Subgroups — #25080391

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145177	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144392	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#19134048	C₂	1	2	yes	maximal, complemented
5	#19134044	C₂	1	2	yes	maximal, complemented
6	#19133992	C₂	1	2	yes	maximal, complemented
7	#19133958	C₂	1	2	yes	maximal, complemented
8	#19133353	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133286	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133285	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3077	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₃⋊C₈	—	2	1	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	#14583302	C₂²	1	1	yes	characteristic, complemented
15	#14583278	C₂²	1	1	yes	characteristic, complemented
16	#14583251	C₂²	1	1	yes	characteristic, complemented
17	#14583249	C₂²	1	1	yes	characteristic, complemented
18	#14583199	—	2	2	no	—
19	#14583189	C₂²	1	2	yes	—
20	#14583179	C₂²	1	2	yes	—
21	#14583138	—	2	1	no	—
22	#14583138	—	2	1	no	—
23	C₄×#10621885	—	2	1	no	—
24	C₄×#10621885	—	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	#14582651	C₂²	1	2	yes	complemented
36	#14582651	C₂²	1	2	yes	complemented
37	#14582648	C₂²	1	2	yes	complemented
38	#14582647	C₂²	1	2	yes	complemented
39	#14582645	C₂²	1	2	yes	complemented
40	#14582644	C₂²	1	2	yes	complemented
41	C₄₃×#533	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#478	—	2	2	no	—
44	C₄₃×#476	C₂²	1	2	yes	—
45	C₄₃×#474	C₂²	1	2	yes	—
46	C₄₃×#428	—	2	1	no	—
47	C₄₃×#423	C₂²	1	1	yes	characteristic
48	C₄₃×#418	—	2	1	no	—
49	C₂×#10621885	—	2	1	no	—
50	C₂×#10621885	—	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	#13063258	—	2	1	no	—
68	#13063258	—	2	1	no	—
69	#13063256	—	2	2	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	#13063249	—	2	1	no	—
75	#13063249	—	2	1	no	—
76	#13063248	—	2	1	no	—
77	#13063248	—	2	1	no	—
78	#13063246	—	2	2	no	—
79	#13063246	—	2	2	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	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₄₃	—	2	1	no	—
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
91	#125×C₄₃	—	2	1	no	—
92	C₂²⋊Q₈×C₄₃	—	2	1	no	—
93	C₂²⋊Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	—	2	1	no	—
95	C₄×Q₈×C₄₃	—	2	1	no	—
96	C₄×D₄×C₄₃	—	2	1	no	—
97	C₄×D₄×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	D₄	1	2	yes	—
99	C₄×D₄×C₄₃	C₂³	1	2	yes	—
100	#117×C₄₃	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#107×C₄₃	—	2	2	no	—
105	#106×C₄₃	—	2	2	no	—
106	C₄⋊C₈×C₄₃	—	2	1	no	—
107	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
108	#102×C₄₃	—	2	2	no	—
109	#102×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	Q₁₆	1	4	yes	complemented
116	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	4	2	no	—
121	C₂²×C₄×C₄₃	—	4	2	no	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
125	C₂×Dic₈₆	—	2	1	no	—
126	C₂×Dic₈₆	—	2	1	no	—
127	M₁₆×C₄₃	—	4	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	1	no	—
134	C₄⋊C₄×C₄₃	—	4	1	no	—
135	C₄⋊C₄×C₄₃	—	4	1	no	—
136	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₄₃	—	2	2	no	—
138	C₂²⋊C₄×C₄₃	—	2	2	no	—
139	C₂²⋊C₄×C₄₃	—	4	1	no	—
140	C₄²×C₄₃	—	4	1	no	—
141	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₄₃	#41	1	1	yes	characteristic
144	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
145	C₂²⋊Dic₄₃	—	4	1	no	—
146	#10621885	—	4	2	no	—
147	#10621885	—	4	2	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	Dic₄₃⋊C₄	—	4	1	no	—
153	Dic₄₃⋊C₄	—	4	1	no	—
154	C₄×Dic₄₃	—	4	1	no	—
155	#10621877	—	4	2	no	—
156	C₂×C₄₃⋊C₈	—	2	2	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	4	1	no	—
160	C₂×C₄₃⋊C₈	—	4	4	no	—
161	C₂×C₄₃⋊C₈	—	4	2	no	—
162	C₂×C₄₃⋊C₈	—	4	4	no	—
163	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₄₃	—	2	2	no	—
168	C₂³×C₄₃	—	2	4	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	#121	1	1	yes	characteristic
172	Q₈×C₄₃	—	4	1	no	—
173	Q₈×C₄₃	—	4	1	no	—
174	Q₈×C₄₃	—	8	1	no	—
175	D₄×C₄₃	—	2	2	no	—
176	D₄×C₄₃	—	2	4	no	—
177	D₄×C₄₃	C₂×Q₁₆	1	4	yes	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	4	4	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
190	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
192	C₂×C₄×C₄₃	#135	1	2	yes	—
193	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂×Dic₄₃	—	4	1	no	—
197	C₂×Dic₄₃	—	4	1	no	—
198	Dic₈₆	—	4	1	no	—
199	Dic₈₆	—	4	1	no	—
200	Dic₈₆	—	8	1	no	—
201	C₈×C₄₃	—	4	2	no	—
202	C₄₃⋊C₈	—	2	1	no	—
203	C₄₃⋊C₈	—	2	1	no	—
204	C₄₃⋊C₈	—	2	1	no	—
205	C₄₃⋊C₈	—	4	2	no	—
206	C₄₃⋊C₈	—	4	2	no	—
207	C₄₃⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
208	#19256	—	43	1	no	maximal, Sylow
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	—	2	4	no	—
212	C₂²×C₄₃	—	4	8	no	—
213	C₂²×C₄₃	—	4	2	no	—
214	C₂²×C₄₃	—	4	2	no	—
215	C₂²×C₄₃	#467	1	2	yes	—
216	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
217	C₄×C₄₃	—	2	1	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	—	8	1	no	—
222	C₄×C₄₃	—	8	1	no	—
223	C₄×C₄₃	#467	1	2	yes	—
224	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
225	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
226	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₄₃	#575	1	1	yes	characteristic
228	Dic₄₃	—	8	1	no	—
229	Dic₄₃	—	8	1	no	—
230	#3170	—	43	1	no	—
231	#3077	—	43	1	no	—
232	#3077	D₄₃	1	1	yes	characteristic
233	C₂×C₈×D₄	—	43	1	no	—
234	#1683	—	43	2	no	—
235	#1683	—	43	2	no	—
236	#1675	—	43	2	no	—
237	#1669	—	43	2	no	—
238	#1567	—	43	1	no	—
239	#1550	—	43	1	no	—
240	#1550	—	43	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	—	4	4	no	—
243	C₂×C₄₃	#3036	1	1	yes	characteristic
244	C₂×C₄₃	C₂×#467	1	1	yes	characteristic
245	C₂×C₄₃	#3067	1	1	yes	characteristic
246	C₂³×C₈	—	86	1	no	—
247	#533	—	43	1	no	—
248	#533	C₂×D₄₃	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
250	#500	—	43	1	no	—
251	#494	—	43	1	no	—
252	#487	—	43	1	no	—
253	#487	—	43	1	no	—
254	#478	—	2	2	no	—
255	#478	—	86	2	no	—
256	#476	—	43	2	no	—
257	#476	C₂×D₄₃	1	2	yes	—
258	#474	—	43	2	no	—
259	#474	C₂×D₄₃	1	2	yes	—
260	#467	—	86	1	no	—
261	#467	—	86	1	no	—
262	C₄×Q₁₆	—	86	1	no	—
263	C₄×Q₁₆	—	86	1	no	—
264	C₈×D₄	—	43	2	no	—
265	C₈×D₄	—	43	2	no	—
266	C₈×D₄	—	86	1	no	—
267	C₈×D₄	—	86	1	no	—
268	#428	—	2	1	no	—
269	#428	—	86	1	no	—
270	#423	—	43	1	no	—
271	#423	C₂×D₄₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	43	1	no	—
273	#418	—	2	1	no	—
274	#418	—	86	1	no	—
275	C₂×C₂²⋊C₈	—	86	1	no	—
276	C₂×C₄×C₈	—	43	1	no	—
277	#335	—	43	2	no	—
278	#335	—	43	2	no	—
279	#333	—	43	2	no	—
280	#333	—	43	2	no	—
281	#332	—	43	2	no	—
282	#332	—	43	2	no	—
283	C₄₃	#19256	1	1	yes	characteristic, complemented, Sylow
284	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂×Q₁₆	—	86	1	no	—
287	C₂×Q₁₆	—	86	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	86	1	no	—
290	C₂²×C₈	—	43	1	no	—
291	C₂²×C₈	—	43	1	no	—
292	C₂²×C₈	—	86	2	no	—
293	C₂²×C₈	—	86	2	no	—
294	C₂²×C₈	—	86	1	no	—
295	C₂²×C₈	—	172	4	no	—
296	C₄⋊Q₈	—	43	1	no	—
297	C₄⋊Q₈	—	43	1	no	—
298	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
299	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
300	#125	—	2	1	no	—
301	#125	—	86	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	86	1	no	—
305	C₂²⋊Q₈	—	86	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	86	1	no	—
309	C₄×Q₈	—	86	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
313	C₄×D₄	C₂²×D₄₃	1	2	yes	—
314	#117	—	2	1	no	—
315	#117	—	86	1	no	—
316	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
319	#107	—	2	2	no	—
320	#107	—	86	1	no	—
321	#107	—	86	1	no	—
322	#107	—	86	2	no	—
323	#106	—	2	2	no	—
324	#106	—	86	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	43	2	no	—
327	C₄⋊C₈	—	43	2	no	—
328	C₄⋊C₈	—	86	1	no	—
329	C₄⋊C₈	—	86	1	no	—
330	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
331	#103	—	86	1	no	—
332	#103	—	86	1	no	—
333	#103	—	86	1	no	—
334	#103	—	86	1	no	—
335	#102	—	2	2	no	—
336	#102	—	2	2	no	—
337	#102	—	86	2	no	—
338	#102	—	86	2	no	—
339	C₂²⋊C₈	—	86	2	no	—
340	C₂²⋊C₈	—	86	2	no	—
341	C₄×C₈	—	43	1	no	—
342	C₄×C₈	—	43	1	no	—
343	C₄×C₈	—	43	1	no	—
344	C₄×C₈	—	43	1	no	—
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	86	1	no	—
349	C₂×Q₈	—	86	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	#10621885	1	4	yes	complemented
353	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
360	C₂²×C₄	#10621900	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
362	Q₁₆	—	172	2	no	—
363	Q₁₆	—	172	2	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	172	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	43	1	no	—
368	C₂×C₈	—	43	1	no	—
369	C₂×C₈	—	43	1	no	—
370	C₂×C₈	—	43	1	no	—
371	C₂×C₈	—	86	2	no	—
372	C₂×C₈	—	86	2	no	—
373	C₂×C₈	—	86	2	no	—
374	C₂×C₈	—	172	4	no	—
375	C₂×C₈	—	172	1	no	—
376	C₂×C₈	—	172	4	no	—
377	C₂×C₈	—	172	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	86	1	no	—
386	C₄⋊C₄	—	86	1	no	—
387	C₄⋊C₄	—	86	1	no	—
388	C₄⋊C₄	—	86	1	no	—
389	C₄⋊C₄	—	172	1	no	—
390	C₄⋊C₄	—	172	1	no	—
391	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	172	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	172	1	no	—
398	C₄²	D₄×D₄₃	1	1	yes	characteristic
399	C₄²	#10621900	1	1	yes	characteristic
400	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
401	C₄²	C₂³×D₄₃	1	1	yes	characteristic
402	C₂³	—	2	2	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	#13063297	1	1	yes	characteristic
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	8	1	no	—
410	Q₈	—	344	1	no	—
411	Q₈	—	172	1	no	—
412	Q₈	—	172	1	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	C₂×#10621885	1	4	yes	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	172	1	no	—
427	C₂×C₄	—	172	1	no	—
428	C₂×C₄	#13063297	1	1	yes	characteristic
429	C₂×C₄	#13063297	1	1	yes	characteristic
430	C₂×C₄	#13063297	1	1	yes	characteristic
431	C₂×C₄	C₂×#10621885	1	2	yes	—
432	C₂×C₄	#13063345	1	2	yes	—
433	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	43	2	no	—
438	C₈	—	86	1	no	—
439	C₈	—	86	1	no	—
440	C₈	—	86	1	no	—
441	C₈	—	172	2	no	—
442	C₈	—	172	2	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	#14583138	1	2	yes	—
450	C₂²	C₂×#13063297	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	—	344	1	no	—
458	C₄	—	344	1	no	—
459	C₄	#14583138	1	2	yes	—
460	C₄	C₂²×#10621885	1	1	yes	characteristic
461	C₄	C₂×#13063345	1	1	yes	characteristic
462	C₄	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
463	C₄	#14583695	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	4	4	no	—
466	C₂	#19144056	1	1	yes	characteristic
467	C₂	C₂×#14583138	1	1	yes	characteristic
468	C₂	#19144312	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3077	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂²×D₄×C₄₃	D₄
hypercenter	#3077	D₄₃
hypocenter	C₄₃	#19256
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3077

Complements

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

N	H ≅ G/N	type
1. #19145177	C₂	semidirect
4. #19134048	C₂	semidirect
5. #19134044	C₂	semidirect
6. #19133992	C₂	semidirect
7. #19133958	C₂	semidirect
8. #19133353	C₂	semidirect
9. #19133286	C₂	semidirect
10. #19133285	C₂	semidirect
14. #14583302	C₂²	semidirect
15. #14583278	C₂²	semidirect
16. #14583251	C₂²	semidirect
17. #14583249	C₂²	semidirect
35. #14582651	C₂²	semidirect
36. #14582651	C₂²	semidirect
37. #14582648	C₂²	semidirect
38. #14582647	C₂²	semidirect
39. #14582645	C₂²	semidirect
40. #14582644	C₂²	semidirect
115. C₂×D₄×C₄₃	Q₁₆	semidirect
283. C₄₃	#19256	semidirect
352. C₂×D₄	#10621885	semidirect

Maximal subgroups

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

subgroup	index
#19145177	2
#19144392	2
C₂×D₄×C₄₃⋊C₈	2
#19134048	2
#19134044	2
#19133992	2
#19133958	2
#19133353	2
#19133286	2
#19133285	2
C₄₃×#3077	2
#19256	43