Subgroups — C₂×C₄₇×#1801 #26060334

Order 12032.

1410 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#423	C₂	1	2	yes	maximal
3	C₂²×#101×C₄₇	C₂	1	2	yes	maximal
4	C₄₇×#1801	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇×#343	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₇	C₂²	1	4	yes	—
8	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
9	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
10	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
11	C₂×C₄×Q₈×C₄₇	C₄	1	4	yes	—
12	C₂×C₄×Q₈×C₄₇	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	C₄	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#423	—	2	4	no	—
18	C₄₇×#423	C₂²	1	8	yes	—
19	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
20	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
21	C₂×#101×C₄₇	—	2	8	no	—
22	C₂×#101×C₄₇	C₂²	1	8	yes	—
23	C₄₇×#343	C₂²	1	8	yes	—
24	C₂²×Q₈×C₄₇	—	2	2	no	—
25	C₂²×Q₈×C₄₇	—	2	2	no	—
26	C₂²×Q₈×C₄₇	—	2	4	no	—
27	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
28	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
29	C₂²×Q₈×C₄₇	Q₈	1	4	yes	—
30	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
31	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₇	—	2	4	no	—
37	C₂×M₁₆×C₄₇	—	2	8	no	—
38	C₂×M₁₆×C₄₇	—	2	8	no	—
39	C₂×M₁₆×C₄₇	C₂³	1	8	yes	—
40	C₂²×C₈×C₄₇	—	2	4	no	—
41	C₄×Q₈×C₄₇	—	2	8	no	—
42	C₄×Q₈×C₄₇	—	2	8	no	—
43	C₄×Q₈×C₄₇	—	2	8	no	—
44	C₄×Q₈×C₄₇	—	2	8	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
50	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
52	C₂×C₄²×C₄₇	—	2	4	no	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	—	2	2	no	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
56	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	D₄	1	2	yes	—
58	C₂×C₄²×C₄₇	D₄	1	2	yes	—
59	C₂×C₄²×C₄₇	D₄	1	4	yes	—
60	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
61	C₄⋊C₈×C₄₇	—	2	8	no	—
62	C₄⋊C₈×C₄₇	—	2	8	no	—
63	#101×C₄₇	—	2	16	no	—
64	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂×Q₈×C₄₇	—	2	4	no	—
66	C₂×Q₈×C₄₇	—	2	4	no	—
67	C₂×Q₈×C₄₇	—	2	8	no	—
68	C₂×Q₈×C₄₇	—	2	8	no	—
69	C₂×Q₈×C₄₇	—	2	8	no	—
70	C₂×Q₈×C₄₇	—	2	8	no	—
71	C₂×Q₈×C₄₇	—	2	4	no	—
72	C₂×Q₈×C₄₇	—	2	4	no	—
73	C₂×Q₈×C₄₇	C₄⋊C₄	1	8	yes	—
74	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
75	C₂×Q₈×C₄₇	C₂×Q₈	1	4	yes	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	4	2	no	—
83	C₂²×C₄×C₄₇	—	4	4	no	—
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₄⋊C₄	1	8	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₄₇	#41	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	M₁₆×C₄₇	—	2	8	no	—
102	M₁₆×C₄₇	—	2	8	no	—
103	M₁₆×C₄₇	—	4	8	no	—
104	C₂×C₈×C₄₇	—	2	8	no	—
105	C₂×C₈×C₄₇	—	4	8	no	—
106	C₄⋊C₄×C₄₇	—	2	16	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	—	2	4	no	—
109	C₄²×C₄₇	—	2	8	no	—
110	C₄²×C₄₇	—	2	8	no	—
111	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
112	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
113	C₄²×C₄₇	C₂×D₄	1	4	yes	—
114	C₄²×C₄₇	C₂×D₄	1	4	yes	—
115	C₂³×C₄₇	—	2	2	no	—
116	C₂³×C₄₇	—	2	2	no	—
117	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
120	C₂³×C₄₇	#117	1	2	yes	—
121	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
122	Q₈×C₄₇	—	2	8	no	—
123	Q₈×C₄₇	—	2	8	no	—
124	Q₈×C₄₇	—	2	16	no	—
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	8	no	—
128	C₂×C₄×C₄₇	—	2	8	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	4	no	—
137	C₂×C₄×C₄₇	—	4	4	no	—
138	C₂×C₄×C₄₇	—	4	4	no	—
139	C₂×C₄×C₄₇	#101	1	4	yes	complemented
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₇	#117	1	2	yes	—
147	C₂×C₄×C₄₇	#121	1	4	yes	—
148	C₂×C₄×C₄₇	#121	1	4	yes	—
149	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
151	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
155	C₈×C₄₇	—	4	8	no	—
156	C₂×#1801	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	—	2	1	no	—
160	C₂²×C₄₇	—	2	1	no	—
161	C₂²×C₄₇	—	2	1	no	—
162	C₂²×C₄₇	—	2	1	no	—
163	C₂²×C₄₇	#380	1	2	yes	—
164	C₂²×C₄₇	#380	1	2	yes	—
165	C₂²×C₄₇	C₂×#101	1	2	yes	—
166	C₂²×C₄₇	#413	1	2	yes	—
167	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	—	2	4	no	—
172	C₄×C₄₇	—	2	8	no	—
173	C₄×C₄₇	—	4	4	no	—
174	C₄×C₄₇	#380	1	4	yes	—
175	C₄×C₄₇	C₂×#101	1	4	yes	complemented
176	C₄×C₄₇	C₂×#121	1	2	yes	—
177	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
178	C₂²×C₄×Q₈	C₂×C₄₇	1	1	yes	characteristic
179	C₂×#423	C₂×C₄₇	1	2	yes	—
180	C₂²×#101	C₂×C₄₇	1	2	yes	—
181	#1801	C₂×C₄₇	1	8	yes	direct product factor
182	C₂×#343	C₂×C₄₇	1	2	yes	—
183	C₂×C₄₇	—	2	1	no	—
184	C₂×C₄₇	—	2	1	no	—
185	C₂×C₄₇	—	2	2	no	—
186	C₂×C₄₇	#1801	1	4	yes	direct product factor
187	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
188	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
189	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
190	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
191	C₂²×M₁₆	C₂²×C₄₇	1	4	yes	—
192	C₂×C₄×Q₈	—	2	2	no	—
193	C₂×C₄×Q₈	—	2	2	no	—
194	C₂×C₄×Q₈	—	2	4	no	—
195	C₂×C₄×Q₈	C₄×C₄₇	1	4	yes	—
196	C₂×C₄×Q₈	C₂²×C₄₇	1	4	yes	—
197	C₂²×C₄⋊C₄	C₄×C₄₇	1	2	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
199	C₂²×C₄²	C₄×C₄₇	1	2	yes	—
200	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
201	#423	—	2	4	no	—
202	#423	C₂²×C₄₇	1	8	yes	—
203	C₂×C₄⋊C₈	—	2	2	no	—
204	C₂×C₄⋊C₈	—	2	2	no	—
205	C₂×#101	—	2	8	no	—
206	C₂×#101	C₂²×C₄₇	1	8	yes	—
207	#343	C₂²×C₄₇	1	8	yes	—
208	C₄₇	C₂×#1801	1	1	yes	characteristic, direct product factor, Sylow
209	C₂²×Q₈	—	2	2	no	—
210	C₂²×Q₈	—	2	2	no	—
211	C₂²×Q₈	—	2	4	no	—
212	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
213	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
214	C₂²×Q₈	Q₈×C₄₇	1	4	yes	—
215	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
216	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
217	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
218	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
219	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	—	2	8	no	—
223	C₂×M₁₆	—	2	8	no	—
224	C₂×M₁₆	C₂³×C₄₇	1	8	yes	—
225	C₂²×C₈	—	2	4	no	—
226	C₄×Q₈	—	2	8	no	—
227	C₄×Q₈	—	2	8	no	—
228	C₄×Q₈	—	2	8	no	—
229	C₄×Q₈	—	2	8	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	C₂×C₄×C₄₇	1	8	yes	—
241	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
242	C₂×C₄²	D₄×C₄₇	1	2	yes	—
243	C₂×C₄²	D₄×C₄₇	1	2	yes	—
244	C₂×C₄²	D₄×C₄₇	1	4	yes	—
245	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
246	C₄⋊C₈	—	2	8	no	—
247	C₄⋊C₈	—	2	8	no	—
248	#101	—	2	16	no	—
249	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	2	8	no	—
253	C₂×Q₈	—	2	8	no	—
254	C₂×Q₈	—	2	8	no	—
255	C₂×Q₈	—	2	8	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	C₄⋊C₄×C₄₇	1	8	yes	—
259	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
260	C₂×Q₈	C₂×Q₈×C₄₇	1	4	yes	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
271	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
272	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
273	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊C₄×C₄₇	1	8	yes	—
275	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
276	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
277	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
283	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
284	C₂²×C₄	#41×C₄₇	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
286	M₁₆	—	2	8	no	—
287	M₁₆	—	2	8	no	—
288	M₁₆	—	4	8	no	—
289	C₂×C₈	—	2	8	no	—
290	C₂×C₈	—	4	8	no	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄²	—	2	8	no	—
295	C₄²	—	2	8	no	—
296	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
297	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
298	C₄²	C₂×D₄×C₄₇	1	4	yes	—
299	C₄²	C₂×D₄×C₄₇	1	4	yes	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
303	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
304	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
305	C₂³	#117×C₄₇	1	2	yes	—
306	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	Q₈	—	2	8	no	—
309	Q₈	—	2	16	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	#101×C₄₇	1	4	yes	complemented
325	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
329	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	8	yes	—
330	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
331	C₂×C₄	#117×C₄₇	1	2	yes	—
332	C₂×C₄	#121×C₄₇	1	4	yes	—
333	C₂×C₄	#121×C₄₇	1	4	yes	—
334	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
335	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
336	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
338	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
340	C₈	—	4	8	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	C₄₇×#380	1	2	yes	—
348	C₂²	C₄₇×#380	1	2	yes	—
349	C₂²	C₂×#101×C₄₇	1	2	yes	—
350	C₂²	C₄₇×#413	1	2	yes	—
351	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
352	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
353	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
354	C₄	—	2	8	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	4	no	—
357	C₄	—	4	4	no	—
358	C₄	C₄₇×#380	1	4	yes	—
359	C₄	C₂×#101×C₄₇	1	4	yes	complemented
360	C₄	C₂×#121×C₄₇	1	2	yes	—
361	C₄	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	—	2	2	no	—
365	C₂	C₄₇×#1801	1	4	yes	direct product factor
366	C₂	C₂×C₄₇×#380	1	1	yes	characteristic
367	C₂	C₂²×#101×C₄₇	1	1	yes	characteristic
368	C₂	C₂×C₄₇×#413	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₄₇×#1801	C₂	direct (N × H)
139. C₂×C₄×C₄₇	#101	semidirect
156. C₂×#1801	C₄₇	direct (N × H)
175. C₄×C₄₇	C₂×#101	semidirect
181. #1801	C₂×C₄₇	direct (N × H)
186. C₂×C₄₇	#1801	direct (N × H)
208. C₄₇	C₂×#1801	direct (N × H)
324. C₂×C₄	#101×C₄₇	semidirect
359. C₄	C₂×#101×C₄₇	semidirect
365. C₂	C₄₇×#1801	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₄₇	2
C₂×C₄₇×#423	2
C₂²×#101×C₄₇	2
C₄₇×#1801	2
C₂×C₄₇×#343	2
C₂×#1801	47

Subgroups — C2×C47×#1801 #26060334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1801 #26060334