Subgroups — C₄×#14583171 #25103482

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583171	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063356	C₂	1	2	yes	maximal
3	C₄×#13063331	C₂	1	1	yes	maximal, characteristic
4	#19135511	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135378	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135247	C₂	1	2	yes	maximal, complemented
7	#19135113	C₂	1	2	yes	maximal
8	#19134660	C₂	1	1	yes	maximal, characteristic
9	C₄×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063244	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	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	#14583171	C₄	1	8	yes	direct product factor
17	#14583004	—	2	2	no	—
18	#14582997	—	2	2	no	—
19	C₄×#10621885	—	2	2	no	—
20	C₄×#10621884	—	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	#14582908	C₂²	1	2	yes	—
25	#14582898	C₂²	1	2	yes	—
26	C₂×#13063244	C₂²	1	2	yes	—
27	C₂×#13063244	C₂²	1	2	yes	—
28	#14582854	C₂²	1	1	yes	characteristic
29	#14582854	C₂²	1	1	yes	characteristic
30	#14582853	—	2	1	no	—
31	#14582853	—	2	1	no	—
32	C₄×#10621877	C₂²	1	2	yes	—
33	C₄×#10621877	C₂²	1	1	yes	characteristic
34	C₄×#10621872	—	2	1	no	—
35	C₄×C₈×D₄₃	—	2	1	no	—
36	#14582668	C₂²	1	2	yes	—
37	#14582668	C₂²	1	2	yes	—
38	#14582664	C₂²	1	2	yes	—
39	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₄₃	—	2	1	no	—
42	C₄×Q₁₆×C₄₃	—	2	1	no	—
43	C₄×Q₁₆×C₄₃	—	2	1	no	—
44	C₄×Q₁₆×C₄₃	—	2	1	no	—
45	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#103×C₄₃	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×#10621898	C₂³	1	1	yes	characteristic
49	#13063356	—	2	4	no	—
50	#13063356	C₂×C₄	1	8	yes	—
51	C₂×#10621885	—	2	2	no	—
52	C₂×#10621884	—	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	—
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	1	yes	characteristic
66	C₄×Dic₈₆	D₄	1	1	yes	characteristic
67	C₄×D₁₇₂	D₄	1	1	yes	characteristic
68	C₄×D₁₇₂	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₃	—	2	1	no	—
70	C₄×C₂²⋊D₄₃	—	2	1	no	—
71	#13063284	C₂³	1	1	yes	characteristic
72	#13063282	—	2	1	no	—
73	C₄²×D₄₃	—	2	1	no	—
74	#13063261	—	2	2	no	—
75	#13063261	C₂×C₄	1	4	yes	complemented
76	#13063258	—	2	2	no	—
77	#13063256	—	2	2	no	—
78	#13063249	—	2	2	no	—
79	#13063249	—	2	2	no	—
80	#13063248	—	2	2	no	—
81	#13063245	—	2	2	no	—
82	#13063244	—	2	4	no	—
83	#13063244	C₂×C₄	1	8	yes	complemented
84	#13063236	—	2	1	no	—
85	#13063236	—	2	2	no	—
86	#13063235	—	2	1	no	—
87	#13063235	—	2	1	no	—
88	C₄×C₄₃⋊C₈	—	2	1	no	—
89	C₄×C₄₃⋊C₈	—	2	2	no	—
90	C₈×Dic₄₃	—	2	1	no	—
91	C₈×Dic₄₃	—	2	1	no	—
92	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
93	C₂×Q₁₆×C₄₃	—	2	1	no	—
94	C₂×Q₁₆×C₄₃	—	2	1	no	—
95	C₂×Q₁₆×C₄₃	—	2	2	no	—
96	C₂×Q₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
97	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₄₃	—	2	2	no	—
100	C₄×Q₈×C₄₃	—	2	2	no	—
101	C₄×Q₈×C₄₃	—	2	2	no	—
102	C₄×Q₈×C₄₃	—	2	2	no	—
103	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
105	C₂×C₄²×C₄₃	—	2	2	no	—
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	#107×C₄₃	—	2	1	no	—
108	#107×C₄₃	—	2	1	no	—
109	#103×C₄₃	—	2	2	no	—
110	#103×C₄₃	—	2	2	no	—
111	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
112	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
113	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
114	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	2	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
126	C₂×C₂²⋊D₄₃	—	2	1	no	—
127	#10621898	—	2	1	no	—
128	#10621898	—	2	1	no	—
129	#10621898	C₂²×C₄	1	2	yes	—
130	#10621898	#41	1	2	yes	—
131	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×D₄₃	—	2	1	no	—
133	C₂×C₄×D₄₃	—	2	1	no	—
134	C₂×C₄×D₄₃	—	2	1	no	—
135	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
136	Q₁₆×C₄₃	—	2	4	no	—
137	Q₁₆×C₄₃	—	2	4	no	—
138	C₂×C₈×C₄₃	—	2	1	no	—
139	C₂×C₈×C₄₃	—	2	1	no	—
140	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₄₃	#41	1	2	yes	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	2	no	—
148	C₄⋊C₄×C₄₃	—	4	2	no	—
149	C₄⋊C₄×C₄₃	—	4	2	no	—
150	C₄²×C₄₃	—	4	2	no	—
151	C₄²×C₄₃	—	4	2	no	—
152	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂²⋊Dic₄₃	—	2	1	no	—
157	#10621885	—	2	8	no	—
158	#10621884	—	2	8	no	—
159	(C₂×D₄₃)⋊C₄	—	2	1	no	—
160	(C₂×D₄₃)⋊C₄	—	2	1	no	—
161	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
162	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
163	Dic₄₃⋊C₄	—	2	1	no	—
164	Dic₄₃⋊C₄	—	2	1	no	—
165	C₄×Dic₄₃	—	2	1	no	—
166	C₄×Dic₄₃	—	2	1	no	—
167	C₄×Dic₄₃	—	2	1	no	—
168	#10621877	—	2	1	no	—
169	#10621877	—	2	1	no	—
170	#10621877	—	2	2	no	—
171	#10621877	—	2	2	no	—
172	#10621877	—	2	2	no	—
173	#10621877	C₂²×C₄	1	2	yes	—
174	#10621877	C₂²×C₄	1	4	yes	—
175	#10621877	#41	1	2	yes	—
176	C₂×C₄₃⋊C₈	—	2	1	no	—
177	C₂×C₄₃⋊C₈	—	2	1	no	—
178	C₂×C₄₃⋊C₈	—	2	2	no	—
179	C₂×C₄₃⋊C₈	—	2	2	no	—
180	#10621872	—	2	4	no	—
181	#10621872	—	2	4	no	—
182	C₈×D₄₃	—	2	4	no	—
183	C₈×D₄₃	—	2	4	no	—
184	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
185	C₂²×D₄₃	—	2	1	no	—
186	Q₈×C₄₃	—	2	4	no	—
187	Q₈×C₄₃	—	2	4	no	—
188	Q₈×C₄₃	—	4	2	no	—
189	Q₈×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	4	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	—	8	2	no	—
197	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
198	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
199	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
200	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
207	C₂²⋊D₄₃	—	2	2	no	—
208	C₂²⋊D₄₃	—	2	2	no	—
209	C₂×Dic₄₃	—	2	1	no	—
210	C₂×Dic₄₃	—	2	1	no	—
211	C₂×Dic₄₃	—	2	1	no	—
212	D₁₇₂	—	2	1	no	—
213	D₁₇₂	C₄×D₄	1	2	yes	—
214	C₄×D₄₃	—	2	2	no	—
215	C₄×D₄₃	—	2	2	no	—
216	C₄×D₄₃	—	4	2	no	—
217	C₄×D₄₃	—	4	2	no	—
218	Dic₈₆	—	2	1	no	—
219	Dic₈₆	C₄×D₄	1	2	yes	—
220	C₈×C₄₃	—	2	1	no	—
221	C₈×C₄₃	—	2	1	no	—
222	C₈×C₄₃	C₄×D₄	1	2	yes	—
223	C₈×C₄₃	C₄×D₄	1	2	yes	—
224	C₄₃⋊C₈	—	2	2	no	—
225	C₄₃⋊C₈	—	2	4	no	—
226	C₄₃⋊C₈	—	2	2	no	—
227	C₄₃⋊C₈	—	4	2	no	—
228	C₄×#473	—	43	1	no	maximal, Sylow
229	C₂²×C₄₃	—	2	1	no	—
230	C₂²×C₄₃	—	2	1	no	—
231	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
232	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
233	C₂²×C₄₃	#529	1	1	yes	characteristic
234	C₂×D₄₃	—	2	2	no	—
235	C₂×D₄₃	—	4	1	no	—
236	C₂×D₄₃	—	4	1	no	—
237	C₄×C₄₃	—	2	1	no	—
238	C₄×C₄₃	—	2	1	no	—
239	C₄×C₄₃	—	2	1	no	—
240	C₄×C₄₃	—	4	4	no	—
241	C₄×C₄₃	—	8	2	no	—
242	C₄×C₄₃	#473	1	2	yes	complemented
243	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₄₃	#525	1	1	yes	characteristic
246	C₄×C₄₃	#532	1	1	yes	characteristic
247	Dic₄₃	—	2	2	no	—
248	Dic₄₃	—	4	1	no	—
249	Dic₄₃	—	4	1	no	—
250	C₂×#473	—	43	1	no	—
251	C₄×#137	—	43	2	no	—
252	C₂×C₄×Q₁₆	D₄₃	1	1	yes	characteristic, complemented
253	C₄×#131	—	43	1	no	—
254	#1979	—	43	1	no	—
255	#1952	—	43	1	no	—
256	#1930	—	43	2	no	—
257	#1908	—	43	2	no	—
258	#1816	—	43	1	no	—
259	C₄×#108	—	43	1	no	—
260	C₄×#101	—	43	2	no	—
261	C₂×C₄₃	—	2	1	no	—
262	C₂×C₄₃	—	2	1	no	—
263	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
264	C₂×C₄₃	C₂×#473	1	1	yes	characteristic
265	C₂×C₄₃	#3067	1	1	yes	characteristic
266	D₄₃	—	4	2	no	—
267	C₂×#137	—	43	2	no	—
268	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
269	C₂×#131	—	43	1	no	—
270	C₂×#131	—	43	1	no	—
271	C₄×#41	—	43	1	no	—
272	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
273	#473	—	43	8	no	—
274	#441	—	86	2	no	—
275	#440	—	86	2	no	—
276	C₄×Q₁₆	—	2	1	no	—
277	C₄×Q₁₆	—	2	1	no	—
278	C₄×Q₁₆	—	2	1	no	—
279	C₄×Q₁₆	—	2	1	no	—
280	C₄×Q₁₆	—	86	2	no	—
281	C₄×SD₁₆	—	86	2	no	—
282	C₂×#108	—	43	1	no	—
283	C₂×#108	—	43	1	no	—
284	#428	—	43	2	no	—
285	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
286	#419	—	43	2	no	—
287	#417	—	43	2	no	—
288	C₂×#103	C₂×D₄₃	1	2	yes	—
289	C₂×#101	—	43	2	no	—
290	C₂×#101	—	43	2	no	—
291	#405	—	43	1	no	—
292	#405	—	43	1	no	—
293	#405	—	86	1	no	—
294	#405	—	86	1	no	—
295	C₄×M₁₆	—	43	1	no	—
296	C₄×M₁₆	—	43	2	no	—
297	C₄×M₁₆	—	86	1	no	—
298	C₂×C₄×C₈	—	86	1	no	—
299	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
300	#343	—	43	2	no	—
301	#343	—	43	2	no	—
302	#341	—	43	2	no	—
303	C₄₃	C₄×#473	1	1	yes	characteristic, complemented, Sylow
304	C₂×#41	—	43	1	no	—
305	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
306	#137	—	43	8	no	—
307	#137	—	86	4	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×Q₁₆	—	2	1	no	—
311	C₂×Q₁₆	—	86	2	no	—
312	C₂×Q₁₆	C₄×D₄₃	1	4	yes	complemented
313	C₂×SD₁₆	—	86	2	no	—
314	#131	—	43	4	no	—
315	#131	—	86	2	no	—
316	#131	—	86	2	no	—
317	#131	—	86	2	no	—
318	C₂×M₁₆	—	43	1	no	—
319	C₂×M₁₆	—	43	1	no	—
320	C₂×M₁₆	—	43	2	no	—
321	C₂×M₁₆	—	43	2	no	—
322	C₂×M₁₆	—	86	1	no	—
323	C₂×M₁₆	—	86	1	no	—
324	C₂²×C₈	—	86	1	no	—
325	C₂²×C₈	—	86	1	no	—
326	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	43	1	no	—
333	C₄×Q₈	—	43	1	no	—
334	C₄×D₄	—	43	1	no	—
335	C₄×D₄	—	43	1	no	—
336	C₄×D₄	—	86	1	no	—
337	C₄×D₄	—	86	1	no	—
338	#117	—	43	1	no	—
339	#117	—	86	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	86	1	no	—
344	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
345	#108	—	43	4	no	—
346	#108	—	86	2	no	—
347	#107	—	2	1	no	—
348	#107	—	2	1	no	—
349	#107	—	86	2	no	—
350	#106	—	86	2	no	—
351	#103	—	2	2	no	—
352	#103	—	2	2	no	—
353	#103	—	86	2	no	—
354	#103	—	86	2	no	—
355	#103	—	86	2	no	—
356	#102	—	86	2	no	—
357	#101	—	43	8	no	—
358	#101	—	86	4	no	—
359	#97	—	86	1	no	—
360	#97	—	86	1	no	—
361	#97	—	86	2	no	—
362	#97	—	86	1	no	—
363	C₄×C₈	—	86	1	no	—
364	C₄×C₈	—	86	1	no	—
365	C₄×C₈	—	86	2	no	—
366	C₄×C₈	—	86	1	no	—
367	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
368	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
369	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
370	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
371	#41	—	43	2	no	—
372	#41	—	43	2	no	—
373	#41	—	86	1	no	—
374	#41	—	86	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	43	1	no	—
381	C₂×Q₈	C₂×C₄×D₄₃	1	4	yes	—
382	C₂×D₄	—	43	1	no	—
383	C₂×D₄	—	86	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	86	1	no	—
387	C₂²×C₄	—	86	1	no	—
388	C₂²×C₄	—	86	1	no	—
389	C₂²×C₄	#10621900	1	1	yes	characteristic
390	C₂²×C₄	#10621900	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
392	Q₁₆	—	2	4	no	—
393	Q₁₆	—	2	4	no	—
394	Q₁₆	—	86	8	no	—
395	SD₁₆	—	86	8	no	—
396	M₁₆	—	43	2	no	—
397	M₁₆	—	43	4	no	—
398	M₁₆	—	43	2	no	—
399	M₁₆	—	86	4	no	—
400	M₁₆	—	86	1	no	—
401	M₁₆	—	86	2	no	—
402	M₁₆	—	86	1	no	—
403	M₁₆	—	86	4	no	—
404	M₁₆	—	86	2	no	—
405	M₁₆	—	86	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	86	4	no	—
409	C₂×C₈	—	86	2	no	—
410	C₂×C₈	—	86	1	no	—
411	C₂×C₈	—	86	1	no	—
412	C₂×C₈	—	86	4	no	—
413	C₂×C₈	—	86	2	no	—
414	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
415	C₂×C₈	#10621898	1	2	yes	—
416	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
417	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
418	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
419	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	43	1	no	—
425	C₄⋊C₄	—	43	1	no	—
426	C₄⋊C₄	—	86	1	no	—
427	C₄⋊C₄	—	86	1	no	—
428	C₂²⋊C₄	—	86	1	no	—
429	C₂²⋊C₄	—	86	1	no	—
430	C₂²⋊C₄	—	86	1	no	—
431	C₄²	—	4	2	no	—
432	C₄²	—	4	2	no	—
433	C₄²	—	86	1	no	—
434	C₄²	—	86	1	no	—
435	C₄²	—	86	1	no	—
436	C₄²	D₄×D₄₃	1	1	yes	characteristic
437	C₄²	D₄×D₄₃	1	1	yes	characteristic
438	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
440	C₂³	—	86	1	no	—
441	C₂³	C₂×#10621900	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	43	2	no	—
447	Q₈	—	86	1	no	—
448	D₄	—	43	2	no	—
449	D₄	—	86	2	no	—
450	D₄	—	86	2	no	—
451	D₄	—	86	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	86	1	no	—
460	C₂×C₄	—	86	2	no	—
461	C₂×C₄	—	86	2	no	—
462	C₂×C₄	—	86	1	no	—
463	C₂×C₄	—	86	1	no	—
464	C₂×C₄	—	172	2	no	—
465	C₂×C₄	—	172	2	no	—
466	C₂×C₄	#13063296	1	1	yes	characteristic
467	C₂×C₄	#13063296	1	1	yes	characteristic
468	C₂×C₄	#13063296	1	1	yes	characteristic
469	C₂×C₄	#13063296	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
471	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
473	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
474	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
475	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
476	C₈	—	2	1	no	—
477	C₈	—	2	1	no	—
478	C₈	—	86	4	no	—
479	C₈	—	86	2	no	—
480	C₈	—	86	2	no	—
481	C₈	—	172	2	no	—
482	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
483	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	86	2	no	—
487	C₂²	—	172	1	no	—
488	C₂²	—	172	1	no	—
489	C₂²	C₄×#10621900	1	1	yes	characteristic
490	C₂²	C₂×#13063296	1	1	yes	characteristic
491	C₂²	#14583431	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	2	no	—
497	C₄	—	86	2	no	—
498	C₄	—	172	1	no	—
499	C₄	—	172	1	no	—
500	C₄	#14583171	1	2	yes	direct product factor
501	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
502	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
503	C₄	#14583406	1	1	yes	characteristic
504	C₄	#14583446	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	172	2	no	—
508	C₂	C₄×#13063296	1	1	yes	characteristic
509	C₂	C₂×#14583171	1	1	yes	characteristic
510	C₂	#19144311	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063296
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂×#10621898	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₄₃
hypocenter	C₄₃	C₄×#473
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #19135511	C₂	semidirect
5. #19135378	C₂	semidirect
6. #19135247	C₂	semidirect
9. C₄×#13063261	C₂	semidirect
10. C₄×#13063244	C₂	semidirect
11. C₂×C₄×Q₁₆×C₄₃	C₂	semidirect
16. #14583171	C₄	direct (N × H)
75. #13063261	C₂×C₄	semidirect
83. #13063244	C₂×C₄	semidirect
96. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
242. C₄×C₄₃	#473	semidirect
252. C₂×C₄×Q₁₆	D₄₃	semidirect
303. C₄₃	C₄×#473	semidirect
312. C₂×Q₁₆	C₄×D₄₃	semidirect
500. C₄	#14583171	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#14583171	2
C₄×#13063356	2
C₄×#13063331	2
#19135511	2
#19135378	2
#19135247	2
#19135113	2
#19134660	2
C₄×#13063261	2
C₄×#13063244	2
C₂×C₄×Q₁₆×C₄₃	2
C₄×#473	43

Subgroups — C4×#14583171 #25103482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14583171 #25103482