Subgroups — #575×Dic₄₇ #27080365

Order 12032.

2842 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#137×Dic₄₇	C₂	1	8	yes	maximal, complemented
3	AGL(1,ℤ/8)×Dic₄₇	C₂	1	8	yes	maximal, complemented
4	#20252189	C₂	1	4	yes	maximal, complemented
5	#135×Dic₄₇	C₂	1	4	yes	maximal, complemented
6	#20251978	C₂	1	1	yes	maximal, characteristic, complemented
7	#20251907	C₂	1	2	yes	maximal, complemented
8	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#575	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	#41×Dic₄₇	—	2	4	no	—
12	#41×Dic₄₇	—	2	2	no	—
13	#41×Dic₄₇	—	2	2	no	—
14	#41×Dic₄₇	C₂²	1	8	yes	—
15	#41×Dic₄₇	C₂²	1	4	yes	complemented
16	#41×Dic₄₇	C₂²	1	4	yes	complemented
17	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	complemented
18	C₂×D₄×Dic₄₇	—	2	4	no	—
19	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
20	C₂×#13093983	—	2	2	no	—
21	C₂×#13093983	C₂²	1	2	yes	—
22	C₂²×C₄×Dic₄₇	—	2	2	no	—
23	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
24	#15689235	C₂²	1	8	yes	complemented
25	#15689230	C₂²	1	8	yes	complemented
26	#15689224	C₂²	1	16	yes	complemented
27	Q₁₆×Dic₄₇	C₂²	1	8	yes	complemented
28	SD₁₆×Dic₄₇	C₂²	1	16	yes	complemented
29	D₈×Dic₄₇	C₂²	1	8	yes	complemented
30	#15689165	C₂²	1	8	yes	complemented
31	#15689161	C₂²	1	4	yes	complemented
32	#15689132	C₂²	1	4	yes	complemented
33	#15689128	C₂²	1	4	yes	complemented
34	#15689124	C₂²	1	8	yes	—
35	#15689119	C₂²	1	8	yes	complemented
36	M₁₆×Dic₄₇	C₂²	1	8	yes	complemented
37	C₂×#13093934	C₂²	1	2	yes	complemented
38	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
39	C₂²×#41×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#575	C₄	1	16	yes	complemented
41	C₂×#137×C₄₇	C₂²	1	4	yes	—
42	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	4	yes	—
43	C₂×#135×C₄₇	C₂²	1	4	yes	—
44	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
45	C₂³×Dic₄₇	—	2	4	no	—
46	C₂³×Dic₄₇	D₄	1	2	yes	—
47	C₂×#10625329	—	2	4	no	—
48	C₂×#10625329	C₂³	1	4	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	Q₈×Dic₄₇	—	2	4	no	—
51	Q₈×Dic₄₇	—	2	4	no	—
52	Q₈×Dic₄₇	C₂³	1	8	yes	—
53	Q₈×Dic₄₇	C₂³	1	8	yes	—
54	D₄×Dic₄₇	—	2	8	no	—
55	D₄×Dic₄₇	—	2	8	no	—
56	D₄×Dic₄₇	—	2	8	no	—
57	D₄×Dic₄₇	—	2	8	no	—
58	D₄×Dic₄₇	—	2	4	no	—
59	D₄×Dic₄₇	—	2	4	no	—
60	D₄×Dic₄₇	C₂³	1	8	yes	—
61	D₄×Dic₄₇	C₂³	1	8	yes	—
62	#13093983	—	2	2	no	—
63	#13093983	—	2	2	no	—
64	#13093983	—	2	8	no	—
65	#13093983	—	2	4	no	—
66	#13093983	—	2	4	no	—
67	#13093983	C₂³	1	4	yes	—
68	#13093983	C₂³	1	4	yes	—
69	C₂×C₄⋊Dic₄₇	—	2	4	no	—
70	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
71	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
72	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
73	C₂×C₄×Dic₄₇	—	2	2	no	—
74	C₂×C₄×Dic₄₇	—	2	4	no	—
75	C₂×C₄×Dic₄₇	—	2	8	no	—
76	C₂×C₄×Dic₄₇	—	2	4	no	—
77	C₂×C₄×Dic₄₇	—	2	4	no	—
78	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
79	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
80	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
81	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
84	#13093958	C₂³	1	8	yes	—
85	#13093956	C₂³	1	8	yes	—
86	#13093948	C₂³	1	16	yes	—
87	#13093945	C₂³	1	16	yes	—
88	#13093934	C₂³	1	8	yes	—
89	C₈×Dic₄₇	C₂³	1	8	yes	—
90	C₂×#41×C₄₇	—	2	2	no	—
91	C₂×#41×C₄₇	—	2	2	no	—
92	C₂×#41×C₄₇	—	2	8	no	—
93	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
94	C₂×#41×C₄₇	C₂³	1	4	yes	—
95	C₂×#41×C₄₇	C₂³	1	4	yes	—
96	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₄₇	—	2	2	no	—
98	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₄₇	—	2	2	no	—
100	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	#137×C₄₇	C₂×C₄	1	32	yes	complemented
102	AGL(1,ℤ/8)×C₄₇	C₂×C₄	1	32	yes	complemented
103	#135×C₄₇	C₂×C₄	1	32	yes	complemented
104	C₂×Q₁₆×C₄₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
106	C₂×D₈×C₄₇	C₂³	1	4	yes	—
107	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
108	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
109	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
110	C₂⁴×C₄₇	—	2	2	no	—
111	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
112	#41×C₄₇	—	2	16	no	—
113	#41×C₄₇	—	2	16	no	—
114	#41×C₄₇	—	2	8	no	—
115	#41×C₄₇	—	2	8	no	—
116	#41×C₄₇	C₂²×C₄	1	16	yes	—
117	#41×C₄₇	C₂²×C₄	1	16	yes	complemented
118	C₂×Q₈×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	2	4	no	—
120	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	complemented
121	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
122	C₂×D₄×C₄₇	—	2	16	no	—
123	C₂×D₄×C₄₇	—	2	4	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	4	no	—
127	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	complemented
128	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	16	no	—
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	#41	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
139	C₂²×Dic₄₇	—	2	4	no	—
140	C₂²×Dic₄₇	—	2	8	no	—
141	C₂²×Dic₄₇	—	2	8	no	—
142	C₂²×Dic₄₇	—	4	4	no	—
143	C₂²×Dic₄₇	—	4	16	no	—
144	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
145	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
146	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
147	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
148	Q₁₆×C₄₇	C₂²×C₄	1	16	yes	complemented
149	SD₁₆×C₄₇	C₂²×C₄	1	32	yes	complemented
150	D₈×C₄₇	C₂²×C₄	1	16	yes	complemented
151	M₁₆×C₄₇	C₂²×C₄	1	16	yes	complemented
152	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	complemented
153	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
154	C₂²⋊Dic₄₇	—	2	4	no	—
155	C₂²⋊Dic₄₇	—	2	4	no	—
156	C₂²⋊Dic₄₇	—	2	8	no	—
157	C₂²⋊Dic₄₇	—	2	8	no	—
158	C₄⋊Dic₄₇	—	2	4	no	—
159	C₄⋊Dic₄₇	—	2	8	no	—
160	C₄⋊Dic₄₇	—	2	8	no	—
161	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
162	C₄×Dic₄₇	—	2	4	no	—
163	C₄×Dic₄₇	—	2	4	no	—
164	C₄×Dic₄₇	—	2	8	no	—
165	C₄×Dic₄₇	—	2	8	no	—
166	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
167	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
168	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
169	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
170	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
171	C₄×Dic₄₇	C₂⁴	1	2	yes	—
172	C₄×Dic₄₇	C₂⁴	1	2	yes	—
173	#10625329	—	2	8	no	—
174	C₂×C₄₇⋊C₈	—	2	4	no	—
175	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
176	C₂³×C₄₇	—	2	8	no	—
177	C₂³×C₄₇	—	2	4	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	—	4	8	no	—
180	C₂³×C₄₇	C₄×D₄	1	4	yes	—
181	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
183	Q₈×C₄₇	—	2	8	no	—
184	Q₈×C₄₇	—	2	4	no	—
185	Q₈×C₄₇	C₂³×C₄	1	8	yes	—
186	D₄×C₄₇	—	2	16	no	—
187	D₄×C₄₇	—	2	16	no	—
188	D₄×C₄₇	—	2	8	no	—
189	D₄×C₄₇	—	2	4	no	—
190	D₄×C₄₇	C₂³×C₄	1	8	yes	—
191	C₂×C₄×C₄₇	—	2	8	no	—
192	C₂×C₄×C₄₇	—	2	4	no	—
193	C₂×C₄×C₄₇	—	2	16	no	—
194	C₂×C₄×C₄₇	—	2	16	no	—
195	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
196	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
197	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
198	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
199	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
203	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
204	C₂×Dic₄₇	—	2	8	no	—
205	C₂×Dic₄₇	—	2	4	no	—
206	C₂×Dic₄₇	—	2	8	no	—
207	C₂×Dic₄₇	—	4	2	no	—
208	C₂×Dic₄₇	—	4	4	no	—
209	C₂×Dic₄₇	—	4	16	no	—
210	C₂×Dic₄₇	—	4	8	no	—
211	C₂×Dic₄₇	—	4	16	no	—
212	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
213	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
214	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
215	C₈×C₄₇	C₂³×C₄	1	8	yes	—
216	C₄₇⋊C₈	—	2	4	no	—
217	C₄×#575	—	47	1	no	maximal, Sylow
218	C₂²×C₄₇	—	2	4	no	—
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	8	no	—
221	C₂²×C₄₇	—	4	4	no	—
222	C₂²×C₄₇	—	4	16	no	—
223	C₂²×C₄₇	—	4	8	no	—
224	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
225	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
226	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
227	C₄×C₄₇	—	2	8	no	—
228	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
229	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
230	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
231	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
232	Dic₄₇	—	2	4	no	—
233	Dic₄₇	—	2	2	no	—
234	Dic₄₇	—	4	8	no	—
235	Dic₄₇	#575	1	4	yes	direct product factor
236	C₂×#575	D₄₇	1	1	yes	characteristic
237	C₂×C₄×#41	—	47	2	no	—
238	C₄×#137	—	47	8	no	—
239	C₄×AGL(1,ℤ/8)	—	47	8	no	—
240	#2943	—	47	4	no	—
241	C₄×#135	—	47	4	no	—
242	#2911	—	47	1	no	—
243	#2896	—	47	2	no	—
244	C₂×C₄×M₁₆	—	47	1	no	—
245	C₂×C₄₇	—	2	4	no	—
246	C₂×C₄₇	—	2	2	no	—
247	C₂×C₄₇	—	4	8	no	—
248	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
249	C₂×C₄₇	C₂×#575	1	2	yes	—
250	C₂²×#41	C₂×D₄₇	1	2	yes	—
251	#575	Dic₄₇	1	16	yes	direct product factor
252	C₂×#137	C₂×D₄₇	1	4	yes	—
253	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	4	yes	—
254	C₂×#135	C₂×D₄₇	1	4	yes	—
255	C₂²×M₁₆	—	47	1	no	—
256	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
257	C₄×#41	—	47	8	no	—
258	C₄×#41	—	47	4	no	—
259	C₄×#41	—	47	4	no	—
260	C₄×#41	—	94	2	no	—
261	C₄×#41	—	94	4	no	—
262	C₄×#41	—	94	2	no	—
263	C₂×C₄×Q₈	—	47	4	no	—
264	C₂×C₄×D₄	—	47	4	no	—
265	C₂×C₄×D₄	—	94	4	no	—
266	C₂×#117	—	47	2	no	—
267	C₂×#117	—	94	2	no	—
268	C₂²×C₄²	—	47	1	no	—
269	C₂²×C₄²	—	94	2	no	—
270	#442	—	47	8	no	—
271	#441	—	47	8	no	—
272	#440	—	47	16	no	—
273	C₄×Q₁₆	—	47	8	no	—
274	C₄×SD₁₆	—	47	16	no	—
275	C₄×D₈	—	47	8	no	—
276	#428	—	47	8	no	—
277	#427	—	47	4	no	—
278	#419	—	47	4	no	—
279	#418	—	47	4	no	—
280	#417	—	47	8	no	—
281	#416	—	47	8	no	—
282	C₄×M₁₆	—	47	8	no	—
283	C₂×#97	—	47	2	no	—
284	C₂×C₄×C₈	—	47	2	no	—
285	C₄₇	C₄×#575	1	1	yes	characteristic, complemented, Sylow
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	8	no	—
289	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
290	C₂×#41	C₂²×D₄₇	1	4	yes	—
291	C₂×#41	C₂²×D₄₇	1	4	yes	—
292	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
295	C₂³×C₄	—	2	2	no	—
296	C₂³×C₄	—	47	2	no	—
297	C₂³×C₄	—	94	4	no	—
298	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
299	#137	C₂×Dic₄₇	1	32	yes	complemented
300	AGL(1,ℤ/8)	C₂×Dic₄₇	1	32	yes	complemented
301	#135	C₂×Dic₄₇	1	32	yes	complemented
302	C₂×Q₁₆	C₂²×D₄₇	1	4	yes	—
303	C₂×SD₁₆	C₂²×D₄₇	1	8	yes	—
304	C₂×D₈	C₂²×D₄₇	1	4	yes	—
305	C₂×M₁₆	—	47	4	no	—
306	C₂×M₁₆	—	94	4	no	—
307	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	complemented
308	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
309	C₂²×C₈	—	47	2	no	—
310	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
311	C₄×Q₈	—	47	8	no	—
312	C₄×Q₈	—	47	8	no	—
313	C₄×Q₈	—	94	4	no	—
314	C₄×Q₈	—	94	4	no	—
315	C₄×D₄	—	47	8	no	—
316	C₄×D₄	—	47	8	no	—
317	C₄×D₄	—	94	4	no	—
318	C₄×D₄	—	94	4	no	—
319	C₄×D₄	—	94	8	no	—
320	C₄×D₄	—	94	8	no	—
321	C₄×D₄	—	94	8	no	—
322	C₄×D₄	—	94	8	no	—
323	#117	—	47	4	no	—
324	#117	—	47	4	no	—
325	#117	—	94	8	no	—
326	#117	—	94	4	no	—
327	#117	—	94	4	no	—
328	#117	—	94	2	no	—
329	#117	—	94	2	no	—
330	C₂×C₄⋊C₄	—	47	4	no	—
331	C₂×C₄⋊C₄	—	94	4	no	—
332	C₂×C₂²⋊C₄	—	94	4	no	—
333	C₂×C₂²⋊C₄	—	94	2	no	—
334	C₂×C₄²	—	47	2	no	—
335	C₂×C₄²	—	47	2	no	—
336	C₂×C₄²	—	47	2	no	—
337	C₂×C₄²	—	47	4	no	—
338	C₂×C₄²	—	47	1	no	—
339	C₂×C₄²	—	47	1	no	—
340	C₂×C₄²	—	94	8	no	—
341	C₂×C₄²	—	94	4	no	—
342	C₂×C₄²	—	94	4	no	—
343	C₂×C₄²	—	94	4	no	—
344	C₂×C₄²	—	94	2	no	—
345	#107	—	47	8	no	—
346	#106	—	47	8	no	—
347	#103	—	47	16	no	—
348	#102	—	47	16	no	—
349	#97	—	47	8	no	—
350	C₄×C₈	—	47	8	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
353	#41	—	2	16	no	—
354	#41	—	2	16	no	—
355	#41	—	2	8	no	—
356	#41	—	2	8	no	—
357	#41	C₂²×Dic₄₇	1	16	yes	—
358	#41	C₂²×Dic₄₇	1	16	yes	complemented
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	complemented
362	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
363	C₂×D₄	—	2	16	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	C₂²×Dic₄₇	1	8	yes	complemented
369	C₂×D₄	C₂³×D₄₇	1	4	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	16	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	47	4	no	—
375	C₂²×C₄	—	47	2	no	—
376	C₂²×C₄	—	47	4	no	—
377	C₂²×C₄	—	47	2	no	—
378	C₂²×C₄	—	94	8	no	—
379	C₂²×C₄	—	94	8	no	—
380	C₂²×C₄	—	94	4	no	—
381	C₂²×C₄	—	188	4	no	—
382	C₂²×C₄	—	188	16	no	—
383	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
384	C₂²×C₄	D₄×D₄₇	1	2	yes	—
385	C₂²×C₄	#10625352	1	4	yes	—
386	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
387	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
388	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
389	Q₁₆	C₂²×Dic₄₇	1	16	yes	complemented
390	SD₁₆	C₂²×Dic₄₇	1	32	yes	complemented
391	D₈	C₂²×Dic₄₇	1	16	yes	complemented
392	M₁₆	—	94	8	no	—
393	M₁₆	C₂²×Dic₄₇	1	16	yes	complemented
394	C₂×C₈	—	47	4	no	—
395	C₂×C₈	—	94	4	no	—
396	C₂×C₈	C₂²×Dic₄₇	1	8	yes	complemented
397	C₂×C₈	C₂³×D₄₇	1	4	yes	—
398	C₄⋊C₄	—	47	8	no	—
399	C₄⋊C₄	—	94	8	no	—
400	C₄⋊C₄	—	94	8	no	—
401	C₄⋊C₄	—	94	4	no	—
402	C₂²⋊C₄	—	94	8	no	—
403	C₂²⋊C₄	—	94	8	no	—
404	C₂²⋊C₄	—	94	4	no	—
405	C₂²⋊C₄	—	94	4	no	—
406	C₄²	—	47	4	no	—
407	C₄²	—	47	4	no	—
408	C₄²	—	47	1	no	—
409	C₄²	—	47	2	no	—
410	C₄²	—	47	1	no	—
411	C₄²	—	47	2	no	—
412	C₄²	—	47	2	no	—
413	C₄²	—	94	8	no	—
414	C₄²	—	94	8	no	—
415	C₄²	—	94	4	no	—
416	C₄²	—	94	4	no	—
417	C₂³	—	2	8	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	8	no	—
421	C₂³	D₄×Dic₄₇	1	4	yes	—
422	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
423	C₂³	C₂×D₄×D₄₇	1	2	yes	—
424	Q₈	—	2	8	no	—
425	Q₈	—	2	4	no	—
426	Q₈	C₂³×Dic₄₇	1	8	yes	—
427	D₄	—	2	16	no	—
428	D₄	—	2	16	no	—
429	D₄	—	2	8	no	—
430	D₄	—	2	4	no	—
431	D₄	C₂³×Dic₄₇	1	8	yes	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	16	no	—
435	C₂×C₄	—	2	16	no	—
436	C₂×C₄	—	47	2	no	—
437	C₂×C₄	—	47	4	no	—
438	C₂×C₄	—	47	2	no	—
439	C₂×C₄	—	94	4	no	—
440	C₂×C₄	—	94	8	no	—
441	C₂×C₄	—	94	8	no	—
442	C₂×C₄	—	188	16	no	—
443	C₂×C₄	—	188	2	no	—
444	C₂×C₄	—	188	4	no	—
445	C₂×C₄	—	188	16	no	—
446	C₂×C₄	—	188	8	no	—
447	C₂×C₄	D₄×Dic₄₇	1	8	yes	—
448	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
449	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
450	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
451	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
452	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625352	1	2	yes	—
454	C₂×C₄	C₂×#10625352	1	4	yes	—
455	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
456	C₈	—	94	4	no	—
457	C₈	C₂³×Dic₄₇	1	8	yes	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	8	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	16	no	—
463	C₂²	—	4	8	no	—
464	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
465	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
466	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
467	C₄	—	2	8	no	—
468	C₄	—	47	4	no	—
469	C₄	—	94	4	no	—
470	C₄	—	94	2	no	—
471	C₄	—	188	8	no	—
472	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
473	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
474	C₄	C₂⁴×Dic₄₇	1	1	yes	characteristic
475	C₄	C₂²×#10625352	1	1	yes	characteristic
476	C₂	—	2	4	no	—
477	C₂	—	2	2	no	—
478	C₂	—	4	8	no	—
479	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
480	C₂	#575×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₂×C₄₇×#575	C₂
socle	C₂²×C₄₇	C₂³×D₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#575	D₄₇
hypocenter	C₄₇	C₄×#575
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#575

Complements

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

N	H ≅ G/N	type
1. C₂×#41×Dic₄₇	C₂	semidirect
2. #137×Dic₄₇	C₂	semidirect
3. AGL(1,ℤ/8)×Dic₄₇	C₂	semidirect
4. #20252189	C₂	semidirect
5. #135×Dic₄₇	C₂	semidirect
6. #20251978	C₂	semidirect
7. #20251907	C₂	semidirect
8. C₂×M₁₆×Dic₄₇	C₂	semidirect
15. #41×Dic₄₇	C₂²	semidirect
16. #41×Dic₄₇	C₂²	semidirect
17. C₂×Q₈×Dic₄₇	C₂²	semidirect
19. C₂×D₄×Dic₄₇	C₂²	semidirect
24. #15689235	C₂²	semidirect
25. #15689230	C₂²	semidirect
26. #15689224	C₂²	semidirect
27. Q₁₆×Dic₄₇	C₂²	semidirect
28. SD₁₆×Dic₄₇	C₂²	semidirect
29. D₈×Dic₄₇	C₂²	semidirect
30. #15689165	C₂²	semidirect
31. #15689161	C₂²	semidirect
32. #15689132	C₂²	semidirect
33. #15689128	C₂²	semidirect
35. #15689119	C₂²	semidirect
36. M₁₆×Dic₄₇	C₂²	semidirect
37. C₂×#13093934	C₂²	semidirect
38. C₂×C₈×Dic₄₇	C₂²	semidirect
40. C₄₇×#575	C₄	semidirect
93. C₂×#41×C₄₇	C₂×C₄	semidirect
101. #137×C₄₇	C₂×C₄	semidirect
102. AGL(1,ℤ/8)×C₄₇	C₂×C₄	semidirect
103. #135×C₄₇	C₂×C₄	semidirect
107. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
117. #41×C₄₇	C₂²×C₄	semidirect
120. C₂×Q₈×C₄₇	C₂²×C₄	semidirect
127. C₂×D₄×C₄₇	C₂²×C₄	semidirect
148. Q₁₆×C₄₇	C₂²×C₄	semidirect
149. SD₁₆×C₄₇	C₂²×C₄	semidirect
150. D₈×C₄₇	C₂²×C₄	semidirect
151. M₁₆×C₄₇	C₂²×C₄	semidirect
152. C₂×C₈×C₄₇	C₂²×C₄	semidirect
235. Dic₄₇	#575	direct (N × H)
251. #575	Dic₄₇	direct (N × H)
285. C₄₇	C₄×#575	semidirect
289. C₂×#41	C₂×Dic₄₇	semidirect
299. #137	C₂×Dic₄₇	semidirect
300. AGL(1,ℤ/8)	C₂×Dic₄₇	semidirect
301. #135	C₂×Dic₄₇	semidirect
307. C₂×M₁₆	C₂×Dic₄₇	semidirect
358. #41	C₂²×Dic₄₇	semidirect
361. C₂×Q₈	C₂²×Dic₄₇	semidirect
368. C₂×D₄	C₂²×Dic₄₇	semidirect
389. Q₁₆	C₂²×Dic₄₇	semidirect
390. SD₁₆	C₂²×Dic₄₇	semidirect
391. D₈	C₂²×Dic₄₇	semidirect
393. M₁₆	C₂²×Dic₄₇	semidirect
396. C₂×C₈	C₂²×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×Dic₄₇	2
#137×Dic₄₇	2
AGL(1,ℤ/8)×Dic₄₇	2
#20252189	2
#135×Dic₄₇	2
#20251978	2
#20251907	2
C₂×M₁₆×Dic₄₇	2
C₂×C₄₇×#575	2
C₄×#575	47

Subgroups — #575×Dic47 #27080365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #575×Dic₄₇ #27080365