Subgroups — #24992776

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583094	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582642	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132478	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132429	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621882	—	2	1	no	—
9	C₂³×C₄₃⋊C₈	—	2	1	no	—
10	C₂×#13063322	C₂²	1	1	yes	characteristic
11	#14583094	—	2	2	no	—
12	#14583094	C₄	1	4	yes	complemented
13	D₄×C₄₃⋊C₈	—	2	2	no	—
14	D₄×C₄₃⋊C₈	—	2	2	no	—
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13063245	—	2	1	no	—
18	C₂×#13063245	—	2	1	no	—
19	C₂×#13063245	—	2	1	no	—
20	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
21	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	#14582642	—	2	2	no	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#102×C₄₃	—	2	1	no	—
26	C₄₃×#384	C₂²	1	1	yes	characteristic
27	C₄₃×#340	—	2	1	no	—
28	C₂²×D₁₇₂	—	2	1	no	—
29	C₂²×D₁₇₂	—	2	1	no	—
30	C₂²×D₁₇₂	—	2	1	no	—
31	C₂×#10621882	—	2	4	no	—
32	C₂×#10621882	—	4	2	no	—
33	C₂×#10621882	—	4	2	no	—
34	C₂²×C₄₃⋊C₈	—	2	4	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	C₂²×C₄₃⋊C₈	—	4	2	no	—
38	C₂²×C₄₃⋊C₈	—	4	2	no	—
39	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
40	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
41	#13063322	—	2	1	no	—
42	#13063322	—	2	1	no	—
43	#13063322	—	2	1	no	—
44	#13063322	C₂×C₄	1	2	yes	—
45	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
46	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
47	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
48	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
49	#13063245	—	2	4	no	—
50	#13063245	—	4	2	no	—
51	#13063245	—	4	2	no	—
52	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
53	C₄×C₄₃⋊C₈	—	2	1	no	—
54	C₄×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	—	2	1	no	—
57	C₂²×C₈×C₄₃	—	2	1	no	—
58	C₄×D₄×C₄₃	—	2	1	no	—
59	C₄×D₄×C₄₃	—	2	1	no	—
60	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
61	C₄×D₄×C₄₃	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	C₄⋊C₈×C₄₃	—	2	1	no	—
70	#102×C₄₃	—	4	2	no	—
71	C₂⁴×C₄₃	—	2	1	no	—
72	C₂³×D₄₃	—	4	1	no	—
73	C₂×D₄×C₄₃	—	2	1	no	—
74	C₂×D₄×C₄₃	—	2	1	no	—
75	C₂×D₄×C₄₃	—	2	1	no	—
76	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
77	C₂×D₄×C₄₃	D₈	1	2	yes	—
78	C₂×D₄×C₄₃	SD₁₆	1	2	yes	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	1	no	—
82	C₂²×C₄×C₄₃	—	4	1	no	—
83	C₂²×C₄×C₄₃	—	4	1	no	—
84	C₂²×C₄×C₄₃	—	4	1	no	—
85	C₂²×C₄×C₄₃	—	4	1	no	—
86	C₂²×C₄×C₄₃	—	4	1	no	—
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
90	C₂×D₁₇₂	—	2	2	no	—
91	C₂×D₁₇₂	—	2	2	no	—
92	C₂×D₁₇₂	—	2	2	no	—
93	C₂×D₁₇₂	—	4	1	no	—
94	C₂×D₁₇₂	—	4	1	no	—
95	C₂×D₁₇₂	—	4	1	no	—
96	C₂×D₁₇₂	—	4	1	no	—
97	C₂×D₁₇₂	—	4	1	no	—
98	C₂×D₁₇₂	—	4	1	no	—
99	C₂×D₁₇₂	—	4	1	no	—
100	C₂×D₁₇₂	—	4	1	no	—
101	C₂×D₁₇₂	—	4	1	no	—
102	C₂×D₁₇₂	—	4	1	no	—
103	C₂×D₁₇₂	—	4	1	no	—
104	C₂×D₁₇₂	—	8	1	no	—
105	C₂×D₁₇₂	—	8	1	no	—
106	C₂×C₈×C₄₃	—	4	1	no	—
107	C₂×C₈×C₄₃	—	4	1	no	—
108	C₂×C₈×C₄₃	—	4	1	no	—
109	C₄⋊C₄×C₄₃	—	2	1	no	—
110	C₄⋊C₄×C₄₃	—	4	1	no	—
111	C₄⋊C₄×C₄₃	—	4	1	no	—
112	C₄⋊C₄×C₄₃	—	4	1	no	—
113	C₄⋊C₄×C₄₃	—	4	1	no	—
114	C₄⋊C₄×C₄₃	—	8	1	no	—
115	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
116	C₂²⋊C₄×C₄₃	—	2	2	no	—
117	C₂²⋊C₄×C₄₃	—	2	2	no	—
118	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₃	#41	1	1	yes	characteristic
122	#10621882	—	4	8	no	—
123	C₂×C₄₃⋊C₈	—	2	1	no	—
124	C₂×C₄₃⋊C₈	—	2	1	no	—
125	C₂×C₄₃⋊C₈	—	2	2	no	—
126	C₂×C₄₃⋊C₈	—	2	1	no	—
127	C₂×C₄₃⋊C₈	—	2	2	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	—	4	8	no	—
131	C₂×C₄₃⋊C₈	—	4	1	no	—
132	C₂×C₄₃⋊C₈	—	4	1	no	—
133	C₂×C₄₃⋊C₈	—	4	1	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	C₂×C₄₃⋊C₈	D₈	1	2	yes	complemented
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	2	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	—	4	1	no	—
142	C₂³×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	#121	1	1	yes	characteristic
144	C₂²×D₄₃	—	4	2	no	—
145	C₂²×D₄₃	—	8	1	no	—
146	C₂²×D₄₃	—	8	1	no	—
147	C₂²×D₄₃	—	8	1	no	—
148	C₂²×D₄₃	—	8	1	no	—
149	C₂²×D₄₃	—	8	1	no	—
150	C₂²×D₄₃	—	8	1	no	—
151	D₄×C₄₃	—	2	2	no	—
152	D₄×C₄₃	—	2	2	no	—
153	D₄×C₄₃	—	2	2	no	—
154	D₄×C₄₃	#102	1	4	yes	complemented
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	8	1	no	—
165	C₂×C₄×C₄₃	—	8	1	no	—
166	C₂×C₄×C₄₃	—	8	1	no	—
167	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
179	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
181	D₁₇₂	—	4	2	no	—
182	D₁₇₂	—	4	2	no	—
183	D₁₇₂	—	4	2	no	—
184	D₁₇₂	—	4	2	no	—
185	D₁₇₂	—	8	2	no	—
186	D₁₇₂	—	8	2	no	—
187	D₁₇₂	—	8	1	no	—
188	D₁₇₂	—	8	1	no	—
189	D₁₇₂	—	8	1	no	—
190	D₁₇₂	—	8	1	no	—
191	C₈×C₄₃	—	8	1	no	—
192	C₄₃⋊C₈	—	2	2	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	C₄₃⋊C₈	—	4	2	no	—
195	C₄₃⋊C₈	—	4	1	no	—
196	#9221	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	2	4	no	—
198	C₂²×C₄₃	—	4	2	no	—
199	C₂²×C₄₃	—	4	2	no	—
200	C₂²×C₄₃	—	4	2	no	—
201	C₂²×C₄₃	—	4	2	no	—
202	C₂²×C₄₃	—	4	2	no	—
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	#386	1	1	yes	characteristic
205	C₂²×C₄₃	#459	1	1	yes	characteristic
206	C₂²×C₄₃	#463	1	1	yes	characteristic
207	C₂²×C₄₃	#465	1	1	yes	characteristic
208	C₂²×C₄₃	#466	1	1	yes	characteristic
209	C₂²×C₄₃	#471	1	1	yes	characteristic
210	C₂²×C₄₃	#472	1	1	yes	characteristic
211	C₂×D₄₃	—	8	2	no	—
212	C₂×D₄₃	—	8	2	no	—
213	C₂×D₄₃	—	8	2	no	—
214	C₂×D₄₃	—	16	1	no	—
215	C₂×D₄₃	—	16	1	no	—
216	C₂×D₄₃	—	16	1	no	—
217	C₂×D₄₃	—	16	1	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	—	16	1	no	—
222	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
223	C₄×C₄₃	#416	1	1	yes	characteristic
224	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
225	C₄×C₄₃	#442	1	1	yes	characteristic
226	C₄×C₄₃	#447	1	1	yes	characteristic
227	C₄×C₄₃	#449	1	1	yes	characteristic
228	C₄×C₄₃	#465	1	1	yes	characteristic
229	C₄×C₄₃	#466	1	1	yes	characteristic
230	C₂×#459	—	43	1	no	—
231	C₂×C₈×D₄	—	43	1	no	—
232	#1957	—	43	1	no	—
233	#1802	D₄₃	1	1	yes	characteristic, complemented
234	C₂×#331	—	43	1	no	—
235	#1296	—	43	1	no	—
236	#1277	—	43	1	no	—
237	C₂×C₄₃	—	4	4	no	—
238	C₂×C₄₃	#1665	1	1	yes	characteristic
239	C₂×C₄₃	#1667	1	1	yes	characteristic
240	C₂×C₄₃	#1677	1	1	yes	characteristic
241	C₂×C₄₃	#1681	1	1	yes	characteristic
242	C₂×C₄₃	#1879	1	1	yes	characteristic
243	C₂×C₄₃	#1893	1	1	yes	characteristic
244	C₂×C₄₃	#1907	1	1	yes	characteristic
245	D₄₃	—	16	2	no	—
246	C₂²×D₈	—	86	1	no	—
247	C₂³×C₈	—	86	1	no	—
248	C₂×#127	—	43	1	no	—
249	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
250	#459	—	43	4	no	—
251	#459	—	86	2	no	—
252	C₈×D₄	—	86	2	no	—
253	C₈×D₄	—	86	2	no	—
254	C₂×C₄⋊C₈	—	43	1	no	—
255	C₂×C₄⋊C₈	—	43	1	no	—
256	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
257	C₂×#102	—	2	1	no	—
258	C₂×#102	—	86	1	no	—
259	C₂×#102	—	86	1	no	—
260	C₂×#102	—	86	1	no	—
261	C₂×C₂²⋊C₈	—	86	1	no	—
262	C₂×C₄×C₈	—	43	1	no	—
263	#384	C₂×D₄₃	1	1	yes	characteristic
264	#340	—	2	1	no	—
265	#331	—	86	2	no	—
266	C₄₃	#9221	1	1	yes	characteristic, complemented, Sylow
267	C₂²×D₄	—	86	1	no	—
268	C₂²×D₄	—	86	1	no	—
269	C₂²×D₄	—	86	1	no	—
270	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂×D₈	—	86	4	no	—
273	C₂×D₈	—	172	2	no	—
274	C₂×D₈	—	172	2	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	—	43	1	no	—
277	C₂²×C₈	—	43	1	no	—
278	C₂²×C₈	—	86	4	no	—
279	C₂²×C₈	—	86	1	no	—
280	C₂²×C₈	—	86	1	no	—
281	C₂²×C₈	—	172	2	no	—
282	C₂²×C₈	—	172	2	no	—
283	#127	—	43	2	no	—
284	#127	—	86	1	no	—
285	#127	—	86	1	no	—
286	#127	—	86	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	C₄×D₄₃	1	2	yes	—
290	C₄×D₄	D₁₇₂	1	2	yes	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	43	2	no	—
300	C₄⋊C₈	—	43	2	no	—
301	C₄⋊C₈	—	86	1	no	—
302	C₄⋊C₈	—	86	1	no	—
303	#102	—	4	2	no	—
304	#102	—	86	4	no	—
305	#102	—	172	2	no	—
306	#102	—	172	2	no	—
307	C₂²⋊C₈	—	86	4	no	—
308	C₄×C₈	—	86	1	no	—
309	C₄×C₈	—	86	1	no	—
310	C₂⁴	—	2	1	no	—
311	C₂⁴	—	172	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	86	2	no	—
316	C₂×D₄	—	86	2	no	—
317	C₂×D₄	—	86	2	no	—
318	C₂×D₄	—	344	1	no	—
319	C₂×D₄	—	344	1	no	—
320	C₂×D₄	—	172	1	no	—
321	C₂×D₄	—	172	1	no	—
322	C₂×D₄	—	172	1	no	—
323	C₂×D₄	—	172	1	no	—
324	C₂×D₄	—	172	1	no	—
325	C₂×D₄	—	172	1	no	—
326	C₂×D₄	—	172	1	no	—
327	C₂×D₄	—	172	1	no	—
328	C₂×D₄	—	172	1	no	—
329	C₂×D₄	—	172	1	no	—
330	C₂×D₄	—	172	1	no	—
331	C₂×D₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
332	C₂×D₄	#10621882	1	2	yes	—
333	C₂×D₄	#10621884	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
343	C₂²×C₄	#10621900	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
345	D₈	—	172	8	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	43	2	no	—
350	C₂×C₈	—	86	1	no	—
351	C₂×C₈	—	86	1	no	—
352	C₂×C₈	—	86	2	no	—
353	C₂×C₈	—	86	1	no	—
354	C₂×C₈	—	86	2	no	—
355	C₂×C₈	—	86	1	no	—
356	C₂×C₈	—	86	1	no	—
357	C₂×C₈	—	172	8	no	—
358	C₂×C₈	—	172	1	no	—
359	C₂×C₈	—	172	1	no	—
360	C₂×C₈	—	172	1	no	—
361	C₂×C₈	—	172	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	8	1	no	—
368	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
372	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
373	C₄²	D₄×D₄₃	1	1	yes	characteristic
374	C₄²	#10621900	1	1	yes	characteristic
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	344	1	no	—
383	C₂³	—	344	1	no	—
384	C₂³	—	344	1	no	—
385	C₂³	—	344	1	no	—
386	C₂³	—	344	1	no	—
387	C₂³	—	344	1	no	—
388	C₂³	—	172	2	no	—
389	C₂³	#13063297	1	1	yes	characteristic
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	344	2	no	—
394	D₄	—	344	2	no	—
395	D₄	—	344	1	no	—
396	D₄	—	344	1	no	—
397	D₄	—	344	1	no	—
398	D₄	—	344	1	no	—
399	D₄	—	172	2	no	—
400	D₄	—	172	2	no	—
401	D₄	—	172	2	no	—
402	D₄	—	172	2	no	—
403	D₄	#13063245	1	4	yes	complemented
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	8	1	no	—
415	C₂×C₄	—	8	1	no	—
416	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
417	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
418	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
419	C₂×C₄	#13063295	1	1	yes	characteristic
420	C₂×C₄	#13063297	1	1	yes	characteristic
421	C₂×C₄	#13063309	1	1	yes	characteristic
422	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
424	C₂×C₄	C₂×#10621884	1	1	yes	characteristic
425	C₂×C₄	#13063345	1	1	yes	characteristic
426	C₂×C₄	#13063345	1	1	yes	characteristic
427	C₂×C₄	#13063346	1	1	yes	characteristic
428	C₂×C₄	#13063349	1	1	yes	characteristic
429	C₂×C₄	#13063352	1	1	yes	characteristic
430	C₈	—	8	1	no	—
431	C₈	—	86	2	no	—
432	C₈	—	172	1	no	—
433	C₈	—	172	2	no	—
434	C₈	—	172	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	344	2	no	—
443	C₂²	—	344	2	no	—
444	C₂²	—	344	2	no	—
445	C₂²	—	688	1	no	—
446	C₂²	—	688	1	no	—
447	C₂²	—	688	1	no	—
448	C₂²	—	688	1	no	—
449	C₂²	#14582776	1	1	yes	characteristic
450	C₂²	#14583092	1	1	yes	characteristic
451	C₂²	#14583116	1	1	yes	characteristic
452	C₂²	#14583130	1	1	yes	characteristic
453	C₂²	#14583133	1	1	yes	characteristic
454	C₂²	#14583164	1	1	yes	characteristic
455	C₂²	#14583167	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	16	1	no	—
460	C₄	C₂×#13063245	1	1	yes	characteristic
461	C₄	#14582893	1	1	yes	characteristic
462	C₄	#14582979	1	1	yes	characteristic
463	C₄	#14583008	1	1	yes	characteristic
464	C₄	#14583034	1	1	yes	characteristic
465	C₄	#14583045	1	1	yes	characteristic
466	C₄	#14583130	1	1	yes	characteristic
467	C₄	#14583133	1	1	yes	characteristic
468	C₂	—	4	4	no	—
469	C₂	—	688	2	no	—
470	C₂	#19133938	1	1	yes	characteristic
471	C₂	#19133948	1	1	yes	characteristic
472	C₂	#19134006	1	1	yes	characteristic
473	C₂	#19134034	1	1	yes	characteristic
474	C₂	#19134941	1	1	yes	characteristic
475	C₂	#19135021	1	1	yes	characteristic
476	C₂	#19135101	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063297
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1802	C₂
socle	C₂³×C₄₃	#121
prime radical	C₂×#14583094	C₂
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1802	D₄₃
hypocenter	C₄₃	#9221
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1802

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
3. #19135400	C₂	semidirect
4. C₂×#14582642	C₂	semidirect
5. #19132478	C₂	semidirect
6. #19132429	C₂	semidirect
7. C₄₃×#1802	C₂	semidirect
12. #14583094	C₄	semidirect
135. C₂×C₄₃⋊C₈	D₈	semidirect
154. D₄×C₄₃	#102	semidirect
233. #1802	D₄₃	semidirect
266. C₄₃	#9221	semidirect
403. D₄	#13063245	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583094	2
C₂×D₄×C₄₃⋊C₈	2
#19135400	2
C₂×#14582642	2
#19132478	2
#19132429	2
C₄₃×#1802	2
#9221	43