Subgroups — C₄₇×#17915 #26057613

Order 12032.

624 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3108	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2966	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1584	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1583	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1579	C₂	1	2	yes	maximal, complemented
7	C₄₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1573	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1483	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#529	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₄₇×#483	C₄	1	1	yes	characteristic
15	C₄₇×#480	C₄	1	1	yes	characteristic
16	C₄₇×#479	C₄	1	2	yes	—
17	C₄₇×#464	C₄	1	2	yes	—
18	C₄₇×#451	C₄	1	1	yes	characteristic
19	C₄₇×#448	C₄	1	1	yes	characteristic
20	C₄₇×#446	C₂²	1	1	yes	characteristic
21	C₈×Q₈×C₄₇	—	2	1	no	—
22	C₈×Q₈×C₄₇	—	2	1	no	—
23	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
24	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
26	C₄×Q₁₆×C₄₇	C₂²	1	2	yes	—
27	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
28	C₄₇×#436	C₂²	1	1	yes	characteristic
29	C₄₇×#435	—	2	1	no	—
30	C₈×D₄×C₄₇	—	2	1	no	—
31	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#433	—	2	1	no	—
33	C₄₇×#432	C₂²	1	1	yes	characteristic
34	C₄₇×#431	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#405	—	2	1	no	—
38	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	—	2	1	no	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#335	C₂²	1	2	yes	—
42	C₄₇×#334	C₂²	1	2	yes	—
43	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₄₇×#322	C₂²	1	2	yes	—
48	C₄₇×#322	C₂²	1	2	yes	—
49	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×M₁₆×C₄₇	—	2	1	no	—
53	C₂×M₁₆×C₄₇	—	2	1	no	—
54	C₂²×C₈×C₄₇	—	2	1	no	—
55	C₂²×C₈×C₄₇	—	2	1	no	—
56	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
58	#126×C₄₇	—	2	1	no	—
59	#125×C₄₇	C₂×C₄	1	1	yes	characteristic
60	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
61	#123×C₄₇	—	2	1	no	—
62	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
63	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₄₇	—	2	1	no	—
65	C₄×Q₈×C₄₇	—	2	1	no	—
66	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
68	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₄₇	—	2	1	no	—
70	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
71	#117×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	—	2	1	no	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	#107×C₄₇	C₂×C₄	1	2	yes	—
77	#106×C₄₇	C₂×C₄	1	2	yes	—
78	C₄⋊C₈×C₄₇	—	2	2	no	—
79	C₄⋊C₈×C₄₇	—	2	2	no	—
80	C₄⋊C₈×C₄₇	—	2	1	no	—
81	C₄⋊C₈×C₄₇	—	2	1	no	—
82	C₄⋊C₈×C₄₇	—	2	1	no	—
83	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
84	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
85	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
87	#103×C₄₇	C₂×C₄	1	2	yes	—
88	#103×C₄₇	C₂×C₄	1	2	yes	—
89	#103×C₄₇	C₂×C₄	1	2	yes	—
90	#102×C₄₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₄₇	—	2	1	no	—
92	C₂²⋊C₈×C₄₇	—	2	1	no	—
93	C₂²⋊C₈×C₄₇	—	2	1	no	—
94	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
96	#97×C₄₇	—	2	1	no	—
97	#97×C₄₇	—	2	1	no	—
98	#97×C₄₇	—	2	1	no	—
99	C₄×C₈×C₄₇	—	2	2	no	—
100	C₄×C₈×C₄₇	—	2	2	no	—
101	C₄×C₈×C₄₇	—	2	1	no	—
102	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
103	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₄₇	C₂³	1	2	yes	—
105	C₄×C₈×C₄₇	C₂³	1	2	yes	—
106	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₄₇	—	2	4	no	—
109	C₂×Q₈×C₄₇	—	2	1	no	—
110	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₄₇	—	2	1	no	—
113	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
120	Q₁₆×C₄₇	—	2	4	no	—
121	SD₁₆×C₄₇	—	2	4	no	—
122	M₁₆×C₄₇	—	4	2	no	—
123	M₁₆×C₄₇	—	4	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	4	1	no	—
130	C₂×C₈×C₄₇	—	4	2	no	—
131	C₂×C₈×C₄₇	—	4	2	no	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	—	2	1	no	—
141	C₄⋊C₄×C₄₇	—	2	1	no	—
142	C₄⋊C₄×C₄₇	—	2	1	no	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	—	2	1	no	—
145	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂²⋊C₄×C₄₇	—	2	1	no	—
149	C₂²⋊C₄×C₄₇	—	2	1	no	—
150	C₂²⋊C₄×C₄₇	—	2	1	no	—
151	C₂²⋊C₄×C₄₇	—	2	1	no	—
152	C₂²⋊C₄×C₄₇	—	2	1	no	—
153	C₄²×C₄₇	—	2	2	no	—
154	C₄²×C₄₇	—	2	2	no	—
155	C₄²×C₄₇	—	2	1	no	—
156	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₇	#41	1	1	yes	characteristic
159	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
162	Q₈×C₄₇	—	2	4	no	—
163	Q₈×C₄₇	—	2	2	no	—
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	#131	1	4	yes	—
166	D₄×C₄₇	—	2	2	no	—
167	D₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	—	2	1	no	—
190	C₈×C₄₇	—	2	1	no	—
191	C₈×C₄₇	—	2	1	no	—
192	C₈×C₄₇	—	4	2	no	—
193	C₈×C₄₇	—	4	1	no	—
194	C₈×C₄₇	—	4	2	no	—
195	C₈×C₄₇	—	4	1	no	—
196	C₈×C₄₇	#137	1	2	yes	—
197	#17915	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	4	1	no	—
201	C₂²×C₄₇	—	4	1	no	—
202	C₂²×C₄₇	—	4	1	no	—
203	C₂²×C₄₇	#444	1	2	yes	—
204	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
205	C₄×C₄₇	—	2	4	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	4	1	no	—
211	C₄×C₄₇	—	4	1	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	C₂×#131	1	2	yes	—
215	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
216	C₄×C₄₇	#575	1	1	yes	characteristic
217	#3108	C₂×C₄₇	1	1	yes	characteristic
218	#2966	C₂×C₄₇	1	1	yes	characteristic
219	C₂×C₈×Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
220	#1584	C₂×C₄₇	1	2	yes	complemented
221	#1583	C₂×C₄₇	1	2	yes	complemented
222	#1579	C₂×C₄₇	1	2	yes	complemented
223	SD₁₆⋊C₈	C₂×C₄₇	1	2	yes	complemented
224	#1573	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#1491	C₂×C₄₇	1	1	yes	characteristic, complemented
226	#1483	C₂×C₄₇	1	1	yes	characteristic
227	#1451	C₂×C₄₇	1	1	yes	characteristic, complemented
228	C₂×C₄₇	—	2	2	no	—
229	C₂×C₄₇	—	8	1	no	—
230	C₂×C₄₇	#2929	1	1	yes	characteristic
231	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
233	#529	C₂²×C₄₇	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
235	#483	C₄×C₄₇	1	1	yes	characteristic
236	#480	C₄×C₄₇	1	1	yes	characteristic
237	#479	C₄×C₄₇	1	2	yes	—
238	#464	C₄×C₄₇	1	2	yes	—
239	#451	C₄×C₄₇	1	1	yes	characteristic
240	#448	C₄×C₄₇	1	1	yes	characteristic
241	#446	C₂²×C₄₇	1	1	yes	characteristic
242	C₈×Q₈	—	2	1	no	—
243	C₈×Q₈	—	2	1	no	—
244	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
245	C₈×Q₈	C₂²×C₄₇	1	1	yes	characteristic
246	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
247	C₄×Q₁₆	C₂²×C₄₇	1	2	yes	—
248	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	—
249	#436	C₂²×C₄₇	1	1	yes	characteristic
250	#435	—	2	1	no	—
251	C₈×D₄	—	2	1	no	—
252	C₈×D₄	C₂²×C₄₇	1	1	yes	characteristic
253	#433	—	2	1	no	—
254	#432	C₂²×C₄₇	1	1	yes	characteristic
255	#431	C₂²×C₄₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	—	2	1	no	—
257	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
258	#405	—	2	1	no	—
259	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
260	C₂×C₄×C₈	—	2	1	no	—
261	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
262	#335	C₂²×C₄₇	1	2	yes	—
263	#334	C₂²×C₄₇	1	2	yes	—
264	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
265	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
266	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
267	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
268	#322	C₂²×C₄₇	1	2	yes	—
269	#322	C₂²×C₄₇	1	2	yes	—
270	C₄₇	#17915	1	1	yes	characteristic, direct product factor, Sylow
271	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
272	C₂×Q₁₆	C₂×C₄×C₄₇	1	2	yes	—
273	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
279	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
280	#126	—	2	1	no	—
281	#125	C₂×C₄×C₄₇	1	1	yes	characteristic
282	#124	C₂×C₄×C₄₇	1	1	yes	characteristic
283	#123	—	2	1	no	—
284	C₂²⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
285	#121	C₂×C₄×C₄₇	1	1	yes	characteristic
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
289	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
290	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
293	#117	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
298	#107	C₂×C₄×C₄₇	1	2	yes	—
299	#106	C₂×C₄×C₄₇	1	2	yes	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	C₂×C₄×C₄₇	1	2	yes	—
306	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
307	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
309	#103	C₂×C₄×C₄₇	1	2	yes	—
310	#103	C₂×C₄×C₄₇	1	2	yes	—
311	#103	C₂×C₄×C₄₇	1	2	yes	—
312	#102	C₂×C₄×C₄₇	1	2	yes	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
317	C₂²⋊C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
318	#97	—	2	1	no	—
319	#97	—	2	1	no	—
320	#97	—	2	1	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
325	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₄₇	1	2	yes	—
327	C₄×C₈	C₂³×C₄₇	1	2	yes	—
328	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
329	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
333	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
341	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
342	Q₁₆	—	2	4	no	—
343	SD₁₆	—	2	4	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
355	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
357	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
358	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
359	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
368	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
379	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
380	C₄²	#41×C₄₇	1	1	yes	characteristic
381	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
382	C₂³	—	2	1	no	—
383	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	2	2	no	—
387	Q₈	#131×C₄₇	1	4	yes	—
388	D₄	—	2	2	no	—
389	D₄	—	4	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
404	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
405	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	1	no	—
418	C₈	#137×C₄₇	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	C₄₇×#444	1	2	yes	—
425	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	1	no	—
435	C₄	C₂×#131×C₄₇	1	2	yes	—
436	C₄	C₂×#137×C₄₇	1	1	yes	characteristic
437	C₄	C₄₇×#575	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	8	1	no	—
440	C₂	C₄₇×#2929	1	1	yes	characteristic
441	C₂	C₄×#137×C₄₇	1	1	yes	characteristic
442	C₂	C₂×C₄₇×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#121×C₄₇	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂×C₄×C₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₈×Q₈×C₄₇	C₂	semidirect
4. C₄₇×#1584	C₂	semidirect
5. C₄₇×#1583	C₂	semidirect
6. C₄₇×#1579	C₂	semidirect
7. C₄₇×SD₁₆⋊C₈	C₂	semidirect
8. C₄₇×#1573	C₂	semidirect
9. C₄₇×#1491	C₂	semidirect
11. C₄₇×#1451	C₂	semidirect
197. #17915	C₄₇	direct (N × H)
219. C₂×C₈×Q₈	C₂×C₄₇	semidirect
220. #1584	C₂×C₄₇	semidirect
221. #1583	C₂×C₄₇	semidirect
222. #1579	C₂×C₄₇	semidirect
223. SD₁₆⋊C₈	C₂×C₄₇	semidirect
224. #1573	C₂×C₄₇	semidirect
225. #1491	C₂×C₄₇	semidirect
227. #1451	C₂×C₄₇	semidirect
270. C₄₇	#17915	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×#3108	2
C₄₇×#2966	2
C₂×C₈×Q₈×C₄₇	2
C₄₇×#1584	2
C₄₇×#1583	2
C₄₇×#1579	2
C₄₇×SD₁₆⋊C₈	2
C₄₇×#1573	2
C₄₇×#1491	2
C₄₇×#1483	2
C₄₇×#1451	2
#17915	47

Subgroups — C47×#17915 #26057613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17915 #26057613