Subgroups — #25099819

Order 11008.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063347	C₂	1	1	yes	maximal, characteristic
2	#19143240	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13063333	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135242	C₂	1	2	yes	maximal, complemented
5	#19135193	C₂	1	2	yes	maximal, complemented
6	#19134923	C₂	1	2	yes	maximal
7	#19134867	C₂	1	2	yes	maximal, complemented
8	C₄×#13063251	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13063251	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#108×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	C₂×#13063333	C₂²	1	2	yes	—
14	C₄×#10621898	C₂²	1	1	yes	characteristic
15	C₄×#10621898	C₂²	1	1	yes	characteristic
16	C₄×Dic₁₇₂	C₄	1	1	yes	characteristic, complemented
17	C₄×Dic₁₇₂	C₄	1	1	yes	characteristic, complemented
18	C₄×#10621873	C₄	1	1	yes	characteristic, complemented
19	C₄×#10621873	C₄	1	1	yes	characteristic, complemented
20	C₄×#10621873	C₄	1	1	yes	characteristic, complemented
21	C₄×#10621873	C₄	1	1	yes	characteristic, complemented
22	C₄×D₃₄₄	C₄	1	1	yes	characteristic, complemented
23	C₄×D₃₄₄	C₄	1	1	yes	characteristic, complemented
24	#14582961	—	2	2	no	—
25	#14582950	—	2	1	no	—
26	#14582950	—	2	1	no	—
27	#14582937	C₂²	1	1	yes	characteristic
28	#14582927	C₂²	1	2	yes	—
29	C₂×#13063251	C₂²	1	2	yes	—
30	C₂×#13063251	C₂²	1	2	yes	—
31	#14582896	C₂²	1	1	yes	characteristic
32	#14582896	C₂²	1	1	yes	characteristic
33	#14582867	C₂²	1	2	yes	—
34	#14582857	C₂²	1	2	yes	—
35	#14582856	—	2	2	no	—
36	C₄×#10621872	—	2	1	no	—
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×C₈×D₄₃	—	2	1	no	—
39	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
40	#14582660	C₂²	1	2	yes	—
41	#14582660	C₂²	1	2	yes	—
42	#14582653	C₂²	1	2	yes	—
43	#14582653	C₂²	1	2	yes	—
44	C₂×#108×C₄₃	C₂²	1	2	yes	—
45	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
48	C₄₃×#341	C₂²	1	2	yes	—
49	C₂×#10621898	C₂³	1	1	yes	characteristic
50	C₂×#10621898	C₂³	1	1	yes	characteristic
51	#13063347	—	2	4	no	—
52	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
53	C₂×#10621873	C₂×C₄	1	1	yes	characteristic
54	C₂×#10621873	C₂×C₄	1	1	yes	characteristic
55	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
56	#13063333	—	2	4	no	—
57	#13063333	—	2	4	no	—
58	C₂×#10621872	—	2	2	no	—
59	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
60	C₂×C₈×D₄₃	—	2	2	no	—
61	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
66	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
67	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
68	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₃	—	2	1	no	—
70	C₄×C₂²⋊D₄₃	—	2	1	no	—
71	C₄×C₂²⋊D₄₃	—	2	1	no	—
72	C₄×C₂²⋊D₄₃	—	2	1	no	—
73	#13063284	C₂³	1	1	yes	characteristic
74	#13063284	C₂³	1	1	yes	characteristic
75	#13063282	—	2	1	no	—
76	#13063282	—	2	1	no	—
77	C₂×C₄×Dic₄₃	—	2	1	no	—
78	C₂×C₄×Dic₄₃	—	2	1	no	—
79	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
80	C₄²×D₄₃	—	2	1	no	—
81	C₄²×D₄₃	—	2	1	no	—
82	#13063259	C₂×C₄	1	1	yes	characteristic
83	#13063259	C₂×C₄	1	1	yes	characteristic
84	#13063257	C₂×C₄	1	1	yes	characteristic
85	#13063257	C₂×C₄	1	1	yes	characteristic
86	Dic₄₃⋊C₈	—	2	2	no	—
87	Dic₄₃⋊C₈	—	2	2	no	—
88	#13063251	—	2	4	no	—
89	#13063251	—	2	4	no	—
90	#13063250	C₂×C₄	1	1	yes	characteristic
91	#13063250	C₂×C₄	1	1	yes	characteristic
92	#13063250	C₂×C₄	1	1	yes	characteristic
93	#13063250	C₂×C₄	1	1	yes	characteristic
94	#13063247	C₂×C₄	1	1	yes	characteristic
95	#13063247	C₂×C₄	1	1	yes	characteristic
96	#13063247	C₂×C₄	1	1	yes	characteristic
97	#13063247	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₄₃)⋊C₈	—	2	2	no	—
99	(C₂×D₄₃)⋊C₈	—	2	2	no	—
100	#13063235	—	2	2	no	—
101	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
102	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
103	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
104	C₈×Dic₄₃	—	2	2	no	—
105	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
106	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
110	#108×C₄₃	—	2	4	no	—
111	#97×C₄₃	—	2	1	no	—
112	#97×C₄₃	—	2	1	no	—
113	C₄×C₈×C₄₃	—	2	1	no	—
114	C₄×C₈×C₄₃	—	2	1	no	—
115	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
116	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
117	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
118	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
122	C₂×C₂²⋊D₄₃	—	2	1	no	—
123	C₂×C₂²⋊D₄₃	—	2	1	no	—
124	C₂²×Dic₄₃	—	2	2	no	—
125	#10621898	—	2	2	no	—
126	#10621898	—	2	2	no	—
127	#10621898	—	2	2	no	—
128	#10621898	#41	1	4	yes	—
129	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
130	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₄₃	—	2	1	no	—
132	C₂×C₄×D₄₃	—	2	1	no	—
133	C₂×C₄×D₄₃	—	2	1	no	—
134	C₂×C₄×D₄₃	—	2	1	no	—
135	C₂×C₄×D₄₃	—	2	1	no	—
136	C₂×C₄×D₄₃	—	2	1	no	—
137	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
139	M₁₆×C₄₃	—	2	2	no	—
140	M₁₆×C₄₃	—	2	2	no	—
141	M₁₆×C₄₃	—	2	2	no	—
142	M₁₆×C₄₃	#41	1	4	yes	—
143	C₂×C₈×C₄₃	—	2	2	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	2	no	—
146	C₂×C₈×C₄₃	—	2	2	no	—
147	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂²⋊Dic₄₃	—	2	1	no	—
156	C₂²⋊Dic₄₃	—	2	1	no	—
157	(C₂×D₄₃)⋊C₄	—	2	1	no	—
158	(C₂×D₄₃)⋊C₄	—	2	1	no	—
159	(C₂×D₄₃)⋊C₄	—	2	1	no	—
160	(C₂×D₄₃)⋊C₄	—	2	1	no	—
161	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
162	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
163	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
165	Dic₄₃⋊C₄	—	2	1	no	—
166	Dic₄₃⋊C₄	—	2	1	no	—
167	Dic₄₃⋊C₄	—	2	1	no	—
168	Dic₄₃⋊C₄	—	2	1	no	—
169	C₄×Dic₄₃	—	2	4	no	—
170	C₄×Dic₄₃	—	2	1	no	—
171	C₄×Dic₄₃	—	2	1	no	—
172	C₄×Dic₄₃	—	2	1	no	—
173	C₄×Dic₄₃	—	2	1	no	—
174	C₄×Dic₄₃	—	2	1	no	—
175	C₄×Dic₄₃	—	2	1	no	—
176	C₄×Dic₄₃	—	2	2	no	—
177	C₄×Dic₄₃	—	2	2	no	—
178	C₄×Dic₄₃	—	4	2	no	—
179	C₂×C₄₃⋊C₈	—	2	2	no	—
180	C₂×C₄₃⋊C₈	—	2	2	no	—
181	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
182	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
183	Dic₁₇₂	—	2	2	no	—
184	D₃₄₄	—	2	2	no	—
185	#10621873	—	2	2	no	—
186	#10621873	—	2	2	no	—
187	#10621872	—	2	8	no	—
188	C₈×D₄₃	—	2	8	no	—
189	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
190	C₂²×D₄₃	—	2	1	no	—
191	C₂²×D₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
201	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
202	C₂²⋊D₄₃	—	2	4	no	—
203	C₂²⋊D₄₃	—	4	2	no	—
204	C₂×Dic₄₃	—	2	1	no	—
205	C₂×Dic₄₃	—	2	4	no	—
206	C₂×Dic₄₃	—	2	1	no	—
207	C₂×Dic₄₃	—	2	1	no	—
208	C₂×Dic₄₃	—	2	1	no	—
209	C₂×Dic₄₃	—	2	1	no	—
210	C₂×Dic₄₃	—	2	1	no	—
211	C₂×Dic₄₃	—	4	2	no	—
212	C₂×Dic₄₃	—	4	2	no	—
213	D₁₇₂	—	2	1	no	—
214	D₁₇₂	—	2	1	no	—
215	D₁₇₂	—	2	1	no	—
216	D₁₇₂	#117	1	2	yes	—
217	C₄×D₄₃	—	2	4	no	—
218	C₄×D₄₃	—	4	2	no	—
219	C₄×D₄₃	—	4	2	no	—
220	C₄×D₄₃	—	4	2	no	—
221	C₄×D₄₃	—	4	2	no	—
222	C₄×D₄₃	—	4	2	no	—
223	Dic₈₆	—	2	1	no	—
224	Dic₈₆	—	2	1	no	—
225	Dic₈₆	—	2	1	no	—
226	Dic₈₆	#117	1	2	yes	—
227	C₈×C₄₃	—	2	1	no	—
228	C₈×C₄₃	—	2	1	no	—
229	C₈×C₄₃	—	2	1	no	—
230	C₈×C₄₃	—	2	1	no	—
231	C₈×C₄₃	—	2	4	no	—
232	C₈×C₄₃	—	4	2	no	—
233	C₄₃⋊C₈	—	2	2	no	—
234	C₄₃⋊C₈	—	2	2	no	—
235	#21137	—	43	1	no	maximal, Sylow
236	C₂²×C₄₃	—	2	1	no	—
237	C₂²×C₄₃	—	2	1	no	—
238	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₂²×C₄₃	#529	1	2	yes	—
240	C₂×D₄₃	—	2	2	no	—
241	C₂×D₄₃	—	4	1	no	—
242	C₂×D₄₃	—	4	1	no	—
243	C₂×D₄₃	—	4	1	no	—
244	C₂×D₄₃	—	4	1	no	—
245	C₂×D₄₃	—	4	1	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	2	1	no	—
248	C₄×C₄₃	#443	1	2	yes	—
249	C₄×C₄₃	#444	1	2	yes	—
250	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
251	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
252	C₄×C₄₃	#525	1	2	yes	—
253	Dic₄₃	—	2	2	no	—
254	Dic₄₃	—	4	4	no	—
255	Dic₄₃	—	4	1	no	—
256	Dic₄₃	—	4	1	no	—
257	Dic₄₃	—	4	1	no	—
258	Dic₄₃	—	4	1	no	—
259	Dic₄₃	—	4	1	no	—
260	C₄×#135	—	43	1	no	—
261	#2922	—	43	1	no	—
262	C₄×#131	—	43	1	no	—
263	#1929	—	43	2	no	—
264	#1922	—	43	2	no	—
265	#1876	—	43	2	no	—
266	#1866	—	43	2	no	—
267	C₄×#108	D₄₃	1	1	yes	characteristic, complemented
268	C₄×#104	—	43	1	no	—
269	C₄×#104	—	43	1	no	—
270	#1744	—	43	1	no	—
271	C₂×C₄₃	—	2	2	no	—
272	C₂×C₄₃	#2290	1	1	yes	characteristic
273	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
274	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
275	D₄₃	—	4	2	no	—
276	D₄₃	—	8	1	no	—
277	C₂×#135	—	43	1	no	—
278	C₂×#131	—	43	2	no	—
279	C₄×#41	—	43	1	no	—
280	C₄×#41	—	43	1	no	—
281	C₄×Q₁₆	—	43	1	no	—
282	C₄×Q₁₆	—	43	1	no	—
283	C₄×SD₁₆	—	43	1	no	—
284	C₄×SD₁₆	—	43	1	no	—
285	C₄×SD₁₆	—	43	1	no	—
286	C₄×SD₁₆	—	43	1	no	—
287	C₄×D₈	—	43	1	no	—
288	C₄×D₈	—	43	1	no	—
289	#433	—	86	2	no	—
290	#431	—	86	1	no	—
291	#431	—	86	1	no	—
292	C₂×#108	C₂×D₄₃	1	2	yes	—
293	#427	—	43	1	no	—
294	#424	—	43	2	no	—
295	C₂×#104	—	43	2	no	—
296	C₂×#104	—	43	2	no	—
297	#416	—	43	1	no	—
298	#416	—	43	1	no	—
299	#408	—	43	2	no	—
300	#405	—	43	2	no	—
301	#405	—	86	2	no	—
302	C₄×M₁₆	—	86	1	no	—
303	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
304	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
305	C₂×C₄×C₈	—	43	1	no	—
306	C₂×C₄×C₈	—	86	1	no	—
307	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
308	C₄³	—	43	1	no	—
309	#341	C₂×D₄₃	1	2	yes	—
310	#339	—	43	2	no	—
311	#339	—	43	2	no	—
312	#336	—	43	2	no	—
313	#336	—	43	2	no	—
314	C₄₃	#21137	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	43	1	no	—
316	C₂×#41	—	43	1	no	—
317	#135	—	86	4	no	—
318	C₂×Q₁₆	—	43	1	no	—
319	C₂×SD₁₆	—	43	1	no	—
320	C₂×SD₁₆	—	43	1	no	—
321	C₂×D₈	—	43	1	no	—
322	#131	—	86	4	no	—
323	#131	—	86	4	no	—
324	C₂×M₁₆	—	86	2	no	—
325	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
326	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
327	C₂²×C₈	—	43	2	no	—
328	C₂²×C₈	—	86	2	no	—
329	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
330	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
331	C₄×Q₈	—	43	1	no	—
332	C₄×Q₈	—	43	1	no	—
333	C₄×Q₈	—	43	1	no	—
334	C₄×Q₈	—	43	1	no	—
335	C₄×D₄	—	43	1	no	—
336	C₄×D₄	—	43	1	no	—
337	C₄×D₄	—	43	1	no	—
338	C₄×D₄	—	43	1	no	—
339	C₄×D₄	—	86	1	no	—
340	C₄×D₄	—	86	1	no	—
341	C₄×D₄	—	86	1	no	—
342	C₄×D₄	—	86	1	no	—
343	#117	—	43	1	no	—
344	#117	—	43	1	no	—
345	#117	—	86	1	no	—
346	#117	—	86	1	no	—
347	C₂×C₄²	—	43	2	no	—
348	C₂×C₄²	—	86	1	no	—
349	C₂×C₄²	—	86	1	no	—
350	C₂×C₄²	—	86	1	no	—
351	C₂×C₄²	—	86	1	no	—
352	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
353	#108	—	2	4	no	—
354	#107	—	43	1	no	—
355	#107	—	43	1	no	—
356	#106	—	43	1	no	—
357	#106	—	43	1	no	—
358	C₄⋊C₈	—	86	2	no	—
359	C₄⋊C₈	—	86	2	no	—
360	#104	—	86	4	no	—
361	#104	—	86	4	no	—
362	#103	—	43	1	no	—
363	#103	—	43	1	no	—
364	#103	—	43	1	no	—
365	#103	—	43	1	no	—
366	#102	—	43	1	no	—
367	#102	—	43	1	no	—
368	#102	—	43	1	no	—
369	#102	—	43	1	no	—
370	C₂²⋊C₈	—	86	2	no	—
371	C₂²⋊C₈	—	86	2	no	—
372	#97	—	2	1	no	—
373	#97	—	2	1	no	—
374	#97	—	86	2	no	—
375	C₄×C₈	—	2	1	no	—
376	C₄×C₈	—	2	1	no	—
377	C₄×C₈	—	43	2	no	—
378	C₄×C₈	—	43	1	no	—
379	C₄×C₈	—	43	1	no	—
380	C₄×C₈	—	86	2	no	—
381	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
382	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
383	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
384	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
385	#41	—	43	4	no	—
386	#41	—	86	2	no	—
387	#41	—	86	2	no	—
388	#41	—	86	2	no	—
389	C₂×Q₈	—	43	1	no	—
390	C₂×Q₈	—	43	1	no	—
391	C₂×D₄	—	43	1	no	—
392	C₂×D₄	—	43	1	no	—
393	C₂×D₄	—	86	1	no	—
394	C₂×D₄	—	86	1	no	—
395	C₂²×C₄	—	86	1	no	—
396	C₂²×C₄	—	86	2	no	—
397	C₂²×C₄	—	86	1	no	—
398	C₂²×C₄	—	86	1	no	—
399	C₂²×C₄	—	86	1	no	—
400	C₂²×C₄	—	86	1	no	—
401	C₂²×C₄	—	86	1	no	—
402	C₂²×C₄	#10621902	1	1	yes	characteristic
403	C₂²×C₄	#10621902	1	1	yes	characteristic
404	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
405	Q₁₆	—	86	2	no	—
406	SD₁₆	—	86	2	no	—
407	SD₁₆	—	86	2	no	—
408	D₈	—	86	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	86	8	no	—
413	M₁₆	#10621898	1	4	yes	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	43	2	no	—
419	C₂×C₈	—	43	2	no	—
420	C₂×C₈	—	86	8	no	—
421	C₂×C₈	—	86	2	no	—
422	C₂×C₈	—	86	2	no	—
423	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
424	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
425	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
426	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
427	C₄⋊C₄	—	43	1	no	—
428	C₄⋊C₄	—	43	1	no	—
429	C₄⋊C₄	—	43	1	no	—
430	C₄⋊C₄	—	43	1	no	—
431	C₄⋊C₄	—	86	1	no	—
432	C₄⋊C₄	—	86	1	no	—
433	C₄⋊C₄	—	86	1	no	—
434	C₄⋊C₄	—	86	1	no	—
435	C₂²⋊C₄	—	86	1	no	—
436	C₂²⋊C₄	—	86	1	no	—
437	C₂²⋊C₄	—	86	1	no	—
438	C₂²⋊C₄	—	86	1	no	—
439	C₂²⋊C₄	—	86	1	no	—
440	C₂²⋊C₄	—	86	1	no	—
441	C₄²	—	86	4	no	—
442	C₄²	—	86	1	no	—
443	C₄²	—	86	1	no	—
444	C₄²	—	86	1	no	—
445	C₄²	—	86	1	no	—
446	C₄²	—	86	1	no	—
447	C₄²	—	86	1	no	—
448	C₄²	—	86	2	no	—
449	C₄²	—	86	2	no	—
450	C₄²	—	172	2	no	—
451	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
452	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
453	C₄²	D₄×D₄₃	1	1	yes	characteristic
454	C₄²	D₄×D₄₃	1	1	yes	characteristic
455	C₂³	—	86	1	no	—
456	C₂³	—	86	1	no	—
457	C₂³	C₂×#10621902	1	1	yes	characteristic
458	Q₈	—	43	2	no	—
459	Q₈	—	86	1	no	—
460	Q₈	—	86	1	no	—
461	Q₈	—	86	1	no	—
462	D₄	—	43	2	no	—
463	D₄	—	86	4	no	—
464	D₄	—	86	1	no	—
465	D₄	—	86	1	no	—
466	D₄	—	86	1	no	—
467	D₄	—	172	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	86	1	no	—
471	C₂×C₄	—	86	4	no	—
472	C₂×C₄	—	86	4	no	—
473	C₂×C₄	—	86	1	no	—
474	C₂×C₄	—	86	1	no	—
475	C₂×C₄	—	86	1	no	—
476	C₂×C₄	—	86	1	no	—
477	C₂×C₄	—	86	1	no	—
478	C₂×C₄	—	172	2	no	—
479	C₂×C₄	—	172	2	no	—
480	C₂×C₄	—	172	2	no	—
481	C₂×C₄	—	172	2	no	—
482	C₂×C₄	—	172	2	no	—
483	C₂×C₄	—	172	2	no	—
484	C₂×C₄	—	172	2	no	—
485	C₂×C₄	#13063287	1	1	yes	characteristic
486	C₂×C₄	#13063287	1	1	yes	characteristic
487	C₂×C₄	#13063287	1	1	yes	characteristic
488	C₂×C₄	#13063287	1	1	yes	characteristic
489	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
491	C₂×C₄	#41×D₄₃	1	2	yes	—
492	C₂×C₄	C₂×#10621898	1	2	yes	—
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	1	no	—
496	C₈	—	2	1	no	—
497	C₈	—	2	4	no	—
498	C₈	—	4	2	no	—
499	C₈	—	86	2	no	—
500	C₈	—	86	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	86	2	no	—
504	C₂²	—	172	1	no	—
505	C₂²	—	172	1	no	—
506	C₂²	—	172	1	no	—
507	C₂²	—	172	1	no	—
508	C₂²	—	172	1	no	—
509	C₂²	C₂×#13063287	1	1	yes	characteristic
510	C₂²	#14583436	1	2	yes	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	86	2	no	—
514	C₄	—	172	4	no	—
515	C₄	—	172	1	no	—
516	C₄	—	172	1	no	—
517	C₄	—	172	1	no	—
518	C₄	—	172	1	no	—
519	C₄	—	172	1	no	—
520	C₄	#14583015	1	2	yes	—
521	C₄	#14583020	1	2	yes	—
522	C₄	#117×D₄₃	1	1	yes	characteristic
523	C₄	C₄×#10621898	1	1	yes	characteristic
524	C₄	#14583408	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	344	1	no	—
527	C₂	—	172	2	no	—
528	C₂	#19137036	1	1	yes	characteristic
529	C₂	C₂×#14583015	1	1	yes	characteristic
530	C₂	C₂×#14583020	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#108×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063347	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#108	D₄₃
hypocenter	C₄₃	#21137
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#108

Complements

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

N	H ≅ G/N	type
2. #19143240	C₂	semidirect
3. C₄×#13063333	C₂	semidirect
4. #19135242	C₂	semidirect
5. #19135193	C₂	semidirect
7. #19134867	C₂	semidirect
8. C₄×#13063251	C₂	semidirect
9. C₄×#13063251	C₂	semidirect
10. #19134340	C₂	semidirect
11. C₄×#108×C₄₃	C₂	semidirect
16. C₄×Dic₁₇₂	C₄	semidirect
17. C₄×Dic₁₇₂	C₄	semidirect
18. C₄×#10621873	C₄	semidirect
19. C₄×#10621873	C₄	semidirect
20. C₄×#10621873	C₄	semidirect
21. C₄×#10621873	C₄	semidirect
22. C₄×D₃₄₄	C₄	semidirect
23. C₄×D₃₄₄	C₄	semidirect
267. C₄×#108	D₄₃	semidirect
314. C₄₃	#21137	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063347	2
#19143240	2
C₄×#13063333	2
#19135242	2
#19135193	2
#19134923	2
#19134867	2
C₄×#13063251	2
#19134340	2
C₄×#108×C₄₃	2
#21137	43