Subgroups — #72320512

Order 1024.

626 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#483859	C₂	1	1	yes	maximal, characteristic
2	#483611	C₂	1	1	yes	maximal, characteristic, complemented
3	#483603	C₂	1	1	yes	maximal, characteristic, complemented
4	#122970	C₂	1	1	yes	maximal, characteristic, complemented
5	#122968	C₂	1	1	yes	maximal, characteristic, complemented
6	#122968	C₂	1	1	yes	maximal, characteristic, complemented
7	#122967	C₂	1	1	yes	maximal, characteristic, complemented
8	#122966	C₂	1	1	yes	maximal, characteristic, complemented
9	#122964	C₂	1	1	yes	maximal, characteristic, complemented
10	#122963	C₂	1	1	yes	maximal, characteristic, complemented
11	#122961	C₂	1	1	yes	maximal, characteristic, complemented
12	#122927	C₂	1	1	yes	maximal, characteristic, complemented
13	#122483	C₂	1	1	yes	maximal, characteristic, complemented
14	#122466	C₂	1	1	yes	maximal, characteristic, complemented
15	#122217	C₂	1	1	yes	maximal, characteristic, complemented
16	#33665	C₄	1	1	yes	characteristic
17	#33483	—	2	1	no	—
18	D₄×M₃₂	—	2	1	no	—
19	#17959	C₂²	1	1	yes	characteristic
20	C₂×C₈×D₈	C₂²	1	1	yes	characteristic
21	#12070	C₄	1	1	yes	characteristic
22	#12070	C₄	1	1	yes	characteristic
23	#12069	C₄	1	1	yes	characteristic
24	#12069	C₄	1	1	yes	characteristic
25	#12064	C₂²	1	1	yes	characteristic
26	#12064	C₂²	1	1	yes	characteristic
27	#12064	C₂²	1	1	yes	characteristic, complemented
28	#12063	—	2	1	no	—
29	#12063	—	2	1	no	—
30	#12062	C₂²	1	1	yes	characteristic
31	#12062	C₂²	1	1	yes	characteristic
32	#12062	C₂²	1	1	yes	characteristic, complemented
33	#12061	C₂²	1	1	yes	characteristic, complemented
34	#12059	C₂²	1	1	yes	characteristic, complemented
35	#12057	—	2	1	no	—
36	#12056	—	2	1	no	—
37	#12045	C₂²	1	1	yes	characteristic
38	#12045	C₂²	1	1	yes	characteristic
39	#12043	C₂²	1	1	yes	characteristic
40	#12043	C₂²	1	1	yes	characteristic
41	#12035	C₄	1	1	yes	characteristic
42	#12012	C₂²	1	1	yes	characteristic
43	#11996	C₂²	1	1	yes	characteristic
44	#11661	C₄	1	1	yes	characteristic
45	#11648	C₄	1	1	yes	characteristic
46	#11614	—	2	1	no	—
47	#11583	—	2	1	no	—
48	#11411	C₂²	1	1	yes	characteristic
49	#11410	C₂²	1	1	yes	characteristic
50	#11402	C₂²	1	1	yes	characteristic
51	#7099	C₂²	1	1	yes	characteristic, complemented
52	#7099	C₂²	1	1	yes	characteristic, complemented
53	#7099	C₂²	1	1	yes	characteristic, complemented
54	#7099	C₂²	1	1	yes	characteristic, complemented
55	#7071	C₂²	1	1	yes	characteristic, complemented
56	#7071	C₂²	1	1	yes	characteristic, complemented
57	#7070	C₂²	1	1	yes	characteristic
58	#7070	C₂²	1	1	yes	characteristic
59	#7070	C₂²	1	1	yes	characteristic
60	#7070	C₂²	1	1	yes	characteristic
61	#7070	C₂²	1	1	yes	characteristic, complemented
62	#7070	C₂²	1	1	yes	characteristic, complemented
63	#7053	C₂²	1	1	yes	characteristic, complemented
64	#7053	C₂²	1	1	yes	characteristic, complemented
65	#7053	C₂²	1	1	yes	characteristic, complemented
66	#7053	C₂²	1	1	yes	characteristic, complemented
67	C₂²×M₃₂	—	4	1	no	—
68	#3168	C₂×C₄	1	1	yes	characteristic
69	#2966	—	2	1	no	—
70	C₂×C₄×D₈	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₄	—	2	1	no	—
72	#2236	C₈	1	1	yes	characteristic
73	#2233	C₈	1	1	yes	characteristic
74	#2228	C₈	1	1	yes	characteristic
75	#2228	C₈	1	1	yes	characteristic
76	#2210	C₈	1	1	yes	characteristic
77	#2210	C₈	1	1	yes	characteristic
78	#2187	C₈	1	1	yes	characteristic
79	#2184	C₈	1	1	yes	characteristic
80	#2183	—	2	1	no	—
81	Q₈×C₁₆	—	2	1	no	—
82	C₄×SD₃₂	C₂×C₄	1	1	yes	characteristic
83	C₄×SD₃₂	C₂×C₄	1	1	yes	characteristic
84	C₄×D₁₆	C₂×C₄	1	1	yes	characteristic
85	C₄×D₁₆	C₂×C₄	1	1	yes	characteristic
86	#2169	—	2	1	no	—
87	#2169	—	2	1	no	—
88	#2169	—	2	1	no	—
89	#2169	—	4	1	no	—
90	#2168	—	4	1	no	—
91	#2168	—	4	1	no	—
92	#2168	—	4	1	no	—
93	D₄×C₁₆	—	2	1	no	—
94	D₄×C₁₆	—	2	1	no	—
95	D₄×C₁₆	—	2	1	no	—
96	#2164	—	4	1	no	—
97	#2162	—	2	1	no	—
98	#2162	—	2	1	no	—
99	#2162	C₂×C₄	1	1	yes	characteristic
100	#2162	C₂×C₄	1	1	yes	characteristic
101	#2150	—	2	1	no	—
102	#2112	—	4	1	no	—
103	#2108	—	4	1	no	—
104	C₄×M₃₂	D₄	1	1	yes	characteristic
105	C₄×M₃₂	D₄	1	1	yes	characteristic
106	#1591	C₂×C₄	1	1	yes	characteristic
107	#1590	—	2	1	no	—
108	#1589	C₂×C₄	1	1	yes	characteristic
109	C₈×Q₁₆	C₂³	1	1	yes	characteristic
110	C₈×SD₁₆	—	2	1	no	—
111	C₈×D₈	—	2	1	no	—
112	C₈×D₈	—	2	1	no	—
113	C₈×D₈	C₂×C₄	1	1	yes	characteristic
114	C₈×D₈	C₂×C₄	1	1	yes	characteristic
115	C₈×D₈	C₂³	1	1	yes	characteristic
116	C₈×D₈	C₂³	1	1	yes	characteristic
117	C₈×D₈	C₂³	1	1	yes	characteristic
118	#1568	C₂×C₄	1	1	yes	characteristic
119	C₂×#335	C₂×C₄	1	1	yes	characteristic
120	#1494	—	2	1	no	—
121	C₂×D₄⋊C₈	—	2	1	no	—
122	C₂×C₈²	C₂³	1	1	yes	characteristic
123	#1372	C₂×C₄	1	1	yes	characteristic
124	#1372	C₂×C₄	1	1	yes	characteristic
125	#1371	C₂×C₄	1	1	yes	characteristic
126	#1371	C₂×C₄	1	1	yes	characteristic
127	#1370	—	2	1	no	—
128	#1367	—	2	1	no	—
129	#1367	C₂³	1	1	yes	characteristic
130	#1367	C₂³	1	1	yes	characteristic
131	#1367	C₂³	1	1	yes	characteristic
132	#1367	C₂³	1	1	yes	characteristic
133	Q₈⋊C₁₆	—	2	1	no	—
134	Q₈⋊C₁₆	—	2	1	no	—
135	#1332	C₂×C₄	1	1	yes	characteristic
136	#1332	C₂×C₄	1	1	yes	characteristic
137	#1331	C₂×C₄	1	1	yes	characteristic
138	#1331	C₂×C₄	1	1	yes	characteristic
139	#1331	C₂×C₄	1	1	yes	characteristic
140	#1331	C₂×C₄	1	1	yes	characteristic
141	#1331	C₂×C₄	1	1	yes	characteristic
142	#1331	C₂×C₄	1	1	yes	characteristic
143	D₄⋊C₁₆	—	2	1	no	—
144	D₄⋊C₁₆	—	2	1	no	—
145	D₄⋊C₁₆	—	2	1	no	—
146	D₄⋊C₁₆	—	2	1	no	—
147	D₄⋊C₁₆	—	2	1	no	—
148	D₄⋊C₁₆	—	2	1	no	—
149	#1312	C₂×C₄	1	1	yes	characteristic
150	#1312	C₂×C₄	1	1	yes	characteristic
151	#1312	D₄	1	1	yes	characteristic
152	#1312	D₄	1	1	yes	characteristic
153	#1312	C₂³	1	1	yes	characteristic
154	#1312	C₂³	1	1	yes	characteristic
155	#1312	C₂³	1	1	yes	characteristic
156	#1312	C₂³	1	1	yes	characteristic
157	#1311	C₂³	1	1	yes	characteristic
158	#1311	C₂³	1	1	yes	characteristic
159	C₈×C₁₆	—	2	1	no	—
160	C₂²×D₈	C₂×C₈	1	1	yes	characteristic
161	C₂³×C₈	—	4	1	no	—
162	#529	—	2	1	no	—
163	C₂×C₄×D₄	—	2	1	no	—
164	C₂×SD₃₂	C₂×C₈	1	1	yes	characteristic
165	C₂×SD₃₂	C₂×C₈	1	1	yes	characteristic
166	C₂×D₁₆	C₂×C₈	1	1	yes	characteristic
167	C₂×D₁₆	C₂×C₈	1	1	yes	characteristic
168	C₂×M₃₂	—	2	1	no	—
169	C₂×M₃₂	—	2	1	no	—
170	C₂×M₃₂	—	4	1	no	—
171	C₂×M₃₂	—	4	1	no	—
172	C₂×M₃₂	—	4	1	no	—
173	C₂×M₃₂	—	4	1	no	—
174	C₂×M₃₂	—	8	4	no	—
175	C₂²×C₁₆	—	4	1	no	—
176	C₂²×C₁₆	—	4	1	no	—
177	C₂²×C₁₆	—	4	1	no	—
178	#499	C₂×C₈	1	1	yes	characteristic
179	#495	C₂×C₈	1	1	yes	characteristic
180	#488	—	2	1	no	—
181	#467	C₂×C₈	1	1	yes	characteristic
182	#466	C₂×C₈	1	1	yes	characteristic
183	#465	—	2	1	no	—
184	#446	—	2	1	no	—
185	C₈×Q₈	—	2	1	no	—
186	C₄×Q₁₆	C₂²×C₄	1	1	yes	characteristic
187	C₄×SD₁₆	—	2	1	no	—
188	C₄×D₈	—	2	1	no	—
189	C₄×D₈	—	2	1	no	—
190	C₄×D₈	C₂×C₈	1	1	yes	characteristic
191	C₄×D₈	C₂×C₈	1	1	yes	characteristic
192	C₄×D₈	C₂²×C₄	1	1	yes	characteristic
193	C₄×D₈	C₂²×C₄	1	1	yes	characteristic
194	C₄×D₈	C₂²×C₄	1	1	yes	characteristic
195	#436	—	2	1	no	—
196	#435	—	4	1	no	—
197	C₈×D₄	—	2	1	no	—
198	C₈×D₄	—	2	1	no	—
199	C₈×D₄	—	2	1	no	—
200	C₈×D₄	—	2	1	no	—
201	C₈×D₄	—	2	1	no	—
202	C₈×D₄	—	4	1	no	—
203	C₈×D₄	—	4	1	no	—
204	C₈×D₄	—	4	1	no	—
205	#433	—	4	1	no	—
206	#432	—	2	1	no	—
207	C₂×#107	C₂×C₈	1	1	yes	characteristic
208	C₂×C₄⋊C₈	—	2	1	no	—
209	C₂×#102	—	2	1	no	—
210	C₂×C₂²⋊C₈	—	4	1	no	—
211	#405	—	4	1	no	—
212	C₂×C₄×C₈	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂×D₄	1	1	yes	characteristic
214	C₂×C₄×C₈	#41	1	1	yes	characteristic
215	#367	C₂×C₈	1	1	yes	characteristic
216	#367	C₂×C₈	1	1	yes	characteristic
217	#366	C₂×C₈	1	1	yes	characteristic
218	#366	C₂×C₈	1	1	yes	characteristic
219	C₄⋊C₁₆	—	2	1	no	—
220	C₄⋊C₁₆	—	2	1	no	—
221	C₄⋊C₁₆	—	2	1	no	—
222	C₄⋊C₁₆	—	2	1	no	—
223	C₄⋊C₁₆	—	2	1	no	—
224	C₄⋊C₁₆	—	4	1	no	—
225	C₄⋊C₁₆	—	4	1	no	—
226	C₄⋊C₁₆	—	4	1	no	—
227	C₄⋊C₁₆	—	4	1	no	—
228	C₄⋊C₁₆	C₂×C₈	1	1	yes	characteristic
229	C₄⋊C₁₆	C₂×C₈	1	1	yes	characteristic
230	#358	C₂×C₈	1	1	yes	characteristic
231	#358	C₂×C₈	1	1	yes	characteristic
232	#357	C₂×C₈	1	1	yes	characteristic
233	#357	C₂×C₈	1	1	yes	characteristic
234	#357	C₂×C₈	1	1	yes	characteristic
235	#357	C₂×C₈	1	1	yes	characteristic
236	#357	C₂×C₈	1	1	yes	characteristic
237	#357	C₂×C₈	1	1	yes	characteristic
238	C₂²⋊C₁₆	—	2	1	no	—
239	C₂²⋊C₁₆	—	4	1	no	—
240	C₂²⋊C₁₆	—	4	1	no	—
241	C₂²⋊C₁₆	—	4	1	no	—
242	C₂²⋊C₁₆	—	4	1	no	—
243	C₂²⋊C₁₆	—	4	1	no	—
244	C₂²⋊C₁₆	—	4	1	no	—
245	C₂²⋊C₁₆	—	4	1	no	—
246	C₂²⋊C₁₆	—	4	1	no	—
247	C₂²⋊C₁₆	C₂×C₈	1	1	yes	characteristic
248	C₂²⋊C₁₆	C₂×C₈	1	1	yes	characteristic
249	#346	—	2	1	no	—
250	#346	—	2	1	no	—
251	#346	—	4	1	no	—
252	C₄×C₁₆	—	2	1	no	—
253	C₄×C₁₆	—	2	1	no	—
254	C₄×C₁₆	—	4	1	no	—
255	C₄×C₁₆	—	4	1	no	—
256	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
257	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
258	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
259	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
260	C₄×C₁₆	C₂×D₄	1	1	yes	characteristic
261	C₄×C₁₆	C₂×D₄	1	1	yes	characteristic
262	C₄×C₁₆	C₂×D₄	1	1	yes	characteristic
263	C₄×C₁₆	C₂×D₄	1	1	yes	characteristic
264	#335	—	2	1	no	—
265	#335	C₂²×C₄	1	1	yes	characteristic
266	#335	C₂²×C₄	1	1	yes	characteristic
267	#335	C₂²×C₄	1	1	yes	characteristic
268	#335	C₂²×C₄	1	1	yes	characteristic
269	#334	—	2	1	no	—
270	Q₈⋊C₈	—	2	1	no	—
271	Q₈⋊C₈	—	2	1	no	—
272	D₄⋊C₈	—	2	1	no	—
273	D₄⋊C₈	—	2	1	no	—
274	D₄⋊C₈	—	2	1	no	—
275	D₄⋊C₈	—	2	1	no	—
276	D₄⋊C₈	—	2	1	no	—
277	D₄⋊C₈	—	2	1	no	—
278	C₈²	C₂²×C₄	1	1	yes	characteristic
279	C₈²	C₂×D₄	1	1	yes	characteristic
280	C₈²	#41	1	1	yes	characteristic
281	C₈²	C₂⁴	1	1	yes	characteristic
282	C₂²×D₄	—	2	1	no	—
283	C₂³×C₄	—	4	1	no	—
284	C₂×Q₁₆	C₂²×C₈	1	1	yes	characteristic
285	C₂×SD₁₆	—	2	1	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	—	2	1	no	—
288	C₂×D₈	—	4	1	no	—
289	C₂×D₈	C₂²×C₈	1	1	yes	characteristic
290	C₂×D₈	C₂²×C₈	1	1	yes	characteristic
291	C₂×D₈	C₂²×C₈	1	1	yes	characteristic
292	C₂×M₁₆	—	4	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	4	1	no	—
295	C₂²×C₈	—	4	1	no	—
296	C₂²×C₈	—	4	1	no	—
297	C₂²×C₈	—	4	1	no	—
298	C₂²×C₈	—	4	1	no	—
299	C₂²×C₈	—	4	1	no	—
300	C₂²×C₈	—	8	2	no	—
301	C₂²×C₈	—	8	2	no	—
302	C₂²×C₈	C₂²×C₈	1	1	yes	characteristic
303	C₂²×C₈	#131	1	1	yes	characteristic
304	C₂²×C₈	AGL(1,ℤ/8)	1	1	yes	characteristic
305	C₂²×C₈	AGL(1,ℤ/8)	1	1	yes	characteristic
306	#126	—	4	1	no	—
307	#125	—	2	1	no	—
308	#124	—	2	1	no	—
309	#123	—	4	1	no	—
310	C₂²⋊Q₈	—	2	1	no	—
311	#121	—	2	1	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	4	1	no	—
319	C₄×D₄	—	4	1	no	—
320	C₄×D₄	—	4	1	no	—
321	#117	—	4	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	4	1	no	—
324	C₂×C₄²	C₄×D₄	1	1	yes	characteristic
325	SD₃₂	—	2	2	no	—
326	SD₃₂	—	4	1	no	—
327	D₁₆	—	2	2	no	—
328	D₁₆	—	4	1	no	—
329	M₃₂	—	4	2	no	—
330	M₃₂	—	8	1	no	—
331	M₃₂	—	8	2	no	—
332	M₃₂	—	8	2	no	—
333	M₃₂	—	8	2	no	—
334	M₃₂	—	8	2	no	—
335	C₂×C₁₆	—	2	1	no	—
336	C₂×C₁₆	—	2	1	no	—
337	C₂×C₁₆	—	2	1	no	—
338	C₂×C₁₆	—	2	1	no	—
339	C₂×C₁₆	—	2	1	no	—
340	C₂×C₁₆	—	2	1	no	—
341	C₂×C₁₆	—	4	1	no	—
342	C₂×C₁₆	—	4	1	no	—
343	C₂×C₁₆	—	4	1	no	—
344	C₂×C₁₆	—	4	1	no	—
345	C₂×C₁₆	—	4	1	no	—
346	C₂×C₁₆	—	4	1	no	—
347	C₂×C₁₆	—	8	2	no	—
348	C₂×C₁₆	—	8	2	no	—
349	C₂×C₁₆	—	8	2	no	—
350	C₂×C₁₆	C₂²×C₈	1	1	yes	characteristic
351	C₂×C₁₆	C₂²×C₈	1	1	yes	characteristic
352	C₂×C₁₆	C₂²×C₈	1	1	yes	characteristic
353	C₂×C₁₆	C₂²×C₈	1	1	yes	characteristic
354	#107	—	2	1	no	—
355	#107	C₂²×C₈	1	1	yes	characteristic
356	#107	C₂²×C₈	1	1	yes	characteristic
357	#107	C₂²×C₈	1	1	yes	characteristic
358	#107	C₂²×C₈	1	1	yes	characteristic
359	#106	—	2	1	no	—
360	C₄⋊C₈	—	2	1	no	—
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	2	1	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	—	4	1	no	—
365	C₄⋊C₈	—	4	1	no	—
366	C₄⋊C₈	—	4	1	no	—
367	#103	—	2	1	no	—
368	#103	—	2	1	no	—
369	#102	—	2	1	no	—
370	#102	—	2	1	no	—
371	#102	—	2	1	no	—
372	#102	—	2	1	no	—
373	#102	—	2	1	no	—
374	#102	—	2	1	no	—
375	C₂²⋊C₈	—	4	1	no	—
376	C₂²⋊C₈	—	4	1	no	—
377	C₂²⋊C₈	—	4	1	no	—
378	C₂²⋊C₈	—	4	1	no	—
379	C₂²⋊C₈	—	4	1	no	—
380	C₂²⋊C₈	—	4	1	no	—
381	C₂²⋊C₈	—	4	1	no	—
382	#97	—	4	1	no	—
383	#97	—	4	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	—	4	1	no	—
386	C₄×C₈	C₄×D₄	1	1	yes	characteristic
387	C₄×C₈	C₄×D₄	1	1	yes	characteristic
388	C₄×C₈	C₄×D₄	1	1	yes	characteristic
389	C₄×C₈	C₂²×C₈	1	1	yes	characteristic
390	C₄×C₈	#131	1	1	yes	characteristic
391	C₄×C₈	AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₄×C₈	AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₄	1	1	yes	characteristic
394	C₄×C₈	C₂²×D₄	1	1	yes	characteristic
395	C₄×C₈	C₂×#41	1	1	yes	characteristic
396	C₂⁴	—	4	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	1	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	—	8	1	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	—	8	2	no	—
412	C₂²×C₄	—	8	2	no	—
413	C₂²×C₄	C₈×D₄	1	1	yes	characteristic
414	C₂²×C₄	#442	1	1	yes	characteristic
415	C₂²×C₄	#444	1	1	yes	characteristic
416	Q₁₆	—	2	1	no	—
417	Q₁₆	—	2	1	no	—
418	SD₁₆	—	8	1	no	—
419	D₈	—	2	1	no	—
420	D₈	—	2	1	no	—
421	D₈	—	2	1	no	—
422	D₈	—	2	1	no	—
423	D₈	—	2	1	no	—
424	D₈	—	4	2	no	—
425	D₈	#504	1	2	yes	—
426	M₁₆	—	8	2	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	4	1	no	—
433	C₂×C₈	—	4	1	no	—
434	C₂×C₈	—	4	1	no	—
435	C₂×C₈	—	4	1	no	—
436	C₂×C₈	—	4	1	no	—
437	C₂×C₈	—	4	1	no	—
438	C₂×C₈	—	8	1	no	—
439	C₂×C₈	—	8	1	no	—
440	C₂×C₈	—	8	1	no	—
441	C₂×C₈	—	8	1	no	—
442	C₂×C₈	—	8	1	no	—
443	C₂×C₈	—	8	1	no	—
444	C₂×C₈	—	8	1	no	—
445	C₂×C₈	—	8	2	no	—
446	C₂×C₈	—	8	2	no	—
447	C₂×C₈	—	8	2	no	—
448	C₂×C₈	C₈×D₄	1	1	yes	characteristic
449	C₂×C₈	C₈×D₄	1	1	yes	characteristic
450	C₂×C₈	#442	1	1	yes	characteristic
451	C₂×C₈	#442	1	1	yes	characteristic
452	C₂×C₈	C₂³×C₈	1	1	yes	characteristic
453	C₂×C₈	C₂×#131	1	1	yes	characteristic
454	C₂×C₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₂×C₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	C₈×D₄	1	1	yes	characteristic
476	C₄²	#442	1	1	yes	characteristic
477	C₄²	#444	1	1	yes	characteristic
478	C₄²	C₂×C₄×D₄	1	1	yes	characteristic
479	C₁₆	—	2	1	no	—
480	C₁₆	—	2	1	no	—
481	C₁₆	—	2	1	no	—
482	C₁₆	—	2	1	no	—
483	C₁₆	—	4	1	no	—
484	C₁₆	—	4	1	no	—
485	C₁₆	—	4	1	no	—
486	C₁₆	—	4	1	no	—
487	C₁₆	—	4	1	no	—
488	C₁₆	—	4	1	no	—
489	C₁₆	—	8	1	no	—
490	C₁₆	—	8	1	no	—
491	C₁₆	—	8	1	no	—
492	C₁₆	—	8	1	no	—
493	C₁₆	—	8	1	no	—
494	C₁₆	—	8	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	8	2	no	—
499	C₂³	—	8	2	no	—
500	C₂³	—	16	1	no	—
501	C₂³	#1580	1	1	yes	characteristic
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	D₄	—	2	2	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	8	2	no	—
511	D₄	—	16	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	1	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	1	no	—
528	C₂×C₄	—	8	1	no	—
529	C₂×C₄	—	8	1	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	#1580	1	1	yes	characteristic
532	C₂×C₄	#1580	1	1	yes	characteristic
533	C₂×C₄	#1580	1	1	yes	characteristic
534	C₂×C₄	C₂×C₈×D₄	1	1	yes	characteristic
535	C₂×C₄	C₂×#442	1	1	yes	characteristic
536	C₂×C₄	C₂×#444	1	1	yes	characteristic
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	8	1	no	—
546	C₈	—	8	1	no	—
547	C₈	—	8	1	no	—
548	C₈	—	8	1	no	—
549	C₈	AGL(1,ℤ/16)	1	2	yes	—
550	C₈	C₂×#504	1	1	yes	characteristic
551	C₈	#3407	1	1	yes	characteristic
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	16	4	no	—
565	C₂²	C₂×#1580	1	1	yes	characteristic
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	#33436	1	1	yes	characteristic
576	C₄	#33442	1	1	yes	characteristic
577	C₄	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
578	C₄	#33468	1	1	yes	characteristic
579	C₂	—	4	1	no	—
580	C₂	—	8	2	no	—
581	C₂	—	16	1	no	—
582	C₂	—	16	1	no	—
583	C₂	#483590	1	1	yes	characteristic
584	C₂	#483601	1	1	yes	characteristic
585	C₂	#483602	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#442
commutator	C₂×C₈	C₂³×C₈
Frattini, cosocle	C₈²	C₂⁴
socle	C₂²	C₂×#1580
prime radical	#2184	C₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #11402 ◁ G
LECS	G ▷ C₈² ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #483611	C₂	semidirect
3. #483603	C₂	semidirect
4. #122970	C₂	semidirect
5. #122968	C₂	semidirect
6. #122968	C₂	semidirect
7. #122967	C₂	semidirect
8. #122966	C₂	semidirect
9. #122964	C₂	semidirect
10. #122963	C₂	semidirect
11. #122961	C₂	semidirect
12. #122927	C₂	semidirect
13. #122483	C₂	semidirect
14. #122466	C₂	semidirect
15. #122217	C₂	semidirect
27. #12064	C₂²	semidirect
32. #12062	C₂²	semidirect
33. #12061	C₂²	semidirect
34. #12059	C₂²	semidirect
51. #7099	C₂²	semidirect
52. #7099	C₂²	semidirect
53. #7099	C₂²	semidirect
54. #7099	C₂²	semidirect
55. #7071	C₂²	semidirect
56. #7071	C₂²	semidirect
61. #7070	C₂²	semidirect
62. #7070	C₂²	semidirect
63. #7053	C₂²	semidirect
64. #7053	C₂²	semidirect
65. #7053	C₂²	semidirect
66. #7053	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#483859	2
#483611	2
#483603	2
#122970	2
#122968	2
#122967	2
#122966	2
#122964	2
#122963	2
#122961	2
#122927	2
#122483	2
#122466	2
#122217	2