Subgroups — C₄₇×#10790 #26050488

Order 12032.

1426 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#104×C₄₇	C₂	1	2	yes	maximal
3	C₂×C₄₇×#339	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₄×#41×C₄₇	—	2	4	no	—
9	C₄×#41×C₄₇	—	2	4	no	—
10	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	complemented
11	C₂×C₄×D₄×C₄₇	—	2	2	no	—
12	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	complemented
13	C₂×#117×C₄₇	—	2	1	no	—
14	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	—	2	1	no	—
16	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#104×C₄₇	—	2	4	no	—
19	C₂×#104×C₄₇	—	2	4	no	—
20	C₂×#104×C₄₇	C₄	1	8	yes	complemented
21	C₂×#95×C₄₇	—	2	2	no	—
22	C₄₇×#339	—	2	4	no	—
23	C₄₇×#336	—	2	1	no	—
24	C₄₇×#336	—	2	1	no	—
25	C₂×#41×C₄₇	—	2	2	no	—
26	C₂×#41×C₄₇	—	2	2	no	—
27	C₂×#41×C₄₇	—	2	1	no	—
28	C₂×#41×C₄₇	—	2	1	no	—
29	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
30	C₂×#41×C₄₇	D₄	1	4	yes	—
31	C₂×#41×C₄₇	D₄	1	2	yes	—
32	C₂×#41×C₄₇	Q₈	1	2	yes	—
33	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₄₇	—	2	1	no	—
35	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	—	2	1	no	—
37	C₂³×C₄×C₄₇	—	2	2	no	—
38	C₂³×C₄×C₄₇	—	2	2	no	—
39	C₂³×C₄×C₄₇	D₄	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₄₇	—	2	2	no	—
42	C₂×M₁₆×C₄₇	—	2	2	no	—
43	C₂×M₁₆×C₄₇	—	2	2	no	—
44	C₂×M₁₆×C₄₇	—	2	2	no	—
45	C₂×M₁₆×C₄₇	—	2	2	no	—
46	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
47	C₂²×C₈×C₄₇	—	2	2	no	—
48	C₄×Q₈×C₄₇	—	2	4	no	—
49	C₄×Q₈×C₄₇	—	2	4	no	—
50	C₄×D₄×C₄₇	—	2	16	no	—
51	C₄×D₄×C₄₇	—	2	4	no	—
52	C₄×D₄×C₄₇	—	2	4	no	—
53	#117×C₄₇	—	2	8	no	—
54	#117×C₄₇	—	2	2	no	—
55	#117×C₄₇	D₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	—	2	8	no	—
61	C₂×C₄²×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂×C₄²×C₄₇	—	2	2	no	—
64	C₂×C₄²×C₄₇	—	2	1	no	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	—	2	2	no	—
70	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
74	#104×C₄₇	—	2	16	no	—
75	#95×C₄₇	—	2	8	no	—
76	C₂⁴×C₄₇	—	2	1	no	—
77	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	2	4	no	—
83	#41×C₄₇	—	2	4	no	—
84	#41×C₄₇	C₂²⋊C₄	1	8	yes	—
85	#41×C₄₇	C₄⋊C₄	1	8	yes	—
86	C₂×Q₈×C₄₇	—	2	1	no	—
87	C₂×Q₈×C₄₇	—	2	1	no	—
88	C₂×Q₈×C₄₇	—	2	1	no	—
89	C₂×Q₈×C₄₇	C₄²	1	2	yes	—
90	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	2	4	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	—	2	1	no	—
98	C₂×D₄×C₄₇	—	2	1	no	—
99	C₂×D₄×C₄₇	C₄²	1	2	yes	—
100	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
101	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	4	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	8	no	—
108	C₂²×C₄×C₄₇	—	2	8	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	—	4	4	no	—
115	C₂²×C₄×C₄₇	—	4	4	no	—
116	C₂²×C₄×C₄₇	—	4	2	no	—
117	C₂²×C₄×C₄₇	—	4	2	no	—
118	C₂²×C₄×C₄₇	—	4	4	no	—
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	#41	1	2	yes	—
131	M₁₆×C₄₇	—	2	4	no	—
132	M₁₆×C₄₇	—	2	4	no	—
133	M₁₆×C₄₇	—	4	2	no	—
134	M₁₆×C₄₇	—	4	2	no	—
135	C₂×C₈×C₄₇	—	2	4	no	—
136	C₂×C₈×C₄₇	—	4	2	no	—
137	C₂×C₈×C₄₇	—	4	2	no	—
138	C₄⋊C₄×C₄₇	—	2	8	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
141	C₂²⋊C₄×C₄₇	—	2	8	no	—
142	C₂²⋊C₄×C₄₇	—	2	4	no	—
143	C₄²×C₄₇	—	2	8	no	—
144	C₄²×C₄₇	—	2	2	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	—	2	2	no	—
147	C₄²×C₄₇	—	2	4	no	—
148	C₄²×C₄₇	—	2	2	no	—
149	C₄²×C₄₇	—	2	4	no	—
150	C₄²×C₄₇	—	2	4	no	—
151	C₄²×C₄₇	—	4	2	no	—
152	C₄²×C₄₇	—	4	2	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂³×C₄₇	C₄×D₄	1	2	yes	—
162	C₂³×C₄₇	#120	1	2	yes	—
163	C₂³×C₄₇	#121	1	1	yes	characteristic
164	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
165	Q₈×C₄₇	—	2	2	no	—
166	Q₈×C₄₇	—	2	2	no	—
167	Q₈×C₄₇	—	2	2	no	—
168	Q₈×C₄₇	#95	1	4	yes	complemented
169	D₄×C₄₇	—	2	8	no	—
170	D₄×C₄₇	—	2	8	no	—
171	D₄×C₄₇	—	2	2	no	—
172	D₄×C₄₇	—	2	2	no	—
173	D₄×C₄₇	—	2	2	no	—
174	D₄×C₄₇	#95	1	4	yes	complemented
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	8	no	—
181	C₂×C₄×C₄₇	—	2	8	no	—
182	C₂×C₄×C₄₇	—	2	8	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	4	8	no	—
188	C₂×C₄×C₄₇	—	4	16	no	—
189	C₂×C₄×C₄₇	—	4	8	no	—
190	C₂×C₄×C₄₇	—	4	4	no	—
191	C₂×C₄×C₄₇	—	4	8	no	—
192	C₂×C₄×C₄₇	—	4	4	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	#104	1	4	yes	complemented
196	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
202	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
203	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₄₇	#120	1	2	yes	—
208	C₂×C₄×C₄₇	#121	1	2	yes	—
209	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
211	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₄×C₄₇	#123	1	2	yes	—
213	C₂×C₄×C₄₇	#123	1	2	yes	—
214	C₈×C₄₇	—	4	4	no	—
215	#10790	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₄₇	—	2	2	no	—
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	2	2	no	—
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	4	no	—
221	C₂²×C₄₇	—	2	4	no	—
222	C₂²×C₄₇	—	4	4	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	—	4	2	no	—
225	C₂²×C₄₇	—	4	4	no	—
226	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₄₇	#379	1	1	yes	characteristic
228	C₂²×C₄₇	#380	1	1	yes	characteristic
229	C₂²×C₄₇	#385	1	2	yes	—
230	C₂²×C₄₇	#386	1	2	yes	—
231	C₂²×C₄₇	C₂×#104	1	2	yes	—
232	C₂²×C₄₇	#421	1	2	yes	—
233	C₄×C₄₇	—	2	4	no	—
234	C₄×C₄₇	—	2	4	no	—
235	C₄×C₄₇	—	4	8	no	—
236	C₄×C₄₇	—	4	2	no	—
237	C₄×C₄₇	—	4	4	no	—
238	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
239	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
240	C₄×C₄₇	#380	1	1	yes	characteristic
241	C₄×C₄₇	#381	1	1	yes	characteristic
242	C₄×C₄₇	#385	1	2	yes	—
243	C₄×C₄₇	#386	1	2	yes	—
244	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic
245	C₂²×#104	C₂×C₄₇	1	2	yes	—
246	C₂×#339	C₂×C₄₇	1	2	yes	complemented
247	#1728	C₂×C₄₇	1	1	yes	characteristic, complemented
248	C₄×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
249	C₂×C₄₇	—	2	2	no	—
250	C₂×C₄₇	—	2	2	no	—
251	C₂×C₄₇	—	4	4	no	—
252	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
253	C₂×C₄₇	C₄×#104	1	1	yes	characteristic
254	C₂×C₄₇	#1759	1	1	yes	characteristic
255	C₂×C₄₇	#1789	1	2	yes	—
256	C₂×C₄₇	#1806	1	2	yes	—
257	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
258	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
259	C₄×#41	—	2	4	no	—
260	C₄×#41	—	2	4	no	—
261	C₂×C₄×Q₈	C₄×C₄₇	1	2	yes	complemented
262	C₂×C₄×D₄	—	2	2	no	—
263	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	complemented
264	C₂×#117	—	2	1	no	—
265	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
266	C₂²×C₄²	—	2	1	no	—
267	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
268	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
269	C₂×#104	—	2	4	no	—
270	C₂×#104	—	2	4	no	—
271	C₂×#104	C₄×C₄₇	1	8	yes	complemented
272	C₂×#95	—	2	2	no	—
273	#339	—	2	4	no	—
274	#336	—	2	1	no	—
275	#336	—	2	1	no	—
276	C₄₇	#10790	1	1	yes	characteristic, direct product factor, Sylow
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	1	no	—
280	C₂×#41	—	2	1	no	—
281	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
282	C₂×#41	D₄×C₄₇	1	4	yes	—
283	C₂×#41	D₄×C₄₇	1	2	yes	—
284	C₂×#41	Q₈×C₄₇	1	2	yes	—
285	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	2	2	no	—
291	C₂³×C₄	D₄×C₄₇	1	2	yes	—
292	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	complemented
299	C₂²×C₈	—	2	2	no	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×D₄	—	2	16	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	4	no	—
305	#117	—	2	8	no	—
306	#117	—	2	2	no	—
307	#117	D₄×C₄₇	1	4	yes	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₄²	—	2	8	no	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
323	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	complemented
324	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
325	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
326	#104	—	2	16	no	—
327	#95	—	2	8	no	—
328	C₂⁴	—	2	1	no	—
329	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	#41	—	2	4	no	—
333	#41	—	2	4	no	—
334	#41	—	2	4	no	—
335	#41	—	2	4	no	—
336	#41	C₂²⋊C₄×C₄₇	1	8	yes	—
337	#41	C₄⋊C₄×C₄₇	1	8	yes	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	C₄²×C₄₇	1	2	yes	—
342	C₂×Q₈	C₂²⋊C₄×C₄₇	1	2	yes	—
343	C₂×Q₈	C₄⋊C₄×C₄₇	1	2	yes	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	C₄²×C₄₇	1	2	yes	—
352	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
353	C₂×D₄	C₄⋊C₄×C₄₇	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
372	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
373	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×Q₈×C₄₇	1	1	yes	characteristic
380	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
381	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
382	C₂²×C₄	#41×C₄₇	1	2	yes	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	4	no	—
385	M₁₆	—	4	2	no	—
386	M₁₆	—	4	2	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	4	2	no	—
389	C₂×C₈	—	4	2	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₄²	—	2	8	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	2	4	no	—
403	C₄²	—	4	2	no	—
404	C₄²	—	4	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
413	C₂³	C₄×D₄×C₄₇	1	2	yes	—
414	C₂³	#120×C₄₇	1	2	yes	—
415	C₂³	#121×C₄₇	1	1	yes	characteristic
416	C₂³	C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	#95×C₄₇	1	4	yes	complemented
421	D₄	—	2	8	no	—
422	D₄	—	2	8	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	2	no	—
425	D₄	—	2	2	no	—
426	D₄	#95×C₄₇	1	4	yes	complemented
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	4	8	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	#104×C₄₇	1	4	yes	complemented
448	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
451	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
454	C₂×C₄	#117×C₄₇	1	1	yes	characteristic
455	C₂×C₄	#117×C₄₇	1	1	yes	characteristic
456	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
457	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
458	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
459	C₂×C₄	#120×C₄₇	1	2	yes	—
460	C₂×C₄	#121×C₄₇	1	2	yes	—
461	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
462	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
463	C₂×C₄	C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
464	C₂×C₄	#123×C₄₇	1	2	yes	—
465	C₂×C₄	#123×C₄₇	1	2	yes	—
466	C₈	—	4	4	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
478	C₂²	C₄₇×#379	1	1	yes	characteristic
479	C₂²	C₄₇×#380	1	1	yes	characteristic
480	C₂²	C₄₇×#385	1	2	yes	—
481	C₂²	C₄₇×#386	1	2	yes	—
482	C₂²	C₂×#104×C₄₇	1	2	yes	—
483	C₂²	C₄₇×#421	1	2	yes	—
484	C₄	—	2	4	no	—
485	C₄	—	2	4	no	—
486	C₄	—	4	8	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	C₂×#95×C₄₇	1	1	yes	characteristic
490	C₄	C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
491	C₄	C₄₇×#380	1	1	yes	characteristic
492	C₄	C₄₇×#381	1	1	yes	characteristic
493	C₄	C₄₇×#385	1	2	yes	—
494	C₄	C₄₇×#386	1	2	yes	—
495	C₂	—	2	2	no	—
496	C₂	—	2	2	no	—
497	C₂	—	4	4	no	—
498	C₂	C₄₇×C₂²⋊#95	1	1	yes	characteristic
499	C₂	C₄×#104×C₄₇	1	1	yes	characteristic
500	C₂	C₄₇×#1759	1	1	yes	characteristic
501	C₂	C₄₇×#1789	1	2	yes	—
502	C₂	C₄₇×#1806	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₇×#339	C₂	semidirect
4. C₄₇×#1728	C₂	semidirect
5. C₄×#95×C₄₇	C₂	semidirect
10. C₂×C₄×Q₈×C₄₇	C₄	semidirect
12. C₂×C₄×D₄×C₄₇	C₄	semidirect
20. C₂×#104×C₄₇	C₄	semidirect
46. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
71. C₂×C₄²×C₄₇	C₂×C₄	semidirect
168. Q₈×C₄₇	#95	semidirect
174. D₄×C₄₇	#95	semidirect
195. C₂×C₄×C₄₇	#104	semidirect
215. #10790	C₄₇	direct (N × H)
246. C₂×#339	C₂×C₄₇	semidirect
247. #1728	C₂×C₄₇	semidirect
248. C₄×#95	C₂×C₄₇	semidirect
261. C₂×C₄×Q₈	C₄×C₄₇	semidirect
263. C₂×C₄×D₄	C₄×C₄₇	semidirect
271. C₂×#104	C₄×C₄₇	semidirect
276. C₄₇	#10790	direct (N × H)
298. C₂×M₁₆	C₂×C₄×C₄₇	semidirect
323. C₂×C₄²	C₂×C₄×C₄₇	semidirect
420. Q₈	#95×C₄₇	semidirect
426. D₄	#95×C₄₇	semidirect
447. C₂×C₄	#104×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₄₇	2
C₂²×#104×C₄₇	2
C₂×C₄₇×#339	2
C₄₇×#1728	2
C₄×#95×C₄₇	2
#10790	47

Subgroups — C47×#10790 #26050488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10790 #26050488