Subgroups — C₈×#13094052 #26185696

Order 12032.

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×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094052	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242213	C₂	1	2	yes	maximal, complemented
5	#20242202	C₂	1	2	yes	maximal, complemented
6	C₈×#10625325	C₂	1	2	yes	maximal, complemented
7	C₈×D₃₇₆	C₂	1	2	yes	maximal, complemented
8	#20242140	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241780	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094052	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	—	2	1	no	—
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
16	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
17	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
18	#15689236	C₄	1	2	yes	—
19	#15689225	C₄	1	2	yes	—
20	C₄×#10625325	C₂²	1	2	yes	—
21	C₄×D₃₇₆	C₂²	1	2	yes	—
22	C₈×D₁₈₈	—	2	1	no	—
23	C₈×D₁₈₈	—	2	1	no	—
24	C₈×D₁₈₈	C₂²	1	2	yes	—
25	C₈×D₁₈₈	C₂²	1	2	yes	—
26	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
27	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
28	C₈×C₂²⋊D₄₇	—	2	1	no	—
29	C₈×C₂²⋊D₄₇	—	2	1	no	—
30	#15689176	C₂²	1	1	yes	characteristic
31	#15689174	—	2	1	no	—
32	#15689165	C₄	1	1	yes	characteristic
33	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	#15689129	C₄	1	1	yes	characteristic
35	#15689125	C₄	1	1	yes	characteristic
36	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688876	C₂²	1	2	yes	complemented
39	#15688874	C₂²	1	2	yes	complemented
40	#15688855	C₂²	1	2	yes	complemented
41	#15688852	C₂²	1	2	yes	—
42	#15688852	C₂²	1	2	yes	—
43	#15688852	C₂²	1	2	yes	complemented
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#322	C₂²	1	2	yes	complemented
48	C₈²×C₄₇	C₂²	1	2	yes	complemented
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₄₇	—	2	1	no	—
52	#13094052	C₈	1	8	yes	direct product factor
53	C₂×#10625325	C₂×C₄	1	2	yes	—
54	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂×C₈×D₄₇	—	2	1	no	—
57	C₂×C₈×D₄₇	—	2	1	no	—
58	C₂×C₈×D₄₇	—	2	2	no	—
59	C₂×C₈×D₄₇	—	2	2	no	—
60	C₂×C₈×D₄₇	—	4	4	no	—
61	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
63	C₄×D₁₈₈	—	2	1	no	—
64	C₄×D₁₈₈	—	2	1	no	—
65	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
66	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
67	C₄×D₁₈₈	C₂³	1	2	yes	—
68	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₇	—	2	1	no	—
70	C₄×C₂²⋊D₄₇	—	2	1	no	—
71	#13093983	C₂×C₄	1	1	yes	characteristic
72	#13093981	—	2	1	no	—
73	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
75	C₄²×D₄₇	—	2	1	no	—
76	#13093958	C₂×C₄	1	2	yes	—
77	#13093956	C₂×C₄	1	2	yes	—
78	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
79	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
81	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
82	Dic₄₇⋊C₈	—	2	1	no	—
83	Dic₄₇⋊C₈	—	2	1	no	—
84	#13093949	C₂×C₄	1	2	yes	—
85	#13093946	C₂×C₄	1	2	yes	—
86	#13093946	C₂×C₄	1	2	yes	—
87	#13093946	C₂×C₄	1	2	yes	—
88	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
89	(C₂×D₄₇)⋊C₈	—	2	2	no	—
90	(C₂×D₄₇)⋊C₈	—	2	2	no	—
91	(C₂×D₄₇)⋊C₈	—	2	1	no	—
92	(C₂×D₄₇)⋊C₈	—	2	1	no	—
93	C₄×C₄₇⋊C₈	—	2	1	no	—
94	C₈×Dic₄₇	—	2	1	no	—
95	C₈×Dic₄₇	—	2	1	no	—
96	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₄₇	—	2	1	no	—
102	C₂²⋊C₈×C₄₇	—	2	1	no	—
103	#97×C₄₇	C₂×C₄	1	2	yes	—
104	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₄₇	C₂³	1	2	yes	—
107	C₄×C₈×C₄₇	C₂³	1	2	yes	—
108	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₂³×D₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₇	—	2	1	no	—
115	C₂²×Dic₄₇	—	2	1	no	—
116	#10625350	—	2	2	no	—
117	#10625350	C₂×C₈	1	4	yes	complemented
118	C₂×D₁₈₈	—	2	1	no	—
119	C₂×D₁₈₈	—	2	2	no	—
120	C₂×D₁₈₈	C₂×C₈	1	4	yes	complemented
121	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
122	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₄₇	—	2	1	no	—
124	C₂×C₄×D₄₇	—	2	1	no	—
125	C₂×C₄×D₄₇	—	2	2	no	—
126	C₂×C₄×D₄₇	—	2	1	no	—
127	C₂×C₄×D₄₇	—	2	2	no	—
128	C₂×C₄×D₄₇	—	4	2	no	—
129	C₂×C₄×D₄₇	—	4	2	no	—
130	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
131	M₁₆×C₄₇	—	2	2	no	—
132	M₁₆×C₄₇	C₂×C₈	1	4	yes	complemented
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	4	1	no	—
136	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₇	#41	1	1	yes	characteristic
145	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂²⋊Dic₄₇	—	2	1	no	—
147	(C₂×D₄₇)⋊C₄	—	2	2	no	—
148	(C₂×D₄₇)⋊C₄	—	2	1	no	—
149	(C₂×D₄₇)⋊C₄	—	2	2	no	—
150	(C₂×D₄₇)⋊C₄	—	2	1	no	—
151	C₄⋊Dic₄₇	—	2	1	no	—
152	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
155	Dic₄₇⋊C₄	—	2	1	no	—
156	Dic₄₇⋊C₄	—	2	1	no	—
157	C₄×Dic₄₇	—	2	1	no	—
158	C₄×Dic₄₇	—	2	1	no	—
159	C₄×Dic₄₇	—	2	1	no	—
160	C₂×C₄₇⋊C₈	—	2	1	no	—
161	C₂×C₄₇⋊C₈	—	2	1	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	—	4	2	no	—
164	D₃₇₆	C₂×C₈	1	8	yes	complemented
165	#10625325	C₂×C₈	1	8	yes	complemented
166	C₈×D₄₇	—	4	2	no	—
167	C₈×D₄₇	—	4	4	no	—
168	C₈×D₄₇	—	4	2	no	—
169	C₈×D₄₇	—	4	4	no	—
170	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂²×D₄₇	—	2	1	no	—
172	C₂²×D₄₇	—	2	2	no	—
173	C₂²×D₄₇	—	2	4	no	—
174	C₂²×D₄₇	—	4	2	no	—
175	C₂²×D₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
183	C₂×C₄×C₄₇	#131	1	2	yes	—
184	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₄₇	—	2	4	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	4	2	no	—
193	D₁₈₈	—	2	2	no	—
194	D₁₈₈	—	2	1	no	—
195	D₁₈₈	—	2	4	no	—
196	D₁₈₈	C₂²×C₈	1	4	yes	—
197	D₁₈₈	C₂²×C₈	1	2	yes	complemented
198	C₄×D₄₇	—	2	4	no	—
199	C₄×D₄₇	—	4	2	no	—
200	C₄×D₄₇	—	4	4	no	—
201	C₄×D₄₇	—	4	2	no	—
202	C₄×D₄₇	—	4	1	no	—
203	C₄×D₄₇	—	4	1	no	—
204	C₄×D₄₇	—	4	2	no	—
205	Dic₉₄	—	2	1	no	—
206	Dic₉₄	C₂²×C₈	1	2	yes	complemented
207	C₈×C₄₇	—	2	2	no	—
208	C₈×C₄₇	—	2	1	no	—
209	C₈×C₄₇	—	2	1	no	—
210	C₈×C₄₇	—	2	1	no	—
211	C₈×C₄₇	—	4	2	no	—
212	C₈×C₄₇	C₂²×C₈	1	4	yes	complemented
213	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	complemented
214	C₄₇⋊C₈	—	4	2	no	—
215	C₄₇⋊C₈	—	4	1	no	—
216	C₄₇⋊C₈	—	4	1	no	—
217	C₈×AGL(1,ℤ/8)	—	47	1	no	maximal, Sylow
218	C₂²×C₄₇	—	2	1	no	—
219	C₂²×C₄₇	—	2	1	no	—
220	C₂²×C₄₇	C₈×D₄	1	2	yes	—
221	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂×D₄₇	—	2	2	no	—
223	C₂×D₄₇	—	2	4	no	—
224	C₂×D₄₇	—	4	8	no	—
225	C₂×D₄₇	—	4	2	no	—
226	C₂×D₄₇	—	4	1	no	—
227	C₂×D₄₇	—	4	1	no	—
228	C₂×D₄₇	—	4	2	no	—
229	C₄×C₄₇	—	2	1	no	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	—	2	1	no	—
232	C₄×C₄₇	C₈×D₄	1	2	yes	—
233	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
234	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
235	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₄×C₄₇	#575	1	1	yes	characteristic
237	Dic₄₇	—	2	2	no	—
238	Dic₄₇	—	4	2	no	—
239	Dic₄₇	—	4	1	no	—
240	Dic₄₇	—	4	1	no	—
241	C₈×#41	—	47	1	no	—
242	C₄×AGL(1,ℤ/8)	—	47	1	no	—
243	C₂×C₈×D₄	—	47	1	no	—
244	#1580	—	47	2	no	—
245	SD₁₆⋊C₈	—	47	2	no	—
246	C₈×SD₁₆	—	47	2	no	—
247	C₈×D₈	—	47	2	no	—
248	#1565	—	47	1	no	—
249	#1478	—	47	1	no	—
250	#1477	—	47	1	no	—
251	C₈×M₁₆	D₄₇	1	1	yes	characteristic, complemented
252	C₂×C₄₇	—	2	2	no	—
253	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
254	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂×C₄₇	#2955	1	1	yes	characteristic
256	D₄₇	—	4	2	no	—
257	D₄₇	—	4	4	no	—
258	C₂×AGL(1,ℤ/8)	—	47	1	no	—
259	C₂³×C₈	—	94	1	no	—
260	C₄×#41	—	47	1	no	—
261	C₂×C₄×D₄	—	47	1	no	—
262	C₈×Q₈	—	47	1	no	—
263	C₈×Q₈	—	47	1	no	—
264	#442	—	47	2	no	—
265	#440	—	47	2	no	—
266	C₄×SD₁₆	—	47	2	no	—
267	C₄×D₈	—	47	2	no	—
268	C₈×D₄	—	47	1	no	—
269	C₈×D₄	—	47	2	no	—
270	C₈×D₄	—	47	2	no	—
271	C₈×D₄	—	47	1	no	—
272	C₈×D₄	—	94	1	no	—
273	C₈×D₄	—	94	1	no	—
274	C₈×D₄	—	94	1	no	—
275	C₈×D₄	—	94	1	no	—
276	#431	—	47	1	no	—
277	#431	—	94	1	no	—
278	#431	C₂×D₄₇	1	1	yes	characteristic
279	#428	—	47	1	no	—
280	C₂×C₄⋊C₈	—	47	1	no	—
281	#418	—	47	1	no	—
282	#417	—	47	1	no	—
283	C₂×C₂²⋊C₈	—	94	1	no	—
284	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
285	C₂×C₄×C₈	—	94	1	no	—
286	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
287	#335	—	47	2	no	—
288	#334	—	47	2	no	—
289	Q₈⋊C₈	—	47	2	no	—
290	D₄⋊C₈	—	47	2	no	—
291	D₄⋊C₈	—	47	2	no	—
292	D₄⋊C₈	—	47	2	no	—
293	#322	C₂×D₄₇	1	2	yes	complemented
294	C₈²	C₂×D₄₇	1	2	yes	complemented
295	C₄₇	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	—	47	1	no	—
297	C₂²×D₄	—	47	1	no	—
298	C₂³×C₄	—	94	1	no	—
299	AGL(1,ℤ/8)	—	47	8	no	—
300	C₂×SD₁₆	—	47	2	no	—
301	C₂×D₈	—	47	2	no	—
302	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
303	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
304	C₂²×C₈	—	94	1	no	—
305	C₂²×C₈	—	94	2	no	—
306	C₂²×C₈	—	94	1	no	—
307	C₂²×C₈	—	94	2	no	—
308	C₂²×C₈	—	94	1	no	—
309	C₂²×C₈	—	188	4	no	—
310	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
311	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
312	C₄×Q₈	—	47	1	no	—
313	C₄×Q₈	—	47	1	no	—
314	C₄×D₄	—	47	2	no	—
315	C₄×D₄	—	47	1	no	—
316	C₄×D₄	—	47	2	no	—
317	C₄×D₄	—	47	1	no	—
318	C₄×D₄	—	94	1	no	—
319	C₄×D₄	—	94	1	no	—
320	C₄×D₄	—	94	1	no	—
321	C₄×D₄	—	94	1	no	—
322	#117	—	47	1	no	—
323	#117	—	94	1	no	—
324	C₂×C₄⋊C₄	—	47	1	no	—
325	C₂×C₂²⋊C₄	—	94	1	no	—
326	C₂×C₄²	—	94	1	no	—
327	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
328	#107	—	47	2	no	—
329	#106	—	47	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	47	1	no	—
332	C₄⋊C₈	—	47	1	no	—
333	C₄⋊C₈	—	47	2	no	—
334	C₄⋊C₈	—	94	1	no	—
335	C₄⋊C₈	—	94	1	no	—
336	C₄⋊C₈	—	94	1	no	—
337	#103	—	47	2	no	—
338	#102	—	47	2	no	—
339	#102	—	47	2	no	—
340	#102	—	47	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	94	1	no	—
343	C₂²⋊C₈	—	94	2	no	—
344	C₂²⋊C₈	—	94	2	no	—
345	C₂²⋊C₈	—	94	1	no	—
346	C₂²⋊C₈	—	94	1	no	—
347	#97	C₄×D₄₇	1	2	yes	—
348	C₄×C₈	—	94	1	no	—
349	C₄×C₈	—	94	1	no	—
350	C₄×C₈	—	94	1	no	—
351	C₄×C₈	D₁₈₈	1	1	yes	characteristic
352	C₄×C₈	D₁₈₈	1	1	yes	characteristic
353	C₄×C₈	C₂²×D₄₇	1	2	yes	—
354	C₄×C₈	C₂²×D₄₇	1	2	yes	—
355	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
357	C₂⁴	—	94	1	no	—
358	#41	—	47	4	no	—
359	#41	—	94	2	no	—
360	C₂×Q₈	—	47	1	no	—
361	C₂×D₄	—	47	4	no	—
362	C₂×D₄	—	47	1	no	—
363	C₂×D₄	—	47	2	no	—
364	C₂×D₄	—	94	1	no	—
365	C₂×D₄	—	94	1	no	—
366	C₂×D₄	—	94	2	no	—
367	C₂²×C₄	—	94	1	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	—	94	1	no	—
370	C₂²×C₄	—	94	2	no	—
371	C₂²×C₄	—	94	1	no	—
372	C₂²×C₄	—	94	2	no	—
373	C₂²×C₄	—	188	2	no	—
374	C₂²×C₄	—	188	2	no	—
375	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
377	C₂²×C₄	#10625350	1	1	yes	characteristic
378	SD₁₆	—	47	8	no	—
379	D₈	—	47	8	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	C₈×D₄₇	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	—	94	1	no	—
386	C₂×C₈	—	94	1	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	—	188	2	no	—
389	C₂×C₈	—	188	4	no	—
390	C₂×C₈	—	188	2	no	—
391	C₂×C₈	—	188	2	no	—
392	C₂×C₈	—	188	4	no	—
393	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
394	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
395	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
396	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
397	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
398	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
399	C₄⋊C₄	—	47	1	no	—
400	C₄⋊C₄	—	47	1	no	—
401	C₄⋊C₄	—	47	2	no	—
402	C₄⋊C₄	—	94	1	no	—
403	C₄⋊C₄	—	94	1	no	—
404	C₄⋊C₄	—	94	1	no	—
405	C₂²⋊C₄	—	94	1	no	—
406	C₂²⋊C₄	—	94	2	no	—
407	C₂²⋊C₄	—	94	1	no	—
408	C₂²⋊C₄	—	94	2	no	—
409	C₂²⋊C₄	—	94	1	no	—
410	C₄²	—	94	1	no	—
411	C₄²	—	94	1	no	—
412	C₄²	—	94	1	no	—
413	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
414	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
415	C₄²	#10625350	1	1	yes	characteristic
416	C₄²	C₂³×D₄₇	1	1	yes	characteristic
417	C₂³	—	94	1	no	—
418	C₂³	—	94	2	no	—
419	C₂³	—	94	4	no	—
420	C₂³	—	188	2	no	—
421	C₂³	—	188	2	no	—
422	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
423	Q₈	—	47	2	no	—
424	Q₈	—	94	1	no	—
425	D₄	—	47	4	no	—
426	D₄	—	47	2	no	—
427	D₄	—	94	4	no	—
428	D₄	—	94	2	no	—
429	D₄	—	94	1	no	—
430	D₄	—	94	4	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	94	1	no	—
435	C₂×C₄	—	94	4	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	—	188	4	no	—
441	C₂×C₄	—	188	2	no	—
442	C₂×C₄	—	188	2	no	—
443	C₂×C₄	—	188	1	no	—
444	C₂×C₄	—	188	1	no	—
445	C₂×C₄	—	188	2	no	—
446	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
447	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
448	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
449	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
450	C₂×C₄	#13094030	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	4	2	no	—
459	C₈	—	188	1	no	—
460	C₈	—	188	2	no	—
461	C₈	—	188	1	no	—
462	C₈	C₂×C₈×D₄₇	1	4	yes	complemented
463	C₈	#13094052	1	2	yes	direct product factor
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	94	2	no	—
467	C₂²	—	94	4	no	—
468	C₂²	—	188	8	no	—
469	C₂²	—	188	2	no	—
470	C₂²	—	188	1	no	—
471	C₂²	—	188	1	no	—
472	C₂²	—	188	2	no	—
473	C₂²	C₈×D₁₈₈	1	2	yes	—
474	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	94	2	no	—
479	C₄	—	188	2	no	—
480	C₄	—	188	1	no	—
481	C₄	—	188	1	no	—
482	C₄	C₈×D₁₈₈	1	2	yes	—
483	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
484	C₄	C₂×#13094030	1	1	yes	characteristic
485	C₄	C₂×#13094052	1	1	yes	characteristic
486	C₄	#15689923	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	188	4	no	—
489	C₂	—	188	2	no	—
490	C₂	C₂×C₈×D₁₈₈	1	1	yes	characteristic
491	C₂	C₄×#13094052	1	1	yes	characteristic
492	C₂	#20252292	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₈₈
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094052	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×M₁₆	D₄₇
hypocenter	C₄₇	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
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×#10625350	C₂	semidirect
3. C₂×C₈×D₁₈₈	C₂	semidirect
4. #20242213	C₂	semidirect
5. #20242202	C₂	semidirect
6. C₈×#10625325	C₂	semidirect
7. C₈×D₃₇₆	C₂	semidirect
8. #20242140	C₂	semidirect
9. #20241780	C₂	semidirect
10. #20241776	C₂	semidirect
11. C₈×M₁₆×C₄₇	C₂	semidirect
16. C₈×Dic₉₄	C₂²	semidirect
17. C₈×Dic₉₄	C₂²	semidirect
26. C₈×D₁₈₈	C₂²	semidirect
27. C₈×D₁₈₈	C₂²	semidirect
38. #15688876	C₂²	semidirect
39. #15688874	C₂²	semidirect
40. #15688855	C₂²	semidirect
43. #15688852	C₂²	semidirect
47. C₄₇×#322	C₂²	semidirect
48. C₈²×C₄₇	C₂²	semidirect
52. #13094052	C₈	direct (N × H)
117. #10625350	C₂×C₈	semidirect
120. C₂×D₁₈₈	C₂×C₈	semidirect
132. M₁₆×C₄₇	C₂×C₈	semidirect
164. D₃₇₆	C₂×C₈	semidirect
165. #10625325	C₂×C₈	semidirect
197. D₁₈₈	C₂²×C₈	semidirect
206. Dic₉₄	C₂²×C₈	semidirect
212. C₈×C₄₇	C₂²×C₈	semidirect
213. C₈×C₄₇	AGL(1,ℤ/8)	semidirect
251. C₈×M₁₆	D₄₇	semidirect
293. #322	C₂×D₄₇	semidirect
294. C₈²	C₂×D₄₇	semidirect
295. C₄₇	C₈×AGL(1,ℤ/8)	semidirect
381. M₁₆	C₈×D₄₇	semidirect
462. C₈	C₂×C₈×D₄₇	semidirect
463. C₈	#13094052	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×#10625350	2
C₄×#13094052	2
C₂×C₈×D₁₈₈	2
#20242213	2
#20242202	2
C₈×#10625325	2
C₈×D₃₇₆	2
#20242140	2
#20241780	2
#20241776	2
C₈×M₁₆×C₄₇	2
C₈×AGL(1,ℤ/8)	47

Subgroups — C8×#13094052 #26185696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13094052 #26185696