Subgroups — #61468

Order 256.

954 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	#3355	C₂	1	2	yes	maximal, complemented
9	#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	#3326	C₂	1	2	yes	maximal, complemented
11	#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	#3322	C₂	1	2	yes	maximal, complemented
13	#3275	C₂	1	2	yes	maximal, complemented
14	#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	#3183	C₂	1	2	yes	maximal, complemented
17	#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	#3114	C₂	1	2	yes	maximal, complemented
19	#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	#3111	C₂	1	2	yes	maximal, complemented
21	#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
24	C₂×#137	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	#559	—	2	1	no	—
27	#559	C₂²	1	1	yes	characteristic
28	#559	C₂²	1	1	yes	characteristic, complemented
29	#557	C₂²	1	1	yes	characteristic, complemented
30	#556	—	2	1	no	—
31	#556	C₂²	1	1	yes	characteristic
32	#554	C₂²	1	1	yes	characteristic
33	#554	C₂²	1	1	yes	characteristic
34	#553	—	2	2	no	—
35	#553	—	2	1	no	—
36	#553	C₂²	1	2	yes	—
37	#553	C₂²	1	2	yes	complemented
38	#551	—	2	2	no	—
39	#550	C₂²	1	1	yes	characteristic
40	#548	C₂²	1	2	yes	complemented
41	#546	—	2	1	no	—
42	#546	C₂²	1	2	yes	—
43	D₄²	C₂²	1	1	yes	characteristic
44	#532	—	2	1	no	—
45	#532	C₂²	1	1	yes	characteristic
46	#532	C₂²	1	1	yes	characteristic, complemented
47	#529	—	2	1	no	—
48	#529	—	2	2	no	—
49	#529	C₂²	1	2	yes	—
50	#529	C₂²	1	2	yes	complemented
51	#525	—	2	2	no	—
52	C₄×#41	—	2	1	no	—
53	C₄×#41	C₂²	1	1	yes	characteristic
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₄×#41	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄	—	2	1	no	—
58	C₂×C₄×D₄	C₂²	1	2	yes	—
59	#499	C₂²	1	2	yes	complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#495	C₂²	1	2	yes	complemented
62	#493	C₂²	1	1	yes	characteristic
63	#488	C₂²	1	2	yes	complemented
64	#488	C₂²	1	2	yes	complemented
65	#486	C₂²	1	1	yes	characteristic
66	#486	C₂²	1	1	yes	characteristic, complemented
67	#485	C₂²	1	2	yes	complemented
68	#483	C₂²	1	2	yes	complemented
69	#482	C₂²	1	2	yes	—
70	#482	C₂²	1	2	yes	complemented
71	#480	C₂²	1	2	yes	complemented
72	#480	C₂²	1	2	yes	complemented
73	#479	C₂²	1	2	yes	complemented
74	#478	C₂²	1	2	yes	—
75	#478	C₂²	1	2	yes	complemented
76	#478	C₂²	1	2	yes	complemented
77	#477	C₂²	1	1	yes	characteristic, complemented
78	#477	C₂²	1	1	yes	characteristic, complemented
79	#475	C₂²	1	1	yes	characteristic, complemented
80	#474	C₂²	1	1	yes	characteristic
81	#470	C₂²	1	2	yes	complemented
82	#469	C₂²	1	2	yes	—
83	#469	C₂²	1	2	yes	complemented
84	#469	C₂²	1	2	yes	complemented
85	#468	C₂²	1	2	yes	—
86	#468	C₂²	1	2	yes	complemented
87	#464	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	—
89	#463	C₂²	1	2	yes	complemented
90	#463	C₂²	1	2	yes	complemented
91	#460	C₂²	1	1	yes	characteristic
92	#460	C₂²	1	1	yes	characteristic
93	#460	C₂²	1	1	yes	characteristic, complemented
94	#459	C₂²	1	1	yes	characteristic
95	#452	C₂²	1	2	yes	complemented
96	#450	C₂²	1	2	yes	—
97	#449	C₂²	1	2	yes	—
98	#449	C₂²	1	2	yes	—
99	#448	C₂²	1	2	yes	complemented
100	#447	C₂²	1	2	yes	—
101	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
103	#442	C₂²	1	2	yes	—
104	#442	C₂²	1	2	yes	complemented
105	#442	C₂²	1	2	yes	complemented
106	#441	C₂²	1	1	yes	characteristic, complemented
107	#441	C₂²	1	1	yes	characteristic, complemented
108	#440	C₂²	1	1	yes	characteristic
109	#440	C₂²	1	1	yes	characteristic
110	#440	C₂²	1	2	yes	complemented
111	#440	C₂²	1	2	yes	complemented
112	#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆	C₂²	1	2	yes	—
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×D₈	C₂²	1	2	yes	—
120	C₄×D₈	C₂²	1	2	yes	complemented
121	#436	C₂²	1	1	yes	characteristic
122	#436	C₂²	1	1	yes	characteristic
123	#436	C₂²	1	2	yes	complemented
124	#436	C₂²	1	2	yes	complemented
125	#432	C₂²	1	2	yes	complemented
126	#432	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	1	yes	characteristic, complemented
128	#428	C₂²	1	2	yes	complemented
129	#419	C₂²	1	1	yes	characteristic, complemented
130	#418	C₂²	1	2	yes	—
131	#417	C₂²	1	1	yes	characteristic
132	#417	C₂²	1	2	yes	complemented
133	C₄×M₁₆	C₂²	1	2	yes	complemented
134	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	D₄	1	1	yes	characteristic
138	C₂×#41	C₂³	1	1	yes	characteristic
139	C₂×#41	C₂³	1	2	yes	—
140	C₂²×Q₈	C₂³	1	1	yes	characteristic
141	C₂²×D₄	—	2	1	no	—
142	C₂²×D₄	C₂³	1	2	yes	—
143	C₂³×C₄	—	2	2	no	—
144	#137	—	2	4	no	—
145	AGL(1,ℤ/8)	—	2	8	no	—
146	C₂×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×D₈	C₂³	1	2	yes	—
154	C₂×D₈	C₂³	1	2	yes	—
155	C₂×D₈	C₂³	1	2	yes	—
156	C₂×M₁₆	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×M₁₆	C₂³	1	1	yes	characteristic
159	C₂×M₁₆	C₂³	1	2	yes	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	#127	—	2	1	no	—
164	#127	C₂³	1	1	yes	characteristic
165	#127	C₂³	1	1	yes	characteristic
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#125	—	2	1	no	—
172	#125	—	2	2	no	—
173	#125	C₂³	1	2	yes	—
174	#125	C₂³	1	2	yes	—
175	#124	—	2	1	no	—
176	#124	—	2	1	no	—
177	#124	—	2	1	no	—
178	#124	—	2	2	no	—
179	#124	—	2	1	no	—
180	#124	—	2	1	no	—
181	#124	C₂³	1	2	yes	—
182	#124	C₂³	1	2	yes	—
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	—	2	2	no	—
189	#123	—	2	2	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂²⋊Q₈	C₂³	1	2	yes	—
196	#121	—	2	2	no	—
197	#121	—	2	2	no	—
198	#121	—	2	2	no	—
199	#121	—	2	1	no	—
200	#121	—	2	1	no	—
201	#121	—	2	1	no	—
202	#121	—	2	2	no	—
203	#121	—	2	2	no	—
204	#121	C₂³	1	2	yes	—
205	#121	C₂³	1	2	yes	—
206	#121	C₂³	1	2	yes	—
207	#121	C₂³	1	2	yes	—
208	#120	—	2	2	no	—
209	#120	—	2	2	no	—
210	C₄×Q₈	—	2	1	no	—
211	C₄×Q₈	—	2	1	no	—
212	C₄×Q₈	—	2	1	no	—
213	C₄×Q₈	—	2	1	no	—
214	C₄×Q₈	D₄	1	1	yes	characteristic
215	C₄×Q₈	C₂³	1	1	yes	characteristic
216	C₄×Q₈	C₂³	1	1	yes	characteristic
217	C₄×Q₈	C₂³	1	1	yes	characteristic
218	C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₄×Q₈	C₂³	1	2	yes	—
222	C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₄×D₄	—	2	1	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	D₄	1	1	yes	characteristic
241	C₄×D₄	D₄	1	2	yes	—
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	2	yes	—
246	C₄×D₄	C₂³	1	1	yes	characteristic
247	C₄×D₄	C₂³	1	2	yes	—
248	C₄×D₄	C₂³	1	2	yes	—
249	C₄×D₄	C₂³	1	1	yes	characteristic
250	C₄×D₄	C₂³	1	2	yes	—
251	#117	—	2	2	no	—
252	#117	—	2	1	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	D₄	1	1	yes	characteristic
256	#117	D₄	1	2	yes	—
257	#117	C₂³	1	1	yes	characteristic
258	#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³	1	2	yes	—
269	C₂×C₄²	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	2	yes	—
272	#107	C₂³	1	1	yes	characteristic
273	#107	C₂³	1	2	yes	—
274	#107	C₂³	1	2	yes	—
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	2	yes	—
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	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	2	yes	—
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#102	C₂³	1	1	yes	characteristic
294	#102	C₂³	1	1	yes	characteristic
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	#97	C₂³	1	1	yes	characteristic
308	#97	C₂³	1	1	yes	characteristic
309	#97	C₂³	1	2	yes	—
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₈	C₂³	1	2	yes	—
313	C₄×C₈	C₂³	1	2	yes	—
314	C₂⁴	—	2	2	no	—
315	#41	—	2	4	no	—
316	#41	—	2	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	1	no	—
320	#41	—	4	4	no	—
321	#41	—	8	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄	C₂×D₄	1	2	yes	—
347	C₂×D₄	C₂⁴	1	2	yes	—
348	C₂×D₄	C₂⁴	1	2	yes	—
349	C₂×D₄	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	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	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	8	4	no	—
363	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄	1	2	yes	—
365	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄	1	2	yes	—
367	C₂²×C₄	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴	1	2	yes	—
369	Q₁₆	—	2	2	no	—
370	Q₁₆	—	2	2	no	—
371	SD₁₆	—	2	4	no	—
372	SD₁₆	—	2	2	no	—
373	SD₁₆	—	4	2	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	#41	1	4	yes	complemented
376	D₈	—	2	4	no	—
377	D₈	—	2	4	no	—
378	D₈	—	4	2	no	—
379	M₁₆	—	2	4	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	4	1	no	—
382	M₁₆	—	4	2	no	—
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₈	C₂⁴	1	2	yes	—
386	C₂×C₈	C₂⁴	1	2	yes	—
387	C₂×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₈	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	2	yes	—
415	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	C₂×D₄	1	2	yes	—
448	C₄²	C₂×D₄	1	1	yes	characteristic
449	C₄²	C₂×D₄	1	2	yes	—
450	C₄²	C₂×D₄	1	1	yes	characteristic
451	C₄²	C₂⁴	1	2	yes	—
452	C₄²	C₂⁴	1	1	yes	characteristic
453	C₄²	C₂⁴	1	1	yes	characteristic
454	C₂³	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	4	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	—	2	1	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	8	1	no	—
471	Q₈	C₂×#41	1	2	yes	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	4	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	8	1	no	—
487	D₄	—	8	1	no	—
488	D₄	—	8	2	no	—
489	D₄	—	8	2	no	—
490	D₄	C₂×#41	1	2	yes	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	1	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄	1	2	yes	—
524	C₂×C₄	C₂²×D₄	1	2	yes	—
525	C₂×C₄	C₂²×D₄	1	2	yes	—
526	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂⁵	1	1	yes	characteristic
529	C₈	—	2	2	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	2	no	—
534	C₈	C₂×#41	1	2	yes	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	8	8	no	—
551	C₂²	C₂³×D₄	1	1	yes	characteristic
552	C₄	—	2	1	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	2	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	#575	1	2	yes	—
569	C₄	C₂²×#41	1	1	yes	characteristic
570	C₄	#585	1	1	yes	characteristic
571	C₂	—	4	1	no	—
572	C₂	—	4	2	no	—
573	C₂	—	4	2	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	2	no	—
576	C₂	D₄×#41	1	1	yes	characteristic
577	C₂	C₂×#575	1	1	yes	characteristic
578	C₂	#3585	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 ◁ C₄×#41 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3481	C₂	semidirect
2. #3480	C₂	semidirect
3. #3396	C₂	semidirect
4. #3381	C₂	semidirect
5. #3365	C₂	semidirect
6. #3361	C₂	semidirect
7. #3356	C₂	semidirect
8. #3355	C₂	semidirect
9. #3333	C₂	semidirect
10. #3326	C₂	semidirect
11. #3324	C₂	semidirect
12. #3322	C₂	semidirect
13. #3275	C₂	semidirect
14. #3274	C₂	semidirect
15. #3184	C₂	semidirect
16. #3183	C₂	semidirect
17. #3115	C₂	semidirect
18. #3114	C₂	semidirect
19. #3112	C₂	semidirect
20. #3111	C₂	semidirect
21. #2971	C₂	semidirect
22. C₄×#137	C₂	semidirect
23. C₄×AGL(1,ℤ/8)	C₂	semidirect
28. #559	C₂²	semidirect
29. #557	C₂²	semidirect
37. #553	C₂²	semidirect
40. #548	C₂²	semidirect
46. #532	C₂²	semidirect
50. #529	C₂²	semidirect
55. C₄×#41	C₂²	semidirect
56. C₂×C₄×Q₈	C₂²	semidirect
59. #499	C₂²	semidirect
60. #498	C₂²	semidirect
61. #495	C₂²	semidirect
63. #488	C₂²	semidirect
64. #488	C₂²	semidirect
66. #486	C₂²	semidirect
67. #485	C₂²	semidirect
68. #483	C₂²	semidirect
70. #482	C₂²	semidirect
71. #480	C₂²	semidirect
72. #480	C₂²	semidirect
73. #479	C₂²	semidirect
75. #478	C₂²	semidirect
76. #478	C₂²	semidirect
77. #477	C₂²	semidirect
78. #477	C₂²	semidirect
79. #475	C₂²	semidirect
81. #470	C₂²	semidirect
83. #469	C₂²	semidirect
84. #469	C₂²	semidirect
86. #468	C₂²	semidirect
87. #464	C₂²	semidirect
89. #463	C₂²	semidirect
90. #463	C₂²	semidirect
93. #460	C₂²	semidirect
95. #452	C₂²	semidirect
99. #448	C₂²	semidirect
101. C₈×Q₈	C₂²	semidirect
102. C₈×Q₈	C₂²	semidirect
104. #442	C₂²	semidirect
105. #442	C₂²	semidirect
106. #441	C₂²	semidirect
107. #441	C₂²	semidirect
110. #440	C₂²	semidirect
111. #440	C₂²	semidirect
112. #440	C₂²	semidirect
113. C₄×Q₁₆	C₂²	semidirect
114. C₄×Q₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
123. #436	C₂²	semidirect
124. #436	C₂²	semidirect
125. #432	C₂²	semidirect
126. #432	C₂²	semidirect
127. #428	C₂²	semidirect
128. #428	C₂²	semidirect
129. #419	C₂²	semidirect
132. #417	C₂²	semidirect
133. C₄×M₁₆	C₂²	semidirect
134. C₄×M₁₆	C₂²	semidirect
375. SD₁₆	#41	semidirect

Maximal subgroups

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

subgroup	index
#3481	2
#3480	2
#3396	2
#3381	2
#3365	2
#3361	2
#3356	2
#3355	2
#3333	2
#3326	2
#3324	2
#3322	2
#3275	2
#3274	2
#3184	2
#3183	2
#3115	2
#3114	2
#3112	2
#3111	2
#2971	2
C₄×#137	2
C₄×AGL(1,ℤ/8)	2