Subgroups — #62552

Order 256.

913 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	#3543	C₂	1	1	yes	maximal, characteristic, complemented
3	#3375	C₂	1	1	yes	maximal, characteristic, complemented
4	#3366	C₂	1	1	yes	maximal, characteristic, complemented
5	#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	#3325	C₂	1	1	yes	maximal, characteristic, complemented
9	#3310	C₂	1	2	yes	maximal, complemented
10	#3306	C₂	1	2	yes	maximal, complemented
11	#3305	C₂	1	1	yes	maximal, characteristic, complemented
12	#3296	C₂	1	2	yes	maximal, complemented
13	#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	#3294	C₂	1	2	yes	maximal, complemented
15	#3241	C₂	1	2	yes	maximal, complemented
16	#3238	C₂	1	1	yes	maximal, characteristic, complemented
17	#3224	C₂	1	2	yes	maximal, complemented
18	#3217	C₂	1	1	yes	maximal, characteristic, complemented
19	#3179	C₂	1	2	yes	maximal, complemented
20	#3168	C₂	1	1	yes	maximal, characteristic, complemented
21	#3136	C₂	1	2	yes	maximal, complemented
22	C₂×#486	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	#559	C₂²	1	1	yes	characteristic
27	Q₈²	C₂²	1	1	yes	characteristic, complemented
28	#555	C₂²	1	1	yes	characteristic, complemented
29	#554	C₂²	1	1	yes	characteristic, complemented
30	#554	C₂²	1	1	yes	characteristic, complemented
31	#552	—	2	1	no	—
32	#552	C₂²	1	2	yes	complemented
33	#550	C₂²	1	1	yes	characteristic
34	#550	C₂²	1	1	yes	characteristic
35	#547	—	2	1	no	—
36	#547	C₂²	1	2	yes	complemented
37	#546	—	2	1	no	—
38	#546	C₂²	1	2	yes	—
39	D₄²	—	2	1	no	—
40	D₄²	C₂²	1	2	yes	—
41	D₄²	C₂²	1	1	yes	characteristic
42	#544	—	2	1	no	—
43	#544	C₂²	1	2	yes	complemented
44	#542	—	2	1	no	—
45	#542	C₂²	1	2	yes	complemented
46	#540	—	2	1	no	—
47	#540	C₂²	1	2	yes	—
48	#536	—	2	2	no	—
49	#535	—	2	1	no	—
50	#535	C₂²	1	2	yes	—
51	#534	—	2	2	no	—
52	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×#127	C₂²	1	1	yes	characteristic
54	#529	C₂²	1	1	yes	characteristic
55	#529	C₂²	1	1	yes	characteristic
56	#529	C₂²	1	1	yes	characteristic, complemented
57	#501	C₂²	1	2	yes	complemented
58	#499	C₂²	1	1	yes	characteristic, complemented
59	#496	C₂²	1	2	yes	complemented
60	#495	C₂²	1	1	yes	characteristic, complemented
61	#490	C₂²	1	2	yes	complemented
62	#490	C₂²	1	2	yes	complemented
63	#489	C₂²	1	2	yes	complemented
64	#489	C₂²	1	2	yes	complemented
65	#488	C₂²	1	2	yes	complemented
66	#488	C₂²	1	1	yes	characteristic, complemented
67	#488	C₂²	1	1	yes	characteristic, complemented
68	#486	C₂²	1	1	yes	characteristic
69	#486	C₂²	1	1	yes	characteristic
70	#486	C₂²	1	1	yes	characteristic, complemented
71	#486	C₂²	1	1	yes	characteristic, complemented
72	#486	C₂²	1	2	yes	complemented
73	#486	C₂²	1	2	yes	complemented
74	#486	C₂²	1	2	yes	complemented
75	#483	C₂²	1	2	yes	complemented
76	#482	C₂²	1	2	yes	complemented
77	#482	C₂²	1	2	yes	complemented
78	#481	C₂²	1	2	yes	complemented
79	#480	C₂²	1	2	yes	—
80	#480	C₂²	1	2	yes	complemented
81	#478	C₂²	1	2	yes	complemented
82	#478	C₂²	1	2	yes	complemented
83	#477	C₂²	1	1	yes	characteristic, complemented
84	#477	C₂²	1	1	yes	characteristic, complemented
85	#476	C₂²	1	1	yes	characteristic, complemented
86	#476	C₂²	1	2	yes	complemented
87	#476	C₂²	1	1	yes	characteristic, complemented
88	#474	C₂²	1	2	yes	complemented
89	#469	C₂²	1	2	yes	complemented
90	#468	C₂²	1	2	yes	complemented
91	#467	C₂²	1	1	yes	characteristic, complemented
92	#466	C₂²	1	1	yes	characteristic
93	#466	C₂²	1	2	yes	complemented
94	#465	C₂²	1	1	yes	characteristic
95	#465	C₂²	1	1	yes	characteristic, complemented
96	#465	C₂²	1	2	yes	complemented
97	#464	C₂²	1	2	yes	complemented
98	#463	C₂²	1	2	yes	complemented
99	#460	C₂²	1	1	yes	characteristic
100	#460	C₂²	1	1	yes	characteristic, complemented
101	#460	C₂²	1	2	yes	complemented
102	#459	C₂²	1	1	yes	characteristic
103	#459	C₂²	1	1	yes	characteristic, complemented
104	#459	C₂²	1	2	yes	complemented
105	#452	C₂²	1	2	yes	complemented
106	#450	C₂²	1	2	yes	complemented
107	#450	C₂²	1	2	yes	complemented
108	#449	C₂²	1	2	yes	complemented
109	#447	C₂²	1	2	yes	complemented
110	#447	C₂²	1	2	yes	complemented
111	#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	#442	C₂²	1	2	yes	complemented
114	#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×D₈	C₂²	1	2	yes	complemented
120	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
121	#436	C₂²	1	1	yes	characteristic, complemented
122	#435	C₂²	1	2	yes	complemented
123	C₈×D₄	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
125	#433	C₂²	1	2	yes	complemented
126	#432	C₂²	1	1	yes	characteristic, complemented
127	#418	C₂²	1	2	yes	complemented
128	#417	C₂²	1	2	yes	complemented
129	#416	C₂²	1	2	yes	complemented
130	C₂×#102	C₂²	1	2	yes	complemented
131	C₂×#102	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
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	2	no	—
137	C₂×#41	C₂³	1	2	yes	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×D₄	—	2	2	no	—
140	C₂²×D₄	—	2	1	no	—
141	C₂²×D₄	—	2	1	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	C₂³	1	2	yes	—
144	C₂²×D₄	C₂³	1	2	yes	—
145	C₂×Q₁₆	C₂³	1	1	yes	characteristic
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×SD₁₆	C₂³	1	2	yes	—
150	C₂×D₈	C₂³	1	2	yes	—
151	C₂×D₈	C₂³	1	1	yes	characteristic
152	C₂×D₈	C₂³	1	2	yes	—
153	C₂×M₁₆	C₂³	1	2	yes	—
154	C₂²×C₈	C₂³	1	1	yes	characteristic
155	C₂²×C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₈	C₂³	1	2	yes	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	C₂³	1	2	yes	—
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	#127	—	2	1	no	—
167	#127	—	2	1	no	—
168	#127	—	2	1	no	—
169	#127	C₂³	1	2	yes	—
170	#127	C₂³	1	1	yes	characteristic
171	#127	C₂³	1	1	yes	characteristic
172	#127	C₂³	1	2	yes	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	1	no	—
176	#126	—	2	1	no	—
177	#126	D₄	1	2	yes	—
178	#125	—	2	1	no	—
179	#125	—	2	2	no	—
180	#125	—	2	2	no	—
181	#125	D₄	1	1	yes	characteristic
182	#125	C₂³	1	1	yes	characteristic
183	#125	C₂³	1	1	yes	characteristic
184	#125	C₂³	1	2	yes	—
185	#124	—	2	1	no	—
186	#124	—	2	2	no	—
187	#124	—	2	2	no	—
188	#124	D₄	1	1	yes	characteristic
189	#124	C₂³	1	1	yes	characteristic
190	#124	C₂³	1	1	yes	characteristic
191	#124	C₂³	1	2	yes	—
192	#123	—	2	2	no	—
193	#123	—	2	1	no	—
194	#123	—	2	1	no	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	#123	—	2	2	no	—
202	#123	D₄	1	2	yes	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	#121	—	2	1	no	—
215	#121	—	2	2	no	—
216	#121	—	2	2	no	—
217	#121	—	2	2	no	—
218	#121	—	2	1	no	—
219	#121	—	2	1	no	—
220	#121	—	2	2	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	#121	C₂³	1	2	yes	—
230	#121	C₂³	1	2	yes	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	#120	—	2	2	no	—
234	#120	—	2	2	no	—
235	#120	—	2	2	no	—
236	#120	—	2	2	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₄×Q₈	C₂³	1	2	yes	—
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₂³	1	1	yes	characteristic
248	C₄×D₄	C₂³	1	1	yes	characteristic
249	C₄×D₄	C₂³	1	2	yes	—
250	C₄×D₄	C₂³	1	2	yes	—
251	C₄×D₄	C₂³	1	2	yes	—
252	C₄×D₄	C₂³	1	2	yes	—
253	C₄×D₄	C₂³	1	1	yes	characteristic
254	#117	—	2	1	no	—
255	#117	—	2	2	no	—
256	#117	—	2	1	no	—
257	#117	—	2	1	no	—
258	#117	C₂³	1	2	yes	—
259	#117	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	1	yes	characteristic
269	#107	C₂³	1	2	yes	—
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	1	yes	characteristic
279	#103	C₂³	1	2	yes	—
280	#103	C₂³	1	1	yes	characteristic
281	#103	C₂³	1	2	yes	—
282	#103	C₂³	1	1	yes	characteristic
283	#103	C₂³	1	1	yes	characteristic
284	#102	C₂³	1	2	yes	—
285	#102	C₂³	1	1	yes	characteristic
286	#102	C₂³	1	2	yes	—
287	#102	C₂³	1	2	yes	—
288	#102	C₂³	1	2	yes	—
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	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	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
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	C₂⁴	—	2	2	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	#41	—	8	4	no	—
317	#41	—	8	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	8	2	no	—
323	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈	C₂⁴	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	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	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	—	8	2	no	—
348	C₂×D₄	—	8	2	no	—
349	C₂×D₄	—	8	4	no	—
350	C₂×D₄	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄	C₂×D₄	1	2	yes	—
352	C₂×D₄	C₂⁴	1	2	yes	—
353	C₂×D₄	C₂⁴	1	1	yes	characteristic
354	C₂×D₄	C₂⁴	1	2	yes	—
355	C₂×D₄	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴	1	2	yes	—
368	Q₁₆	—	4	1	no	—
369	SD₁₆	—	4	2	no	—
370	SD₁₆	—	4	1	no	—
371	SD₁₆	—	4	1	no	—
372	SD₁₆	—	4	2	no	—
373	D₈	—	4	2	no	—
374	D₈	—	4	1	no	—
375	D₈	—	4	2	no	—
376	M₁₆	—	4	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	4	1	no	—
380	C₂×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₈	C₂⁴	1	2	yes	—
385	C₂×C₈	C₂⁴	1	2	yes	—
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	—	2	1	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	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂×D₄	1	2	yes	—
407	C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄	C₂⁴	1	2	yes	—
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	2	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	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	C₂×D₄	1	1	yes	characteristic
446	C₄²	C₂×D₄	1	1	yes	characteristic
447	C₄²	C₂⁴	1	1	yes	characteristic
448	C₄²	C₂⁴	1	1	yes	characteristic
449	C₄²	C₂⁴	1	2	yes	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	—	8	2	no	—
460	C₂³	C₂²×D₄	1	2	yes	—
461	C₂³	C₂²×D₄	1	1	yes	characteristic
462	Q₈	—	2	2	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	8	1	no	—
468	Q₈	—	8	2	no	—
469	Q₈	—	8	1	no	—
470	Q₈	—	8	2	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	1	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	4	2	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	1	no	—
488	D₄	—	8	2	no	—
489	D₄	—	8	1	no	—
490	D₄	—	8	2	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	C₂²×D₄	1	2	yes	—
520	C₂×C₄	C₂²×D₄	1	2	yes	—
521	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄	1	2	yes	—
526	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂⁵	1	1	yes	characteristic
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	2	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	16	4	no	—
552	C₂²	—	16	4	no	—
553	C₂²	#576	1	2	yes	—
554	C₂²	C₂³×D₄	1	1	yes	characteristic
555	C₄	—	2	2	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	#577	1	2	yes	—
571	C₄	#585	1	1	yes	characteristic
572	C₄	#585	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	1	no	—
576	C₂	—	8	2	no	—
577	C₂	—	8	2	no	—
578	C₂	—	8	1	no	—
579	C₂	#3500	1	1	yes	characteristic
580	C₂	C₂×#576	1	1	yes	characteristic
581	C₂	C₂×#577	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. #3544	C₂	semidirect
2. #3543	C₂	semidirect
3. #3375	C₂	semidirect
4. #3366	C₂	semidirect
5. #3362	C₂	semidirect
6. #3361	C₂	semidirect
7. #3333	C₂	semidirect
8. #3325	C₂	semidirect
9. #3310	C₂	semidirect
10. #3306	C₂	semidirect
11. #3305	C₂	semidirect
12. #3296	C₂	semidirect
13. #3295	C₂	semidirect
14. #3294	C₂	semidirect
15. #3241	C₂	semidirect
16. #3238	C₂	semidirect
17. #3224	C₂	semidirect
18. #3217	C₂	semidirect
19. #3179	C₂	semidirect
20. #3168	C₂	semidirect
21. #3136	C₂	semidirect
22. C₂×#486	C₂	semidirect
23. #2966	C₂	semidirect
27. Q₈²	C₂²	semidirect
28. #555	C₂²	semidirect
29. #554	C₂²	semidirect
30. #554	C₂²	semidirect
32. #552	C₂²	semidirect
36. #547	C₂²	semidirect
43. #544	C₂²	semidirect
45. #542	C₂²	semidirect
52. C₂×C₄⋊Q₈	C₂²	semidirect
56. #529	C₂²	semidirect
57. #501	C₂²	semidirect
58. #499	C₂²	semidirect
59. #496	C₂²	semidirect
60. #495	C₂²	semidirect
61. #490	C₂²	semidirect
62. #490	C₂²	semidirect
63. #489	C₂²	semidirect
64. #489	C₂²	semidirect
65. #488	C₂²	semidirect
66. #488	C₂²	semidirect
67. #488	C₂²	semidirect
70. #486	C₂²	semidirect
71. #486	C₂²	semidirect
72. #486	C₂²	semidirect
73. #486	C₂²	semidirect
74. #486	C₂²	semidirect
75. #483	C₂²	semidirect
76. #482	C₂²	semidirect
77. #482	C₂²	semidirect
78. #481	C₂²	semidirect
80. #480	C₂²	semidirect
81. #478	C₂²	semidirect
82. #478	C₂²	semidirect
83. #477	C₂²	semidirect
84. #477	C₂²	semidirect
85. #476	C₂²	semidirect
86. #476	C₂²	semidirect
87. #476	C₂²	semidirect
88. #474	C₂²	semidirect
89. #469	C₂²	semidirect
90. #468	C₂²	semidirect
91. #467	C₂²	semidirect
93. #466	C₂²	semidirect
95. #465	C₂²	semidirect
96. #465	C₂²	semidirect
97. #464	C₂²	semidirect
98. #463	C₂²	semidirect
100. #460	C₂²	semidirect
101. #460	C₂²	semidirect
103. #459	C₂²	semidirect
104. #459	C₂²	semidirect
105. #452	C₂²	semidirect
106. #450	C₂²	semidirect
107. #450	C₂²	semidirect
108. #449	C₂²	semidirect
109. #447	C₂²	semidirect
110. #447	C₂²	semidirect
111. #446	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
113. #442	C₂²	semidirect
114. #440	C₂²	semidirect
115. C₄×Q₁₆	C₂²	semidirect
116. C₄×SD₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
119. C₄×D₈	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
121. #436	C₂²	semidirect
122. #435	C₂²	semidirect
123. C₈×D₄	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
126. #432	C₂²	semidirect
127. #418	C₂²	semidirect
128. #417	C₂²	semidirect
129. #416	C₂²	semidirect
130. C₂×#102	C₂²	semidirect
131. C₂×#102	C₂²	semidirect
132. C₂×#102	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
#3544	2
#3543	2
#3375	2
#3366	2
#3362	2
#3361	2
#3333	2
#3325	2
#3310	2
#3306	2
#3305	2
#3296	2
#3295	2
#3294	2
#3241	2
#3238	2
#3224	2
#3217	2
#3179	2
#3168	2
#3136	2
C₂×#486	2
#2966	2