Subgroups — #7624824

Order 512.

1342 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62266	C₂	1	2	yes	maximal, complemented
2	#33908	C₂	1	1	yes	maximal, characteristic, complemented
3	#33906	C₂	1	1	yes	maximal, characteristic, complemented
4	#33903	C₂	1	1	yes	maximal, characteristic, complemented
5	#33901	C₂	1	1	yes	maximal, characteristic, complemented
6	#33886	C₂	1	2	yes	maximal, complemented
7	#33877	C₂	1	2	yes	maximal, complemented
8	#33876	C₂	1	2	yes	maximal, complemented
9	#33873	C₂	1	2	yes	maximal, complemented
10	#33853	C₂	1	1	yes	maximal, characteristic, complemented
11	#33846	C₂	1	1	yes	maximal, characteristic, complemented
12	#33846	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	#33823	C₂	1	2	yes	maximal, complemented
15	#33764	C₂	1	2	yes	maximal, complemented
16	#33760	C₂	1	2	yes	maximal, complemented
17	#33740	C₂	1	1	yes	maximal, characteristic, complemented
18	#33739	C₂	1	1	yes	maximal, characteristic, complemented
19	#33610	C₂	1	1	yes	maximal, characteristic, complemented
20	#33607	C₂	1	1	yes	maximal, characteristic, complemented
21	#33600	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#2215	C₂	1	1	yes	maximal, characteristic, complemented
23	#33432	C₂	1	1	yes	maximal, characteristic, complemented
24	#3542	—	2	2	no	—
25	C₂×#508	C₂²	1	1	yes	characteristic, complemented
26	C₂×#508	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₁₆	C₂²	1	1	yes	characteristic
28	C₂²×D₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×#504	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₁₆	C₂²	1	1	yes	characteristic, complemented
31	#3341	C₂²	1	2	yes	complemented
32	#3339	C₂²	1	2	yes	complemented
33	#3336	C₂²	1	2	yes	—
34	#3334	C₂²	1	2	yes	complemented
35	#3319	—	2	2	no	—
36	#3310	—	2	2	no	—
37	#3309	—	2	2	no	—
38	#3306	—	2	2	no	—
39	#3287	C₂²	1	2	yes	complemented
40	#3280	C₂²	1	2	yes	complemented
41	#3280	C₂²	1	2	yes	complemented
42	D₄×D₈	C₂²	1	2	yes	—
43	#3257	—	2	2	no	—
44	#3198	—	2	2	no	—
45	#3194	—	2	2	no	—
46	#3176	C₂²	1	2	yes	complemented
47	#3175	C₂²	1	2	yes	complemented
48	#3061	C₂²	1	2	yes	complemented
49	#3058	C₂²	1	2	yes	complemented
50	#3050	C₂²	1	2	yes	complemented
51	C₂×#466	C₂²	1	2	yes	complemented
52	#2929	C₂²	1	1	yes	characteristic
53	#2253	C₂²	1	1	yes	characteristic, complemented
54	#2252	C₂²	1	1	yes	characteristic, complemented
55	#2249	C₂²	1	1	yes	characteristic, complemented
56	#2246	C₂²	1	1	yes	characteristic, complemented
57	#2244	C₂²	1	2	yes	complemented
58	#2243	C₂²	1	2	yes	complemented
59	#2237	C₂²	1	2	yes	complemented
60	#2235	C₂²	1	2	yes	complemented
61	#2234	C₂²	1	2	yes	complemented
62	#2234	C₂²	1	2	yes	complemented
63	#2234	C₂²	1	2	yes	complemented
64	#2233	C₂²	1	2	yes	complemented
65	#2232	C₂²	1	2	yes	complemented
66	#2232	C₂²	1	2	yes	complemented
67	#2229	C₂²	1	2	yes	complemented
68	#2228	C₂²	1	2	yes	complemented
69	#2226	C₂²	1	2	yes	complemented
70	#2224	C₂²	1	2	yes	complemented
71	#2220	C₂²	1	2	yes	complemented
72	#2220	C₂²	1	2	yes	complemented
73	#2220	C₂²	1	2	yes	complemented
74	#2218	C₂²	1	2	yes	complemented
75	#2218	C₂²	1	2	yes	complemented
76	#2218	C₂²	1	2	yes	complemented
77	#2217	C₂²	1	2	yes	complemented
78	#2217	C₂²	1	2	yes	complemented
79	#2216	C₂²	1	1	yes	characteristic, complemented
80	#2216	C₂²	1	1	yes	characteristic, complemented
81	#2216	C₂²	1	1	yes	characteristic, complemented
82	#2215	C₂²	1	1	yes	characteristic
83	#2215	C₂²	1	1	yes	characteristic
84	#2215	C₂²	1	1	yes	characteristic
85	#2215	C₂²	1	2	yes	complemented
86	#2215	C₂²	1	1	yes	characteristic, complemented
87	#2215	C₂²	1	1	yes	characteristic, complemented
88	#2215	C₂²	1	1	yes	characteristic, complemented
89	#2215	C₂²	1	1	yes	characteristic, complemented
90	#2215	C₂²	1	2	yes	complemented
91	#2215	C₂²	1	1	yes	characteristic, complemented
92	#2215	C₂²	1	1	yes	characteristic, complemented
93	#2210	C₂²	1	2	yes	complemented
94	#2210	C₂²	1	2	yes	complemented
95	#2207	C₂²	1	2	yes	complemented
96	#2206	C₂²	1	2	yes	complemented
97	#2187	C₂²	1	2	yes	complemented
98	#2187	C₂²	1	2	yes	complemented
99	#2186	C₂²	1	2	yes	complemented
100	#2186	C₂²	1	2	yes	complemented
101	#2186	C₂²	1	2	yes	complemented
102	#2186	C₂²	1	2	yes	complemented
103	#2184	C₂²	1	2	yes	—
104	#2184	C₂²	1	2	yes	complemented
105	#2177	C₂²	1	2	yes	complemented
106	#2175	C₂²	1	2	yes	complemented
107	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₁₆	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₁₆	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₁₆	C₂²	1	1	yes	characteristic, complemented
111	#2168	C₂²	1	1	yes	characteristic
112	#2168	C₂²	1	1	yes	characteristic, complemented
113	#2168	C₂²	1	1	yes	characteristic, complemented
114	#2168	C₂²	1	1	yes	characteristic, complemented
115	D₄×C₁₆	C₂²	1	1	yes	characteristic
116	D₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
117	D₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
118	D₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
119	#2158	C₂²	1	1	yes	characteristic, complemented
120	#2158	C₂²	1	1	yes	characteristic, complemented
121	C₂×#366	C₂²	1	1	yes	characteristic, complemented
122	C₂×#366	C₂²	1	1	yes	characteristic, complemented
123	#2151	C₂²	1	1	yes	characteristic, complemented
124	#2140	C₂²	1	2	yes	complemented
125	#2139	C₂²	1	2	yes	complemented
126	#2138	C₂²	1	2	yes	complemented
127	C₂×#357	C₂²	1	2	yes	complemented
128	#2113	C₂²	1	1	yes	characteristic, complemented
129	#2112	C₂²	1	1	yes	characteristic, complemented
130	#2108	C₂²	1	1	yes	characteristic, complemented
131	C₂×#135	C₂³	1	2	yes	—
132	C₂×#135	C₂³	1	2	yes	—
133	C₂²×D₈	C₂³	1	2	yes	—
134	C₂²×D₈	C₂³	1	2	yes	—
135	C₂×#131	C₂³	1	1	yes	characteristic
136	C₂³×C₈	C₂³	1	1	yes	characteristic
137	#562	—	4	2	no	—
138	#560	—	4	2	no	—
139	#555	—	2	2	no	—
140	#553	—	2	2	no	—
141	#552	—	2	2	no	—
142	#551	—	4	2	no	—
143	#550	—	2	2	no	—
144	#547	—	2	2	no	—
145	#546	—	2	2	no	—
146	#546	—	2	2	no	—
147	#546	—	4	2	no	—
148	D₄²	—	2	2	no	—
149	#542	—	2	2	no	—
150	#540	—	2	2	no	—
151	#540	—	4	2	no	—
152	#538	—	4	2	no	—
153	#537	—	2	2	no	—
154	#535	—	2	2	no	—
155	#535	—	4	2	no	—
156	#534	—	4	2	no	—
157	#525	—	2	2	no	—
158	#525	D₄	1	1	yes	characteristic
159	C₂×#121	—	2	2	no	—
160	#508	—	4	2	no	—
161	#508	—	4	2	no	—
162	C₂×Q₃₂	C₂³	1	1	yes	characteristic
163	C₂×SD₃₂	C₂³	1	2	yes	—
164	C₂×SD₃₂	C₂³	1	2	yes	—
165	C₂×SD₃₂	C₂³	1	2	yes	—
166	C₂×D₁₆	—	4	2	no	—
167	C₂×D₁₆	—	4	2	no	—
168	C₂×D₁₆	C₂³	1	1	yes	characteristic
169	C₂×D₁₆	C₂³	1	1	yes	characteristic
170	C₂×D₁₆	C₂³	1	1	yes	characteristic
171	C₂×D₁₆	C₂³	1	2	yes	—
172	C₂×D₁₆	C₂³	1	2	yes	—
173	C₂×D₁₆	C₂³	1	2	yes	—
174	#504	—	4	2	no	—
175	C₂×M₃₂	C₂³	1	1	yes	characteristic
176	C₂×M₃₂	C₂³	1	1	yes	characteristic
177	C₂×M₃₂	C₂³	1	1	yes	characteristic
178	C₂×M₃₂	C₂³	1	1	yes	characteristic
179	C₂²×C₁₆	—	4	2	no	—
180	C₂²×C₁₆	C₂³	1	1	yes	characteristic
181	C₂²×C₁₆	C₂³	1	1	yes	characteristic
182	C₂²×C₁₆	C₂³	1	1	yes	characteristic
183	C₂²×C₁₆	C₂³	1	1	yes	characteristic
184	C₂²×C₁₆	C₂³	1	1	yes	characteristic
185	C₂²×C₁₆	C₂³	1	1	yes	characteristic
186	C₂²×C₁₆	C₂³	1	1	yes	characteristic
187	C₂²×C₁₆	C₂³	1	1	yes	characteristic
188	#500	C₂³	1	2	yes	—
189	#499	C₂³	1	2	yes	—
190	#495	C₂³	1	2	yes	—
191	#493	C₂³	1	2	yes	—
192	#490	—	2	2	no	—
193	#489	—	2	2	no	—
194	#485	—	2	2	no	—
195	#483	—	2	2	no	—
196	#482	—	2	2	no	—
197	#482	—	2	2	no	—
198	#482	—	2	2	no	—
199	#481	—	2	2	no	—
200	#480	—	2	2	no	—
201	#480	—	2	2	no	—
202	#479	—	2	2	no	—
203	#478	—	2	2	no	—
204	#476	—	2	2	no	—
205	#474	—	2	2	no	—
206	#469	—	2	2	no	—
207	#469	—	2	2	no	—
208	#469	—	2	2	no	—
209	#468	—	2	2	no	—
210	#468	—	2	2	no	—
211	#468	—	2	2	no	—
212	#467	C₂³	1	2	yes	—
213	#467	C₂³	1	2	yes	—
214	#467	C₂³	1	2	yes	—
215	#466	—	2	2	no	—
216	#466	—	2	2	no	—
217	#466	C₂³	1	2	yes	—
218	#466	C₂³	1	2	yes	—
219	#466	C₂³	1	2	yes	—
220	#466	C₂³	1	2	yes	—
221	#466	C₂³	1	2	yes	—
222	#466	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	#465	—	2	2	no	—
228	#463	—	2	2	no	—
229	#463	—	2	2	no	—
230	#460	—	2	2	no	—
231	#459	—	2	2	no	—
232	#450	—	2	2	no	—
233	#450	—	2	2	no	—
234	#449	—	2	2	no	—
235	#449	—	2	2	no	—
236	#449	—	2	2	no	—
237	#449	—	2	2	no	—
238	#447	—	2	2	no	—
239	#447	—	2	2	no	—
240	#442	—	2	2	no	—
241	#440	—	2	2	no	—
242	C₄×Q₁₆	C₂³	1	2	yes	—
243	C₄×D₈	C₂³	1	2	yes	—
244	C₄×D₈	C₂³	1	2	yes	—
245	C₄×D₈	C₂³	1	2	yes	—
246	#435	D₄	1	1	yes	characteristic
247	#435	D₄	1	1	yes	characteristic
248	#435	D₄	1	1	yes	characteristic
249	#435	D₄	1	1	yes	characteristic
250	C₈×D₄	C₂³	1	1	yes	characteristic
251	C₈×D₄	C₂³	1	1	yes	characteristic
252	C₈×D₄	C₂³	1	1	yes	characteristic
253	C₈×D₄	C₂³	1	1	yes	characteristic
254	#427	C₂³	1	2	yes	—
255	#427	C₂³	1	2	yes	—
256	C₂×#107	C₂³	1	2	yes	—
257	C₂×#107	C₂³	1	2	yes	—
258	#424	D₄	1	1	yes	characteristic
259	#418	—	2	2	no	—
260	#417	—	2	2	no	—
261	#416	—	2	2	no	—
262	C₂×#102	—	2	2	no	—
263	#408	D₄	1	1	yes	characteristic
264	#407	D₄	1	1	yes	characteristic
265	#405	C₂³	1	1	yes	characteristic
266	#367	C₂³	1	2	yes	—
267	#367	C₂³	1	2	yes	—
268	#367	C₂³	1	2	yes	—
269	#366	C₂³	1	1	yes	characteristic
270	#366	C₂³	1	1	yes	characteristic
271	#366	C₂³	1	1	yes	characteristic
272	#366	C₂³	1	2	yes	—
273	#366	C₂³	1	2	yes	—
274	#366	C₂³	1	1	yes	characteristic
275	#366	C₂³	1	2	yes	—
276	C₄⋊C₁₆	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	#358	C₂³	1	2	yes	—
281	#358	C₂³	1	2	yes	—
282	#358	C₂³	1	2	yes	—
283	#358	C₂³	1	2	yes	—
284	#357	C₂³	1	2	yes	—
285	#357	C₂³	1	2	yes	—
286	#357	C₂³	1	2	yes	—
287	#357	C₂³	1	2	yes	—
288	#357	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	#357	C₂³	1	2	yes	—
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	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
302	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
303	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
304	#346	C₂³	1	1	yes	characteristic
305	#346	C₂³	1	1	yes	characteristic
306	C₄×C₁₆	C₂³	1	1	yes	characteristic
307	C₄×C₁₆	C₂³	1	1	yes	characteristic
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	4	2	no	—
311	C₂×#41	C₂×D₄	1	1	yes	characteristic
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	4	2	no	—
315	C₂²×D₄	—	4	2	no	—
316	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
317	#135	—	4	2	no	—
318	#135	—	4	2	no	—
319	#135	—	4	2	no	—
320	#135	—	4	2	no	—
321	C₂×Q₁₆	C₂⁴	1	2	yes	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	4	2	no	—
329	C₂×D₈	—	4	2	no	—
330	C₂×D₈	—	4	2	no	—
331	C₂×D₈	—	4	2	no	—
332	C₂×D₈	C₂⁴	1	2	yes	—
333	C₂×D₈	C₂⁴	1	2	yes	—
334	C₂×D₈	C₂⁴	1	2	yes	—
335	#131	—	4	1	no	—
336	#131	—	4	1	no	—
337	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
338	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
339	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
340	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₈	—	4	1	no	—
342	C₂²×C₈	—	4	1	no	—
343	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₈	C₂⁴	1	1	yes	characteristic
347	C₂²×C₈	C₂⁴	1	1	yes	characteristic
348	C₂²×C₈	C₂⁴	1	1	yes	characteristic
349	C₂²×C₈	C₂⁴	1	1	yes	characteristic
350	C₂²×C₈	C₂⁴	1	1	yes	characteristic
351	C₄⋊Q₈	—	2	2	no	—
352	#127	—	2	2	no	—
353	#127	—	4	2	no	—
354	#127	—	4	2	no	—
355	#126	—	4	2	no	—
356	#126	—	4	2	no	—
357	#126	—	4	2	no	—
358	#125	—	2	2	no	—
359	#125	—	4	2	no	—
360	#124	—	2	2	no	—
361	#124	—	4	2	no	—
362	#124	—	4	2	no	—
363	#124	—	4	2	no	—
364	#124	—	4	2	no	—
365	#123	—	4	2	no	—
366	#123	—	4	2	no	—
367	#123	—	4	2	no	—
368	#123	—	4	2	no	—
369	#123	—	4	2	no	—
370	#123	—	4	2	no	—
371	#123	—	4	2	no	—
372	#123	—	4	2	no	—
373	#123	—	4	2	no	—
374	#123	—	4	2	no	—
375	#123	D₈	1	1	yes	characteristic
376	#123	D₈	1	1	yes	characteristic
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	4	2	no	—
381	C₂²⋊Q₈	—	4	2	no	—
382	C₂²⋊Q₈	—	4	2	no	—
383	C₂²⋊Q₈	D₈	1	1	yes	characteristic
384	C₂²⋊Q₈	D₈	1	1	yes	characteristic
385	#121	—	2	2	no	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	—	2	2	no	—
390	#121	—	2	2	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	2	no	—
394	#121	—	4	2	no	—
395	#121	—	4	2	no	—
396	#121	—	4	2	no	—
397	#121	—	4	2	no	—
398	#121	—	4	2	no	—
399	#121	—	4	2	no	—
400	#121	—	4	2	no	—
401	#121	—	4	2	no	—
402	#121	—	4	2	no	—
403	#121	—	4	2	no	—
404	#121	—	4	2	no	—
405	#121	—	4	2	no	—
406	#121	—	4	2	no	—
407	#121	—	4	2	no	—
408	#121	D₈	1	1	yes	characteristic
409	#121	D₈	1	1	yes	characteristic
410	#120	—	4	2	no	—
411	#120	—	4	2	no	—
412	#120	—	4	2	no	—
413	#120	—	4	2	no	—
414	#120	—	4	2	no	—
415	#120	—	4	2	no	—
416	#120	—	4	2	no	—
417	#120	D₈	1	1	yes	characteristic
418	#120	D₈	1	1	yes	characteristic
419	C₄×Q₈	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	4	2	no	—
424	C₄×D₄	—	4	2	no	—
425	C₄×D₄	—	4	2	no	—
426	C₄×D₄	—	4	2	no	—
427	C₄×D₄	C₂×D₄	1	1	yes	characteristic
428	C₄×D₄	C₂×D₄	1	1	yes	characteristic
429	C₄×D₄	C₂×D₄	1	1	yes	characteristic
430	C₄×D₄	C₂×D₄	1	1	yes	characteristic
431	#117	—	2	2	no	—
432	#117	—	2	2	no	—
433	#117	—	4	2	no	—
434	#117	—	4	2	no	—
435	#117	C₂×D₄	1	1	yes	characteristic
436	C₂×C₄⋊C₄	—	2	2	no	—
437	C₂×C₄⋊C₄	—	2	2	no	—
438	C₂×C₂²⋊C₄	—	4	2	no	—
439	C₂×C₂²⋊C₄	—	4	2	no	—
440	C₂×C₂²⋊C₄	—	4	2	no	—
441	Q₃₂	—	2	2	no	—
442	SD₃₂	—	4	2	no	—
443	SD₃₂	—	4	2	no	—
444	SD₃₂	—	4	2	no	—
445	D₁₆	—	2	2	no	—
446	D₁₆	—	2	2	no	—
447	D₁₆	—	2	2	no	—
448	D₁₆	—	4	2	no	—
449	D₁₆	—	4	2	no	—
450	D₁₆	—	4	2	no	—
451	M₃₂	—	4	1	no	—
452	M₃₂	—	4	1	no	—
453	M₃₂	—	4	1	no	—
454	M₃₂	—	4	1	no	—
455	C₂×C₁₆	—	2	2	no	—
456	C₂×C₁₆	—	2	2	no	—
457	C₂×C₁₆	—	2	2	no	—
458	C₂×C₁₆	—	2	2	no	—
459	C₂×C₁₆	—	2	2	no	—
460	C₂×C₁₆	—	4	1	no	—
461	C₂×C₁₆	—	4	1	no	—
462	C₂×C₁₆	—	4	1	no	—
463	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
464	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
465	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
466	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
467	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
468	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
469	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
470	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
471	#107	—	2	2	no	—
472	#107	—	2	2	no	—
473	#107	—	2	2	no	—
474	#107	C₂⁴	1	2	yes	—
475	#107	C₂⁴	1	2	yes	—
476	#107	C₂⁴	1	2	yes	—
477	#107	C₂⁴	1	2	yes	—
478	#106	—	2	2	no	—
479	#106	—	2	2	no	—
480	#106	—	2	2	no	—
481	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
482	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
483	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
484	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
485	#103	—	2	2	no	—
486	#103	—	2	2	no	—
487	#103	—	2	2	no	—
488	#103	—	2	2	no	—
489	#102	—	2	2	no	—
490	#102	—	2	2	no	—
491	#102	—	2	2	no	—
492	#102	—	2	2	no	—
493	#102	—	2	2	no	—
494	#102	—	2	2	no	—
495	#102	—	2	2	no	—
496	#102	—	2	2	no	—
497	#102	—	2	2	no	—
498	#102	—	2	2	no	—
499	#102	—	2	2	no	—
500	#102	—	2	2	no	—
501	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
502	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
503	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
504	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
505	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
506	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
507	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
508	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
509	#97	C₂×D₄	1	1	yes	characteristic
510	#97	C₂×D₄	1	1	yes	characteristic
511	C₄×C₈	C₂⁴	1	1	yes	characteristic
512	C₄×C₈	C₂⁴	1	1	yes	characteristic
513	C₂⁴	—	4	2	no	—
514	C₂⁴	—	4	2	no	—
515	C₂⁴	C₂×D₈	1	1	yes	characteristic
516	#41	—	4	1	no	—
517	#41	—	4	1	no	—
518	#41	—	8	2	no	—
519	#41	—	8	2	no	—
520	#41	—	8	2	no	—
521	#41	—	8	2	no	—
522	#41	—	16	4	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	—	4	2	no	—
525	C₂×Q₈	C₂×D₈	1	1	yes	characteristic
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	4	2	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	—	4	2	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	4	2	no	—
537	C₂×D₄	—	4	2	no	—
538	C₂×D₄	—	4	2	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	—	8	2	no	—
545	C₂×D₄	—	8	2	no	—
546	C₂×D₄	—	8	2	no	—
547	C₂×D₄	—	8	2	no	—
548	C₂×D₄	—	16	4	no	—
549	C₂×D₄	—	16	4	no	—
550	C₂×D₄	C₂×D₈	1	1	yes	characteristic
551	C₂×D₄	C₂×D₈	1	1	yes	characteristic
552	C₂×D₄	C₂×D₈	1	1	yes	characteristic
553	C₂×D₄	C₂×D₈	1	1	yes	characteristic
554	C₂×D₄	C₂×D₈	1	1	yes	characteristic
555	C₂×D₄	C₂×D₈	1	1	yes	characteristic
556	C₂×D₄	C₂×D₈	1	1	yes	characteristic
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	1	no	—
559	C₂²×C₄	—	4	2	no	—
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	C₂×D₈	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
569	C₂²×C₄	C₂²×D₄	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	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
574	Q₁₆	—	2	2	no	—
575	Q₁₆	—	2	2	no	—
576	SD₁₆	—	8	2	no	—
577	SD₁₆	—	8	2	no	—
578	SD₁₆	—	8	2	no	—
579	D₈	—	2	2	no	—
580	D₈	—	2	2	no	—
581	D₈	—	2	2	no	—
582	D₈	—	2	2	no	—
583	D₈	—	2	2	no	—
584	D₈	—	2	2	no	—
585	D₈	—	8	2	no	—
586	D₈	—	8	2	no	—
587	D₈	—	8	2	no	—
588	M₁₆	—	4	1	no	—
589	M₁₆	—	4	1	no	—
590	M₁₆	—	4	1	no	—
591	M₁₆	—	4	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	4	1	no	—
603	C₂×C₈	—	4	1	no	—
604	C₂×C₈	—	4	1	no	—
605	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
608	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	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	C₂×D₈	1	1	yes	characteristic
627	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
631	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
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	C₂×D₈	1	1	yes	characteristic
652	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
653	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
654	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
655	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
656	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
657	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
658	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
659	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
660	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
661	C₄²	—	4	2	no	—
662	C₄²	—	4	2	no	—
663	C₄²	—	4	2	no	—
664	C₄²	C₂²×D₄	1	1	yes	characteristic
665	C₄²	C₂²×D₄	1	1	yes	characteristic
666	C₁₆	—	2	1	no	—
667	C₁₆	—	2	1	no	—
668	C₁₆	—	2	1	no	—
669	C₁₆	—	2	1	no	—
670	C₁₆	—	2	1	no	—
671	C₁₆	—	2	1	no	—
672	C₁₆	—	2	1	no	—
673	C₁₆	H(5,𝔽₂)	1	2	yes	—
674	C₂³	—	2	2	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	8	4	no	—
681	C₂³	—	16	2	no	—
682	C₂³	—	16	2	no	—
683	C₂³	—	16	2	no	—
684	C₂³	—	16	2	no	—
685	C₂³	—	16	2	no	—
686	C₂³	C₂²×D₈	1	1	yes	characteristic
687	C₂³	C₂²×D₈	1	1	yes	characteristic
688	C₂³	C₂²×D₈	1	1	yes	characteristic
689	C₂³	C₂²×D₈	1	1	yes	characteristic
690	C₂³	C₂²×D₈	1	1	yes	characteristic
691	Q₈	—	4	1	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	4	2	no	—
694	Q₈	—	16	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	1	no	—
701	D₄	—	4	1	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	2	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	8	4	no	—
709	D₄	—	16	2	no	—
710	D₄	—	16	2	no	—
711	D₄	—	16	2	no	—
712	D₄	—	16	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	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	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	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	8	4	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	—	16	2	no	—
747	C₂×C₄	—	16	2	no	—
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	—	2	1	no	—
765	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
766	C₈	#585	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	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	8	2	no	—
783	C₂²	—	8	2	no	—
784	C₂²	—	8	2	no	—
785	C₂²	—	8	2	no	—
786	C₂²	—	8	2	no	—
787	C₂²	—	8	2	no	—
788	C₂²	—	8	2	no	—
789	C₂²	—	8	2	no	—
790	C₂²	—	8	2	no	—
791	C₂²	—	32	4	no	—
792	C₂²	—	32	4	no	—
793	C₂²	#3415	1	2	yes	—
794	C₂²	C₂³×D₈	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	8	2	no	—
805	C₄	—	8	2	no	—
806	C₄	—	8	2	no	—
807	C₄	—	8	2	no	—
808	C₄	—	8	2	no	—
809	C₄	#3496	1	1	yes	characteristic
810	C₄	#3584	1	1	yes	characteristic
811	C₂	—	2	2	no	—
812	C₂	—	4	1	no	—
813	C₂	—	4	1	no	—
814	C₂	—	4	1	no	—
815	C₂	—	4	1	no	—
816	C₂	—	16	2	no	—
817	C₂	—	16	2	no	—
818	C₂	—	16	2	no	—
819	C₂	#62245	1	1	yes	characteristic
820	C₂	C₂×#3415	1	1	yes	characteristic
821	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 ◁ #525 ◁ #2929 ◁ 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. #62266	C₂	semidirect
2. #33908	C₂	semidirect
3. #33906	C₂	semidirect
4. #33903	C₂	semidirect
5. #33901	C₂	semidirect
6. #33886	C₂	semidirect
7. #33877	C₂	semidirect
8. #33876	C₂	semidirect
9. #33873	C₂	semidirect
10. #33853	C₂	semidirect
11. #33846	C₂	semidirect
12. #33846	C₂	semidirect
13. D₄×D₁₆	C₂	semidirect
14. #33823	C₂	semidirect
15. #33764	C₂	semidirect
16. #33760	C₂	semidirect
17. #33740	C₂	semidirect
18. #33739	C₂	semidirect
19. #33610	C₂	semidirect
20. #33607	C₂	semidirect
21. #33600	C₂	semidirect
22. C₂×#2215	C₂	semidirect
23. #33432	C₂	semidirect
25. C₂×#508	C₂²	semidirect
26. C₂×#508	C₂²	semidirect
28. C₂²×D₁₆	C₂²	semidirect
29. C₂×#504	C₂²	semidirect
30. C₂³×C₁₆	C₂²	semidirect
31. #3341	C₂²	semidirect
32. #3339	C₂²	semidirect
34. #3334	C₂²	semidirect
39. #3287	C₂²	semidirect
40. #3280	C₂²	semidirect
41. #3280	C₂²	semidirect
46. #3176	C₂²	semidirect
47. #3175	C₂²	semidirect
48. #3061	C₂²	semidirect
49. #3058	C₂²	semidirect
50. #3050	C₂²	semidirect
51. C₂×#466	C₂²	semidirect
53. #2253	C₂²	semidirect
54. #2252	C₂²	semidirect
55. #2249	C₂²	semidirect
56. #2246	C₂²	semidirect
57. #2244	C₂²	semidirect
58. #2243	C₂²	semidirect
59. #2237	C₂²	semidirect
60. #2235	C₂²	semidirect
61. #2234	C₂²	semidirect
62. #2234	C₂²	semidirect
63. #2234	C₂²	semidirect
64. #2233	C₂²	semidirect
65. #2232	C₂²	semidirect
66. #2232	C₂²	semidirect
67. #2229	C₂²	semidirect
68. #2228	C₂²	semidirect
69. #2226	C₂²	semidirect
70. #2224	C₂²	semidirect
71. #2220	C₂²	semidirect
72. #2220	C₂²	semidirect
73. #2220	C₂²	semidirect
74. #2218	C₂²	semidirect
75. #2218	C₂²	semidirect
76. #2218	C₂²	semidirect
77. #2217	C₂²	semidirect
78. #2217	C₂²	semidirect
79. #2216	C₂²	semidirect
80. #2216	C₂²	semidirect
81. #2216	C₂²	semidirect
85. #2215	C₂²	semidirect
86. #2215	C₂²	semidirect
87. #2215	C₂²	semidirect
88. #2215	C₂²	semidirect
89. #2215	C₂²	semidirect
90. #2215	C₂²	semidirect
91. #2215	C₂²	semidirect
92. #2215	C₂²	semidirect
93. #2210	C₂²	semidirect
94. #2210	C₂²	semidirect
95. #2207	C₂²	semidirect
96. #2206	C₂²	semidirect
97. #2187	C₂²	semidirect
98. #2187	C₂²	semidirect
99. #2186	C₂²	semidirect
100. #2186	C₂²	semidirect
101. #2186	C₂²	semidirect
102. #2186	C₂²	semidirect
104. #2184	C₂²	semidirect
105. #2177	C₂²	semidirect
106. #2175	C₂²	semidirect
107. C₄×Q₃₂	C₂²	semidirect
108. C₄×D₁₆	C₂²	semidirect
109. C₄×D₁₆	C₂²	semidirect
110. C₄×D₁₆	C₂²	semidirect
112. #2168	C₂²	semidirect
113. #2168	C₂²	semidirect
114. #2168	C₂²	semidirect
116. D₄×C₁₆	C₂²	semidirect
117. D₄×C₁₆	C₂²	semidirect
118. D₄×C₁₆	C₂²	semidirect
119. #2158	C₂²	semidirect
120. #2158	C₂²	semidirect
121. C₂×#366	C₂²	semidirect
122. C₂×#366	C₂²	semidirect
123. #2151	C₂²	semidirect
124. #2140	C₂²	semidirect
125. #2139	C₂²	semidirect
126. #2138	C₂²	semidirect
127. C₂×#357	C₂²	semidirect
128. #2113	C₂²	semidirect
129. #2112	C₂²	semidirect
130. #2108	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#62266	2
#33908	2
#33906	2
#33903	2
#33901	2
#33886	2
#33877	2
#33876	2
#33873	2
#33853	2
#33846	2
D₄×D₁₆	2
#33823	2
#33764	2
#33760	2
#33740	2
#33739	2
#33610	2
#33607	2
#33600	2
C₂×#2215	2
#33432	2