Subgroups — #61866

Order 256.

803 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3555	C₂	1	1	yes	maximal, characteristic
2	#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	#3390	C₂	1	2	yes	maximal, complemented
4	#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	#3385	C₂	1	1	yes	maximal, characteristic, complemented
6	#3383	C₂	1	2	yes	maximal, complemented
7	Q₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	#3377	C₂	1	2	yes	maximal, complemented
10	#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	#3364	C₂	1	1	yes	maximal, characteristic, complemented
13	#3364	C₂	1	2	yes	maximal, complemented
14	#3363	C₂	1	1	yes	maximal, characteristic, complemented
15	#3243	C₂	1	2	yes	maximal
16	#3242	C₂	1	2	yes	maximal, complemented
17	#3233	C₂	1	1	yes	maximal, characteristic
18	#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	#3127	C₂	1	2	yes	maximal, complemented
20	#3121	C₂	1	2	yes	maximal
21	#3108	C₂	1	1	yes	maximal, characteristic
22	#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	#563	—	2	2	no	—
25	Q₈²	—	2	1	no	—
26	Q₈²	C₂²	1	1	yes	characteristic
27	Q₈²	C₂²	1	1	yes	characteristic
28	Q₈²	C₂²	1	1	yes	characteristic
29	#557	—	2	1	no	—
30	#557	—	2	2	no	—
31	#557	C₂²	1	1	yes	characteristic
32	#557	C₂²	1	1	yes	characteristic
33	#557	C₂²	1	2	yes	—
34	#557	C₂²	1	1	yes	characteristic
35	#557	C₂²	1	2	yes	—
36	#557	C₂²	1	2	yes	—
37	#556	—	2	1	no	—
38	#556	C₂²	1	1	yes	characteristic
39	#556	C₂²	1	2	yes	—
40	#554	C₂²	1	1	yes	characteristic
41	#552	—	2	1	no	—
42	#544	—	2	1	no	—
43	#544	—	2	2	no	—
44	#544	C₂²	1	2	yes	—
45	#542	C₂²	1	2	yes	—
46	#541	—	2	1	no	—
47	#541	—	2	2	no	—
48	#541	C₂²	1	2	yes	—
49	#533	—	2	1	no	—
50	#533	—	2	1	no	—
51	#533	C₂²	1	1	yes	characteristic
52	#533	C₂²	1	1	yes	characteristic
53	#533	C₂²	1	1	yes	characteristic
54	#529	C₂²	1	1	yes	characteristic
55	#519	C₂²	1	2	yes	—
56	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	—
58	#501	C₂²	1	2	yes	—
59	#500	C₂²	1	2	yes	—
60	#500	C₂²	1	1	yes	characteristic
61	#499	C₂²	1	2	yes	—
62	#499	C₂²	1	2	yes	—
63	#498	C₂²	1	1	yes	characteristic
64	#491	C₂²	1	2	yes	—
65	#489	C₂²	1	2	yes	—
66	#488	C₂²	1	2	yes	—
67	#488	C₂²	1	2	yes	—
68	#487	C₂²	1	2	yes	—
69	#487	C₂²	1	1	yes	characteristic
70	#487	C₂²	1	1	yes	characteristic
71	#485	C₂²	1	2	yes	—
72	#485	C₂²	1	2	yes	—
73	#485	C₂²	1	2	yes	—
74	#484	C₂²	1	2	yes	—
75	#483	C₂²	1	1	yes	characteristic
76	#482	C₂²	1	2	yes	—
77	#480	C₂²	1	1	yes	characteristic
78	#479	C₂²	1	1	yes	characteristic
79	#479	C₂²	1	1	yes	characteristic
80	#479	C₂²	1	2	yes	—
81	#479	C₂²	1	2	yes	—
82	#479	C₂²	1	2	yes	—
83	#479	C₂²	1	2	yes	—
84	#479	C₂²	1	2	yes	—
85	#479	C₂²	1	2	yes	—
86	#479	C₂²	1	2	yes	—
87	#478	C₂²	1	2	yes	—
88	#477	C₂²	1	1	yes	characteristic
89	#477	C₂²	1	1	yes	characteristic
90	#477	C₂²	1	1	yes	characteristic
91	#477	C₂²	1	2	yes	—
92	#477	C₂²	1	2	yes	—
93	#477	C₂²	1	2	yes	—
94	#476	C₂²	1	1	yes	characteristic
95	#475	C₂²	1	2	yes	—
96	#475	C₂²	1	1	yes	characteristic
97	#475	C₂²	1	2	yes	—
98	#474	C₂²	1	1	yes	characteristic
99	#474	C₂²	1	2	yes	—
100	#464	C₂²	1	1	yes	characteristic
101	#464	C₂²	1	1	yes	characteristic
102	#464	C₂²	1	2	yes	—
103	#464	C₂²	1	2	yes	—
104	#462	C₂²	1	1	yes	characteristic
105	#462	C₂²	1	1	yes	characteristic
106	#462	C₂²	1	2	yes	—
107	#462	C₂²	1	2	yes	—
108	#451	C₂²	1	2	yes	—
109	#451	C₂²	1	1	yes	characteristic
110	#448	C₂²	1	1	yes	characteristic
111	#446	C₂²	1	1	yes	characteristic
112	#446	C₂²	1	1	yes	characteristic
113	#446	C₂²	1	2	yes	—
114	C₈×Q₈	C₂²	1	1	yes	characteristic
115	C₈×Q₈	C₂²	1	1	yes	characteristic
116	C₈×Q₈	C₂²	1	2	yes	—
117	#441	C₂²	1	2	yes	—
118	#441	C₂²	1	2	yes	—
119	#441	C₂²	1	2	yes	—
120	#440	C₂²	1	2	yes	—
121	C₄×Q₁₆	C₂²	1	2	yes	—
122	C₄×Q₁₆	C₂²	1	2	yes	—
123	C₄×Q₁₆	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆	C₂²	1	2	yes	—
125	C₄×Q₁₆	C₂²	1	1	yes	characteristic
126	C₄×Q₁₆	C₂²	1	2	yes	—
127	C₄×Q₁₆	C₂²	1	2	yes	—
128	C₄×SD₁₆	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆	C₂²	1	2	yes	—
131	#433	C₂²	1	2	yes	—
132	#433	C₂²	1	2	yes	—
133	#431	C₂²	1	1	yes	characteristic
134	#431	C₂²	1	1	yes	characteristic
135	C₂²×Q₈	C₂³	1	1	yes	characteristic
136	C₂×Q₁₆	C₂³	1	2	yes	—
137	C₂×Q₁₆	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆	C₂³	1	2	yes	—
139	C₂×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×SD₁₆	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈	—	2	1	no	—
143	C₄⋊Q₈	—	2	1	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	—	2	1	no	—
148	C₄⋊Q₈	—	2	1	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	1	no	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	—	2	2	no	—
154	C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈	C₂³	1	2	yes	—
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	2	yes	—
163	C₄⋊Q₈	C₂³	1	2	yes	—
164	#126	—	2	2	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	1	no	—
171	#125	—	2	2	no	—
172	#125	—	2	2	no	—
173	#125	—	2	2	no	—
174	#125	—	2	2	no	—
175	#125	—	2	2	no	—
176	#125	—	2	2	no	—
177	#125	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	—	2	2	no	—
180	#125	—	2	2	no	—
181	#125	—	2	2	no	—
182	#125	—	2	2	no	—
183	#125	—	2	2	no	—
184	#125	—	2	1	no	—
185	#125	D₄	1	2	yes	—
186	#125	C₂³	1	1	yes	characteristic
187	#125	C₂³	1	2	yes	—
188	#125	C₂³	1	2	yes	—
189	#125	C₂³	1	2	yes	—
190	#125	C₂³	1	2	yes	—
191	#124	—	2	2	no	—
192	#124	C₂³	1	1	yes	characteristic
193	#124	C₂³	1	2	yes	—
194	#123	—	2	1	no	—
195	#123	—	2	2	no	—
196	C₂²⋊Q₈	—	2	1	no	—
197	C₂²⋊Q₈	—	2	1	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	no	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈	D₄	1	2	yes	—
209	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	#121	C₂³	1	1	yes	characteristic
212	C₄×Q₈	—	2	1	no	—
213	C₄×Q₈	—	2	1	no	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	—	2	1	no	—
216	C₄×Q₈	—	2	2	no	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	—	2	2	no	—
219	C₄×Q₈	—	2	2	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	2	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	—	2	1	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₄×Q₈	C₂³	1	2	yes	—
233	C₄×Q₈	C₂³	1	2	yes	—
234	C₄×Q₈	C₂³	1	2	yes	—
235	C₄×Q₈	C₂³	1	2	yes	—
236	C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₄×Q₈	C₂³	1	2	yes	—
238	C₄×Q₈	C₂³	1	2	yes	—
239	C₄×Q₈	C₂³	1	2	yes	—
240	C₄×Q₈	C₂³	1	2	yes	—
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×Q₈	C₂³	1	2	yes	—
243	C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	C₂³	1	1	yes	characteristic
246	C₄×D₄	C₂³	1	2	yes	—
247	#117	—	2	1	no	—
248	#117	—	2	2	no	—
249	#117	—	2	1	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	—	2	1	no	—
253	#117	C₂³	1	2	yes	—
254	#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³	1	1	yes	characteristic
260	#107	C₂³	1	2	yes	—
261	#107	C₂³	1	2	yes	—
262	#107	C₂³	1	2	yes	—
263	#107	C₂³	1	2	yes	—
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	2	yes	—
268	#106	C₂³	1	1	yes	characteristic
269	#106	C₂³	1	2	yes	—
270	#106	C₂³	1	1	yes	characteristic
271	#106	C₂³	1	2	yes	—
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₄⋊C₈	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	#103	C₂³	1	2	yes	—
283	#103	C₂³	1	1	yes	characteristic
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	2	yes	—
302	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	#97	C₂³	1	2	yes	—
306	#97	C₂³	1	2	yes	—
307	C₄×C₈	C₂³	1	1	yes	characteristic
308	C₄×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₈	C₂³	1	2	yes	—
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈	C₂×D₄	1	2	yes	—
324	C₂×Q₈	C₂⁴	1	2	yes	—
325	C₂×Q₈	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴	1	1	yes	characteristic
337	Q₁₆	—	2	4	no	—
338	Q₁₆	—	2	2	no	—
339	Q₁₆	—	2	4	no	—
340	Q₁₆	—	2	2	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	2	2	no	—
343	C₂×C₈	C₂⁴	1	1	yes	characteristic
344	C₂×C₈	C₂⁴	1	2	yes	—
345	C₂×C₈	C₂⁴	1	1	yes	characteristic
346	C₂×C₈	C₂⁴	1	1	yes	characteristic
347	C₂×C₈	C₂⁴	1	2	yes	—
348	C₂×C₈	C₂⁴	1	1	yes	characteristic
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
386	C₄⋊C₄	C₂×D₄	1	2	yes	—
387	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₄⋊C₄	C₂×D₄	1	2	yes	—
389	C₄⋊C₄	C₂×D₄	1	2	yes	—
390	C₄⋊C₄	C₂×D₄	1	2	yes	—
391	C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₄⋊C₄	C₂⁴	1	2	yes	—
395	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄	C₂⁴	1	2	yes	—
398	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄	C₂⁴	1	2	yes	—
400	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	C₂×D₄	1	2	yes	—
412	C₂²⋊C₄	C₂×D₄	1	2	yes	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	C₂×D₄	1	1	yes	characteristic
428	C₄²	C₂×D₄	1	1	yes	characteristic
429	C₄²	C₂⁴	1	1	yes	characteristic
430	C₄²	C₂⁴	1	1	yes	characteristic
431	C₄²	C₂⁴	1	2	yes	—
432	C₄²	C₂⁴	1	2	yes	—
433	C₂³	—	2	1	no	—
434	C₂³	C₂²×D₄	1	1	yes	characteristic
435	Q₈	—	2	4	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	1	no	—
439	Q₈	—	2	1	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	2	1	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	2	1	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	8	1	no	—
447	Q₈	—	8	1	no	—
448	Q₈	—	8	2	no	—
449	Q₈	—	8	2	no	—
450	Q₈	—	8	2	no	—
451	Q₈	2₋¹⁺⁴	1	2	yes	—
452	Q₈	2₋¹⁺⁴	1	2	yes	—
453	D₄	—	2	1	no	—
454	D₄	—	2	1	no	—
455	D₄	—	8	1	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	8	1	no	—
475	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄	1	2	yes	—
478	C₂×C₄	C₂²×D₄	1	2	yes	—
479	C₂×C₄	C₂²×D₄	1	2	yes	—
480	C₂×C₄	C₂²×D₄	1	2	yes	—
481	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂⁵	1	1	yes	characteristic
485	C₈	—	2	1	no	—
486	C₈	—	2	1	no	—
487	C₈	—	2	1	no	—
488	C₈	—	2	2	no	—
489	C₈	—	2	1	no	—
490	C₈	—	2	2	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	C₂³×D₄	1	1	yes	characteristic
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	2	no	—
517	C₄	#578	1	2	yes	—
518	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
519	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂	—	4	1	no	—
521	C₂	—	8	1	no	—
522	C₂	#3486	1	1	yes	characteristic
523	C₂	C₂×#578	1	1	yes	characteristic
524	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #533 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #3502	C₂	semidirect
3. #3390	C₂	semidirect
4. #3387	C₂	semidirect
5. #3385	C₂	semidirect
6. #3383	C₂	semidirect
7. Q₈×Q₁₆	C₂	semidirect
8. #3381	C₂	semidirect
9. #3377	C₂	semidirect
10. #3374	C₂	semidirect
11. #3369	C₂	semidirect
12. #3364	C₂	semidirect
13. #3364	C₂	semidirect
14. #3363	C₂	semidirect
16. #3242	C₂	semidirect
18. #3231	C₂	semidirect
19. #3127	C₂	semidirect
22. #3104	C₂	semidirect
23. #2986	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3555	2
#3502	2
#3390	2
#3387	2
#3385	2
#3383	2
Q₈×Q₁₆	2
#3381	2
#3377	2
#3374	2
#3369	2
#3364	2
#3363	2
#3243	2
#3242	2
#3233	2
#3231	2
#3127	2
#3121	2
#3108	2
#3104	2
#2986	2