Subgroups — #62215

Order 256.

881 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	#3347	C₂	1	2	yes	maximal, complemented
9	#3341	C₂	1	2	yes	maximal, complemented
10	#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	#3319	C₂	1	2	yes	maximal, complemented
13	#3297	C₂	1	2	yes	maximal, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3257	C₂	1	2	yes	maximal, complemented
16	#3245	C₂	1	1	yes	maximal, characteristic, complemented
17	#3243	C₂	1	2	yes	maximal, complemented
18	#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	#3122	C₂	1	2	yes	maximal, complemented
20	#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	#3081	C₂	1	2	yes	maximal, complemented
22	#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	#562	—	2	2	no	—
25	#559	C₂²	1	1	yes	characteristic
26	#556	C₂²	1	1	yes	characteristic
27	#555	C₂²	1	1	yes	characteristic
28	#555	C₂²	1	2	yes	—
29	#555	C₂²	1	2	yes	complemented
30	#554	C₂²	1	1	yes	characteristic, complemented
31	#553	C₂²	1	2	yes	complemented
32	#552	—	2	1	no	—
33	#551	—	2	2	no	—
34	D₄×Q₈	C₂²	1	1	yes	characteristic
35	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	#548	—	2	1	no	—
37	#548	—	2	1	no	—
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	2	no	—
44	#542	C₂²	1	2	yes	—
45	#540	C₂²	1	2	yes	complemented
46	#538	—	2	2	no	—
47	#537	—	2	1	no	—
48	#536	—	2	1	no	—
49	#533	C₂²	1	1	yes	characteristic, complemented
50	#532	C₂²	1	1	yes	characteristic
51	#532	C₂²	1	1	yes	characteristic, complemented
52	#529	—	2	1	no	—
53	#529	C₂²	1	1	yes	characteristic
54	C₂×#124	—	2	1	no	—
55	#518	C₂²	1	2	yes	—
56	C₄×#41	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#500	C₂²	1	2	yes	complemented
59	#500	C₂²	1	1	yes	characteristic, complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#489	C₂²	1	2	yes	complemented
62	#488	C₂²	1	2	yes	complemented
63	#486	C₂²	1	1	yes	characteristic
64	#486	C₂²	1	1	yes	characteristic
65	#485	C₂²	1	2	yes	complemented
66	#484	C₂²	1	2	yes	complemented
67	#482	C₂²	1	2	yes	—
68	#482	C₂²	1	2	yes	complemented
69	#482	C₂²	1	1	yes	characteristic, complemented
70	#482	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#482	C₂²	1	1	yes	characteristic, complemented
73	#482	C₂²	1	2	yes	complemented
74	#480	C₂²	1	2	yes	—
75	#479	C₂²	1	2	yes	complemented
76	#478	C₂²	1	2	yes	—
77	#478	C₂²	1	2	yes	—
78	#478	C₂²	1	2	yes	complemented
79	#478	C₂²	1	2	yes	complemented
80	#478	C₂²	1	2	yes	complemented
81	#477	C₂²	1	1	yes	characteristic, complemented
82	#477	C₂²	1	1	yes	characteristic, complemented
83	#476	C₂²	1	1	yes	characteristic
84	#476	C₂²	1	1	yes	characteristic
85	#476	C₂²	1	2	yes	complemented
86	#476	C₂²	1	2	yes	complemented
87	#475	C₂²	1	1	yes	characteristic, complemented
88	#474	C₂²	1	1	yes	characteristic
89	#474	C₂²	1	2	yes	—
90	#474	C₂²	1	2	yes	complemented
91	#474	C₂²	1	1	yes	characteristic, complemented
92	#474	C₂²	1	2	yes	complemented
93	#474	C₂²	1	1	yes	characteristic, complemented
94	#469	C₂²	1	2	yes	—
95	#468	C₂²	1	2	yes	complemented
96	#466	C₂²	1	2	yes	—
97	#466	C₂²	1	2	yes	complemented
98	#466	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#463	C₂²	1	2	yes	complemented
101	#463	C₂²	1	2	yes	complemented
102	#460	C₂²	1	1	yes	characteristic, complemented
103	#459	C₂²	1	1	yes	characteristic
104	#459	C₂²	1	1	yes	characteristic
105	#459	C₂²	1	1	yes	characteristic
106	#459	C₂²	1	2	yes	complemented
107	#449	C₂²	1	1	yes	characteristic
108	#449	C₂²	1	1	yes	characteristic
109	#447	C₂²	1	2	yes	—
110	#447	C₂²	1	2	yes	—
111	#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	#442	C₂²	1	2	yes	—
114	#442	C₂²	1	2	yes	complemented
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈	C₂²	1	1	yes	characteristic
118	C₄×D₈	C₂²	1	1	yes	characteristic
119	C₄×D₈	C₂²	1	2	yes	—
120	C₄×D₈	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	#431	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	2	yes	complemented
128	#427	C₂²	1	2	yes	complemented
129	#427	C₂²	1	2	yes	complemented
130	#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	#418	C₂²	1	2	yes	—
133	#416	C₂²	1	2	yes	—
134	C₂×#102	C₂²	1	2	yes	—
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	C₂³	1	1	yes	characteristic
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×Q₈	—	2	1	no	—
141	C₂²×D₄	—	2	1	no	—
142	C₂²×D₄	C₂³	1	2	yes	—
143	C₂×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×D₈	C₂³	1	1	yes	characteristic
146	C₂×D₈	C₂³	1	1	yes	characteristic
147	C₂×D₈	C₂³	1	2	yes	—
148	C₂×D₈	C₂³	1	2	yes	—
149	C₂×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₂²×C₈	C₂³	1	2	yes	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈	C₂³	1	2	yes	—
158	C₄⋊Q₈	C₂³	1	2	yes	—
159	#127	C₂³	1	1	yes	characteristic
160	#127	C₂³	1	1	yes	characteristic
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
163	#126	—	2	2	no	—
164	#126	D₄	1	2	yes	—
165	#125	—	2	2	no	—
166	#125	D₄	1	1	yes	characteristic
167	#125	C₂³	1	2	yes	—
168	#125	C₂³	1	2	yes	—
169	#124	—	2	1	no	—
170	#124	—	2	1	no	—
171	#124	—	2	2	no	—
172	#124	—	2	2	no	—
173	#124	—	2	2	no	—
174	#124	—	2	2	no	—
175	#124	—	2	2	no	—
176	#124	—	2	2	no	—
177	#124	—	2	1	no	—
178	#124	—	2	1	no	—
179	#124	D₄	1	1	yes	characteristic
180	#124	C₂³	1	2	yes	—
181	#123	—	2	2	no	—
182	#123	—	2	2	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	D₄	1	2	yes	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	—	2	1	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	2	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	D₄	1	1	yes	characteristic
202	C₂²⋊Q₈	C₂³	1	2	yes	—
203	#121	—	2	1	no	—
204	#121	—	2	2	no	—
205	#121	—	2	2	no	—
206	#121	—	2	2	no	—
207	#121	—	2	1	no	—
208	#121	—	2	1	no	—
209	#121	—	2	1	no	—
210	#121	—	2	2	no	—
211	#121	—	2	2	no	—
212	#121	—	2	2	no	—
213	#121	D₄	1	1	yes	characteristic
214	#121	C₂³	1	2	yes	—
215	#121	C₂³	1	1	yes	characteristic
216	#121	C₂³	1	1	yes	characteristic
217	#121	C₂³	1	2	yes	—
218	#121	C₂³	1	2	yes	—
219	#121	C₂³	1	2	yes	—
220	#120	—	2	2	no	—
221	#120	—	2	2	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	2	yes	—
239	C₄×D₄	C₂³	1	2	yes	—
240	C₄×D₄	C₂³	1	2	yes	—
241	C₄×D₄	C₂³	1	1	yes	characteristic
242	C₄×D₄	C₂³	1	1	yes	characteristic
243	C₄×D₄	C₂³	1	2	yes	—
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	1	yes	characteristic
246	C₄×D₄	C₂³	1	2	yes	—
247	#117	—	2	2	no	—
248	#117	—	2	1	no	—
249	#117	—	2	2	no	—
250	#117	—	2	1	no	—
251	#117	C₂³	1	1	yes	characteristic
252	#117	C₂³	1	2	yes	—
253	#117	C₂³	1	2	yes	—
254	#117	C₂³	1	2	yes	—
255	#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂³	1	1	yes	characteristic
263	#107	C₂³	1	2	yes	—
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	1	yes	characteristic
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	2	yes	—
271	#106	C₂³	1	1	yes	characteristic
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	2	yes	—
277	C₄⋊C₈	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
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	2	yes	—
293	#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	#97	C₂³	1	2	yes	—
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	—	2	2	no	—
314	#41	—	4	1	no	—
315	#41	—	8	2	no	—
316	#41	—	8	2	no	—
317	#41	—	8	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×Q₈	—	8	2	no	—
326	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	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	2	yes	—
346	C₂×D₄	C₂⁴	1	1	yes	characteristic
347	C₂×D₄	C₂⁴	1	1	yes	characteristic
348	C₂×D₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴	1	2	yes	—
364	SD₁₆	—	4	1	no	—
365	SD₁₆	—	4	1	no	—
366	D₈	—	2	2	no	—
367	D₈	—	2	2	no	—
368	D₈	—	4	2	no	—
369	D₈	—	4	2	no	—
370	M₁₆	—	4	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₈	C₂⁴	1	1	yes	characteristic
375	C₂×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₈	C₂⁴	1	2	yes	—
378	C₂×C₈	C₂⁴	1	2	yes	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₄⋊C₄	C₂⁴	1	2	yes	—
400	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	2	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	1	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	C₂×D₄	1	1	yes	characteristic
440	C₄²	C₂×D₄	1	1	yes	characteristic
441	C₄²	C₂⁴	1	1	yes	characteristic
442	C₄²	C₂⁴	1	2	yes	—
443	C₄²	C₂⁴	1	1	yes	characteristic
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	8	2	no	—
450	C₂³	—	8	2	no	—
451	C₂³	C₂²×D₄	1	2	yes	—
452	C₂³	C₂²×D₄	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	2	1	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	8	1	no	—
459	Q₈	—	8	2	no	—
460	Q₈	—	8	2	no	—
461	Q₈	—	8	1	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	1	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	4	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	8	1	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	1	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	2	no	—
483	D₄	2₋¹⁺⁴	1	2	yes	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	8	1	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	—	8	2	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
515	C₂×C₄	C₂²×D₄	1	2	yes	—
516	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄	C₂⁵	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	2	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	2	no	—
523	C₈	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	16	4	no	—
543	C₂²	C₂³×D₄	1	1	yes	characteristic
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	2	no	—
559	C₄	#576	1	2	yes	—
560	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	C₄	#585	1	1	yes	characteristic
562	C₂	—	4	1	no	—
563	C₂	—	4	2	no	—
564	C₂	—	4	2	no	—
565	C₂	—	8	1	no	—
566	C₂	—	8	1	no	—
567	C₂	—	8	2	no	—
568	C₂	#3489	1	1	yes	characteristic
569	C₂	C₂×#576	1	1	yes	characteristic
570	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
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. #3547	C₂	semidirect
2. #3514	C₂	semidirect
3. #3384	C₂	semidirect
4. Q₈×D₈	C₂	semidirect
5. #3373	C₂	semidirect
6. #3361	C₂	semidirect
7. #3353	C₂	semidirect
8. #3347	C₂	semidirect
9. #3341	C₂	semidirect
10. #3340	C₂	semidirect
11. #3325	C₂	semidirect
12. #3319	C₂	semidirect
13. #3297	C₂	semidirect
14. #3294	C₂	semidirect
15. #3257	C₂	semidirect
16. #3245	C₂	semidirect
17. #3243	C₂	semidirect
18. #3228	C₂	semidirect
19. #3122	C₂	semidirect
20. #3106	C₂	semidirect
21. #3081	C₂	semidirect
22. #3076	C₂	semidirect
23. #2994	C₂	semidirect
29. #555	C₂²	semidirect
30. #554	C₂²	semidirect
31. #553	C₂²	semidirect
35. D₄×Q₈	C₂²	semidirect
42. #544	C₂²	semidirect
45. #540	C₂²	semidirect
49. #533	C₂²	semidirect
51. #532	C₂²	semidirect
57. #501	C₂²	semidirect
58. #500	C₂²	semidirect
59. #500	C₂²	semidirect
60. #498	C₂²	semidirect
61. #489	C₂²	semidirect
62. #488	C₂²	semidirect
65. #485	C₂²	semidirect
66. #484	C₂²	semidirect
68. #482	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
72. #482	C₂²	semidirect
73. #482	C₂²	semidirect
75. #479	C₂²	semidirect
78. #478	C₂²	semidirect
79. #478	C₂²	semidirect
80. #478	C₂²	semidirect
81. #477	C₂²	semidirect
82. #477	C₂²	semidirect
85. #476	C₂²	semidirect
86. #476	C₂²	semidirect
87. #475	C₂²	semidirect
90. #474	C₂²	semidirect
91. #474	C₂²	semidirect
92. #474	C₂²	semidirect
93. #474	C₂²	semidirect
95. #468	C₂²	semidirect
97. #466	C₂²	semidirect
98. #466	C₂²	semidirect
99. #465	C₂²	semidirect
100. #463	C₂²	semidirect
101. #463	C₂²	semidirect
102. #460	C₂²	semidirect
106. #459	C₂²	semidirect
111. #446	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
114. #442	C₂²	semidirect
115. C₄×SD₁₆	C₂²	semidirect
116. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
122. #435	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
126. #431	C₂²	semidirect
127. #428	C₂²	semidirect
128. #427	C₂²	semidirect
129. #427	C₂²	semidirect
130. #424	C₂²	semidirect
131. 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
#3547	2
#3514	2
#3384	2
Q₈×D₈	2
#3373	2
#3361	2
#3353	2
#3347	2
#3341	2
#3340	2
#3325	2
#3319	2
#3297	2
#3294	2
#3257	2
#3245	2
#3243	2
#3228	2
#3122	2
#3106	2
#3081	2
#3076	2
#2994	2