Subgroups — #61863

Order 256.

865 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	#3389	C₂	1	2	yes	maximal, complemented
4	#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	#3384	C₂	1	1	yes	maximal, characteristic, complemented
6	#3381	C₂	1	1	yes	maximal, characteristic, complemented
7	#3380	C₂	1	2	yes	maximal, complemented
8	Q₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#3373	C₂	1	1	yes	maximal, characteristic, complemented
10	#3370	C₂	1	2	yes	maximal, complemented
11	#3366	C₂	1	1	yes	maximal, characteristic, complemented
12	#3361	C₂	1	1	yes	maximal, characteristic, complemented
13	#3361	C₂	1	2	yes	maximal, complemented
14	#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	#3243	C₂	1	2	yes	maximal, complemented
16	#3241	C₂	1	2	yes	maximal, complemented
17	#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	#3122	C₂	1	2	yes	maximal, complemented
20	#3118	C₂	1	2	yes	maximal, complemented
21	#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	#562	—	2	2	no	—
25	#559	C₂²	1	2	yes	complemented
26	#559	C₂²	1	1	yes	characteristic, complemented
27	#557	C₂²	1	1	yes	characteristic, complemented
28	#554	—	2	1	no	—
29	#554	—	2	2	no	—
30	#554	C₂²	1	1	yes	characteristic
31	#554	C₂²	1	2	yes	—
32	#554	C₂²	1	1	yes	characteristic
33	#554	C₂²	1	2	yes	—
34	#554	C₂²	1	2	yes	complemented
35	#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈	—	2	1	no	—
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	D₄×Q₈	C₂²	1	1	yes	characteristic
39	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	#548	—	2	1	no	—
41	#547	—	2	1	no	—
42	#544	C₂²	1	2	yes	—
43	#543	—	2	2	no	—
44	#542	—	2	1	no	—
45	#542	C₂²	1	2	yes	—
46	#540	C₂²	1	2	yes	—
47	#539	—	2	2	no	—
48	#536	—	2	1	no	—
49	#533	C₂²	1	1	yes	characteristic
50	#533	C₂²	1	1	yes	characteristic
51	#532	C₂²	1	1	yes	characteristic
52	#529	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈	—	2	1	no	—
54	C₂×C₂²⋊Q₈	—	2	1	no	—
55	#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#501	C₂²	1	2	yes	complemented
59	#500	C₂²	1	2	yes	complemented
60	#500	C₂²	1	1	yes	characteristic, complemented
61	#499	C₂²	1	2	yes	complemented
62	#499	C₂²	1	2	yes	complemented
63	#498	C₂²	1	1	yes	characteristic, complemented
64	#490	C₂²	1	2	yes	complemented
65	#489	C₂²	1	2	yes	complemented
66	#488	C₂²	1	2	yes	complemented
67	#488	C₂²	1	2	yes	complemented
68	#486	C₂²	1	2	yes	complemented
69	#486	C₂²	1	1	yes	characteristic, complemented
70	#486	C₂²	1	1	yes	characteristic, complemented
71	#485	C₂²	1	2	yes	—
72	#484	C₂²	1	1	yes	characteristic
73	#482	C₂²	1	2	yes	—
74	#482	C₂²	1	2	yes	—
75	#482	C₂²	1	2	yes	—
76	#481	C₂²	1	1	yes	characteristic
77	#480	C₂²	1	2	yes	—
78	#479	C₂²	1	2	yes	complemented
79	#478	C₂²	1	1	yes	characteristic
80	#478	C₂²	1	1	yes	characteristic
81	#478	C₂²	1	2	yes	—
82	#478	C₂²	1	2	yes	—
83	#478	C₂²	1	2	yes	complemented
84	#478	C₂²	1	2	yes	complemented
85	#478	C₂²	1	2	yes	complemented
86	#478	C₂²	1	2	yes	complemented
87	#478	C₂²	1	2	yes	complemented
88	#477	C₂²	1	1	yes	characteristic, complemented
89	#477	C₂²	1	2	yes	complemented
90	#476	C₂²	1	2	yes	—
91	#476	C₂²	1	1	yes	characteristic, complemented
92	#476	C₂²	1	2	yes	complemented
93	#475	C₂²	1	1	yes	characteristic, complemented
94	#474	C₂²	1	1	yes	characteristic
95	#474	C₂²	1	1	yes	characteristic
96	#474	C₂²	1	2	yes	—
97	#474	C₂²	1	1	yes	characteristic, complemented
98	#474	C₂²	1	2	yes	complemented
99	#474	C₂²	1	2	yes	complemented
100	#463	C₂²	1	1	yes	characteristic
101	#463	C₂²	1	1	yes	characteristic
102	#463	C₂²	1	2	yes	—
103	#463	C₂²	1	2	yes	—
104	#459	C₂²	1	1	yes	characteristic
105	#459	C₂²	1	1	yes	characteristic
106	#459	C₂²	1	2	yes	—
107	#459	C₂²	1	2	yes	—
108	#450	C₂²	1	1	yes	characteristic
109	#447	C₂²	1	2	yes	—
110	#447	C₂²	1	1	yes	characteristic
111	#446	C₂²	1	1	yes	characteristic, complemented
112	#446	C₂²	1	2	yes	complemented
113	#446	C₂²	1	1	yes	characteristic, complemented
114	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈	C₂²	1	2	yes	complemented
117	#442	C₂²	1	2	yes	—
118	#442	C₂²	1	2	yes	—
119	#442	C₂²	1	2	yes	—
120	#440	C₂²	1	2	yes	—
121	C₄×SD₁₆	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆	C₂²	1	2	yes	—
124	C₄×D₈	C₂²	1	2	yes	—
125	C₄×D₈	C₂²	1	2	yes	—
126	C₄×D₈	C₂²	1	1	yes	characteristic
127	C₄×D₈	C₂²	1	2	yes	—
128	C₄×D₈	C₂²	1	1	yes	characteristic
129	C₄×D₈	C₂²	1	2	yes	—
130	C₄×D₈	C₂²	1	2	yes	—
131	#433	C₂²	1	2	yes	—
132	#433	C₂²	1	2	yes	—
133	#431	C₂²	1	1	yes	characteristic
134	#431	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂²×Q₈	—	2	1	no	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₄	—	2	1	no	—
142	C₂×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×D₈	C₂³	1	2	yes	—
145	C₂×D₈	C₂³	1	1	yes	characteristic
146	C₂×D₈	C₂³	1	2	yes	—
147	C₂×D₈	C₂³	1	1	yes	characteristic
148	C₄⋊Q₈	—	2	1	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	D₄	1	1	yes	characteristic
151	C₄⋊Q₈	D₄	1	1	yes	characteristic
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	2	yes	—
156	C₄⋊Q₈	C₂³	1	2	yes	—
157	C₄⋊Q₈	C₂³	1	2	yes	—
158	#127	C₂³	1	1	yes	characteristic
159	#127	C₂³	1	2	yes	—
160	#126	—	2	2	no	—
161	#126	—	2	1	no	—
162	#125	—	2	2	no	—
163	#125	—	2	2	no	—
164	#125	D₄	1	2	yes	—
165	#125	C₂³	1	1	yes	characteristic
166	#125	C₂³	1	2	yes	—
167	#125	C₂³	1	2	yes	—
168	#125	C₂³	1	2	yes	—
169	#125	C₂³	1	2	yes	—
170	#124	—	2	1	no	—
171	#124	—	2	2	no	—
172	#124	—	2	2	no	—
173	#124	—	2	1	no	—
174	#124	C₂³	1	1	yes	characteristic
175	#124	C₂³	1	2	yes	—
176	#123	—	2	1	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	#123	—	2	2	no	—
183	C₂²⋊Q₈	—	2	1	no	—
184	C₂²⋊Q₈	—	2	1	no	—
185	C₂²⋊Q₈	—	2	2	no	—
186	C₂²⋊Q₈	—	2	2	no	—
187	C₂²⋊Q₈	—	2	2	no	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	1	no	—
199	C₂²⋊Q₈	—	2	2	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈	D₄	1	2	yes	—
210	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	#121	—	2	1	no	—
212	#121	—	2	2	no	—
213	#121	—	2	1	no	—
214	#121	—	2	2	no	—
215	#121	—	2	2	no	—
216	#121	C₂³	1	1	yes	characteristic
217	#121	C₂³	1	2	yes	—
218	C₄×Q₈	—	2	1	no	—
219	C₄×Q₈	—	2	1	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₄×Q₈	C₂³	1	2	yes	—
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×Q₈	C₂³	1	2	yes	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
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	2	yes	—
239	C₄×D₄	C₂³	1	2	yes	—
240	C₄×D₄	C₂³	1	2	yes	—
241	C₄×D₄	C₂³	1	2	yes	—
242	C₄×D₄	C₂³	1	1	yes	characteristic
243	C₄×D₄	C₂³	1	2	yes	—
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	2	yes	—
246	C₄×D₄	C₂³	1	2	yes	—
247	#117	—	2	1	no	—
248	#117	C₂³	1	2	yes	—
249	#117	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	C₂³	1	1	yes	characteristic
260	#107	C₂³	1	2	yes	—
261	#107	C₂³	1	2	yes	—
262	#107	C₂³	1	2	yes	—
263	#107	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	2	yes	—
268	#106	C₂³	1	2	yes	—
269	#106	C₂³	1	1	yes	characteristic
270	#106	C₂³	1	1	yes	characteristic
271	#106	C₂³	1	2	yes	—
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₄⋊C₈	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
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	#102	C₂³	1	1	yes	characteristic
287	#102	C₂³	1	2	yes	—
288	#102	C₂³	1	1	yes	characteristic
289	#102	C₂³	1	2	yes	—
290	#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	1	yes	characteristic
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	#97	C₂³	1	2	yes	—
306	#97	C₂³	1	2	yes	—
307	C₄×C₈	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	1	no	—
313	#41	—	8	2	no	—
314	#41	—	8	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×Q₈	—	8	2	no	—
323	C₂×Q₈	—	8	2	no	—
324	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈	C₂×D₄	1	2	yes	—
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	C₂⁴	1	1	yes	characteristic
338	C₂×D₄	C₂⁴	1	2	yes	—
339	C₂×D₄	C₂⁴	1	1	yes	characteristic
340	C₂×D₄	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	8	2	no	—
356	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴	1	1	yes	characteristic
359	SD₁₆	—	2	2	no	—
360	SD₁₆	—	2	2	no	—
361	D₈	—	2	4	no	—
362	D₈	—	2	2	no	—
363	D₈	—	2	4	no	—
364	D₈	—	2	2	no	—
365	C₂×C₈	C₂⁴	1	1	yes	characteristic
366	C₂×C₈	C₂⁴	1	2	yes	—
367	C₂×C₈	C₂⁴	1	1	yes	characteristic
368	C₂×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₈	C₂⁴	1	2	yes	—
370	C₂×C₈	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₄⋊C₄	C₂⁴	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	1	yes	characteristic
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₂²⋊C₄	—	2	2	no	—
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	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	C₂×D₄	1	1	yes	characteristic
434	C₄²	C₂×D₄	1	1	yes	characteristic
435	C₄²	C₂⁴	1	1	yes	characteristic
436	C₄²	C₂⁴	1	1	yes	characteristic
437	C₄²	C₂⁴	1	2	yes	—
438	C₄²	C₂⁴	1	2	yes	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	8	1	no	—
445	C₂³	—	8	1	no	—
446	C₂³	C₂²×D₄	1	1	yes	characteristic
447	Q₈	—	2	2	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	4	2	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	8	1	no	—
455	Q₈	—	8	2	no	—
456	Q₈	—	8	2	no	—
457	Q₈	—	8	2	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	2	1	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	2	no	—
465	D₄	—	4	2	no	—
466	D₄	—	8	1	no	—
467	D₄	—	8	2	no	—
468	D₄	—	8	2	no	—
469	D₄	—	8	1	no	—
470	D₄	—	8	2	no	—
471	D₄	2₋¹⁺⁴	1	2	yes	—
472	D₄	2₋¹⁺⁴	1	2	yes	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	—	8	2	no	—
490	C₂×C₄	—	8	2	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	—	8	1	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	—	8	2	no	—
496	C₂×C₄	—	8	2	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	—	8	1	no	—
499	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄	1	2	yes	—
501	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄	1	2	yes	—
505	C₂×C₄	C₂²×D₄	1	2	yes	—
506	C₂×C₄	C₂²×D₄	1	2	yes	—
507	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄	C₂⁵	1	1	yes	characteristic
509	C₈	—	2	2	no	—
510	C₈	—	2	1	no	—
511	C₈	—	2	2	no	—
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	8	4	no	—
531	C₂²	C₂³×D₄	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	#576	1	2	yes	—
549	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
550	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
551	C₂	—	4	1	no	—
552	C₂	—	4	2	no	—
553	C₂	—	4	2	no	—
554	C₂	—	8	2	no	—
555	C₂	—	8	1	no	—
556	C₂	#3486	1	1	yes	characteristic
557	C₂	C₂×#576	1	1	yes	characteristic
558	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 ◁ #533 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3554	C₂	semidirect
2. #3501	C₂	semidirect
3. #3389	C₂	semidirect
4. #3386	C₂	semidirect
5. #3384	C₂	semidirect
6. #3381	C₂	semidirect
7. #3380	C₂	semidirect
8. Q₈×D₈	C₂	semidirect
9. #3373	C₂	semidirect
10. #3370	C₂	semidirect
11. #3366	C₂	semidirect
12. #3361	C₂	semidirect
13. #3361	C₂	semidirect
14. #3358	C₂	semidirect
15. #3243	C₂	semidirect
16. #3241	C₂	semidirect
17. #3233	C₂	semidirect
18. #3228	C₂	semidirect
19. #3122	C₂	semidirect
20. #3118	C₂	semidirect
21. #3105	C₂	semidirect
22. #3100	C₂	semidirect
23. #2986	C₂	semidirect
25. #559	C₂²	semidirect
26. #559	C₂²	semidirect
27. #557	C₂²	semidirect
34. #554	C₂²	semidirect
35. #550	C₂²	semidirect
39. D₄×Q₈	C₂²	semidirect
57. #501	C₂²	semidirect
58. #501	C₂²	semidirect
59. #500	C₂²	semidirect
60. #500	C₂²	semidirect
61. #499	C₂²	semidirect
62. #499	C₂²	semidirect
63. #498	C₂²	semidirect
64. #490	C₂²	semidirect
65. #489	C₂²	semidirect
66. #488	C₂²	semidirect
67. #488	C₂²	semidirect
68. #486	C₂²	semidirect
69. #486	C₂²	semidirect
70. #486	C₂²	semidirect
78. #479	C₂²	semidirect
83. #478	C₂²	semidirect
84. #478	C₂²	semidirect
85. #478	C₂²	semidirect
86. #478	C₂²	semidirect
87. #478	C₂²	semidirect
88. #477	C₂²	semidirect
89. #477	C₂²	semidirect
91. #476	C₂²	semidirect
92. #476	C₂²	semidirect
93. #475	C₂²	semidirect
97. #474	C₂²	semidirect
98. #474	C₂²	semidirect
99. #474	C₂²	semidirect
111. #446	C₂²	semidirect
112. #446	C₂²	semidirect
113. #446	C₂²	semidirect
114. C₈×Q₈	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
116. C₈×Q₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3554	2
#3501	2
#3389	2
#3386	2
#3384	2
#3381	2
#3380	2
Q₈×D₈	2
#3373	2
#3370	2
#3366	2
#3361	2
#3358	2
#3243	2
#3241	2
#3233	2
#3228	2
#3122	2
#3118	2
#3105	2
#3100	2
#2986	2