Subgroups — C₄₇×#29987 #26069685

Order 12032.

718 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2094	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#2093	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#2059	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2025	C₂	1	2	yes	maximal
9	C₄₇×#1949	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1804	C₂	1	2	yes	maximal
12	C₂×#125×C₄₇	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₇	—	2	1	no	—
15	C₂×#107×C₄₇	C₂²	1	2	yes	—
16	C₂×#106×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₂×#102×C₄₇	C₂²	1	2	yes	—
19	C₂×#102×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#390	C₂²	1	1	yes	characteristic
21	C₄₇×#390	C₂²	1	1	yes	characteristic
22	C₄₇×#389	—	2	1	no	—
23	C₄₇×#389	—	2	1	no	—
24	C₄₇×#389	—	2	1	no	—
25	C₄₇×#389	—	2	1	no	—
26	C₄₇×#389	C₂²	1	1	yes	characteristic
27	C₄₇×#389	C₂²	1	1	yes	characteristic
28	C₄₇×#388	—	2	1	no	—
29	C₄₇×#388	—	2	1	no	—
30	C₄₇×#384	C₂²	1	1	yes	characteristic
31	C₄₇×#384	C₂²	1	1	yes	characteristic
32	C₄₇×#382	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
35	C₄³×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#340	C₂²	1	2	yes	—
37	C₄₇×#340	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₄₇×#336	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	—	2	1	no	—
45	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
47	#125×C₄₇	—	4	2	no	—
48	#125×C₄₇	—	4	2	no	—
49	C₄×D₄×C₄₇	—	2	2	no	—
50	C₄×D₄×C₄₇	Q₈	1	4	yes	—
51	#117×C₄₇	—	4	4	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄²×C₄₇	—	2	1	no	—
71	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	#107×C₄₇	—	4	2	no	—
79	#106×C₄₇	—	4	2	no	—
80	C₄⋊C₈×C₄₇	—	2	4	no	—
81	#102×C₄₇	—	4	2	no	—
82	#102×C₄₇	—	4	2	no	—
83	#95×C₄₇	—	2	1	no	—
84	#95×C₄₇	—	2	1	no	—
85	#95×C₄₇	—	2	1	no	—
86	#95×C₄₇	—	2	2	no	—
87	#95×C₄₇	—	2	2	no	—
88	C₂⁴×C₄₇	—	2	1	no	—
89	C₂×D₄×C₄₇	—	2	1	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	—	4	2	no	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	1	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	4	2	no	—
122	C₄⋊C₄×C₄₇	—	4	2	no	—
123	C₄⋊C₄×C₄₇	—	4	2	no	—
124	C₄⋊C₄×C₄₇	—	4	4	no	—
125	C₄⋊C₄×C₄₇	—	4	4	no	—
126	C₄⋊C₄×C₄₇	—	4	2	no	—
127	C₄⋊C₄×C₄₇	—	4	2	no	—
128	C₄⋊C₄×C₄₇	—	4	2	no	—
129	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
130	C₂²⋊C₄×C₄₇	—	2	4	no	—
131	C₂²⋊C₄×C₄₇	—	4	2	no	—
132	C₂²⋊C₄×C₄₇	—	4	2	no	—
133	C₂²⋊C₄×C₄₇	—	4	2	no	—
134	C₂²⋊C₄×C₄₇	—	4	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	2	2	no	—
138	C₄²×C₄₇	—	2	2	no	—
139	C₄²×C₄₇	—	4	1	no	—
140	C₄²×C₄₇	—	4	1	no	—
141	C₄²×C₄₇	—	4	2	no	—
142	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
143	C₄²×C₄₇	#41	1	2	yes	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	4	1	no	—
146	C₂³×C₄₇	—	4	1	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	1	no	—
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
185	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₄₇	#135	1	2	yes	—
187	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
188	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
191	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
192	C₈×C₄₇	—	4	2	no	—
193	C₈×C₄₇	—	4	2	no	—
194	#29987	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	—	8	1	no	—
199	C₂²×C₄₇	—	8	1	no	—
200	C₂²×C₄₇	—	8	1	no	—
201	C₂²×C₄₇	—	8	1	no	—
202	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
203	C₂²×C₄₇	#535	1	1	yes	characteristic
204	C₂²×C₄₇	#536	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂²×C₄₇	#575	1	1	yes	characteristic
208	C₂²×C₄₇	#575	1	1	yes	characteristic
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	4	2	no	—
214	C₄×C₄₇	—	4	1	no	—
215	C₄×C₄₇	—	4	1	no	—
216	C₄×C₄₇	—	8	2	no	—
217	C₄×C₄₇	—	8	1	no	—
218	C₄×C₄₇	—	8	2	no	—
219	C₄×C₄₇	—	8	1	no	—
220	C₄×C₄₇	#542	1	2	yes	—
221	C₄×C₄₇	#544	1	2	yes	—
222	#2859	C₂×C₄₇	1	1	yes	characteristic, complemented
223	#2293	C₂×C₄₇	1	1	yes	characteristic
224	#2100	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#2099	C₂×C₄₇	1	1	yes	characteristic, complemented
226	#2094	C₂×C₄₇	1	1	yes	characteristic
227	#2093	C₂×C₄₇	1	1	yes	characteristic
228	#2059	C₂×C₄₇	1	2	yes	complemented
229	#2025	C₂×C₄₇	1	2	yes	—
230	#1949	C₂×C₄₇	1	2	yes	complemented
231	#1831	C₂×C₄₇	1	1	yes	characteristic, complemented
232	#1804	C₂×C₄₇	1	2	yes	—
233	C₂×C₄₇	—	8	2	no	—
234	C₂×C₄₇	#2628	1	1	yes	characteristic
235	C₂×C₄₇	#3076	1	1	yes	characteristic
236	C₂×C₄₇	#3077	1	1	yes	characteristic
237	C₂×C₄₇	#3207	1	1	yes	characteristic
238	C₂×C₄₇	#3219	1	1	yes	characteristic
239	C₂×C₄₇	#3232	1	1	yes	characteristic
240	C₂×C₄₇	#3234	1	1	yes	characteristic
241	C₂×#125	C₂²×C₄₇	1	2	yes	—
242	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
243	C₂×#117	—	2	1	no	—
244	C₂×#107	C₂²×C₄₇	1	2	yes	—
245	C₂×#106	C₂²×C₄₇	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
247	C₂×#102	C₂²×C₄₇	1	2	yes	—
248	C₂×#102	C₂²×C₄₇	1	2	yes	—
249	#390	C₂²×C₄₇	1	1	yes	characteristic
250	#390	C₂²×C₄₇	1	1	yes	characteristic
251	#389	—	2	1	no	—
252	#389	—	2	1	no	—
253	#389	—	2	1	no	—
254	#389	—	2	1	no	—
255	#389	C₂²×C₄₇	1	1	yes	characteristic
256	#389	C₂²×C₄₇	1	1	yes	characteristic
257	#388	—	2	1	no	—
258	#388	—	2	1	no	—
259	#384	C₂²×C₄₇	1	1	yes	characteristic
260	#384	C₂²×C₄₇	1	1	yes	characteristic
261	#382	C₂²×C₄₇	1	2	yes	—
262	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	—	2	1	no	—
264	C₄³	C₂²×C₄₇	1	1	yes	characteristic
265	#340	C₂²×C₄₇	1	2	yes	—
266	#340	C₂²×C₄₇	1	2	yes	—
267	#340	C₂²×C₄₇	1	2	yes	—
268	#340	C₂²×C₄₇	1	2	yes	—
269	#336	C₂²×C₄₇	1	2	yes	—
270	#336	C₂²×C₄₇	1	1	yes	characteristic
271	#336	C₂²×C₄₇	1	1	yes	characteristic
272	C₄₇	#29987	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
276	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
277	#125	—	4	2	no	—
278	#125	—	4	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	Q₈×C₄₇	1	4	yes	—
281	#117	—	4	4	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
302	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
303	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
304	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
308	#107	—	4	2	no	—
309	#106	—	4	2	no	—
310	C₄⋊C₈	—	2	4	no	—
311	#102	—	4	2	no	—
312	#102	—	4	2	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	C₂⁴	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	C₂×Q₈×C₄₇	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₂×Q₈×C₄₇	1	2	yes	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	4	2	no	—
372	C₄²	C₂×Q₈×C₄₇	1	2	yes	—
373	C₄²	#41×C₄₇	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
382	D₄	—	2	4	no	—
383	D₄	—	4	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
415	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
416	C₂×C₄	#135×C₄₇	1	2	yes	—
417	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
418	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
420	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
421	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
432	C₂²	C₄₇×#535	1	1	yes	characteristic
433	C₂²	C₄₇×#536	1	1	yes	characteristic
434	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
435	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
436	C₂²	C₄₇×#575	1	1	yes	characteristic
437	C₂²	C₄₇×#575	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	1	no	—
449	C₄	C₄₇×#542	1	2	yes	—
450	C₄	C₄₇×#544	1	2	yes	—
451	C₂	—	8	2	no	—
452	C₂	C₄₇×#2628	1	1	yes	characteristic
453	C₂	C₄₇×#3076	1	1	yes	characteristic
454	C₂	C₄₇×#3077	1	1	yes	characteristic
455	C₂	C₄₇×#3207	1	1	yes	characteristic
456	C₂	C₄₇×#3219	1	1	yes	characteristic
457	C₂	C₄₇×#3232	1	1	yes	characteristic
458	C₂	C₄₇×#3234	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×D₄×C₄₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₄³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#2859	C₂	semidirect
3. C₄₇×#2100	C₂	semidirect
4. C₄₇×#2099	C₂	semidirect
7. C₄₇×#2059	C₂	semidirect
9. C₄₇×#1949	C₂	semidirect
10. C₄₇×#1831	C₂	semidirect
194. #29987	C₄₇	direct (N × H)
222. #2859	C₂×C₄₇	semidirect
224. #2100	C₂×C₄₇	semidirect
225. #2099	C₂×C₄₇	semidirect
228. #2059	C₂×C₄₇	semidirect
230. #1949	C₂×C₄₇	semidirect
231. #1831	C₂×C₄₇	semidirect
272. C₄₇	#29987	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#2859	2
C₄₇×#2293	2
C₄₇×#2100	2
C₄₇×#2099	2
C₄₇×#2094	2
C₄₇×#2093	2
C₄₇×#2059	2
C₄₇×#2025	2
C₄₇×#1949	2
C₄₇×#1831	2
C₄₇×#1804	2
#29987	47

Subgroups — C47×#29987 #26069685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29987 #26069685