Subgroups — #61380

Order 256.

867 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	#3390	C₂	1	2	yes	maximal, complemented
4	#3389	C₂	1	2	yes	maximal, complemented
5	#3388	C₂	1	2	yes	maximal, complemented
6	#3388	C₂	1	2	yes	maximal, complemented
7	#3387	C₂	1	2	yes	maximal, complemented
8	#3386	C₂	1	2	yes	maximal, complemented
9	#3385	C₂	1	2	yes	maximal, complemented
10	#3384	C₂	1	2	yes	maximal, complemented
11	#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#501	C₂	1	1	yes	maximal, characteristic, complemented
14	#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	#3084	C₂	1	1	yes	maximal, characteristic, complemented
16	#3083	C₂	1	1	yes	maximal, characteristic, complemented
17	#3083	C₂	1	1	yes	maximal, characteristic, complemented
18	#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	#3079	C₂	1	1	yes	maximal, characteristic, complemented
20	#2961	C₂	1	1	yes	maximal, characteristic, complemented
21	#2952	C₂	1	1	yes	maximal, characteristic
22	#2951	C₂	1	1	yes	maximal, characteristic
23	#2943	C₂	1	1	yes	maximal, characteristic
24	C₂×#135	C₂²	1	1	yes	characteristic
25	Q₈²	C₂²	1	2	yes	—
26	#557	C₂²	1	2	yes	—
27	#557	C₂²	1	2	yes	—
28	#557	C₂²	1	2	yes	—
29	#554	—	2	2	no	—
30	#554	—	2	2	no	—
31	#554	—	2	2	no	—
32	#554	C₂²	1	2	yes	—
33	#554	C₂²	1	2	yes	—
34	#554	C₂²	1	2	yes	—
35	D₄×Q₈	—	2	2	no	—
36	D₄×Q₈	C₂²	1	2	yes	—
37	#544	—	2	1	no	—
38	#544	—	2	1	no	—
39	#544	—	2	1	no	—
40	#544	—	2	1	no	—
41	#544	C₂²	1	1	yes	characteristic
42	#544	C₂²	1	1	yes	characteristic
43	#544	C₂²	1	1	yes	characteristic
44	#544	C₂²	1	1	yes	characteristic
45	#533	—	2	1	no	—
46	#533	—	2	1	no	—
47	#533	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈	—	2	1	no	—
49	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
50	C₂×#125	—	2	1	no	—
51	C₂×#125	C₂²	1	1	yes	characteristic
52	#520	C₂²	1	1	yes	characteristic
53	#520	C₂²	1	1	yes	characteristic
54	#520	C₂²	1	1	yes	characteristic
55	#520	C₂²	1	1	yes	characteristic
56	C₄×#41	C₂²	1	1	yes	characteristic
57	C₄×#41	C₂²	1	1	yes	characteristic
58	#501	C₂²	1	2	yes	—
59	#501	C₂²	1	2	yes	—
60	#501	C₂²	1	2	yes	—
61	#501	C₂²	1	2	yes	—
62	#501	C₂²	1	2	yes	—
63	#501	C₂²	1	2	yes	—
64	#501	C₂²	1	2	yes	—
65	#501	C₂²	1	2	yes	—
66	#500	C₂²	1	2	yes	—
67	#499	C₂²	1	2	yes	—
68	#499	C₂²	1	2	yes	—
69	#498	C₂²	1	2	yes	—
70	#479	C₂²	1	2	yes	—
71	#479	C₂²	1	2	yes	—
72	#479	C₂²	1	2	yes	—
73	#479	C₂²	1	2	yes	—
74	#479	C₂²	1	2	yes	—
75	#479	C₂²	1	2	yes	—
76	#478	C₂²	1	2	yes	—
77	#478	C₂²	1	2	yes	—
78	#478	C₂²	1	2	yes	—
79	#478	C₂²	1	2	yes	—
80	#478	C₂²	1	2	yes	—
81	#478	C₂²	1	2	yes	—
82	#477	C₂²	1	2	yes	—
83	#477	C₂²	1	2	yes	—
84	#477	C₂²	1	2	yes	—
85	#476	C₂²	1	2	yes	—
86	#476	C₂²	1	2	yes	—
87	#476	C₂²	1	2	yes	—
88	#475	C₂²	1	2	yes	—
89	#475	C₂²	1	2	yes	—
90	#475	C₂²	1	2	yes	—
91	#474	C₂²	1	2	yes	—
92	#474	C₂²	1	2	yes	—
93	#474	C₂²	1	2	yes	—
94	#446	C₂²	1	2	yes	—
95	#446	C₂²	1	2	yes	—
96	#446	C₂²	1	2	yes	—
97	#446	C₂²	1	2	yes	—
98	#442	C₂²	1	1	yes	characteristic
99	#442	C₂²	1	2	yes	—
100	#442	C₂²	1	1	yes	characteristic
101	#441	C₂²	1	1	yes	characteristic
102	#441	C₂²	1	2	yes	—
103	#441	C₂²	1	1	yes	characteristic
104	#440	C₂²	1	1	yes	characteristic
105	#440	C₂²	1	2	yes	—
106	#440	C₂²	1	1	yes	characteristic
107	#440	C₂²	1	2	yes	—
108	#440	C₂²	1	1	yes	characteristic
109	#440	C₂²	1	1	yes	characteristic
110	C₄×Q₁₆	C₂²	1	2	yes	—
111	C₄×SD₁₆	C₂²	1	2	yes	—
112	C₄×SD₁₆	C₂²	1	2	yes	—
113	C₄×D₈	C₂²	1	2	yes	—
114	#428	C₂²	1	1	yes	characteristic
115	#428	C₂²	1	1	yes	characteristic
116	#428	C₂²	1	1	yes	characteristic
117	#428	C₂²	1	1	yes	characteristic
118	#427	C₂²	1	1	yes	characteristic
119	C₂×#107	C₂²	1	1	yes	characteristic
120	C₂×#107	C₂²	1	1	yes	characteristic
121	C₂×#106	C₂²	1	1	yes	characteristic
122	C₂×#106	C₂²	1	1	yes	characteristic
123	#424	C₂²	1	1	yes	characteristic
124	#424	C₂²	1	1	yes	characteristic
125	#423	C₂²	1	1	yes	characteristic
126	#417	C₂²	1	1	yes	characteristic
127	#417	C₂²	1	1	yes	characteristic
128	#417	C₂²	1	1	yes	characteristic
129	#417	C₂²	1	1	yes	characteristic
130	#416	C₂²	1	1	yes	characteristic
131	#416	C₂²	1	1	yes	characteristic
132	#405	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic
134	C₂×#97	C₂²	1	1	yes	characteristic
135	C₂×#41	C₂³	1	1	yes	characteristic
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂²×Q₈	—	2	2	no	—
138	C₂²×Q₈	—	2	1	no	—
139	#135	Q₈	1	8	yes	complemented
140	C₂×Q₁₆	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×D₈	C₂³	1	1	yes	characteristic
144	C₂×M₁₆	C₂³	1	1	yes	characteristic
145	C₂×M₁₆	C₂³	1	1	yes	characteristic
146	C₂²×C₈	C₂³	1	1	yes	characteristic
147	C₂²×C₈	C₂³	1	1	yes	characteristic
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄⋊Q₈	—	2	1	no	—
152	C₄⋊Q₈	—	2	1	no	—
153	C₄⋊Q₈	—	2	2	no	—
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	D₄	1	1	yes	characteristic
161	C₄⋊Q₈	D₄	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	2	yes	—
163	C₄⋊Q₈	C₂³	1	2	yes	—
164	C₄⋊Q₈	C₂³	1	2	yes	—
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	C₄⋊Q₈	C₂³	1	2	yes	—
167	C₄⋊Q₈	C₂³	1	2	yes	—
168	#125	—	2	1	no	—
169	#125	—	2	1	no	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	1	no	—
173	#125	—	2	1	no	—
174	#125	—	2	2	no	—
175	#125	—	2	2	no	—
176	#125	—	2	2	no	—
177	#125	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	—	2	1	no	—
180	#125	D₄	1	1	yes	characteristic
181	#125	D₄	1	1	yes	characteristic
182	#125	C₂³	1	2	yes	—
183	#125	C₂³	1	2	yes	—
184	#125	C₂³	1	2	yes	—
185	#125	C₂³	1	2	yes	—
186	#125	C₂³	1	2	yes	—
187	#125	C₂³	1	2	yes	—
188	C₂²⋊Q₈	—	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	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	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	D₄	1	2	yes	—
205	C₂²⋊Q₈	D₄	1	2	yes	—
206	C₄×Q₈	—	2	2	no	—
207	C₄×Q₈	—	2	2	no	—
208	C₄×Q₈	—	2	2	no	—
209	C₄×Q₈	—	2	2	no	—
210	C₄×Q₈	C₂³	1	1	yes	characteristic
211	C₄×Q₈	C₂³	1	1	yes	characteristic
212	C₄×Q₈	C₂³	1	1	yes	characteristic
213	C₄×Q₈	C₂³	1	1	yes	characteristic
214	C₄×Q₈	C₂³	1	2	yes	—
215	C₄×Q₈	C₂³	1	2	yes	—
216	C₄×Q₈	C₂³	1	2	yes	—
217	C₄×Q₈	C₂³	1	2	yes	—
218	C₄×Q₈	C₂³	1	2	yes	—
219	C₄×Q₈	C₂³	1	2	yes	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	1	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	C₂³	1	1	yes	characteristic
229	C₄×D₄	C₂³	1	1	yes	characteristic
230	C₄×D₄	C₂³	1	1	yes	characteristic
231	C₄×D₄	C₂³	1	1	yes	characteristic
232	C₄×D₄	C₂³	1	2	yes	—
233	C₄×D₄	C₂³	1	2	yes	—
234	C₄×D₄	C₂³	1	2	yes	—
235	C₄×D₄	C₂³	1	2	yes	—
236	#117	—	2	1	no	—
237	#117	—	2	1	no	—
238	#117	—	2	1	no	—
239	#117	—	2	1	no	—
240	#117	—	2	1	no	—
241	#117	—	2	1	no	—
242	#117	C₂³	1	1	yes	characteristic
243	#117	C₂³	1	1	yes	characteristic
244	#117	C₂³	1	1	yes	characteristic
245	#117	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂³	1	1	yes	characteristic
263	#107	C₂³	1	2	yes	—
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	1	yes	characteristic
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	2	yes	—
276	#106	C₂³	1	2	yes	—
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	1	yes	characteristic
279	#106	C₂³	1	2	yes	—
280	#106	C₂³	1	2	yes	—
281	#106	C₂³	1	2	yes	—
282	#106	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	C₄⋊C₈	C₂³	1	2	yes	—
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₄⋊C₈	C₂³	1	2	yes	—
287	C₄⋊C₈	C₂³	1	2	yes	—
288	C₄⋊C₈	C₂³	1	2	yes	—
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
297	#102	C₂³	1	1	yes	characteristic
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	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#97	C₂³	1	1	yes	characteristic
306	#97	C₂³	1	1	yes	characteristic
307	#97	C₂³	1	1	yes	characteristic
308	#97	C₂³	1	1	yes	characteristic
309	#97	C₂³	1	2	yes	—
310	#97	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	2	yes	—
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	#41	C₂×Q₈	1	4	yes	—
316	#41	C₂×Q₈	1	4	yes	complemented
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	8	2	no	—
324	C₂×Q₈	—	8	4	no	—
325	C₂×Q₈	C₂×D₄	1	2	yes	—
326	C₂×Q₈	C₂×D₄	1	2	yes	—
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈	C₂⁴	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂⁴	1	1	yes	characteristic
332	C₂×D₄	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴	1	1	yes	characteristic
350	Q₁₆	C₂×Q₈	1	4	yes	complemented
351	SD₁₆	C₂×Q₈	1	4	yes	complemented
352	SD₁₆	C₂×Q₈	1	4	yes	complemented
353	D₈	C₂×Q₈	1	4	yes	complemented
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	C₂×Q₈	1	4	yes	complemented
358	C₂×C₈	C₂⁴	1	2	yes	—
359	C₂×C₈	C₂⁴	1	2	yes	—
360	C₂×C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₈	C₂⁴	1	1	yes	characteristic
362	C₂×C₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₈	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	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	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	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	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄	C₂⁴	1	2	yes	—
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	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	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	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	C₂×D₄	1	1	yes	characteristic
435	C₄²	C₂×D₄	1	1	yes	characteristic
436	C₄²	C₂⁴	1	2	yes	—
437	C₄²	C₂⁴	1	2	yes	—
438	C₄²	C₂⁴	1	1	yes	characteristic
439	C₄²	C₂⁴	1	1	yes	characteristic
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	C₂²×D₄	1	1	yes	characteristic
443	Q₈	—	2	1	no	—
444	Q₈	—	2	1	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	4	no	—
448	Q₈	—	8	2	no	—
449	Q₈	—	8	2	no	—
450	Q₈	—	8	2	no	—
451	Q₈	—	8	2	no	—
452	Q₈	—	8	2	no	—
453	Q₈	C₂²×Q₈	1	2	yes	—
454	Q₈	C₂²×Q₈	1	2	yes	—
455	D₄	—	2	4	no	—
456	D₄	—	2	4	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	1	no	—
459	D₄	C₂²×Q₈	1	2	yes	—
460	D₄	C₂²×Q₈	1	2	yes	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	8	1	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	—	8	1	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	—	8	1	no	—
484	C₂×C₄	—	8	1	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	—	8	1	no	—
487	C₂×C₄	C₂²×D₄	1	2	yes	—
488	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄	1	2	yes	—
493	C₂×C₄	C₂²×D₄	1	2	yes	—
494	C₂×C₄	C₂²×D₄	1	2	yes	—
495	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄	C₂²×Q₈	1	2	yes	—
497	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
498	C₂×C₄	C₂⁵	1	1	yes	characteristic
499	C₈	—	2	1	no	—
500	C₈	—	2	1	no	—
501	C₈	—	2	2	no	—
502	C₈	—	2	2	no	—
503	C₈	C₂²×Q₈	1	2	yes	—
504	C₈	C₂²×Q₈	1	2	yes	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	D₄×Q₈	1	2	yes	—
514	C₂²	C₂³×D₄	1	1	yes	characteristic
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	1	no	—
533	C₄	D₄×Q₈	1	2	yes	—
534	C₄	C₂³×Q₈	1	1	yes	characteristic
535	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
536	C₂	—	2	2	no	—
537	C₂	—	4	2	no	—
538	C₂	—	4	2	no	—
539	C₂	C₂×D₄×Q₈	1	1	yes	characteristic
540	C₂	#3585	1	1	yes	characteristic
541	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	C₂×#135	C₂²
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. #3504	C₂	semidirect
2. #3503	C₂	semidirect
3. #3390	C₂	semidirect
4. #3389	C₂	semidirect
5. #3388	C₂	semidirect
6. #3388	C₂	semidirect
7. #3387	C₂	semidirect
8. #3386	C₂	semidirect
9. #3385	C₂	semidirect
10. #3384	C₂	semidirect
11. #3164	C₂	semidirect
12. #3163	C₂	semidirect
13. C₂×#501	C₂	semidirect
14. #3084	C₂	semidirect
15. #3084	C₂	semidirect
16. #3083	C₂	semidirect
17. #3083	C₂	semidirect
18. #3080	C₂	semidirect
19. #3079	C₂	semidirect
20. #2961	C₂	semidirect
139. #135	Q₈	semidirect
316. #41	C₂×Q₈	semidirect
350. Q₁₆	C₂×Q₈	semidirect
351. SD₁₆	C₂×Q₈	semidirect
352. SD₁₆	C₂×Q₈	semidirect
353. D₈	C₂×Q₈	semidirect
357. C₂×C₈	C₂×Q₈	semidirect

Maximal subgroups

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

subgroup	index
#3504	2
#3503	2
#3390	2
#3389	2
#3388	2
#3387	2
#3386	2
#3385	2
#3384	2
#3164	2
#3163	2
C₂×#501	2
#3084	2
#3083	2
#3080	2
#3079	2
#2961	2
#2952	2
#2951	2
#2943	2