Subgroups — #62563

Order 256.

862 conjugacy classes of subgroups.

The subgroup lattice has 567 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, complemented
2	#3546	C₂	1	1	yes	maximal, characteristic
3	#3369	C₂	1	1	yes	maximal, characteristic, complemented
4	#3368	C₂	1	1	yes	maximal, characteristic, complemented
5	#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	#3317	C₂	1	2	yes	maximal, complemented
10	#3311	C₂	1	2	yes	maximal, complemented
11	#3304	C₂	1	2	yes	maximal, complemented
12	#3302	C₂	1	1	yes	maximal, characteristic, complemented
13	#3296	C₂	1	2	yes	maximal, complemented
14	#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	#3244	C₂	1	2	yes	maximal, complemented
16	#3235	C₂	1	1	yes	maximal, characteristic, complemented
17	#3222	C₂	1	2	yes	maximal, complemented
18	#3216	C₂	1	1	yes	maximal, characteristic, complemented
19	#3178	C₂	1	2	yes	maximal, complemented
20	#3167	C₂	1	1	yes	maximal, characteristic, complemented
21	#3136	C₂	1	2	yes	maximal, complemented
22	#3131	C₂	1	1	yes	maximal, characteristic, complemented
23	#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	#563	—	2	2	no	—
25	#560	—	2	2	no	—
26	Q₈²	C₂²	1	1	yes	characteristic, complemented
27	#557	—	2	1	no	—
28	#557	C₂²	1	1	yes	characteristic, complemented
29	#556	—	2	1	no	—
30	#556	C₂²	1	1	yes	characteristic
31	#556	C₂²	1	1	yes	characteristic
32	#556	C₂²	1	2	yes	complemented
33	#554	C₂²	1	1	yes	characteristic
34	#553	—	2	1	no	—
35	#552	C₂²	1	2	yes	complemented
36	#550	C₂²	1	2	yes	—
37	#550	C₂²	1	1	yes	characteristic
38	#547	C₂²	1	1	yes	characteristic
39	#546	—	2	1	no	—
40	#546	C₂²	1	2	yes	—
41	D₄²	C₂²	1	1	yes	characteristic
42	#544	C₂²	1	2	yes	complemented
43	#542	—	2	1	no	—
44	#542	C₂²	1	2	yes	—
45	#541	—	2	2	no	—
46	#541	—	2	1	no	—
47	#541	C₂²	1	2	yes	complemented
48	#538	—	2	2	no	—
49	#537	—	2	1	no	—
50	#535	—	2	1	no	—
51	#535	C₂²	1	2	yes	—
52	#533	C₂²	1	1	yes	characteristic, complemented
53	#533	C₂²	1	1	yes	characteristic, complemented
54	#532	C₂²	1	1	yes	characteristic
55	#532	C₂²	1	1	yes	characteristic
56	#529	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#498	C₂²	1	1	yes	characteristic, complemented
59	#497	C₂²	1	2	yes	complemented
60	#492	C₂²	1	1	yes	characteristic
61	#490	C₂²	1	2	yes	—
62	#490	C₂²	1	2	yes	complemented
63	#489	C₂²	1	2	yes	—
64	#489	C₂²	1	2	yes	complemented
65	#488	C₂²	1	2	yes	—
66	#488	C₂²	1	2	yes	complemented
67	#488	C₂²	1	2	yes	complemented
68	#487	C₂²	1	1	yes	characteristic, complemented
69	#487	C₂²	1	1	yes	characteristic, complemented
70	#487	C₂²	1	1	yes	characteristic, complemented
71	#486	C₂²	1	1	yes	characteristic
72	#486	C₂²	1	1	yes	characteristic
73	#486	C₂²	1	1	yes	characteristic
74	#486	C₂²	1	2	yes	complemented
75	#485	C₂²	1	2	yes	complemented
76	#483	C₂²	1	2	yes	complemented
77	#482	C₂²	1	2	yes	—
78	#482	C₂²	1	2	yes	—
79	#482	C₂²	1	2	yes	complemented
80	#481	C₂²	1	2	yes	—
81	#479	C₂²	1	2	yes	complemented
82	#478	C₂²	1	2	yes	complemented
83	#476	C₂²	1	1	yes	characteristic
84	#476	C₂²	1	1	yes	characteristic, complemented
85	#476	C₂²	1	2	yes	complemented
86	#475	C₂²	1	2	yes	complemented
87	#474	C₂²	1	1	yes	characteristic
88	#474	C₂²	1	1	yes	characteristic, complemented
89	#470	C₂²	1	2	yes	complemented
90	#468	C₂²	1	2	yes	—
91	#467	C₂²	1	2	yes	complemented
92	#465	C₂²	1	1	yes	characteristic
93	#465	C₂²	1	1	yes	characteristic
94	#465	C₂²	1	2	yes	—
95	#465	C₂²	1	1	yes	characteristic, complemented
96	#465	C₂²	1	1	yes	characteristic, complemented
97	#464	C₂²	1	2	yes	—
98	#464	C₂²	1	2	yes	—
99	#462	C₂²	1	1	yes	characteristic, complemented
100	#462	C₂²	1	1	yes	characteristic, complemented
101	#460	C₂²	1	1	yes	characteristic
102	#460	C₂²	1	1	yes	characteristic
103	#460	C₂²	1	2	yes	complemented
104	#460	C₂²	1	2	yes	complemented
105	#452	C₂²	1	2	yes	complemented
106	#452	C₂²	1	2	yes	complemented
107	#452	C₂²	1	2	yes	complemented
108	#452	C₂²	1	2	yes	complemented
109	#450	C₂²	1	2	yes	—
110	#450	C₂²	1	2	yes	—
111	#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	#441	C₂²	1	2	yes	complemented
114	#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆	C₂²	1	2	yes	complemented
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆	C₂²	1	2	yes	complemented
121	#436	C₂²	1	1	yes	characteristic
122	#435	C₂²	1	2	yes	complemented
123	C₈×D₄	C₂²	1	1	yes	characteristic
124	C₈×D₄	C₂²	1	2	yes	complemented
125	#433	C₂²	1	2	yes	complemented
126	#432	C₂²	1	1	yes	characteristic, complemented
127	#418	C₂²	1	2	yes	—
128	#417	C₂²	1	2	yes	complemented
129	#416	C₂²	1	2	yes	complemented
130	#416	C₂²	1	2	yes	complemented
131	#416	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	—
133	#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	C₂³	1	2	yes	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂²×D₄	—	2	1	no	—
140	C₂²×D₄	C₂³	1	2	yes	—
141	C₂×Q₁₆	C₂³	1	2	yes	—
142	C₂×Q₁₆	C₂³	1	2	yes	—
143	C₂×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆	C₂³	1	2	yes	—
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₈	C₂³	1	2	yes	—
153	C₄⋊Q₈	—	2	1	no	—
154	C₄⋊Q₈	—	2	2	no	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	2	yes	—
164	#127	—	2	2	no	—
165	#127	C₂³	1	1	yes	characteristic
166	#127	C₂³	1	1	yes	characteristic
167	#127	C₂³	1	2	yes	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#126	D₄	1	2	yes	—
177	#125	—	2	2	no	—
178	#125	—	2	2	no	—
179	#125	—	2	2	no	—
180	#125	—	2	1	no	—
181	#125	—	2	2	no	—
182	#125	—	2	2	no	—
183	#125	—	2	1	no	—
184	#125	D₄	1	1	yes	characteristic
185	#125	C₂³	1	2	yes	—
186	#125	C₂³	1	2	yes	—
187	#124	—	2	1	no	—
188	#124	—	2	2	no	—
189	#124	—	2	2	no	—
190	#124	—	2	1	no	—
191	#124	D₄	1	1	yes	characteristic
192	#124	C₂³	1	2	yes	—
193	#124	C₂³	1	2	yes	—
194	#123	—	2	2	no	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	#123	D₄	1	2	yes	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	no	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	1	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	#121	—	2	1	no	—
214	#121	—	2	1	no	—
215	#121	—	2	1	no	—
216	#121	—	2	1	no	—
217	#121	—	2	1	no	—
218	#121	—	2	2	no	—
219	#121	—	2	2	no	—
220	#121	—	2	1	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	D₄	1	1	yes	characteristic
226	#121	C₂³	1	1	yes	characteristic
227	#121	C₂³	1	1	yes	characteristic
228	#121	C₂³	1	2	yes	—
229	#120	—	2	2	no	—
230	#120	—	2	2	no	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×Q₈	C₂³	1	2	yes	—
243	C₄×Q₈	C₂³	1	2	yes	—
244	C₄×Q₈	C₂³	1	2	yes	—
245	C₄×Q₈	C₂³	1	1	yes	characteristic
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	C₂³	1	1	yes	characteristic
252	C₄×D₄	C₂³	1	1	yes	characteristic
253	C₄×D₄	C₂³	1	2	yes	—
254	C₄×D₄	C₂³	1	1	yes	characteristic
255	C₄×D₄	C₂³	1	2	yes	—
256	#117	—	2	1	no	—
257	#117	—	2	1	no	—
258	#117	—	2	2	no	—
259	#117	C₂³	1	2	yes	—
260	#117	C₂³	1	2	yes	—
261	#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#106	C₂³	1	1	yes	characteristic
269	#106	C₂³	1	1	yes	characteristic
270	#106	C₂³	1	1	yes	characteristic
271	#106	C₂³	1	1	yes	characteristic
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	2	yes	—
277	C₄⋊C₈	C₂³	1	2	yes	—
278	#103	C₂³	1	2	yes	—
279	#103	C₂³	1	2	yes	—
280	#103	C₂³	1	2	yes	—
281	#103	C₂³	1	2	yes	—
282	#103	C₂³	1	2	yes	—
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#102	C₂³	1	1	yes	characteristic
289	#102	C₂³	1	2	yes	—
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	1	yes	characteristic
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	1	yes	characteristic
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂²⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	—	2	2	no	—
313	#41	—	4	2	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	8	2	no	—
318	#41	—	8	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈	C₂⁴	1	2	yes	—
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	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	8	2	no	—
343	C₂×D₄	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄	C₂×D₄	1	2	yes	—
345	C₂×D₄	C₂⁴	1	1	yes	characteristic
346	C₂×D₄	C₂⁴	1	2	yes	—
347	C₂×D₄	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴	1	2	yes	—
358	Q₁₆	—	4	2	no	—
359	Q₁₆	—	4	2	no	—
360	SD₁₆	—	4	1	no	—
361	SD₁₆	—	4	1	no	—
362	SD₁₆	—	4	1	no	—
363	SD₁₆	—	4	1	no	—
364	SD₁₆	—	4	2	no	—
365	SD₁₆	—	4	2	no	—
366	M₁₆	—	4	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₈	C₂⁴	1	1	yes	characteristic
372	C₂×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₈	C₂⁴	1	2	yes	—
375	C₂×C₈	C₂⁴	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₄⋊C₄	C₂×D₄	1	2	yes	—
405	C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	C₂×D₄	1	1	yes	characteristic
442	C₄²	C₂×D₄	1	1	yes	characteristic
443	C₄²	C₂⁴	1	1	yes	characteristic
444	C₄²	C₂⁴	1	1	yes	characteristic
445	C₄²	C₂⁴	1	2	yes	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	8	2	no	—
450	C₂³	—	8	2	no	—
451	C₂³	—	8	2	no	—
452	C₂³	C₂²×D₄	1	2	yes	—
453	C₂³	C₂²×D₄	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	1	no	—
457	Q₈	—	2	1	no	—
458	Q₈	—	2	1	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	8	1	no	—
463	Q₈	—	8	1	no	—
464	Q₈	—	8	2	no	—
465	Q₈	—	8	1	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	1	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	1	no	—
476	D₄	—	8	1	no	—
477	D₄	—	8	2	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	1	no	—
480	D₄	—	8	2	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	2	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	1	no	—
485	D₄	—	8	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	—	8	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄	1	2	yes	—
509	C₂×C₄	C₂²×D₄	1	2	yes	—
510	C₂×C₄	C₂²×D₄	1	2	yes	—
511	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂⁵	1	1	yes	characteristic
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	16	4	no	—
538	C₂²	C₂³×D₄	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	2	no	—
555	C₄	#577	1	2	yes	—
556	C₄	#585	1	1	yes	characteristic
557	C₄	#585	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	4	2	no	—
560	C₂	—	8	1	no	—
561	C₂	—	8	2	no	—
562	C₂	—	8	1	no	—
563	C₂	#3500	1	1	yes	characteristic
564	C₂	C₂×#577	1	1	yes	characteristic
565	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3555	C₂	semidirect
3. #3369	C₂	semidirect
4. #3368	C₂	semidirect
5. #3364	C₂	semidirect
6. #3362	C₂	semidirect
7. #3331	C₂	semidirect
8. #3324	C₂	semidirect
9. #3317	C₂	semidirect
10. #3311	C₂	semidirect
11. #3304	C₂	semidirect
12. #3302	C₂	semidirect
13. #3296	C₂	semidirect
14. #3295	C₂	semidirect
15. #3244	C₂	semidirect
16. #3235	C₂	semidirect
17. #3222	C₂	semidirect
18. #3216	C₂	semidirect
19. #3178	C₂	semidirect
20. #3167	C₂	semidirect
21. #3136	C₂	semidirect
22. #3131	C₂	semidirect
23. #2966	C₂	semidirect
26. Q₈²	C₂²	semidirect
28. #557	C₂²	semidirect
32. #556	C₂²	semidirect
35. #552	C₂²	semidirect
42. #544	C₂²	semidirect
47. #541	C₂²	semidirect
52. #533	C₂²	semidirect
53. #533	C₂²	semidirect
57. #501	C₂²	semidirect
58. #498	C₂²	semidirect
59. #497	C₂²	semidirect
62. #490	C₂²	semidirect
64. #489	C₂²	semidirect
66. #488	C₂²	semidirect
67. #488	C₂²	semidirect
68. #487	C₂²	semidirect
69. #487	C₂²	semidirect
70. #487	C₂²	semidirect
74. #486	C₂²	semidirect
75. #485	C₂²	semidirect
76. #483	C₂²	semidirect
79. #482	C₂²	semidirect
81. #479	C₂²	semidirect
82. #478	C₂²	semidirect
84. #476	C₂²	semidirect
85. #476	C₂²	semidirect
86. #475	C₂²	semidirect
88. #474	C₂²	semidirect
89. #470	C₂²	semidirect
91. #467	C₂²	semidirect
95. #465	C₂²	semidirect
96. #465	C₂²	semidirect
99. #462	C₂²	semidirect
100. #462	C₂²	semidirect
103. #460	C₂²	semidirect
104. #460	C₂²	semidirect
105. #452	C₂²	semidirect
106. #452	C₂²	semidirect
107. #452	C₂²	semidirect
108. #452	C₂²	semidirect
111. #446	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
113. #441	C₂²	semidirect
114. #440	C₂²	semidirect
115. C₄×Q₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
119. C₄×SD₁₆	C₂²	semidirect
120. C₄×SD₁₆	C₂²	semidirect
122. #435	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
126. #432	C₂²	semidirect
128. #417	C₂²	semidirect
129. #416	C₂²	semidirect
130. #416	C₂²	semidirect
131. #416	C₂²	semidirect
133. #405	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3555	2
#3546	2
#3369	2
#3368	2
#3364	2
#3362	2
#3331	2
#3324	2
#3317	2
#3311	2
#3304	2
#3302	2
#3296	2
#3295	2
#3244	2
#3235	2
#3222	2
#3216	2
#3178	2
#3167	2
#3136	2
#3131	2
#2966	2