Subgroups — C₄₇×#25057 #26064755

Order 12032.

722 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2538	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2092	C₂	1	2	yes	maximal
4	C₄₇×#2085	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1925	C₂	1	2	yes	maximal
8	C₄₇×#1921	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×#102×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
13	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#107×C₄₇	C₂²	1	2	yes	—
16	C₂×#107×C₄₇	C₂²	1	2	yes	—
17	C₂×#106×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#102×C₄₇	C₂²	1	2	yes	—
21	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#396	—	2	2	no	—
24	C₄₇×#391	—	2	1	no	—
25	C₄₇×#390	C₂²	1	2	yes	—
26	C₄₇×#389	C₂²	1	2	yes	—
27	C₄₇×#387	—	2	2	no	—
28	C₄₇×#384	C₂²	1	1	yes	characteristic
29	C₄₇×#384	C₂²	1	1	yes	characteristic
30	C₄₇×#382	C₂²	1	2	yes	—
31	C₄₇×#380	—	2	1	no	—
32	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
33	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₄₇×#340	C₂²	1	1	yes	characteristic
36	C₄₇×#340	C₂²	1	1	yes	characteristic
37	C₄₇×#340	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₄₇×#336	C₂²	1	2	yes	—
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	—	2	1	no	—
44	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
47	C₂²⋊Q₈×C₄₇	—	4	4	no	—
48	C₄×Q₈×C₄₇	—	2	2	no	—
49	C₄×Q₈×C₄₇	—	2	2	no	—
50	C₄×D₄×C₄₇	—	2	2	no	—
51	C₄×D₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	—	2	1	no	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	#107×C₄₇	—	2	4	no	—
72	#107×C₄₇	—	4	2	no	—
73	#106×C₄₇	—	4	2	no	—
74	C₄⋊C₈×C₄₇	—	2	2	no	—
75	#102×C₄₇	—	2	2	no	—
76	#102×C₄₇	—	4	2	no	—
77	#102×C₄₇	Q₈	1	4	yes	complemented
78	C₄×C₈×C₄₇	—	2	2	no	—
79	#95×C₄₇	—	2	2	no	—
80	#95×C₄₇	—	2	1	no	—
81	#95×C₄₇	—	2	2	no	—
82	#95×C₄₇	—	2	2	no	—
83	#95×C₄₇	—	2	2	no	—
84	C₂⁴×C₄₇	—	2	1	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	1	no	—
89	C₂×D₄×C₄₇	—	2	1	no	—
90	C₂×D₄×C₄₇	—	2	1	no	—
91	C₂×D₄×C₄₇	—	2	1	no	—
92	C₂×D₄×C₄₇	—	2	1	no	—
93	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	—	4	2	no	—
101	C₂²×C₄×C₄₇	—	4	2	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₄₇	#41	1	2	yes	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	1	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	4	4	no	—
128	C₄⋊C₄×C₄₇	—	4	2	no	—
129	C₄⋊C₄×C₄₇	—	4	2	no	—
130	C₄⋊C₄×C₄₇	—	8	1	no	—
131	C₄⋊C₄×C₄₇	—	8	1	no	—
132	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
133	C₂²⋊C₄×C₄₇	—	4	4	no	—
134	C₂²⋊C₄×C₄₇	—	4	2	no	—
135	C₂²⋊C₄×C₄₇	—	8	2	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	2	2	no	—
138	C₄²×C₄₇	—	4	2	no	—
139	C₄²×C₄₇	—	8	2	no	—
140	C₄²×C₄₇	#41	1	2	yes	—
141	C₄²×C₄₇	#41	1	2	yes	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	4	1	no	—
144	C₂³×C₄₇	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₇	—	4	4	no	—
151	D₄×C₄₇	—	2	2	no	—
152	D₄×C₄₇	—	2	2	no	—
153	D₄×C₄₇	—	4	1	no	—
154	D₄×C₄₇	—	4	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	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	1	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	8	4	no	—
179	C₂×C₄×C₄₇	#123	1	2	yes	—
180	C₂×C₄×C₄₇	#123	1	2	yes	—
181	C₂×C₄×C₄₇	#135	1	2	yes	—
182	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	2	2	no	—
191	C₈×C₄₇	—	4	2	no	—
192	#25057	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₄₇	—	4	2	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	8	1	no	—
197	C₂²×C₄₇	—	8	1	no	—
198	C₂²×C₄₇	—	8	1	no	—
199	C₂²×C₄₇	—	8	1	no	—
200	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
201	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
202	C₂²×C₄₇	#550	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₂²×C₄₇	#576	1	1	yes	characteristic
206	C₂²×C₄₇	#578	1	1	yes	characteristic
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	4	2	no	—
209	C₄×C₄₇	—	4	2	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	—	8	1	no	—
212	C₄×C₄₇	—	8	1	no	—
213	C₄×C₄₇	—	8	2	no	—
214	C₄×C₄₇	—	8	2	no	—
215	C₄×C₄₇	#482	1	4	yes	—
216	C₄×C₄₇	#533	1	1	yes	characteristic
217	C₄×C₄₇	#542	1	1	yes	characteristic
218	C₄×C₄₇	#552	1	1	yes	characteristic
219	C₄×C₄₇	#554	1	1	yes	characteristic
220	#2538	C₂×C₄₇	1	1	yes	characteristic
221	#2355	C₂×C₄₇	1	1	yes	characteristic, complemented
222	#2092	C₂×C₄₇	1	2	yes	—
223	#2085	C₂×C₄₇	1	2	yes	complemented
224	#1984	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#1948	C₂×C₄₇	1	1	yes	characteristic, complemented
226	#1925	C₂×C₄₇	1	2	yes	—
227	#1921	C₂×C₄₇	1	2	yes	complemented
228	#1845	C₂×C₄₇	1	1	yes	characteristic, complemented
229	#1802	C₂×C₄₇	1	1	yes	characteristic
230	C₄×#102	C₂×C₄₇	1	1	yes	characteristic
231	C₂×C₄₇	—	8	2	no	—
232	C₂×C₄₇	#2423	1	1	yes	characteristic
233	C₂×C₄₇	C₂×#482	1	1	yes	characteristic
234	C₂×C₄₇	#3098	1	1	yes	characteristic
235	C₂×C₄₇	#3380	1	1	yes	characteristic
236	C₂×C₄₇	#3386	1	1	yes	characteristic
237	C₂×C₄₇	#3393	1	1	yes	characteristic
238	C₂×C₄₇	#3399	1	1	yes	characteristic
239	C₂×C₂²⋊Q₈	—	2	1	no	—
240	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
242	C₂×#107	C₂²×C₄₇	1	2	yes	—
243	C₂×#107	C₂²×C₄₇	1	2	yes	—
244	C₂×#106	C₂²×C₄₇	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
246	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
247	C₂×#102	C₂²×C₄₇	1	2	yes	—
248	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
250	#396	—	2	2	no	—
251	#391	—	2	1	no	—
252	#390	C₂²×C₄₇	1	2	yes	—
253	#389	C₂²×C₄₇	1	2	yes	—
254	#387	—	2	2	no	—
255	#384	C₂²×C₄₇	1	1	yes	characteristic
256	#384	C₂²×C₄₇	1	1	yes	characteristic
257	#382	C₂²×C₄₇	1	2	yes	—
258	#380	—	2	1	no	—
259	C₄×C₄⋊C₄	—	2	1	no	—
260	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
261	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
262	#340	C₂²×C₄₇	1	2	yes	—
263	#340	C₂²×C₄₇	1	1	yes	characteristic
264	#340	C₂²×C₄₇	1	1	yes	characteristic
265	#340	C₂²×C₄₇	1	2	yes	—
266	#336	C₂²×C₄₇	1	2	yes	—
267	#336	C₂²×C₄₇	1	2	yes	—
268	C₄₇	#25057	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
273	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
275	C₂²⋊Q₈	—	4	4	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
286	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
298	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
299	#107	—	2	4	no	—
300	#107	—	4	2	no	—
301	#106	—	4	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	4	2	no	—
305	#102	Q₈×C₄₇	1	4	yes	complemented
306	C₄×C₈	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	1	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₂⁴	—	2	1	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂×Q₈×C₄₇	1	2	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₂×Q₈×C₄₇	1	2	yes	—
343	C₂×C₈	#41×C₄₇	1	2	yes	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	8	1	no	—
359	C₄⋊C₄	—	8	1	no	—
360	C₄⋊C₄	C₂×Q₈×C₄₇	1	2	yes	—
361	C₂²⋊C₄	—	4	4	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	8	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	2	no	—
367	C₄²	—	8	2	no	—
368	C₄²	#41×C₄₇	1	2	yes	—
369	C₄²	#41×C₄₇	1	2	yes	—
370	C₂³	—	2	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
378	Q₈	—	4	4	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	8	4	no	—
407	C₂×C₄	#123×C₄₇	1	2	yes	—
408	C₂×C₄	#123×C₄₇	1	2	yes	—
409	C₂×C₄	#135×C₄₇	1	2	yes	—
410	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
411	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
415	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
416	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
428	C₂²	D₄×Q₈×C₄₇	1	1	yes	characteristic
429	C₂²	C₄₇×#550	1	1	yes	characteristic
430	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
431	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
432	C₂²	C₄₇×#576	1	1	yes	characteristic
433	C₂²	C₄₇×#578	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	C₄₇×#482	1	4	yes	—
443	C₄	C₄₇×#533	1	1	yes	characteristic
444	C₄	C₄₇×#542	1	1	yes	characteristic
445	C₄	C₄₇×#552	1	1	yes	characteristic
446	C₄	C₄₇×#554	1	1	yes	characteristic
447	C₂	—	8	2	no	—
448	C₂	C₄₇×#2423	1	1	yes	characteristic
449	C₂	C₂×C₄₇×#482	1	1	yes	characteristic
450	C₂	C₄₇×#3098	1	1	yes	characteristic
451	C₂	C₄₇×#3380	1	1	yes	characteristic
452	C₂	C₄₇×#3386	1	1	yes	characteristic
453	C₂	C₄₇×#3393	1	1	yes	characteristic
454	C₂	C₄₇×#3399	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 ◁ C₂×C₄×Q₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2355	C₂	semidirect
4. C₄₇×#2085	C₂	semidirect
5. C₄₇×#1984	C₂	semidirect
6. C₄₇×#1948	C₂	semidirect
8. C₄₇×#1921	C₂	semidirect
9. C₄₇×#1845	C₂	semidirect
77. #102×C₄₇	Q₈	semidirect
192. #25057	C₄₇	direct (N × H)
221. #2355	C₂×C₄₇	semidirect
223. #2085	C₂×C₄₇	semidirect
224. #1984	C₂×C₄₇	semidirect
225. #1948	C₂×C₄₇	semidirect
227. #1921	C₂×C₄₇	semidirect
228. #1845	C₂×C₄₇	semidirect
268. C₄₇	#25057	direct (N × H)
305. #102	Q₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#2538	2
C₄₇×#2355	2
C₄₇×#2092	2
C₄₇×#2085	2
C₄₇×#1984	2
C₄₇×#1948	2
C₄₇×#1925	2
C₄₇×#1921	2
C₄₇×#1845	2
C₄₇×#1802	2
C₄×#102×C₄₇	2
#25057	47

Subgroups — C47×#25057 #26064755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25057 #26064755