Subgroups — #61343

Order 256.

908 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	#3376	C₂	1	2	yes	maximal, complemented
4	#3376	C₂	1	2	yes	maximal, complemented
5	#3373	C₂	1	2	yes	maximal, complemented
6	#3370	C₂	1	2	yes	maximal, complemented
7	#3370	C₂	1	2	yes	maximal, complemented
8	#3367	C₂	1	2	yes	maximal, complemented
9	#3361	C₂	1	2	yes	maximal, complemented
10	#3360	C₂	1	2	yes	maximal, complemented
11	#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	#3137	C₂	1	1	yes	maximal, characteristic, complemented
13	#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	#3041	C₂	1	1	yes	maximal, characteristic
19	C₂×#463	C₂	1	1	yes	maximal, characteristic, complemented
20	#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	#2949	C₂	1	1	yes	maximal, characteristic, complemented
22	#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂²×D₈	C₂²	1	1	yes	characteristic
27	#559	C₂²	1	2	yes	complemented
28	#559	C₂²	1	2	yes	complemented
29	#556	C₂²	1	2	yes	complemented
30	#556	C₂²	1	2	yes	complemented
31	#554	—	2	1	no	—
32	#554	—	2	1	no	—
33	#554	—	2	1	no	—
34	#554	C₂²	1	2	yes	complemented
35	#554	C₂²	1	2	yes	complemented
36	#554	C₂²	1	2	yes	complemented
37	#551	—	2	2	no	—
38	#551	—	2	2	no	—
39	D₄×Q₈	—	2	1	no	—
40	D₄×Q₈	C₂²	1	2	yes	complemented
41	#544	C₂²	1	1	yes	characteristic
42	#544	C₂²	1	1	yes	characteristic
43	#543	—	2	2	no	—
44	#542	—	2	1	no	—
45	#542	—	2	1	no	—
46	#536	C₂²	1	1	yes	characteristic
47	#535	C₂²	1	1	yes	characteristic
48	#533	C₂²	1	1	yes	characteristic
49	#533	C₂²	1	1	yes	characteristic
50	#529	—	2	1	no	—
51	#529	—	2	1	no	—
52	C₂×#124	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈	—	2	2	no	—
54	#519	C₂²	1	1	yes	characteristic
55	#518	C₂²	1	1	yes	characteristic
56	#518	C₂²	1	1	yes	characteristic
57	#518	C₂²	1	1	yes	characteristic
58	C₄×#41	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
60	#491	C₂²	1	2	yes	complemented
61	#490	C₂²	1	2	yes	complemented
62	#489	C₂²	1	2	yes	complemented
63	#489	C₂²	1	2	yes	complemented
64	#489	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	#488	C₂²	1	2	yes	complemented
69	#488	C₂²	1	2	yes	complemented
70	#487	C₂²	1	2	yes	complemented
71	#486	C₂²	1	2	yes	complemented
72	#479	C₂²	1	1	yes	characteristic, complemented
73	#479	C₂²	1	1	yes	characteristic, complemented
74	#479	C₂²	1	2	yes	complemented
75	#479	C₂²	1	2	yes	complemented
76	#478	C₂²	1	1	yes	characteristic, complemented
77	#478	C₂²	1	1	yes	characteristic, complemented
78	#478	C₂²	1	2	yes	complemented
79	#478	C₂²	1	2	yes	complemented
80	#477	C₂²	1	1	yes	characteristic, complemented
81	#477	C₂²	1	2	yes	complemented
82	#476	C₂²	1	1	yes	characteristic, complemented
83	#476	C₂²	1	2	yes	complemented
84	#475	C₂²	1	1	yes	characteristic, complemented
85	#475	C₂²	1	2	yes	complemented
86	#474	C₂²	1	1	yes	characteristic, complemented
87	#474	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	—
89	#463	C₂²	1	2	yes	—
90	#463	C₂²	1	2	yes	—
91	#463	C₂²	1	2	yes	—
92	#463	C₂²	1	2	yes	—
93	#463	C₂²	1	2	yes	—
94	#463	C₂²	1	2	yes	complemented
95	#463	C₂²	1	2	yes	complemented
96	#461	C₂²	1	2	yes	complemented
97	#461	C₂²	1	2	yes	complemented
98	#459	C₂²	1	2	yes	—
99	#459	C₂²	1	2	yes	—
100	#446	C₂²	1	2	yes	complemented
101	#446	C₂²	1	2	yes	complemented
102	#446	C₂²	1	2	yes	complemented
103	C₈×Q₈	C₂²	1	2	yes	complemented
104	#442	C₂²	1	2	yes	—
105	#442	C₂²	1	2	yes	—
106	#442	C₂²	1	2	yes	complemented
107	#440	C₂²	1	2	yes	complemented
108	#440	C₂²	1	2	yes	complemented
109	#440	C₂²	1	2	yes	complemented
110	C₄×SD₁₆	C₂²	1	2	yes	complemented
111	C₄×SD₁₆	C₂²	1	2	yes	complemented
112	C₄×SD₁₆	C₂²	1	2	yes	complemented
113	C₄×D₈	C₂²	1	2	yes	—
114	C₄×D₈	C₂²	1	2	yes	—
115	C₄×D₈	C₂²	1	2	yes	complemented
116	#428	C₂²	1	1	yes	characteristic
117	#427	C₂²	1	1	yes	characteristic
118	#427	C₂²	1	1	yes	characteristic
119	#424	C₂²	1	1	yes	characteristic
120	#424	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
122	#419	C₂²	1	1	yes	characteristic
123	#419	C₂²	1	1	yes	characteristic
124	#418	C₂²	1	1	yes	characteristic
125	#418	C₂²	1	1	yes	characteristic
126	#418	C₂²	1	1	yes	characteristic
127	#417	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic
129	#416	C₂²	1	1	yes	characteristic
130	C₂×#103	C₂²	1	1	yes	characteristic
131	C₂×#102	C₂²	1	1	yes	characteristic
132	#405	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×#41	C₂³	1	1	yes	characteristic
136	C₂²×Q₈	—	2	2	no	—
137	C₂²×Q₈	C₂³	1	1	yes	characteristic
138	C₂²×D₄	C₂³	1	1	yes	characteristic
139	C₂²×D₄	C₂³	1	1	yes	characteristic
140	C₂³×C₄	—	2	1	no	—
141	AGL(1,ℤ/8)	—	2	4	no	—
142	C₂×SD₁₆	—	2	4	no	—
143	C₂×SD₁₆	C₂³	1	2	yes	—
144	C₂×SD₁₆	C₂³	1	2	yes	—
145	C₂×SD₁₆	C₂³	1	2	yes	—
146	C₂×D₈	—	2	4	no	—
147	C₂×D₈	C₂³	1	2	yes	—
148	C₂×D₈	C₂³	1	2	yes	—
149	C₂×D₈	C₂³	1	2	yes	—
150	C₂×M₁₆	C₂³	1	1	yes	characteristic
151	C₂×M₁₆	C₂³	1	1	yes	characteristic
152	C₂²×C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₈	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₄⋊Q₈	C₂³	1	2	yes	—
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	2	yes	—
163	#127	C₂³	1	2	yes	—
164	#126	—	2	2	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#125	—	2	1	no	—
169	#125	—	2	1	no	—
170	#125	D₄	1	1	yes	characteristic
171	#125	D₄	1	1	yes	characteristic
172	#125	C₂³	1	1	yes	characteristic
173	#125	C₂³	1	1	yes	characteristic
174	#125	C₂³	1	2	yes	—
175	#125	C₂³	1	2	yes	—
176	#124	—	2	2	no	—
177	#124	—	2	2	no	—
178	#124	—	2	1	no	—
179	#124	—	2	1	no	—
180	#124	C₂³	1	2	yes	—
181	#124	C₂³	1	2	yes	—
182	#124	C₂³	1	2	yes	—
183	#124	C₂³	1	2	yes	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	1	no	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	D₄	1	2	yes	—
210	C₂²⋊Q₈	D₄	1	2	yes	—
211	#121	—	2	1	no	—
212	#121	—	2	1	no	—
213	#120	—	2	2	no	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	—	2	1	no	—
216	C₄×Q₈	—	2	1	no	—
217	C₄×Q₈	—	2	1	no	—
218	C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₄×Q₈	C₂³	1	2	yes	—
221	C₄×Q₈	C₂³	1	2	yes	—
222	C₄×Q₈	C₂³	1	2	yes	—
223	C₄×Q₈	C₂³	1	2	yes	—
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	2	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	C₂³	1	2	yes	—
237	C₄×D₄	C₂³	1	2	yes	—
238	C₄×D₄	C₂³	1	1	yes	characteristic
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	1	2	yes	—
241	C₄×D₄	C₂³	1	2	yes	—
242	C₄×D₄	C₂³	1	2	yes	—
243	C₄×D₄	C₂³	1	2	yes	—
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	2	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	—	2	2	no	—
249	#117	—	2	1	no	—
250	#117	C₂³	1	1	yes	characteristic
251	#117	C₂³	1	1	yes	characteristic
252	#117	C₂³	1	1	yes	characteristic
253	#117	C₂³	1	1	yes	characteristic
254	#117	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	1	yes	characteristic
268	#107	C₂³	1	1	yes	characteristic
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	2	yes	—
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	1	yes	characteristic
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	2	yes	—
277	C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	C₄⋊C₈	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	2	yes	—
308	#102	C₂³	1	2	yes	—
309	#97	C₂³	1	2	yes	—
310	#97	C₂³	1	2	yes	—
311	#97	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	2	yes	—
313	C₄×C₈	C₂³	1	2	yes	—
314	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	—	2	1	no	—
316	C₂⁴	—	2	1	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	8	4	no	—
327	C₂×Q₈	C₂×D₄	1	2	yes	—
328	C₂×Q₈	C₂×D₄	1	2	yes	—
329	C₂×Q₈	C₂⁴	1	2	yes	—
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	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	#41	1	4	yes	—
340	C₂×D₄	C₂⁴	1	2	yes	—
341	C₂×D₄	C₂⁴	1	1	yes	characteristic
342	C₂×D₄	C₂⁴	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	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	—	2	2	no	—
356	C₂²×C₄	—	8	2	no	—
357	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴	1	1	yes	characteristic
360	SD₁₆	—	2	4	no	—
361	SD₁₆	—	2	4	no	—
362	SD₁₆	—	2	4	no	—
363	D₈	—	2	4	no	—
364	D₈	—	2	4	no	—
365	D₈	—	2	4	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	C₂⁴	1	2	yes	—
371	C₂×C₈	C₂⁴	1	1	yes	characteristic
372	C₂×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₈	C₂⁴	1	2	yes	—
374	C₂×C₈	C₂⁴	1	1	yes	characteristic
375	C₂×C₈	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	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	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
400	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₄⋊C₄	C₂×D₄	1	2	yes	—
405	C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	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	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	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	2	yes	—
446	C₄²	C₂⁴	1	2	yes	—
447	C₄²	C₂⁴	1	1	yes	characteristic
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	8	1	no	—
454	C₂³	—	8	1	no	—
455	C₂³	—	8	1	no	—
456	C₂³	—	8	1	no	—
457	C₂³	C₂²×D₄	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	2	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	1	no	—
467	Q₈	—	8	2	no	—
468	Q₈	—	8	2	no	—
469	D₄	—	2	4	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	1	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	8	2	no	—
478	D₄	—	8	2	no	—
479	D₄	C₂×#41	1	4	yes	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	8	1	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	—	8	2	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	1	no	—
504	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄	1	2	yes	—
507	C₂×C₄	C₂²×D₄	1	2	yes	—
508	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄	1	2	yes	—
511	C₂×C₄	C₂²×D₄	1	2	yes	—
512	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂×#41	1	2	yes	—
514	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
515	C₂×C₄	C₂⁵	1	1	yes	characteristic
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	8	4	no	—
534	C₂²	—	16	2	no	—
535	C₂²	#548	1	2	yes	—
536	C₂²	C₂³×D₄	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	2	no	—
554	C₄	#548	1	2	yes	—
555	C₄	C₂²×#41	1	1	yes	characteristic
556	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
557	C₂	—	2	2	no	—
558	C₂	—	4	4	no	—
559	C₂	—	8	1	no	—
560	C₂	—	8	2	no	—
561	C₂	C₂×#548	1	1	yes	characteristic
562	C₂	#3584	1	1	yes	characteristic
563	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3041	C₂
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. #3510	C₂	semidirect
2. #3501	C₂	semidirect
3. #3376	C₂	semidirect
4. #3376	C₂	semidirect
5. #3373	C₂	semidirect
6. #3370	C₂	semidirect
7. #3370	C₂	semidirect
8. #3367	C₂	semidirect
9. #3361	C₂	semidirect
10. #3360	C₂	semidirect
11. #3140	C₂	semidirect
12. #3137	C₂	semidirect
13. #3136	C₂	semidirect
14. #3082	C₂	semidirect
15. #3081	C₂	semidirect
16. #3076	C₂	semidirect
17. #3042	C₂	semidirect
19. C₂×#463	C₂	semidirect
20. #2962	C₂	semidirect
21. #2949	C₂	semidirect
22. #2948	C₂	semidirect
23. C₄×AGL(1,ℤ/8)	C₂	semidirect
27. #559	C₂²	semidirect
28. #559	C₂²	semidirect
29. #556	C₂²	semidirect
30. #556	C₂²	semidirect
34. #554	C₂²	semidirect
35. #554	C₂²	semidirect
36. #554	C₂²	semidirect
40. D₄×Q₈	C₂²	semidirect
60. #491	C₂²	semidirect
61. #490	C₂²	semidirect
62. #489	C₂²	semidirect
63. #489	C₂²	semidirect
64. #489	C₂²	semidirect
65. #489	C₂²	semidirect
66. #488	C₂²	semidirect
67. #488	C₂²	semidirect
68. #488	C₂²	semidirect
69. #488	C₂²	semidirect
70. #487	C₂²	semidirect
71. #486	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
74. #479	C₂²	semidirect
75. #479	C₂²	semidirect
76. #478	C₂²	semidirect
77. #478	C₂²	semidirect
78. #478	C₂²	semidirect
79. #478	C₂²	semidirect
80. #477	C₂²	semidirect
81. #477	C₂²	semidirect
82. #476	C₂²	semidirect
83. #476	C₂²	semidirect
84. #475	C₂²	semidirect
85. #475	C₂²	semidirect
86. #474	C₂²	semidirect
87. #474	C₂²	semidirect
94. #463	C₂²	semidirect
95. #463	C₂²	semidirect
96. #461	C₂²	semidirect
97. #461	C₂²	semidirect
100. #446	C₂²	semidirect
101. #446	C₂²	semidirect
102. #446	C₂²	semidirect
103. C₈×Q₈	C₂²	semidirect
106. #442	C₂²	semidirect
107. #440	C₂²	semidirect
108. #440	C₂²	semidirect
109. #440	C₂²	semidirect
110. C₄×SD₁₆	C₂²	semidirect
111. C₄×SD₁₆	C₂²	semidirect
112. C₄×SD₁₆	C₂²	semidirect
115. C₄×D₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3510	2
#3501	2
#3376	2
#3373	2
#3370	2
#3367	2
#3361	2
#3360	2
#3140	2
#3137	2
#3136	2
#3082	2
#3081	2
#3076	2
#3042	2
#3041	2
C₂×#463	2
#2962	2
#2949	2
#2948	2
C₄×AGL(1,ℤ/8)	2