Subgroups — #72231988

Order 2048.

761 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72231957	C₂	1	1	yes	maximal, characteristic
2	#72231942	C₂	1	2	yes	maximal, complemented
3	#72231941	C₂	1	1	yes	maximal, characteristic
4	#72231939	C₂	1	1	yes	maximal, characteristic, complemented
5	#72231938	C₂	1	1	yes	maximal, characteristic
6	#72231936	C₂	1	1	yes	maximal, characteristic, complemented
7	#72231935	C₂	1	2	yes	maximal, complemented
8	#72231932	C₂	1	2	yes	maximal, complemented
9	#72231929	C₂	1	1	yes	maximal, characteristic, complemented
10	#72231929	C₂	1	2	yes	maximal, complemented
11	#72225212	C₂	1	1	yes	maximal, characteristic, complemented
12	#512789	C₄	1	1	yes	characteristic
13	#512789	C₄	1	1	yes	characteristic
14	#483380	—	2	1	no	—
15	#483351	—	2	1	no	—
16	#479943	C₂²	1	1	yes	characteristic
17	#149513	C₂²	1	1	yes	characteristic
18	#149513	C₂²	1	2	yes	—
19	#149509	C₄	1	1	yes	characteristic
20	#149509	C₄	1	2	yes	—
21	#149509	C₄	1	1	yes	characteristic
22	#149509	C₄	1	2	yes	—
23	#149495	C₂²	1	1	yes	characteristic
24	#149495	C₂²	1	2	yes	—
25	#122927	—	2	1	no	—
26	#122926	—	2	2	no	—
27	#122925	—	2	2	no	—
28	#122924	—	2	1	no	—
29	#122922	C₂²	1	2	yes	—
30	#122922	C₂²	1	2	yes	—
31	#122921	C₂²	1	1	yes	characteristic
32	#122921	C₂²	1	1	yes	characteristic
33	#122919	C₂²	1	1	yes	characteristic
34	#122919	C₂²	1	2	yes	—
35	C₂×#7099	C₂²	1	1	yes	characteristic
36	C₂×#7099	C₂²	1	2	yes	—
37	#93877	C₂²	1	2	yes	—
38	#93877	C₂²	1	2	yes	—
39	#93877	C₂²	1	2	yes	—
40	#93877	C₂²	1	2	yes	—
41	#93877	C₂²	1	1	yes	characteristic
42	#93877	C₂²	1	2	yes	—
43	#93877	C₂²	1	2	yes	—
44	#93877	C₂²	1	1	yes	characteristic
45	#93877	C₂²	1	1	yes	characteristic
46	#93877	C₂²	1	1	yes	characteristic
47	#33504	—	4	1	no	—
48	C₁₆×#41	C₂×C₄	1	1	yes	characteristic
49	C₁₆×#41	Q₈	1	1	yes	characteristic
50	#33423	—	4	1	no	—
51	C₈×#131	D₄	1	1	yes	characteristic
52	Q₈×C₃₂	—	2	1	no	—
53	Q₈×C₃₂	C₈	1	1	yes	characteristic
54	Q₈×C₃₂	C₈	1	1	yes	characteristic
55	#13646	—	2	1	no	—
56	#13646	—	2	2	no	—
57	#13646	C₈	1	1	yes	characteristic
58	#13646	C₈	1	2	yes	—
59	#13646	C₈	1	1	yes	characteristic
60	#13646	C₈	1	2	yes	—
61	#13640	C₂×C₄	1	1	yes	characteristic
62	#13640	C₂×C₄	1	2	yes	—
63	#13640	C₂×C₄	1	1	yes	characteristic
64	#13640	C₂×C₄	1	2	yes	—
65	C₄×M₆₄	C₂×C₄	1	1	yes	characteristic
66	C₄×M₆₄	C₂×C₄	1	2	yes	—
67	C₄×M₆₄	C₂×C₄	1	1	yes	characteristic
68	C₄×M₆₄	C₂×C₄	1	2	yes	—
69	#12018	—	4	1	no	—
70	#12016	—	4	2	no	—
71	#12014	—	4	2	no	—
72	#12013	—	2	2	no	—
73	#12013	—	2	2	no	—
74	#12012	—	2	2	no	—
75	#12012	—	2	1	no	—
76	#12005	—	4	1	no	—
77	#11996	—	2	1	no	—
78	#11996	—	2	1	no	—
79	C₂×#1367	—	2	1	no	—
80	C₂×#1367	—	2	2	no	—
81	#11411	D₄	1	1	yes	characteristic
82	#11411	D₄	1	2	yes	—
83	#11408	C₂×C₄	1	2	yes	—
84	#11408	C₂×C₄	1	1	yes	characteristic
85	#11408	Q₈	1	2	yes	—
86	#11408	Q₈	1	1	yes	characteristic
87	C₂×#1311	C₂³	1	1	yes	characteristic
88	C₂×#1311	C₂³	1	2	yes	—
89	#7332	C₂×C₄	1	2	yes	—
90	#7332	C₂×C₄	1	2	yes	—
91	#7332	C₂×C₄	1	2	yes	—
92	#7330	C₂×C₄	1	1	yes	characteristic
93	#7330	C₂×C₄	1	2	yes	—
94	#7330	C₂×C₄	1	1	yes	characteristic
95	#7330	C₂×C₄	1	2	yes	—
96	#7330	C₂³	1	2	yes	—
97	#7330	C₂³	1	1	yes	characteristic
98	#7330	C₂³	1	1	yes	characteristic
99	#7099	—	2	1	no	—
100	#7099	—	2	2	no	—
101	#7099	—	2	2	no	—
102	#7099	—	2	1	no	—
103	#7099	—	2	1	no	—
104	#7099	—	2	1	no	—
105	#7099	—	2	2	no	—
106	#7099	—	2	2	no	—
107	#7099	C₂³	1	1	yes	characteristic
108	#7099	C₂³	1	1	yes	characteristic
109	#7099	C₂³	1	2	yes	—
110	#7099	C₂³	1	1	yes	characteristic
111	#7099	C₂³	1	2	yes	—
112	#7099	C₂³	1	1	yes	characteristic
113	C₈×#41	C₄⋊C₄	1	1	yes	characteristic
114	C₈×#41	SD₁₆	1	1	yes	characteristic
115	C₄×#131	SD₁₆	1	1	yes	characteristic
116	C₂×M₆₄	—	2	1	no	—
117	C₂×M₆₄	—	2	2	no	—
118	C₂×M₆₄	C₂×C₈	1	1	yes	characteristic
119	C₂×M₆₄	C₂×C₈	1	2	yes	—
120	C₂×M₆₄	C₂×C₈	1	1	yes	characteristic
121	C₂×M₆₄	C₂×C₈	1	2	yes	—
122	#2183	—	8	1	no	—
123	Q₈×C₁₆	—	2	1	no	—
124	Q₈×C₁₆	C₂×C₈	1	1	yes	characteristic
125	Q₈×C₁₆	M₁₆	1	1	yes	characteristic
126	#2168	—	8	2	no	—
127	D₄×C₁₆	—	2	1	no	—
128	D₄×C₁₆	—	2	2	no	—
129	D₄×C₁₆	—	8	1	no	—
130	D₄×C₁₆	C₂×C₈	1	1	yes	characteristic
131	D₄×C₁₆	C₂×C₈	1	2	yes	—
132	D₄×C₁₆	M₁₆	1	1	yes	characteristic
133	D₄×C₁₆	M₁₆	1	2	yes	—
134	#2164	—	8	2	no	—
135	#2163	—	4	2	no	—
136	#2163	—	4	2	no	—
137	#2162	—	4	2	no	—
138	#2162	—	4	1	no	—
139	#2162	C₄⋊C₄	1	1	yes	characteristic
140	#2162	C₄⋊C₄	1	2	yes	—
141	#2162	C₄⋊C₄	1	1	yes	characteristic
142	#2162	C₄⋊C₄	1	2	yes	—
143	#2150	—	4	1	no	—
144	#2150	—	4	1	no	—
145	C₂×C₄⋊C₁₆	—	4	1	no	—
146	C₂×C₄⋊C₁₆	—	4	2	no	—
147	#2113	—	8	1	no	—
148	#2108	—	8	1	no	—
149	C₂×C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₆	C₂²×C₄	1	2	yes	—
151	C₂×C₄×C₁₆	C₂×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₆	C₂×Q₈	1	2	yes	—
153	#1450	SD₁₆	1	1	yes	characteristic
154	#1450	SD₁₆	1	2	yes	—
155	C₈×M₁₆	C₄⋊C₄	1	2	yes	—
156	C₈×M₁₆	C₄⋊C₄	1	1	yes	characteristic
157	C₈×M₁₆	SD₁₆	1	2	yes	—
158	C₈×M₁₆	SD₁₆	1	1	yes	characteristic
159	C₂×C₈²	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈²	C₂×D₄	1	2	yes	—
161	C₄⋊C₃₂	—	2	1	no	—
162	C₄⋊C₃₂	—	2	2	no	—
163	C₄⋊C₃₂	C₂×C₈	1	1	yes	characteristic
164	C₄⋊C₃₂	C₂×C₈	1	2	yes	—
165	C₄⋊C₃₂	C₂×C₈	1	1	yes	characteristic
166	C₄⋊C₃₂	C₂×C₈	1	2	yes	—
167	C₂²⋊C₃₂	—	2	1	no	—
168	C₂²⋊C₃₂	—	2	2	no	—
169	C₂²⋊C₃₂	C₂×C₈	1	2	yes	—
170	C₂²⋊C₃₂	C₂×C₈	1	2	yes	—
171	C₂²⋊C₃₂	C₂×C₈	1	2	yes	—
172	#1397	C₂²×C₄	1	2	yes	—
173	#1397	C₂²×C₄	1	1	yes	characteristic
174	#1397	C₂²×C₄	1	1	yes	characteristic
175	#1397	C₂²×C₄	1	2	yes	—
176	#1397	C₂²×C₄	1	1	yes	characteristic
177	#1397	C₂²×C₄	1	1	yes	characteristic
178	C₄×C₃₂	—	2	1	no	—
179	C₄×C₃₂	—	2	2	no	—
180	C₄×C₃₂	C₂×C₈	1	1	yes	characteristic
181	C₄×C₃₂	C₂×C₈	1	2	yes	—
182	C₄×C₃₂	C₂×C₈	1	1	yes	characteristic
183	C₄×C₃₂	C₂×C₈	1	2	yes	—
184	#1370	—	4	2	no	—
185	#1370	—	4	2	no	—
186	#1370	—	4	1	no	—
187	#1370	—	4	2	no	—
188	#1367	—	2	1	no	—
189	#1367	—	2	2	no	—
190	#1367	—	2	1	no	—
191	#1367	—	2	1	no	—
192	#1367	—	2	2	no	—
193	#1367	—	2	1	no	—
194	#1367	—	4	1	no	—
195	#1367	—	4	2	no	—
196	#1367	—	4	1	no	—
197	#1367	—	4	1	no	—
198	#1312	C₄⋊C₄	1	2	yes	—
199	#1312	C₄⋊C₄	1	2	yes	—
200	#1312	C₄⋊C₄	1	2	yes	—
201	#1311	C₂²×C₄	1	1	yes	characteristic
202	#1311	C₂²×C₄	1	2	yes	—
203	#1311	C₂×D₄	1	1	yes	characteristic
204	#1311	C₂×D₄	1	2	yes	—
205	#1311	C₂×Q₈	1	1	yes	characteristic
206	#1311	C₂×Q₈	1	2	yes	—
207	#1311	C₂⁴	1	1	yes	characteristic
208	C₂×#131	—	2	1	no	—
209	C₄×#41	#106	1	1	yes	characteristic
210	C₂×M₃₂	—	8	1	no	—
211	C₂×M₃₂	—	8	1	no	—
212	C₂²×C₁₆	—	2	1	no	—
213	C₂²×C₁₆	—	2	2	no	—
214	C₂²×C₁₆	—	8	1	no	—
215	C₂²×C₁₆	—	8	2	no	—
216	C₂²×C₁₆	C₂²×C₈	1	1	yes	characteristic
217	C₂²×C₁₆	C₂²×C₈	1	2	yes	—
218	C₂²×C₁₆	C₂×M₁₆	1	1	yes	characteristic
219	C₂²×C₁₆	C₂×M₁₆	1	2	yes	—
220	C₈×Q₈	—	2	1	no	—
221	C₈×Q₈	C₄⋊C₈	1	1	yes	characteristic
222	C₈×Q₈	#108	1	1	yes	characteristic
223	C₈×D₄	—	2	1	no	—
224	C₈×D₄	—	2	2	no	—
225	C₈×D₄	C₄⋊C₈	1	1	yes	characteristic
226	C₈×D₄	C₄⋊C₈	1	2	yes	—
227	C₈×D₄	#108	1	1	yes	characteristic
228	C₈×D₄	#108	1	2	yes	—
229	#431	#106	1	1	yes	characteristic
230	#431	#106	1	2	yes	—
231	#431	#106	1	2	yes	—
232	#431	#106	1	1	yes	characteristic
233	#405	—	2	1	no	—
234	#405	—	2	2	no	—
235	C₄×M₁₆	#106	1	1	yes	characteristic
236	C₄×M₁₆	#106	1	2	yes	—
237	C₂×C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂×C₄⋊C₄	1	2	yes	—
239	C₂×C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂×SD₁₆	1	2	yes	—
241	C₂×C₄×C₈	C₂×SD₁₆	1	2	yes	—
242	C₂×C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
243	M₆₄	—	2	2	no	—
244	M₆₄	—	2	4	no	—
245	M₆₄	—	4	1	no	—
246	M₆₄	—	4	2	no	—
247	M₆₄	—	4	2	no	—
248	M₆₄	—	4	4	no	—
249	C₂×C₃₂	—	2	1	no	—
250	C₂×C₃₂	—	2	1	no	—
251	C₂×C₃₂	—	2	2	no	—
252	C₂×C₃₂	C₂²×C₈	1	1	yes	characteristic
253	C₂×C₃₂	C₂²×C₈	1	1	yes	characteristic
254	C₂×C₃₂	C₂²×C₈	1	2	yes	—
255	C₂×C₃₂	C₂²×C₈	1	1	yes	characteristic
256	C₂×C₃₂	C₂²×C₈	1	2	yes	—
257	C₂×C₃₂	C₂²×C₈	1	1	yes	characteristic
258	C₄⋊C₁₆	—	2	1	no	—
259	C₄⋊C₁₆	—	2	2	no	—
260	C₄⋊C₁₆	—	4	1	no	—
261	C₄⋊C₁₆	—	4	2	no	—
262	C₄⋊C₁₆	—	4	1	no	—
263	C₄⋊C₁₆	—	4	1	no	—
264	C₄⋊C₁₆	—	4	2	no	—
265	C₄⋊C₁₆	—	4	1	no	—
266	C₄⋊C₁₆	—	8	1	no	—
267	C₄⋊C₁₆	—	8	2	no	—
268	C₄⋊C₁₆	—	8	1	no	—
269	C₄⋊C₁₆	—	8	1	no	—
270	C₄⋊C₁₆	C₄⋊C₈	1	1	yes	characteristic
271	C₄⋊C₁₆	C₄⋊C₈	1	2	yes	—
272	C₄⋊C₁₆	C₄⋊C₈	1	1	yes	characteristic
273	C₄⋊C₁₆	C₄⋊C₈	1	2	yes	—
274	C₂²⋊C₁₆	—	2	1	no	—
275	C₂²⋊C₁₆	—	2	2	no	—
276	C₂²⋊C₁₆	—	8	2	no	—
277	C₂²⋊C₁₆	—	8	2	no	—
278	C₂²⋊C₁₆	—	8	1	no	—
279	C₂²⋊C₁₆	—	8	2	no	—
280	C₂²⋊C₁₆	C₄⋊C₈	1	2	yes	—
281	C₂²⋊C₁₆	C₄⋊C₈	1	2	yes	—
282	C₂²⋊C₁₆	C₄⋊C₈	1	2	yes	—
283	#346	—	8	2	no	—
284	#346	—	8	2	no	—
285	C₄×C₁₆	—	2	1	no	—
286	C₄×C₁₆	—	2	2	no	—
287	C₄×C₁₆	—	8	2	no	—
288	C₄×C₁₆	—	8	1	no	—
289	C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
290	C₄×C₁₆	C₂×C₄⋊C₄	1	2	yes	—
291	C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
292	C₄×C₁₆	C₂×C₄⋊C₄	1	2	yes	—
293	C₄×C₁₆	C₂²×C₈	1	1	yes	characteristic
294	C₄×C₁₆	C₂²×C₈	1	2	yes	—
295	C₄×C₁₆	C₂×M₁₆	1	1	yes	characteristic
296	C₄×C₁₆	C₂×M₁₆	1	2	yes	—
297	C₄×C₁₆	C₂³×C₄	1	1	yes	characteristic
298	C₄×C₁₆	C₂²×Q₈	1	1	yes	characteristic
299	#322	#106	1	2	yes	—
300	#322	#106	1	2	yes	—
301	#322	#106	1	2	yes	—
302	C₈²	C₂×C₄⋊C₄	1	1	yes	characteristic
303	C₈²	C₂×C₄⋊C₄	1	2	yes	—
304	C₈²	C₂×SD₁₆	1	1	yes	characteristic
305	C₈²	C₂×SD₁₆	1	2	yes	—
306	C₈²	C₂×SD₁₆	1	1	yes	characteristic
307	C₈²	C₂×SD₁₆	1	2	yes	—
308	C₈²	C₂²×D₄	1	1	yes	characteristic
309	C₂×#41	#365	1	1	yes	characteristic
310	#131	—	8	2	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	1	no	—
317	C₂²×C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
318	C₂²×C₈	C₂×C₄⋊C₈	1	2	yes	—
319	C₂²×C₈	C₂×#108	1	1	yes	characteristic
320	C₂²×C₈	C₂×#108	1	2	yes	—
321	C₄×Q₈	#334	1	1	yes	characteristic
322	C₄×Q₈	#365	1	1	yes	characteristic
323	C₄×D₄	#334	1	1	yes	characteristic
324	C₄×D₄	#334	1	2	yes	—
325	C₄×D₄	#365	1	1	yes	characteristic
326	C₄×D₄	#365	1	2	yes	—
327	#117	#365	1	1	yes	characteristic
328	#117	#365	1	2	yes	—
329	C₂×C₄²	C₂×#106	1	1	yes	characteristic
330	C₂×C₄²	C₂×#106	1	2	yes	—
331	M₃₂	—	16	2	no	—
332	M₃₂	—	32	1	no	—
333	C₂×C₁₆	—	2	1	no	—
334	C₂×C₁₆	—	2	2	no	—
335	C₂×C₁₆	—	2	1	no	—
336	C₂×C₁₆	—	2	2	no	—
337	C₂×C₁₆	—	2	1	no	—
338	C₂×C₁₆	—	2	1	no	—
339	C₂×C₁₆	—	2	2	no	—
340	C₂×C₁₆	—	4	1	no	—
341	C₂×C₁₆	—	4	2	no	—
342	C₂×C₁₆	—	8	1	no	—
343	C₂×C₁₆	—	8	2	no	—
344	C₂×C₁₆	—	8	1	no	—
345	C₂×C₁₆	—	8	1	no	—
346	C₂×C₁₆	—	8	2	no	—
347	C₂×C₁₆	—	8	1	no	—
348	C₂×C₁₆	—	8	1	no	—
349	C₂×C₁₆	—	8	2	no	—
350	C₂×C₁₆	—	16	2	no	—
351	C₂×C₁₆	—	32	2	no	—
352	C₂×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
353	C₂×C₁₆	C₂×C₄⋊C₈	1	2	yes	—
354	C₂×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
355	C₂×C₁₆	C₂×C₄⋊C₈	1	2	yes	—
356	C₂×C₁₆	C₂³×C₈	1	1	yes	characteristic
357	C₂×C₁₆	C₂²×M₁₆	1	1	yes	characteristic
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	—	2	2	no	—
360	C₄⋊C₈	#334	1	2	yes	—
361	C₄⋊C₈	#334	1	1	yes	characteristic
362	C₄⋊C₈	#334	1	2	yes	—
363	C₄⋊C₈	#334	1	1	yes	characteristic
364	C₂²⋊C₈	—	2	2	no	—
365	C₂²⋊C₈	—	2	1	no	—
366	C₂²⋊C₈	#334	1	2	yes	—
367	C₂²⋊C₈	#334	1	2	yes	—
368	C₂²⋊C₈	#334	1	2	yes	—
369	#97	—	2	2	no	—
370	#97	—	2	1	no	—
371	C₄×C₈	—	2	2	no	—
372	C₄×C₈	—	2	1	no	—
373	C₄×C₈	—	2	2	no	—
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	C₂×C₄⋊C₈	1	2	yes	—
376	C₄×C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
377	C₄×C₈	C₂×#106	1	1	yes	characteristic
378	C₄×C₈	C₂×#106	1	2	yes	—
379	C₄×C₈	C₂×#106	1	1	yes	characteristic
380	C₄×C₈	C₂×#106	1	2	yes	—
381	C₄×C₈	C₂×#106	1	1	yes	characteristic
382	C₄×C₈	C₂×#106	1	2	yes	—
383	C₄×C₈	C₂×#108	1	2	yes	—
384	C₄×C₈	C₂×#108	1	1	yes	characteristic
385	C₄×C₈	C₂²×C₄⋊C₄	1	1	yes	characteristic
386	C₄×C₈	C₂²×SD₁₆	1	1	yes	characteristic
387	C₄×C₈	C₂²×SD₁₆	1	1	yes	characteristic
388	C₃₂	—	2	2	no	—
389	C₃₂	—	2	1	no	—
390	C₃₂	—	2	2	no	—
391	C₃₂	—	2	1	no	—
392	C₃₂	—	2	2	no	—
393	C₃₂	—	2	1	no	—
394	C₃₂	—	4	1	no	—
395	C₃₂	—	4	2	no	—
396	C₃₂	#504	1	2	yes	—
397	#41	—	4	2	no	—
398	C₂×Q₈	#1368	1	1	yes	characteristic
399	C₂×D₄	#1368	1	1	yes	characteristic
400	C₂×D₄	#1368	1	2	yes	—
401	C₂²×C₄	C₂×#334	1	1	yes	characteristic
402	C₂²×C₄	C₂×#334	1	2	yes	—
403	C₂²×C₄	C₂×#365	1	1	yes	characteristic
404	C₂²×C₄	C₂×#365	1	2	yes	—
405	C₂²×C₄	C₂×#365	1	1	yes	characteristic
406	C₂²×C₄	C₂×#365	1	2	yes	—
407	M₁₆	—	4	2	no	—
408	M₁₆	—	8	2	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	4	1	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	—	4	2	no	—
422	C₂×C₈	—	8	2	no	—
423	C₂×C₈	—	8	1	no	—
424	C₂×C₈	—	8	2	no	—
425	C₂×C₈	C₂×#334	1	1	yes	characteristic
426	C₂×C₈	C₂×#334	1	2	yes	—
427	C₂×C₈	C₂×#334	1	1	yes	characteristic
428	C₂×C₈	C₂×#334	1	2	yes	—
429	C₂×C₈	C₂²×C₄⋊C₈	1	1	yes	characteristic
430	C₂×C₈	C₂²×#108	1	1	yes	characteristic
431	C₄⋊C₄	#1368	1	2	yes	—
432	C₄⋊C₄	#1368	1	1	yes	characteristic
433	C₄⋊C₄	#1368	1	2	yes	—
434	C₄⋊C₄	#1368	1	1	yes	characteristic
435	C₂²⋊C₄	#1368	1	2	yes	—
436	C₂²⋊C₄	#1368	1	2	yes	—
437	C₂²⋊C₄	#1368	1	2	yes	—
438	C₄²	C₂×#334	1	2	yes	—
439	C₄²	C₂×#334	1	1	yes	characteristic
440	C₄²	C₂×#365	1	2	yes	—
441	C₄²	C₂×#365	1	1	yes	characteristic
442	C₄²	C₂×#365	1	2	yes	—
443	C₄²	C₂×#365	1	1	yes	characteristic
444	C₄²	C₂²×#106	1	1	yes	characteristic
445	C₁₆	—	2	1	no	—
446	C₁₆	—	2	2	no	—
447	C₁₆	—	2	1	no	—
448	C₁₆	—	2	1	no	—
449	C₁₆	—	2	2	no	—
450	C₁₆	—	4	1	no	—
451	C₁₆	—	4	2	no	—
452	C₁₆	—	4	1	no	—
453	C₁₆	—	16	1	no	—
454	C₁₆	—	16	1	no	—
455	C₁₆	—	16	1	no	—
456	C₁₆	—	16	1	no	—
457	C₁₆	—	16	2	no	—
458	C₁₆	—	16	2	no	—
459	C₁₆	C₂×#504	1	1	yes	characteristic
460	C₁₆	#3407	1	1	yes	characteristic
461	C₂³	C₂×#1368	1	1	yes	characteristic
462	C₂³	C₂×#1368	1	2	yes	—
463	Q₈	—	2	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	4	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	C₂×#1368	1	2	yes	—
475	C₂×C₄	C₂×#1368	1	1	yes	characteristic
476	C₂×C₄	C₂×#1368	1	2	yes	—
477	C₂×C₄	C₂×#1368	1	2	yes	—
478	C₂×C₄	C₂×#1368	1	1	yes	characteristic
479	C₂×C₄	C₂×#1368	1	1	yes	characteristic
480	C₂×C₄	C₂²×#334	1	1	yes	characteristic
481	C₂×C₄	C₂²×#365	1	1	yes	characteristic
482	C₂×C₄	C₂²×#365	1	1	yes	characteristic
483	C₈	—	2	1	no	—
484	C₈	—	2	2	no	—
485	C₈	—	2	1	no	—
486	C₈	—	2	1	no	—
487	C₈	—	2	2	no	—
488	C₈	—	4	1	no	—
489	C₈	—	4	1	no	—
490	C₈	—	4	1	no	—
491	C₈	—	4	2	no	—
492	C₈	—	4	1	no	—
493	C₈	—	4	2	no	—
494	C₈	#33398	1	1	yes	characteristic
495	C₈	#33401	1	1	yes	characteristic
496	C₂²	—	2	1	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	C₂²×#1368	1	1	yes	characteristic
503	C₄	—	2	1	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	1	no	—
510	C₄	#151024	1	2	yes	—
511	C₄	#483325	1	1	yes	characteristic
512	C₄	#483327	1	1	yes	characteristic
513	C₂	—	4	1	no	—
514	C₂	—	4	2	no	—
515	C₂	C₂×#151024	1	1	yes	characteristic
516	C₂	#72224974	1	1	yes	characteristic
517	C₂	#72231934	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1368
commutator	C₂×C₁₆	C₂³×C₈
Frattini, cosocle	#1311	C₂⁴
prime radical	C₂×#41	#365
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ C₈×#131 ◁ #479943 ◁ G
LECS	G ▷ #1311 ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #72231942	C₂	semidirect
4. #72231939	C₂	semidirect
6. #72231936	C₂	semidirect
7. #72231935	C₂	semidirect
8. #72231932	C₂	semidirect
9. #72231929	C₂	semidirect
10. #72231929	C₂	semidirect
11. #72225212	C₂	semidirect

Maximal subgroups

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

subgroup	index
#72231957	2
#72231942	2
#72231941	2
#72231939	2
#72231938	2
#72231936	2
#72231935	2
#72231932	2
#72231929	2
#72225212	2