Subgroups — #25080372

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145150	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144392	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134020	C₂	1	2	yes	maximal, complemented
5	#19134002	C₂	1	2	yes	maximal, complemented
6	#19133968	C₂	1	2	yes	maximal, complemented
7	#19133934	C₂	1	2	yes	maximal, complemented
8	#19133350	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133286	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133272	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3036	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₃⋊C₈	—	2	1	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	#14583295	C₂²	1	1	yes	characteristic, complemented
15	#14583271	C₂²	1	1	yes	characteristic, complemented
16	#14583251	C₂²	1	1	yes	characteristic, complemented
17	#14583245	C₂²	1	1	yes	characteristic, complemented
18	#14583199	—	2	2	no	—
19	#14583189	C₂²	1	2	yes	—
20	#14583179	C₂²	1	2	yes	—
21	#14583126	—	2	1	no	—
22	#14583126	—	2	1	no	—
23	C₄×#10621883	—	2	1	no	—
24	C₄×#10621883	—	2	1	no	—
25	D₄×C₄₃⋊C₈	—	2	1	no	—
26	D₄×C₄₃⋊C₈	—	2	1	no	—
27	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
28	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
29	#14582939	—	2	1	no	—
30	#14582923	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	#14582904	—	2	1	no	—
33	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
34	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	#14582649	C₂²	1	2	yes	complemented
36	#14582649	C₂²	1	2	yes	complemented
37	#14582647	C₂²	1	2	yes	complemented
38	#14582645	C₂²	1	2	yes	complemented
39	#14582644	C₂²	1	2	yes	complemented
40	#14582643	C₂²	1	2	yes	complemented
41	C₂×AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
42	C₄₃×#532	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#463	—	2	2	no	—
45	C₄₃×#461	C₂²	1	2	yes	—
46	C₄₃×#459	C₂²	1	2	yes	—
47	C₄₃×#423	C₂²	1	1	yes	characteristic
48	C₄₃×#417	—	2	1	no	—
49	C₂×#10621883	—	2	1	no	—
50	C₂×#10621883	—	2	1	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂²×C₄₃⋊C₈	—	2	2	no	—
54	C₂²×C₄₃⋊C₈	—	2	2	no	—
55	C₂²×C₄₃⋊C₈	—	4	4	no	—
56	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063325	C₂³	1	1	yes	characteristic
60	#13063317	—	2	1	no	—
61	#13063304	—	2	1	no	—
62	#13063304	—	2	1	no	—
63	C₄×Dic₈₆	—	2	1	no	—
64	C₄×Dic₈₆	—	2	1	no	—
65	#13063284	—	2	1	no	—
66	#13063258	—	2	2	no	—
67	#13063256	—	2	2	no	—
68	#13063256	—	2	1	no	—
69	#13063256	—	2	1	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
72	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
74	#13063248	—	2	1	no	—
75	#13063248	—	2	1	no	—
76	#13063246	—	2	2	no	—
77	#13063246	—	2	2	no	—
78	#13063246	—	2	1	no	—
79	#13063246	—	2	1	no	—
80	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
81	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
82	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×#41×C₄₃	—	2	1	no	—
87	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂³×C₄×C₄₃	—	2	1	no	—
89	AGL(1,ℤ/8)×C₄₃	—	4	4	no	—
90	C₂×SD₁₆×C₄₃	—	2	2	no	—
91	C₂×D₈×C₄₃	—	2	2	no	—
92	C₂×M₁₆×C₄₃	—	2	1	no	—
93	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
94	#127×C₄₃	C₂³	1	1	yes	characteristic
95	#124×C₄₃	—	2	1	no	—
96	#121×C₄₃	—	2	1	no	—
97	#121×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	—	2	1	no	—
99	C₄×D₄×C₄₃	—	2	1	no	—
100	C₄×D₄×C₄₃	—	2	1	no	—
101	C₄×D₄×C₄₃	—	2	1	no	—
102	C₄×D₄×C₄₃	D₄	1	2	yes	—
103	C₄×D₄×C₄₃	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₄₃	—	2	1	no	—
108	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
109	#103×C₄₃	—	2	2	no	—
110	#102×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	#41×C₄₃	—	4	2	no	—
113	#41×C₄₃	—	4	2	no	—
114	C₂×Q₈×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	1	no	—
118	C₂×D₄×C₄₃	—	2	1	no	—
119	C₂×D₄×C₄₃	—	2	1	no	—
120	C₂×D₄×C₄₃	—	4	1	no	—
121	C₂×D₄×C₄₃	SD₁₆	1	4	yes	complemented
122	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	4	2	no	—
127	C₂²×C₄×C₄₃	—	4	2	no	—
128	C₂²×C₄×C₄₃	—	4	1	no	—
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
132	C₂×Dic₈₆	—	2	1	no	—
133	C₂×Dic₈₆	—	2	1	no	—
134	SD₁₆×C₄₃	—	4	4	no	—
135	D₈×C₄₃	—	4	4	no	—
136	M₁₆×C₄₃	—	4	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	—	2	1	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₄₃	—	2	2	no	—
143	C₂²⋊C₄×C₄₃	—	2	2	no	—
144	C₂²⋊C₄×C₄₃	—	4	1	no	—
145	C₂²⋊C₄×C₄₃	—	4	1	no	—
146	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₄₃	#41	1	1	yes	characteristic
149	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
150	C₂²⋊Dic₄₃	—	4	1	no	—
151	#10621883	—	4	2	no	—
152	#10621883	—	4	2	no	—
153	C₄⋊Dic₄₃	—	2	1	no	—
154	C₄⋊Dic₄₃	—	2	1	no	—
155	C₄⋊Dic₄₃	—	2	1	no	—
156	C₄⋊Dic₄₃	—	2	1	no	—
157	Dic₄₃⋊C₄	—	4	1	no	—
158	Dic₄₃⋊C₄	—	4	1	no	—
159	C₄×Dic₄₃	—	4	1	no	—
160	#10621877	—	4	2	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	2	2	no	—
163	C₂×C₄₃⋊C₈	—	2	2	no	—
164	C₂×C₄₃⋊C₈	—	4	1	no	—
165	C₂×C₄₃⋊C₈	—	4	4	no	—
166	C₂×C₄₃⋊C₈	—	4	2	no	—
167	C₂×C₄₃⋊C₈	—	4	4	no	—
168	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	—	2	4	no	—
174	C₂³×C₄₃	—	4	2	no	—
175	C₂³×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	—	4	1	no	—
177	C₂³×C₄₃	#121	1	1	yes	characteristic
178	Q₈×C₄₃	—	4	1	no	—
179	Q₈×C₄₃	—	4	1	no	—
180	D₄×C₄₃	—	2	2	no	—
181	D₄×C₄₃	—	2	4	no	—
182	D₄×C₄₃	—	4	1	no	—
183	D₄×C₄₃	—	4	1	no	—
184	D₄×C₄₃	—	4	1	no	—
185	D₄×C₄₃	—	4	1	no	—
186	D₄×C₄₃	—	8	1	no	—
187	D₄×C₄₃	—	8	2	no	—
188	D₄×C₄₃	C₂×SD₁₆	1	4	yes	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	2	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	4	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	—	4	1	no	—
198	C₂×C₄×C₄₃	—	8	2	no	—
199	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
200	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
201	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₄₃	#135	1	2	yes	—
204	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
207	C₂×Dic₄₃	—	4	1	no	—
208	C₂×Dic₄₃	—	4	1	no	—
209	Dic₈₆	—	4	1	no	—
210	Dic₈₆	—	4	1	no	—
211	Dic₈₆	—	8	1	no	—
212	C₈×C₄₃	—	4	2	no	—
213	C₄₃⋊C₈	—	2	1	no	—
214	C₄₃⋊C₈	—	2	1	no	—
215	C₄₃⋊C₈	—	2	1	no	—
216	C₄₃⋊C₈	—	4	2	no	—
217	C₄₃⋊C₈	—	4	2	no	—
218	C₄₃⋊C₈	AGL(1,ℤ/8)	1	2	yes	complemented
219	#19254	—	43	1	no	maximal, Sylow
220	C₂²×C₄₃	—	2	1	no	—
221	C₂²×C₄₃	—	2	1	no	—
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	4	8	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	4	2	no	—
226	C₂²×C₄₃	—	8	1	no	—
227	C₂²×C₄₃	—	8	1	no	—
228	C₂²×C₄₃	—	8	1	no	—
229	C₂²×C₄₃	#465	1	2	yes	—
230	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	—	2	1	no	—
234	C₄×C₄₃	—	4	2	no	—
235	C₄×C₄₃	—	8	1	no	—
236	C₄×C₄₃	#465	1	2	yes	—
237	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
238	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
239	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₄×C₄₃	#575	1	1	yes	characteristic
241	Dic₄₃	—	8	1	no	—
242	Dic₄₃	—	8	1	no	—
243	#3167	—	43	1	no	—
244	#3077	—	43	1	no	—
245	#3036	D₄₃	1	1	yes	characteristic
246	C₂×C₈×D₄	—	43	1	no	—
247	#1679	—	43	2	no	—
248	#1677	—	43	2	no	—
249	#1671	—	43	2	no	—
250	#1665	—	43	2	no	—
251	#1566	—	43	1	no	—
252	#1550	—	43	1	no	—
253	#1547	—	43	1	no	—
254	C₂×C₄₃	—	2	2	no	—
255	C₂×C₄₃	—	4	4	no	—
256	C₂×C₄₃	—	16	1	no	—
257	C₂×C₄₃	#3036	1	1	yes	characteristic
258	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
259	C₂×C₄₃	#3067	1	1	yes	characteristic
260	C₂×AGL(1,ℤ/8)	—	2	1	no	—
261	C₂³×C₈	—	86	1	no	—
262	#533	—	43	1	no	—
263	#532	C₂×D₄₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
265	#498	—	43	1	no	—
266	#492	—	43	1	no	—
267	#487	—	43	1	no	—
268	#486	—	43	1	no	—
269	#478	—	86	2	no	—
270	#476	—	43	2	no	—
271	#474	—	43	2	no	—
272	#465	—	86	1	no	—
273	#465	—	86	1	no	—
274	#463	—	2	2	no	—
275	#461	C₂×D₄₃	1	2	yes	—
276	#459	C₂×D₄₃	1	2	yes	—
277	C₄×SD₁₆	—	86	1	no	—
278	C₄×SD₁₆	—	86	1	no	—
279	C₈×D₄	—	43	2	no	—
280	C₈×D₄	—	43	2	no	—
281	C₈×D₄	—	86	1	no	—
282	C₈×D₄	—	86	1	no	—
283	#428	—	86	1	no	—
284	#423	—	43	1	no	—
285	#423	C₂×D₄₃	1	1	yes	characteristic
286	C₂×C₄⋊C₈	—	43	1	no	—
287	#418	—	86	1	no	—
288	#417	—	2	1	no	—
289	C₂×C₂²⋊C₈	—	86	1	no	—
290	C₂×C₄×C₈	—	43	1	no	—
291	#334	—	43	2	no	—
292	#334	—	43	2	no	—
293	#333	—	43	2	no	—
294	#332	—	43	2	no	—
295	#332	—	43	2	no	—
296	#331	—	43	2	no	—
297	C₄₃	#19254	1	1	yes	characteristic, complemented, Sylow
298	C₂×#41	—	2	1	no	—
299	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	AGL(1,ℤ/8)	—	4	4	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	86	1	no	—
304	C₂×SD₁₆	—	86	1	no	—
305	C₂×D₈	—	2	2	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	86	1	no	—
308	C₂²×C₈	—	43	1	no	—
309	C₂²×C₈	—	43	1	no	—
310	C₂²×C₈	—	86	2	no	—
311	C₂²×C₈	—	86	2	no	—
312	C₂²×C₈	—	86	1	no	—
313	C₂²×C₈	—	172	4	no	—
314	C₄⋊Q₈	—	43	1	no	—
315	C₄⋊Q₈	—	43	1	no	—
316	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
317	#127	C₂²×D₄₃	1	1	yes	characteristic
318	#125	—	86	1	no	—
319	#124	—	2	1	no	—
320	C₂²⋊Q₈	—	86	1	no	—
321	C₂²⋊Q₈	—	86	1	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	C₄×Q₈	—	86	1	no	—
325	C₄×Q₈	—	86	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
331	C₄×D₄	C₂²×D₄₃	1	2	yes	—
332	#117	—	86	1	no	—
333	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
336	#107	—	86	2	no	—
337	#106	—	86	1	no	—
338	#106	—	86	1	no	—
339	#106	—	86	2	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	43	2	no	—
342	C₄⋊C₈	—	43	2	no	—
343	C₄⋊C₈	—	86	1	no	—
344	C₄⋊C₈	—	86	1	no	—
345	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
346	#103	—	2	2	no	—
347	#103	—	86	1	no	—
348	#103	—	86	1	no	—
349	#102	—	2	2	no	—
350	#102	—	86	1	no	—
351	#102	—	86	1	no	—
352	#102	—	86	2	no	—
353	#102	—	86	2	no	—
354	C₂²⋊C₈	—	86	2	no	—
355	C₂²⋊C₈	—	86	2	no	—
356	C₄×C₈	—	43	1	no	—
357	C₄×C₈	—	43	1	no	—
358	C₄×C₈	—	43	1	no	—
359	C₄×C₈	—	43	1	no	—
360	C₂⁴	—	2	1	no	—
361	#41	—	4	2	no	—
362	#41	—	4	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	86	1	no	—
365	C₂×Q₈	—	86	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	#10621883	1	4	yes	complemented
373	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
381	C₂²×C₄	#10621900	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
383	SD₁₆	—	4	4	no	—
384	SD₁₆	—	172	2	no	—
385	SD₁₆	—	172	2	no	—
386	D₈	—	4	4	no	—
387	M₁₆	—	4	2	no	—
388	M₁₆	—	172	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	43	1	no	—
391	C₂×C₈	—	43	1	no	—
392	C₂×C₈	—	43	1	no	—
393	C₂×C₈	—	43	1	no	—
394	C₂×C₈	—	86	2	no	—
395	C₂×C₈	—	86	2	no	—
396	C₂×C₈	—	86	2	no	—
397	C₂×C₈	—	172	4	no	—
398	C₂×C₈	—	172	1	no	—
399	C₂×C₈	—	172	4	no	—
400	C₂×C₈	—	172	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	86	1	no	—
405	C₄⋊C₄	—	86	1	no	—
406	C₄⋊C₄	—	86	1	no	—
407	C₄⋊C₄	—	86	1	no	—
408	C₄⋊C₄	—	172	1	no	—
409	C₄⋊C₄	—	172	1	no	—
410	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	172	1	no	—
416	C₄²	—	172	1	no	—
417	C₄²	D₄×D₄₃	1	1	yes	characteristic
418	C₄²	#10621900	1	1	yes	characteristic
419	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
420	C₄²	C₂³×D₄₃	1	1	yes	characteristic
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	1	no	—
426	C₂³	#13063297	1	1	yes	characteristic
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	344	1	no	—
430	Q₈	—	172	1	no	—
431	Q₈	—	172	1	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	2	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	8	1	no	—
439	D₄	—	8	2	no	—
440	D₄	C₂×#10621883	1	4	yes	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	—	172	1	no	—
452	C₂×C₄	—	172	1	no	—
453	C₂×C₄	#13063297	1	1	yes	characteristic
454	C₂×C₄	#13063297	1	1	yes	characteristic
455	C₂×C₄	#13063297	1	1	yes	characteristic
456	C₂×C₄	C₂×#10621883	1	2	yes	—
457	C₂×C₄	#13063345	1	2	yes	—
458	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
460	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
461	C₈	—	4	2	no	—
462	C₈	—	43	2	no	—
463	C₈	—	86	1	no	—
464	C₈	—	86	1	no	—
465	C₈	—	86	1	no	—
466	C₈	—	172	2	no	—
467	C₈	—	172	2	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	4	8	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	#14583126	1	2	yes	—
478	C₂²	C₂×#13063297	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	344	1	no	—
485	C₄	—	344	1	no	—
486	C₄	#14583126	1	2	yes	—
487	C₄	C₂²×#10621883	1	1	yes	characteristic
488	C₄	C₂×#13063345	1	1	yes	characteristic
489	C₄	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
490	C₄	#14583695	1	1	yes	characteristic
491	C₂	—	2	2	no	—
492	C₂	—	4	4	no	—
493	C₂	—	16	1	no	—
494	C₂	#19144056	1	1	yes	characteristic
495	C₂	C₂×#14583126	1	1	yes	characteristic
496	C₂	#19144312	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting, prime radical	C₄₃×#3036	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#3036	D₄₃
hypocenter	C₄₃	#19254
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3036

Complements

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

N	H ≅ G/N	type
1. #19145150	C₂	semidirect
2. #19144392	C₂	semidirect
3. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
4. #19134020	C₂	semidirect
5. #19134002	C₂	semidirect
6. #19133968	C₂	semidirect
7. #19133934	C₂	semidirect
8. #19133350	C₂	semidirect
9. #19133286	C₂	semidirect
10. #19133272	C₂	semidirect
14. #14583295	C₂²	semidirect
15. #14583271	C₂²	semidirect
16. #14583251	C₂²	semidirect
17. #14583245	C₂²	semidirect
35. #14582649	C₂²	semidirect
36. #14582649	C₂²	semidirect
37. #14582647	C₂²	semidirect
38. #14582645	C₂²	semidirect
39. #14582644	C₂²	semidirect
40. #14582643	C₂²	semidirect
121. C₂×D₄×C₄₃	SD₁₆	semidirect
218. C₄₃⋊C₈	AGL(1,ℤ/8)	semidirect
297. C₄₃	#19254	semidirect
372. C₂×D₄	#10621883	semidirect

Maximal subgroups

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

subgroup	index
#19145150	2
#19144392	2
C₂×D₄×C₄₃⋊C₈	2
#19134020	2
#19134002	2
#19133968	2
#19133934	2
#19133350	2
#19133286	2
#19133272	2
C₄₃×#3036	2
#19254	43