Subgroups — #7624992

Order 512.

1375 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62434	C₂	1	2	yes	maximal, complemented
2	#33968	C₂	1	2	yes	maximal, complemented
3	#33963	C₂	1	1	yes	maximal, characteristic, complemented
4	#33960	C₂	1	1	yes	maximal, characteristic, complemented
5	#33853	C₂	1	1	yes	maximal, characteristic, complemented
6	#33851	C₂	1	1	yes	maximal, characteristic, complemented
7	#33851	C₂	1	1	yes	maximal, characteristic, complemented
8	#33849	C₂	1	1	yes	maximal, characteristic, complemented
9	#33846	C₂	1	1	yes	maximal, characteristic, complemented
10	#33846	C₂	1	1	yes	maximal, characteristic, complemented
11	#33841	C₂	1	2	yes	maximal, complemented
12	#33837	C₂	1	2	yes	maximal, complemented
13	#33833	C₂	1	2	yes	maximal, complemented
14	#33788	C₂	1	2	yes	maximal, complemented
15	#33787	C₂	1	2	yes	maximal, complemented
16	#33785	C₂	1	2	yes	maximal, complemented
17	#33741	C₂	1	1	yes	maximal, characteristic, complemented
18	#33740	C₂	1	1	yes	maximal, characteristic, complemented
19	#33735	C₂	1	1	yes	maximal, characteristic, complemented
20	#33721	C₂	1	1	yes	maximal, characteristic, complemented
21	#33720	C₂	1	1	yes	maximal, characteristic, complemented
22	#33713	C₂	1	1	yes	maximal, characteristic, complemented
23	#33480	C₂	1	1	yes	maximal, characteristic, complemented
24	#3562	—	2	2	no	—
25	C₂×#510	C₂²	1	2	yes	complemented
26	C₂×#509	C₂²	1	2	yes	—
27	C₂×#508	C₂²	1	1	yes	characteristic
28	C₂×#508	C₂²	1	1	yes	characteristic
29	C₂×#508	C₂²	1	1	yes	characteristic
30	C₂×#508	C₂²	1	2	yes	complemented
31	C₂×#508	C₂²	1	1	yes	characteristic, complemented
32	C₂²×Q₃₂	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₁₆	C₂²	1	1	yes	characteristic
34	#3401	—	2	2	no	—
35	#3396	C₂²	1	2	yes	complemented
36	#3393	C₂²	1	2	yes	complemented
37	#3287	C₂²	1	2	yes	complemented
38	#3285	C₂²	1	2	yes	—
39	#3285	C₂²	1	2	yes	complemented
40	#3283	C₂²	1	2	yes	—
41	#3280	C₂²	1	2	yes	—
42	#3280	C₂²	1	2	yes	—
43	#3275	—	2	2	no	—
44	#3271	—	2	2	no	—
45	#3267	—	2	2	no	—
46	#3222	—	2	2	no	—
47	#3221	—	2	2	no	—
48	#3219	—	2	2	no	—
49	#3177	C₂²	1	2	yes	—
50	#3176	C₂²	1	2	yes	complemented
51	#3168	C₂²	1	2	yes	complemented
52	#3156	C₂²	1	2	yes	complemented
53	#3155	C₂²	1	2	yes	—
54	#3147	C₂²	1	2	yes	complemented
55	#2966	C₂²	1	1	yes	characteristic
56	#2253	C₂²	1	1	yes	characteristic, complemented
57	#2251	C₂²	1	2	yes	complemented
58	#2251	C₂²	1	2	yes	complemented
59	#2250	C₂²	1	2	yes	—
60	#2250	C₂²	1	2	yes	—
61	#2249	C₂²	1	1	yes	characteristic
62	#2249	C₂²	1	1	yes	characteristic
63	#2249	C₂²	1	1	yes	characteristic
64	#2249	C₂²	1	1	yes	characteristic
65	#2249	C₂²	1	2	yes	complemented
66	#2249	C₂²	1	1	yes	characteristic, complemented
67	#2248	C₂²	1	2	yes	complemented
68	#2247	C₂²	1	1	yes	characteristic, complemented
69	#2247	C₂²	1	1	yes	characteristic, complemented
70	#2246	C₂²	1	1	yes	characteristic
71	#2246	C₂²	1	1	yes	characteristic
72	#2245	C₂²	1	2	yes	complemented
73	#2244	C₂²	1	2	yes	complemented
74	#2242	C₂²	1	2	yes	complemented
75	#2219	C₂²	1	2	yes	—
76	#2218	C₂²	1	2	yes	complemented
77	#2217	C₂²	1	2	yes	complemented
78	#2216	C₂²	1	1	yes	characteristic
79	#2216	C₂²	1	1	yes	characteristic
80	#2216	C₂²	1	1	yes	characteristic, complemented
81	#2215	C₂²	1	1	yes	characteristic
82	#2215	C₂²	1	1	yes	characteristic
83	#2215	C₂²	1	1	yes	characteristic, complemented
84	#2211	C₂²	1	2	yes	complemented
85	#2211	C₂²	1	2	yes	complemented
86	#2211	C₂²	1	2	yes	complemented
87	#2211	C₂²	1	2	yes	complemented
88	#2210	C₂²	1	2	yes	—
89	#2210	C₂²	1	2	yes	—
90	#2210	C₂²	1	2	yes	complemented
91	#2210	C₂²	1	2	yes	complemented
92	#2208	C₂²	1	2	yes	complemented
93	#2208	C₂²	1	2	yes	complemented
94	#2207	C₂²	1	2	yes	complemented
95	#2207	C₂²	1	2	yes	complemented
96	#2189	C₂²	1	2	yes	—
97	#2189	C₂²	1	2	yes	—
98	#2189	C₂²	1	2	yes	complemented
99	#2189	C₂²	1	2	yes	complemented
100	#2187	C₂²	1	2	yes	—
101	#2187	C₂²	1	2	yes	—
102	#2186	C₂²	1	2	yes	—
103	#2186	C₂²	1	2	yes	—
104	#2186	C₂²	1	2	yes	complemented
105	#2186	C₂²	1	2	yes	complemented
106	#2185	C₂²	1	2	yes	complemented
107	#2185	C₂²	1	2	yes	complemented
108	#2183	C₂²	1	1	yes	characteristic, complemented
109	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
110	#2177	C₂²	1	2	yes	complemented
111	#2176	C₂²	1	2	yes	complemented
112	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₃₂	C₂²	1	2	yes	complemented
116	C₄×D₁₆	C₂²	1	1	yes	characteristic
117	C₄×D₁₆	C₂²	1	1	yes	characteristic
118	C₄×D₁₆	C₂²	1	1	yes	characteristic, complemented
119	#2169	C₂²	1	1	yes	characteristic
120	#2168	C₂²	1	1	yes	characteristic
121	#2168	C₂²	1	1	yes	characteristic, complemented
122	D₄×C₁₆	C₂²	1	1	yes	characteristic
123	D₄×C₁₆	C₂²	1	1	yes	characteristic
124	D₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
125	#2164	C₂²	1	1	yes	characteristic
126	#2164	C₂²	1	1	yes	characteristic, complemented
127	#2163	C₂²	1	1	yes	characteristic, complemented
128	#2108	C₂²	1	1	yes	characteristic
129	#2108	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
131	C₂×#137	—	2	2	no	—
132	C₂×AGL(1,ℤ/8)	—	2	2	no	—
133	C₂×#135	—	2	2	no	—
134	C₂×#135	C₂³	1	2	yes	—
135	C₂×#135	C₂³	1	2	yes	—
136	C₂×#135	C₂³	1	2	yes	—
137	C₂×#135	C₂³	1	2	yes	—
138	C₂²×Q₁₆	C₂³	1	2	yes	—
139	C₂²×D₈	C₂³	1	2	yes	—
140	#562	—	4	2	no	—
141	#560	—	4	2	no	—
142	#559	—	2	2	no	—
143	#556	—	2	2	no	—
144	#553	—	4	2	no	—
145	#551	—	4	2	no	—
146	#550	—	2	2	no	—
147	#548	—	2	2	no	—
148	#548	—	2	2	no	—
149	#547	—	2	2	no	—
150	#546	—	2	2	no	—
151	#546	—	2	2	no	—
152	#541	—	2	2	no	—
153	#540	—	2	2	no	—
154	#540	—	4	2	no	—
155	#539	—	4	2	no	—
156	#538	—	4	2	no	—
157	#538	—	4	2	no	—
158	#536	—	2	2	no	—
159	#535	—	2	2	no	—
160	#532	—	2	2	no	—
161	#529	—	2	2	no	—
162	#529	D₄	1	1	yes	characteristic
163	#510	—	4	4	no	—
164	#509	—	4	4	no	—
165	#508	—	4	2	no	—
166	#508	—	4	2	no	—
167	#508	—	4	2	no	—
168	#508	—	4	2	no	—
169	#508	—	4	4	no	—
170	C₂×Q₃₂	—	4	2	no	—
171	C₂×Q₃₂	C₂³	1	1	yes	characteristic
172	C₂×Q₃₂	C₂³	1	1	yes	characteristic
173	C₂×Q₃₂	C₂³	1	1	yes	characteristic
174	C₂×Q₃₂	C₂³	1	2	yes	—
175	C₂×Q₃₂	C₂³	1	2	yes	—
176	C₂×Q₃₂	C₂³	1	2	yes	—
177	C₂×SD₃₂	C₂³	1	2	yes	—
178	C₂×SD₃₂	C₂³	1	2	yes	—
179	C₂×SD₃₂	C₂³	1	2	yes	—
180	C₂×SD₃₂	C₂³	1	2	yes	—
181	C₂×SD₃₂	C₂³	1	2	yes	—
182	C₂×SD₃₂	C₂³	1	2	yes	—
183	C₂×SD₃₂	C₂³	1	2	yes	—
184	C₂×SD₃₂	C₂³	1	2	yes	—
185	C₂×SD₃₂	C₂³	1	2	yes	—
186	C₂×D₁₆	—	4	2	no	—
187	C₂×D₁₆	C₂³	1	1	yes	characteristic
188	C₂×D₁₆	C₂³	1	1	yes	characteristic
189	C₂×D₁₆	C₂³	1	1	yes	characteristic
190	C₂×D₁₆	C₂³	1	2	yes	—
191	C₂×D₁₆	C₂³	1	2	yes	—
192	C₂×D₁₆	C₂³	1	2	yes	—
193	C₂×M₃₂	C₂³	1	1	yes	characteristic
194	C₂×M₃₂	C₂³	1	1	yes	characteristic
195	C₂²×C₁₆	C₂³	1	1	yes	characteristic
196	C₂²×C₁₆	C₂³	1	1	yes	characteristic
197	C₂²×C₁₆	C₂³	1	1	yes	characteristic
198	C₂²×C₁₆	C₂³	1	1	yes	characteristic
199	#499	C₂³	1	2	yes	—
200	#497	—	2	2	no	—
201	#497	—	2	2	no	—
202	#496	—	2	2	no	—
203	#496	—	2	2	no	—
204	#495	—	2	2	no	—
205	#495	C₂³	1	2	yes	—
206	#495	C₂³	1	2	yes	—
207	#495	C₂³	1	2	yes	—
208	#495	C₂³	1	2	yes	—
209	#495	C₂³	1	2	yes	—
210	#494	C₂³	1	2	yes	—
211	#494	C₂³	1	2	yes	—
212	#493	C₂³	1	2	yes	—
213	#493	C₂³	1	2	yes	—
214	#492	—	2	2	no	—
215	#491	—	2	2	no	—
216	#490	—	2	2	no	—
217	#488	—	2	2	no	—
218	#470	—	2	2	no	—
219	#469	—	2	2	no	—
220	#467	C₂³	1	2	yes	—
221	#467	C₂³	1	2	yes	—
222	#467	C₂³	1	2	yes	—
223	#466	C₂³	1	2	yes	—
224	#466	C₂³	1	2	yes	—
225	#466	C₂³	1	2	yes	—
226	#465	—	2	2	no	—
227	#464	—	2	2	no	—
228	#464	—	2	2	no	—
229	#464	—	2	2	no	—
230	#464	—	2	2	no	—
231	#463	—	2	2	no	—
232	#463	—	2	2	no	—
233	#463	—	2	2	no	—
234	#463	—	2	2	no	—
235	#461	—	2	2	no	—
236	#461	—	2	2	no	—
237	#460	—	2	2	no	—
238	#460	—	2	2	no	—
239	#452	—	2	2	no	—
240	#452	—	2	2	no	—
241	#452	—	2	2	no	—
242	#452	—	2	2	no	—
243	#450	—	2	2	no	—
244	#450	—	2	2	no	—
245	#449	—	2	2	no	—
246	#449	—	2	2	no	—
247	#449	—	2	2	no	—
248	#449	—	2	2	no	—
249	#448	—	2	2	no	—
250	#448	—	2	2	no	—
251	#446	D₄	1	1	yes	characteristic
252	C₈×Q₈	C₂³	1	1	yes	characteristic
253	#442	—	2	2	no	—
254	#441	—	2	2	no	—
255	C₄×Q₁₆	C₂³	1	2	yes	—
256	C₄×Q₁₆	C₂³	1	2	yes	—
257	C₄×Q₁₆	C₂³	1	2	yes	—
258	C₄×SD₁₆	—	2	2	no	—
259	C₄×D₈	C₂³	1	2	yes	—
260	C₄×D₈	C₂³	1	2	yes	—
261	C₄×D₈	C₂³	1	2	yes	—
262	#436	D₄	1	1	yes	characteristic
263	#435	D₄	1	1	yes	characteristic
264	#435	D₄	1	1	yes	characteristic
265	C₈×D₄	C₂³	1	1	yes	characteristic
266	C₈×D₄	C₂³	1	1	yes	characteristic
267	C₈×D₄	C₂³	1	1	yes	characteristic
268	#433	D₄	1	1	yes	characteristic
269	#433	D₄	1	1	yes	characteristic
270	#432	D₄	1	1	yes	characteristic
271	#405	C₂³	1	1	yes	characteristic
272	#405	C₂³	1	1	yes	characteristic
273	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
274	#367	C₂³	1	2	yes	—
275	#366	C₂³	1	1	yes	characteristic
276	#366	C₂³	1	1	yes	characteristic
277	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
278	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
279	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
280	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
281	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
282	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
283	#358	C₂³	1	2	yes	—
284	#358	C₂³	1	2	yes	—
285	#358	C₂³	1	2	yes	—
286	#358	C₂³	1	2	yes	—
287	#358	C₂³	1	2	yes	—
288	#358	C₂³	1	2	yes	—
289	#357	C₂³	1	2	yes	—
290	#357	C₂³	1	2	yes	—
291	#357	C₂³	1	2	yes	—
292	#357	C₂³	1	2	yes	—
293	#357	C₂³	1	2	yes	—
294	#357	C₂³	1	2	yes	—
295	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
296	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
297	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
298	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
299	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
300	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
301	#346	C₂³	1	1	yes	characteristic
302	#346	C₂³	1	1	yes	characteristic
303	#346	C₂³	1	1	yes	characteristic
304	#346	C₂³	1	1	yes	characteristic
305	C₄×C₁₆	C₂³	1	1	yes	characteristic
306	C₄×C₁₆	C₂³	1	1	yes	characteristic
307	C₄×C₁₆	C₂³	1	1	yes	characteristic
308	C₄×C₁₆	C₂³	1	1	yes	characteristic
309	C₄×C₁₆	C₂³	1	1	yes	characteristic
310	C₄×C₁₆	C₂³	1	1	yes	characteristic
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	2	no	—
314	C₂×#41	—	2	2	no	—
315	C₂²×Q₈	—	2	2	no	—
316	C₂²×D₄	—	2	2	no	—
317	#137	—	8	4	no	—
318	AGL(1,ℤ/8)	—	8	4	no	—
319	#135	—	4	2	no	—
320	#135	—	4	2	no	—
321	#135	—	4	2	no	—
322	#135	—	4	2	no	—
323	#135	—	4	2	no	—
324	#135	—	4	2	no	—
325	#135	—	4	2	no	—
326	#135	—	4	2	no	—
327	#135	—	8	4	no	—
328	C₂×Q₁₆	—	2	2	no	—
329	C₂×Q₁₆	—	2	2	no	—
330	C₂×Q₁₆	—	2	2	no	—
331	C₂×Q₁₆	—	4	2	no	—
332	C₂×Q₁₆	—	4	2	no	—
333	C₂×Q₁₆	C₂⁴	1	2	yes	—
334	C₂×Q₁₆	C₂⁴	1	2	yes	—
335	C₂×Q₁₆	C₂⁴	1	2	yes	—
336	C₂×SD₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×SD₁₆	—	2	2	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×D₈	—	2	2	no	—
346	C₂×D₈	—	2	2	no	—
347	C₂×D₈	—	2	2	no	—
348	C₂×D₈	—	4	2	no	—
349	C₂×D₈	—	4	2	no	—
350	C₂×D₈	C₂⁴	1	2	yes	—
351	C₂×D₈	C₂⁴	1	2	yes	—
352	C₂×D₈	C₂⁴	1	2	yes	—
353	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
354	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₈	C₂⁴	1	1	yes	characteristic
357	C₂²×C₈	C₂⁴	1	1	yes	characteristic
358	C₂²×C₈	C₂⁴	1	1	yes	characteristic
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	#127	—	2	2	no	—
362	#127	—	2	2	no	—
363	#127	—	4	2	no	—
364	#126	—	4	2	no	—
365	#126	—	4	2	no	—
366	#126	—	4	2	no	—
367	#126	—	4	2	no	—
368	#126	—	4	2	no	—
369	#126	D₈	1	1	yes	characteristic
370	#126	D₈	1	1	yes	characteristic
371	#125	—	2	2	no	—
372	#125	—	4	2	no	—
373	#125	—	4	2	no	—
374	#125	D₈	1	1	yes	characteristic
375	#124	—	2	2	no	—
376	#124	—	2	2	no	—
377	#124	—	2	2	no	—
378	#124	—	2	2	no	—
379	#124	—	2	2	no	—
380	#124	—	4	2	no	—
381	#124	—	4	2	no	—
382	#124	—	4	2	no	—
383	#124	D₈	1	1	yes	characteristic
384	#123	—	4	2	no	—
385	#123	—	4	2	no	—
386	#123	—	4	2	no	—
387	#123	—	4	2	no	—
388	#123	—	4	2	no	—
389	#123	—	4	2	no	—
390	#123	—	4	2	no	—
391	#123	—	4	2	no	—
392	#123	—	4	2	no	—
393	#123	—	4	2	no	—
394	#123	—	4	2	no	—
395	#123	D₈	1	1	yes	characteristic
396	#123	D₈	1	1	yes	characteristic
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	4	2	no	—
401	C₂²⋊Q₈	—	4	2	no	—
402	C₂²⋊Q₈	—	4	2	no	—
403	C₂²⋊Q₈	—	4	2	no	—
404	C₂²⋊Q₈	—	4	2	no	—
405	C₂²⋊Q₈	D₈	1	1	yes	characteristic
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	4	2	no	—
410	#121	—	4	2	no	—
411	#121	—	4	2	no	—
412	#121	—	4	2	no	—
413	#121	—	4	2	no	—
414	#121	—	4	2	no	—
415	#121	—	4	2	no	—
416	#121	—	4	2	no	—
417	#121	—	4	2	no	—
418	#121	—	4	2	no	—
419	#121	—	4	2	no	—
420	#121	—	4	2	no	—
421	#121	—	4	2	no	—
422	#121	D₈	1	1	yes	characteristic
423	#120	—	4	2	no	—
424	#120	—	4	2	no	—
425	#120	—	4	2	no	—
426	#120	—	4	2	no	—
427	C₄×Q₈	—	2	2	no	—
428	C₄×Q₈	—	2	2	no	—
429	C₄×Q₈	—	2	2	no	—
430	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	4	2	no	—
435	C₄×D₄	—	4	2	no	—
436	C₄×D₄	—	4	2	no	—
437	C₄×D₄	—	4	2	no	—
438	C₄×D₄	—	4	2	no	—
439	C₄×D₄	—	4	2	no	—
440	C₄×D₄	—	4	2	no	—
441	C₄×D₄	C₂×D₄	1	1	yes	characteristic
442	C₄×D₄	C₂×D₄	1	1	yes	characteristic
443	C₄×D₄	C₂×D₄	1	1	yes	characteristic
444	#117	—	4	2	no	—
445	#117	—	4	2	no	—
446	#117	C₂×D₄	1	1	yes	characteristic
447	#117	C₂×D₄	1	1	yes	characteristic
448	C₂×C₄⋊C₄	—	4	2	no	—
449	C₂×C₂²⋊C₄	—	4	2	no	—
450	C₂×C₂²⋊C₄	—	4	2	no	—
451	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
452	Q₃₂	—	2	2	no	—
453	Q₃₂	—	2	2	no	—
454	Q₃₂	—	2	2	no	—
455	Q₃₂	—	2	4	no	—
456	Q₃₂	—	4	2	no	—
457	Q₃₂	—	4	2	no	—
458	SD₃₂	—	2	4	no	—
459	SD₃₂	—	4	2	no	—
460	SD₃₂	—	4	2	no	—
461	SD₃₂	—	4	2	no	—
462	SD₃₂	—	4	2	no	—
463	SD₃₂	—	4	2	no	—
464	SD₃₂	—	4	2	no	—
465	SD₃₂	—	4	2	no	—
466	SD₃₂	—	4	2	no	—
467	D₁₆	—	2	2	no	—
468	D₁₆	—	2	2	no	—
469	D₁₆	—	2	2	no	—
470	D₁₆	—	2	4	no	—
471	D₁₆	—	4	2	no	—
472	D₁₆	—	4	2	no	—
473	M₃₂	—	2	2	no	—
474	M₃₂	—	2	2	no	—
475	C₂×C₁₆	—	2	2	no	—
476	C₂×C₁₆	—	2	2	no	—
477	C₂×C₁₆	—	2	2	no	—
478	C₂×C₁₆	—	2	2	no	—
479	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
480	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
481	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
482	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
483	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
484	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
485	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
486	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
487	#107	C₂⁴	1	2	yes	—
488	#107	C₂⁴	1	2	yes	—
489	#106	—	2	2	no	—
490	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
491	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
492	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
493	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
494	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
495	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
496	#103	—	2	2	no	—
497	#103	—	2	2	no	—
498	#103	—	2	2	no	—
499	#103	—	2	2	no	—
500	#103	—	2	2	no	—
501	#103	—	2	2	no	—
502	#102	—	2	2	no	—
503	#102	—	2	2	no	—
504	#102	—	2	2	no	—
505	#102	—	2	2	no	—
506	#102	—	2	2	no	—
507	#102	—	2	2	no	—
508	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
509	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
510	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
511	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
512	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
513	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
514	#97	C₂×D₄	1	1	yes	characteristic
515	#97	C₂×D₄	1	1	yes	characteristic
516	#97	C₂×D₄	1	1	yes	characteristic
517	#97	C₂×D₄	1	1	yes	characteristic
518	C₄×C₈	C₂×D₄	1	1	yes	characteristic
519	C₄×C₈	C₂×D₄	1	1	yes	characteristic
520	C₄×C₈	C₂⁴	1	1	yes	characteristic
521	C₄×C₈	C₂⁴	1	1	yes	characteristic
522	C₄×C₈	C₂⁴	1	1	yes	characteristic
523	C₄×C₈	C₂⁴	1	1	yes	characteristic
524	C₂⁴	—	4	2	no	—
525	#41	—	8	2	no	—
526	#41	—	8	2	no	—
527	#41	—	8	2	no	—
528	#41	—	8	2	no	—
529	#41	—	8	2	no	—
530	#41	—	8	2	no	—
531	#41	—	8	2	no	—
532	#41	—	8	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	4	2	no	—
537	C₂×Q₈	—	8	2	no	—
538	C₂×Q₈	—	8	2	no	—
539	C₂×Q₈	C₂×D₈	1	1	yes	characteristic
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	2	no	—
547	C₂×D₄	—	4	2	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	—	4	2	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	—	4	2	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	8	2	no	—
556	C₂×D₄	—	8	2	no	—
557	C₂×D₄	C₂×D₈	1	1	yes	characteristic
558	C₂×D₄	C₂×D₈	1	1	yes	characteristic
559	C₂×D₄	C₂×D₈	1	1	yes	characteristic
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
570	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
573	Q₁₆	—	2	2	no	—
574	Q₁₆	—	2	2	no	—
575	Q₁₆	—	2	2	no	—
576	Q₁₆	—	2	2	no	—
577	Q₁₆	—	2	2	no	—
578	Q₁₆	—	2	2	no	—
579	Q₁₆	—	4	4	no	—
580	Q₁₆	—	8	2	no	—
581	Q₁₆	—	8	2	no	—
582	SD₁₆	—	4	4	no	—
583	SD₁₆	—	8	2	no	—
584	SD₁₆	—	8	2	no	—
585	SD₁₆	—	8	2	no	—
586	SD₁₆	—	8	2	no	—
587	SD₁₆	—	8	2	no	—
588	SD₁₆	—	8	2	no	—
589	SD₁₆	—	8	2	no	—
590	SD₁₆	—	8	2	no	—
591	D₈	—	2	2	no	—
592	D₈	—	2	2	no	—
593	D₈	—	2	2	no	—
594	D₈	—	2	2	no	—
595	D₈	—	2	2	no	—
596	D₈	—	2	2	no	—
597	D₈	—	4	4	no	—
598	D₈	—	8	2	no	—
599	D₈	—	8	2	no	—
600	M₁₆	—	2	2	no	—
601	M₁₆	—	2	2	no	—
602	C₂×C₈	—	2	2	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
611	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
613	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
614	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
615	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
616	C₂×C₈	C₂⁵	1	1	yes	characteristic
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
632	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
636	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
640	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
661	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
662	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
663	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
664	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
665	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
666	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
667	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
668	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
669	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
670	C₄²	—	4	2	no	—
671	C₄²	—	4	2	no	—
672	C₄²	—	4	2	no	—
673	C₄²	C₂×D₈	1	1	yes	characteristic
674	C₄²	C₂×D₈	1	1	yes	characteristic
675	C₄²	C₂²×D₄	1	1	yes	characteristic
676	C₄²	C₂²×D₄	1	1	yes	characteristic
677	C₄²	C₂²×D₄	1	1	yes	characteristic
678	C₄²	C₂²×D₄	1	1	yes	characteristic
679	C₁₆	—	2	1	no	—
680	C₁₆	—	2	1	no	—
681	C₁₆	—	2	1	no	—
682	C₁₆	—	2	1	no	—
683	C₁₆	—	2	1	no	—
684	C₁₆	—	2	1	no	—
685	C₁₆	H(5,𝔽₂)	1	2	yes	—
686	C₁₆	H(5,𝔽₂)	1	2	yes	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	16	2	no	—
691	C₂³	—	16	2	no	—
692	C₂³	—	16	2	no	—
693	C₂³	C₂²×D₈	1	1	yes	characteristic
694	C₂³	C₂²×D₈	1	1	yes	characteristic
695	C₂³	C₂²×D₈	1	1	yes	characteristic
696	Q₈	—	4	1	no	—
697	Q₈	—	4	2	no	—
698	Q₈	—	4	2	no	—
699	Q₈	—	4	2	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	2	no	—
702	Q₈	—	4	2	no	—
703	Q₈	—	16	2	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	1	no	—
707	D₄	—	4	2	no	—
708	D₄	—	4	2	no	—
709	D₄	—	4	2	no	—
710	D₄	—	4	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	4	2	no	—
713	D₄	—	16	2	no	—
714	D₄	—	16	2	no	—
715	D₄	—	16	2	no	—
716	D₄	—	16	2	no	—
717	D₄	—	16	2	no	—
718	D₄	—	16	2	no	—
719	D₄	—	16	2	no	—
720	D₄	—	16	2	no	—
721	D₄	—	16	2	no	—
722	D₄	—	16	2	no	—
723	D₄	—	16	2	no	—
724	D₄	—	16	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	16	2	no	—
739	C₂×C₄	—	16	2	no	—
740	C₂×C₄	—	16	2	no	—
741	C₂×C₄	—	16	2	no	—
742	C₂×C₄	—	16	2	no	—
743	C₂×C₄	—	16	2	no	—
744	C₂×C₄	—	16	2	no	—
745	C₂×C₄	—	16	2	no	—
746	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
757	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
758	C₈	—	2	1	no	—
759	C₈	—	2	1	no	—
760	C₈	—	2	1	no	—
761	C₈	—	2	1	no	—
762	C₈	—	2	1	no	—
763	C₈	—	2	1	no	—
764	C₈	#576	1	2	yes	—
765	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
766	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	8	2	no	—
777	C₂²	—	8	2	no	—
778	C₂²	—	8	2	no	—
779	C₂²	—	8	2	no	—
780	C₂²	—	8	2	no	—
781	C₂²	—	8	2	no	—
782	C₂²	—	8	2	no	—
783	C₂²	—	8	2	no	—
784	C₂²	—	8	2	no	—
785	C₂²	—	32	4	no	—
786	C₂²	C₂³×D₈	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	8	2	no	—
799	C₄	—	8	2	no	—
800	C₄	—	8	2	no	—
801	C₄	—	8	2	no	—
802	C₄	—	8	2	no	—
803	C₄	#3498	1	1	yes	characteristic
804	C₄	C₂×#576	1	1	yes	characteristic
805	C₂	—	4	1	no	—
806	C₂	—	4	1	no	—
807	C₂	—	4	1	no	—
808	C₂	—	16	2	no	—
809	C₂	—	16	2	no	—
810	C₂	—	16	2	no	—
811	C₂	#62415	1	1	yes	characteristic
812	C₂	#62635	1	1	yes	characteristic
813	C₂	#62635	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁵
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966 ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #62434	C₂	semidirect
2. #33968	C₂	semidirect
3. #33963	C₂	semidirect
4. #33960	C₂	semidirect
5. #33853	C₂	semidirect
6. #33851	C₂	semidirect
7. #33851	C₂	semidirect
8. #33849	C₂	semidirect
9. #33846	C₂	semidirect
10. #33846	C₂	semidirect
11. #33841	C₂	semidirect
12. #33837	C₂	semidirect
13. #33833	C₂	semidirect
14. #33788	C₂	semidirect
15. #33787	C₂	semidirect
16. #33785	C₂	semidirect
17. #33741	C₂	semidirect
18. #33740	C₂	semidirect
19. #33735	C₂	semidirect
20. #33721	C₂	semidirect
21. #33720	C₂	semidirect
22. #33713	C₂	semidirect
23. #33480	C₂	semidirect
25. C₂×#510	C₂²	semidirect
30. C₂×#508	C₂²	semidirect
31. C₂×#508	C₂²	semidirect
32. C₂²×Q₃₂	C₂²	semidirect
35. #3396	C₂²	semidirect
36. #3393	C₂²	semidirect
37. #3287	C₂²	semidirect
39. #3285	C₂²	semidirect
50. #3176	C₂²	semidirect
51. #3168	C₂²	semidirect
52. #3156	C₂²	semidirect
54. #3147	C₂²	semidirect
56. #2253	C₂²	semidirect
57. #2251	C₂²	semidirect
58. #2251	C₂²	semidirect
65. #2249	C₂²	semidirect
66. #2249	C₂²	semidirect
67. #2248	C₂²	semidirect
68. #2247	C₂²	semidirect
69. #2247	C₂²	semidirect
72. #2245	C₂²	semidirect
73. #2244	C₂²	semidirect
74. #2242	C₂²	semidirect
76. #2218	C₂²	semidirect
77. #2217	C₂²	semidirect
80. #2216	C₂²	semidirect
83. #2215	C₂²	semidirect
84. #2211	C₂²	semidirect
85. #2211	C₂²	semidirect
86. #2211	C₂²	semidirect
87. #2211	C₂²	semidirect
90. #2210	C₂²	semidirect
91. #2210	C₂²	semidirect
92. #2208	C₂²	semidirect
93. #2208	C₂²	semidirect
94. #2207	C₂²	semidirect
95. #2207	C₂²	semidirect
98. #2189	C₂²	semidirect
99. #2189	C₂²	semidirect
104. #2186	C₂²	semidirect
105. #2186	C₂²	semidirect
106. #2185	C₂²	semidirect
107. #2185	C₂²	semidirect
108. #2183	C₂²	semidirect
109. Q₈×C₁₆	C₂²	semidirect
110. #2177	C₂²	semidirect
111. #2176	C₂²	semidirect
112. C₄×Q₃₂	C₂²	semidirect
113. C₄×Q₃₂	C₂²	semidirect
114. C₄×Q₃₂	C₂²	semidirect
115. C₄×SD₃₂	C₂²	semidirect
118. C₄×D₁₆	C₂²	semidirect
121. #2168	C₂²	semidirect
124. D₄×C₁₆	C₂²	semidirect
126. #2164	C₂²	semidirect
127. #2163	C₂²	semidirect
129. #2108	C₂²	semidirect
130. C₂×C₄×C₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#62434	2
#33968	2
#33963	2
#33960	2
#33853	2
#33851	2
#33849	2
#33846	2
#33841	2
#33837	2
#33833	2
#33788	2
#33787	2
#33785	2
#33741	2
#33740	2
#33735	2
#33721	2
#33720	2
#33713	2
#33480	2