	—
144	C₂×D₄×C₄₃	—	2	8	no	—
145	C₂×D₄×C₄₃	—	2	16	no	—
146	C₂×D₄×C₄₃	—	4	8	no	—
147	C₂×D₄×C₄₃	—	4	8	no	—
148	C₂×D₄×C₄₃	—	4	32	no	—
149	C₂×D₄×C₄₃	—	4	16	no	—
150	C₂×D₄×C₄₃	—	4	32	no	—
151	C₂×D₄×C₄₃	C₂×D₄	1	16	yes	complemented
152	C₂²×C₄×C₄₃	—	2	8	no	—
153	C₂²×C₄×C₄₃	—	2	16	no	—
154	C₂²×C₄×C₄₃	—	2	2	no	—
155	C₂²×C₄×C₄₃	—	2	4	no	—
156	C₂²×C₄×C₄₃	—	2	2	no	—
157	C₂²×C₄×C₄₃	—	2	4	no	—
158	C₂²×C₄×C₄₃	—	2	2	no	—
159	C₂²×C₄×C₄₃	—	2	4	no	—
160	C₂²×C₄×C₄₃	—	2	4	no	—
161	C₂²×C₄×C₄₃	—	2	16	no	—
162	C₂²×C₄×C₄₃	—	2	2	no	—
163	C₂²×C₄×C₄₃	—	2	4	no	—
164	C₂²×C₄×C₄₃	—	2	4	no	—
165	C₂²×C₄×C₄₃	—	2	4	no	—
166	C₂²×C₄×C₄₃	—	2	4	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	—	2	4	no	—
171	C₂²×C₄×C₄₃	—	4	16	no	—
172	C₂²×C₄×C₄₃	—	4	8	no	—
173	C₂²×C₄×C₄₃	—	4	8	no	—
174	C₂²×C₄×C₄₃	—	4	8	no	—
175	C₂²×C₄×C₄₃	—	4	32	no	—
176	C₂²×C₄×C₄₃	—	4	16	no	—
177	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₄₃	C₂×D₄	1	16	yes	complemented
181	C₂²×C₄×C₄₃	#41	1	8	yes	—
182	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
190	C₄⋊C₄×C₄₃	—	2	8	no	—
191	C₄⋊C₄×C₄₃	—	2	16	no	—
192	C₄⋊C₄×C₄₃	—	2	8	no	—
193	C₂²⋊C₄×C₄₃	—	2	8	no	—
194	C₂²⋊C₄×C₄₃	—	2	16	no	—
195	C₂²⋊C₄×C₄₃	—	2	16	no	—
196	C₂²⋊C₄×C₄₃	—	2	16	no	—
197	C₂²⋊C₄×C₄₃	—	2	8	no	—
198	C₂²⋊C₄×C₄₃	—	2	16	no	—
199	C₂²⋊C₄×C₄₃	—	4	8	no	—
200	C₄²×C₄₃	—	2	8	no	—
201	C₂³×C₄₃	—	2	8	no	—
202	C₂³×C₄₃	—	2	8	no	—
203	C₂³×C₄₃	—	2	16	no	—
204	C₂³×C₄₃	—	2	16	no	—
205	C₂³×C₄₃	—	2	4	no	—
206	C₂³×C₄₃	—	2	4	no	—
207	C₂³×C₄₃	—	2	8	no	—
208	C₂³×C₄₃	—	2	16	no	—
209	C₂³×C₄₃	—	2	2	no	—
210	C₂³×C₄₃	—	2	2	no	—
211	C₂³×C₄₃	—	2	4	no	—
212	C₂³×C₄₃	—	2	4	no	—
213	C₂³×C₄₃	—	2	4	no	—
214	C₂³×C₄₃	—	2	4	no	—
215	C₂³×C₄₃	—	2	4	no	—
216	C₂³×C₄₃	—	2	4	no	—
217	C₂³×C₄₃	—	2	4	no	—
218	C₂³×C₄₃	—	2	4	no	—
219	C₂³×C₄₃	—	2	4	no	—
220	C₂³×C₄₃	—	4	4	no	—
221	C₂³×C₄₃	—	4	4	no	—
222	C₂³×C₄₃	—	4	8	no	—
223	C₂³×C₄₃	—	4	8	no	—
224	C₂³×C₄₃	—	4	8	no	—
225	C₂³×C₄₃	—	4	8	no	—
226	C₂³×C₄₃	—	4	8	no	—
227	C₂³×C₄₃	—	4	8	no	—
228	C₂³×C₄₃	—	4	8	no	—
229	C₂³×C₄₃	—	4	8	no	—
230	C₂³×C₄₃	#121	1	16	yes	—
231	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
232	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
233	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
234	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
235	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
236	C₂³×C₄₃	C₂×#41	1	4	yes	—
237	C₂³×C₄₃	C₂×#41	1	2	yes	—
238	C₂³×C₄₃	C₂×#41	1	4	yes	—
239	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
240	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
241	D₄×C₄₃	—	2	32	no	—
242	D₄×C₄₃	—	4	32	no	—
243	D₄×C₄₃	—	4	16	no	—
244	D₄×C₄₃	—	4	32	no	—
245	C₂×C₄×C₄₃	—	2	8	no	—
246	C₂×C₄×C₄₃	—	2	8	no	—
247	C₂×C₄×C₄₃	—	2	8	no	—
248	C₂×C₄×C₄₃	—	2	16	no	—
249	C₂×C₄×C₄₃	—	2	2	no	—
250	C₂×C₄×C₄₃	—	2	4	no	—
251	C₂×C₄×C₄₃	—	2	2	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	2	no	—
256	C₂×C₄×C₄₃	—	2	4	no	—
257	C₂×C₄×C₄₃	—	2	2	no	—
258	C₂×C₄×C₄₃	—	2	4	no	—
259	C₂×C₄×C₄₃	—	2	4	no	—
260	C₂×C₄×C₄₃	—	2	4	no	—
261	C₂×C₄×C₄₃	—	2	4	no	—
262	C₂×C₄×C₄₃	—	2	4	no	—
263	C₂×C₄×C₄₃	—	2	4	no	—
264	C₂×C₄×C₄₃	—	2	4	no	—
265	C₂×C₄×C₄₃	—	4	16	no	—
266	C₂×C₄×C₄₃	—	4	32	no	—
267	C₂×C₄×C₄₃	—	4	16	no	—
268	C₂×C₄×C₄₃	—	4	8	no	—
269	C₂×C₄×C₄₃	—	4	4	no	—
270	C₂×C₄×C₄₃	—	4	4	no	—
271	C₂×C₄×C₄₃	—	4	8	no	—
272	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
273	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
274	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₄₃	C₂×#41	1	8	yes	—
276	C₂×#2543	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂²×C₄₃	—	2	4	no	—
278	C₂²×C₄₃	—	2	4	no	—
279	C₂²×C₄₃	—	2	8	no	—
280	C₂²×C₄₃	—	2	8	no	—
281	C₂²×C₄₃	—	2	32	no	—
282	C₂²×C₄₃	—	2	4	no	—
283	C₂²×C₄₃	—	2	8	no	—
284	C₂²×C₄₃	—	4	2	no	—
285	C₂²×C₄₃	—	4	2	no	—
286	C₂²×C₄₃	—	4	4	no	—
287	C₂²×C₄₃	—	4	16	no	—
288	C₂²×C₄₃	—	4	4	no	—
289	C₂²×C₄₃	—	4	4	no	—
290	C₂²×C₄₃	—	4	4	no	—
291	C₂²×C₄₃	—	4	4	no	—
292	C₂²×C₄₃	—	4	4	no	—
293	C₂²×C₄₃	—	4	4	no	—
294	C₂²×C₄₃	—	4	4	no	—
295	C₂²×C₄₃	—	8	16	no	—
296	C₂²×C₄₃	C₂×#121	1	8	yes	—
297	C₂²×C₄₃	C₂×#121	1	4	yes	—
298	C₂²×C₄₃	#532	1	4	yes	—
299	C₂²×C₄₃	#534	1	4	yes	—
300	C₂²×C₄₃	#546	1	8	yes	—
301	C₂²×C₄₃	#553	1	8	yes	—
302	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
303	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
304	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
305	C₂²×C₄₃	C₂²×#41	1	2	yes	—
306	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
307	C₄×C₄₃	—	2	4	no	—
308	C₄×C₄₃	—	2	4	no	—
309	C₄×C₄₃	—	2	4	no	—
310	C₄×C₄₃	—	2	8	no	—
311	C₄×C₄₃	—	4	4	no	—
312	C₄×C₄₃	—	4	2	no	—
313	C₄×C₄₃	—	4	2	no	—
314	C₄×C₄₃	—	4	4	no	—
315	C₂²×#121	C₂×C₄₃	1	2	yes	complemented
316	C₂²×#121	C₂×C₄₃	1	1	yes	characteristic, complemented
317	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic, complemented
318	#2543	C₂×C₄₃	1	16	yes	direct product factor
319	C₂×#398	C₂×C₄₃	1	1	yes	characteristic, complemented
320	C₂×#397	C₂×C₄₃	1	1	yes	characteristic, complemented
321	C₂×#394	C₂×C₄₃	1	1	yes	characteristic, complemented
322	C₂×#392	C₂×C₄₃	1	1	yes	characteristic, complemented
323	C₂×#388	C₂×C₄₃	1	2	yes	complemented
324	C₂×#386	C₂×C₄₃	1	2	yes	complemented
325	C₂×#386	C₂×C₄₃	1	2	yes	complemented
326	C₂²×#95	C₂×C₄₃	1	1	yes	characteristic, complemented
327	C₂×C₄₃	—	2	8	no	—
328	C₂×C₄₃	—	4	4	no	—
329	C₂×C₄₃	—	8	4	no	—
330	C₂×C₄₃	#2543	1	8	yes	direct product factor
331	C₂×C₄₃	C₂²×#121	1	1	yes	characteristic
332	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
333	C₂×C₄₃	C₂×#534	1	1	yes	characteristic
334	C₂×C₄₃	C₂×#546	1	2	yes	—
335	C₂×C₄₃	C₂×#553	1	2	yes	—
336	C₂³×D₄	C₂²×C₄₃	1	2	yes	—
337	C₂³×D₄	C₂²×C₄₃	1	2	yes	—
338	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
339	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
340	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
341	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
342	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
343	C₂×#121	—	2	16	no	—
344	C₂×#121	—	2	8	no	—
345	C₂×#121	C₂²×C₄₃	1	8	yes	complemented
346	C₂×#121	C₂²×C₄₃	1	16	yes	complemented
347	C₂×C₄×D₄	—	2	8	no	—
348	C₂×C₄×D₄	C₂²×C₄₃	1	8	yes	complemented
349	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
350	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
351	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
352	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
355	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
356	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
358	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
359	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
360	#398	C₂²×C₄₃	1	8	yes	complemented
361	#397	C₂²×C₄₃	1	8	yes	complemented
362	#394	C₂²×C₄₃	1	8	yes	complemented
363	#392	C₂²×C₄₃	1	8	yes	complemented
364	#388	C₂²×C₄₃	1	16	yes	complemented
365	#386	C₂²×C₄₃	1	16	yes	complemented
366	#386	C₂²×C₄₃	1	16	yes	complemented
367	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
368	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
369	C₂×#95	C₂²×C₄₃	1	2	yes	—
370	C₂×#95	C₂²×C₄₃	1	2	yes	—
371	C₂×#95	C₂²×C₄₃	1	2	yes	—
372	C₂×#95	C₂²×C₄₃	1	8	yes	complemented
373	C₄₃	C₂×#2543	1	1	yes	characteristic, direct product factor, Sylow
374	C₂⁵	C₂³×C₄₃	1	2	yes	—
375	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
376	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
377	C₂²×D₄	—	2	4	no	—
378	C₂²×D₄	—	2	4	no	—
379	C₂²×D₄	—	2	8	no	—
380	C₂²×D₄	—	2	8	no	—
381	C₂²×D₄	—	2	8	no	—
382	C₂²×D₄	—	2	8	no	—
383	C₂²×D₄	—	2	4	no	—
384	C₂²×D₄	—	2	8	no	—
385	C₂²×D₄	—	4	4	no	—
386	C₂²×D₄	—	4	4	no	—
387	C₂²×D₄	D₄×C₄₃	1	8	yes	complemented
388	C₂²×D₄	C₂³×C₄₃	1	8	yes	—
389	C₂²×D₄	C₂³×C₄₃	1	8	yes	—
390	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
391	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
392	C₂³×C₄	—	2	8	no	—
393	C₂³×C₄	—	2	4	no	—
394	C₂³×C₄	—	2	8	no	—
395	C₂³×C₄	—	4	4	no	—
396	C₂³×C₄	—	4	4	no	—
397	C₂³×C₄	—	4	4	no	—
398	C₂³×C₄	D₄×C₄₃	1	8	yes	complemented
399	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
402	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
403	C₂³×C₄	C₂³×C₄₃	1	8	yes	—
404	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
408	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
409	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
410	#121	—	2	64	no	—
411	#121	—	2	32	no	—
412	C₄×D₄	—	2	32	no	—
413	C₂×C₄⋊C₄	—	2	4	no	—
414	C₂×C₄⋊C₄	—	2	8	no	—
415	C₂×C₄⋊C₄	—	2	4	no	—
416	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
418	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
419	C₂×C₂²⋊C₄	—	2	4	no	—
420	C₂×C₂²⋊C₄	—	2	8	no	—
421	C₂×C₂²⋊C₄	—	2	4	no	—
422	C₂×C₂²⋊C₄	—	2	8	no	—
423	C₂×C₂²⋊C₄	—	2	8	no	—
424	C₂×C₂²⋊C₄	—	2	8	no	—
425	C₂×C₂²⋊C₄	—	4	4	no	—
426	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
433	C₂×C₄²	—	2	4	no	—
434	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
435	#95	C₂³×C₄₃	1	8	yes	—
436	#95	C₂³×C₄₃	1	4	yes	—
437	#95	C₂³×C₄₃	1	4	yes	—
438	#95	C₂³×C₄₃	1	8	yes	—
439	#95	C₂³×C₄₃	1	8	yes	—
440	C₂⁴	—	2	4	no	—
441	C₂⁴	—	2	4	no	—
442	C₂⁴	—	2	2	no	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	4	no	—
445	C₂⁴	—	2	4	no	—
446	C₂⁴	—	2	4	no	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	2	4	no	—
450	C₂⁴	—	2	4	no	—
451	C₂⁴	—	2	4	no	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
454	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
455	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
456	C₂⁴	#41×C₄₃	1	4	yes	—
457	C₂⁴	C₂⁴×C₄₃	1	4	yes	—
458	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
459	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
460	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
461	C₂×D₄	—	2	32	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	16	no	—
465	C₂×D₄	—	2	16	no	—
466	C₂×D₄	—	2	16	no	—
467	C₂×D₄	—	2	16	no	—
468	C₂×D₄	—	2	8	no	—
469	C₂×D₄	—	2	16	no	—
470	C₂×D₄	—	4	8	no	—
471	C₂×D₄	—	4	8	no	—
472	C₂×D₄	—	4	32	no	—
473	C₂×D₄	—	4	16	no	—
474	C₂×D₄	—	4	32	no	—
475	C₂×D₄	C₂×D₄×C₄₃	1	16	yes	complemented
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	4	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	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	16	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	8	no	—
494	C₂²×C₄	—	2	16	no	—
495	C₂²×C₄	—	4	8	no	—
496	C₂²×C₄	—	4	8	no	—
497	C₂²×C₄	—	4	8	no	—
498	C₂²×C₄	—	4	16	no	—
499	C₂²×C₄	—	4	32	no	—
500	C₂²×C₄	—	4	16	no	—
501	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
502	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
503	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
504	C₂²×C₄	C₂×D₄×C₄₃	1	16	yes	complemented
505	C₂²×C₄	#41×C₄₃	1	8	yes	—
506	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
514	C₄⋊C₄	—	2	8	no	—
515	C₄⋊C₄	—	2	16	no	—
516	C₄⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	16	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	2	16	no	—
523	C₂²⋊C₄	—	4	8	no	—
524	C₄²	—	2	8	no	—
525	C₂³	—	2	8	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	16	no	—
528	C₂³	—	2	16	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	8	no	—
532	C₂³	—	2	16	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	4	4	no	—
545	C₂³	—	4	4	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	4	8	no	—
550	C₂³	—	4	8	no	—
551	C₂³	—	4	8	no	—
552	C₂³	—	4	8	no	—
553	C₂³	—	4	8	no	—
554	C₂³	#121×C₄₃	1	16	yes	—
555	C₂³	C₂²×D₄×C₄₃	1	4	yes	—
556	C₂³	C₂²×D₄×C₄₃	1	4	yes	—
557	C₂³	C₂²×D₄×C₄₃	1	4	yes	—
558	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
559	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
560	C₂³	C₂×#41×C₄₃	1	4	yes	—
561	C₂³	C₂×#41×C₄₃	1	2	yes	—
562	C₂³	C₂×#41×C₄₃	1	4	yes	—
563	C₂³	H(5,𝔽₂)×C₄₃	1	4	yes	—
564	C₂³	C₂⁵×C₄₃	1	1	yes	characteristic
565	D₄	—	2	32	no	—
566	D₄	—	4	32	no	—
567	D₄	—	4	16	no	—
568	D₄	—	4	32	no	—
569	C₂×C₄	—	2	8	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	16	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	4	16	no	—
590	C₂×C₄	—	4	32	no	—
591	C₂×C₄	—	4	16	no	—
592	C₂×C₄	—	4	8	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
597	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
598	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
599	C₂×C₄	C₂×#41×C₄₃	1	8	yes	—
600	C₂²	—	2	4	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	8	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	2	32	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	8	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	16	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	4	4	no	—
618	C₂²	—	8	16	no	—
619	C₂²	C₂×#121×C₄₃	1	8	yes	—
620	C₂²	C₂×#121×C₄₃	1	4	yes	—
621	C₂²	C₄₃×#532	1	4	yes	—
622	C₂²	C₄₃×#534	1	4	yes	—
623	C₂²	C₄₃×#546	1	8	yes	—
624	C₂²	C₄₃×#553	1	8	yes	—
625	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
626	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
627	C₂²	C₂²×#41×C₄₃	1	1	yes	characteristic
628	C₂²	C₂²×#41×C₄₃	1	2	yes	—
629	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	2	yes	—
630	C₄	—	2	4	no	—
631	C₄	—	2	4	no	—
632	C₄	—	2	4	no	—
633	C₄	—	2	8	no	—
634	C₄	—	4	4	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	4	no	—
638	C₂	—	2	8	no	—
639	C₂	—	4	4	no	—
640	C₂	—	8	4	no	—
641	C₂	C₄₃×#2543	1	8	yes	direct product factor
642	C₂	C₂²×#121×C₄₃	1	1	yes	characteristic
643	C₂	C₂×C₄₃×#532	1	1	yes	characteristic
644	C₂	C₂×C₄₃×#534	1	1	yes	characteristic
645	C₂	C₂×C₄₃×#546	1	2	yes	—
646	C₂	C₂×C₄₃×#553	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#121×C₄₃	C₂	semidirect
2. C₂²×#121×C₄₃	C₂	semidirect
3. C₂²×C₄×D₄×C₄₃	C₂	semidirect
4. C₄₃×#2543	C₂	direct (N × H)
5. C₂×C₄₃×#398	C₂	semidirect
6. C₂×C₄₃×#397	C₂	semidirect
7. C₂×C₄₃×#394	C₂	semidirect
8. C₂×C₄₃×#392	C₂	semidirect
9. C₂×C₄₃×#388	C₂	semidirect
10. C₂×C₄₃×#386	C₂	semidirect
11. C₂×C₄₃×#386	C₂	semidirect
12. C₂²×#95×C₄₃	C₂	semidirect
22. C₂×#121×C₄₃	C₂²	semidirect
23. C₂×#121×C₄₃	C₂²	semidirect
25. C₂×C₄×D₄×C₄₃	C₂²	semidirect
37. C₄₃×#398	C₂²	semidirect
38. C₄₃×#397	C₂²	semidirect
39. C₄₃×#394	C₂²	semidirect
40. C₄₃×#392	C₂²	semidirect
41. C₄₃×#388	C₂²	semidirect
42. C₄₃×#386	C₂²	semidirect
43. C₄₃×#386	C₂²	semidirect
49. C₂×#95×C₄₃	C₂²	semidirect
63. C₂²×D₄×C₄₃	D₄	semidirect
74. C₂³×C₄×C₄₃	D₄	semidirect
151. C₂×D₄×C₄₃	C₂×D₄	semidirect
180. C₂²×C₄×C₄₃	C₂×D₄	semidirect
276. C₂×#2543	C₄₃	direct (N × H)
315. C₂²×#121	C₂×C₄₃	semidirect
316. C₂²×#121	C₂×C₄₃	semidirect
317. C₂²×C₄×D₄	C₂×C₄₃	semidirect
318. #2543	C₂×C₄₃	direct (N × H)
319. C₂×#398	C₂×C₄₃	semidirect
320. C₂×#397	C₂×C₄₃	semidirect
321. C₂×#394	C₂×C₄₃	semidirect
322. C₂×#392	C₂×C₄₃	semidirect
323. C₂×#388	C₂×C₄₃	semidirect
324. C₂×#386	C₂×C₄₃	semidirect
325. C₂×#386	C₂×C₄₃	semidirect
326. C₂²×#95	C₂×C₄₃	semidirect
330. C₂×C₄₃	#2543	direct (N × H)
345. C₂×#121	C₂²×C₄₃	semidirect
346. C₂×#121	C₂²×C₄₃	semidirect
348. C₂×C₄×D₄	C₂²×C₄₃	semidirect
360. #398	C₂²×C₄₃	semidirect
361. #397	C₂²×C₄₃	semidirect
362. #394	C₂²×C₄₃	semidirect
363. #392	C₂²×C₄₃	semidirect
364. #388	C₂²×C₄₃	semidirect
365. #386	C₂²×C₄₃	semidirect
366. #386	C₂²×C₄₃	semidirect
372. C₂×#95	C₂²×C₄₃	semidirect
373. C₄₃	C₂×#2543	direct (N × H)
387. C₂²×D₄	D₄×C₄₃	semidirect
398. C₂³×C₄	D₄×C₄₃	semidirect
475. C₂×D₄	C₂×D₄×C₄₃	semidirect
504. C₂²×C₄	C₂×D₄×C₄₃	semidirect
641. C₂	C₄₃×#2543	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#121×C₄₃	2
C₂²×C₄×D₄×C₄₃	2
C₄₃×#2543	2
C₂×C₄₃×#398	2
C₂×C₄₃×#397	2
C₂×C₄₃×#394	2
C₂×C₄₃×#392	2
C₂×C₄₃×#388	2
C₂×C₄₃×#386	2
C₂²×#95×C₄₃	2
C₂×#2543	43

Subgroups — C2×C43×#2543 #24954835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#2543 #24954835