Subgroups — #61734

Order 256.

885 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	#3350	C₂	1	2	yes	maximal, complemented
6	#3349	C₂	1	2	yes	maximal, complemented
7	#3341	C₂	1	1	yes	maximal, characteristic, complemented
8	#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	#3330	C₂	1	1	yes	maximal, characteristic, complemented
11	#3317	C₂	1	2	yes	maximal, complemented
12	#3309	C₂	1	2	yes	maximal, complemented
13	#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	#3197	C₂	1	2	yes	maximal, complemented
18	#3191	C₂	1	2	yes	maximal, complemented
19	#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	#3093	C₂	1	2	yes	maximal, complemented
22	#3091	C₂	1	2	yes	maximal, complemented
23	#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	—	2	2	no	—
25	#556	C₂²	1	1	yes	characteristic
26	#556	C₂²	1	2	yes	—
27	#555	C₂²	1	1	yes	characteristic
28	#555	C₂²	1	1	yes	characteristic
29	#555	C₂²	1	1	yes	characteristic
30	#554	C₂²	1	1	yes	characteristic
31	#553	—	2	1	no	—
32	#553	—	2	1	no	—
33	#553	C₂²	1	2	yes	—
34	#552	—	2	1	no	—
35	#552	C₂²	1	2	yes	—
36	#551	—	2	2	no	—
37	#550	C₂²	1	2	yes	—
38	#547	C₂²	1	1	yes	characteristic
39	#547	C₂²	1	1	yes	characteristic
40	#547	C₂²	1	1	yes	characteristic
41	#546	—	2	1	no	—
42	#538	—	2	2	no	—
43	#535	—	2	1	no	—
44	#533	C₂²	1	1	yes	characteristic
45	#533	C₂²	1	1	yes	characteristic
46	#532	C₂²	1	1	yes	characteristic
47	#529	—	2	2	no	—
48	#529	—	2	1	no	—
49	#525	C₂²	1	2	yes	—
50	#525	C₂²	1	2	yes	—
51	#525	C₂²	1	2	yes	—
52	#520	—	2	1	no	—
53	C₄×#41	—	2	1	no	—
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
56	C₂×#117	C₂²	1	2	yes	—
57	#501	C₂²	1	2	yes	complemented
58	#500	C₂²	1	1	yes	characteristic, complemented
59	#498	C₂²	1	1	yes	characteristic, complemented
60	#490	C₂²	1	2	yes	complemented
61	#487	C₂²	1	1	yes	characteristic, complemented
62	#487	C₂²	1	1	yes	characteristic, complemented
63	#485	C₂²	1	2	yes	—
64	#485	C₂²	1	2	yes	—
65	#485	C₂²	1	2	yes	—
66	#485	C₂²	1	2	yes	complemented
67	#485	C₂²	1	2	yes	complemented
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#484	C₂²	1	2	yes	complemented
71	#483	C₂²	1	2	yes	complemented
72	#482	C₂²	1	1	yes	characteristic
73	#482	C₂²	1	2	yes	—
74	#482	C₂²	1	1	yes	characteristic
75	#482	C₂²	1	2	yes	—
76	#482	C₂²	1	2	yes	complemented
77	#482	C₂²	1	2	yes	complemented
78	#482	C₂²	1	2	yes	complemented
79	#482	C₂²	1	2	yes	complemented
80	#481	C₂²	1	2	yes	complemented
81	#480	C₂²	1	2	yes	complemented
82	#479	C₂²	1	2	yes	complemented
83	#479	C₂²	1	2	yes	complemented
84	#477	C₂²	1	1	yes	characteristic, complemented
85	#477	C₂²	1	1	yes	characteristic, complemented
86	#476	C₂²	1	1	yes	characteristic, complemented
87	#476	C₂²	1	1	yes	characteristic, complemented
88	#476	C₂²	1	1	yes	characteristic, complemented
89	#476	C₂²	1	1	yes	characteristic, complemented
90	#474	C₂²	1	1	yes	characteristic, complemented
91	#474	C₂²	1	1	yes	characteristic, complemented
92	#470	C₂²	1	2	yes	complemented
93	#469	C₂²	1	2	yes	complemented
94	#468	C₂²	1	2	yes	complemented
95	#468	C₂²	1	2	yes	complemented
96	#467	C₂²	1	2	yes	complemented
97	#466	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#462	C₂²	1	1	yes	characteristic, complemented
101	#461	C₂²	1	1	yes	characteristic, complemented
102	#460	C₂²	1	1	yes	characteristic, complemented
103	#459	C₂²	1	1	yes	characteristic, complemented
104	#452	C₂²	1	2	yes	—
105	#452	C₂²	1	2	yes	complemented
106	#452	C₂²	1	2	yes	complemented
107	#449	C₂²	1	1	yes	characteristic
108	#449	C₂²	1	1	yes	characteristic
109	#449	C₂²	1	2	yes	complemented
110	#449	C₂²	1	2	yes	complemented
111	#441	C₂²	1	2	yes	complemented
112	#440	C₂²	1	2	yes	complemented
113	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
117	#436	C₂²	1	1	yes	characteristic
118	#436	C₂²	1	1	yes	characteristic
119	#435	C₂²	1	2	yes	—
120	#435	C₂²	1	2	yes	—
121	C₈×D₄	C₂²	1	1	yes	characteristic
122	C₈×D₄	C₂²	1	1	yes	characteristic
123	#432	C₂²	1	1	yes	characteristic
124	#431	C₂²	1	1	yes	characteristic
125	#428	C₂²	1	2	yes	complemented
126	#428	C₂²	1	2	yes	complemented
127	#427	C₂²	1	2	yes	complemented
128	#427	C₂²	1	2	yes	complemented
129	#417	C₂²	1	2	yes	complemented
130	#417	C₂²	1	2	yes	complemented
131	#416	C₂²	1	2	yes	complemented
132	#416	C₂²	1	2	yes	complemented
133	#407	C₂²	1	2	yes	—
134	C₂×C₂²⋊C₈	C₂²	1	2	yes	—
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂×#41	C₂³	1	2	yes	—
139	C₂×#41	C₂³	1	2	yes	—
140	C₂²×D₄	D₄	1	1	yes	characteristic
141	C₂³×C₄	C₂³	1	2	yes	—
142	C₂×Q₁₆	C₂³	1	2	yes	—
143	C₂×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆	C₂³	1	2	yes	—
146	C₂×D₈	C₂³	1	1	yes	characteristic
147	C₂×D₈	C₂³	1	1	yes	characteristic
148	C₂×M₁₆	C₂³	1	2	yes	—
149	C₂×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₂²×C₈	C₂³	1	2	yes	—
152	C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	#127	—	2	2	no	—
158	#127	C₂³	1	1	yes	characteristic
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
163	#126	—	2	2	no	—
164	#125	—	2	2	no	—
165	#125	—	2	1	no	—
166	#125	—	2	1	no	—
167	#125	C₂³	1	2	yes	—
168	#124	—	2	1	no	—
169	#124	—	2	2	no	—
170	#124	—	2	2	no	—
171	#124	—	2	2	no	—
172	#124	—	2	2	no	—
173	#124	—	2	1	no	—
174	#123	—	2	2	no	—
175	#123	—	2	2	no	—
176	#123	—	2	2	no	—
177	#123	—	2	2	no	—
178	#123	—	2	2	no	—
179	#123	—	2	2	no	—
180	#123	—	2	2	no	—
181	#123	—	2	2	no	—
182	C₂²⋊Q₈	—	2	1	no	—
183	C₂²⋊Q₈	—	2	1	no	—
184	C₂²⋊Q₈	—	2	1	no	—
185	C₂²⋊Q₈	—	2	1	no	—
186	C₂²⋊Q₈	—	2	2	no	—
187	C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₂²⋊Q₈	C₂³	1	2	yes	—
192	#121	—	2	2	no	—
193	#121	—	2	1	no	—
194	#121	—	2	1	no	—
195	#121	—	2	1	no	—
196	#121	—	2	1	no	—
197	#121	—	2	1	no	—
198	#121	—	2	1	no	—
199	#121	—	2	2	no	—
200	#121	—	2	2	no	—
201	#121	C₂³	1	1	yes	characteristic
202	#121	C₂³	1	1	yes	characteristic
203	#121	C₂³	1	2	yes	—
204	#121	C₂³	1	2	yes	—
205	#121	C₂³	1	2	yes	—
206	#121	C₂³	1	2	yes	—
207	#120	—	2	2	no	—
208	#120	—	2	2	no	—
209	#120	—	2	2	no	—
210	C₄×Q₈	—	2	1	no	—
211	C₄×Q₈	—	2	2	no	—
212	C₄×Q₈	—	2	1	no	—
213	C₄×Q₈	—	2	1	no	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	C₂³	1	1	yes	characteristic
216	C₄×Q₈	C₂³	1	1	yes	characteristic
217	C₄×Q₈	C₂³	1	2	yes	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	2	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	D₄	1	1	yes	characteristic
231	C₄×D₄	D₄	1	1	yes	characteristic
232	C₄×D₄	D₄	1	2	yes	—
233	C₄×D₄	C₂³	1	1	yes	characteristic
234	C₄×D₄	C₂³	1	1	yes	characteristic
235	C₄×D₄	C₂³	1	1	yes	characteristic
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	1	yes	characteristic
239	C₄×D₄	C₂³	1	2	yes	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	1	no	—
243	#117	—	2	1	no	—
244	#117	—	2	1	no	—
245	#117	—	2	1	no	—
246	#117	—	2	2	no	—
247	#117	—	2	1	no	—
248	#117	C₂³	1	1	yes	characteristic
249	#117	C₂³	1	2	yes	—
250	#117	C₂³	1	2	yes	—
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	2	yes	—
253	#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	D₄	1	2	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	1	yes	characteristic
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	1	yes	characteristic
269	#107	C₂³	1	2	yes	—
270	#107	C₂³	1	2	yes	—
271	#106	C₂³	1	1	yes	characteristic
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	2	yes	—
277	#106	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	#103	C₂³	1	2	yes	—
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	2	yes	—
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	2	yes	—
291	#102	C₂³	1	1	yes	characteristic
292	#102	C₂³	1	1	yes	characteristic
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	1	yes	characteristic
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	2	yes	—
302	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂²⋊C₈	C₂³	1	2	yes	—
309	#97	C₂³	1	2	yes	—
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₂⁴	C₂×D₄	1	2	yes	—
313	#41	—	4	1	no	—
314	#41	—	4	1	no	—
315	#41	—	4	4	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	4	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	C₂⁴	1	2	yes	—
326	C₂×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄	C₂×D₄	1	2	yes	—
342	C₂×D₄	C₂⁴	1	1	yes	characteristic
343	C₂×D₄	C₂⁴	1	1	yes	characteristic
344	C₂×D₄	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄	1	2	yes	—
358	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄	1	2	yes	—
360	C₂²×C₄	C₂×D₄	1	2	yes	—
361	C₂²×C₄	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴	1	2	yes	—
363	C₂²×C₄	C₂⁴	1	2	yes	—
364	Q₁₆	—	4	2	no	—
365	SD₁₆	—	4	1	no	—
366	SD₁₆	—	4	2	no	—
367	SD₁₆	—	4	1	no	—
368	D₈	—	4	1	no	—
369	D₈	—	4	1	no	—
370	M₁₆	—	4	2	no	—
371	M₁₆	—	4	2	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	C₂⁴	1	1	yes	characteristic
375	C₂×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₈	C₂⁴	1	2	yes	—
379	C₂×C₈	C₂⁴	1	2	yes	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	1	2	yes	—
404	C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	C₂×D₄	1	1	yes	characteristic
443	C₄²	C₂×D₄	1	1	yes	characteristic
444	C₄²	C₂⁴	1	1	yes	characteristic
445	C₄²	C₂⁴	1	1	yes	characteristic
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	C₂²×D₄	1	2	yes	—
453	C₂³	C₂²×D₄	1	1	yes	characteristic
454	C₂³	C₂²×D₄	1	2	yes	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	1	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	8	1	no	—
462	Q₈	—	8	1	no	—
463	D₄	—	2	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	1	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	1	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	4	no	—
477	D₄	—	8	1	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	2	no	—
480	D₄	—	8	2	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	8	1	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	8	2	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄	1	2	yes	—
514	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄	1	2	yes	—
517	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂⁵	1	1	yes	characteristic
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	2	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	8	4	no	—
545	C₂²	C₂³×D₄	1	1	yes	characteristic
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	#575	1	2	yes	—
562	C₄	#585	1	1	yes	characteristic
563	C₄	#585	1	1	yes	characteristic
564	C₂	—	4	2	no	—
565	C₂	—	4	2	no	—
566	C₂	—	4	1	no	—
567	C₂	—	8	1	no	—
568	C₂	—	8	1	no	—
569	C₂	—	8	1	no	—
570	C₂	#3485	1	1	yes	characteristic
571	C₂	C₂×#575	1	1	yes	characteristic
572	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3506	C₂	semidirect
2. #3475	C₂	semidirect
3. #3357	C₂	semidirect
4. #3354	C₂	semidirect
5. #3350	C₂	semidirect
6. #3349	C₂	semidirect
7. #3341	C₂	semidirect
8. #3340	C₂	semidirect
9. #3331	C₂	semidirect
10. #3330	C₂	semidirect
11. #3317	C₂	semidirect
12. #3309	C₂	semidirect
13. #3303	C₂	semidirect
14. #3302	C₂	semidirect
15. #3235	C₂	semidirect
16. #3231	C₂	semidirect
17. #3197	C₂	semidirect
18. #3191	C₂	semidirect
19. #3116	C₂	semidirect
20. #3106	C₂	semidirect
21. #3093	C₂	semidirect
22. #3091	C₂	semidirect
23. #2974	C₂	semidirect
57. #501	C₂²	semidirect
58. #500	C₂²	semidirect
59. #498	C₂²	semidirect
60. #490	C₂²	semidirect
61. #487	C₂²	semidirect
62. #487	C₂²	semidirect
66. #485	C₂²	semidirect
67. #485	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #484	C₂²	semidirect
71. #483	C₂²	semidirect
76. #482	C₂²	semidirect
77. #482	C₂²	semidirect
78. #482	C₂²	semidirect
79. #482	C₂²	semidirect
80. #481	C₂²	semidirect
81. #480	C₂²	semidirect
82. #479	C₂²	semidirect
83. #479	C₂²	semidirect
84. #477	C₂²	semidirect
85. #477	C₂²	semidirect
86. #476	C₂²	semidirect
87. #476	C₂²	semidirect
88. #476	C₂²	semidirect
89. #476	C₂²	semidirect
90. #474	C₂²	semidirect
91. #474	C₂²	semidirect
92. #470	C₂²	semidirect
93. #469	C₂²	semidirect
94. #468	C₂²	semidirect
95. #468	C₂²	semidirect
96. #467	C₂²	semidirect
97. #466	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
100. #462	C₂²	semidirect
101. #461	C₂²	semidirect
102. #460	C₂²	semidirect
103. #459	C₂²	semidirect
105. #452	C₂²	semidirect
106. #452	C₂²	semidirect
109. #449	C₂²	semidirect
110. #449	C₂²	semidirect
111. #441	C₂²	semidirect
112. #440	C₂²	semidirect
113. C₄×SD₁₆	C₂²	semidirect
114. C₄×SD₁₆	C₂²	semidirect
115. C₄×D₈	C₂²	semidirect
116. C₄×D₈	C₂²	semidirect
125. #428	C₂²	semidirect
126. #428	C₂²	semidirect
127. #427	C₂²	semidirect
128. #427	C₂²	semidirect
129. #417	C₂²	semidirect
130. #417	C₂²	semidirect
131. #416	C₂²	semidirect
132. #416	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3506	2
#3475	2
#3357	2
#3354	2
#3350	2
#3349	2
#3341	2
#3340	2
#3331	2
#3330	2
#3317	2
#3309	2
#3303	2
#3302	2
#3235	2
#3231	2
#3197	2
#3191	2
#3116	2
#3106	2
#3093	2
#3091	2
#2974	2