Subgroups — #72319213

Order 1024.

772 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#483553	C₂	1	1	yes	maximal, characteristic
2	#483466	C₂	1	1	yes	maximal, characteristic, complemented
3	#483463	C₂	1	1	yes	maximal, characteristic, complemented
4	#225783	C₂	1	1	yes	maximal, characteristic
5	#225720	C₂	1	1	yes	maximal, characteristic
6	#140496	C₂	1	1	yes	maximal, characteristic, complemented
7	#140494	C₂	1	1	yes	maximal, characteristic, complemented
8	#136464	C₂	1	1	yes	maximal, characteristic, complemented
9	#136464	C₂	1	1	yes	maximal, characteristic, complemented
10	#136463	C₂	1	1	yes	maximal, characteristic, complemented
11	#136462	C₂	1	1	yes	maximal, characteristic, complemented
12	#135792	C₂	1	1	yes	maximal, characteristic, complemented
13	#135074	C₂	1	1	yes	maximal, characteristic, complemented
14	#135073	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×#365	C₂	1	1	yes	maximal, characteristic, complemented
16	#33485	C₂²	1	1	yes	characteristic
17	#33484	C₂²	1	1	yes	characteristic
18	#22688	—	2	1	no	—
19	#18057	—	2	1	no	—
20	C₈×#135	C₂²	1	1	yes	characteristic
21	#17835	C₂²	1	1	yes	characteristic
22	#17834	C₂²	1	1	yes	characteristic
23	#17826	C₂²	1	1	yes	characteristic
24	#17826	C₂²	1	1	yes	characteristic
25	C₄×#365	C₂²	1	1	yes	characteristic
26	#12053	C₄	1	1	yes	characteristic, complemented
27	#12053	C₄	1	1	yes	characteristic, complemented
28	#12051	C₄	1	1	yes	characteristic, complemented
29	#12051	C₄	1	1	yes	characteristic, complemented
30	C₁₆×SD₁₆	C₄	1	1	yes	characteristic, complemented
31	C₁₆×SD₁₆	C₄	1	1	yes	characteristic, complemented
32	#12038	C₄	1	1	yes	characteristic, complemented
33	#12038	C₄	1	1	yes	characteristic, complemented
34	#12030	—	2	1	no	—
35	#12030	—	2	1	no	—
36	#12030	C₂²	1	1	yes	characteristic
37	#12030	C₂²	1	1	yes	characteristic
38	#12029	—	2	1	no	—
39	#12029	C₂²	1	1	yes	characteristic
40	#12029	C₂²	1	1	yes	characteristic
41	#12028	—	2	1	no	—
42	#12020	—	2	1	no	—
43	#12020	C₂²	1	1	yes	characteristic
44	#12020	C₂²	1	1	yes	characteristic
45	#12020	C₂²	1	1	yes	characteristic
46	#12020	C₂²	1	1	yes	characteristic
47	#12019	—	2	1	no	—
48	#12013	C₂²	1	1	yes	characteristic
49	#12000	—	2	1	no	—
50	#12000	C₂²	1	1	yes	characteristic
51	C₂×#1368	—	2	1	no	—
52	#11615	C₂²	1	1	yes	characteristic
53	#11615	C₂²	1	1	yes	characteristic
54	C₈×M₃₂	C₂²	1	1	yes	characteristic
55	#9633	—	2	1	no	—
56	#9628	—	2	1	no	—
57	#8904	—	2	1	no	—
58	#8904	—	2	1	no	—
59	#8899	—	2	1	no	—
60	#8898	—	2	1	no	—
61	#8822	C₂²	1	1	yes	characteristic
62	#8822	C₂²	1	1	yes	characteristic
63	#8670	C₂²	1	1	yes	characteristic
64	#8670	C₂²	1	1	yes	characteristic
65	#8666	C₂²	1	1	yes	characteristic
66	#8666	C₂²	1	1	yes	characteristic
67	C₈×#108	C₂²	1	1	yes	characteristic
68	C₈×#106	C₂²	1	1	yes	characteristic
69	#7302	C₂²	1	1	yes	characteristic
70	#7302	C₂²	1	1	yes	characteristic
71	#7300	C₂²	1	1	yes	characteristic
72	#7300	C₂²	1	1	yes	characteristic
73	#7174	C₂²	1	1	yes	characteristic
74	#7173	C₂²	1	1	yes	characteristic
75	#2991	—	2	1	no	—
76	#2990	—	2	1	no	—
77	C₈×#41	C₂³	1	1	yes	characteristic
78	C₈×#41	C₂³	1	1	yes	characteristic
79	C₂×#443	—	4	1	no	—
80	C₄×#135	D₄	1	1	yes	characteristic
81	#2906	—	2	1	no	—
82	#2906	—	2	1	no	—
83	#2183	C₂×C₄	1	1	yes	characteristic
84	#2183	C₂×C₄	1	1	yes	characteristic
85	Q₈×C₁₆	C₂×C₄	1	1	yes	characteristic
86	Q₈×C₁₆	C₂×C₄	1	1	yes	characteristic
87	#2169	—	2	1	no	—
88	#2169	—	2	1	no	—
89	#2169	C₂×C₄	1	1	yes	characteristic
90	#2169	C₂×C₄	1	1	yes	characteristic
91	#2168	—	2	1	no	—
92	#2168	—	2	1	no	—
93	D₄×C₁₆	C₂×C₄	1	1	yes	characteristic
94	D₄×C₁₆	C₂×C₄	1	1	yes	characteristic
95	#2163	—	2	1	no	—
96	#2163	—	2	1	no	—
97	#2163	C₂³	1	1	yes	characteristic
98	#2163	C₂³	1	1	yes	characteristic
99	C₂×#365	—	2	1	no	—
100	C₄×M₃₂	—	2	1	no	—
101	C₄×M₃₂	C₂³	1	1	yes	characteristic
102	C₄×M₃₂	C₂³	1	1	yes	characteristic
103	C₂×#346	—	2	1	no	—
104	#1945	—	4	1	no	—
105	#1866	—	4	1	no	—
106	#1866	—	4	1	no	—
107	#1848	—	2	1	no	—
108	#1848	—	2	1	no	—
109	#1806	—	2	1	no	—
110	#1806	—	2	1	no	—
111	C₄×#108	C₂³	1	1	yes	characteristic
112	C₄×#106	C₂³	1	1	yes	characteristic
113	C₈×C₄⋊C₄	—	2	1	no	—
114	#1590	—	4	1	no	—
115	#1587	—	4	1	no	—
116	#1586	—	4	1	no	—
117	C₈×Q₁₆	C₂×C₄	1	1	yes	characteristic
118	C₈×Q₁₆	Q₈	1	1	yes	characteristic
119	C₈×SD₁₆	—	4	1	no	—
120	C₈×SD₁₆	C₂×C₄	1	1	yes	characteristic
121	C₈×SD₁₆	C₂×C₄	1	1	yes	characteristic
122	C₈×SD₁₆	Q₈	1	1	yes	characteristic
123	C₈×SD₁₆	Q₈	1	1	yes	characteristic
124	C₈×D₈	C₂×C₄	1	1	yes	characteristic
125	C₈×D₈	Q₈	1	1	yes	characteristic
126	#1574	—	2	1	no	—
127	#1574	—	2	1	no	—
128	#1574	—	4	1	no	—
129	#1573	—	4	1	no	—
130	#1570	—	2	1	no	—
131	#1570	—	2	1	no	—
132	#1570	—	4	1	no	—
133	#1570	—	4	1	no	—
134	#1568	—	2	1	no	—
135	#1566	—	2	1	no	—
136	#1566	—	2	1	no	—
137	#1566	—	2	1	no	—
138	#1566	—	2	1	no	—
139	#1566	—	2	1	no	—
140	#1566	C₂³	1	1	yes	characteristic
141	#1566	C₂³	1	1	yes	characteristic
142	#1566	C₂³	1	1	yes	characteristic
143	#1566	C₂³	1	1	yes	characteristic
144	#1564	—	2	1	no	—
145	#1564	D₄	1	1	yes	characteristic
146	#1564	C₂³	1	1	yes	characteristic
147	C₂×#334	—	2	1	no	—
148	C₂×#334	—	2	1	no	—
149	C₂×#334	—	2	1	no	—
150	C₂×#334	C₂³	1	1	yes	characteristic
151	#1489	—	2	1	no	—
152	#1489	—	2	1	no	—
153	#1476	D₄	1	1	yes	characteristic
154	#1476	D₄	1	1	yes	characteristic
155	C₈×M₁₆	—	2	1	no	—
156	C₂×C₈²	C₂³	1	1	yes	characteristic
157	#1383	—	2	1	no	—
158	#1370	C₂×C₄	1	1	yes	characteristic
159	#1370	C₂×C₄	1	1	yes	characteristic
160	#1368	—	2	1	no	—
161	#1368	—	2	1	no	—
162	#1368	—	2	1	no	—
163	#1368	—	2	1	no	—
164	#1368	—	2	1	no	—
165	#1368	—	2	1	no	—
166	#1368	—	2	1	no	—
167	#1368	—	2	1	no	—
168	#1368	—	2	1	no	—
169	#1368	—	2	1	no	—
170	#1368	—	2	1	no	—
171	#1368	—	2	1	no	—
172	#1368	—	4	1	no	—
173	#1368	—	4	1	no	—
174	#1368	D₄	1	1	yes	characteristic
175	#1368	D₄	1	1	yes	characteristic
176	#1368	D₄	1	1	yes	characteristic
177	#1368	D₄	1	1	yes	characteristic
178	#1367	C₂×C₄	1	1	yes	characteristic
179	#1367	C₂×C₄	1	1	yes	characteristic
180	Q₈⋊C₁₆	C₂×C₄	1	1	yes	characteristic
181	Q₈⋊C₁₆	C₂×C₄	1	1	yes	characteristic
182	Q₈⋊C₁₆	C₂×C₄	1	1	yes	characteristic
183	Q₈⋊C₁₆	C₂×C₄	1	1	yes	characteristic
184	D₄⋊C₁₆	C₂×C₄	1	1	yes	characteristic
185	D₄⋊C₁₆	C₂×C₄	1	1	yes	characteristic
186	D₄⋊C₁₆	C₂×C₄	1	1	yes	characteristic
187	D₄⋊C₁₆	C₂×C₄	1	1	yes	characteristic
188	#1311	C₂×C₄	1	1	yes	characteristic
189	#1311	C₂×C₄	1	1	yes	characteristic
190	C₈×C₁₆	C₂×C₄	1	1	yes	characteristic
191	C₈×C₁₆	C₂×C₄	1	1	yes	characteristic
192	#1303	—	2	1	no	—
193	#1303	—	2	1	no	—
194	#1299	—	2	1	no	—
195	#1299	—	2	1	no	—
196	#1279	—	2	1	no	—
197	#1278	—	2	1	no	—
198	C₂×#135	SD₁₆	1	1	yes	characteristic
199	C₂×#131	—	4	1	no	—
200	C₂×#131	—	4	1	no	—
201	C₄×#41	C₂×D₄	1	1	yes	characteristic
202	C₄×#41	C₂×D₄	1	1	yes	characteristic
203	C₂×M₃₂	—	2	1	no	—
204	C₂×M₃₂	—	2	1	no	—
205	C₂×M₃₂	—	2	1	no	—
206	C₂×M₃₂	#41	1	1	yes	characteristic
207	C₂×M₃₂	#41	1	1	yes	characteristic
208	C₂²×C₁₆	—	2	1	no	—
209	C₂²×C₁₆	—	2	1	no	—
210	#446	—	4	1	no	—
211	C₈×Q₈	—	4	1	no	—
212	C₈×Q₈	C₂²×C₄	1	1	yes	characteristic
213	C₈×Q₈	C₂²×C₄	1	1	yes	characteristic
214	C₈×Q₈	C₂×Q₈	1	1	yes	characteristic
215	C₈×Q₈	C₂×Q₈	1	1	yes	characteristic
216	#443	—	8	4	no	—
217	C₄×Q₁₆	C₄⋊C₄	1	1	yes	characteristic
218	C₄×Q₁₆	SD₁₆	1	1	yes	characteristic
219	C₄×SD₁₆	C₄⋊C₄	1	1	yes	characteristic
220	C₄×SD₁₆	C₄⋊C₄	1	1	yes	characteristic
221	C₄×SD₁₆	SD₁₆	1	1	yes	characteristic
222	C₄×SD₁₆	SD₁₆	1	1	yes	characteristic
223	C₄×D₈	C₄⋊C₄	1	1	yes	characteristic
224	C₄×D₈	SD₁₆	1	1	yes	characteristic
225	#436	—	4	1	no	—
226	#436	—	8	1	no	—
227	#435	—	8	1	no	—
228	C₈×D₄	—	2	1	no	—
229	C₈×D₄	—	2	1	no	—
230	C₈×D₄	—	2	1	no	—
231	C₈×D₄	—	2	1	no	—
232	C₈×D₄	—	4	1	no	—
233	C₈×D₄	C₂²×C₄	1	1	yes	characteristic
234	C₈×D₄	C₂²×C₄	1	1	yes	characteristic
235	C₈×D₄	C₂×Q₈	1	1	yes	characteristic
236	C₈×D₄	C₂×Q₈	1	1	yes	characteristic
237	#432	—	4	1	no	—
238	#431	—	2	1	no	—
239	#431	—	2	1	no	—
240	#431	—	2	1	no	—
241	#431	—	4	1	no	—
242	#431	C₂×D₄	1	1	yes	characteristic
243	#431	C₂×D₄	1	1	yes	characteristic
244	C₂×#108	—	2	1	no	—
245	C₂×#108	—	4	1	no	—
246	C₂×#108	—	4	1	no	—
247	C₂×#108	—	8	1	no	—
248	#427	SD₁₆	1	1	yes	characteristic
249	C₂×#106	—	2	1	no	—
250	#424	—	4	1	no	—
251	#424	—	4	1	no	—
252	#424	—	8	1	no	—
253	#424	—	8	1	no	—
254	#423	—	2	1	no	—
255	#423	—	2	1	no	—
256	#423	—	2	1	no	—
257	#423	—	2	1	no	—
258	#423	—	4	1	no	—
259	#423	—	4	1	no	—
260	#423	—	4	1	no	—
261	C₂×C₄⋊C₈	—	2	1	no	—
262	C₂×C₄⋊C₈	—	4	1	no	—
263	C₂×C₄⋊C₈	—	4	1	no	—
264	C₂×C₄⋊C₈	—	4	1	no	—
265	C₂×#104	—	4	1	no	—
266	C₂×#104	—	4	1	no	—
267	#416	SD₁₆	1	1	yes	characteristic
268	#416	SD₁₆	1	1	yes	characteristic
269	C₄×M₁₆	—	2	1	no	—
270	C₂×C₄×C₈	—	2	1	no	—
271	C₂×C₄×C₈	—	2	1	no	—
272	C₂×C₄×C₈	—	4	1	no	—
273	C₂×C₄×C₈	C₂×D₄	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂×D₄	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂⁴	1	1	yes	characteristic
276	C₄×C₄⋊C₄	—	2	1	no	—
277	#365	—	2	4	no	—
278	C₄⋊C₁₆	—	2	1	no	—
279	C₄⋊C₁₆	—	2	1	no	—
280	C₄⋊C₁₆	—	2	1	no	—
281	C₄⋊C₁₆	—	2	1	no	—
282	C₄⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
283	C₄⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
284	C₄⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
285	C₄⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
286	C₂²⋊C₁₆	—	2	1	no	—
287	C₂²⋊C₁₆	—	2	1	no	—
288	C₂²⋊C₁₆	—	2	1	no	—
289	C₂²⋊C₁₆	—	2	1	no	—
290	C₂²⋊C₁₆	—	2	1	no	—
291	C₂²⋊C₁₆	—	2	1	no	—
292	#346	—	2	1	no	—
293	#346	—	2	1	no	—
294	#346	—	2	1	no	—
295	#346	—	2	1	no	—
296	#346	—	2	1	no	—
297	#346	C₂×D₄	1	1	yes	characteristic
298	#346	C₂×D₄	1	1	yes	characteristic
299	C₄×C₁₆	—	2	1	no	—
300	C₄×C₁₆	—	2	1	no	—
301	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
302	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
303	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
304	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
305	#341	—	2	1	no	—
306	#340	—	2	1	no	—
307	#339	—	4	1	no	—
308	#339	—	4	1	no	—
309	#336	—	4	1	no	—
310	#335	—	2	1	no	—
311	#335	—	4	1	no	—
312	#335	—	4	1	no	—
313	#335	C₄⋊C₄	1	1	yes	characteristic
314	#335	C₄⋊C₄	1	1	yes	characteristic
315	#334	—	2	1	no	—
316	#334	—	2	1	no	—
317	#334	—	2	1	no	—
318	#334	—	2	1	no	—
319	#334	—	2	1	no	—
320	#334	—	2	1	no	—
321	#334	—	2	1	no	—
322	#334	—	2	1	no	—
323	#334	—	2	1	no	—
324	#334	—	4	1	no	—
325	#334	—	4	1	no	—
326	#334	—	4	1	no	—
327	#334	—	4	1	no	—
328	#334	—	4	1	no	—
329	#334	—	4	1	no	—
330	#334	—	4	1	no	—
331	#334	—	4	1	no	—
332	#334	—	8	1	no	—
333	#334	C₄⋊C₄	1	1	yes	characteristic
334	#334	C₄⋊C₄	1	1	yes	characteristic
335	#334	C₂×D₄	1	1	yes	characteristic
336	#334	C₂×D₄	1	1	yes	characteristic
337	#334	C₂×D₄	1	1	yes	characteristic
338	#334	C₂×D₄	1	1	yes	characteristic
339	Q₈⋊C₈	—	4	1	no	—
340	Q₈⋊C₈	—	4	1	no	—
341	Q₈⋊C₈	C₄⋊C₄	1	1	yes	characteristic
342	Q₈⋊C₈	C₄⋊C₄	1	1	yes	characteristic
343	Q₈⋊C₈	C₄⋊C₄	1	1	yes	characteristic
344	Q₈⋊C₈	C₄⋊C₄	1	1	yes	characteristic
345	D₄⋊C₈	—	4	1	no	—
346	D₄⋊C₈	—	4	1	no	—
347	D₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
348	D₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
349	D₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
350	D₄⋊C₈	C₄⋊C₄	1	1	yes	characteristic
351	#322	—	4	1	no	—
352	C₈²	—	4	1	no	—
353	C₈²	C₂²×C₄	1	1	yes	characteristic
354	C₈²	C₂²×C₄	1	1	yes	characteristic
355	C₈²	C₂×Q₈	1	1	yes	characteristic
356	C₈²	C₂×Q₈	1	1	yes	characteristic
357	C₂×#41	C₂×SD₁₆	1	1	yes	characteristic
358	C₂×#41	C₂×SD₁₆	1	1	yes	characteristic
359	#135	—	2	4	no	—
360	C₂×Q₁₆	#106	1	1	yes	characteristic
361	C₂×SD₁₆	#106	1	1	yes	characteristic
362	C₂×SD₁₆	#106	1	1	yes	characteristic
363	C₂×D₈	#106	1	1	yes	characteristic
364	#131	—	8	2	no	—
365	#131	—	8	2	no	—
366	#131	—	16	1	no	—
367	#131	—	16	1	no	—
368	C₂×M₁₆	—	4	1	no	—
369	C₂×M₁₆	—	4	1	no	—
370	C₂×M₁₆	—	4	1	no	—
371	C₂×M₁₆	—	4	1	no	—
372	C₂×M₁₆	—	4	1	no	—
373	C₂×M₁₆	—	8	1	no	—
374	C₂×M₁₆	—	8	1	no	—
375	C₂×M₁₆	—	8	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	4	1	no	—
382	C₂²×C₈	—	8	1	no	—
383	C₂²×C₈	—	8	1	no	—
384	C₂²×C₈	—	8	1	no	—
385	C₂²×C₈	C₂×SD₁₆	1	1	yes	characteristic
386	C₂²×C₈	C₂×SD₁₆	1	1	yes	characteristic
387	C₂²×C₈	C₂×#41	1	1	yes	characteristic
388	C₂²×C₈	2₋¹⁺⁴	1	1	yes	characteristic
389	C₄×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
390	C₄×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
391	C₄×Q₈	C₂×SD₁₆	1	1	yes	characteristic
392	C₄×Q₈	C₂×SD₁₆	1	1	yes	characteristic
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
398	C₄×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
399	C₄×D₄	C₂×SD₁₆	1	1	yes	characteristic
400	C₄×D₄	C₂×SD₁₆	1	1	yes	characteristic
401	#117	—	2	1	no	—
402	#117	—	2	1	no	—
403	#117	C₂×SD₁₆	1	1	yes	characteristic
404	#117	C₂×SD₁₆	1	1	yes	characteristic
405	C₂×C₄⋊C₄	—	4	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	4	1	no	—
409	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
410	M₃₂	—	2	2	no	—
411	M₃₂	—	4	1	no	—
412	M₃₂	—	4	2	no	—
413	M₃₂	—	4	2	no	—
414	M₃₂	—	8	1	no	—
415	C₂×C₁₆	—	2	1	no	—
416	C₂×C₁₆	—	2	1	no	—
417	C₂×C₁₆	—	2	1	no	—
418	C₂×C₁₆	—	2	1	no	—
419	C₂×C₁₆	—	2	1	no	—
420	C₂×C₁₆	—	2	1	no	—
421	C₂×C₁₆	—	4	2	no	—
422	C₂×C₁₆	—	8	1	no	—
423	C₂×C₁₆	C₄×D₄	1	1	yes	characteristic
424	C₂×C₁₆	C₄×D₄	1	1	yes	characteristic
425	C₂×C₁₆	C₄×D₄	1	1	yes	characteristic
426	C₂×C₁₆	C₄×D₄	1	1	yes	characteristic
427	#108	—	2	2	no	—
428	#108	—	4	1	no	—
429	#108	—	8	2	no	—
430	#108	—	16	1	no	—
431	#108	—	16	2	no	—
432	#107	#106	1	1	yes	characteristic
433	#107	#106	1	1	yes	characteristic
434	#106	—	2	2	no	—
435	#106	—	4	1	no	—
436	#106	#106	1	1	yes	characteristic
437	#106	#106	1	1	yes	characteristic
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	C₄⋊C₈	—	2	1	no	—
441	C₄⋊C₈	—	2	1	no	—
442	C₄⋊C₈	—	2	1	no	—
443	C₄⋊C₈	—	2	1	no	—
444	C₄⋊C₈	—	2	1	no	—
445	C₄⋊C₈	—	2	1	no	—
446	C₄⋊C₈	—	4	1	no	—
447	C₄⋊C₈	—	4	1	no	—
448	C₄⋊C₈	—	4	1	no	—
449	C₄⋊C₈	—	4	1	no	—
450	C₄⋊C₈	—	4	1	no	—
451	C₄⋊C₈	—	4	1	no	—
452	C₄⋊C₈	—	4	1	no	—
453	C₄⋊C₈	—	4	1	no	—
454	C₄⋊C₈	—	4	1	no	—
455	C₄⋊C₈	—	8	1	no	—
456	C₄⋊C₈	—	8	1	no	—
457	C₄⋊C₈	—	8	1	no	—
458	C₄⋊C₈	—	8	1	no	—
459	C₄⋊C₈	—	8	1	no	—
460	C₄⋊C₈	—	8	1	no	—
461	C₄⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
462	C₄⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
463	C₄⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
464	C₄⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
465	#104	—	8	2	no	—
466	#104	—	8	2	no	—
467	#103	#106	1	1	yes	characteristic
468	#103	#106	1	1	yes	characteristic
469	#103	#106	1	1	yes	characteristic
470	#103	#106	1	1	yes	characteristic
471	#102	#106	1	1	yes	characteristic
472	#102	#106	1	1	yes	characteristic
473	#102	#106	1	1	yes	characteristic
474	#102	#106	1	1	yes	characteristic
475	C₂²⋊C₈	—	2	1	no	—
476	C₂²⋊C₈	—	2	1	no	—
477	C₂²⋊C₈	—	2	1	no	—
478	C₂²⋊C₈	—	2	1	no	—
479	C₂²⋊C₈	—	2	1	no	—
480	C₂²⋊C₈	—	2	1	no	—
481	C₂²⋊C₈	—	4	1	no	—
482	C₂²⋊C₈	—	8	1	no	—
483	C₂²⋊C₈	—	8	1	no	—
484	#97	—	4	1	no	—
485	#97	—	8	1	no	—
486	C₄×C₈	—	2	1	no	—
487	C₄×C₈	—	2	1	no	—
488	C₄×C₈	—	2	1	no	—
489	C₄×C₈	—	2	1	no	—
490	C₄×C₈	—	2	1	no	—
491	C₄×C₈	—	2	1	no	—
492	C₄×C₈	—	2	1	no	—
493	C₄×C₈	—	4	1	no	—
494	C₄×C₈	—	4	1	no	—
495	C₄×C₈	—	8	1	no	—
496	C₄×C₈	—	8	2	no	—
497	C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
498	C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
499	C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
500	C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
501	C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
502	C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
503	C₄×C₈	C₂³×C₄	1	1	yes	characteristic
504	C₄×C₈	C₂²×D₄	1	1	yes	characteristic
505	C₄×C₈	C₂²×Q₈	1	1	yes	characteristic
506	C₄×C₈	H(5,𝔽₂)	1	1	yes	characteristic
507	#95	—	4	1	no	—
508	#41	—	2	2	no	—
509	#41	—	2	2	no	—
510	#41	—	4	1	no	—
511	#41	—	4	1	no	—
512	C₂×Q₈	C₂×#106	1	1	yes	characteristic
513	C₂×Q₈	C₂×#106	1	1	yes	characteristic
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	C₂×#106	1	1	yes	characteristic
517	C₂×D₄	C₂×#106	1	1	yes	characteristic
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	8	1	no	—
525	C₂²×C₄	#547	1	1	yes	characteristic
526	C₂²×C₄	C₂²×SD₁₆	1	1	yes	characteristic
527	C₂²×C₄	#577	1	1	yes	characteristic
528	Q₁₆	—	2	2	no	—
529	SD₁₆	—	2	2	no	—
530	SD₁₆	#365	1	4	yes	complemented
531	D₈	—	2	2	no	—
532	M₁₆	—	4	2	no	—
533	M₁₆	—	8	1	no	—
534	M₁₆	—	8	1	no	—
535	M₁₆	—	8	1	no	—
536	M₁₆	—	8	1	no	—
537	M₁₆	—	8	1	no	—
538	M₁₆	—	16	2	no	—
539	M₁₆	—	16	2	no	—
540	M₁₆	—	16	1	no	—
541	M₁₆	—	16	1	no	—
542	M₁₆	—	32	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	2	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	4	1	no	—
553	C₂×C₈	—	4	1	no	—
554	C₂×C₈	—	4	2	no	—
555	C₂×C₈	—	4	1	no	—
556	C₂×C₈	—	4	1	no	—
557	C₂×C₈	—	4	1	no	—
558	C₂×C₈	—	4	1	no	—
559	C₂×C₈	—	4	1	no	—
560	C₂×C₈	—	4	1	no	—
561	C₂×C₈	—	4	1	no	—
562	C₂×C₈	—	4	1	no	—
563	C₂×C₈	—	8	1	no	—
564	C₂×C₈	—	8	1	no	—
565	C₂×C₈	—	8	1	no	—
566	C₂×C₈	—	8	1	no	—
567	C₂×C₈	—	8	1	no	—
568	C₂×C₈	—	8	1	no	—
569	C₂×C₈	—	8	1	no	—
570	C₂×C₈	—	8	1	no	—
571	C₂×C₈	—	8	1	no	—
572	C₂×C₈	—	16	2	no	—
573	C₂×C₈	—	16	2	no	—
574	C₂×C₈	—	32	1	no	—
575	C₂×C₈	C₂×#106	1	1	yes	characteristic
576	C₂×C₈	C₂×#106	1	1	yes	characteristic
577	C₂×C₈	C₂×#106	1	1	yes	characteristic
578	C₂×C₈	C₂×#106	1	1	yes	characteristic
579	C₂×C₈	C₂×C₄×D₄	1	1	yes	characteristic
580	C₂×C₈	#520	1	1	yes	characteristic
581	C₂×C₈	D₄×Q₈	1	1	yes	characteristic
582	C₂×C₈	#554	1	1	yes	characteristic
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	8	1	no	—
589	C₄⋊C₄	C₂×#106	1	1	yes	characteristic
590	C₄⋊C₄	C₂×#106	1	1	yes	characteristic
591	C₄⋊C₄	C₂×#106	1	1	yes	characteristic
592	C₄⋊C₄	C₂×#106	1	1	yes	characteristic
593	C₂²⋊C₄	—	2	1	no	—
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	8	1	no	—
606	C₄²	—	8	1	no	—
607	C₄²	C₂²×C₄⋊C₄	1	1	yes	characteristic
608	C₄²	D₄²	1	1	yes	characteristic
609	C₄²	C₂²×SD₁₆	1	1	yes	characteristic
610	C₄²	#577	1	1	yes	characteristic
611	C₁₆	—	2	2	no	—
612	C₁₆	—	2	1	no	—
613	C₁₆	—	2	1	no	—
614	C₁₆	—	2	1	no	—
615	C₁₆	—	4	1	no	—
616	C₁₆	—	4	1	no	—
617	C₁₆	—	4	1	no	—
618	C₁₆	—	4	1	no	—
619	C₁₆	—	4	1	no	—
620	C₁₆	#443	1	2	yes	complemented
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	#3335	1	1	yes	characteristic
624	Q₈	—	2	1	no	—
625	Q₈	—	2	1	no	—
626	Q₈	—	2	1	no	—
627	Q₈	C₂×#365	1	2	yes	—
628	D₄	—	2	1	no	—
629	D₄	—	2	1	no	—
630	D₄	—	2	1	no	—
631	D₄	—	4	2	no	—
632	D₄	—	4	2	no	—
633	D₄	C₂×#365	1	2	yes	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	8	1	no	—
652	C₂×C₄	—	8	1	no	—
653	C₂×C₄	—	8	2	no	—
654	C₂×C₄	—	16	1	no	—
655	C₂×C₄	—	16	1	no	—
656	C₂×C₄	D₄×C₄⋊C₄	1	1	yes	characteristic
657	C₂×C₄	C₂²×#106	1	1	yes	characteristic
658	C₂×C₄	#2912	1	1	yes	characteristic
659	C₂×C₄	D₄×SD₁₆	1	1	yes	characteristic
660	C₂×C₄	D₄×SD₁₆	1	1	yes	characteristic
661	C₂×C₄	#3335	1	1	yes	characteristic
662	C₈	—	2	2	no	—
663	C₈	—	2	1	no	—
664	C₈	—	2	1	no	—
665	C₈	—	2	1	no	—
666	C₈	—	2	1	no	—
667	C₈	—	2	1	no	—
668	C₈	—	2	1	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₈	—	8	1	no	—
675	C₈	—	8	1	no	—
676	C₈	—	8	1	no	—
677	C₈	—	8	1	no	—
678	C₈	—	8	2	no	—
679	C₈	—	16	1	no	—
680	C₈	—	16	1	no	—
681	C₈	—	16	1	no	—
682	C₈	—	16	1	no	—
683	C₈	C₂×#365	1	2	yes	—
684	C₈	C₂×#443	1	1	yes	characteristic
685	C₈	#2957	1	1	yes	characteristic
686	C₂²	—	2	1	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	D₄×#106	1	1	yes	characteristic
696	C₄	—	2	1	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	16	2	no	—
707	C₄	#22688	1	1	yes	characteristic
708	C₄	#22694	1	1	yes	characteristic
709	C₄	C₂²×#365	1	1	yes	characteristic
710	C₄	#33404	1	1	yes	characteristic
711	C₂	—	4	1	no	—
712	C₂	—	4	2	no	—
713	C₂	—	8	1	no	—
714	C₂	#225720	1	1	yes	characteristic
715	C₂	D₄×#365	1	1	yes	characteristic
716	C₂	#497838	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₄×#106
commutator	C₄×C₈	C₂³×C₄
Frattini, cosocle	C₂×C₄×C₈	C₂⁴
prime radical	C₂×#135	SD₁₆
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#135 ◁ G
LECS	G ▷ C₂×C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #483466	C₂	semidirect
3. #483463	C₂	semidirect
6. #140496	C₂	semidirect
7. #140494	C₂	semidirect
8. #136464	C₂	semidirect
9. #136464	C₂	semidirect
10. #136463	C₂	semidirect
11. #136462	C₂	semidirect
12. #135792	C₂	semidirect
13. #135074	C₂	semidirect
14. #135073	C₂	semidirect
15. C₈×#365	C₂	semidirect
26. #12053	C₄	semidirect
27. #12053	C₄	semidirect
28. #12051	C₄	semidirect
29. #12051	C₄	semidirect
30. C₁₆×SD₁₆	C₄	semidirect
31. C₁₆×SD₁₆	C₄	semidirect
32. #12038	C₄	semidirect
33. #12038	C₄	semidirect
530. SD₁₆	#365	semidirect
620. C₁₆	#443	semidirect

Maximal subgroups

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

subgroup	index
#483553	2
#483466	2
#483463	2
#225783	2
#225720	2
#140496	2
#140494	2
#136464	2
#136463	2
#136462	2
#135792	2
#135074	2
#135073	2
C₈×#365	2