Subgroups — AGL(1,ℤ/8)×#92420 #30612303

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#92420	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#92420	C₂	1	1	yes	maximal, characteristic, complemented
3	#21461415	C₂	1	2	yes	maximal, complemented
4	SD₁₆⋊#92420	C₂	1	2	yes	maximal, complemented
5	SD₁₆×#92420	C₂	1	2	yes	maximal, complemented
6	D₈×#92420	C₂	1	2	yes	maximal, complemented
7	#21461370	C₂	1	1	yes	maximal, characteristic, complemented
8	#21461118	C₂	1	1	yes	maximal, characteristic, complemented
9	#21461114	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#92420	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×Dic₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×#92420	—	2	1	no	—
13	Q₈×#92420	C₂²	1	1	yes	characteristic, complemented
14	Q₈×#92420	C₂²	1	1	yes	characteristic, complemented
15	D₄×#92420	—	2	1	no	—
16	D₄×#92420	—	2	1	no	—
17	D₄×#92420	—	2	1	no	—
18	D₄×#92420	—	2	1	no	—
19	D₄×#92420	C₂²	1	2	yes	—
20	D₄×#92420	C₂²	1	2	yes	—
21	D₄×#92420	C₂²	1	1	yes	characteristic, complemented
22	D₄×#92420	C₂²	1	1	yes	characteristic, complemented
23	#16840778	—	2	1	no	—
24	#16840778	C₂²	1	1	yes	characteristic
25	#16840778	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#92420	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#92420	—	2	1	no	—
28	C₂×C₄×#92420	—	2	1	no	—
29	C₂×C₄×#92420	C₂²	1	1	yes	characteristic
30	#16840625	C₂²	1	2	yes	complemented
31	#16840623	C₂²	1	2	yes	complemented
32	Q₈⋊#92420	C₂²	1	2	yes	complemented
33	D₄⋊#92420	C₂²	1	2	yes	—
34	D₄⋊#92420	C₂²	1	2	yes	—
35	D₄⋊#92420	C₂²	1	2	yes	complemented
36	#16840603	C₂²	1	2	yes	complemented
37	C₈×#92420	C₂²	1	2	yes	complemented
38	#41×Dic₆₁	C₂²	1	1	yes	characteristic
39	C₂×D₄×Dic₆₁	C₂²	1	1	yes	characteristic
40	#16839874	C₄	1	2	yes	—
41	#16839863	C₄	1	2	yes	—
42	SD₁₆×Dic₆₁	C₂²	1	2	yes	—
43	D₈×Dic₆₁	C₂²	1	2	yes	—
44	#16839804	C₄	1	1	yes	characteristic
45	#16839767	C₄	1	1	yes	characteristic
46	#16839763	C₄	1	1	yes	characteristic
47	M₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
48	C₂×AGL(1,ℤ/8)×C₆₁	C₄	1	1	yes	characteristic
49	C₂²×#92420	—	2	1	no	—
50	C₂²×#92420	—	2	1	no	—
51	C₂²×#92420	—	2	1	no	—
52	C₂²×#92420	—	2	2	no	—
53	C₂²×#92420	—	2	2	no	—
54	C₂²×#92420	—	4	4	no	—
55	C₂²×#92420	D₄	1	1	yes	characteristic
56	C₂²×#92420	D₄	1	1	yes	characteristic
57	C₄⋊#92420	—	2	1	no	—
58	C₄⋊#92420	—	2	1	no	—
59	C₄⋊#92420	—	2	1	no	—
60	C₄⋊#92420	—	2	1	no	—
61	C₄⋊#92420	C₂³	1	2	yes	—
62	C₄⋊#92420	C₂³	1	1	yes	characteristic
63	C₄⋊#92420	C₂³	1	1	yes	characteristic
64	C₂²⋊#92420	—	2	1	no	—
65	C₂²⋊#92420	—	2	1	no	—
66	C₂²⋊#92420	—	2	2	no	—
67	C₂²⋊#92420	—	2	2	no	—
68	C₂²⋊#92420	—	2	1	no	—
69	C₂²⋊#92420	—	2	1	no	—
70	C₄×#92420	—	2	1	no	—
71	C₄×#92420	—	2	1	no	—
72	C₄×#92420	—	2	1	no	—
73	C₄×#92420	D₄	1	1	yes	characteristic
74	C₄×#92420	D₄	1	1	yes	characteristic
75	C₄×#92420	C₂³	1	2	yes	—
76	C₄×#92420	C₂³	1	1	yes	characteristic
77	C₄×#92420	C₂³	1	1	yes	characteristic
78	C₂³×Dic₆₁	—	2	1	no	—
79	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
80	Q₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
81	Q₈×Dic₆₁	C₂³	1	1	yes	characteristic
82	D₄×Dic₆₁	—	2	1	no	—
83	D₄×Dic₆₁	—	2	1	no	—
84	D₄×Dic₆₁	—	2	1	no	—
85	D₄×Dic₆₁	—	2	1	no	—
86	D₄×Dic₆₁	C₂×C₄	1	2	yes	—
87	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
88	D₄×Dic₆₁	C₂³	1	2	yes	—
89	D₄×Dic₆₁	C₂³	1	1	yes	characteristic
90	#14519736	—	2	1	no	—
91	#14519736	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊Dic₆₁	—	2	1	no	—
94	C₂×C₄×Dic₆₁	—	2	1	no	—
95	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
96	#14519711	C₂×C₄	1	2	yes	—
97	#14519709	C₂×C₄	1	2	yes	—
98	#14519701	C₂×C₄	1	2	yes	—
99	#14519698	C₂×C₄	1	2	yes	—
100	#14519698	C₂×C₄	1	2	yes	—
101	#14519698	C₂×C₄	1	2	yes	—
102	#14519687	C₂×C₄	1	2	yes	—
103	C₈×Dic₆₁	C₂³	1	2	yes	—
104	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
105	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
106	AGL(1,ℤ/8)×C₆₁	C₈	1	8	yes	complemented
107	C₂×SD₁₆×C₆₁	C₂×C₄	1	2	yes	—
108	C₂×D₈×C₆₁	C₂×C₄	1	2	yes	—
109	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
110	C₂⁴×C₆₁	—	2	1	no	—
111	#41×C₆₁	—	2	2	no	—
112	#41×C₆₁	C₂×C₈	1	4	yes	complemented
113	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₆₁	—	2	1	no	—
115	C₂×D₄×C₆₁	—	2	1	no	—
116	C₂×D₄×C₆₁	—	2	2	no	—
117	C₂×D₄×C₆₁	C₂×C₈	1	4	yes	complemented
118	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
119	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₆₁	—	2	1	no	—
123	C₂²×Dic₆₁	—	2	2	no	—
124	C₂²×Dic₆₁	—	2	1	no	—
125	C₂²×Dic₆₁	—	2	2	no	—
126	C₂²×Dic₆₁	—	2	1	no	—
127	C₂²×Dic₆₁	—	4	2	no	—
128	C₂²×Dic₆₁	—	4	2	no	—
129	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×Dic₆₁	#41	1	1	yes	characteristic
131	C₂×#92420	—	2	2	no	—
132	C₂×#92420	—	2	1	no	—
133	C₂×#92420	—	2	1	no	—
134	C₂×#92420	—	2	2	no	—
135	C₂×#92420	—	2	2	no	—
136	C₂×#92420	—	4	1	no	—
137	C₂×#92420	—	4	2	no	—
138	C₂×#92420	—	4	4	no	—
139	C₂×#92420	—	4	2	no	—
140	C₂×#92420	—	4	2	no	—
141	C₂×#92420	—	4	4	no	—
142	C₂×#92420	C₂×D₄	1	1	yes	characteristic
143	C₂×#92420	C₂×D₄	1	1	yes	characteristic
144	C₂×#92420	C₂×D₄	1	1	yes	characteristic
145	C₂×#92420	C₂×D₄	1	1	yes	characteristic
146	SD₁₆×C₆₁	C₂×C₈	1	8	yes	complemented
147	D₈×C₆₁	C₂×C₈	1	8	yes	complemented
148	M₁₆×C₆₁	C₂×C₈	1	4	yes	complemented
149	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
150	C₂²⋊Dic₆₁	—	2	1	no	—
151	C₂²⋊Dic₆₁	—	2	2	no	—
152	C₂²⋊Dic₆₁	—	2	1	no	—
153	C₂²⋊Dic₆₁	—	2	2	no	—
154	C₂²⋊Dic₆₁	—	2	1	no	—
155	C₄⋊Dic₆₁	—	2	1	no	—
156	C₄⋊Dic₆₁	—	2	1	no	—
157	C₄⋊Dic₆₁	—	2	1	no	—
158	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
161	C₄×Dic₆₁	—	2	1	no	—
162	C₄×Dic₆₁	—	2	1	no	—
163	C₄×Dic₆₁	—	2	1	no	—
164	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
166	C₄×Dic₆₁	#41	1	1	yes	characteristic
167	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
168	#11758194	—	2	2	no	—
169	C₂×#92418	C₂²×C₄	1	2	yes	—
170	C₂³×C₆₁	—	2	1	no	—
171	C₂³×C₆₁	—	2	2	no	—
172	C₂³×C₆₁	—	2	4	no	—
173	C₂³×C₆₁	—	4	2	no	—
174	C₂³×C₆₁	—	4	2	no	—
175	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
176	Q₈×C₆₁	—	2	1	no	—
177	Q₈×C₆₁	C₂²×C₈	1	2	yes	complemented
178	D₄×C₆₁	—	2	4	no	—
179	D₄×C₆₁	—	2	2	no	—
180	D₄×C₆₁	—	2	1	no	—
181	D₄×C₆₁	—	2	4	no	—
182	D₄×C₆₁	C₂²×C₈	1	4	yes	—
183	D₄×C₆₁	C₂²×C₈	1	2	yes	complemented
184	C₂×C₄×C₆₁	—	2	1	no	—
185	C₂×C₄×C₆₁	—	2	4	no	—
186	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
188	C₂×C₄×C₆₁	#131	1	2	yes	—
189	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
190	C₂×Dic₆₁	—	2	1	no	—
191	C₂×Dic₆₁	—	2	1	no	—
192	C₂×Dic₆₁	—	2	1	no	—
193	C₂×Dic₆₁	—	2	1	no	—
194	C₂×Dic₆₁	—	2	2	no	—
195	C₂×Dic₆₁	—	4	1	no	—
196	C₂×Dic₆₁	—	4	2	no	—
197	C₂×Dic₆₁	—	4	4	no	—
198	C₂×Dic₆₁	—	4	2	no	—
199	C₂×Dic₆₁	—	4	2	no	—
200	C₂×Dic₆₁	—	4	1	no	—
201	C₂×Dic₆₁	—	4	1	no	—
202	C₂×Dic₆₁	—	4	2	no	—
203	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
204	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
205	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×Dic₆₁	C₂×#41	1	1	yes	characteristic
207	#92420	—	2	1	no	—
208	#92420	—	2	1	no	—
209	#92420	—	2	1	no	—
210	#92420	—	4	2	no	—
211	#92420	—	4	1	no	—
212	#92420	—	4	2	no	—
213	#92420	—	4	1	no	—
214	#92420	AGL(1,ℤ/8)	1	2	yes	direct product factor
215	C₈×C₆₁	C₂²×C₈	1	4	yes	complemented
216	#92418	—	2	2	no	—
217	C₈×AGL(1,ℤ/8)	—	61	1	no	maximal, Sylow
218	C₂²×C₆₁	—	2	1	no	—
219	C₂²×C₆₁	—	2	1	no	—
220	C₂²×C₆₁	—	2	2	no	—
221	C₂²×C₆₁	—	2	4	no	—
222	C₂²×C₆₁	—	4	8	no	—
223	C₂²×C₆₁	—	4	2	no	—
224	C₂²×C₆₁	—	4	1	no	—
225	C₂²×C₆₁	—	4	1	no	—
226	C₂²×C₆₁	—	4	2	no	—
227	C₂²×C₆₁	C₈×D₄	1	2	yes	—
228	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
229	C₄×C₆₁	—	2	2	no	—
230	C₄×C₆₁	C₈×D₄	1	2	yes	—
231	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
232	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
233	Dic₆₁	—	2	1	no	—
234	Dic₆₁	—	2	1	no	—
235	Dic₆₁	—	2	1	no	—
236	Dic₆₁	—	4	1	no	—
237	Dic₆₁	—	4	2	no	—
238	Dic₆₁	—	4	1	no	—
239	Dic₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	Dic₆₁	#575	1	1	yes	characteristic
241	C₈×#41	—	61	1	no	—
242	C₄×AGL(1,ℤ/8)	—	61	1	no	—
243	C₂×C₈×D₄	—	61	1	no	—
244	#1580	—	61	2	no	—
245	SD₁₆⋊C₈	—	61	2	no	—
246	C₈×SD₁₆	—	61	2	no	—
247	C₈×D₈	—	61	2	no	—
248	#1565	—	61	1	no	—
249	#1478	—	61	1	no	—
250	#1477	—	61	1	no	—
251	C₈×M₁₆	—	61	1	no	—
252	C₂×C₆₁	—	2	2	no	—
253	C₂×C₆₁	—	4	2	no	—
254	C₂×C₆₁	—	4	4	no	—
255	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
256	C₂×C₆₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₂×C₆₁	#2955	1	1	yes	characteristic
258	C₂×AGL(1,ℤ/8)	#6923	1	1	yes	characteristic
259	C₂³×C₈	—	122	1	no	—
260	C₄×#41	—	61	1	no	—
261	C₂×C₄×D₄	—	61	1	no	—
262	C₈×Q₈	—	61	1	no	—
263	C₈×Q₈	—	61	1	no	—
264	#442	—	61	2	no	—
265	#440	—	61	2	no	—
266	C₄×SD₁₆	—	61	2	no	—
267	C₄×D₈	—	61	2	no	—
268	C₈×D₄	—	61	1	no	—
269	C₈×D₄	—	61	2	no	—
270	C₈×D₄	—	61	2	no	—
271	C₈×D₄	—	61	1	no	—
272	C₈×D₄	—	122	1	no	—
273	C₈×D₄	—	122	1	no	—
274	C₈×D₄	—	122	1	no	—
275	C₈×D₄	—	122	1	no	—
276	#431	—	61	1	no	—
277	#431	—	61	1	no	—
278	#431	—	122	1	no	—
279	#428	—	61	1	no	—
280	C₂×C₄⋊C₈	—	61	1	no	—
281	#418	—	61	1	no	—
282	#417	—	61	1	no	—
283	C₂×C₂²⋊C₈	—	122	1	no	—
284	C₄×M₁₆	—	61	1	no	—
285	C₂×C₄×C₈	—	61	1	no	—
286	C₂×C₄×C₈	—	122	1	no	—
287	#335	—	61	2	no	—
288	#334	—	61	2	no	—
289	Q₈⋊C₈	—	61	2	no	—
290	D₄⋊C₈	—	61	2	no	—
291	D₄⋊C₈	—	61	2	no	—
292	D₄⋊C₈	—	61	2	no	—
293	#322	—	61	2	no	—
294	C₈²	—	61	2	no	—
295	C₆₁	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	C₂×#6923	1	1	yes	characteristic
297	C₂²×D₄	C₂×#6923	1	1	yes	characteristic
298	C₂³×C₄	—	122	1	no	—
299	AGL(1,ℤ/8)	#92420	1	8	yes	direct product factor
300	C₂×SD₁₆	C₂×#6923	1	2	yes	—
301	C₂×D₈	C₂×#6923	1	2	yes	—
302	C₂×M₁₆	—	61	1	no	—
303	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
304	C₂²×C₈	—	61	1	no	—
305	C₂²×C₈	—	61	1	no	—
306	C₂²×C₈	—	122	2	no	—
307	C₂²×C₈	—	122	2	no	—
308	C₂²×C₈	—	122	1	no	—
309	C₂²×C₈	—	122	1	no	—
310	C₂²×C₈	—	122	1	no	—
311	C₂²×C₈	—	244	4	no	—
312	C₄×Q₈	—	61	1	no	—
313	C₄×Q₈	—	61	1	no	—
314	C₄×D₄	—	61	2	no	—
315	C₄×D₄	—	61	2	no	—
316	C₄×D₄	—	61	1	no	—
317	C₄×D₄	—	61	1	no	—
318	C₄×D₄	—	122	1	no	—
319	C₄×D₄	—	122	1	no	—
320	C₄×D₄	—	122	1	no	—
321	C₄×D₄	—	122	1	no	—
322	#117	—	61	1	no	—
323	#117	—	122	1	no	—
324	C₂×C₄⋊C₄	—	61	1	no	—
325	C₂×C₂²⋊C₄	—	122	1	no	—
326	C₂×C₄²	—	61	1	no	—
327	C₂×C₄²	—	122	1	no	—
328	#107	—	61	2	no	—
329	#106	—	61	2	no	—
330	C₄⋊C₈	—	61	1	no	—
331	C₄⋊C₈	—	61	1	no	—
332	C₄⋊C₈	—	61	2	no	—
333	C₄⋊C₈	—	122	1	no	—
334	C₄⋊C₈	—	122	1	no	—
335	C₄⋊C₈	—	122	1	no	—
336	C₄⋊C₈	—	122	1	no	—
337	#103	—	61	2	no	—
338	#102	—	61	2	no	—
339	#102	—	61	2	no	—
340	#102	—	61	2	no	—
341	C₂²⋊C₈	—	122	2	no	—
342	C₂²⋊C₈	—	122	2	no	—
343	C₂²⋊C₈	—	122	1	no	—
344	C₂²⋊C₈	—	122	1	no	—
345	C₂²⋊C₈	—	122	1	no	—
346	C₂²⋊C₈	—	122	1	no	—
347	#97	—	61	2	no	—
348	C₄×C₈	—	61	1	no	—
349	C₄×C₈	—	61	1	no	—
350	C₄×C₈	—	61	1	no	—
351	C₄×C₈	—	61	1	no	—
352	C₄×C₈	—	61	2	no	—
353	C₄×C₈	—	61	2	no	—
354	C₄×C₈	—	122	1	no	—
355	C₄×C₈	—	122	1	no	—
356	C₄×C₈	—	122	1	no	—
357	C₂⁴	—	2	1	no	—
358	#41	—	2	2	no	—
359	#41	C₂×#92420	1	4	yes	complemented
360	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	C₂×#92420	1	4	yes	complemented
365	C₂×D₄	C₂²×#6923	1	2	yes	—
366	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	61	1	no	—
369	C₂²×C₄	—	61	1	no	—
370	C₂²×C₄	—	122	1	no	—
371	C₂²×C₄	—	122	2	no	—
372	C₂²×C₄	—	122	1	no	—
373	C₂²×C₄	—	122	2	no	—
374	C₂²×C₄	—	122	1	no	—
375	C₂²×C₄	—	244	2	no	—
376	C₂²×C₄	—	244	2	no	—
377	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
378	SD₁₆	C₂×#92420	1	8	yes	complemented
379	D₈	C₂×#92420	1	8	yes	complemented
380	M₁₆	—	122	2	no	—
381	M₁₆	C₂×#92420	1	4	yes	complemented
382	C₂×C₈	—	61	1	no	—
383	C₂×C₈	—	61	1	no	—
384	C₂×C₈	—	61	1	no	—
385	C₂×C₈	—	61	1	no	—
386	C₂×C₈	—	61	2	no	—
387	C₂×C₈	—	122	2	no	—
388	C₂×C₈	—	122	2	no	—
389	C₂×C₈	—	122	1	no	—
390	C₂×C₈	—	122	1	no	—
391	C₂×C₈	—	122	2	no	—
392	C₂×C₈	—	244	4	no	—
393	C₂×C₈	—	244	2	no	—
394	C₂×C₈	—	244	1	no	—
395	C₂×C₈	—	244	4	no	—
396	C₂×C₈	—	244	2	no	—
397	C₂×C₈	—	244	2	no	—
398	C₂×C₈	C₂²×#6923	1	2	yes	—
399	C₄⋊C₄	—	61	1	no	—
400	C₄⋊C₄	—	61	1	no	—
401	C₄⋊C₄	—	61	2	no	—
402	C₄⋊C₄	—	122	1	no	—
403	C₄⋊C₄	—	122	1	no	—
404	C₄⋊C₄	—	122	1	no	—
405	C₂²⋊C₄	—	122	2	no	—
406	C₂²⋊C₄	—	122	2	no	—
407	C₂²⋊C₄	—	122	1	no	—
408	C₂²⋊C₄	—	122	1	no	—
409	C₂²⋊C₄	—	122	1	no	—
410	C₄²	—	61	1	no	—
411	C₄²	—	61	1	no	—
412	C₄²	—	61	1	no	—
413	C₄²	—	61	1	no	—
414	C₄²	—	122	1	no	—
415	C₄²	—	122	1	no	—
416	C₄²	—	122	1	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	D₄×#6923	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	C₂²×#92420	1	2	yes	complemented
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	1	no	—
429	D₄	C₂²×#92420	1	4	yes	—
430	D₄	C₂²×#92420	1	2	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	61	1	no	—
434	C₂×C₄	—	61	1	no	—
435	C₂×C₄	—	61	1	no	—
436	C₂×C₄	—	61	1	no	—
437	C₂×C₄	—	122	1	no	—
438	C₂×C₄	—	122	1	no	—
439	C₂×C₄	—	122	1	no	—
440	C₂×C₄	—	122	1	no	—
441	C₂×C₄	—	122	2	no	—
442	C₂×C₄	—	244	2	no	—
443	C₂×C₄	—	244	1	no	—
444	C₂×C₄	—	244	1	no	—
445	C₂×C₄	—	244	2	no	—
446	C₂×C₄	—	244	1	no	—
447	C₂×C₄	—	244	2	no	—
448	C₂×C₄	—	244	4	no	—
449	C₂×C₄	—	244	2	no	—
450	C₂×C₄	D₄×#6923	1	1	yes	characteristic
451	C₂×C₄	C₂²×#92420	1	2	yes	—
452	C₂×C₄	#14519864	1	2	yes	—
453	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
454	C₈	—	61	2	no	—
455	C₈	—	122	1	no	—
456	C₈	—	122	1	no	—
457	C₈	—	122	1	no	—
458	C₈	—	122	2	no	—
459	C₈	—	244	1	no	—
460	C₈	—	244	1	no	—
461	C₈	—	244	2	no	—
462	C₈	—	244	2	no	—
463	C₈	C₂²×#92420	1	4	yes	complemented
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	2	no	—
473	C₂²	D₄×#92420	1	2	yes	—
474	C₂²	C₂×D₄×#6923	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	61	1	no	—
477	C₄	—	61	1	no	—
478	C₄	—	122	1	no	—
479	C₄	—	122	1	no	—
480	C₄	—	122	1	no	—
481	C₄	—	244	1	no	—
482	C₄	—	244	2	no	—
483	C₄	—	244	1	no	—
484	C₄	D₄×#92420	1	2	yes	—
485	C₄	C₂³×#92420	1	1	yes	characteristic
486	C₄	C₂×#14519864	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	4	no	—
489	C₂	—	4	2	no	—
490	C₂	C₂×D₄×#92420	1	1	yes	characteristic
491	C₂	AGL(1,ℤ/8)×#6923	1	1	yes	characteristic
492	C₂	#21462591	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×#6923
commutator	C₄×C₆₁	C₂³×C₈
Frattini	C₂×C₄	C₂³×#6923
Fitting, prime radical	C₂×AGL(1,ℤ/8)×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄×D₄
cosocle	C₄×Dic₆₁	C₂⁴
hypercenter	C₂×AGL(1,ℤ/8)	#6923
hypocenter	C₆₁	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #41×#92420	C₂	semidirect
2. C₂×D₄×#92420	C₂	semidirect
3. #21461415	C₂	semidirect
4. SD₁₆⋊#92420	C₂	semidirect
5. SD₁₆×#92420	C₂	semidirect
6. D₈×#92420	C₂	semidirect
7. #21461370	C₂	semidirect
8. #21461118	C₂	semidirect
9. #21461114	C₂	semidirect
10. M₁₆×#92420	C₂	semidirect
13. Q₈×#92420	C₂²	semidirect
14. Q₈×#92420	C₂²	semidirect
21. D₄×#92420	C₂²	semidirect
22. D₄×#92420	C₂²	semidirect
30. #16840625	C₂²	semidirect
31. #16840623	C₂²	semidirect
32. Q₈⋊#92420	C₂²	semidirect
35. D₄⋊#92420	C₂²	semidirect
36. #16840603	C₂²	semidirect
37. C₈×#92420	C₂²	semidirect
106. AGL(1,ℤ/8)×C₆₁	C₈	semidirect
112. #41×C₆₁	C₂×C₈	semidirect
117. C₂×D₄×C₆₁	C₂×C₈	semidirect
146. SD₁₆×C₆₁	C₂×C₈	semidirect
147. D₈×C₆₁	C₂×C₈	semidirect
148. M₁₆×C₆₁	C₂×C₈	semidirect
177. Q₈×C₆₁	C₂²×C₈	semidirect
183. D₄×C₆₁	C₂²×C₈	semidirect
214. #92420	AGL(1,ℤ/8)	direct (N × H)
215. C₈×C₆₁	C₂²×C₈	semidirect
295. C₆₁	C₈×AGL(1,ℤ/8)	semidirect
299. AGL(1,ℤ/8)	#92420	direct (N × H)
359. #41	C₂×#92420	semidirect
364. C₂×D₄	C₂×#92420	semidirect
378. SD₁₆	C₂×#92420	semidirect
379. D₈	C₂×#92420	semidirect
381. M₁₆	C₂×#92420	semidirect
424. Q₈	C₂²×#92420	semidirect
430. D₄	C₂²×#92420	semidirect
463. C₈	C₂²×#92420	semidirect

Maximal subgroups

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

subgroup	index
#41×#92420	2
C₂×D₄×#92420	2
#21461415	2
SD₁₆⋊#92420	2
SD₁₆×#92420	2
D₈×#92420	2
#21461370	2
#21461118	2
#21461114	2
M₁₆×#92420	2
AGL(1,ℤ/8)×Dic₆₁	2
C₈×AGL(1,ℤ/8)	61