Subgroups — C₂×C₄₃×#1439 #24933853

Order 11008.

4926 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₄₃	C₂	1	2	yes	maximal
3	C₂³×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#95×C₄₃	C₂	1	2	yes	maximal, complemented
5	C₂²×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1439	C₂	1	8	yes	maximal, direct product factor
7	C₂⁶×C₄₃	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	—	2	8	no	—
13	C₂²×C₄⋊C₄×C₄₃	—	2	4	no	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	complemented
15	C₂²×C₂²⋊C₄×C₄₃	—	2	8	no	—
16	C₂²×C₂²⋊C₄×C₄₃	—	2	8	no	—
17	C₂²×C₂²⋊C₄×C₄₃	—	2	8	no	—
18	C₂²×C₂²⋊C₄×C₄₃	—	2	4	no	—
19	C₂²×C₂²⋊C₄×C₄₃	—	2	4	no	—
20	C₂²×C₂²⋊C₄×C₄₃	C₄	1	8	yes	complemented
21	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	8	yes	—
22	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
23	C₂×#95×C₄₃	—	2	8	no	—
24	C₂×#95×C₄₃	—	2	4	no	—
25	C₂×#95×C₄₃	C₂²	1	8	yes	complemented
26	C₂×#95×C₄₃	C₂²	1	4	yes	complemented
27	C₂⁵×C₄₃	—	2	2	no	—
28	C₂⁵×C₄₃	—	2	2	no	—
29	C₂⁵×C₄₃	—	2	4	no	—
30	C₂⁵×C₄₃	—	2	4	no	—
31	C₂⁵×C₄₃	—	2	2	no	—
32	C₂⁵×C₄₃	—	2	2	no	—
33	C₂⁵×C₄₃	—	2	4	no	—
34	C₂⁵×C₄₃	—	2	4	no	—
35	C₂⁵×C₄₃	C₂×C₄	1	4	yes	—
36	C₂⁵×C₄₃	D₄	1	4	yes	—
37	C₂⁵×C₄₃	Q₈	1	4	yes	—
38	C₂⁵×C₄₃	C₂³	1	2	yes	—
39	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	—	2	4	no	—
41	C₂³×C₄×C₄₃	—	2	4	no	—
42	C₂³×C₄×C₄₃	—	2	2	no	—
43	C₂³×C₄×C₄₃	—	2	2	no	—
44	C₂³×C₄×C₄₃	—	2	4	no	—
45	C₂³×C₄×C₄₃	—	2	4	no	—
46	C₂³×C₄×C₄₃	—	2	4	no	—
47	C₂³×C₄×C₄₃	—	2	4	no	—
48	C₂³×C₄×C₄₃	—	2	4	no	—
49	C₂³×C₄×C₄₃	—	2	4	no	—
50	C₂³×C₄×C₄₃	—	2	4	no	—
51	C₂³×C₄×C₄₃	—	2	4	no	—
52	C₂³×C₄×C₄₃	—	2	4	no	—
53	C₂³×C₄×C₄₃	—	2	4	no	—
54	C₂³×C₄×C₄₃	—	2	4	no	—
55	C₂³×C₄×C₄₃	—	2	4	no	—
56	C₂³×C₄×C₄₃	—	2	4	no	—
57	C₂³×C₄×C₄₃	—	2	4	no	—
58	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
59	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
60	C₂³×C₄×C₄₃	D₄	1	8	yes	—
61	C₂³×C₄×C₄₃	D₄	1	8	yes	—
62	C₂³×C₄×C₄₃	D₄	1	4	yes	—
63	C₂³×C₄×C₄₃	D₄	1	4	yes	—
64	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	—	2	32	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	16	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	64	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	32	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
78	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	16	yes	complemented
79	#95×C₄₃	—	2	16	no	—
80	#95×C₄₃	—	2	8	no	—
81	C₂⁴×C₄₃	—	2	8	no	—
82	C₂⁴×C₄₃	—	2	8	no	—
83	C₂⁴×C₄₃	—	2	16	no	—
84	C₂⁴×C₄₃	—	2	16	no	—
85	C₂⁴×C₄₃	—	2	16	no	—
86	C₂⁴×C₄₃	—	2	8	no	—
87	C₂⁴×C₄₃	—	2	8	no	—
88	C₂⁴×C₄₃	—	2	8	no	—
89	C₂⁴×C₄₃	—	2	8	no	—
90	C₂⁴×C₄₃	—	2	16	no	—
91	C₂⁴×C₄₃	—	2	16	no	—
92	C₂⁴×C₄₃	—	2	16	no	—
93	C₂⁴×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	—	2	2	no	—
95	C₂⁴×C₄₃	—	2	4	no	—
96	C₂⁴×C₄₃	—	2	4	no	—
97	C₂⁴×C₄₃	—	2	2	no	—
98	C₂⁴×C₄₃	—	2	2	no	—
99	C₂⁴×C₄₃	—	2	4	no	—
100	C₂⁴×C₄₃	—	2	4	no	—
101	C₂⁴×C₄₃	—	4	4	no	—
102	C₂⁴×C₄₃	—	4	8	no	—
103	C₂⁴×C₄₃	—	4	8	no	—
104	C₂⁴×C₄₃	—	4	8	no	—
105	C₂⁴×C₄₃	—	4	4	no	—
106	C₂⁴×C₄₃	—	4	8	no	—
107	C₂⁴×C₄₃	—	4	8	no	—
108	C₂⁴×C₄₃	—	4	4	no	—
109	C₂⁴×C₄₃	—	4	8	no	—
110	C₂⁴×C₄₃	—	4	4	no	—
111	C₂⁴×C₄₃	C₄⋊C₄	1	16	yes	complemented
112	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
113	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
115	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
116	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
117	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
118	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
119	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
120	C₂⁴×C₄₃	C₂×Q₈	1	4	yes	—
121	C₂⁴×C₄₃	C₂×Q₈	1	2	yes	—
122	C₂⁴×C₄₃	#41	1	2	yes	—
123	C₂⁴×C₄₃	#41	1	2	yes	—
124	C₂⁴×C₄₃	#41	1	4	yes	—
125	C₂⁴×C₄₃	#41	1	4	yes	—
126	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	—	2	8	no	—
128	C₂²×C₄×C₄₃	—	2	16	no	—
129	C₂²×C₄×C₄₃	—	2	16	no	—
130	C₂²×C₄×C₄₃	—	2	8	no	—
131	C₂²×C₄×C₄₃	—	2	16	no	—
132	C₂²×C₄×C₄₃	—	2	16	no	—
133	C₂²×C₄×C₄₃	—	2	16	no	—
134	C₂²×C₄×C₄₃	—	2	16	no	—
135	C₂²×C₄×C₄₃	—	2	16	no	—
136	C₂²×C₄×C₄₃	—	2	16	no	—
137	C₂²×C₄×C₄₃	—	2	8	no	—
138	C₂²×C₄×C₄₃	—	2	16	no	—
139	C₂²×C₄×C₄₃	—	2	4	no	—
140	C₂²×C₄×C₄₃	—	2	4	no	—
141	C₂²×C₄×C₄₃	—	2	4	no	—
142	C₂²×C₄×C₄₃	—	2	4	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	4	no	—
147	C₂²×C₄×C₄₃	—	2	4	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	4	no	—
152	C₂²×C₄×C₄₃	—	2	4	no	—
153	C₂²×C₄×C₄₃	—	2	4	no	—
154	C₂²×C₄×C₄₃	—	2	4	no	—
155	C₂²×C₄×C₄₃	—	2	4	no	—
156	C₂²×C₄×C₄₃	—	2	4	no	—
157	C₂²×C₄×C₄₃	—	4	8	no	—
158	C₂²×C₄×C₄₃	—	4	8	no	—
159	C₂²×C₄×C₄₃	—	4	8	no	—
160	C₂²×C₄×C₄₃	—	4	8	no	—
161	C₂²×C₄×C₄₃	—	4	8	no	—
162	C₂²×C₄×C₄₃	—	4	8	no	—
163	C₂²×C₄×C₄₃	—	4	8	no	—
164	C₂²×C₄×C₄₃	—	4	8	no	—
165	C₂²×C₄×C₄₃	—	4	4	no	—
166	C₂²×C₄×C₄₃	—	4	4	no	—
167	C₂²×C₄×C₄₃	—	4	8	no	—
168	C₂²×C₄×C₄₃	C₂²⋊C₄	1	16	yes	complemented
169	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
172	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
173	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
175	C₄⋊C₄×C₄₃	—	2	32	no	—
176	C₂²⋊C₄×C₄₃	—	2	64	no	—
177	C₂²⋊C₄×C₄₃	—	2	32	no	—
178	C₂³×C₄₃	—	2	4	no	—
179	C₂³×C₄₃	—	2	4	no	—
180	C₂³×C₄₃	—	2	8	no	—
181	C₂³×C₄₃	—	2	8	no	—
182	C₂³×C₄₃	—	2	8	no	—
183	C₂³×C₄₃	—	2	4	no	—
184	C₂³×C₄₃	—	2	4	no	—
185	C₂³×C₄₃	—	2	4	no	—
186	C₂³×C₄₃	—	2	4	no	—
187	C₂³×C₄₃	—	2	8	no	—
188	C₂³×C₄₃	—	2	8	no	—
189	C₂³×C₄₃	—	2	8	no	—
190	C₂³×C₄₃	—	2	32	no	—
191	C₂³×C₄₃	—	2	64	no	—
192	C₂³×C₄₃	—	4	2	no	—
193	C₂³×C₄₃	—	4	4	no	—
194	C₂³×C₄₃	—	4	4	no	—
195	C₂³×C₄₃	—	4	4	no	—
196	C₂³×C₄₃	—	4	4	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	—	4	4	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	4	no	—
201	C₂³×C₄₃	—	4	2	no	—
202	C₂³×C₄₃	—	4	16	no	—
203	C₂³×C₄₃	—	4	32	no	—
204	C₂³×C₄₃	—	4	16	no	—
205	C₂³×C₄₃	—	4	16	no	—
206	C₂³×C₄₃	—	4	16	no	—
207	C₂³×C₄₃	—	4	32	no	—
208	C₂³×C₄₃	—	4	32	no	—
209	C₂³×C₄₃	—	4	16	no	—
210	C₂³×C₄₃	—	4	16	no	—
211	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
212	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
213	C₂³×C₄₃	C₂×C₄⋊C₄	1	8	yes	complemented
214	C₂³×C₄₃	#117	1	4	yes	—
215	C₂³×C₄₃	C₄×D₄	1	8	yes	—
216	C₂³×C₄₃	C₄×D₄	1	8	yes	—
217	C₂³×C₄₃	#120	1	8	yes	—
218	C₂³×C₄₃	#120	1	4	yes	—
219	C₂³×C₄₃	#121	1	4	yes	—
220	C₂³×C₄₃	#121	1	4	yes	—
221	C₂³×C₄₃	#121	1	8	yes	—
222	C₂³×C₄₃	#121	1	8	yes	—
223	C₂³×C₄₃	#121	1	8	yes	—
224	C₂³×C₄₃	C₂²⋊Q₈	1	4	yes	—
225	C₂³×C₄₃	C₂²⋊Q₈	1	4	yes	—
226	C₂³×C₄₃	C₂²⋊Q₈	1	8	yes	—
227	C₂³×C₄₃	C₂²⋊Q₈	1	8	yes	—
228	C₂³×C₄₃	#123	1	8	yes	—
229	C₂³×C₄₃	#123	1	4	yes	—
230	C₂³×C₄₃	#123	1	8	yes	—
231	C₂³×C₄₃	#124	1	8	yes	—
232	C₂³×C₄₃	#124	1	4	yes	—
233	C₂³×C₄₃	#126	1	8	yes	—
234	C₂³×C₄₃	#127	1	4	yes	—
235	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
236	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
237	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
238	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
239	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
240	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
241	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
242	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
243	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
244	C₂³×C₄₃	C₂×#41	1	2	yes	—
245	C₂³×C₄₃	C₂×#41	1	2	yes	—
246	C₂×C₄×C₄₃	—	2	8	no	—
247	C₂×C₄×C₄₃	—	2	4	no	—
248	C₂×C₄×C₄₃	—	2	8	no	—
249	C₂×C₄×C₄₃	—	2	4	no	—
250	C₂×C₄×C₄₃	—	2	32	no	—
251	C₂×C₄×C₄₃	—	2	4	no	—
252	C₂×C₄×C₄₃	—	2	8	no	—
253	C₂×C₄×C₄₃	—	2	8	no	—
254	C₂×C₄×C₄₃	—	2	8	no	—
255	C₂×C₄×C₄₃	—	2	8	no	—
256	C₂×C₄×C₄₃	—	2	8	no	—
257	C₂×C₄×C₄₃	—	2	8	no	—
258	C₂×C₄×C₄₃	—	2	8	no	—
259	C₂×C₄×C₄₃	—	4	4	no	—
260	C₂×C₄×C₄₃	—	4	4	no	—
261	C₂×C₄×C₄₃	—	4	4	no	—
262	C₂×C₄×C₄₃	—	4	4	no	—
263	C₂×C₄×C₄₃	—	4	4	no	—
264	C₂×C₄×C₄₃	—	4	4	no	—
265	C₂×C₄×C₄₃	—	4	4	no	—
266	C₂×C₄×C₄₃	—	4	4	no	—
267	C₂×C₄×C₄₃	—	4	2	no	—
268	C₂×C₄×C₄₃	—	4	4	no	—
269	C₂×C₄×C₄₃	—	4	2	no	—
270	C₂×C₄×C₄₃	—	4	16	no	—
271	C₂×C₄×C₄₃	—	4	32	no	—
272	C₂×C₄×C₄₃	—	4	32	no	—
273	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	complemented
274	C₂×#1439	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂²×C₄₃	—	2	8	no	—
276	C₂²×C₄₃	—	2	16	no	—
277	C₂²×C₄₃	—	4	4	no	—
278	C₂²×C₄₃	—	4	4	no	—
279	C₂²×C₄₃	—	4	8	no	—
280	C₂²×C₄₃	—	4	8	no	—
281	C₂²×C₄₃	—	4	4	no	—
282	C₂²×C₄₃	—	4	4	no	—
283	C₂²×C₄₃	—	4	64	no	—
284	C₂²×C₄₃	—	4	4	no	—
285	C₂²×C₄₃	—	4	8	no	—
286	C₂²×C₄₃	—	4	4	no	—
287	C₂²×C₄₃	#380	1	8	yes	—
288	C₂²×C₄₃	#385	1	16	yes	—
289	C₂²×C₄₃	#386	1	8	yes	—
290	C₂²×C₄₃	#388	1	16	yes	—
291	C₂²×C₄₃	#390	1	8	yes	—
292	C₂²×C₄₃	#392	1	8	yes	—
293	C₂²×C₄₃	#393	1	8	yes	—
294	C₂²×C₄₃	#394	1	16	yes	—
295	C₂²×C₄₃	#396	1	16	yes	—
296	C₂²×C₄₃	#397	1	8	yes	—
297	C₂²×C₄₃	#399	1	8	yes	—
298	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
300	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
301	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
302	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
303	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
304	C₂²×C₄₃	C₂×#120	1	2	yes	—
305	C₂²×C₄₃	C₂×#121	1	2	yes	—
306	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
307	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
308	C₂²×C₄₃	C₂×#121	1	2	yes	—
309	C₂²×C₄₃	C₂×#121	1	2	yes	—
310	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
311	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
312	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
313	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
314	C₂²×C₄₃	C₂×#123	1	2	yes	—
315	C₂²×C₄₃	C₂×#123	1	2	yes	—
316	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
317	C₂²×C₄₃	C₂×#124	1	2	yes	—
318	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
319	C₂²×C₄₃	C₂×#126	1	2	yes	—
320	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
321	C₄×C₄₃	—	2	8	no	—
322	C₄×C₄₃	—	4	8	no	—
323	C₄×C₄₃	—	4	8	no	—
324	C₄×C₄₃	—	4	4	no	—
325	C₂³×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
326	C₂³×C₂²⋊C₄	C₂×C₄₃	1	2	yes	—
327	C₂³×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic
328	C₂²×#95	C₂×C₄₃	1	2	yes	complemented
329	C₂²×#95	C₂×C₄₃	1	1	yes	characteristic, complemented
330	#1439	C₂×C₄₃	1	8	yes	direct product factor
331	C₂×C₄₃	—	4	8	no	—
332	C₂×C₄₃	#1439	1	16	yes	direct product factor
333	C₂×C₄₃	C₂×#380	1	1	yes	characteristic
334	C₂×C₄₃	C₂×#385	1	2	yes	—
335	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
336	C₂×C₄₃	C₂×#388	1	2	yes	—
337	C₂×C₄₃	C₂×#390	1	1	yes	characteristic
338	C₂×C₄₃	C₂×#392	1	1	yes	characteristic
339	C₂×C₄₃	C₂×#393	1	1	yes	characteristic
340	C₂×C₄₃	C₂×#394	1	2	yes	—
341	C₂×C₄₃	C₂×#396	1	2	yes	—
342	C₂×C₄₃	C₂×#397	1	1	yes	characteristic
343	C₂×C₄₃	C₂×#399	1	1	yes	characteristic
344	C₂⁶	C₂²×C₄₃	1	1	yes	characteristic
345	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
346	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
347	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
348	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
349	C₂²×C₄⋊C₄	—	2	8	no	—
350	C₂²×C₄⋊C₄	—	2	4	no	—
351	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	complemented
352	C₂²×C₂²⋊C₄	—	2	8	no	—
353	C₂²×C₂²⋊C₄	—	2	8	no	—
354	C₂²×C₂²⋊C₄	—	2	8	no	—
355	C₂²×C₂²⋊C₄	—	2	4	no	—
356	C₂²×C₂²⋊C₄	—	2	4	no	—
357	C₂²×C₂²⋊C₄	C₄×C₄₃	1	8	yes	complemented
358	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	8	yes	—
359	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
360	C₂×#95	—	2	8	no	—
361	C₂×#95	—	2	4	no	—
362	C₂×#95	C₂²×C₄₃	1	8	yes	complemented
363	C₂×#95	C₂²×C₄₃	1	4	yes	complemented
364	C₄₃	C₂×#1439	1	1	yes	characteristic, direct product factor, Sylow
365	C₂⁵	—	2	2	no	—
366	C₂⁵	—	2	2	no	—
367	C₂⁵	—	2	4	no	—
368	C₂⁵	—	2	4	no	—
369	C₂⁵	—	2	2	no	—
370	C₂⁵	—	2	2	no	—
371	C₂⁵	—	2	4	no	—
372	C₂⁵	—	2	4	no	—
373	C₂⁵	C₂×C₄×C₄₃	1	4	yes	—
374	C₂⁵	D₄×C₄₃	1	4	yes	—
375	C₂⁵	Q₈×C₄₃	1	4	yes	—
376	C₂⁵	C₂³×C₄₃	1	2	yes	—
377	C₂⁵	C₂³×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	2	no	—
382	C₂³×C₄	—	2	4	no	—
383	C₂³×C₄	—	2	4	no	—
384	C₂³×C₄	—	2	4	no	—
385	C₂³×C₄	—	2	4	no	—
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	—	2	4	no	—
388	C₂³×C₄	—	2	4	no	—
389	C₂³×C₄	—	2	4	no	—
390	C₂³×C₄	—	2	4	no	—
391	C₂³×C₄	—	2	4	no	—
392	C₂³×C₄	—	2	4	no	—
393	C₂³×C₄	—	2	4	no	—
394	C₂³×C₄	—	2	4	no	—
395	C₂³×C₄	—	2	4	no	—
396	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
397	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
398	C₂³×C₄	D₄×C₄₃	1	8	yes	—
399	C₂³×C₄	D₄×C₄₃	1	8	yes	—
400	C₂³×C₄	D₄×C₄₃	1	4	yes	—
401	C₂³×C₄	D₄×C₄₃	1	4	yes	—
402	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
403	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
404	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
405	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
406	C₂×C₄⋊C₄	—	2	32	no	—
407	C₂×C₄⋊C₄	—	2	16	no	—
408	C₂×C₄⋊C₄	—	2	8	no	—
409	C₂×C₂²⋊C₄	—	2	64	no	—
410	C₂×C₂²⋊C₄	—	2	16	no	—
411	C₂×C₂²⋊C₄	—	2	32	no	—
412	C₂×C₂²⋊C₄	—	2	16	no	—
413	C₂×C₂²⋊C₄	—	2	16	no	—
414	C₂×C₂²⋊C₄	—	2	8	no	—
415	C₂×C₂²⋊C₄	—	2	8	no	—
416	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	16	yes	complemented
417	#95	—	2	16	no	—
418	#95	—	2	8	no	—
419	C₂⁴	—	2	8	no	—
420	C₂⁴	—	2	8	no	—
421	C₂⁴	—	2	16	no	—
422	C₂⁴	—	2	16	no	—
423	C₂⁴	—	2	16	no	—
424	C₂⁴	—	2	8	no	—
425	C₂⁴	—	2	8	no	—
426	C₂⁴	—	2	8	no	—
427	C₂⁴	—	2	8	no	—
428	C₂⁴	—	2	16	no	—
429	C₂⁴	—	2	16	no	—
430	C₂⁴	—	2	16	no	—
431	C₂⁴	—	2	2	no	—
432	C₂⁴	—	2	2	no	—
433	C₂⁴	—	2	4	no	—
434	C₂⁴	—	2	4	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	2	no	—
437	C₂⁴	—	2	4	no	—
438	C₂⁴	—	2	4	no	—
439	C₂⁴	—	4	4	no	—
440	C₂⁴	—	4	8	no	—
441	C₂⁴	—	4	8	no	—
442	C₂⁴	—	4	8	no	—
443	C₂⁴	—	4	4	no	—
444	C₂⁴	—	4	8	no	—
445	C₂⁴	—	4	8	no	—
446	C₂⁴	—	4	4	no	—
447	C₂⁴	—	4	8	no	—
448	C₂⁴	—	4	4	no	—
449	C₂⁴	C₄⋊C₄×C₄₃	1	16	yes	complemented
450	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
451	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
452	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
453	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
454	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
455	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
456	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
457	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
458	C₂⁴	C₂×Q₈×C₄₃	1	4	yes	—
459	C₂⁴	C₂×Q₈×C₄₃	1	2	yes	—
460	C₂⁴	#41×C₄₃	1	2	yes	—
461	C₂⁴	#41×C₄₃	1	2	yes	—
462	C₂⁴	#41×C₄₃	1	4	yes	—
463	C₂⁴	#41×C₄₃	1	4	yes	—
464	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
465	C₂²×C₄	—	2	16	no	—
466	C₂²×C₄	—	2	8	no	—
467	C₂²×C₄	—	2	16	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	16	no	—
473	C₂²×C₄	—	2	16	no	—
474	C₂²×C₄	—	2	16	no	—
475	C₂²×C₄	—	2	16	no	—
476	C₂²×C₄	—	2	16	no	—
477	C₂²×C₄	—	2	16	no	—
478	C₂²×C₄	—	2	16	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	2	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	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	4	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	4	8	no	—
496	C₂²×C₄	—	4	8	no	—
497	C₂²×C₄	—	4	8	no	—
498	C₂²×C₄	—	4	8	no	—
499	C₂²×C₄	—	4	8	no	—
500	C₂²×C₄	—	4	8	no	—
501	C₂²×C₄	—	4	8	no	—
502	C₂²×C₄	—	4	4	no	—
503	C₂²×C₄	—	4	8	no	—
504	C₂²×C₄	—	4	4	no	—
505	C₂²×C₄	—	4	8	no	—
506	C₂²×C₄	C₂²⋊C₄×C₄₃	1	16	yes	complemented
507	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
508	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
509	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
510	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
511	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
512	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
513	C₄⋊C₄	—	2	32	no	—
514	C₂²⋊C₄	—	2	64	no	—
515	C₂²⋊C₄	—	2	32	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	8	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	8	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	8	no	—
528	C₂³	—	2	32	no	—
529	C₂³	—	2	64	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	4	no	—
532	C₂³	—	4	4	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	4	16	no	—
541	C₂³	—	4	32	no	—
542	C₂³	—	4	16	no	—
543	C₂³	—	4	16	no	—
544	C₂³	—	4	16	no	—
545	C₂³	—	4	32	no	—
546	C₂³	—	4	32	no	—
547	C₂³	—	4	16	no	—
548	C₂³	—	4	16	no	—
549	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
550	C₂³	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
551	C₂³	C₂×C₄⋊C₄×C₄₃	1	8	yes	complemented
552	C₂³	#117×C₄₃	1	4	yes	—
553	C₂³	C₄×D₄×C₄₃	1	8	yes	—
554	C₂³	C₄×D₄×C₄₃	1	8	yes	—
555	C₂³	#120×C₄₃	1	8	yes	—
556	C₂³	#120×C₄₃	1	4	yes	—
557	C₂³	#121×C₄₃	1	4	yes	—
558	C₂³	#121×C₄₃	1	4	yes	—
559	C₂³	#121×C₄₃	1	8	yes	—
560	C₂³	#121×C₄₃	1	8	yes	—
561	C₂³	#121×C₄₃	1	8	yes	—
562	C₂³	C₂²⋊Q₈×C₄₃	1	4	yes	—
563	C₂³	C₂²⋊Q₈×C₄₃	1	4	yes	—
564	C₂³	C₂²⋊Q₈×C₄₃	1	8	yes	—
565	C₂³	C₂²⋊Q₈×C₄₃	1	8	yes	—
566	C₂³	#123×C₄₃	1	8	yes	—
567	C₂³	#123×C₄₃	1	4	yes	—
568	C₂³	#123×C₄₃	1	8	yes	—
569	C₂³	#124×C₄₃	1	8	yes	—
570	C₂³	#124×C₄₃	1	4	yes	—
571	C₂³	#126×C₄₃	1	8	yes	—
572	C₂³	#127×C₄₃	1	4	yes	—
573	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
574	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
575	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
576	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
577	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
578	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
579	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
580	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
581	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
582	C₂³	C₂×#41×C₄₃	1	2	yes	—
583	C₂³	C₂×#41×C₄₃	1	2	yes	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	32	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	8	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	8	no	—
594	C₂×C₄	—	2	8	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	4	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	4	4	no	—
601	C₂×C₄	—	4	4	no	—
602	C₂×C₄	—	4	4	no	—
603	C₂×C₄	—	4	4	no	—
604	C₂×C₄	—	4	4	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	16	no	—
609	C₂×C₄	—	4	32	no	—
610	C₂×C₄	—	4	32	no	—
611	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	complemented
612	C₂²	—	2	8	no	—
613	C₂²	—	2	16	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	8	no	—
617	C₂²	—	4	8	no	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	64	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	4	8	no	—
623	C₂²	—	4	4	no	—
624	C₂²	C₄₃×#380	1	8	yes	—
625	C₂²	C₄₃×#385	1	16	yes	—
626	C₂²	C₄₃×#386	1	8	yes	—
627	C₂²	C₄₃×#388	1	16	yes	—
628	C₂²	C₄₃×#390	1	8	yes	—
629	C₂²	C₄₃×#392	1	8	yes	—
630	C₂²	C₄₃×#393	1	8	yes	—
631	C₂²	C₄₃×#394	1	16	yes	—
632	C₂²	C₄₃×#396	1	16	yes	—
633	C₂²	C₄₃×#397	1	8	yes	—
634	C₂²	C₄₃×#399	1	8	yes	—
635	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
636	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
637	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
638	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
639	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
640	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
641	C₂²	C₂×#120×C₄₃	1	2	yes	—
642	C₂²	C₂×#121×C₄₃	1	2	yes	—
643	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
644	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
645	C₂²	C₂×#121×C₄₃	1	2	yes	—
646	C₂²	C₂×#121×C₄₃	1	2	yes	—
647	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
648	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
649	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
650	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
651	C₂²	C₂×#123×C₄₃	1	2	yes	—
652	C₂²	C₂×#123×C₄₃	1	2	yes	—
653	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
654	C₂²	C₂×#124×C₄₃	1	2	yes	—
655	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
656	C₂²	C₂×#126×C₄₃	1	2	yes	—
657	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
658	C₄	—	2	8	no	—
659	C₄	—	4	8	no	—
660	C₄	—	4	8	no	—
661	C₄	—	4	4	no	—
662	C₂	—	4	8	no	—
663	C₂	C₄₃×#1439	1	16	yes	direct product factor
664	C₂	C₂×C₄₃×#380	1	1	yes	characteristic
665	C₂	C₂×C₄₃×#385	1	2	yes	—
666	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
667	C₂	C₂×C₄₃×#388	1	2	yes	—
668	C₂	C₂×C₄₃×#390	1	1	yes	characteristic
669	C₂	C₂×C₄₃×#392	1	1	yes	characteristic
670	C₂	C₂×C₄₃×#393	1	1	yes	characteristic
671	C₂	C₂×C₄₃×#394	1	2	yes	—
672	C₂	C₂×C₄₃×#396	1	2	yes	—
673	C₂	C₂×C₄₃×#397	1	1	yes	characteristic
674	C₂	C₂×C₄₃×#399	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵×C₄₃	C₂³
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
prime radical	C₂⁶×C₄₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄⋊C₄×C₄₃	C₂	semidirect
4. C₂²×#95×C₄₃	C₂	semidirect
5. C₂²×#95×C₄₃	C₂	semidirect
6. C₄₃×#1439	C₂	direct (N × H)
14. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
20. C₂²×C₂²⋊C₄×C₄₃	C₄	semidirect
25. C₂×#95×C₄₃	C₂²	semidirect
26. C₂×#95×C₄₃	C₂²	semidirect
78. C₂×C₂²⋊C₄×C₄₃	C₂×C₄	semidirect
111. C₂⁴×C₄₃	C₄⋊C₄	semidirect
168. C₂²×C₄×C₄₃	C₂²⋊C₄	semidirect
213. C₂³×C₄₃	C₂×C₄⋊C₄	semidirect
273. C₂×C₄×C₄₃	C₂×C₂²⋊C₄	semidirect
274. C₂×#1439	C₄₃	direct (N × H)
325. C₂³×C₄⋊C₄	C₂×C₄₃	semidirect
328. C₂²×#95	C₂×C₄₃	semidirect
329. C₂²×#95	C₂×C₄₃	semidirect
330. #1439	C₂×C₄₃	direct (N × H)
332. C₂×C₄₃	#1439	direct (N × H)
351. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
357. C₂²×C₂²⋊C₄	C₄×C₄₃	semidirect
362. C₂×#95	C₂²×C₄₃	semidirect
363. C₂×#95	C₂²×C₄₃	semidirect
364. C₄₃	C₂×#1439	direct (N × H)
416. C₂×C₂²⋊C₄	C₂×C₄×C₄₃	semidirect
449. C₂⁴	C₄⋊C₄×C₄₃	semidirect
506. C₂²×C₄	C₂²⋊C₄×C₄₃	semidirect
551. C₂³	C₂×C₄⋊C₄×C₄₃	semidirect
611. C₂×C₄	C₂×C₂²⋊C₄×C₄₃	semidirect
663. C₂	C₄₃×#1439	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×C₄⋊C₄×C₄₃	2
C₂³×C₂²⋊C₄×C₄₃	2
C₂²×#95×C₄₃	2
C₄₃×#1439	2
C₂×#1439	43

Subgroups — C2×C43×#1439 #24933853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1439 #24933853