Subgroups — #575×D₄₇ #20258130

Order 6016.

1484 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₄₇	C₂	1	2	yes	maximal, complemented
2	#15689923	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689922	C₂	1	4	yes	maximal, complemented
4	#15689921	C₂	1	2	yes	maximal, complemented
5	#15689920	C₂	1	4	yes	maximal, complemented
6	#15689919	C₂	1	4	yes	maximal, complemented
7	#137×D₄₇	C₂	1	4	yes	maximal, complemented
8	AGL(1,ℤ/8)×D₄₇	C₂	1	4	yes	maximal, complemented
9	#135×D₄₇	C₂	1	4	yes	maximal, complemented
10	C₂×M₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#575	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625354	C₂²	1	2	yes	complemented
13	C₂×#10625350	—	2	2	no	—
14	C₂×#10625350	C₂²	1	2	yes	complemented
15	C₂×#10625352	—	2	2	no	—
16	C₂×#10625352	C₂²	1	2	yes	complemented
17	#41×D₄₇	—	2	2	no	—
18	#41×D₄₇	—	2	2	no	—
19	#41×D₄₇	—	2	2	no	—
20	#41×D₄₇	—	2	2	no	—
21	#41×D₄₇	C₂²	1	4	yes	—
22	#41×D₄₇	C₂²	1	4	yes	complemented
23	#41×D₄₇	C₂²	1	4	yes	complemented
24	#41×D₄₇	C₂²	1	4	yes	complemented
25	C₂×Q₈×D₄₇	C₂²	1	2	yes	complemented
26	C₂×D₄×D₄₇	—	2	2	no	—
27	C₂×D₄×D₄₇	C₂²	1	2	yes	complemented
28	C₂²×C₄×D₄₇	—	2	2	no	—
29	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
30	#13094057	C₂²	1	4	yes	complemented
31	#13094056	C₂²	1	8	yes	complemented
32	#13094055	C₂²	1	4	yes	complemented
33	#13094054	C₂²	1	4	yes	complemented
34	#13094053	C₂²	1	8	yes	complemented
35	#13094052	C₂²	1	4	yes	complemented
36	#13094051	C₂²	1	8	yes	complemented
37	#13094050	C₂²	1	4	yes	complemented
38	#13094049	C₂²	1	4	yes	complemented
39	#13094048	C₂²	1	8	yes	complemented
40	#13094047	C₂²	1	4	yes	complemented
41	#13094046	C₂²	1	4	yes	complemented
42	#13094045	C₂²	1	8	yes	complemented
43	#13094044	C₂²	1	8	yes	complemented
44	#13094043	C₂²	1	4	yes	complemented
45	Q₁₆×D₄₇	C₂²	1	4	yes	complemented
46	SD₁₆×D₄₇	C₂²	1	8	yes	complemented
47	D₈×D₄₇	C₂²	1	4	yes	complemented
48	C₂×#10625329	C₂²	1	1	yes	characteristic, complemented
49	C₂×#10625324	C₂²	1	2	yes	complemented
50	M₁₆×D₄₇	C₂²	1	4	yes	complemented
51	M₁₆×D₄₇	C₂²	1	4	yes	complemented
52	C₂×C₈×D₄₇	C₂²	1	2	yes	complemented
53	C₂×#41×C₄₇	C₂²	1	2	yes	complemented
54	#137×C₄₇	C₂²	1	4	yes	complemented
55	AGL(1,ℤ/8)×C₄₇	C₂²	1	4	yes	complemented
56	#135×C₄₇	C₂²	1	4	yes	complemented
57	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
58	C₂³×D₄₇	—	2	2	no	—
59	C₂³×D₄₇	D₄	1	1	yes	characteristic
60	#41×C₄₇	—	2	2	no	—
61	#41×C₄₇	—	2	2	no	—
62	#41×C₄₇	C₂³	1	4	yes	—
63	#41×C₄₇	C₂³	1	4	yes	complemented
64	C₂×Q₈×C₄₇	C₂³	1	2	yes	complemented
65	C₂×D₄×C₄₇	—	2	2	no	—
66	C₂×D₄×C₄₇	C₂³	1	2	yes	complemented
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₄₇	—	2	2	no	—
70	C₂×C₂²⋊D₄₇	—	2	2	no	—
71	C₂×C₂²⋊D₄₇	—	2	2	no	—
72	C₂²×Dic₄₇	—	2	2	no	—
73	C₂²×Dic₄₇	D₄	1	1	yes	characteristic
74	#10625354	—	2	2	no	—
75	#10625354	—	2	2	no	—
76	#10625354	C₂³	1	4	yes	—
77	#10625354	C₂³	1	4	yes	complemented
78	Q₈×D₄₇	—	2	2	no	—
79	Q₈×D₄₇	—	2	2	no	—
80	Q₈×D₄₇	C₂³	1	4	yes	—
81	Q₈×D₄₇	C₂³	1	4	yes	complemented
82	#10625352	—	2	4	no	—
83	#10625352	—	2	4	no	—
84	#10625352	—	2	4	no	—
85	#10625352	—	2	4	no	—
86	#10625352	—	2	2	no	—
87	#10625352	—	2	2	no	—
88	#10625352	C₂³	1	4	yes	—
89	#10625352	C₂³	1	4	yes	complemented
90	D₄×D₄₇	—	2	4	no	—
91	D₄×D₄₇	—	2	4	no	—
92	D₄×D₄₇	—	2	4	no	—
93	D₄×D₄₇	—	2	4	no	—
94	D₄×D₄₇	—	2	2	no	—
95	D₄×D₄₇	—	2	2	no	—
96	D₄×D₄₇	C₂³	1	4	yes	—
97	D₄×D₄₇	C₂³	1	4	yes	complemented
98	#10625350	—	2	2	no	—
99	#10625350	—	2	2	no	—
100	#10625350	—	2	4	no	—
101	#10625350	—	2	4	no	—
102	#10625350	—	2	4	no	—
103	#10625350	—	2	4	no	—
104	#10625350	C₂³	1	4	yes	—
105	#10625350	C₂³	1	4	yes	complemented
106	C₂×D₁₈₈	—	2	2	no	—
107	C₂×D₁₈₈	C₂³	1	2	yes	complemented
108	C₂×C₄×D₄₇	—	2	2	no	—
109	C₂×C₄×D₄₇	—	2	2	no	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×C₄×D₄₇	—	2	4	no	—
112	C₂×C₄×D₄₇	—	2	4	no	—
113	C₂×C₄×D₄₇	—	2	4	no	—
114	C₂×C₄×D₄₇	—	2	4	no	—
115	C₂×C₄×D₄₇	D₄	1	2	yes	—
116	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
117	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
118	C₂×C₄×D₄₇	D₄	1	2	yes	—
119	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
120	C₂×C₄×D₄₇	C₂³	1	2	yes	—
121	C₂×C₄×D₄₇	C₂³	1	2	yes	—
122	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
123	C₂×Dic₉₄	—	2	2	no	—
124	C₂×Dic₉₄	C₂³	1	2	yes	complemented
125	Q₁₆×C₄₇	C₂³	1	4	yes	complemented
126	SD₁₆×C₄₇	C₂³	1	8	yes	complemented
127	D₈×C₄₇	C₂³	1	4	yes	complemented
128	M₁₆×C₄₇	C₂³	1	4	yes	complemented
129	C₂×C₈×C₄₇	C₂³	1	2	yes	complemented
130	#10625337	C₂³	1	8	yes	complemented
131	#10625336	C₂³	1	8	yes	complemented
132	#10625335	C₂³	1	8	yes	complemented
133	#10625334	C₂³	1	8	yes	complemented
134	#10625329	C₂³	1	4	yes	complemented
135	C₂×C₄₇⋊C₈	C₂³	1	2	yes	complemented
136	Dic₁₈₈	C₂³	1	4	yes	complemented
137	D₃₇₆	C₂³	1	4	yes	complemented
138	#10625325	C₂³	1	8	yes	complemented
139	#10625324	C₂³	1	8	yes	complemented
140	C₈×D₄₇	C₂³	1	4	yes	—
141	C₈×D₄₇	C₂³	1	4	yes	complemented
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×D₄₇	—	2	2	no	—
145	C₂²×D₄₇	—	2	4	no	—
146	C₂²×D₄₇	—	2	4	no	—
147	C₂²×D₄₇	—	4	2	no	—
148	C₂²×D₄₇	—	4	8	no	—
149	C₂²×D₄₇	C₂×D₄	1	2	yes	—
150	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×D₄₇	C₂×D₄	1	2	yes	—
152	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
153	Q₈×C₄₇	—	2	2	no	—
154	Q₈×C₄₇	C₂⁴	1	4	yes	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	2	4	no	—
157	D₄×C₄₇	—	2	2	no	—
158	D₄×C₄₇	C₂⁴	1	4	yes	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
166	C₂²⋊D₄₇	—	2	4	no	—
167	C₂²⋊D₄₇	—	2	4	no	—
168	C₂²⋊D₄₇	—	2	4	no	—
169	C₂²⋊D₄₇	—	2	4	no	—
170	C₂²⋊D₄₇	—	2	4	no	—
171	C₂²⋊D₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	2	4	no	—
175	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
176	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
177	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
178	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
179	D₁₈₈	—	2	4	no	—
180	D₁₈₈	—	2	4	no	—
181	D₁₈₈	—	2	2	no	—
182	D₁₈₈	C₂⁴	1	4	yes	—
183	C₄×D₄₇	—	2	4	no	—
184	C₄×D₄₇	—	2	4	no	—
185	C₄×D₄₇	—	2	4	no	—
186	C₄×D₄₇	—	2	4	no	—
187	C₄×D₄₇	—	2	4	no	—
188	C₄×D₄₇	—	2	4	no	—
189	C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
190	C₄×D₄₇	C₂×D₄	1	2	yes	—
191	C₄×D₄₇	C₂×D₄	1	2	yes	—
192	C₄×D₄₇	C₂×D₄	1	2	yes	—
193	C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
194	C₄×D₄₇	C₂×D₄	1	2	yes	—
195	C₄×D₄₇	C₂×D₄	1	2	yes	—
196	C₄×D₄₇	C₂⁴	1	1	yes	characteristic
197	C₄×D₄₇	C₂⁴	1	1	yes	characteristic
198	C₄×D₄₇	C₂⁴	1	2	yes	—
199	Dic₉₄	—	2	2	no	—
200	Dic₉₄	—	2	4	no	—
201	Dic₉₄	—	2	4	no	—
202	Dic₉₄	C₂⁴	1	4	yes	—
203	C₈×C₄₇	C₂⁴	1	4	yes	—
204	C₄₇⋊C₈	C₂⁴	1	4	yes	—
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	4	1	no	—
207	C₂²×C₄₇	—	4	4	no	—
208	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
209	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×D₄₇	—	2	4	no	—
211	C₂×D₄₇	—	2	2	no	—
212	C₂×D₄₇	—	2	4	no	—
213	C₂×D₄₇	—	4	1	no	—
214	C₂×D₄₇	—	4	2	no	—
215	C₂×D₄₇	—	4	8	no	—
216	C₂×D₄₇	—	4	4	no	—
217	C₂×D₄₇	—	4	8	no	—
218	C₂×D₄₇	C₂²×D₄	1	2	yes	—
219	C₂×D₄₇	C₂²×D₄	1	1	yes	characteristic
220	C₂×D₄₇	C₂²×D₄	1	1	yes	characteristic
221	C₄×C₄₇	—	2	4	no	—
222	C₄×C₄₇	C₂²×D₄	1	2	yes	—
223	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
224	C₄×C₄₇	C₂⁵	1	1	yes	characteristic
225	Dic₄₇	—	2	4	no	—
226	Dic₄₇	C₂²×D₄	1	1	yes	characteristic
227	Dic₄₇	C₂²×D₄	1	2	yes	—
228	Dic₄₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×#575	—	47	1	no	maximal, Sylow
230	C₂×C₄₇	—	2	2	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	4	4	no	—
233	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
234	D₄₇	—	2	2	no	—
235	D₄₇	—	2	1	no	—
236	D₄₇	—	4	4	no	—
237	D₄₇	#575	1	2	yes	direct product factor
238	C₂²×#41	—	47	2	no	—
239	#575	—	47	2	no	—
240	#575	—	47	4	no	—
241	#575	—	47	4	no	—
242	#575	—	47	4	no	—
243	#575	—	47	1	no	—
244	#575	D₄₇	1	1	yes	characteristic, direct product factor
245	C₂×#137	—	47	4	no	—
246	C₂×AGL(1,ℤ/8)	—	47	4	no	—
247	C₂×#135	—	47	4	no	—
248	C₂²×M₁₆	—	47	1	no	—
249	C₄₇	C₂×#575	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	47	4	no	—
251	C₂×#41	—	47	4	no	—
252	C₂×#41	—	47	4	no	—
253	C₂×#41	—	47	4	no	—
254	C₂×#41	—	47	2	no	—
255	C₂×#41	—	47	2	no	—
256	C₂×#41	—	47	2	no	—
257	C₂×#41	—	94	2	no	—
258	C₂×#41	—	94	2	no	—
259	C₂×#41	—	94	2	no	—
260	C₂×#41	—	94	2	no	—
261	C₂×#41	—	94	2	no	—
262	C₂×#41	—	94	2	no	—
263	C₂×#41	C₂×D₄₇	1	2	yes	complemented
264	C₂²×Q₈	—	47	2	no	—
265	C₂²×D₄	—	47	2	no	—
266	C₂²×D₄	—	94	2	no	—
267	C₂³×C₄	—	47	1	no	—
268	C₂³×C₄	—	94	2	no	—
269	#137	—	47	4	no	—
270	#137	—	47	4	no	—
271	#137	—	47	8	no	—
272	#137	—	47	8	no	—
273	#137	—	47	4	no	—
274	#137	C₂×D₄₇	1	4	yes	complemented
275	AGL(1,ℤ/8)	—	47	4	no	—
276	AGL(1,ℤ/8)	—	47	4	no	—
277	AGL(1,ℤ/8)	—	47	8	no	—
278	AGL(1,ℤ/8)	—	47	8	no	—
279	AGL(1,ℤ/8)	—	47	4	no	—
280	AGL(1,ℤ/8)	C₂×D₄₇	1	4	yes	complemented
281	#135	—	47	8	no	—
282	#135	—	47	4	no	—
283	#135	—	47	8	no	—
284	#135	—	47	4	no	—
285	#135	—	47	4	no	—
286	#135	C₂×D₄₇	1	4	yes	complemented
287	C₂×Q₁₆	—	47	4	no	—
288	C₂×SD₁₆	—	47	8	no	—
289	C₂×D₈	—	47	4	no	—
290	C₂×M₁₆	—	47	1	no	—
291	C₂×M₁₆	—	47	4	no	—
292	C₂×M₁₆	—	47	4	no	—
293	C₂×M₁₆	—	47	2	no	—
294	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
295	C₂²×C₈	—	47	2	no	—
296	C₂⁴	—	47	1	no	—
297	C₂⁴	—	94	2	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	—	47	4	no	—
301	#41	—	47	4	no	—
302	#41	—	47	4	no	—
303	#41	—	47	4	no	—
304	#41	—	47	4	no	—
305	#41	—	47	4	no	—
306	#41	—	94	4	no	—
307	#41	—	94	4	no	—
308	#41	—	94	4	no	—
309	#41	—	94	4	no	—
310	#41	—	94	4	no	—
311	#41	—	94	4	no	—
312	#41	—	94	4	no	—
313	#41	—	94	4	no	—
314	#41	—	94	2	no	—
315	#41	—	94	2	no	—
316	#41	—	94	2	no	—
317	#41	—	94	2	no	—
318	#41	—	94	2	no	—
319	#41	—	94	2	no	—
320	#41	C₂²×D₄₇	1	4	yes	—
321	#41	C₂²×D₄₇	1	4	yes	complemented
322	C₂×Q₈	—	47	4	no	—
323	C₂×Q₈	—	47	4	no	—
324	C₂×Q₈	—	47	2	no	—
325	C₂×Q₈	—	94	2	no	—
326	C₂×Q₈	—	94	2	no	—
327	C₂×Q₈	—	94	2	no	—
328	C₂×Q₈	C₂²×D₄₇	1	2	yes	complemented
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	47	4	no	—
331	C₂×D₄	—	47	4	no	—
332	C₂×D₄	—	47	2	no	—
333	C₂×D₄	—	94	2	no	—
334	C₂×D₄	—	94	2	no	—
335	C₂×D₄	—	94	2	no	—
336	C₂×D₄	—	94	2	no	—
337	C₂×D₄	—	94	4	no	—
338	C₂×D₄	—	94	4	no	—
339	C₂×D₄	—	94	4	no	—
340	C₂×D₄	—	94	4	no	—
341	C₂×D₄	—	94	2	no	—
342	C₂×D₄	—	94	2	no	—
343	C₂×D₄	C₂²×D₄₇	1	2	yes	complemented
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	47	1	no	—
346	C₂²×C₄	—	47	2	no	—
347	C₂²×C₄	—	47	2	no	—
348	C₂²×C₄	—	47	1	no	—
349	C₂²×C₄	—	47	1	no	—
350	C₂²×C₄	—	47	1	no	—
351	C₂²×C₄	—	47	2	no	—
352	C₂²×C₄	—	47	2	no	—
353	C₂²×C₄	—	47	1	no	—
354	C₂²×C₄	—	94	2	no	—
355	C₂²×C₄	—	94	4	no	—
356	C₂²×C₄	—	94	4	no	—
357	C₂²×C₄	—	94	4	no	—
358	C₂²×C₄	—	94	4	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	94	2	no	—
361	C₂²×C₄	—	94	2	no	—
362	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
363	Q₁₆	—	47	8	no	—
364	Q₁₆	—	47	4	no	—
365	Q₁₆	C₂²×D₄₇	1	4	yes	complemented
366	SD₁₆	—	47	8	no	—
367	SD₁₆	—	47	8	no	—
368	SD₁₆	—	47	8	no	—
369	SD₁₆	C₂²×D₄₇	1	8	yes	complemented
370	D₈	—	47	8	no	—
371	D₈	—	47	4	no	—
372	D₈	C₂²×D₄₇	1	4	yes	complemented
373	M₁₆	—	47	4	no	—
374	M₁₆	—	47	8	no	—
375	M₁₆	C₂²×D₄₇	1	4	yes	complemented
376	C₂×C₈	—	47	2	no	—
377	C₂×C₈	—	47	4	no	—
378	C₂×C₈	—	47	4	no	—
379	C₂×C₈	C₂²×D₄₇	1	2	yes	complemented
380	C₂³	—	2	2	no	—
381	C₂³	—	47	2	no	—
382	C₂³	—	47	1	no	—
383	C₂³	—	47	1	no	—
384	C₂³	—	47	2	no	—
385	C₂³	—	94	4	no	—
386	C₂³	—	94	4	no	—
387	C₂³	—	94	2	no	—
388	C₂³	—	188	2	no	—
389	C₂³	—	188	8	no	—
390	C₂³	D₄×D₄₇	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	47	4	no	—
393	Q₈	—	94	4	no	—
394	Q₈	—	94	4	no	—
395	Q₈	—	94	2	no	—
396	Q₈	C₂³×D₄₇	1	4	yes	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	47	4	no	—
401	D₄	—	94	4	no	—
402	D₄	—	94	4	no	—
403	D₄	—	94	4	no	—
404	D₄	—	94	4	no	—
405	D₄	—	94	4	no	—
406	D₄	—	94	4	no	—
407	D₄	—	94	4	no	—
408	D₄	—	94	4	no	—
409	D₄	—	94	2	no	—
410	D₄	C₂³×D₄₇	1	4	yes	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	47	2	no	—
415	C₂×C₄	—	47	2	no	—
416	C₂×C₄	—	47	1	no	—
417	C₂×C₄	—	47	1	no	—
418	C₂×C₄	—	47	2	no	—
419	C₂×C₄	—	47	2	no	—
420	C₂×C₄	—	47	2	no	—
421	C₂×C₄	—	47	2	no	—
422	C₂×C₄	—	47	1	no	—
423	C₂×C₄	—	47	2	no	—
424	C₂×C₄	—	47	1	no	—
425	C₂×C₄	—	47	1	no	—
426	C₂×C₄	—	47	1	no	—
427	C₂×C₄	—	47	2	no	—
428	C₂×C₄	—	94	4	no	—
429	C₂×C₄	—	94	4	no	—
430	C₂×C₄	—	94	4	no	—
431	C₂×C₄	—	94	4	no	—
432	C₂×C₄	—	94	4	no	—
433	C₂×C₄	—	94	4	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	4	no	—
436	C₂×C₄	—	94	4	no	—
437	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
438	C₂×C₄	D₄×D₄₇	1	2	yes	—
439	C₂×C₄	C₂³×D₄₇	1	2	yes	—
440	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
441	C₈	—	47	4	no	—
442	C₈	C₂³×D₄₇	1	4	yes	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	47	1	no	—
447	C₂²	—	47	2	no	—
448	C₂²	—	47	1	no	—
449	C₂²	—	94	4	no	—
450	C₂²	—	94	2	no	—
451	C₂²	—	94	4	no	—
452	C₂²	—	188	2	no	—
453	C₂²	—	188	1	no	—
454	C₂²	—	188	4	no	—
455	C₂²	—	188	8	no	—
456	C₂²	—	188	8	no	—
457	C₂²	C₂×D₄×D₄₇	1	2	yes	—
458	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	47	1	no	—
461	C₄	—	47	2	no	—
462	C₄	—	47	1	no	—
463	C₄	—	94	4	no	—
464	C₄	C₂×D₄×D₄₇	1	2	yes	—
465	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
466	C₄	C₂⁴×D₄₇	1	1	yes	characteristic
467	C₂	—	2	2	no	—
468	C₂	—	2	1	no	—
469	C₂	—	4	4	no	—
470	C₂	—	47	2	no	—
471	C₂	—	94	2	no	—
472	C₂	—	94	1	no	—
473	C₂	—	188	4	no	—
474	C₂	C₂²×D₄×D₄₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₄₇	C₂	semidirect
2. #15689923	C₂	semidirect
3. #15689922	C₂	semidirect
4. #15689921	C₂	semidirect
5. #15689920	C₂	semidirect
6. #15689919	C₂	semidirect
7. #137×D₄₇	C₂	semidirect
8. AGL(1,ℤ/8)×D₄₇	C₂	semidirect
9. #135×D₄₇	C₂	semidirect
10. C₂×M₁₆×D₄₇	C₂	semidirect
11. C₄₇×#575	C₂	semidirect
12. C₂×#10625354	C₂²	semidirect
14. C₂×#10625350	C₂²	semidirect
16. C₂×#10625352	C₂²	semidirect
22. #41×D₄₇	C₂²	semidirect
23. #41×D₄₇	C₂²	semidirect
24. #41×D₄₇	C₂²	semidirect
25. C₂×Q₈×D₄₇	C₂²	semidirect
27. C₂×D₄×D₄₇	C₂²	semidirect
30. #13094057	C₂²	semidirect
31. #13094056	C₂²	semidirect
32. #13094055	C₂²	semidirect
33. #13094054	C₂²	semidirect
34. #13094053	C₂²	semidirect
35. #13094052	C₂²	semidirect
36. #13094051	C₂²	semidirect
37. #13094050	C₂²	semidirect
38. #13094049	C₂²	semidirect
39. #13094048	C₂²	semidirect
40. #13094047	C₂²	semidirect
41. #13094046	C₂²	semidirect
42. #13094045	C₂²	semidirect
43. #13094044	C₂²	semidirect
44. #13094043	C₂²	semidirect
45. Q₁₆×D₄₇	C₂²	semidirect
46. SD₁₆×D₄₇	C₂²	semidirect
47. D₈×D₄₇	C₂²	semidirect
48. C₂×#10625329	C₂²	semidirect
49. C₂×#10625324	C₂²	semidirect
50. M₁₆×D₄₇	C₂²	semidirect
51. M₁₆×D₄₇	C₂²	semidirect
52. C₂×C₈×D₄₇	C₂²	semidirect
53. C₂×#41×C₄₇	C₂²	semidirect
54. #137×C₄₇	C₂²	semidirect
55. AGL(1,ℤ/8)×C₄₇	C₂²	semidirect
56. #135×C₄₇	C₂²	semidirect
57. C₂×M₁₆×C₄₇	C₂²	semidirect
63. #41×C₄₇	C₂³	semidirect
64. C₂×Q₈×C₄₇	C₂³	semidirect
66. C₂×D₄×C₄₇	C₂³	semidirect
77. #10625354	C₂³	semidirect
81. Q₈×D₄₇	C₂³	semidirect
89. #10625352	C₂³	semidirect
97. D₄×D₄₇	C₂³	semidirect
105. #10625350	C₂³	semidirect
107. C₂×D₁₈₈	C₂³	semidirect
124. C₂×Dic₉₄	C₂³	semidirect
125. Q₁₆×C₄₇	C₂³	semidirect
126. SD₁₆×C₄₇	C₂³	semidirect
127. D₈×C₄₇	C₂³	semidirect
128. M₁₆×C₄₇	C₂³	semidirect
129. C₂×C₈×C₄₇	C₂³	semidirect
130. #10625337	C₂³	semidirect
131. #10625336	C₂³	semidirect
132. #10625335	C₂³	semidirect
133. #10625334	C₂³	semidirect
134. #10625329	C₂³	semidirect
135. C₂×C₄₇⋊C₈	C₂³	semidirect
136. Dic₁₈₈	C₂³	semidirect
137. D₃₇₆	C₂³	semidirect
138. #10625325	C₂³	semidirect
139. #10625324	C₂³	semidirect
141. C₈×D₄₇	C₂³	semidirect
237. D₄₇	#575	direct (N × H)
244. #575	D₄₇	direct (N × H)
249. C₄₇	C₂×#575	semidirect
263. C₂×#41	C₂×D₄₇	semidirect
274. #137	C₂×D₄₇	semidirect
280. AGL(1,ℤ/8)	C₂×D₄₇	semidirect
286. #135	C₂×D₄₇	semidirect
294. C₂×M₁₆	C₂×D₄₇	semidirect
321. #41	C₂²×D₄₇	semidirect
328. C₂×Q₈	C₂²×D₄₇	semidirect
343. C₂×D₄	C₂²×D₄₇	semidirect
365. Q₁₆	C₂²×D₄₇	semidirect
369. SD₁₆	C₂²×D₄₇	semidirect
372. D₈	C₂²×D₄₇	semidirect
375. M₁₆	C₂²×D₄₇	semidirect
379. C₂×C₈	C₂²×D₄₇	semidirect

Subgroups — #575×D47 #20258130

Conjugacy classes of subgroups

Complements

Subgroups — #575×D₄₇ #20258130