Subgroups — #25103493

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583166	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063351	C₂	1	2	yes	maximal, complemented
3	#19143020	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135506	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135373	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135254	C₂	1	2	yes	maximal, complemented
7	#19135106	C₂	1	2	yes	maximal, complemented
8	#19134655	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134501	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063242	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063351	C₂²	1	2	yes	—
13	C₂×#13063331	C₂²	1	1	yes	characteristic
14	C₂×#13063331	C₂²	1	1	yes	characteristic
15	C₄×#10621898	C₂²	1	1	yes	characteristic
16	#14583166	C₄	1	8	yes	complemented
17	#14583009	—	2	2	no	—
18	#14582999	—	2	2	no	—
19	C₄×#10621883	—	2	2	no	—
20	C₄×#10621882	—	2	2	no	—
21	C₂×#13063261	C₂²	1	1	yes	characteristic
22	C₂×#13063261	C₂²	1	1	yes	characteristic
23	#14582939	C₂²	1	2	yes	—
24	#14582904	C₂²	1	2	yes	—
25	#14582898	C₂²	1	2	yes	—
26	C₂×#13063242	C₂²	1	2	yes	—
27	C₂×#13063242	C₂²	1	2	yes	—
28	#14582856	—	2	1	no	—
29	#14582856	—	2	1	no	—
30	#14582854	C₂²	1	1	yes	characteristic
31	#14582854	C₂²	1	1	yes	characteristic
32	C₄×#10621877	C₂²	1	2	yes	—
33	C₄×#10621877	C₂²	1	1	yes	characteristic
34	#14582851	—	2	1	no	—
35	#97×D₄₃	—	2	1	no	—
36	#14582668	C₂²	1	2	yes	—
37	#14582668	C₂²	1	2	yes	—
38	#14582664	C₂²	1	2	yes	—
39	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
41	C₄₃×#442	—	2	1	no	—
42	C₄₃×#442	—	2	1	no	—
43	C₄₃×#442	—	2	1	no	—
44	C₄₃×#442	—	2	1	no	—
45	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#102×C₄₃	C₂²	1	2	yes	—
47	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×#10621898	C₂³	1	1	yes	characteristic
49	#13063351	—	2	4	no	—
50	#13063351	C₂×C₄	1	8	yes	complemented
51	C₂×#10621883	—	2	2	no	—
52	C₂×#10621882	—	2	2	no	—
53	#13063331	—	2	2	no	—
54	#13063331	—	2	2	no	—
55	#13063331	—	2	2	no	—
56	#13063331	C₂×C₄	1	4	yes	complemented
57	C₂×#10621877	C₂³	1	2	yes	—
58	C₂×#10621877	C₂³	1	1	yes	characteristic
59	C₂×#10621877	C₂³	1	2	yes	—
60	C₂×#10621877	C₂³	1	1	yes	characteristic
61	C₂×#10621872	—	2	1	no	—
62	C₂×#10621872	—	2	1	no	—
63	C₂×C₈×D₄₃	—	2	1	no	—
64	C₂×C₈×D₄₃	—	2	1	no	—
65	C₄×Dic₈₆	D₄	1	2	yes	—
66	C₄×D₁₇₂	D₄	1	2	yes	—
67	C₄×C₂²⋊D₄₃	—	2	2	no	—
68	#13063284	C₂³	1	1	yes	characteristic
69	#13063282	—	2	1	no	—
70	C₄²×D₄₃	—	2	1	no	—
71	#13063261	—	2	2	no	—
72	#13063261	C₂×C₄	1	4	yes	complemented
73	#13063258	—	2	2	no	—
74	#13063256	—	2	2	no	—
75	#13063248	—	2	2	no	—
76	#13063246	—	2	2	no	—
77	#13063246	—	2	2	no	—
78	#13063245	—	2	2	no	—
79	#13063242	—	2	4	no	—
80	#13063242	C₂×C₄	1	8	yes	complemented
81	#13063236	—	2	1	no	—
82	#13063236	—	2	2	no	—
83	#13063235	—	2	1	no	—
84	#13063235	—	2	1	no	—
85	C₄×C₄₃⋊C₈	—	2	1	no	—
86	C₄×C₄₃⋊C₈	—	2	2	no	—
87	C₈×Dic₄₃	—	2	1	no	—
88	C₈×Dic₄₃	—	2	1	no	—
89	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₄₃	—	2	2	no	—
91	C₂×D₈×C₄₃	—	2	1	no	—
92	C₂×D₈×C₄₃	—	2	1	no	—
93	C₂×D₈×C₄₃	—	2	2	no	—
94	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	complemented
95	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₄₃	—	2	2	no	—
98	C₄×D₄×C₄₃	—	2	2	no	—
99	C₄×D₄×C₄₃	—	2	2	no	—
100	C₄×D₄×C₄₃	—	2	2	no	—
101	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#106×C₄₃	—	2	1	no	—
105	#106×C₄₃	—	2	1	no	—
106	#102×C₄₃	—	2	2	no	—
107	#102×C₄₃	—	2	2	no	—
108	#97×C₄₃	D₄	1	1	yes	characteristic
109	#97×C₄₃	D₄	1	1	yes	characteristic
110	#97×C₄₃	D₄	1	1	yes	characteristic
111	#97×C₄₃	D₄	1	1	yes	characteristic
112	C₂⁴×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	4	2	no	—
121	C₂²×C₄×C₄₃	—	4	2	no	—
122	C₂²×C₄×C₄₃	—	8	4	no	—
123	C₂²×C₄×C₄₃	#41	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₃	—	2	1	no	—
126	#10621898	—	2	1	no	—
127	#10621898	—	2	1	no	—
128	#10621898	C₂²×C₄	1	2	yes	—
129	#10621898	#41	1	2	yes	—
130	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×D₄₃	—	2	1	no	—
132	C₂×C₄×D₄₃	—	2	2	no	—
133	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
134	D₈×C₄₃	—	2	4	no	—
135	D₈×C₄₃	—	2	4	no	—
136	C₂×C₈×C₄₃	—	2	1	no	—
137	C₂×C₈×C₄₃	—	2	1	no	—
138	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₄₃	#41	1	2	yes	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	2	2	no	—
146	C₂²⋊C₄×C₄₃	—	4	2	no	—
147	C₂²⋊C₄×C₄₃	—	4	2	no	—
148	C₄²×C₄₃	C₂×D₄	1	2	yes	—
149	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂²⋊Dic₄₃	—	2	1	no	—
152	#10621883	—	2	8	no	—
153	#10621882	—	2	8	no	—
154	(C₂×D₄₃)⋊C₄	—	2	2	no	—
155	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
156	Dic₄₃⋊C₄	—	2	2	no	—
157	C₄×Dic₄₃	—	2	2	no	—
158	C₄×Dic₄₃	—	2	1	no	—
159	#10621877	—	2	1	no	—
160	#10621877	—	2	1	no	—
161	#10621877	—	2	2	no	—
162	#10621877	—	2	2	no	—
163	#10621877	—	2	2	no	—
164	#10621877	C₂²×C₄	1	2	yes	—
165	#10621877	C₂²×C₄	1	4	yes	—
166	#10621877	#41	1	2	yes	—
167	C₂×C₄₃⋊C₈	—	2	1	no	—
168	C₂×C₄₃⋊C₈	—	2	1	no	—
169	C₂×C₄₃⋊C₈	—	2	2	no	—
170	C₂×C₄₃⋊C₈	—	2	2	no	—
171	#10621872	—	2	4	no	—
172	#10621872	—	2	4	no	—
173	C₈×D₄₃	—	2	4	no	—
174	C₈×D₄₃	—	2	4	no	—
175	C₂³×C₄₃	—	2	4	no	—
176	C₂³×C₄₃	—	4	2	no	—
177	C₂³×C₄₃	—	4	2	no	—
178	C₂³×C₄₃	—	8	2	no	—
179	C₂³×C₄₃	—	8	2	no	—
180	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂²×D₄₃	—	2	1	no	—
182	D₄×C₄₃	—	2	4	no	—
183	D₄×C₄₃	—	2	4	no	—
184	D₄×C₄₃	—	4	2	no	—
185	D₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	8	4	no	—
189	C₂×C₄×C₄₃	—	8	4	no	—
190	C₂×C₄×C₄₃	—	8	2	no	—
191	C₂×C₄×C₄₃	#121	1	2	yes	—
192	C₂×C₄×C₄₃	#121	1	2	yes	—
193	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
199	C₂²⋊D₄₃	—	2	2	no	—
200	C₂²⋊D₄₃	—	2	2	no	—
201	C₂×Dic₄₃	—	2	1	no	—
202	C₂×Dic₄₃	—	2	2	no	—
203	D₁₇₂	—	2	1	no	—
204	D₁₇₂	C₄×D₄	1	2	yes	—
205	C₄×D₄₃	—	2	2	no	—
206	C₄×D₄₃	—	2	2	no	—
207	C₄×D₄₃	—	8	2	no	—
208	Dic₈₆	—	2	1	no	—
209	Dic₈₆	C₄×D₄	1	2	yes	—
210	C₈×C₄₃	—	2	1	no	—
211	C₈×C₄₃	—	2	1	no	—
212	C₈×C₄₃	C₄×D₄	1	2	yes	—
213	C₈×C₄₃	C₄×D₄	1	2	yes	—
214	C₄₃⋊C₈	—	2	2	no	—
215	C₄₃⋊C₈	—	2	4	no	—
216	C₄₃⋊C₈	—	2	2	no	—
217	C₄₃⋊C₈	—	4	2	no	—
218	#21555	—	43	1	no	maximal, Sylow
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	4	4	no	—
221	C₂²×C₄₃	—	8	4	no	—
222	C₂²×C₄₃	—	8	4	no	—
223	C₂²×C₄₃	—	8	2	no	—
224	C₂²×C₄₃	—	8	2	no	—
225	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
226	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
227	C₂²×C₄₃	#529	1	1	yes	characteristic
228	C₂×D₄₃	—	2	2	no	—
229	C₂×D₄₃	—	4	2	no	—
230	C₄×C₄₃	—	2	2	no	—
231	C₄×C₄₃	—	2	2	no	—
232	C₄×C₄₃	—	8	2	no	—
233	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
234	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₄₃	#525	1	1	yes	characteristic
236	C₄×C₄₃	#532	1	1	yes	characteristic
237	Dic₄₃	—	2	2	no	—
238	Dic₄₃	—	4	2	no	—
239	C₂×#472	—	43	1	no	—
240	C₄×AGL(1,ℤ/8)	—	43	2	no	—
241	C₂×#442	D₄₃	1	1	yes	characteristic, complemented
242	#2875	—	43	1	no	—
243	#1978	—	43	1	no	—
244	#1951	—	43	1	no	—
245	#1931	—	43	2	no	—
246	#1907	—	43	2	no	—
247	#1815	—	43	1	no	—
248	#1778	—	43	1	no	—
249	C₄×#100	—	43	2	no	—
250	C₂×C₄₃	—	2	1	no	—
251	C₂×C₄₃	—	2	1	no	—
252	C₂×C₄₃	—	8	4	no	—
253	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
254	C₂×C₄₃	#3068	1	2	yes	—
255	D₄₃	—	4	2	no	—
256	C₂×AGL(1,ℤ/8)	—	43	2	no	—
257	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
258	C₂×#131	—	43	1	no	—
259	C₂×#131	—	43	1	no	—
260	C₄×#41	—	43	1	no	—
261	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
262	#472	—	43	8	no	—
263	#442	—	2	1	no	—
264	#442	—	2	1	no	—
265	#442	—	2	1	no	—
266	#442	—	2	1	no	—
267	#442	—	86	2	no	—
268	#440	—	86	2	no	—
269	C₄×SD₁₆	—	86	2	no	—
270	C₄×D₈	—	86	2	no	—
271	C₂×#108	—	43	1	no	—
272	C₂×#108	—	43	1	no	—
273	#428	—	43	2	no	—
274	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
275	#418	—	43	2	no	—
276	#417	—	43	2	no	—
277	C₂×#102	C₂×D₄₃	1	2	yes	—
278	C₂×#100	—	43	2	no	—
279	C₂×#100	—	43	2	no	—
280	#405	—	43	1	no	—
281	#405	—	43	1	no	—
282	#405	—	86	1	no	—
283	#405	—	86	1	no	—
284	C₄×M₁₆	—	43	1	no	—
285	C₄×M₁₆	—	43	2	no	—
286	C₄×M₁₆	—	86	1	no	—
287	C₂×#97	—	86	1	no	—
288	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
289	#343	—	43	2	no	—
290	#343	—	43	2	no	—
291	#341	—	43	2	no	—
292	C₄₃	#21555	1	1	yes	characteristic, complemented, Sylow
293	C₂×#41	—	43	1	no	—
294	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
295	C₂³×C₄	—	2	2	no	—
296	AGL(1,ℤ/8)	—	43	8	no	—
297	AGL(1,ℤ/8)	—	86	4	no	—
298	C₂×SD₁₆	—	86	2	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	1	no	—
301	C₂×D₈	—	2	1	no	—
302	C₂×D₈	—	86	2	no	—
303	C₂×D₈	C₄×D₄₃	1	4	yes	complemented
304	#131	—	43	4	no	—
305	#131	—	86	2	no	—
306	#131	—	86	2	no	—
307	#131	—	86	2	no	—
308	C₂×M₁₆	—	43	1	no	—
309	C₂×M₁₆	—	43	1	no	—
310	C₂×M₁₆	—	43	2	no	—
311	C₂×M₁₆	—	43	2	no	—
312	C₂×M₁₆	—	86	1	no	—
313	C₂×M₁₆	—	86	1	no	—
314	C₂²×C₈	—	86	1	no	—
315	C₂²×C₈	—	86	1	no	—
316	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
318	C₄×Q₈	—	43	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	43	2	no	—
324	C₄×D₄	—	86	2	no	—
325	#117	—	43	1	no	—
326	#117	—	86	1	no	—
327	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₄²	—	86	1	no	—
330	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
331	#108	—	43	4	no	—
332	#108	—	86	2	no	—
333	#107	—	86	2	no	—
334	#106	—	2	1	no	—
335	#106	—	2	1	no	—
336	#106	—	86	2	no	—
337	#103	—	86	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	#102	—	86	2	no	—
341	#102	—	86	2	no	—
342	#102	—	86	2	no	—
343	#100	—	43	8	no	—
344	#100	—	86	4	no	—
345	#97	—	86	1	no	—
346	#97	—	86	1	no	—
347	#97	—	86	2	no	—
348	#97	—	86	1	no	—
349	#97	C₂²⋊D₄₃	1	1	yes	characteristic
350	#97	C₂²⋊D₄₃	1	1	yes	characteristic
351	#97	C₂²⋊D₄₃	1	1	yes	characteristic
352	#97	C₂²⋊D₄₃	1	1	yes	characteristic
353	C₄×C₈	—	86	1	no	—
354	C₄×C₈	—	86	1	no	—
355	C₄×C₈	—	86	2	no	—
356	C₄×C₈	—	86	1	no	—
357	C₂⁴	—	2	2	no	—
358	#41	—	43	2	no	—
359	#41	—	43	2	no	—
360	#41	—	86	1	no	—
361	#41	—	86	1	no	—
362	C₂×Q₈	—	43	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	43	1	no	—
369	C₂×D₄	—	86	1	no	—
370	C₂×D₄	C₂×C₄×D₄₃	1	4	yes	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	8	4	no	—
375	C₂²×C₄	—	86	1	no	—
376	C₂²×C₄	—	86	2	no	—
377	C₂²×C₄	#10621900	1	2	yes	—
378	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
379	SD₁₆	—	86	8	no	—
380	D₈	—	2	4	no	—
381	D₈	—	2	4	no	—
382	D₈	—	86	8	no	—
383	M₁₆	—	43	2	no	—
384	M₁₆	—	43	4	no	—
385	M₁₆	—	43	2	no	—
386	M₁₆	—	86	4	no	—
387	M₁₆	—	86	1	no	—
388	M₁₆	—	86	2	no	—
389	M₁₆	—	86	1	no	—
390	M₁₆	—	86	4	no	—
391	M₁₆	—	86	2	no	—
392	M₁₆	—	86	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	86	4	no	—
396	C₂×C₈	—	86	2	no	—
397	C₂×C₈	—	86	1	no	—
398	C₂×C₈	—	86	1	no	—
399	C₂×C₈	—	86	4	no	—
400	C₂×C₈	—	86	2	no	—
401	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
402	C₂×C₈	#10621898	1	2	yes	—
403	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
404	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
405	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
406	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	43	2	no	—
410	C₄⋊C₄	—	86	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	86	1	no	—
414	C₂²⋊C₄	—	86	2	no	—
415	C₄²	—	86	2	no	—
416	C₄²	—	86	1	no	—
417	C₄²	D₄×D₄₃	1	2	yes	—
418	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
419	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
420	C₂³	—	2	4	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	8	2	no	—
424	C₂³	—	8	2	no	—
425	C₂³	—	86	1	no	—
426	C₂³	C₂×#10621900	1	1	yes	characteristic
427	Q₈	—	43	2	no	—
428	Q₈	—	86	1	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	43	2	no	—
434	D₄	—	86	2	no	—
435	D₄	—	86	2	no	—
436	D₄	—	86	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	4	no	—
440	C₂×C₄	—	8	4	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	—	86	1	no	—
443	C₂×C₄	—	86	2	no	—
444	C₂×C₄	—	86	2	no	—
445	C₂×C₄	—	86	2	no	—
446	C₂×C₄	—	344	2	no	—
447	C₂×C₄	#13063296	1	2	yes	—
448	C₂×C₄	#13063296	1	2	yes	—
449	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
450	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
452	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
453	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
454	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	86	4	no	—
458	C₈	—	86	2	no	—
459	C₈	—	86	2	no	—
460	C₈	—	172	2	no	—
461	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
462	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	8	4	no	—
466	C₂²	—	8	4	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	86	2	no	—
470	C₂²	—	172	2	no	—
471	C₂²	C₄×#10621900	1	1	yes	characteristic
472	C₂²	C₂×#13063296	1	1	yes	characteristic
473	C₂²	#14583431	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	8	2	no	—
477	C₄	—	86	2	no	—
478	C₄	—	172	2	no	—
479	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
480	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
481	C₄	#14583406	1	1	yes	characteristic
482	C₄	#14583446	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	4	no	—
486	C₂	—	172	2	no	—
487	C₂	C₄×#13063296	1	1	yes	characteristic
488	C₂	#19144319	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#442	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂×#14583166	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#442	D₄₃
hypocenter	C₄₃	#21555
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#442

Complements

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

N	H ≅ G/N	type
2. C₄×#13063351	C₂	semidirect
3. #19143020	C₂	semidirect
4. #19135506	C₂	semidirect
5. #19135373	C₂	semidirect
6. #19135254	C₂	semidirect
7. #19135106	C₂	semidirect
8. #19134655	C₂	semidirect
9. #19134501	C₂	semidirect
10. C₄×#13063242	C₂	semidirect
11. C₂×C₄₃×#442	C₂	semidirect
16. #14583166	C₄	semidirect
50. #13063351	C₂×C₄	semidirect
56. #13063331	C₂×C₄	semidirect
72. #13063261	C₂×C₄	semidirect
80. #13063242	C₂×C₄	semidirect
94. C₂×D₈×C₄₃	C₂×C₄	semidirect
241. C₂×#442	D₄₃	semidirect
292. C₄₃	#21555	semidirect
303. C₂×D₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583166	2
C₄×#13063351	2
#19143020	2
#19135506	2
#19135373	2
#19135254	2
#19135106	2
#19134655	2
#19134501	2
C₄×#13063242	2
C₂×C₄₃×#442	2
#21555	43