Subgroups — #61811

Order 256.

894 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	#3353	C₂	1	1	yes	maximal, characteristic, complemented
4	#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	#3347	C₂	1	2	yes	maximal, complemented
6	#3346	C₂	1	2	yes	maximal, complemented
7	#3342	C₂	1	1	yes	maximal, characteristic, complemented
8	#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	#3319	C₂	1	2	yes	maximal, complemented
12	#3314	C₂	1	2	yes	maximal, complemented
13	#3304	C₂	1	1	yes	maximal, characteristic, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3239	C₂	1	1	yes	maximal, characteristic, complemented
16	#3226	C₂	1	1	yes	maximal, characteristic, complemented
17	#3203	C₂	1	2	yes	maximal, complemented
18	#3198	C₂	1	2	yes	maximal, complemented
19	#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	#3098	C₂	1	2	yes	maximal, complemented
22	#3096	C₂	1	2	yes	maximal, complemented
23	#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	#560	—	2	2	no	—
25	#556	C₂²	1	1	yes	characteristic
26	#556	C₂²	1	1	yes	characteristic
27	#556	C₂²	1	1	yes	characteristic, complemented
28	#555	C₂²	1	2	yes	complemented
29	#554	C₂²	1	2	yes	complemented
30	#553	—	2	2	no	—
31	#553	C₂²	1	2	yes	—
32	#550	—	2	1	no	—
33	#550	C₂²	1	1	yes	characteristic
34	#548	—	2	1	no	—
35	#548	—	2	1	no	—
36	#547	C₂²	1	1	yes	characteristic
37	#547	C₂²	1	1	yes	characteristic
38	#547	C₂²	1	1	yes	characteristic, complemented
39	#546	—	2	1	no	—
40	#546	C₂²	1	2	yes	—
41	D₄²	C₂²	1	1	yes	characteristic
42	#542	—	2	1	no	—
43	#542	—	2	2	no	—
44	#538	—	2	2	no	—
45	#537	C₂²	1	2	yes	—
46	#537	C₂²	1	2	yes	complemented
47	#535	—	2	1	no	—
48	#535	C₂²	1	2	yes	—
49	#533	—	2	1	no	—
50	#532	—	2	1	no	—
51	#532	C₂²	1	1	yes	characteristic
52	#532	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	#529	C₂²	1	1	yes	characteristic
55	#520	C₂²	1	2	yes	complemented
56	C₄×#41	C₂²	1	1	yes	characteristic, complemented
57	#501	C₂²	1	2	yes	complemented
58	#500	C₂²	1	1	yes	characteristic, complemented
59	#500	C₂²	1	1	yes	characteristic, complemented
60	#489	C₂²	1	2	yes	—
61	#486	C₂²	1	1	yes	characteristic
62	#486	C₂²	1	1	yes	characteristic
63	#485	C₂²	1	2	yes	complemented
64	#485	C₂²	1	2	yes	complemented
65	#485	C₂²	1	1	yes	characteristic, complemented
66	#484	C₂²	1	2	yes	complemented
67	#484	C₂²	1	2	yes	complemented
68	#484	C₂²	1	2	yes	complemented
69	#482	C₂²	1	2	yes	—
70	#482	C₂²	1	1	yes	characteristic
71	#482	C₂²	1	2	yes	—
72	#482	C₂²	1	2	yes	complemented
73	#482	C₂²	1	2	yes	complemented
74	#482	C₂²	1	2	yes	complemented
75	#481	C₂²	1	2	yes	—
76	#481	C₂²	1	2	yes	complemented
77	#480	C₂²	1	2	yes	—
78	#480	C₂²	1	2	yes	—
79	#480	C₂²	1	2	yes	complemented
80	#480	C₂²	1	2	yes	complemented
81	#480	C₂²	1	2	yes	complemented
82	#479	C₂²	1	1	yes	characteristic, complemented
83	#478	C₂²	1	1	yes	characteristic, complemented
84	#475	C₂²	1	1	yes	characteristic, complemented
85	#475	C₂²	1	1	yes	characteristic, complemented
86	#475	C₂²	1	1	yes	characteristic, complemented
87	#474	C₂²	1	1	yes	characteristic
88	#474	C₂²	1	1	yes	characteristic
89	#474	C₂²	1	1	yes	characteristic, complemented
90	#474	C₂²	1	2	yes	complemented
91	#474	C₂²	1	2	yes	complemented
92	#469	C₂²	1	2	yes	complemented
93	#468	C₂²	1	2	yes	—
94	#468	C₂²	1	2	yes	—
95	#468	C₂²	1	2	yes	complemented
96	#467	C₂²	1	2	yes	complemented
97	#466	C₂²	1	2	yes	—
98	#466	C₂²	1	2	yes	—
99	#465	C₂²	1	2	yes	complemented
100	#464	C₂²	1	1	yes	characteristic
101	#463	C₂²	1	1	yes	characteristic
102	#460	C₂²	1	1	yes	characteristic
103	#459	C₂²	1	1	yes	characteristic
104	#452	C₂²	1	1	yes	characteristic, complemented
105	#452	C₂²	1	2	yes	complemented
106	#450	C₂²	1	2	yes	—
107	#449	C₂²	1	1	yes	characteristic
108	#449	C₂²	1	2	yes	complemented
109	#449	C₂²	1	2	yes	complemented
110	#447	C₂²	1	2	yes	—
111	#442	C₂²	1	2	yes	complemented
112	#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈	C₂²	1	1	yes	characteristic
117	#436	C₂²	1	1	yes	characteristic
118	#436	C₂²	1	1	yes	characteristic, complemented
119	#435	C₂²	1	2	yes	complemented
120	#435	C₂²	1	2	yes	complemented
121	C₈×D₄	C₂²	1	1	yes	characteristic
122	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
123	#432	C₂²	1	1	yes	characteristic, complemented
124	#431	C₂²	1	1	yes	characteristic, complemented
125	#428	C₂²	1	2	yes	complemented
126	#428	C₂²	1	2	yes	complemented
127	#427	C₂²	1	2	yes	complemented
128	C₂×#107	C₂²	1	2	yes	complemented
129	#418	C₂²	1	2	yes	—
130	#417	C₂²	1	2	yes	complemented
131	#416	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	—
133	#408	C₂²	1	2	yes	complemented
134	#408	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	—	2	1	no	—
139	C₂×#41	C₂³	1	1	yes	characteristic
140	C₂×#41	C₂³	1	2	yes	—
141	C₂×#41	C₂³	1	2	yes	—
142	C₂²×Q₈	—	2	1	no	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	C₂³	1	2	yes	—
145	C₂×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×D₈	C₂³	1	1	yes	characteristic
150	C₂×D₈	C₂³	1	2	yes	—
151	C₂×M₁₆	C₂³	1	2	yes	—
152	C₂×M₁₆	C₂³	1	2	yes	—
153	C₂²×C₈	C₂³	1	2	yes	—
154	C₂²×C₈	C₂³	1	2	yes	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	—	2	1	no	—
157	C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	2	yes	—
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	#127	—	2	1	no	—
163	#127	—	2	2	no	—
164	#127	D₄	1	1	yes	characteristic
165	#127	C₂³	1	1	yes	characteristic
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	1	no	—
171	#125	—	2	2	no	—
172	#125	C₂³	1	1	yes	characteristic
173	#124	—	2	2	no	—
174	#124	—	2	1	no	—
175	#124	—	2	1	no	—
176	#124	—	2	1	no	—
177	#124	—	2	2	no	—
178	#124	—	2	2	no	—
179	#124	—	2	1	no	—
180	#124	D₄	1	2	yes	—
181	#124	C₂³	1	1	yes	characteristic
182	#123	—	2	1	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	C₂²⋊Q₈	—	2	2	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
196	C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂²⋊Q₈	C₂³	1	2	yes	—
199	#121	—	2	2	no	—
200	#121	—	2	2	no	—
201	#121	—	2	2	no	—
202	#121	—	2	2	no	—
203	#121	—	2	2	no	—
204	#121	—	2	2	no	—
205	#121	—	2	2	no	—
206	#121	—	2	2	no	—
207	#121	—	2	1	no	—
208	#121	—	2	1	no	—
209	#121	—	2	2	no	—
210	#121	—	2	2	no	—
211	#121	D₄	1	1	yes	characteristic
212	#121	D₄	1	1	yes	characteristic
213	#121	D₄	1	2	yes	—
214	#121	C₂³	1	1	yes	characteristic
215	#121	C₂³	1	2	yes	—
216	#121	C₂³	1	2	yes	—
217	#121	C₂³	1	2	yes	—
218	#121	C₂³	1	2	yes	—
219	#121	C₂³	1	2	yes	—
220	#121	C₂³	1	2	yes	—
221	#120	—	2	2	no	—
222	#120	—	2	2	no	—
223	#120	—	2	2	no	—
224	#120	—	2	2	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₄×D₄	—	2	2	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	C₂³	1	1	yes	characteristic
243	C₄×D₄	C₂³	1	1	yes	characteristic
244	C₄×D₄	C₂³	1	1	yes	characteristic
245	C₄×D₄	C₂³	1	2	yes	—
246	C₄×D₄	C₂³	1	1	yes	characteristic
247	C₄×D₄	C₂³	1	2	yes	—
248	C₄×D₄	C₂³	1	1	yes	characteristic
249	#117	—	2	2	no	—
250	#117	—	2	1	no	—
251	#117	—	2	1	no	—
252	#117	C₂³	1	1	yes	characteristic
253	#117	C₂³	1	2	yes	—
254	#117	C₂³	1	2	yes	—
255	#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄	—	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	#107	C₂³	1	2	yes	—
272	#107	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	1	yes	characteristic
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	1	yes	characteristic
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#102	C₂³	1	1	yes	characteristic
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
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	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
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	—	2	2	no	—
313	#41	—	4	2	no	—
314	#41	—	4	2	no	—
315	#41	—	4	1	no	—
316	#41	—	4	1	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	8	2	no	—
320	#41	—	8	2	no	—
321	#41	—	8	2	no	—
322	#41	—	8	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	8	2	no	—
328	C₂×Q₈	C₂×D₄	1	2	yes	—
329	C₂×Q₈	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	8	2	no	—
346	C₂×D₄	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄	C₂×D₄	1	2	yes	—
349	C₂×D₄	C₂×D₄	1	2	yes	—
350	C₂×D₄	C₂×D₄	1	2	yes	—
351	C₂×D₄	C₂×D₄	1	2	yes	—
352	C₂×D₄	C₂⁴	1	1	yes	characteristic
353	C₂×D₄	C₂⁴	1	2	yes	—
354	C₂×D₄	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴	1	2	yes	—
369	C₂²×C₄	C₂⁴	1	2	yes	—
370	Q₁₆	—	4	1	no	—
371	SD₁₆	—	4	2	no	—
372	SD₁₆	—	4	1	no	—
373	SD₁₆	—	4	1	no	—
374	D₈	—	4	1	no	—
375	D₈	—	4	2	no	—
376	M₁₆	—	4	2	no	—
377	M₁₆	—	4	2	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₈	C₂⁴	1	2	yes	—
385	C₂×C₈	C₂⁴	1	2	yes	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	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	2	yes	—
404	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄	C₂⁴	1	2	yes	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	C₂×D₄	1	1	yes	characteristic
446	C₄²	C₂×D₄	1	1	yes	characteristic
447	C₄²	C₂⁴	1	1	yes	characteristic
448	C₄²	C₂⁴	1	1	yes	characteristic
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	8	2	no	—
453	C₂³	—	8	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	C₂²×D₄	1	2	yes	—
456	C₂³	C₂²×D₄	1	2	yes	—
457	C₂³	C₂²×D₄	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	8	2	no	—
467	D₄	—	2	2	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	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	8	1	no	—
482	D₄	—	8	2	no	—
483	D₄	—	8	1	no	—
484	D₄	—	8	2	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	2	no	—
488	D₄	—	8	2	no	—
489	D₄	—	8	2	no	—
490	D₄	—	8	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	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	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	C₂²×D₄	1	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂⁵	1	1	yes	characteristic
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	2	no	—
529	C₈	—	2	2	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	16	4	no	—
551	C₂²	C₂³×D₄	1	1	yes	characteristic
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	#576	1	2	yes	—
568	C₄	#585	1	1	yes	characteristic
569	C₄	#585	1	1	yes	characteristic
570	C₂	—	4	1	no	—
571	C₂	—	4	2	no	—
572	C₂	—	4	2	no	—
573	C₂	—	8	1	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	1	no	—
576	C₂	#3485	1	1	yes	characteristic
577	C₂	C₂×#576	1	1	yes	characteristic
578	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 ◁ #532 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3546	C₂	semidirect
2. #3511	C₂	semidirect
3. #3353	C₂	semidirect
4. #3353	C₂	semidirect
5. #3347	C₂	semidirect
6. #3346	C₂	semidirect
7. #3342	C₂	semidirect
8. #3334	C₂	semidirect
9. #3332	C₂	semidirect
10. #3324	C₂	semidirect
11. #3319	C₂	semidirect
12. #3314	C₂	semidirect
13. #3304	C₂	semidirect
14. #3294	C₂	semidirect
15. #3239	C₂	semidirect
16. #3226	C₂	semidirect
17. #3203	C₂	semidirect
18. #3198	C₂	semidirect
19. #3115	C₂	semidirect
20. #3102	C₂	semidirect
21. #3098	C₂	semidirect
22. #3096	C₂	semidirect
23. #2981	C₂	semidirect
27. #556	C₂²	semidirect
28. #555	C₂²	semidirect
29. #554	C₂²	semidirect
38. #547	C₂²	semidirect
46. #537	C₂²	semidirect
53. C₂×C₄⋊Q₈	C₂²	semidirect
55. #520	C₂²	semidirect
56. C₄×#41	C₂²	semidirect
57. #501	C₂²	semidirect
58. #500	C₂²	semidirect
59. #500	C₂²	semidirect
63. #485	C₂²	semidirect
64. #485	C₂²	semidirect
65. #485	C₂²	semidirect
66. #484	C₂²	semidirect
67. #484	C₂²	semidirect
68. #484	C₂²	semidirect
72. #482	C₂²	semidirect
73. #482	C₂²	semidirect
74. #482	C₂²	semidirect
76. #481	C₂²	semidirect
79. #480	C₂²	semidirect
80. #480	C₂²	semidirect
81. #480	C₂²	semidirect
82. #479	C₂²	semidirect
83. #478	C₂²	semidirect
84. #475	C₂²	semidirect
85. #475	C₂²	semidirect
86. #475	C₂²	semidirect
89. #474	C₂²	semidirect
90. #474	C₂²	semidirect
91. #474	C₂²	semidirect
92. #469	C₂²	semidirect
95. #468	C₂²	semidirect
96. #467	C₂²	semidirect
99. #465	C₂²	semidirect
104. #452	C₂²	semidirect
105. #452	C₂²	semidirect
108. #449	C₂²	semidirect
109. #449	C₂²	semidirect
111. #442	C₂²	semidirect
112. #440	C₂²	semidirect
113. C₄×Q₁₆	C₂²	semidirect
115. C₄×SD₁₆	C₂²	semidirect
118. #436	C₂²	semidirect
119. #435	C₂²	semidirect
120. #435	C₂²	semidirect
122. C₈×D₄	C₂²	semidirect
123. #432	C₂²	semidirect
124. #431	C₂²	semidirect
125. #428	C₂²	semidirect
126. #428	C₂²	semidirect
127. #427	C₂²	semidirect
128. C₂×#107	C₂²	semidirect
130. #417	C₂²	semidirect
131. #416	C₂²	semidirect
133. #408	C₂²	semidirect
134. #408	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3546	2
#3511	2
#3353	2
#3347	2
#3346	2
#3342	2
#3334	2
#3332	2
#3324	2
#3319	2
#3314	2
#3304	2
#3294	2
#3239	2
#3226	2
#3203	2
#3198	2
#3115	2
#3102	2
#3098	2
#3096	2
#2981	2