Subgroups — #24991200

Order 11008.

636 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10621882	C₂	1	1	yes	maximal, characteristic
2	#19135389	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582626	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132429	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621882	C₄	1	1	yes	characteristic
9	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
10	C₄×#10621882	—	2	2	no	—
11	C₄×#10621882	—	2	2	no	—
12	C₂×#13063258	C₄	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13063246	C₄	1	1	yes	characteristic
15	C₂×#13063245	C₄	1	1	yes	characteristic
16	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
17	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
18	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	D₄⋊(C₄₃⋊C₈)	—	2	2	no	—
21	#14582626	—	2	2	no	—
22	C₂²×M₁₆×C₄₃	—	2	1	no	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#436	—	2	2	no	—
25	C₄₃×#436	—	2	2	no	—
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
28	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₃	—	2	1	no	—
31	C₂×#10621882	—	2	2	no	—
32	C₂×#10621882	—	2	2	no	—
33	C₂×#10621882	—	2	2	no	—
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₄×D₁₇₂	—	2	1	no	—
39	C₄×D₁₇₂	—	2	1	no	—
40	C₄×D₁₇₂	—	2	1	no	—
41	C₄×D₁₇₂	—	2	1	no	—
42	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
44	#13063258	—	2	2	no	—
45	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
46	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
47	#13063246	—	2	2	no	—
48	#13063245	—	2	2	no	—
49	(C₂×D₄₃)⋊C₈	—	4	2	no	—
50	(C₂×D₄₃)⋊C₈	—	4	2	no	—
51	C₄×C₄₃⋊C₈	—	2	1	no	—
52	C₄×C₄₃⋊C₈	—	2	1	no	—
53	C₄×C₄₃⋊C₈	—	2	1	no	—
54	C₄×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	—	2	1	no	—
57	C₂×M₁₆×C₄₃	—	2	4	no	—
58	C₂×M₁₆×C₄₃	—	4	2	no	—
59	C₂×M₁₆×C₄₃	—	4	2	no	—
60	C₂²×C₈×C₄₃	—	2	1	no	—
61	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
63	C₄×D₄×C₄₃	—	2	1	no	—
64	C₄×D₄×C₄₃	—	2	1	no	—
65	C₄×D₄×C₄₃	D₄	1	2	yes	—
66	C₄×D₄×C₄₃	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₃	—	2	1	no	—
71	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
72	C₂²⋊C₈×C₄₃	—	2	4	no	—
73	C₄×C₈×C₄₃	—	2	1	no	—
74	C₄×C₈×C₄₃	—	2	1	no	—
75	C₂⁴×C₄₃	—	2	1	no	—
76	C₂³×D₄₃	—	2	1	no	—
77	C₂×D₄×C₄₃	—	2	1	no	—
78	C₂×D₄×C₄₃	—	2	1	no	—
79	C₂×D₄×C₄₃	—	2	1	no	—
80	C₂×D₄×C₄₃	—	2	1	no	—
81	C₂×D₄×C₄₃	—	2	1	no	—
82	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	—	4	1	no	—
87	C₂²×C₄×C₄₃	—	4	1	no	—
88	C₂²×C₄×C₄₃	—	4	1	no	—
89	C₂²×C₄×C₄₃	—	4	1	no	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
93	C₂²×Dic₄₃	—	2	1	no	—
94	C₂×D₁₇₂	—	2	1	no	—
95	C₂×D₁₇₂	—	2	1	no	—
96	C₂×D₁₇₂	—	2	1	no	—
97	C₂×D₁₇₂	—	2	1	no	—
98	C₂×D₁₇₂	—	2	1	no	—
99	C₂×D₁₇₂	M₁₆	1	2	yes	complemented
100	C₂×C₄×D₄₃	—	4	1	no	—
101	C₂×C₄×D₄₃	—	4	1	no	—
102	C₂×C₄×D₄₃	—	4	1	no	—
103	C₂×C₄×D₄₃	—	4	1	no	—
104	C₂×C₄×D₄₃	—	4	1	no	—
105	C₂×C₄×D₄₃	—	4	1	no	—
106	M₁₆×C₄₃	—	4	8	no	—
107	C₂×C₈×C₄₃	—	2	1	no	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	2	1	no	—
112	C₂×C₈×C₄₃	—	2	1	no	—
113	C₂×C₈×C₄₃	—	4	1	no	—
114	C₂×C₈×C₄₃	—	4	1	no	—
115	C₂×C₈×C₄₃	D₈	1	2	yes	complemented
116	C₄⋊C₄×C₄₃	—	2	1	no	—
117	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
118	C₂²⋊C₄×C₄₃	—	2	2	no	—
119	C₂²⋊C₄×C₄₃	—	2	2	no	—
120	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₃	#41	1	1	yes	characteristic
124	#10621882	—	2	8	no	—
125	(C₂×D₄₃)⋊C₄	—	4	1	no	—
126	(C₂×D₄₃)⋊C₄	—	4	1	no	—
127	C₄⋊Dic₄₃	—	2	1	no	—
128	C₄⋊Dic₄₃	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	—	2	1	no	—
131	C₂×C₄₃⋊C₈	—	2	2	no	—
132	C₂×C₄₃⋊C₈	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	—	4	1	no	—
136	C₂×C₄₃⋊C₈	—	4	1	no	—
137	C₂×C₄₃⋊C₈	—	4	1	no	—
138	C₂×C₄₃⋊C₈	—	4	1	no	—
139	C₂×C₄₃⋊C₈	—	4	1	no	—
140	C₂×C₄₃⋊C₈	M₁₆	1	2	yes	complemented
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	—	4	1	no	—
144	C₂³×C₄₃	—	4	1	no	—
145	C₂³×C₄₃	—	4	1	no	—
146	C₂³×C₄₃	—	4	1	no	—
147	C₂³×C₄₃	—	4	1	no	—
148	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
149	C₂²×D₄₃	—	2	2	no	—
150	C₂²×D₄₃	—	4	1	no	—
151	C₂²×D₄₃	—	4	1	no	—
152	C₂²×D₄₃	—	4	1	no	—
153	C₂²×D₄₃	—	4	1	no	—
154	C₂²×D₄₃	—	4	1	no	—
155	C₂²×D₄₃	—	4	1	no	—
156	D₄×C₄₃	—	2	2	no	—
157	D₄×C₄₃	—	2	2	no	—
158	D₄×C₄₃	—	4	1	no	—
159	D₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
181	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×Dic₄₃	—	4	1	no	—
184	C₂×Dic₄₃	—	4	1	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	D₁₇₂	—	2	2	no	—
187	D₁₇₂	—	2	2	no	—
188	D₁₇₂	—	4	1	no	—
189	D₁₇₂	—	4	1	no	—
190	C₄×D₄₃	—	8	1	no	—
191	C₄×D₄₃	—	8	1	no	—
192	C₄×D₄₃	—	8	1	no	—
193	C₄×D₄₃	—	8	1	no	—
194	C₈×C₄₃	—	2	2	no	—
195	C₈×C₄₃	—	4	2	no	—
196	C₈×C₄₃	—	4	1	no	—
197	C₄₃⋊C₈	—	2	2	no	—
198	C₄₃⋊C₈	—	4	2	no	—
199	C₄₃⋊C₈	—	4	1	no	—
200	C₄₃⋊C₈	—	8	1	no	—
201	#8951	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	4	2	no	—
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	8	1	no	—
206	C₂²×C₄₃	—	8	1	no	—
207	C₂²×C₄₃	—	8	1	no	—
208	C₂²×C₄₃	—	8	1	no	—
209	C₂²×C₄₃	#386	1	1	yes	characteristic
210	C₂²×C₄₃	#435	1	1	yes	characteristic
211	C₂²×C₄₃	#436	1	1	yes	characteristic
212	C₂²×C₄₃	C₄×D₈	1	1	yes	characteristic
213	C₂²×C₄₃	#442	1	1	yes	characteristic
214	C₂²×C₄₃	#443	1	1	yes	characteristic
215	C₂²×C₄₃	#444	1	1	yes	characteristic
216	C₂×D₄₃	—	4	2	no	—
217	C₂×D₄₃	—	4	2	no	—
218	C₂×D₄₃	—	4	2	no	—
219	C₂×D₄₃	—	8	1	no	—
220	C₂×D₄₃	—	8	1	no	—
221	C₂×D₄₃	—	8	1	no	—
222	C₂×D₄₃	—	8	1	no	—
223	C₄×C₄₃	—	2	1	no	—
224	C₄×C₄₃	—	2	1	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	#407	1	1	yes	characteristic
227	C₄×C₄₃	#408	1	1	yes	characteristic
228	C₄×C₄₃	#435	1	1	yes	characteristic
229	C₄×C₄₃	#436	1	1	yes	characteristic
230	C₄×C₄₃	#447	1	1	yes	characteristic
231	C₄×C₄₃	#449	1	1	yes	characteristic
232	C₄×C₄₃	#459	1	1	yes	characteristic
233	C₄×C₄₃	#463	1	1	yes	characteristic
234	Dic₄₃	—	8	1	no	—
235	C₂×C₄×D₈	—	43	1	no	—
236	C₂×#436	D₄₃	1	1	yes	characteristic, complemented
237	#1954	—	43	1	no	—
238	C₂×D₄⋊C₈	—	43	1	no	—
239	C₂×D₄⋊C₈	—	43	1	no	—
240	#1277	—	43	1	no	—
241	#1273	—	43	1	no	—
242	C₂×C₄₃	—	8	2	no	—
243	C₂×C₄₃	#1581	1	1	yes	characteristic
244	C₂×C₄₃	#1586	1	1	yes	characteristic
245	C₂×C₄₃	#1589	1	1	yes	characteristic
246	C₂×C₄₃	#1594	1	1	yes	characteristic
247	C₂×C₄₃	#1870	1	1	yes	characteristic
248	C₂×C₄₃	#1876	1	1	yes	characteristic
249	C₂×C₄₃	#1879	1	1	yes	characteristic
250	D₄₃	—	8	2	no	—
251	C₂²×D₈	—	43	1	no	—
252	C₂²×M₁₆	—	2	1	no	—
253	C₂×C₄×D₄	—	43	1	no	—
254	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
255	C₄×D₈	—	86	2	no	—
256	C₄×D₈	—	86	2	no	—
257	#436	—	2	2	no	—
258	#436	—	2	2	no	—
259	C₂×#107	—	43	1	no	—
260	C₂×C₄⋊C₈	—	43	1	no	—
261	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
262	C₂×#102	—	43	1	no	—
263	C₂×#102	—	43	1	no	—
264	C₂×C₂²⋊C₈	—	2	1	no	—
265	C₂×C₂²⋊C₈	—	86	1	no	—
266	C₂×C₂²⋊C₈	—	86	1	no	—
267	C₂×C₄×C₈	—	43	1	no	—
268	C₂×C₄×C₈	—	43	1	no	—
269	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
270	D₄⋊C₈	—	86	2	no	—
271	D₄⋊C₈	—	86	2	no	—
272	C₄₃	#8951	1	1	yes	characteristic, complemented, Sylow
273	C₂²×D₄	—	43	1	no	—
274	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	86	1	no	—
277	C₂×D₈	—	86	2	no	—
278	C₂×D₈	—	86	2	no	—
279	C₂×D₈	—	86	2	no	—
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	—	4	2	no	—
282	C₂×M₁₆	—	4	2	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	43	1	no	—
285	C₂²×C₈	—	43	1	no	—
286	C₂²×C₈	—	86	1	no	—
287	C₂²×C₈	—	86	1	no	—
288	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	86	1	no	—
293	C₄×D₄	—	86	1	no	—
294	C₄×D₄	—	86	1	no	—
295	C₄×D₄	—	86	1	no	—
296	C₄×D₄	D₁₇₂	1	2	yes	—
297	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
298	C₂×C₄⋊C₄	—	43	1	no	—
299	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	86	1	no	—
302	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
303	#107	—	86	2	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	86	1	no	—
306	C₄⋊C₈	—	86	1	no	—
307	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
308	#102	—	86	2	no	—
309	#102	—	86	2	no	—
310	C₂²⋊C₈	—	2	4	no	—
311	C₂²⋊C₈	—	172	2	no	—
312	C₂²⋊C₈	—	172	2	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	86	1	no	—
316	C₄×C₈	—	86	1	no	—
317	C₄×C₈	—	86	1	no	—
318	C₄×C₈	—	86	1	no	—
319	C₂⁴	—	2	1	no	—
320	C₂⁴	—	86	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	43	2	no	—
327	C₂×D₄	—	86	1	no	—
328	C₂×D₄	—	86	1	no	—
329	C₂×D₄	—	86	1	no	—
330	C₂×D₄	—	86	1	no	—
331	C₂×D₄	—	86	1	no	—
332	C₂×D₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	86	1	no	—
341	C₂²×C₄	—	172	1	no	—
342	C₂²×C₄	—	172	1	no	—
343	C₂²×C₄	—	172	1	no	—
344	C₂²×C₄	—	172	1	no	—
345	C₂²×C₄	—	172	1	no	—
346	C₂²×C₄	—	172	1	no	—
347	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
348	C₂²×C₄	#10621898	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
350	D₈	—	86	8	no	—
351	M₁₆	—	4	8	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	43	2	no	—
361	C₂×C₈	—	86	1	no	—
362	C₂×C₈	—	86	1	no	—
363	C₂×C₈	—	86	2	no	—
364	C₂×C₈	—	86	1	no	—
365	C₂×C₈	—	86	1	no	—
366	C₂×C₈	—	86	1	no	—
367	C₂×C₈	—	172	1	no	—
368	C₂×C₈	—	172	1	no	—
369	C₂×C₈	—	172	1	no	—
370	C₂×C₈	—	172	1	no	—
371	C₂×C₈	—	172	1	no	—
372	C₂×C₈	#10621882	1	2	yes	complemented
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	86	1	no	—
375	C₄⋊C₄	—	86	1	no	—
376	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	172	1	no	—
380	C₂²⋊C₄	—	172	1	no	—
381	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
382	C₄²	#10621898	1	1	yes	characteristic
383	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
384	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	86	2	no	—
393	C₂³	—	172	1	no	—
394	C₂³	—	172	1	no	—
395	C₂³	—	172	1	no	—
396	C₂³	—	172	1	no	—
397	C₂³	—	172	1	no	—
398	C₂³	—	172	1	no	—
399	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	86	2	no	—
405	D₄	—	86	2	no	—
406	D₄	—	172	1	no	—
407	D₄	—	172	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	344	1	no	—
418	C₂×C₄	—	344	1	no	—
419	C₂×C₄	—	344	1	no	—
420	C₂×C₄	—	344	1	no	—
421	C₂×C₄	—	172	1	no	—
422	C₂×C₄	—	172	1	no	—
423	C₂×C₄	—	172	1	no	—
424	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
425	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
426	C₂×C₄	#13063294	1	1	yes	characteristic
427	C₂×C₄	#13063299	1	1	yes	characteristic
428	C₂×C₄	#13063299	1	1	yes	characteristic
429	C₂×C₄	#13063308	1	1	yes	characteristic
430	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
431	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
432	C₂×C₄	#13063333	1	1	yes	characteristic
433	C₂×C₄	#13063333	1	1	yes	characteristic
434	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
435	C₂×C₄	#13063345	1	1	yes	characteristic
436	C₂×C₄	#13063350	1	1	yes	characteristic
437	C₂×C₄	#13063351	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	86	2	no	—
442	C₈	—	344	1	no	—
443	C₈	—	172	2	no	—
444	C₈	—	172	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	344	1	no	—
453	C₂²	—	344	1	no	—
454	C₂²	—	344	1	no	—
455	C₂²	—	344	1	no	—
456	C₂²	—	172	2	no	—
457	C₂²	—	172	2	no	—
458	C₂²	—	172	2	no	—
459	C₂²	#14582778	1	1	yes	characteristic
460	C₂²	#14582968	1	1	yes	characteristic
461	C₂²	#14582975	1	1	yes	characteristic
462	C₂²	C₄×#10621882	1	1	yes	characteristic
463	C₂²	#14583009	1	1	yes	characteristic
464	C₂²	#14583014	1	1	yes	characteristic
465	C₂²	#14583019	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	344	1	no	—
470	C₄	#14582862	1	1	yes	characteristic
471	C₄	#14582867	1	1	yes	characteristic
472	C₄	#14582968	1	1	yes	characteristic
473	C₄	#14582975	1	1	yes	characteristic
474	C₄	#14583033	1	1	yes	characteristic
475	C₄	#14583044	1	1	yes	characteristic
476	C₄	#14583094	1	1	yes	characteristic
477	C₄	#14583114	1	1	yes	characteristic
478	C₂	—	8	2	no	—
479	C₂	—	344	2	no	—
480	C₂	#19133422	1	1	yes	characteristic
481	C₂	#19133457	1	1	yes	characteristic
482	C₂	#19133478	1	1	yes	characteristic
483	C₂	#19133507	1	1	yes	characteristic
484	C₂	#19134892	1	1	yes	characteristic
485	C₂	#19134922	1	1	yes	characteristic
486	C₂	#19134943	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#436	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂²×#10621882	C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#436	D₄₃
hypocenter	C₄₃	#8951
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
2. #19135389	C₂	semidirect
3. C₂×D₄⋊(C₄₃⋊C₈)	C₂	semidirect
4. C₂×#14582626	C₂	semidirect
5. #19132429	C₂	semidirect
6. C₄₃⋊#1273	C₂	semidirect
7. C₂×C₄₃×#436	C₂	semidirect
99. C₂×D₁₇₂	M₁₆	semidirect
115. C₂×C₈×C₄₃	D₈	semidirect
140. C₂×C₄₃⋊C₈	M₁₆	semidirect
236. C₂×#436	D₄₃	semidirect
272. C₄₃	#8951	semidirect
372. C₂×C₈	#10621882	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10621882	2
#19135389	2
C₂×D₄⋊(C₄₃⋊C₈)	2
C₂×#14582626	2
#19132429	2
C₄₃⋊#1273	2
C₂×C₄₃×#436	2
#8951	43