Subgroups — C₂×C₄₇×#1804 #26060340

Order 12032.

1942 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₄₇	C₂	1	2	yes	maximal
4	C₂×C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1804	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#340	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₇	—	2	1	no	—
9	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₄₇	—	2	2	no	—
11	C₂×C₄×D₄×C₄₇	—	2	4	no	—
12	C₂×C₄×D₄×C₄₇	C₄	1	8	yes	complemented
13	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₄₇	—	2	4	no	—
19	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	complemented
20	C₂×#102×C₄₇	—	2	8	no	—
21	C₂×#102×C₄₇	C₂²	1	8	yes	—
22	C₄₇×#382	—	2	2	no	—
23	C₄₇×#382	C₂²	1	4	yes	complemented
24	C₂×#95×C₄₇	—	2	1	no	—
25	C₂×#95×C₄₇	—	2	1	no	—
26	C₄₇×#340	C₂²	1	8	yes	complemented
27	C₂⁵×C₄₇	—	2	1	no	—
28	C₂²×D₄×C₄₇	—	2	1	no	—
29	C₂²×D₄×C₄₇	—	2	2	no	—
30	C₂²×D₄×C₄₇	—	2	2	no	—
31	C₂²×D₄×C₄₇	—	2	2	no	—
32	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
33	C₂²×D₄×C₄₇	D₄	1	4	yes	—
34	C₂²×D₄×C₄₇	Q₈	1	4	yes	—
35	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
36	C₂³×C₄×C₄₇	—	2	1	no	—
37	C₂³×C₄×C₄₇	—	2	8	no	—
38	C₂³×C₄×C₄₇	—	2	4	no	—
39	C₂³×C₄×C₄₇	—	2	2	no	—
40	C₂³×C₄×C₄₇	—	4	8	no	—
41	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	—	2	4	no	—
45	C₂²×C₈×C₄₇	—	2	4	no	—
46	C₂²×C₈×C₄₇	—	2	4	no	—
47	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
48	C₄×D₄×C₄₇	—	2	16	no	—
49	C₄×D₄×C₄₇	—	2	8	no	—
50	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
51	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
61	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₄₇	D₄	1	2	yes	—
63	C₂×C₄²×C₄₇	D₄	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
65	C₄⋊C₈×C₄₇	—	2	8	no	—
66	#102×C₄₇	—	2	16	no	—
67	#95×C₄₇	—	2	4	no	—
68	#95×C₄₇	—	2	4	no	—
69	C₂⁴×C₄₇	—	2	4	no	—
70	C₂⁴×C₄₇	—	2	4	no	—
71	C₂⁴×C₄₇	—	2	4	no	—
72	C₂⁴×C₄₇	—	2	2	no	—
73	C₂⁴×C₄₇	—	4	4	no	—
74	C₂⁴×C₄₇	—	4	4	no	—
75	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂×D₄×C₄₇	—	2	4	no	—
77	C₂×D₄×C₄₇	—	2	8	no	—
78	C₂×D₄×C₄₇	—	2	8	no	—
79	C₂×D₄×C₄₇	—	2	4	no	—
80	C₂×D₄×C₄₇	—	2	8	no	—
81	C₂×D₄×C₄₇	—	2	4	no	—
82	C₂×D₄×C₄₇	—	2	2	no	—
83	C₂×D₄×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	C₄⋊C₄	1	16	yes	—
86	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
87	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
88	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	16	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	4	16	no	—
96	C₂²×C₄×C₄₇	—	4	32	no	—
97	C₂²×C₄×C₄₇	—	4	4	no	—
98	C₂²×C₄×C₄₇	—	4	4	no	—
99	C₂²×C₄×C₄₇	—	4	4	no	—
100	C₂²×C₄×C₄₇	—	4	4	no	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₄₇	#41	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₄₇	—	2	4	no	—
114	C₂×C₈×C₄₇	—	2	4	no	—
115	C₂×C₈×C₄₇	—	2	4	no	—
116	C₂×C₈×C₄₇	—	4	8	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	—	2	4	no	—
121	C₄⋊C₄×C₄₇	—	4	4	no	—
122	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₄₇	—	2	16	no	—
124	C₄²×C₄₇	C₂²⋊C₄	1	8	yes	—
125	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
126	C₄²×C₄₇	C₂×D₄	1	4	yes	—
127	C₂³×C₄₇	—	2	4	no	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	2	4	no	—
130	C₂³×C₄₇	—	2	16	no	—
131	C₂³×C₄₇	—	4	4	no	—
132	C₂³×C₄₇	—	4	4	no	—
133	C₂³×C₄₇	—	4	8	no	—
134	C₂³×C₄₇	—	4	8	no	—
135	C₂³×C₄₇	—	4	16	no	—
136	C₂³×C₄₇	—	4	16	no	—
137	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂³×C₄₇	#121	1	2	yes	—
139	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
140	C₂³×C₄₇	#135	1	4	yes	—
141	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
142	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	D₄×C₄₇	—	2	4	no	—
144	D₄×C₄₇	—	2	4	no	—
145	D₄×C₄₇	—	2	4	no	—
146	D₄×C₄₇	—	2	16	no	—
147	D₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	8	no	—
151	C₂×C₄×C₄₇	—	2	8	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	4	32	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	8	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	4	4	no	—
159	C₂×C₄×C₄₇	—	8	8	no	—
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
164	C₂×C₄×C₄₇	#117	1	4	yes	—
165	C₂×C₄×C₄₇	#121	1	4	yes	—
166	C₂×C₄×C₄₇	#121	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
168	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₈×C₄₇	—	4	4	no	—
176	C₂×#1804	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₄₇	—	2	8	no	—
178	C₂²×C₄₇	—	4	8	no	—
179	C₂²×C₄₇	—	4	32	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	8	no	—
183	C₂²×C₄₇	#380	1	4	yes	—
184	C₂²×C₄₇	#416	1	4	yes	—
185	C₂²×C₄₇	#418	1	4	yes	—
186	C₂²×C₄₇	#463	1	8	yes	—
187	C₂²×C₄₇	#478	1	8	yes	—
188	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#135	1	2	yes	—
192	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
193	C₄×C₄₇	—	2	4	no	—
194	C₄×C₄₇	—	2	4	no	—
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	—	8	4	no	—
197	C₄×C₄₇	#380	1	4	yes	—
198	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
201	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
203	C₂²×C₄⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
204	C₂²×#102	C₂×C₄₇	1	2	yes	—
205	C₂×#382	C₂×C₄₇	1	1	yes	characteristic, complemented
206	#1804	C₂×C₄₇	1	8	yes	direct product factor
207	C₂×#340	C₂×C₄₇	1	2	yes	complemented
208	C₂×C₄₇	—	4	8	no	—
209	C₂×C₄₇	#1804	1	8	yes	direct product factor
210	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
212	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
213	C₂×C₄₇	C₂×#463	1	2	yes	—
214	C₂×C₄₇	C₂×#478	1	2	yes	—
215	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
216	C₂⁴×C₄	—	2	1	no	—
217	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
218	C₂×C₄×D₄	—	2	2	no	—
219	C₂×C₄×D₄	—	2	4	no	—
220	C₂×C₄×D₄	C₄×C₄₇	1	8	yes	complemented
221	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
224	C₂²×C₂²⋊C₄	—	2	1	no	—
225	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
226	C₂×C₄⋊C₈	—	2	4	no	—
227	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
228	C₂×#102	—	2	8	no	—
229	C₂×#102	C₂²×C₄₇	1	8	yes	—
230	#382	—	2	2	no	—
231	#382	C₂²×C₄₇	1	4	yes	complemented
232	C₂×#95	—	2	1	no	—
233	C₂×#95	—	2	1	no	—
234	#340	C₂²×C₄₇	1	8	yes	complemented
235	C₄₇	C₂×#1804	1	1	yes	characteristic, direct product factor, Sylow
236	C₂⁵	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
242	C₂²×D₄	D₄×C₄₇	1	4	yes	—
243	C₂²×D₄	Q₈×C₄₇	1	4	yes	—
244	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	8	no	—
247	C₂³×C₄	—	2	4	no	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	—	4	8	no	—
250	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
251	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	—	2	4	no	—
255	C₂²×C₈	—	2	4	no	—
256	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
257	C₄×D₄	—	2	16	no	—
258	C₄×D₄	—	2	8	no	—
259	C₄×D₄	C₂×C₄×C₄₇	1	16	yes	complemented
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
266	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
267	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	8	no	—
269	C₂×C₂²⋊C₄	—	2	4	no	—
270	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
271	C₂×C₄²	D₄×C₄₇	1	2	yes	—
272	C₂×C₄²	D₄×C₄₇	1	4	yes	—
273	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
274	C₄⋊C₈	—	2	8	no	—
275	#102	—	2	16	no	—
276	#95	—	2	4	no	—
277	#95	—	2	4	no	—
278	C₂⁴	—	2	4	no	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	—	2	4	no	—
281	C₂⁴	—	2	2	no	—
282	C₂⁴	—	4	4	no	—
283	C₂⁴	—	4	4	no	—
284	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	C₄⋊C₄×C₄₇	1	16	yes	—
295	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
296	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
297	C₂×D₄	C₂×Q₈×C₄₇	1	4	yes	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	4	16	no	—
305	C₂²×C₄	—	4	32	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
311	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
312	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
318	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
319	C₂²×C₄	#41×C₄₇	1	2	yes	—
320	C₂²×C₄	#41×C₄₇	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	4	8	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
332	C₂²⋊C₄	—	2	16	no	—
333	C₄²	C₂²⋊C₄×C₄₇	1	8	yes	—
334	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
335	C₄²	C₂×D₄×C₄₇	1	4	yes	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	16	no	—
340	C₂³	—	4	16	no	—
341	C₂³	—	4	16	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	8	no	—
346	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
347	C₂³	#121×C₄₇	1	2	yes	—
348	C₂³	C₂²⋊Q₈×C₄₇	1	2	yes	—
349	C₂³	#135×C₄₇	1	4	yes	—
350	C₂³	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
351	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
352	D₄	—	2	4	no	—
353	D₄	—	2	4	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	16	no	—
356	D₄	C₂×C₄⋊C₄×C₄₇	1	8	yes	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	32	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	8	8	no	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
372	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
373	C₂×C₄	#117×C₄₇	1	4	yes	—
374	C₂×C₄	#121×C₄₇	1	4	yes	—
375	C₂×C₄	#121×C₄₇	1	2	yes	—
376	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
377	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
378	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
384	C₈	—	4	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	32	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	C₄₇×#380	1	4	yes	—
392	C₂²	C₄₇×#416	1	4	yes	—
393	C₂²	C₄₇×#418	1	4	yes	—
394	C₂²	C₄₇×#463	1	8	yes	—
395	C₂²	C₄₇×#478	1	8	yes	—
396	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
397	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
398	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
399	C₂²	C₂×#135×C₄₇	1	2	yes	—
400	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
401	C₄	—	2	4	no	—
402	C₄	—	2	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	4	no	—
405	C₄	C₄₇×#380	1	4	yes	—
406	C₄	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
407	C₄	C₂×#117×C₄₇	1	1	yes	characteristic
408	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
409	C₄	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
410	C₂	—	4	8	no	—
411	C₂	C₄₇×#1804	1	8	yes	direct product factor
412	C₂	C₂×C₄₇×#380	1	1	yes	characteristic
413	C₂	C₂×C₄₇×#416	1	1	yes	characteristic
414	C₂	C₂×C₄₇×#418	1	1	yes	characteristic
415	C₂	C₂×C₄₇×#463	1	2	yes	—
416	C₂	C₂×C₄₇×#478	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊C₈×C₄₇	C₂	semidirect
4. C₂×C₄₇×#382	C₂	semidirect
5. C₄₇×#1804	C₂	direct (N × H)
6. C₂×C₄₇×#340	C₂	semidirect
12. C₂×C₄×D₄×C₄₇	C₄	semidirect
19. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
23. C₄₇×#382	C₂²	semidirect
26. C₄₇×#340	C₂²	semidirect
50. C₄×D₄×C₄₇	C₂×C₄	semidirect
176. C₂×#1804	C₄₇	direct (N × H)
203. C₂²×C₄⋊C₈	C₂×C₄₇	semidirect
205. C₂×#382	C₂×C₄₇	semidirect
206. #1804	C₂×C₄₇	direct (N × H)
207. C₂×#340	C₂×C₄₇	semidirect
209. C₂×C₄₇	#1804	direct (N × H)
220. C₂×C₄×D₄	C₄×C₄₇	semidirect
227. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
231. #382	C₂²×C₄₇	semidirect
234. #340	C₂²×C₄₇	semidirect
235. C₄₇	C₂×#1804	direct (N × H)
259. C₄×D₄	C₂×C₄×C₄₇	semidirect
411. C₂	C₄₇×#1804	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×D₄×C₄₇	2
C₂²×C₄⋊C₈×C₄₇	2
C₂²×#102×C₄₇	2
C₂×C₄₇×#382	2
C₄₇×#1804	2
C₂×C₄₇×#340	2
C₂×#1804	47

Subgroups — C2×C47×#1804 #26060340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1804 #26060340