Subgroups — #203675

Order 512.

706 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21978	C₂	1	1	yes	maximal, characteristic
2	#20549	C₂	1	1	yes	maximal, characteristic
3	C₄×#424	C₂	1	1	yes	maximal, characteristic
4	C₂×#1569	C₂	1	1	yes	maximal, characteristic
5	C₂×#1568	C₂	1	1	yes	maximal, characteristic
6	#9606	C₂	1	1	yes	maximal, characteristic, complemented
7	#9606	C₂	1	1	yes	maximal, characteristic, complemented
8	#9605	C₂	1	1	yes	maximal, characteristic, complemented
9	#9604	C₂	1	1	yes	maximal, characteristic, complemented
10	#9603	C₂	1	1	yes	maximal, characteristic, complemented
11	#9603	C₂	1	1	yes	maximal, characteristic, complemented
12	#9602	C₂	1	1	yes	maximal, characteristic, complemented
13	#9601	C₂	1	1	yes	maximal, characteristic, complemented
14	#7876	C₂	1	1	yes	maximal, characteristic
15	#7874	C₂	1	1	yes	maximal, characteristic
16	C₂×#432	C₂²	1	1	yes	characteristic
17	C₂×#432	C₂²	1	1	yes	characteristic
18	C₂×#424	C₄	1	1	yes	characteristic
19	C₂×#424	C₄	1	1	yes	characteristic
20	C₂×#423	C₂²	1	1	yes	characteristic
21	C₂×#423	C₂²	1	1	yes	characteristic
22	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
24	C₄×#117	C₂²	1	1	yes	characteristic
25	#1940	—	2	1	no	—
26	#1940	—	2	1	no	—
27	#1851	—	2	1	no	—
28	#1851	—	2	1	no	—
29	#1842	C₂²	1	1	yes	characteristic
30	#1842	C₂²	1	1	yes	characteristic
31	#1831	C₂²	1	1	yes	characteristic
32	#1831	C₂²	1	1	yes	characteristic
33	#1771	—	2	1	no	—
34	#1771	—	2	1	no	—
35	#1768	C₄	1	1	yes	characteristic
36	#1768	C₄	1	1	yes	characteristic
37	#1768	C₄	1	1	yes	characteristic
38	#1768	C₄	1	1	yes	characteristic
39	#1767	C₂²	1	1	yes	characteristic
40	#1767	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	#1753	—	2	1	no	—
48	#1753	—	2	1	no	—
49	#1729	C₄	1	1	yes	characteristic
50	#1729	C₄	1	1	yes	characteristic
51	#1569	—	2	4	no	—
52	#1568	—	2	4	no	—
53	C₂×#335	C₂²	1	1	yes	characteristic
54	C₂×#335	C₂²	1	1	yes	characteristic
55	C₂×#335	C₂²	1	1	yes	characteristic
56	C₂×#335	C₂²	1	1	yes	characteristic
57	C₂×#334	C₂²	1	1	yes	characteristic
58	C₂×#334	C₂²	1	1	yes	characteristic
59	C₂×#334	C₂²	1	1	yes	characteristic
60	C₂×#334	C₂²	1	1	yes	characteristic
61	#1277	C₂²	1	1	yes	characteristic
62	#1277	C₂²	1	1	yes	characteristic
63	#1277	C₂²	1	1	yes	characteristic
64	#1277	C₂²	1	1	yes	characteristic
65	#1277	C₂²	1	1	yes	characteristic
66	#1277	C₂²	1	1	yes	characteristic
67	#1277	C₂²	1	1	yes	characteristic
68	#1277	C₂²	1	1	yes	characteristic
69	C₂²×M₁₆	—	2	1	no	—
70	C₂²×M₁₆	—	2	1	no	—
71	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₈	C₂×C₄	1	1	yes	characteristic
75	C₂×#117	C₂×C₄	1	1	yes	characteristic
76	C₂×#117	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₄²	C₂³	1	1	yes	characteristic
78	#432	—	2	2	no	—
79	#432	—	2	2	no	—
80	#432	—	2	2	no	—
81	#432	D₄	1	4	yes	—
82	#424	—	2	4	no	—
83	#424	—	2	4	no	—
84	#423	—	2	2	no	—
85	#423	—	2	2	no	—
86	#423	—	2	2	no	—
87	#423	Q₈	1	4	yes	—
88	C₂×C₄⋊C₈	—	2	1	no	—
89	C₂×C₄⋊C₈	—	2	1	no	—
90	C₂×C₄⋊C₈	—	2	1	no	—
91	C₂×C₄⋊C₈	—	2	1	no	—
92	C₂×C₄⋊C₈	—	2	1	no	—
93	C₂×C₄⋊C₈	—	2	1	no	—
94	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₈	—	2	1	no	—
111	C₂×C₂²⋊C₈	—	2	1	no	—
112	C₄×M₁₆	—	2	2	no	—
113	C₄×M₁₆	—	2	2	no	—
114	C₂×#97	—	2	1	no	—
115	C₂×#97	—	2	1	no	—
116	C₂×#97	—	2	1	no	—
117	C₂×#97	—	2	1	no	—
118	C₂×#97	C₂×C₄	1	1	yes	characteristic
119	C₂×#97	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄×C₈	—	2	2	no	—
121	C₂×C₄×C₈	—	2	2	no	—
122	C₂×C₄×C₈	—	2	1	no	—
123	C₂×C₄×C₈	—	2	1	no	—
124	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
128	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
129	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
130	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
131	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
132	C₄×C₄⋊C₄	Q₈	1	1	yes	characteristic
133	C₄×C₄⋊C₄	Q₈	1	1	yes	characteristic
134	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
135	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
136	C₄×C₂²⋊C₄	Q₈	1	1	yes	characteristic
137	C₄×C₂²⋊C₄	Q₈	1	1	yes	characteristic
138	#376	C₂×C₄	1	1	yes	characteristic
139	#376	C₂×C₄	1	1	yes	characteristic
140	C₄³	C₂³	1	1	yes	characteristic
141	C₄³	C₂³	1	1	yes	characteristic
142	#336	—	2	1	no	—
143	#336	—	2	1	no	—
144	#336	—	2	1	no	—
145	#336	—	2	1	no	—
146	#336	—	2	1	no	—
147	#336	—	2	1	no	—
148	#336	—	2	1	no	—
149	#336	—	2	1	no	—
150	#336	C₂×C₄	1	1	yes	characteristic
151	#336	C₂×C₄	1	1	yes	characteristic
152	#336	C₂×C₄	1	1	yes	characteristic
153	#336	C₂×C₄	1	1	yes	characteristic
154	#336	C₂×C₄	1	1	yes	characteristic
155	#336	C₂×C₄	1	1	yes	characteristic
156	#336	C₂×C₄	1	1	yes	characteristic
157	#336	C₂×C₄	1	1	yes	characteristic
158	#335	—	2	2	no	—
159	#335	—	2	2	no	—
160	#335	—	2	2	no	—
161	#335	—	2	2	no	—
162	#334	—	2	2	no	—
163	#334	—	2	2	no	—
164	#334	—	2	2	no	—
165	#334	—	2	2	no	—
166	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
167	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
168	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
169	C₂×M₁₆	—	2	2	no	—
170	C₂×M₁₆	—	2	2	no	—
171	C₂×M₁₆	—	2	4	no	—
172	C₂×M₁₆	—	2	2	no	—
173	C₂×M₁₆	—	2	2	no	—
174	C₂×M₁₆	—	4	1	no	—
175	C₂×M₁₆	—	4	1	no	—
176	C₂×M₁₆	—	4	2	no	—
177	C₂×M₁₆	—	8	1	no	—
178	C₂×M₁₆	—	8	1	no	—
179	C₂×M₁₆	—	8	1	no	—
180	C₂×M₁₆	—	8	1	no	—
181	C₂²×C₈	—	2	2	no	—
182	C₂²×C₈	—	2	2	no	—
183	C₂²×C₈	—	2	1	no	—
184	C₂²×C₈	—	2	1	no	—
185	C₂²×C₈	—	2	1	no	—
186	C₂²×C₈	—	2	1	no	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	—	2	2	no	—
189	C₂²×C₈	—	2	1	no	—
190	C₂²×C₈	—	2	1	no	—
191	C₂²×C₈	—	2	1	no	—
192	C₂²×C₈	—	2	1	no	—
193	C₂²×C₈	—	4	1	no	—
194	C₂²×C₈	—	4	1	no	—
195	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
203	#117	—	2	2	no	—
204	#117	—	2	2	no	—
205	#117	—	4	1	no	—
206	#117	—	4	1	no	—
207	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
215	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
221	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
222	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
223	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
224	C₂×C₄²	C₂×D₄	1	2	yes	—
225	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
226	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
227	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
228	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
229	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
230	C₂×C₄²	C₂×Q₈	1	2	yes	—
231	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
232	C₂×C₄²	#41	1	2	yes	—
233	C₂×C₄²	#41	1	2	yes	—
234	C₂×C₄²	C₂⁴	1	1	yes	characteristic
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	4	no	—
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	4	2	no	—
255	C₄⋊C₈	—	8	1	no	—
256	C₄⋊C₈	—	8	1	no	—
257	C₄⋊C₈	—	8	1	no	—
258	C₄⋊C₈	—	8	1	no	—
259	C₄⋊C₈	M₁₆	1	4	yes	complemented
260	C₄⋊C₈	M₁₆	1	4	yes	complemented
261	C₄⋊C₈	C₂×D₄	1	2	yes	—
262	C₄⋊C₈	C₂×D₄	1	2	yes	—
263	C₄⋊C₈	C₂×Q₈	1	2	yes	—
264	C₄⋊C₈	C₂×Q₈	1	2	yes	—
265	C₂²⋊C₈	—	2	4	no	—
266	C₂²⋊C₈	—	4	2	no	—
267	#97	—	2	2	no	—
268	#97	—	2	2	no	—
269	#97	—	2	4	no	—
270	#97	—	4	2	no	—
271	#97	—	8	1	no	—
272	#97	—	8	1	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	2	2	no	—
275	C₄×C₈	—	2	1	no	—
276	C₄×C₈	—	2	1	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	—	8	1	no	—
284	C₄×C₈	—	8	1	no	—
285	#95	C₄⋊C₄	1	1	yes	characteristic
286	#95	C₄⋊C₄	1	1	yes	characteristic
287	#95	C₄⋊C₄	1	1	yes	characteristic
288	#95	C₄⋊C₄	1	1	yes	characteristic
289	#95	C₄⋊C₄	1	1	yes	characteristic
290	#95	C₄⋊C₄	1	1	yes	characteristic
291	#95	C₄⋊C₄	1	1	yes	characteristic
292	#95	C₄⋊C₄	1	1	yes	characteristic
293	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
315	C₂²×C₄	C₄×D₄	1	2	yes	—
316	C₂²×C₄	C₄×Q₈	1	2	yes	—
317	C₂²×C₄	#121	1	2	yes	—
318	C₂²×C₄	C₂²⋊Q₈	1	2	yes	—
319	C₂²×C₄	#125	1	2	yes	—
320	C₂²×C₄	C₄⋊Q₈	1	2	yes	—
321	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
324	M₁₆	—	4	4	no	—
325	M₁₆	—	4	4	no	—
326	M₁₆	—	8	4	no	—
327	M₁₆	—	8	4	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	—	4	4	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	C₂×M₁₆	1	2	yes	—
375	C₂×C₈	C₂×M₁₆	1	2	yes	—
376	C₂×C₈	C₂×M₁₆	1	2	yes	—
377	C₂×C₈	C₂×M₁₆	1	2	yes	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	4	1	no	—
403	C₄²	—	4	1	no	—
404	C₄²	C₄×D₄	1	2	yes	—
405	C₄²	C₄×Q₈	1	2	yes	—
406	C₄²	#121	1	2	yes	—
407	C₄²	C₂²⋊Q₈	1	2	yes	—
408	C₄²	#125	1	2	yes	—
409	C₄²	C₄⋊Q₈	1	2	yes	—
410	C₄²	C₂×M₁₆	1	2	yes	—
411	C₄²	C₂×M₁₆	1	2	yes	—
412	C₄²	C₂²×D₄	1	1	yes	characteristic
413	C₄²	C₂²×Q₈	1	1	yes	characteristic
414	C₄²	C₂×#41	1	1	yes	characteristic
415	C₄²	C₂×#41	1	1	yes	characteristic
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	#389	1	2	yes	—
423	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	#389	1	2	yes	—
465	C₂×C₄	#389	1	2	yes	—
466	C₂×C₄	#389	1	2	yes	—
467	C₂×C₄	#423	1	2	yes	—
468	C₂×C₄	#423	1	2	yes	—
469	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
470	C₂×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
471	C₂×C₄	C₂×#121	1	1	yes	characteristic
472	C₂×C₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
473	C₂×C₄	C₂×#125	1	1	yes	characteristic
474	C₂×C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
475	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
476	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
477	C₂×C₄	#568	1	1	yes	characteristic
478	C₂×C₄	#568	1	1	yes	characteristic
479	C₂×C₄	#576	1	1	yes	characteristic
480	C₂×C₄	#577	1	1	yes	characteristic
481	C₂×C₄	#577	1	1	yes	characteristic
482	C₂×C₄	#578	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	2	2	no	—
486	C₈	—	2	2	no	—
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₈	—	4	1	no	—
490	C₈	—	4	1	no	—
491	C₈	—	4	1	no	—
492	C₈	—	4	1	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₈	—	8	1	no	—
496	C₈	—	8	1	no	—
497	C₈	—	8	1	no	—
498	C₈	—	8	1	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	C₂×#389	1	1	yes	characteristic
507	C₂²	C₂×#423	1	1	yes	characteristic
508	C₂²	#2905	1	1	yes	characteristic
509	C₂²	#2912	1	1	yes	characteristic
510	C₂²	#2913	1	1	yes	characteristic
511	C₂²	#2916	1	1	yes	characteristic
512	C₂²	#2916	1	1	yes	characteristic
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	D₄×M₁₆	1	1	yes	characteristic
527	C₄	D₄×M₁₆	1	1	yes	characteristic
528	C₄	Q₈×M₁₆	1	1	yes	characteristic
529	C₄	Q₈×M₁₆	1	1	yes	characteristic
530	C₄	#3045	1	1	yes	characteristic
531	C₄	#3046	1	1	yes	characteristic
532	C₄	#3081	1	1	yes	characteristic
533	C₄	#3082	1	1	yes	characteristic
534	C₂	—	4	2	no	—
535	C₂	#17798	1	1	yes	characteristic
536	C₂	#17799	1	1	yes	characteristic
537	C₂	#17824	1	1	yes	characteristic
538	C₂	#17825	1	1	yes	characteristic
539	C₂	#21146	1	1	yes	characteristic
540	C₂	#21175	1	1	yes	characteristic
541	C₂	#21178	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄
commutator	C₂²×C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂³	C₂²×C₄⋊C₄
prime radical	C₂⁴	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
6. #9606	C₂	semidirect
7. #9606	C₂	semidirect
8. #9605	C₂	semidirect
9. #9604	C₂	semidirect
10. #9603	C₂	semidirect
11. #9603	C₂	semidirect
12. #9602	C₂	semidirect
13. #9601	C₂	semidirect
259. C₄⋊C₈	M₁₆	semidirect
260. C₄⋊C₈	M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#21978	2
#20549	2
C₄×#424	2
C₂×#1569	2
C₂×#1568	2
#9606	2
#9605	2
#9604	2
#9603	2
#9602	2
#9601	2
#7876	2
#7874	2