Subgroups — C₄₇×#21769 #26061467

Order 12032.

1558 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1895	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1894	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1874	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1872	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1825	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1788	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
13	C₄₇×#525	—	2	4	no	—
14	C₄₇×#525	C₄	1	8	yes	complemented
15	C₂×#123×C₄₇	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#120×C₄₇	—	2	1	no	—
21	C₂×C₄×D₄×C₄₇	—	2	1	no	—
22	C₂×C₄×D₄×C₄₇	—	2	1	no	—
23	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
26	C₂×#103×C₄₇	C₂²	1	4	yes	complemented
27	C₂×#102×C₄₇	C₂²	1	4	yes	complemented
28	C₄₇×#407	—	2	4	no	—
29	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
31	C₄₇×#380	—	2	1	no	—
32	C₄₇×#380	—	2	1	no	—
33	C₄₇×#380	C₂²	1	2	yes	—
34	C₄₇×#380	C₂²	1	2	yes	—
35	C₂×#95×C₄₇	—	2	1	no	—
36	C₄₇×#340	C₂²	1	4	yes	complemented
37	C₄₇×#340	C₂²	1	4	yes	complemented
38	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
39	C₂×#41×C₄₇	—	2	2	no	—
40	C₂×#41×C₄₇	—	4	4	no	—
41	C₂×#41×C₄₇	C₂×C₄	1	4	yes	complemented
42	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₄₇	—	2	1	no	—
44	C₂²×D₄×C₄₇	—	2	1	no	—
45	C₂²×D₄×C₄₇	—	2	1	no	—
46	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	—	2	1	no	—
48	C₂³×C₄×C₄₇	—	2	2	no	—
49	C₂³×C₄×C₄₇	—	4	4	no	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	D₄	1	4	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₄₇	—	2	4	no	—
59	C₂×M₁₆×C₄₇	—	4	4	no	—
60	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
61	#123×C₄₇	—	2	8	no	—
62	C₂²⋊Q₈×C₄₇	—	2	2	no	—
63	C₂²⋊Q₈×C₄₇	—	2	2	no	—
64	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
65	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
66	#121×C₄₇	—	2	2	no	—
67	#121×C₄₇	—	2	2	no	—
68	#121×C₄₇	C₂×C₄	1	4	yes	—
69	#121×C₄₇	C₂×C₄	1	4	yes	complemented
70	#120×C₄₇	—	2	8	no	—
71	C₄×D₄×C₄₇	—	2	8	no	—
72	C₄×D₄×C₄₇	—	2	8	no	—
73	#117×C₄₇	—	2	2	no	—
74	#117×C₄₇	C₂×C₄	1	4	yes	complemented
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	#103×C₄₇	—	4	4	no	—
92	#102×C₄₇	—	4	4	no	—
93	C₂²⋊C₈×C₄₇	—	2	4	no	—
94	C₂²⋊C₈×C₄₇	—	2	4	no	—
95	#95×C₄₇	—	2	2	no	—
96	#95×C₄₇	—	2	2	no	—
97	C₂⁴×C₄₇	—	2	2	no	—
98	C₂⁴×C₄₇	—	2	2	no	—
99	C₂⁴×C₄₇	—	2	1	no	—
100	C₂⁴×C₄₇	—	4	2	no	—
101	C₂⁴×C₄₇	—	4	2	no	—
102	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
103	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
106	#41×C₄₇	—	4	8	no	—
107	#41×C₄₇	—	4	8	no	—
108	C₂×Q₈×C₄₇	—	2	1	no	—
109	C₂×Q₈×C₄₇	—	2	4	no	—
110	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₇	—	2	4	no	—
112	C₂×D₄×C₄₇	—	2	4	no	—
113	C₂×D₄×C₄₇	—	2	4	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	—	2	4	no	—
116	C₂×D₄×C₄₇	—	4	4	no	—
117	C₂×D₄×C₄₇	—	4	4	no	—
118	C₂×D₄×C₄₇	—	4	2	no	—
119	C₂×D₄×C₄₇	—	4	2	no	—
120	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	—	2	4	no	—
122	C₂²×C₄×C₄₇	—	2	4	no	—
123	C₂²×C₄×C₄₇	—	2	4	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	—	2	4	no	—
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	4	8	no	—
130	C₂²×C₄×C₄₇	—	4	8	no	—
131	C₂²×C₄×C₄₇	—	4	2	no	—
132	C₂²×C₄×C₄₇	—	4	2	no	—
133	C₂²×C₄×C₄₇	—	4	2	no	—
134	C₂²×C₄×C₄₇	—	4	4	no	—
135	C₂²×C₄×C₄₇	—	4	4	no	—
136	C₂²×C₄×C₄₇	—	4	4	no	—
137	C₂²×C₄×C₄₇	—	4	4	no	—
138	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
139	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
140	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
151	M₁₆×C₄₇	—	4	8	no	—
152	C₂×C₈×C₄₇	—	2	4	no	—
153	C₂×C₈×C₄₇	—	2	4	no	—
154	C₂×C₈×C₄₇	—	2	4	no	—
155	C₄⋊C₄×C₄₇	—	2	4	no	—
156	C₄⋊C₄×C₄₇	—	2	4	no	—
157	C₄⋊C₄×C₄₇	—	2	1	no	—
158	C₄⋊C₄×C₄₇	—	2	1	no	—
159	C₄⋊C₄×C₄₇	—	2	4	no	—
160	C₄⋊C₄×C₄₇	—	2	4	no	—
161	C₄⋊C₄×C₄₇	—	4	4	no	—
162	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
163	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
164	C₂²⋊C₄×C₄₇	—	2	4	no	—
165	C₂²⋊C₄×C₄₇	—	2	4	no	—
166	C₂²⋊C₄×C₄₇	—	2	4	no	—
167	C₂²⋊C₄×C₄₇	—	2	4	no	—
168	C₂²⋊C₄×C₄₇	—	2	4	no	—
169	C₂²⋊C₄×C₄₇	—	4	4	no	—
170	C₂²⋊C₄×C₄₇	—	4	4	no	—
171	C₄²×C₄₇	—	2	4	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	2	no	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	1	no	—
177	C₂³×C₄₇	—	2	1	no	—
178	C₂³×C₄₇	—	2	1	no	—
179	C₂³×C₄₇	—	2	1	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	2	8	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	4	4	no	—
185	C₂³×C₄₇	—	4	4	no	—
186	C₂³×C₄₇	—	4	8	no	—
187	C₂³×C₄₇	—	4	8	no	—
188	C₂³×C₄₇	—	4	2	no	—
189	C₂³×C₄₇	—	4	1	no	—
190	C₂³×C₄₇	—	4	1	no	—
191	C₂³×C₄₇	—	4	2	no	—
192	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
196	C₂³×C₄₇	#137	1	2	yes	—
197	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₄₇	—	2	4	no	—
199	Q₈×C₄₇	—	4	2	no	—
200	D₄×C₄₇	—	2	4	no	—
201	D₄×C₄₇	—	4	8	no	—
202	D₄×C₄₇	—	4	8	no	—
203	D₄×C₄₇	—	4	8	no	—
204	D₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	4	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	4	4	no	—
218	C₂×C₄×C₄₇	—	4	4	no	—
219	C₂×C₄×C₄₇	—	4	4	no	—
220	C₂×C₄×C₄₇	—	4	8	no	—
221	C₂×C₄×C₄₇	—	4	2	no	—
222	C₂×C₄×C₄₇	—	4	1	no	—
223	C₂×C₄×C₄₇	—	4	1	no	—
224	C₂×C₄×C₄₇	—	4	2	no	—
225	C₂×C₄×C₄₇	—	4	4	no	—
226	C₂×C₄×C₄₇	—	4	4	no	—
227	C₂×C₄×C₄₇	—	4	4	no	—
228	C₂×C₄×C₄₇	—	8	8	no	—
229	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
232	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
235	C₈×C₄₇	—	4	4	no	—
236	#21769	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₄₇	—	2	2	no	—
238	C₂²×C₄₇	—	2	2	no	—
239	C₂²×C₄₇	—	2	4	no	—
240	C₂²×C₄₇	—	2	4	no	—
241	C₂²×C₄₇	—	2	2	no	—
242	C₂²×C₄₇	—	2	2	no	—
243	C₂²×C₄₇	—	2	2	no	—
244	C₂²×C₄₇	—	2	2	no	—
245	C₂²×C₄₇	—	2	2	no	—
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	4	16	no	—
248	C₂²×C₄₇	—	4	2	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	—	4	2	no	—
252	C₂²×C₄₇	—	4	2	no	—
253	C₂²×C₄₇	—	4	2	no	—
254	C₂²×C₄₇	—	4	2	no	—
255	C₂²×C₄₇	—	8	2	no	—
256	C₂²×C₄₇	—	8	2	no	—
257	C₂²×C₄₇	#417	1	4	yes	—
258	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₄₇	#534	1	2	yes	—
260	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
262	C₂²×C₄₇	#575	1	2	yes	—
263	C₄×C₄₇	—	2	2	no	—
264	C₄×C₄₇	—	2	2	no	—
265	C₄×C₄₇	—	2	2	no	—
266	C₄×C₄₇	—	4	2	no	—
267	C₄×C₄₇	—	4	2	no	—
268	C₄×C₄₇	—	4	2	no	—
269	C₄×C₄₇	—	8	4	no	—
270	C₄×C₄₇	#518	1	2	yes	—
271	C₄×C₄₇	#534	1	2	yes	—
272	C₂×#525	C₂×C₄₇	1	1	yes	characteristic
273	C₂×#407	C₂×C₄₇	1	1	yes	characteristic, complemented
274	C₂×#380	C₂×C₄₇	1	1	yes	characteristic, complemented
275	#1895	C₂×C₄₇	1	2	yes	complemented
276	#1894	C₂×C₄₇	1	2	yes	complemented
277	#1874	C₂×C₄₇	1	2	yes	complemented
278	#1872	C₂×C₄₇	1	2	yes	complemented
279	#1825	C₂×C₄₇	1	2	yes	complemented
280	#1788	C₂×C₄₇	1	2	yes	complemented
281	C₂×C₄₇	—	2	4	no	—
282	C₂×C₄₇	—	4	2	no	—
283	C₂×C₄₇	—	4	2	no	—
284	C₂×C₄₇	—	8	2	no	—
285	C₂×C₄₇	#2308	1	1	yes	characteristic
286	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
287	C₂×C₄₇	#2896	1	1	yes	characteristic
288	C₂×C₄₇	#3194	1	2	yes	—
289	C₂×C₄₇	#3196	1	2	yes	—
290	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
291	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
292	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
293	#525	—	2	4	no	—
294	#525	C₄×C₄₇	1	8	yes	complemented
295	C₂×#123	—	2	1	no	—
296	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
297	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
298	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
299	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
300	C₂×#120	—	2	1	no	—
301	C₂×C₄×D₄	—	2	1	no	—
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
305	C₂²×C₂²⋊C₄	—	2	1	no	—
306	C₂×#103	C₂²×C₄₇	1	4	yes	complemented
307	C₂×#102	C₂²×C₄₇	1	4	yes	complemented
308	#407	—	2	4	no	—
309	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
311	#380	—	2	1	no	—
312	#380	—	2	1	no	—
313	#380	C₂²×C₄₇	1	2	yes	—
314	#380	C₂²×C₄₇	1	2	yes	—
315	C₂×#95	—	2	1	no	—
316	#340	C₂²×C₄₇	1	4	yes	complemented
317	#340	C₂²×C₄₇	1	4	yes	complemented
318	C₄₇	#21769	1	1	yes	characteristic, direct product factor, Sylow
319	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	4	4	no	—
322	C₂×#41	C₂×C₄×C₄₇	1	4	yes	complemented
323	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	—	2	2	no	—
330	C₂³×C₄	—	4	4	no	—
331	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
332	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
333	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
334	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
335	C₂³×C₄	D₄×C₄₇	1	4	yes	—
336	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
339	C₂×M₁₆	—	2	4	no	—
340	C₂×M₁₆	—	4	4	no	—
341	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
342	#123	—	2	8	no	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
346	C₂²⋊Q₈	C₂×C₄×C₄₇	1	4	yes	complemented
347	#121	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	C₂×C₄×C₄₇	1	4	yes	—
350	#121	C₂×C₄×C₄₇	1	4	yes	complemented
351	#120	—	2	8	no	—
352	C₄×D₄	—	2	8	no	—
353	C₄×D₄	—	2	8	no	—
354	#117	—	2	2	no	—
355	#117	C₂×C₄×C₄₇	1	4	yes	complemented
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	4	4	no	—
360	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	4	4	no	—
371	C₂×C₄²	—	2	1	no	—
372	#103	—	4	4	no	—
373	#102	—	4	4	no	—
374	C₂²⋊C₈	—	2	4	no	—
375	C₂²⋊C₈	—	2	4	no	—
376	#95	—	2	2	no	—
377	#95	—	2	2	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	4	2	no	—
382	C₂⁴	—	4	2	no	—
383	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
384	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
385	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
386	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
387	#41	—	4	8	no	—
388	#41	—	4	8	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	—	4	8	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	—	4	4	no	—
419	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
420	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
421	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
422	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
423	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
424	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
432	M₁₆	—	4	8	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	4	no	—
435	C₂×C₈	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	4	4	no	—
443	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
444	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₄²	—	2	4	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	4	no	—
466	C₂³	—	4	4	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	4	8	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	2	no	—
473	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
474	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
475	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
476	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
477	C₂³	#137×C₄₇	1	2	yes	—
478	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
479	Q₈	—	2	4	no	—
480	Q₈	—	4	2	no	—
481	D₄	—	2	4	no	—
482	D₄	—	4	8	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	8	8	no	—
510	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
511	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
512	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
513	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
515	C₂×C₄	H(5,𝔽₂)×C₄₇	1	4	yes	—
516	C₈	—	4	4	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	4	16	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	8	2	no	—
536	C₂²	—	8	2	no	—
537	C₂²	C₄₇×#417	1	4	yes	—
538	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
539	C₂²	C₄₇×#534	1	2	yes	—
540	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
541	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
542	C₂²	C₄₇×#575	1	2	yes	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	8	4	no	—
550	C₄	C₄₇×#518	1	2	yes	—
551	C₄	C₄₇×#534	1	2	yes	—
552	C₂	—	2	4	no	—
553	C₂	—	4	2	no	—
554	C₂	—	4	2	no	—
555	C₂	—	8	2	no	—
556	C₂	C₄₇×#2308	1	1	yes	characteristic
557	C₂	C₂×C₄₇×#417	1	1	yes	characteristic
558	C₂	C₄₇×#2896	1	1	yes	characteristic
559	C₂	C₄₇×#3194	1	2	yes	—
560	C₂	C₄₇×#3196	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#407	C₂	semidirect
3. C₂×C₄₇×#380	C₂	semidirect
4. C₄₇×#1895	C₂	semidirect
5. C₄₇×#1894	C₂	semidirect
6. C₄₇×#1874	C₂	semidirect
7. C₄₇×#1872	C₂	semidirect
8. C₄₇×#1825	C₂	semidirect
9. C₄₇×#1788	C₂	semidirect
14. C₄₇×#525	C₄	semidirect
26. C₂×#103×C₄₇	C₂²	semidirect
27. C₂×#102×C₄₇	C₂²	semidirect
36. C₄₇×#340	C₂²	semidirect
37. C₄₇×#340	C₂²	semidirect
41. C₂×#41×C₄₇	C₂×C₄	semidirect
65. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
69. #121×C₄₇	C₂×C₄	semidirect
74. #117×C₄₇	C₂×C₄	semidirect
236. #21769	C₄₇	direct (N × H)
273. C₂×#407	C₂×C₄₇	semidirect
274. C₂×#380	C₂×C₄₇	semidirect
275. #1895	C₂×C₄₇	semidirect
276. #1894	C₂×C₄₇	semidirect
277. #1874	C₂×C₄₇	semidirect
278. #1872	C₂×C₄₇	semidirect
279. #1825	C₂×C₄₇	semidirect
280. #1788	C₂×C₄₇	semidirect
294. #525	C₄×C₄₇	semidirect
306. C₂×#103	C₂²×C₄₇	semidirect
307. C₂×#102	C₂²×C₄₇	semidirect
316. #340	C₂²×C₄₇	semidirect
317. #340	C₂²×C₄₇	semidirect
318. C₄₇	#21769	direct (N × H)
322. C₂×#41	C₂×C₄×C₄₇	semidirect
346. C₂²⋊Q₈	C₂×C₄×C₄₇	semidirect
350. #121	C₂×C₄×C₄₇	semidirect
355. #117	C₂×C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#525	2
C₂×C₄₇×#407	2
C₂×C₄₇×#380	2
C₄₇×#1895	2
C₄₇×#1894	2
C₄₇×#1874	2
C₄₇×#1872	2
C₄₇×#1825	2
C₄₇×#1788	2
#21769	47

Subgroups — C47×#21769 #26061467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21769 #26061467