Subgroups — #62618

Order 256.

883 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	#3368	C₂	1	1	yes	maximal, characteristic, complemented
4	#3367	C₂	1	1	yes	maximal, characteristic, complemented
5	#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	#3333	C₂	1	2	yes	maximal, complemented
8	#3330	C₂	1	1	yes	maximal, characteristic, complemented
9	#3324	C₂	1	1	yes	maximal, characteristic, complemented
10	#3322	C₂	1	2	yes	maximal, complemented
11	#3314	C₂	1	2	yes	maximal, complemented
12	#3309	C₂	1	2	yes	maximal, complemented
13	#3302	C₂	1	1	yes	maximal, characteristic, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3243	C₂	1	2	yes	maximal, complemented
16	#3226	C₂	1	1	yes	maximal, characteristic, complemented
17	#3224	C₂	1	2	yes	maximal, complemented
18	#3212	C₂	1	1	yes	maximal, characteristic, complemented
19	#3175	C₂	1	2	yes	maximal, complemented
20	#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	#3141	C₂	1	1	yes	maximal, characteristic, complemented
22	#3136	C₂	1	2	yes	maximal, complemented
23	#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	#563	—	2	2	no	—
25	#560	—	2	2	no	—
26	#557	C₂²	1	1	yes	characteristic, complemented
27	#556	C₂²	1	1	yes	characteristic
28	#556	C₂²	1	1	yes	characteristic
29	#554	C₂²	1	2	yes	complemented
30	#553	—	2	1	no	—
31	#553	C₂²	1	2	yes	complemented
32	#550	C₂²	1	2	yes	—
33	#550	C₂²	1	1	yes	characteristic
34	D₄×Q₈	—	2	1	no	—
35	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	#548	—	2	1	no	—
37	#547	C₂²	1	1	yes	characteristic
38	#547	C₂²	1	1	yes	characteristic
39	#546	—	2	1	no	—
40	#546	C₂²	1	2	yes	—
41	D₄²	C₂²	1	1	yes	characteristic
42	#544	C₂²	1	2	yes	complemented
43	#542	C₂²	1	2	yes	—
44	#542	C₂²	1	2	yes	complemented
45	#541	—	2	1	no	—
46	#539	—	2	2	no	—
47	#538	—	2	2	no	—
48	#537	—	2	1	no	—
49	#536	—	2	1	no	—
50	#535	—	2	1	no	—
51	#535	C₂²	1	2	yes	—
52	#532	C₂²	1	1	yes	characteristic
53	#532	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	#529	C₂²	1	1	yes	characteristic
56	#529	C₂²	1	1	yes	characteristic, complemented
57	#501	C₂²	1	1	yes	characteristic, complemented
58	#500	C₂²	1	2	yes	complemented
59	#496	C₂²	1	1	yes	characteristic
60	#495	C₂²	1	2	yes	complemented
61	#490	C₂²	1	1	yes	characteristic
62	#490	C₂²	1	2	yes	complemented
63	#489	C₂²	1	2	yes	—
64	#489	C₂²	1	2	yes	complemented
65	#489	C₂²	1	2	yes	complemented
66	#489	C₂²	1	1	yes	characteristic, complemented
67	#488	C₂²	1	2	yes	—
68	#488	C₂²	1	2	yes	complemented
69	#487	C₂²	1	1	yes	characteristic, complemented
70	#487	C₂²	1	1	yes	characteristic, complemented
71	#486	C₂²	1	1	yes	characteristic
72	#486	C₂²	1	1	yes	characteristic
73	#486	C₂²	1	2	yes	—
74	#486	C₂²	1	2	yes	complemented
75	#485	C₂²	1	2	yes	complemented
76	#484	C₂²	1	2	yes	complemented
77	#482	C₂²	1	2	yes	—
78	#480	C₂²	1	2	yes	—
79	#480	C₂²	1	2	yes	—
80	#480	C₂²	1	2	yes	complemented
81	#479	C₂²	1	2	yes	complemented
82	#478	C₂²	1	2	yes	complemented
83	#477	C₂²	1	2	yes	complemented
84	#474	C₂²	1	1	yes	characteristic
85	#474	C₂²	1	1	yes	characteristic
86	#474	C₂²	1	1	yes	characteristic, complemented
87	#474	C₂²	1	1	yes	characteristic, complemented
88	#474	C₂²	1	2	yes	complemented
89	#469	C₂²	1	1	yes	characteristic
90	#469	C₂²	1	1	yes	characteristic, complemented
91	#468	C₂²	1	2	yes	—
92	#468	C₂²	1	1	yes	characteristic
93	#468	C₂²	1	2	yes	complemented
94	#468	C₂²	1	1	yes	characteristic, complemented
95	#467	C₂²	1	2	yes	complemented
96	#466	C₂²	1	2	yes	—
97	#464	C₂²	1	2	yes	—
98	#463	C₂²	1	2	yes	—
99	#462	C₂²	1	1	yes	characteristic, complemented
100	#461	C₂²	1	1	yes	characteristic, complemented
101	#460	C₂²	1	1	yes	characteristic
102	#460	C₂²	1	2	yes	complemented
103	#459	C₂²	1	1	yes	characteristic
104	#459	C₂²	1	2	yes	complemented
105	#452	C₂²	1	2	yes	complemented
106	#452	C₂²	1	2	yes	complemented
107	#450	C₂²	1	2	yes	—
108	#449	C₂²	1	2	yes	complemented
109	#449	C₂²	1	2	yes	complemented
110	#447	C₂²	1	2	yes	—
111	#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	#440	C₂²	1	2	yes	complemented
114	#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆	C₂²	1	2	yes	complemented
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈	C₂²	1	1	yes	characteristic
119	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈	C₂²	1	2	yes	complemented
121	#436	C₂²	1	1	yes	characteristic
122	#436	C₂²	1	2	yes	complemented
123	#435	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic
125	#433	C₂²	1	2	yes	complemented
126	#431	C₂²	1	1	yes	characteristic, complemented
127	#418	C₂²	1	2	yes	—
128	#417	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	C₂×#102	C₂²	1	2	yes	—
133	#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂×#41	C₂³	1	2	yes	—
140	C₂²×Q₈	—	2	1	no	—
141	C₂²×Q₈	—	2	1	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	C₂³	1	2	yes	—
144	C₂×Q₁₆	C₂³	1	2	yes	—
145	C₂×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	C₂³	1	2	yes	—
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×D₈	C₂³	1	1	yes	characteristic
150	C₂×D₈	C₂³	1	2	yes	—
151	C₂×D₈	C₂³	1	1	yes	characteristic
152	C₂×M₁₆	C₂³	1	1	yes	characteristic
153	C₂×M₁₆	C₂³	1	1	yes	characteristic
154	C₂×M₁₆	C₂³	1	2	yes	—
155	C₂²×C₈	C₂³	1	2	yes	—
156	C₄⋊Q₈	—	2	1	no	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	#127	—	2	2	no	—
167	#127	C₂³	1	1	yes	characteristic
168	#127	C₂³	1	1	yes	characteristic
169	#127	C₂³	1	2	yes	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	1	no	—
176	#126	D₄	1	2	yes	—
177	#125	—	2	2	no	—
178	#125	—	2	2	no	—
179	#125	—	2	2	no	—
180	#125	D₄	1	1	yes	characteristic
181	#125	C₂³	1	1	yes	characteristic
182	#125	C₂³	1	2	yes	—
183	#124	—	2	1	no	—
184	#124	—	2	2	no	—
185	#124	—	2	2	no	—
186	#124	—	2	1	no	—
187	#124	D₄	1	1	yes	characteristic
188	#124	C₂³	1	1	yes	characteristic
189	#124	C₂³	1	2	yes	—
190	#124	C₂³	1	2	yes	—
191	#123	—	2	1	no	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	#123	D₄	1	2	yes	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	1	no	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	#121	—	2	1	no	—
214	#121	—	2	2	no	—
215	#121	—	2	1	no	—
216	#121	—	2	1	no	—
217	#121	—	2	1	no	—
218	#121	—	2	1	no	—
219	#121	—	2	2	no	—
220	#121	—	2	2	no	—
221	#121	—	2	1	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	—	2	2	no	—
226	#121	D₄	1	1	yes	characteristic
227	#121	C₂³	1	1	yes	characteristic
228	#121	C₂³	1	1	yes	characteristic
229	#121	C₂³	1	1	yes	characteristic
230	#121	C₂³	1	2	yes	—
231	#121	C₂³	1	2	yes	—
232	#120	—	2	2	no	—
233	#120	—	2	2	no	—
234	#120	—	2	2	no	—
235	#120	—	2	2	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₄×Q₈	C₂³	1	2	yes	—
240	C₄×Q₈	C₂³	1	2	yes	—
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	C₂³	1	1	yes	characteristic
250	C₄×D₄	C₂³	1	1	yes	characteristic
251	C₄×D₄	C₂³	1	1	yes	characteristic
252	C₄×D₄	C₂³	1	2	yes	—
253	C₄×D₄	C₂³	1	2	yes	—
254	C₄×D₄	C₂³	1	1	yes	characteristic
255	C₄×D₄	C₂³	1	2	yes	—
256	#117	—	2	1	no	—
257	#117	—	2	1	no	—
258	#117	C₂³	1	2	yes	—
259	#117	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	1	yes	characteristic
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	#107	C₂³	1	2	yes	—
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	1	yes	characteristic
274	C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₄⋊C₈	C₂³	1	2	yes	—
277	C₄⋊C₈	C₂³	1	2	yes	—
278	#103	C₂³	1	2	yes	—
279	#103	C₂³	1	2	yes	—
280	#103	C₂³	1	2	yes	—
281	#103	C₂³	1	2	yes	—
282	#103	C₂³	1	2	yes	—
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#102	C₂³	1	1	yes	characteristic
287	#102	C₂³	1	2	yes	—
288	#102	C₂³	1	2	yes	—
289	#102	C₂³	1	2	yes	—
290	#102	C₂³	1	1	yes	characteristic
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	1	yes	characteristic
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	1	yes	characteristic
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	#97	C₂³	1	1	yes	characteristic
306	#97	C₂³	1	1	yes	characteristic
307	#97	C₂³	1	2	yes	—
308	C₄×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	—	2	2	no	—
313	#41	—	4	2	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	8	2	no	—
318	#41	—	8	2	no	—
319	#41	—	8	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	8	2	no	—
326	C₂×Q₈	—	8	2	no	—
327	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈	C₂⁴	1	2	yes	—
329	C₂×Q₈	C₂⁴	1	1	yes	characteristic
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄	C₂×D₄	1	2	yes	—
349	C₂×D₄	C₂⁴	1	1	yes	characteristic
350	C₂×D₄	C₂⁴	1	2	yes	—
351	C₂×D₄	C₂⁴	1	1	yes	characteristic
352	C₂×D₄	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴	1	2	yes	—
366	Q₁₆	—	4	2	no	—
367	SD₁₆	—	4	1	no	—
368	SD₁₆	—	4	1	no	—
369	SD₁₆	—	4	2	no	—
370	SD₁₆	—	4	2	no	—
371	D₈	—	4	2	no	—
372	D₈	—	4	1	no	—
373	D₈	—	4	1	no	—
374	M₁₆	—	4	1	no	—
375	M₁₆	—	4	1	no	—
376	M₁₆	—	4	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₂×C₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₈	C₂⁴	1	2	yes	—
380	C₂×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₈	C₂⁴	1	2	yes	—
382	C₂×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₄⋊C₄	C₂×D₄	1	2	yes	—
407	C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄	C₂⁴	1	2	yes	—
412	C₄⋊C₄	C₂⁴	1	2	yes	—
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	1	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	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	C₂×D₄	1	1	yes	characteristic
445	C₄²	C₂×D₄	1	1	yes	characteristic
446	C₄²	C₂⁴	1	1	yes	characteristic
447	C₄²	C₂⁴	1	1	yes	characteristic
448	C₄²	C₂⁴	1	2	yes	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	8	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	C₂²×D₄	1	2	yes	—
457	C₂³	C₂²×D₄	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	8	2	no	—
466	Q₈	—	8	2	no	—
467	Q₈	—	8	1	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	1	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	8	1	no	—
481	D₄	—	8	1	no	—
482	D₄	—	8	2	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	1	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	2	no	—
488	D₄	—	8	2	no	—
489	D₄	—	8	1	no	—
490	D₄	—	8	1	no	—
491	D₄	—	8	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	8	2	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	C₂²×D₄	1	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄	1	2	yes	—
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂⁵	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	2	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	16	4	no	—
549	C₂²	C₂³×D₄	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	2	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	#576	1	2	yes	—
566	C₄	#585	1	1	yes	characteristic
567	C₄	#585	1	1	yes	characteristic
568	C₂	—	4	1	no	—
569	C₂	—	4	2	no	—
570	C₂	—	8	1	no	—
571	C₂	—	8	1	no	—
572	C₂	—	8	2	no	—
573	C₂	—	8	1	no	—
574	C₂	#3500	1	1	yes	characteristic
575	C₂	C₂×#576	1	1	yes	characteristic
576	C₂	#3586	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 ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3552	C₂	semidirect
2. #3546	C₂	semidirect
3. #3368	C₂	semidirect
4. #3367	C₂	semidirect
5. #3364	C₂	semidirect
6. #3358	C₂	semidirect
7. #3333	C₂	semidirect
8. #3330	C₂	semidirect
9. #3324	C₂	semidirect
10. #3322	C₂	semidirect
11. #3314	C₂	semidirect
12. #3309	C₂	semidirect
13. #3302	C₂	semidirect
14. #3294	C₂	semidirect
15. #3243	C₂	semidirect
16. #3226	C₂	semidirect
17. #3224	C₂	semidirect
18. #3212	C₂	semidirect
19. #3175	C₂	semidirect
20. #3171	C₂	semidirect
21. #3141	C₂	semidirect
22. #3136	C₂	semidirect
23. #2969	C₂	semidirect
26. #557	C₂²	semidirect
29. #554	C₂²	semidirect
31. #553	C₂²	semidirect
35. D₄×Q₈	C₂²	semidirect
42. #544	C₂²	semidirect
44. #542	C₂²	semidirect
54. C₂×C₄⋊Q₈	C₂²	semidirect
56. #529	C₂²	semidirect
57. #501	C₂²	semidirect
58. #500	C₂²	semidirect
60. #495	C₂²	semidirect
62. #490	C₂²	semidirect
64. #489	C₂²	semidirect
65. #489	C₂²	semidirect
66. #489	C₂²	semidirect
68. #488	C₂²	semidirect
69. #487	C₂²	semidirect
70. #487	C₂²	semidirect
74. #486	C₂²	semidirect
75. #485	C₂²	semidirect
76. #484	C₂²	semidirect
80. #480	C₂²	semidirect
81. #479	C₂²	semidirect
82. #478	C₂²	semidirect
83. #477	C₂²	semidirect
86. #474	C₂²	semidirect
87. #474	C₂²	semidirect
88. #474	C₂²	semidirect
90. #469	C₂²	semidirect
93. #468	C₂²	semidirect
94. #468	C₂²	semidirect
95. #467	C₂²	semidirect
99. #462	C₂²	semidirect
100. #461	C₂²	semidirect
102. #460	C₂²	semidirect
104. #459	C₂²	semidirect
105. #452	C₂²	semidirect
106. #452	C₂²	semidirect
108. #449	C₂²	semidirect
109. #449	C₂²	semidirect
111. #446	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
113. #440	C₂²	semidirect
114. #440	C₂²	semidirect
115. C₄×Q₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
119. C₄×D₈	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
122. #436	C₂²	semidirect
123. #435	C₂²	semidirect
125. #433	C₂²	semidirect
126. #431	C₂²	semidirect
128. #417	C₂²	semidirect
129. #417	C₂²	semidirect
130. #417	C₂²	semidirect
131. #416	C₂²	semidirect
133. #405	C₂²	semidirect
134. C₄×M₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3552	2
#3546	2
#3368	2
#3367	2
#3364	2
#3358	2
#3333	2
#3330	2
#3324	2
#3322	2
#3314	2
#3309	2
#3302	2
#3294	2
#3243	2
#3226	2
#3224	2
#3212	2
#3175	2
#3171	2
#3141	2
#3136	2
#2969	2