Subgroups — C₈×#15668040 #36523846

Order 22784.

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	C₈×#13083574	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668040	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019077	C₂	1	2	yes	maximal, complemented
5	#26019066	C₂	1	2	yes	maximal, complemented
6	C₈×#13083563	C₂	1	2	yes	maximal, complemented
7	C₈×D₇₁₂	C₂	1	2	yes	maximal, complemented
8	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018644	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018640	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668040	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₈₉	—	2	1	no	—
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
16	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
17	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
18	#19151711	C₄	1	2	yes	—
19	#19151700	C₄	1	2	yes	—
20	C₄×#13083563	C₂²	1	2	yes	—
21	C₄×D₇₁₂	C₂²	1	2	yes	—
22	C₈×D₃₅₆	—	2	1	no	—
23	C₈×D₃₅₆	—	2	1	no	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	C₈×D₃₅₆	C₂²	1	2	yes	—
26	C₈×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
27	C₈×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
28	C₈×C₂²⋊D₈₉	—	2	1	no	—
29	C₈×C₂²⋊D₈₉	—	2	1	no	—
30	#19151651	C₂²	1	1	yes	characteristic
31	#19151649	—	2	1	no	—
32	#19151640	C₄	1	1	yes	characteristic
33	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
34	#19151604	C₄	1	1	yes	characteristic
35	#19151600	C₄	1	1	yes	characteristic
36	C₂×#15667924	—	2	1	no	—
37	C₄×C₈×D₈₉	—	2	1	no	—
38	#19151351	C₂²	1	2	yes	complemented
39	#19151349	C₂²	1	2	yes	complemented
40	#19151330	C₂²	1	2	yes	complemented
41	#19151327	C₂²	1	2	yes	—
42	#19151327	C₂²	1	2	yes	—
43	#19151327	C₂²	1	2	yes	complemented
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#322×C₈₉	C₂²	1	2	yes	complemented
48	C₈²×C₈₉	C₂²	1	2	yes	complemented
49	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₈₉	—	2	1	no	—
52	#15668040	C₈	1	8	yes	direct product factor
53	C₂×#13083563	C₂×C₄	1	2	yes	—
54	C₂×D₇₁₂	C₂×C₄	1	2	yes	—
55	C₂²×#10623494	—	2	1	no	—
56	C₂×C₈×D₈₉	—	2	1	no	—
57	C₂×C₈×D₈₉	—	2	1	no	—
58	C₂×C₈×D₈₉	—	2	2	no	—
59	C₂×C₈×D₈₉	—	2	2	no	—
60	C₂×C₈×D₈₉	—	4	4	no	—
61	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
63	C₄×D₃₅₆	—	2	1	no	—
64	C₄×D₃₅₆	—	2	1	no	—
65	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
66	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
67	C₄×D₃₅₆	C₂³	1	2	yes	—
68	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₈₉	—	2	1	no	—
70	C₄×C₂²⋊D₈₉	—	2	1	no	—
71	#15667971	C₂×C₄	1	1	yes	characteristic
72	#15667969	—	2	1	no	—
73	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083551	—	2	1	no	—
75	C₄²×D₈₉	—	2	1	no	—
76	#15667946	C₂×C₄	1	2	yes	—
77	#15667944	C₂×C₄	1	2	yes	—
78	C₄⋊#10623494	—	2	1	no	—
79	C₄⋊#10623494	C₂³	1	2	yes	—
80	C₄⋊#10623494	C₂³	1	1	yes	characteristic
81	C₄⋊#10623494	C₂³	1	1	yes	characteristic
82	#15667941	—	2	1	no	—
83	#15667941	—	2	1	no	—
84	#15667937	C₂×C₄	1	2	yes	—
85	#15667934	C₂×C₄	1	2	yes	—
86	#15667934	C₂×C₄	1	2	yes	—
87	#15667934	C₂×C₄	1	2	yes	—
88	C₂²⋊#10623494	—	2	1	no	—
89	#15667924	—	2	1	no	—
90	#15667924	—	2	1	no	—
91	#15667924	—	2	2	no	—
92	#15667924	—	2	2	no	—
93	C₄×#10623494	—	2	1	no	—
94	C₈×Dic₈₉	—	2	1	no	—
95	C₈×Dic₈₉	—	2	1	no	—
96	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
97	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	—	2	1	no	—
102	C₂²⋊C₈×C₈₉	—	2	1	no	—
103	#97×C₈₉	C₂×C₄	1	2	yes	—
104	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
105	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
106	C₄×C₈×C₈₉	C₂³	1	2	yes	—
107	C₄×C₈×C₈₉	C₂³	1	2	yes	—
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂³×D₈₉	—	2	1	no	—
111	#13083574	—	2	2	no	—
112	#13083574	C₂×C₈	1	4	yes	complemented
113	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₃₅₆	—	2	1	no	—
115	C₂×D₃₅₆	—	2	2	no	—
116	C₂×D₃₅₆	C₂×C₈	1	4	yes	complemented
117	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
118	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊D₈₉	—	2	1	no	—
120	C₂²×Dic₈₉	—	2	1	no	—
121	C₂×C₄×D₈₉	—	2	1	no	—
122	C₂×C₄×D₈₉	—	2	1	no	—
123	C₂×C₄×D₈₉	—	2	2	no	—
124	C₂×C₄×D₈₉	—	2	1	no	—
125	C₂×C₄×D₈₉	—	2	2	no	—
126	C₂×C₄×D₈₉	—	4	2	no	—
127	C₂×C₄×D₈₉	—	4	2	no	—
128	#13083563	C₂×C₈	1	8	yes	complemented
129	D₇₁₂	C₂×C₈	1	8	yes	complemented
130	C₂×#10623494	—	2	2	no	—
131	C₂×#10623494	—	2	1	no	—
132	C₂×#10623494	—	2	1	no	—
133	C₂×#10623494	—	4	2	no	—
134	C₈×D₈₉	—	4	2	no	—
135	C₈×D₈₉	—	4	4	no	—
136	C₈×D₈₉	—	4	2	no	—
137	C₈×D₈₉	—	4	4	no	—
138	C₄⋊Dic₈₉	—	2	1	no	—
139	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
142	#13083553	—	2	1	no	—
143	#13083553	—	2	1	no	—
144	C₂²⋊Dic₈₉	—	2	1	no	—
145	#13083551	—	2	1	no	—
146	#13083551	—	2	2	no	—
147	#13083551	—	2	1	no	—
148	#13083551	—	2	2	no	—
149	C₄×Dic₈₉	—	2	1	no	—
150	C₄×Dic₈₉	—	2	1	no	—
151	C₄×Dic₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
155	M₁₆×C₈₉	—	2	2	no	—
156	M₁₆×C₈₉	C₂×C₈	1	4	yes	complemented
157	C₂×C₈×C₈₉	—	2	2	no	—
158	C₂×C₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	—	4	1	no	—
160	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₈₉	#41	1	1	yes	characteristic
169	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
171	C₂²×D₈₉	—	2	1	no	—
172	C₂²×D₈₉	—	2	2	no	—
173	C₂²×D₈₉	—	2	4	no	—
174	C₂²×D₈₉	—	4	2	no	—
175	C₂²×D₈₉	—	4	2	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
183	C₂×C₄×C₈₉	#131	1	2	yes	—
184	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₈₉	—	2	4	no	—
188	C₂×Dic₈₉	—	2	1	no	—
189	C₂×Dic₈₉	—	2	1	no	—
190	C₂×Dic₈₉	—	2	1	no	—
191	C₂×Dic₈₉	—	2	2	no	—
192	C₂×Dic₈₉	—	4	2	no	—
193	D₃₅₆	—	2	2	no	—
194	D₃₅₆	—	2	1	no	—
195	D₃₅₆	—	2	4	no	—
196	D₃₅₆	C₂²×C₈	1	4	yes	—
197	D₃₅₆	C₂²×C₈	1	2	yes	complemented
198	C₄×D₈₉	—	2	4	no	—
199	C₄×D₈₉	—	4	2	no	—
200	C₄×D₈₉	—	4	4	no	—
201	C₄×D₈₉	—	4	2	no	—
202	C₄×D₈₉	—	4	1	no	—
203	C₄×D₈₉	—	4	1	no	—
204	C₄×D₈₉	—	4	2	no	—
205	Dic₁₇₈	—	2	1	no	—
206	Dic₁₇₈	C₂²×C₈	1	2	yes	complemented
207	C₈×C₈₉	—	2	2	no	—
208	C₈×C₈₉	—	2	1	no	—
209	C₈×C₈₉	—	2	1	no	—
210	C₈×C₈₉	—	2	1	no	—
211	C₈×C₈₉	—	4	2	no	—
212	C₈×C₈₉	C₂²×C₈	1	4	yes	complemented
213	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
214	#10623494	—	4	2	no	—
215	#10623494	—	4	1	no	—
216	#10623494	—	4	1	no	—
217	C₂²×C₈₉	—	2	1	no	—
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	C₈×D₄	1	2	yes	—
220	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂×D₈₉	—	2	2	no	—
222	C₂×D₈₉	—	2	4	no	—
223	C₂×D₈₉	—	4	8	no	—
224	C₂×D₈₉	—	4	2	no	—
225	C₂×D₈₉	—	4	1	no	—
226	C₂×D₈₉	—	4	1	no	—
227	C₂×D₈₉	—	4	2	no	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	C₈×D₄	1	2	yes	—
232	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
233	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
234	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₄×C₈₉	#575	1	1	yes	characteristic
236	Dic₈₉	—	2	2	no	—
237	Dic₈₉	—	4	2	no	—
238	Dic₈₉	—	4	1	no	—
239	Dic₈₉	—	4	1	no	—
240	C₈×AGL(1,ℤ/8)	—	89	1	no	maximal, Sylow
241	C₂×C₈₉	—	2	2	no	—
242	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
243	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
244	C₂×C₈₉	#2955	1	1	yes	characteristic
245	D₈₉	—	4	2	no	—
246	D₈₉	—	4	4	no	—
247	C₈×#41	—	89	1	no	—
248	C₄×AGL(1,ℤ/8)	—	89	1	no	—
249	C₂×C₈×D₄	—	89	1	no	—
250	#1580	—	89	2	no	—
251	SD₁₆⋊C₈	—	89	2	no	—
252	C₈×SD₁₆	—	89	2	no	—
253	C₈×D₈	—	89	2	no	—
254	#1565	—	89	1	no	—
255	#1478	—	89	1	no	—
256	#1477	—	89	1	no	—
257	C₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
258	C₈₉	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
259	C₂×AGL(1,ℤ/8)	—	89	1	no	—
260	C₂³×C₈	—	178	1	no	—
261	C₄×#41	—	89	1	no	—
262	C₂×C₄×D₄	—	89	1	no	—
263	C₈×Q₈	—	89	1	no	—
264	C₈×Q₈	—	89	1	no	—
265	#442	—	89	2	no	—
266	#440	—	89	2	no	—
267	C₄×SD₁₆	—	89	2	no	—
268	C₄×D₈	—	89	2	no	—
269	C₈×D₄	—	89	1	no	—
270	C₈×D₄	—	89	2	no	—
271	C₈×D₄	—	89	2	no	—
272	C₈×D₄	—	89	1	no	—
273	C₈×D₄	—	178	1	no	—
274	C₈×D₄	—	178	1	no	—
275	C₈×D₄	—	178	1	no	—
276	C₈×D₄	—	178	1	no	—
277	#431	—	89	1	no	—
278	#431	—	178	1	no	—
279	#431	C₂×D₈₉	1	1	yes	characteristic
280	#428	—	89	1	no	—
281	C₂×C₄⋊C₈	—	89	1	no	—
282	#418	—	89	1	no	—
283	#417	—	89	1	no	—
284	C₂×C₂²⋊C₈	—	178	1	no	—
285	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
286	C₂×C₄×C₈	—	178	1	no	—
287	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
288	#335	—	89	2	no	—
289	#334	—	89	2	no	—
290	Q₈⋊C₈	—	89	2	no	—
291	D₄⋊C₈	—	89	2	no	—
292	D₄⋊C₈	—	89	2	no	—
293	D₄⋊C₈	—	89	2	no	—
294	#322	C₂×D₈₉	1	2	yes	complemented
295	C₈²	C₂×D₈₉	1	2	yes	complemented
296	C₂×#41	—	89	1	no	—
297	C₂²×D₄	—	89	1	no	—
298	C₂³×C₄	—	178	1	no	—
299	AGL(1,ℤ/8)	—	89	8	no	—
300	C₂×SD₁₆	—	89	2	no	—
301	C₂×D₈	—	89	2	no	—
302	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
303	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
304	C₂²×C₈	—	356	4	no	—
305	C₂²×C₈	—	178	1	no	—
306	C₂²×C₈	—	178	2	no	—
307	C₂²×C₈	—	178	1	no	—
308	C₂²×C₈	—	178	2	no	—
309	C₂²×C₈	—	178	1	no	—
310	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
311	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
312	C₄×Q₈	—	89	1	no	—
313	C₄×Q₈	—	89	1	no	—
314	C₄×D₄	—	89	2	no	—
315	C₄×D₄	—	89	1	no	—
316	C₄×D₄	—	89	2	no	—
317	C₄×D₄	—	89	1	no	—
318	C₄×D₄	—	178	1	no	—
319	C₄×D₄	—	178	1	no	—
320	C₄×D₄	—	178	1	no	—
321	C₄×D₄	—	178	1	no	—
322	#117	—	89	1	no	—
323	#117	—	178	1	no	—
324	C₂×C₄⋊C₄	—	89	1	no	—
325	C₂×C₂²⋊C₄	—	178	1	no	—
326	C₂×C₄²	—	178	1	no	—
327	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
328	#107	—	89	2	no	—
329	#106	—	89	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	89	1	no	—
332	C₄⋊C₈	—	89	1	no	—
333	C₄⋊C₈	—	89	2	no	—
334	C₄⋊C₈	—	178	1	no	—
335	C₄⋊C₈	—	178	1	no	—
336	C₄⋊C₈	—	178	1	no	—
337	#103	—	89	2	no	—
338	#102	—	89	2	no	—
339	#102	—	89	2	no	—
340	#102	—	89	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	178	1	no	—
343	C₂²⋊C₈	—	178	2	no	—
344	C₂²⋊C₈	—	178	2	no	—
345	C₂²⋊C₈	—	178	1	no	—
346	C₂²⋊C₈	—	178	1	no	—
347	#97	C₄×D₈₉	1	2	yes	—
348	C₄×C₈	—	178	1	no	—
349	C₄×C₈	—	178	1	no	—
350	C₄×C₈	—	178	1	no	—
351	C₄×C₈	D₃₅₆	1	1	yes	characteristic
352	C₄×C₈	D₃₅₆	1	1	yes	characteristic
353	C₄×C₈	C₂²×D₈₉	1	2	yes	—
354	C₄×C₈	C₂²×D₈₉	1	2	yes	—
355	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
357	C₂⁴	—	178	1	no	—
358	#41	—	89	4	no	—
359	#41	—	178	2	no	—
360	C₂×Q₈	—	89	1	no	—
361	C₂×D₄	—	89	4	no	—
362	C₂×D₄	—	89	1	no	—
363	C₂×D₄	—	89	2	no	—
364	C₂×D₄	—	178	1	no	—
365	C₂×D₄	—	178	1	no	—
366	C₂×D₄	—	178	2	no	—
367	C₂²×C₄	—	356	2	no	—
368	C₂²×C₄	—	356	2	no	—
369	C₂²×C₄	—	178	1	no	—
370	C₂²×C₄	—	178	1	no	—
371	C₂²×C₄	—	178	2	no	—
372	C₂²×C₄	—	178	1	no	—
373	C₂²×C₄	—	178	2	no	—
374	C₂²×C₄	—	178	1	no	—
375	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
377	C₂²×C₄	#13083574	1	1	yes	characteristic
378	SD₁₆	—	89	8	no	—
379	D₈	—	89	8	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	C₈×D₈₉	1	4	yes	complemented
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	1	no	—
385	C₂×C₈	—	356	4	no	—
386	C₂×C₈	—	356	2	no	—
387	C₂×C₈	—	356	2	no	—
388	C₂×C₈	—	356	4	no	—
389	C₂×C₈	—	356	2	no	—
390	C₂×C₈	—	178	1	no	—
391	C₂×C₈	—	178	1	no	—
392	C₂×C₈	—	178	2	no	—
393	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
394	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
395	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
396	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
397	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
398	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
399	C₄⋊C₄	—	89	1	no	—
400	C₄⋊C₄	—	89	1	no	—
401	C₄⋊C₄	—	89	2	no	—
402	C₄⋊C₄	—	178	1	no	—
403	C₄⋊C₄	—	178	1	no	—
404	C₄⋊C₄	—	178	1	no	—
405	C₂²⋊C₄	—	178	1	no	—
406	C₂²⋊C₄	—	178	2	no	—
407	C₂²⋊C₄	—	178	1	no	—
408	C₂²⋊C₄	—	178	2	no	—
409	C₂²⋊C₄	—	178	1	no	—
410	C₄²	—	178	1	no	—
411	C₄²	—	178	1	no	—
412	C₄²	—	178	1	no	—
413	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
414	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
415	C₄²	#13083574	1	1	yes	characteristic
416	C₄²	C₂³×D₈₉	1	1	yes	characteristic
417	C₂³	—	356	2	no	—
418	C₂³	—	356	2	no	—
419	C₂³	—	178	4	no	—
420	C₂³	—	178	1	no	—
421	C₂³	—	178	2	no	—
422	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
423	Q₈	—	89	2	no	—
424	Q₈	—	178	1	no	—
425	D₄	—	89	4	no	—
426	D₄	—	89	2	no	—
427	D₄	—	178	4	no	—
428	D₄	—	178	4	no	—
429	D₄	—	178	2	no	—
430	D₄	—	178	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	356	4	no	—
435	C₂×C₄	—	356	2	no	—
436	C₂×C₄	—	356	2	no	—
437	C₂×C₄	—	356	2	no	—
438	C₂×C₄	—	356	1	no	—
439	C₂×C₄	—	356	1	no	—
440	C₂×C₄	—	356	2	no	—
441	C₂×C₄	—	178	1	no	—
442	C₂×C₄	—	178	1	no	—
443	C₂×C₄	—	178	2	no	—
444	C₂×C₄	—	178	1	no	—
445	C₂×C₄	—	178	4	no	—
446	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
447	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
448	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
449	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
450	C₂×C₄	#15668018	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
453	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	356	2	no	—
460	C₈	—	356	1	no	—
461	C₈	—	356	1	no	—
462	C₈	C₂×C₈×D₈₉	1	4	yes	complemented
463	C₈	#15668040	1	2	yes	direct product factor
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	356	8	no	—
467	C₂²	—	356	2	no	—
468	C₂²	—	356	1	no	—
469	C₂²	—	356	1	no	—
470	C₂²	—	356	2	no	—
471	C₂²	—	178	2	no	—
472	C₂²	—	178	4	no	—
473	C₂²	C₈×D₃₅₆	1	2	yes	—
474	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	356	2	no	—
479	C₄	—	356	1	no	—
480	C₄	—	356	1	no	—
481	C₄	—	178	2	no	—
482	C₄	C₈×D₃₅₆	1	2	yes	—
483	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
484	C₄	C₂×#15668018	1	1	yes	characteristic
485	C₄	C₂×#15668040	1	1	yes	characteristic
486	C₄	#19152398	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	356	4	no	—
489	C₂	—	356	2	no	—
490	C₂	C₂×C₈×D₃₅₆	1	1	yes	characteristic
491	C₂	C₄×#15668040	1	1	yes	characteristic
492	C₂	#26029156	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₅₆
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×M₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668040	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×M₁₆	D₈₉
hypocenter	C₈₉	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₈×#13083574	C₂	semidirect
3. C₂×C₈×D₃₅₆	C₂	semidirect
4. #26019077	C₂	semidirect
5. #26019066	C₂	semidirect
6. C₈×#13083563	C₂	semidirect
7. C₈×D₇₁₂	C₂	semidirect
8. #26019004	C₂	semidirect
9. #26018644	C₂	semidirect
10. #26018640	C₂	semidirect
11. C₈×M₁₆×C₈₉	C₂	semidirect
16. C₈×Dic₁₇₈	C₂²	semidirect
17. C₈×Dic₁₇₈	C₂²	semidirect
26. C₈×D₃₅₆	C₂²	semidirect
27. C₈×D₃₅₆	C₂²	semidirect
38. #19151351	C₂²	semidirect
39. #19151349	C₂²	semidirect
40. #19151330	C₂²	semidirect
43. #19151327	C₂²	semidirect
47. #322×C₈₉	C₂²	semidirect
48. C₈²×C₈₉	C₂²	semidirect
52. #15668040	C₈	direct (N × H)
112. #13083574	C₂×C₈	semidirect
116. C₂×D₃₅₆	C₂×C₈	semidirect
128. #13083563	C₂×C₈	semidirect
129. D₇₁₂	C₂×C₈	semidirect
156. M₁₆×C₈₉	C₂×C₈	semidirect
197. D₃₅₆	C₂²×C₈	semidirect
206. Dic₁₇₈	C₂²×C₈	semidirect
212. C₈×C₈₉	C₂²×C₈	semidirect
213. C₈×C₈₉	AGL(1,ℤ/8)	semidirect
257. C₈×M₁₆	D₈₉	semidirect
258. C₈₉	C₈×AGL(1,ℤ/8)	semidirect
294. #322	C₂×D₈₉	semidirect
295. C₈²	C₂×D₈₉	semidirect
381. M₁₆	C₈×D₈₉	semidirect
462. C₈	C₂×C₈×D₈₉	semidirect
463. C₈	#15668040	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#13083574	2
C₄×#15668040	2
C₂×C₈×D₃₅₆	2
#26019077	2
#26019066	2
C₈×#13083563	2
C₈×D₇₁₂	2
#26019004	2
#26018644	2
#26018640	2
C₈×M₁₆×C₈₉	2
C₈×AGL(1,ℤ/8)	89

Subgroups — C8×#15668040 #36523846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#15668040 #36523846