Subgroups — #61385

Order 256.

879 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	#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	#3389	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	#3386	C₂	1	2	yes	maximal, complemented
8	#3384	C₂	1	2	yes	maximal, complemented
9	#3381	C₂	1	2	yes	maximal, complemented
10	#3380	C₂	1	2	yes	maximal, complemented
11	#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	#3164	C₂	1	1	yes	maximal, characteristic, complemented
13	#3163	C₂	1	1	yes	maximal, characteristic, complemented
14	#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	#3083	C₂	1	1	yes	maximal, characteristic, complemented
16	#3081	C₂	1	1	yes	maximal, characteristic, complemented
17	#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	#3076	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#478	C₂	1	1	yes	maximal, characteristic, complemented
20	#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	#2946	C₂	1	1	yes	maximal, characteristic
22	#2946	C₂	1	1	yes	maximal, characteristic
23	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
24	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	#557	C₂²	1	2	yes	complemented
26	#557	C₂²	1	2	yes	complemented
27	#554	—	2	1	no	—
28	#554	—	2	1	no	—
29	#554	—	2	1	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	#554	C₂²	1	2	yes	complemented
36	#554	C₂²	1	2	yes	complemented
37	D₄×Q₈	—	2	1	no	—
38	D₄×Q₈	C₂²	1	2	yes	—
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	#543	—	2	2	no	—
46	#533	—	2	1	no	—
47	#533	C₂²	1	1	yes	characteristic
48	#533	C₂²	1	1	yes	characteristic
49	C₂×#125	—	2	1	no	—
50	C₂×#125	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈	—	2	2	no	—
52	#520	C₂²	1	1	yes	characteristic
53	#520	C₂²	1	1	yes	characteristic
54	#518	C₂²	1	1	yes	characteristic
55	#518	C₂²	1	1	yes	characteristic
56	C₄×#41	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
58	#501	C₂²	1	2	yes	complemented
59	#501	C₂²	1	2	yes	complemented
60	#501	C₂²	1	2	yes	complemented
61	#501	C₂²	1	2	yes	complemented
62	#501	C₂²	1	2	yes	complemented
63	#501	C₂²	1	2	yes	complemented
64	#500	C₂²	1	2	yes	complemented
65	#499	C₂²	1	2	yes	complemented
66	#499	C₂²	1	2	yes	complemented
67	#499	C₂²	1	2	yes	complemented
68	#499	C₂²	1	2	yes	complemented
69	#498	C₂²	1	2	yes	complemented
70	#479	C₂²	1	1	yes	characteristic, complemented
71	#479	C₂²	1	1	yes	characteristic, complemented
72	#479	C₂²	1	2	yes	complemented
73	#479	C₂²	1	2	yes	complemented
74	#478	C₂²	1	2	yes	—
75	#478	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	#478	C₂²	1	1	yes	characteristic, complemented
83	#478	C₂²	1	1	yes	characteristic, complemented
84	#478	C₂²	1	2	yes	complemented
85	#478	C₂²	1	2	yes	complemented
86	#477	C₂²	1	1	yes	characteristic, complemented
87	#477	C₂²	1	2	yes	complemented
88	#476	C₂²	1	2	yes	—
89	#476	C₂²	1	2	yes	—
90	#476	C₂²	1	1	yes	characteristic, complemented
91	#476	C₂²	1	2	yes	complemented
92	#475	C₂²	1	1	yes	characteristic, complemented
93	#475	C₂²	1	2	yes	complemented
94	#474	C₂²	1	2	yes	—
95	#474	C₂²	1	2	yes	—
96	#474	C₂²	1	1	yes	characteristic, complemented
97	#474	C₂²	1	2	yes	complemented
98	#446	C₂²	1	2	yes	complemented
99	#446	C₂²	1	2	yes	complemented
100	#446	C₂²	1	2	yes	complemented
101	C₈×Q₈	C₂²	1	2	yes	complemented
102	#442	C₂²	1	2	yes	—
103	#442	C₂²	1	2	yes	—
104	#442	C₂²	1	2	yes	—
105	#440	C₂²	1	2	yes	—
106	#440	C₂²	1	2	yes	—
107	#440	C₂²	1	2	yes	—
108	C₄×SD₁₆	C₂²	1	2	yes	—
109	C₄×SD₁₆	C₂²	1	2	yes	—
110	C₄×SD₁₆	C₂²	1	2	yes	—
111	C₄×D₈	C₂²	1	2	yes	—
112	C₄×D₈	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	#428	C₂²	1	1	yes	characteristic
119	#427	C₂²	1	1	yes	characteristic
120	#427	C₂²	1	1	yes	characteristic
121	C₂×#107	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	C₂×C₄⋊C₈	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×#102	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×D₄	C₂³	1	1	yes	characteristic
138	C₂³×C₄	—	2	1	no	—
139	AGL(1,ℤ/8)	Q₈	1	8	yes	complemented
140	C₂×SD₁₆	C₂³	1	2	yes	—
141	C₂×D₈	C₂³	1	2	yes	—
142	C₂×M₁₆	C₂³	1	1	yes	characteristic
143	C₂×M₁₆	C₂³	1	1	yes	characteristic
144	C₂²×C₈	C₂³	1	1	yes	characteristic
145	C₂²×C₈	C₂³	1	1	yes	characteristic
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	—	2	1	no	—
149	C₄⋊Q₈	—	2	1	no	—
150	C₄⋊Q₈	—	2	1	no	—
151	C₄⋊Q₈	—	2	1	no	—
152	C₄⋊Q₈	D₄	1	1	yes	characteristic
153	C₄⋊Q₈	D₄	1	1	yes	characteristic
154	C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	2	yes	—
157	C₄⋊Q₈	C₂³	1	2	yes	—
158	C₄⋊Q₈	C₂³	1	2	yes	—
159	C₄⋊Q₈	C₂³	1	2	yes	—
160	#125	—	2	1	no	—
161	#125	—	2	1	no	—
162	#125	—	2	2	no	—
163	#125	—	2	2	no	—
164	#125	—	2	2	no	—
165	#125	—	2	2	no	—
166	#125	—	2	1	no	—
167	#125	—	2	1	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	2	yes	—
173	#125	C₂³	1	2	yes	—
174	#125	C₂³	1	1	yes	characteristic
175	#125	C₂³	1	1	yes	characteristic
176	#125	C₂³	1	2	yes	—
177	#125	C₂³	1	2	yes	—
178	#125	C₂³	1	2	yes	—
179	#125	C₂³	1	2	yes	—
180	C₂²⋊Q₈	—	2	2	no	—
181	C₂²⋊Q₈	—	2	2	no	—
182	C₂²⋊Q₈	—	2	2	no	—
183	C₂²⋊Q₈	—	2	2	no	—
184	C₂²⋊Q₈	—	2	2	no	—
185	C₂²⋊Q₈	—	2	1	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	—	2	2	no	—
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	1	no	—
209	C₄×Q₈	—	2	1	no	—
210	C₄×Q₈	C₂³	1	1	yes	characteristic
211	C₄×Q₈	C₂³	1	1	yes	characteristic
212	C₄×Q₈	C₂³	1	2	yes	—
213	C₄×Q₈	C₂³	1	2	yes	—
214	C₄×Q₈	C₂³	1	2	yes	—
215	C₄×Q₈	C₂³	1	2	yes	—
216	C₄×D₄	—	2	1	no	—
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	2	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	C₂³	1	2	yes	—
227	C₄×D₄	C₂³	1	2	yes	—
228	C₄×D₄	C₂³	1	1	yes	characteristic
229	C₄×D₄	C₂³	1	1	yes	characteristic
230	C₄×D₄	C₂³	1	2	yes	—
231	C₄×D₄	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
240	#117	C₂³	1	1	yes	characteristic
241	#117	C₂³	1	1	yes	characteristic
242	#117	C₂³	1	1	yes	characteristic
243	#117	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
260	C₂×C₄²	C₂³	1	1	yes	characteristic
261	#107	C₂³	1	2	yes	—
262	#107	C₂³	1	2	yes	—
263	#107	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	1	yes	characteristic
265	#107	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	2	yes	—
270	#107	C₂³	1	2	yes	—
271	#107	C₂³	1	2	yes	—
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	2	yes	—
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	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₄⋊C₈	C₂³	1	2	yes	—
288	C₄⋊C₈	C₂³	1	2	yes	—
289	C₄⋊C₈	C₂³	1	2	yes	—
290	C₄⋊C₈	C₂³	1	2	yes	—
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
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	#102	C₂³	1	1	yes	characteristic
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#97	C₂³	1	2	yes	—
308	#97	C₂³	1	2	yes	—
309	#97	C₂³	1	2	yes	—
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	2	yes	—
313	C₂⁴	—	2	1	no	—
314	#41	—	2	2	no	—
315	#41	C₂×Q₈	1	4	yes	complemented
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	—	2	2	no	—
322	C₂×Q₈	—	8	4	no	—
323	C₂×Q₈	C₂×D₄	1	2	yes	—
324	C₂×Q₈	C₂×D₄	1	2	yes	—
325	C₂×Q₈	C₂⁴	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	C₂×Q₈	1	4	yes	—
330	C₂×D₄	C₂⁴	1	1	yes	characteristic
331	C₂×D₄	C₂⁴	1	2	yes	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	8	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	SD₁₆	C₂×Q₈	1	8	yes	complemented
351	D₈	C₂×Q₈	1	8	yes	complemented
352	M₁₆	—	2	2	no	—
353	M₁₆	C₂×Q₈	1	4	yes	complemented
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₈	C₂⁴	1	2	yes	—
359	C₂×C₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₈	C₂⁴	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	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	2	no	—
370	C₄⋊C₄	—	2	2	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	1	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	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₄⋊C₄	C₂⁴	1	2	yes	—
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	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	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	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	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄	C₂×D₄	1	2	yes	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	C₂×D₄	1	1	yes	characteristic
433	C₄²	C₂×D₄	1	1	yes	characteristic
434	C₄²	C₂⁴	1	1	yes	characteristic
435	C₄²	C₂⁴	1	2	yes	—
436	C₄²	C₂⁴	1	2	yes	—
437	C₄²	C₂⁴	1	1	yes	characteristic
438	C₂³	—	2	1	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	8	1	no	—
442	C₂³	—	8	1	no	—
443	C₂³	C₂²×D₄	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	8	1	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	D₄	—	2	4	no	—
455	D₄	—	2	4	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	1	no	—
458	D₄	C₂²×Q₈	1	2	yes	—
459	D₄	C₂²×Q₈	1	4	yes	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	8	1	no	—
475	C₂×C₄	—	8	2	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	—	8	2	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	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄	1	2	yes	—
489	C₂×C₄	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
495	C₂×C₄	C₂²×Q₈	1	2	yes	—
496	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
497	C₂×C₄	C₂⁵	1	1	yes	characteristic
498	C₈	—	2	1	no	—
499	C₈	—	2	1	no	—
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	—	2	2	no	—
503	C₈	C₂²×Q₈	1	4	yes	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	8	4	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	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	1	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	4	no	—
539	C₂	C₂×D₄×Q₈	1	1	yes	characteristic
540	C₂	#3584	1	1	yes	characteristic
541	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	C₂×AGL(1,ℤ/8)	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. #3501	C₂	semidirect
3. #3389	C₂	semidirect
4. #3389	C₂	semidirect
5. #3388	C₂	semidirect
6. #3388	C₂	semidirect
7. #3386	C₂	semidirect
8. #3384	C₂	semidirect
9. #3381	C₂	semidirect
10. #3380	C₂	semidirect
11. #3166	C₂	semidirect
12. #3164	C₂	semidirect
13. #3163	C₂	semidirect
14. #3084	C₂	semidirect
15. #3083	C₂	semidirect
16. #3081	C₂	semidirect
17. #3081	C₂	semidirect
18. #3076	C₂	semidirect
19. C₂×#478	C₂	semidirect
20. #2962	C₂	semidirect
25. #557	C₂²	semidirect
26. #557	C₂²	semidirect
35. #554	C₂²	semidirect
36. #554	C₂²	semidirect
58. #501	C₂²	semidirect
59. #501	C₂²	semidirect
60. #501	C₂²	semidirect
61. #501	C₂²	semidirect
62. #501	C₂²	semidirect
63. #501	C₂²	semidirect
64. #500	C₂²	semidirect
65. #499	C₂²	semidirect
66. #499	C₂²	semidirect
67. #499	C₂²	semidirect
68. #499	C₂²	semidirect
69. #498	C₂²	semidirect
70. #479	C₂²	semidirect
71. #479	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
82. #478	C₂²	semidirect
83. #478	C₂²	semidirect
84. #478	C₂²	semidirect
85. #478	C₂²	semidirect
86. #477	C₂²	semidirect
87. #477	C₂²	semidirect
90. #476	C₂²	semidirect
91. #476	C₂²	semidirect
92. #475	C₂²	semidirect
93. #475	C₂²	semidirect
96. #474	C₂²	semidirect
97. #474	C₂²	semidirect
98. #446	C₂²	semidirect
99. #446	C₂²	semidirect
100. #446	C₂²	semidirect
101. C₈×Q₈	C₂²	semidirect
139. AGL(1,ℤ/8)	Q₈	semidirect
315. #41	C₂×Q₈	semidirect
350. SD₁₆	C₂×Q₈	semidirect
351. D₈	C₂×Q₈	semidirect
353. M₁₆	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
#3501	2
#3389	2
#3388	2
#3386	2
#3384	2
#3381	2
#3380	2
#3166	2
#3164	2
#3163	2
#3084	2
#3083	2
#3081	2
#3076	2
C₂×#478	2
#2962	2
#2946	2
C₄×AGL(1,ℤ/8)	2