Subgroups — C₈×#14556149 #31966827

Order 18176.

750 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11765866	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#11765864	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14556149	C₂	1	1	yes	maximal, characteristic
4	C₈×#11765855	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587144	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#11765854	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11765850	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587132	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587085	C₂	1	1	yes	maximal, characteristic, complemented
12	#22586721	C₂	1	1	yes	maximal, characteristic, complemented
13	#22586719	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈²×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14556149	C₄	1	1	yes	characteristic
17	C₄×#11765866	C₂²	1	1	yes	characteristic
18	C₄×#11765864	C₂²	1	1	yes	characteristic
19	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
21	#17986123	C₂²	1	1	yes	characteristic
22	C₄×#11765855	C₂²	1	1	yes	characteristic
23	#17986091	C₄	1	1	yes	characteristic
24	C₄×#11765854	C₂²	1	1	yes	characteristic
25	SD₁₆×Dic₇₁	C₄	1	1	yes	characteristic
26	#17986086	C₄	1	1	yes	characteristic
27	C₄×#11765850	C₂²	1	1	yes	characteristic
28	#17986079	C₄	1	1	yes	characteristic
29	C₈×D₂₈₄	—	2	1	no	—
30	C₈×D₂₈₄	C₂²	1	1	yes	characteristic
31	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
32	#17986064	—	2	1	no	—
33	#17986064	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₇₁	—	2	1	no	—
35	(C₂²⋊D₇₁)⋊C₈	—	2	1	no	—
36	#17986051	—	2	1	no	—
37	#17986051	C₂²	1	1	yes	characteristic
38	#17986051	C₂²	1	1	yes	characteristic
39	#17986049	—	2	1	no	—
40	#17986034	C₄	1	1	yes	characteristic
41	#17985994	C₄	1	1	yes	characteristic
42	#17985992	C₄	1	1	yes	characteristic
43	C₂×C₈×Dic₇₁	—	2	1	no	—
44	C₄×C₈×D₇₁	—	2	1	no	—
45	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
48	#17985751	C₂²	1	1	yes	characteristic
49	#17985751	C₂²	1	1	yes	characteristic
50	#17985750	C₂²	1	1	yes	characteristic
51	#17985731	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
53	#17985729	C₂²	1	1	yes	characteristic
54	#17985728	C₂²	1	1	yes	characteristic
55	D₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
56	#17985726	C₂²	1	1	yes	characteristic
57	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
58	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
59	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
63	#334×C₇₁	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
66	C₈²×C₇₁	C₂²	1	1	yes	characteristic
67	C₂×#11765866	C₂×C₄	1	1	yes	characteristic
68	C₂×#11765864	C₂×C₄	1	1	yes	characteristic
69	#14556149	C₈	1	8	yes	direct product factor
70	C₂×#11765855	C₂×C₄	1	1	yes	characteristic
71	C₂×#11765854	C₂×C₄	1	1	yes	characteristic
72	C₂×#11765850	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₇₁⋊C₈	—	2	1	no	—
74	C₂×C₈×D₇₁	—	2	1	no	—
75	C₂×C₈×D₇₁	—	2	1	no	—
76	C₂×C₈×D₇₁	—	2	1	no	—
77	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
80	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
81	Q₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
83	#14556093	C₂×C₄	1	1	yes	characteristic
84	C₄×D₂₈₄	—	2	1	no	—
85	C₄×D₂₈₄	C₂³	1	1	yes	characteristic
86	D₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
87	#14556090	—	2	1	no	—
88	#14556090	C₂×C₄	1	1	yes	characteristic
89	C₄×C₂²⋊D₇₁	—	2	1	no	—
90	(C₂²⋊D₇₁)⋊C₄	—	2	1	no	—
91	#14556086	—	2	1	no	—
92	#14556086	C₂×C₄	1	1	yes	characteristic
93	#14556086	C₂×C₄	1	1	yes	characteristic
94	#14556084	—	2	1	no	—
95	C₂×C₄×Dic₇₁	—	2	1	no	—
96	C₄²×D₇₁	—	2	1	no	—
97	C₄²×D₇₁	C₂³	1	1	yes	characteristic
98	#14556061	C₂×C₄	1	1	yes	characteristic
99	#14556061	C₂×C₄	1	1	yes	characteristic
100	#14556060	C₂×C₄	1	1	yes	characteristic
101	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
102	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
103	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
104	Dic₇₁⋊C₈	—	2	1	no	—
105	Dic₇₁⋊C₈	—	2	1	no	—
106	#14556053	C₂×C₄	1	1	yes	characteristic
107	#14556052	C₂×C₄	1	1	yes	characteristic
108	#14556051	C₂×C₄	1	1	yes	characteristic
109	#14556050	C₂×C₄	1	1	yes	characteristic
110	#14556049	C₂×C₄	1	1	yes	characteristic
111	#14556048	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
113	(C₂×D₇₁)⋊C₈	—	2	1	no	—
114	(C₂×D₇₁)⋊C₈	—	2	1	no	—
115	(C₂×D₇₁)⋊C₈	—	2	1	no	—
116	(C₂×D₇₁)⋊C₈	—	2	1	no	—
117	C₄×C₇₁⋊C₈	—	2	1	no	—
118	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
119	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
120	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
121	C₈×Dic₇₁	—	2	1	no	—
122	C₈×Dic₇₁	—	2	1	no	—
123	C₈×Dic₇₁	—	2	1	no	—
124	C₈×Dic₇₁	—	2	1	no	—
125	C₈×Dic₇₁	—	2	1	no	—
126	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₇₁	D₄	1	1	yes	characteristic
129	C₈×Dic₇₁	D₄	1	1	yes	characteristic
130	C₂×SD₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
131	C₂²×C₈×C₇₁	—	2	1	no	—
132	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
134	#106×C₇₁	C₂×C₄	1	1	yes	characteristic
135	C₄⋊C₈×C₇₁	—	2	1	no	—
136	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
138	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
139	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₇₁	—	2	1	no	—
141	C₄×C₈×C₇₁	—	2	1	no	—
142	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
145	#11765866	—	2	2	no	—
146	#11765866	C₂×C₈	1	4	yes	complemented
147	#11765864	—	2	2	no	—
148	#11765864	C₂×C₈	1	4	yes	complemented
149	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₂₈₄	—	2	1	no	—
151	C₂×D₂₈₄	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₂²⋊D₇₁	—	2	1	no	—
153	C₂²×Dic₇₁	—	2	1	no	—
154	C₂²×Dic₇₁	—	2	1	no	—
155	C₂×C₄×D₇₁	—	2	1	no	—
156	C₂×C₄×D₇₁	—	2	1	no	—
157	C₂×C₄×D₇₁	—	2	1	no	—
158	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
161	#11765855	C₂×C₈	1	4	yes	complemented
162	#11765854	C₂×C₈	1	4	yes	complemented
163	#11765850	C₂×C₈	1	4	yes	complemented
164	C₂×C₇₁⋊C₈	—	2	1	no	—
165	C₂×C₇₁⋊C₈	—	2	1	no	—
166	C₂×C₇₁⋊C₈	—	2	1	no	—
167	C₂×C₇₁⋊C₈	—	4	2	no	—
168	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₈×D₇₁	—	2	4	no	—
173	C₈×D₇₁	—	2	2	no	—
174	C₈×D₇₁	—	2	2	no	—
175	C₈×D₇₁	—	2	2	no	—
176	C₈×D₇₁	—	4	2	no	—
177	C₈×D₇₁	—	4	2	no	—
178	C₈×D₇₁	C₂×C₈	1	4	yes	complemented
179	C₄⋊Dic₇₁	—	2	1	no	—
180	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
182	Dic₇₁⋊C₄	—	2	1	no	—
183	Dic₇₁⋊C₄	—	2	1	no	—
184	C₂²⋊Dic₇₁	—	2	1	no	—
185	(C₂×D₇₁)⋊C₄	—	2	1	no	—
186	(C₂×D₇₁)⋊C₄	—	2	1	no	—
187	(C₂×D₇₁)⋊C₄	—	2	1	no	—
188	(C₂×D₇₁)⋊C₄	—	2	1	no	—
189	C₄×Dic₇₁	—	2	1	no	—
190	C₄×Dic₇₁	—	2	1	no	—
191	C₄×Dic₇₁	—	2	1	no	—
192	C₄×Dic₇₁	—	2	1	no	—
193	C₄×Dic₇₁	—	2	1	no	—
194	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
196	C₄×Dic₇₁	#41	1	1	yes	characteristic
197	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
198	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₁	—	2	1	no	—
200	SD₁₆×C₇₁	C₂×C₈	1	4	yes	complemented
201	C₂×C₈×C₇₁	—	2	1	no	—
202	C₂×C₈×C₇₁	—	2	1	no	—
203	C₂×C₈×C₇₁	—	2	1	no	—
204	C₂×C₈×C₇₁	—	4	2	no	—
205	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₇₁	—	2	1	no	—
210	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
211	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
212	C₂²⋊C₄×C₇₁	—	2	1	no	—
213	C₄²×C₇₁	—	2	1	no	—
214	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
215	C₂³×C₇₁	—	2	1	no	—
216	C₂²×D₇₁	—	2	1	no	—
217	C₂²×D₇₁	C₄×D₄	1	1	yes	characteristic
218	Q₈×C₇₁	—	2	1	no	—
219	Q₈×C₇₁	C₂²×C₈	1	2	yes	—
220	D₄×C₇₁	—	2	1	no	—
221	D₄×C₇₁	C₂²×C₈	1	2	yes	—
222	C₂×C₄×C₇₁	—	2	1	no	—
223	C₂×C₄×C₇₁	—	2	1	no	—
224	C₂×C₄×C₇₁	—	2	1	no	—
225	C₂×C₄×C₇₁	—	4	1	no	—
226	C₂×C₄×C₇₁	—	4	1	no	—
227	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
230	C₂²⋊D₇₁	—	2	4	no	—
231	C₂×Dic₇₁	—	2	1	no	—
232	C₂×Dic₇₁	—	2	4	no	—
233	C₂×Dic₇₁	—	2	1	no	—
234	C₂×Dic₇₁	—	2	1	no	—
235	C₂×Dic₇₁	—	4	2	no	—
236	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
237	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
238	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
239	D₂₈₄	—	2	4	no	—
240	D₂₈₄	—	2	1	no	—
241	D₂₈₄	C₂²×C₈	1	2	yes	—
242	C₄×D₇₁	—	2	1	no	—
243	C₄×D₇₁	—	2	1	no	—
244	C₄×D₇₁	—	2	4	no	—
245	C₄×D₇₁	—	2	2	no	—
246	C₄×D₇₁	—	4	1	no	—
247	C₄×D₇₁	—	4	1	no	—
248	C₄×D₇₁	—	4	2	no	—
249	C₄×D₇₁	C₂²×C₈	1	2	yes	—
250	C₄×D₇₁	#131	1	2	yes	—
251	Dic₁₄₂	—	2	1	no	—
252	Dic₁₄₂	C₂²×C₈	1	2	yes	—
253	C₈×C₇₁	—	2	2	no	—
254	C₈×C₇₁	—	2	1	no	—
255	C₈×C₇₁	—	2	1	no	—
256	C₈×C₇₁	—	4	1	no	—
257	C₈×C₇₁	—	4	1	no	—
258	C₈×C₇₁	C₂²×C₈	1	2	yes	—
259	C₈×C₇₁	#135	1	2	yes	complemented
260	C₇₁⋊C₈	—	2	2	no	—
261	C₇₁⋊C₈	—	2	1	no	—
262	C₇₁⋊C₈	—	2	1	no	—
263	C₇₁⋊C₈	—	4	1	no	—
264	C₇₁⋊C₈	—	4	1	no	—
265	C₇₁⋊C₈	C₂²×C₈	1	2	yes	—
266	C₇₁⋊C₈	#135	1	2	yes	complemented
267	C₂²×C₇₁	—	2	2	no	—
268	C₂²×C₇₁	—	4	1	no	—
269	C₂²×C₇₁	—	4	1	no	—
270	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂×D₇₁	—	2	1	no	—
272	C₂×D₇₁	—	2	1	no	—
273	C₂×D₇₁	—	2	2	no	—
274	C₂×D₇₁	—	4	1	no	—
275	C₂×D₇₁	—	4	1	no	—
276	C₂×D₇₁	C₈×D₄	1	2	yes	—
277	C₄×C₇₁	—	2	2	no	—
278	C₄×C₇₁	—	2	1	no	—
279	C₄×C₇₁	—	4	1	no	—
280	C₄×C₇₁	—	4	1	no	—
281	C₄×C₇₁	C₂³×C₈	1	1	yes	characteristic
282	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
283	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
284	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
285	Dic₇₁	—	2	2	no	—
286	Dic₇₁	—	2	1	no	—
287	Dic₇₁	—	4	1	no	—
288	Dic₇₁	—	4	1	no	—
289	Dic₇₁	C₈×D₄	1	2	yes	—
290	Dic₇₁	#443	1	2	yes	—
291	C₈×#135	—	71	1	no	maximal, Sylow
292	C₂×C₇₁	—	4	2	no	—
293	C₂×C₇₁	C₂×C₈×D₄	1	1	yes	characteristic
294	C₂×C₇₁	C₄×#135	1	1	yes	characteristic
295	C₂×C₇₁	C₂×#443	1	1	yes	characteristic
296	D₇₁	—	2	2	no	—
297	D₇₁	—	4	2	no	—
298	C₈×#41	—	71	1	no	—
299	C₈×#41	—	71	1	no	—
300	C₄×#135	—	71	1	no	—
301	C₈×Q₁₆	—	71	1	no	—
302	C₈×Q₁₆	—	71	1	no	—
303	C₈×SD₁₆	—	71	1	no	—
304	C₈×SD₁₆	—	71	1	no	—
305	C₈×SD₁₆	—	71	1	no	—
306	C₈×SD₁₆	D₇₁	1	1	yes	characteristic, complemented
307	C₈×D₈	—	71	1	no	—
308	C₈×D₈	—	71	1	no	—
309	#1564	—	71	1	no	—
310	#1476	—	71	1	no	—
311	#1476	—	71	1	no	—
312	C₂×C₈²	—	71	1	no	—
313	C₇₁	C₈×#135	1	1	yes	characteristic, complemented, Sylow
314	C₂×#135	—	71	1	no	—
315	C₄×#41	—	71	1	no	—
316	C₄×#41	—	71	1	no	—
317	C₈×Q₈	—	71	1	no	—
318	C₈×Q₈	—	71	1	no	—
319	C₈×Q₈	—	71	1	no	—
320	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic
321	C₄×Q₁₆	—	71	1	no	—
322	C₄×Q₁₆	—	71	1	no	—
323	C₄×SD₁₆	—	71	1	no	—
324	C₄×SD₁₆	—	71	1	no	—
325	C₄×SD₁₆	—	71	1	no	—
326	C₄×SD₁₆	C₂×D₇₁	1	1	yes	characteristic
327	C₄×D₈	—	71	1	no	—
328	C₄×D₈	—	71	1	no	—
329	C₈×D₄	—	71	1	no	—
330	C₈×D₄	—	71	1	no	—
331	C₈×D₄	—	71	1	no	—
332	C₈×D₄	—	142	1	no	—
333	C₈×D₄	—	142	1	no	—
334	C₈×D₄	—	142	1	no	—
335	C₈×D₄	—	142	1	no	—
336	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
337	#431	—	71	1	no	—
338	#431	—	71	1	no	—
339	#431	—	142	1	no	—
340	#431	—	142	1	no	—
341	#427	—	71	1	no	—
342	#416	—	71	1	no	—
343	#416	—	71	1	no	—
344	C₂×C₄×C₈	—	71	1	no	—
345	C₂×C₄×C₈	—	71	1	no	—
346	C₂×C₄×C₈	—	71	1	no	—
347	C₂×C₄×C₈	—	142	1	no	—
348	C₂×C₄×C₈	—	142	1	no	—
349	#335	—	71	1	no	—
350	#335	—	71	1	no	—
351	#334	—	71	1	no	—
352	#334	C₂×D₇₁	1	1	yes	characteristic
353	Q₈⋊C₈	—	71	1	no	—
354	Q₈⋊C₈	—	71	1	no	—
355	Q₈⋊C₈	—	71	1	no	—
356	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
357	D₄⋊C₈	—	71	1	no	—
358	D₄⋊C₈	—	71	1	no	—
359	D₄⋊C₈	—	71	1	no	—
360	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
361	C₈²	—	71	1	no	—
362	C₈²	—	71	1	no	—
363	C₈²	—	71	1	no	—
364	C₈²	C₂×D₇₁	1	1	yes	characteristic
365	C₂×#41	—	71	1	no	—
366	C₂×#41	—	71	1	no	—
367	#135	—	71	8	no	—
368	C₂×Q₁₆	—	71	1	no	—
369	C₂×SD₁₆	—	71	1	no	—
370	C₂×SD₁₆	C₄×D₇₁	1	1	yes	characteristic
371	C₂×D₈	—	71	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	71	1	no	—
374	C₂²×C₈	—	71	1	no	—
375	C₂²×C₈	—	71	1	no	—
376	C₂²×C₈	—	71	1	no	—
377	C₂²×C₈	—	142	1	no	—
378	C₂²×C₈	—	142	1	no	—
379	C₂²×C₈	—	142	1	no	—
380	C₂²×C₈	—	142	1	no	—
381	C₄×Q₈	—	71	1	no	—
382	C₄×Q₈	—	71	1	no	—
383	C₄×Q₈	—	71	1	no	—
384	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
385	C₄×D₄	—	71	1	no	—
386	C₄×D₄	—	71	1	no	—
387	C₄×D₄	—	71	1	no	—
388	C₄×D₄	—	142	1	no	—
389	C₄×D₄	—	142	1	no	—
390	C₄×D₄	—	142	1	no	—
391	C₄×D₄	—	142	1	no	—
392	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
393	#117	—	71	1	no	—
394	#117	—	71	1	no	—
395	#117	—	142	1	no	—
396	#117	—	142	1	no	—
397	C₂×C₄²	—	71	1	no	—
398	C₂×C₄²	—	142	1	no	—
399	C₂×C₄²	—	142	1	no	—
400	#107	—	71	1	no	—
401	#107	—	71	1	no	—
402	#106	—	71	1	no	—
403	#106	C₄×D₇₁	1	1	yes	characteristic
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	71	1	no	—
406	C₄⋊C₈	—	71	1	no	—
407	C₄⋊C₈	—	142	1	no	—
408	C₄⋊C₈	—	142	1	no	—
409	C₄⋊C₈	—	142	1	no	—
410	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
411	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
412	#103	—	71	1	no	—
413	#103	—	71	1	no	—
414	#103	—	71	1	no	—
415	#103	C₄×D₇₁	1	1	yes	characteristic
416	#102	—	71	1	no	—
417	#102	—	71	1	no	—
418	#102	—	71	1	no	—
419	#102	C₄×D₇₁	1	1	yes	characteristic
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	142	1	no	—
422	C₂²⋊C₈	—	142	1	no	—
423	C₂²⋊C₈	—	142	1	no	—
424	C₂²⋊C₈	—	142	1	no	—
425	C₂²⋊C₈	—	142	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	71	1	no	—
428	C₄×C₈	—	71	1	no	—
429	C₄×C₈	—	71	1	no	—
430	C₄×C₈	—	71	1	no	—
431	C₄×C₈	—	71	1	no	—
432	C₄×C₈	—	71	1	no	—
433	C₄×C₈	—	71	1	no	—
434	C₄×C₈	—	142	1	no	—
435	C₄×C₈	—	142	1	no	—
436	C₄×C₈	—	142	1	no	—
437	C₄×C₈	—	142	1	no	—
438	C₄×C₈	—	142	1	no	—
439	C₄×C₈	—	142	1	no	—
440	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
441	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
442	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
443	#41	—	71	4	no	—
444	#41	—	71	4	no	—
445	#41	—	142	2	no	—
446	#41	—	142	2	no	—
447	C₂×Q₈	—	71	1	no	—
448	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
449	C₂×D₄	—	71	1	no	—
450	C₂×D₄	—	142	1	no	—
451	C₂×D₄	—	142	1	no	—
452	C₂×D₄	C₂×C₄×D₇₁	1	1	yes	characteristic
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	71	1	no	—
455	C₂²×C₄	—	71	1	no	—
456	C₂²×C₄	—	71	1	no	—
457	C₂²×C₄	—	142	1	no	—
458	C₂²×C₄	—	142	1	no	—
459	C₂²×C₄	—	142	1	no	—
460	C₂²×C₄	—	142	1	no	—
461	C₂²×C₄	—	142	1	no	—
462	Q₁₆	—	71	4	no	—
463	SD₁₆	—	71	4	no	—
464	SD₁₆	C₈×D₇₁	1	4	yes	complemented
465	D₈	—	71	4	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	4	2	no	—
470	C₂×C₈	—	284	2	no	—
471	C₂×C₈	—	284	2	no	—
472	C₂×C₈	—	284	2	no	—
473	C₂×C₈	—	71	1	no	—
474	C₂×C₈	—	71	1	no	—
475	C₂×C₈	—	71	4	no	—
476	C₂×C₈	—	71	1	no	—
477	C₂×C₈	—	71	1	no	—
478	C₂×C₈	—	142	2	no	—
479	C₂×C₈	—	142	2	no	—
480	C₂×C₈	—	142	4	no	—
481	C₂×C₈	—	142	1	no	—
482	C₂×C₈	—	142	1	no	—
483	C₂×C₈	—	142	1	no	—
484	C₂×C₈	—	142	2	no	—
485	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
486	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
487	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
488	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	71	1	no	—
491	C₄⋊C₄	—	71	1	no	—
492	C₄⋊C₄	—	142	1	no	—
493	C₄⋊C₄	—	142	1	no	—
494	C₄⋊C₄	—	142	1	no	—
495	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
496	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	142	1	no	—
499	C₂²⋊C₄	—	142	1	no	—
500	C₂²⋊C₄	—	142	1	no	—
501	C₂²⋊C₄	—	142	1	no	—
502	C₂²⋊C₄	—	142	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	71	1	no	—
505	C₄²	—	71	1	no	—
506	C₄²	—	71	1	no	—
507	C₄²	—	142	1	no	—
508	C₄²	—	142	1	no	—
509	C₄²	—	142	1	no	—
510	C₄²	—	142	1	no	—
511	C₄²	—	142	1	no	—
512	C₄²	C₂³×D₇₁	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	71	1	no	—
515	C₂³	—	142	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	71	2	no	—
518	Q₈	—	142	1	no	—
519	Q₈	C₂×C₈×D₇₁	1	2	yes	—
520	D₄	—	2	1	no	—
521	D₄	—	71	2	no	—
522	D₄	—	142	4	no	—
523	D₄	—	142	4	no	—
524	D₄	—	142	1	no	—
525	D₄	C₂×C₈×D₇₁	1	2	yes	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	284	2	no	—
532	C₂×C₄	—	284	2	no	—
533	C₂×C₄	—	284	1	no	—
534	C₂×C₄	—	284	1	no	—
535	C₂×C₄	—	71	1	no	—
536	C₂×C₄	—	71	1	no	—
537	C₂×C₄	—	71	2	no	—
538	C₂×C₄	—	71	2	no	—
539	C₂×C₄	—	71	1	no	—
540	C₂×C₄	—	142	2	no	—
541	C₂×C₄	—	142	4	no	—
542	C₂×C₄	—	142	1	no	—
543	C₂×C₄	—	142	1	no	—
544	C₂×C₄	—	142	4	no	—
545	C₂×C₄	—	142	1	no	—
546	C₂×C₄	—	142	1	no	—
547	C₂×C₄	—	142	1	no	—
548	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
549	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
550	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	284	1	no	—
557	C₈	—	284	1	no	—
558	C₈	—	71	2	no	—
559	C₈	—	71	2	no	—
560	C₈	—	142	2	no	—
561	C₈	—	142	1	no	—
562	C₈	—	142	1	no	—
563	C₈	C₂×C₈×D₇₁	1	2	yes	—
564	C₈	#14556149	1	2	yes	direct product factor
565	C₂²	—	2	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	284	1	no	—
569	C₂²	—	284	1	no	—
570	C₂²	—	71	2	no	—
571	C₂²	—	142	2	no	—
572	C₂²	—	142	1	no	—
573	C₂²	—	142	1	no	—
574	C₂²	C₄×D₄×D₇₁	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	284	1	no	—
580	C₄	—	284	1	no	—
581	C₄	—	71	2	no	—
582	C₄	—	71	2	no	—
583	C₄	—	142	2	no	—
584	C₄	—	142	1	no	—
585	C₄	C₂²×C₈×D₇₁	1	1	yes	characteristic
586	C₄	#131×D₇₁	1	1	yes	characteristic
587	C₄	#135×D₇₁	1	1	yes	characteristic
588	C₄	C₂×#14556149	1	1	yes	characteristic
589	C₂	—	4	2	no	—
590	C₂	—	284	2	no	—
591	C₂	—	142	2	no	—
592	C₂	C₈×D₄×D₇₁	1	1	yes	characteristic
593	C₂	C₄×#14556149	1	1	yes	characteristic
594	C₂	#443×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₇₁
commutator	C₄×C₇₁	C₂³×C₈
Frattini	C₄²	C₂³×D₇₁
Fitting	C₈×SD₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	C₂×#14556149	C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	C₈×SD₁₆	D₇₁
hypocenter	C₇₁	C₈×#135
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₈×#11765866	C₂	semidirect
2. C₈×#11765864	C₂	semidirect
4. C₈×#11765855	C₂	semidirect
5. #22587144	C₂	semidirect
6. C₈×#11765854	C₂	semidirect
7. SD₁₆×C₇₁⋊C₈	C₂	semidirect
8. #22587139	C₂	semidirect
9. C₈×#11765850	C₂	semidirect
10. #22587132	C₂	semidirect
11. #22587085	C₂	semidirect
12. #22586721	C₂	semidirect
13. #22586719	C₂	semidirect
14. C₈²×D₇₁	C₂	semidirect
15. C₈×SD₁₆×C₇₁	C₂	semidirect
69. #14556149	C₈	direct (N × H)
146. #11765866	C₂×C₈	semidirect
148. #11765864	C₂×C₈	semidirect
161. #11765855	C₂×C₈	semidirect
162. #11765854	C₂×C₈	semidirect
163. #11765850	C₂×C₈	semidirect
178. C₈×D₇₁	C₂×C₈	semidirect
200. SD₁₆×C₇₁	C₂×C₈	semidirect
259. C₈×C₇₁	#135	semidirect
266. C₇₁⋊C₈	#135	semidirect
306. C₈×SD₁₆	D₇₁	semidirect
313. C₇₁	C₈×#135	semidirect
464. SD₁₆	C₈×D₇₁	semidirect
564. C₈	#14556149	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×#11765866	2
C₈×#11765864	2
C₄×#14556149	2
C₈×#11765855	2
#22587144	2
C₈×#11765854	2
SD₁₆×C₇₁⋊C₈	2
#22587139	2
C₈×#11765850	2
#22587132	2
#22587085	2
#22586721	2
#22586719	2
C₈²×D₇₁	2
C₈×SD₁₆×C₇₁	2
C₈×#135	71

Subgroups — C8×#14556149 #31966827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#14556149 #31966827