Subgroups — C₄₇×#23883 #26063581

Order 12032.

1696 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3025	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3022	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#3005	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2010	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2009	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1909	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1904	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1891	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1795	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#585	C₂²	1	1	yes	characteristic
13	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
15	C₄₇×#577	—	2	4	no	—
16	C₄₇×#576	—	2	4	no	—
17	C₄₇×#575	—	2	2	no	—
18	C₄₇×#575	C₂²	1	2	yes	—
19	C₂×#137×C₄₇	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
21	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
22	C₄₇×#568	C₂²	1	1	yes	characteristic
23	C₄₇×#547	—	2	2	no	—
24	C₄₇×#547	—	2	2	no	—
25	C₄₇×#546	—	2	2	no	—
26	C₄₇×#546	—	2	2	no	—
27	C₄₇×#536	C₂²	1	1	yes	characteristic
28	C₄₇×#536	C₂²	1	1	yes	characteristic, complemented
29	C₄₇×#534	—	2	2	no	—
30	C₄₇×#525	C₂²	1	1	yes	characteristic
31	C₄₇×#525	C₂²	1	1	yes	characteristic, complemented
32	C₄₇×#525	C₂²	1	2	yes	complemented
33	C₂×#123×C₄₇	—	2	2	no	—
34	C₄₇×#518	C₂²	1	1	yes	characteristic, complemented
35	C₄₇×#458	—	2	2	no	—
36	C₄₇×B(4,𝔽₂)	—	2	2	no	—
37	C₄₇×#456	—	2	2	no	—
38	C₄₇×#455	—	2	2	no	—
39	C₄₇×#452	—	2	4	no	—
40	C₄₇×#449	—	2	4	no	—
41	C₄₇×#421	C₂²	1	2	yes	complemented
42	C₄₇×#421	C₂²	1	2	yes	complemented
43	C₄₇×#419	C₂²	1	2	yes	complemented
44	C₄₇×#418	C₂²	1	2	yes	complemented
45	C₄₇×#413	C₂²	1	1	yes	characteristic
46	C₄₇×#410	C₂²	1	1	yes	characteristic
47	C₄₇×#410	C₂²	1	2	yes	complemented
48	C₄₇×#407	C₂²	1	2	yes	complemented
49	C₄₇×#344	C₂²	1	2	yes	complemented
50	C₄₇×H(3,ℤ/4)	C₂²	1	2	yes	complemented
51	2₋¹⁺⁴×C₄₇	—	2	2	no	—
52	2₋¹⁺⁴×C₄₇	—	2	1	no	—
53	H(5,𝔽₂)×C₄₇	—	2	2	no	—
54	H(5,𝔽₂)×C₄₇	—	2	4	no	—
55	H(5,𝔽₂)×C₄₇	—	2	2	no	—
56	H(5,𝔽₂)×C₄₇	—	2	1	no	—
57	H(5,𝔽₂)×C₄₇	—	4	2	no	—
58	C₂×#41×C₄₇	—	2	2	no	—
59	C₂×#41×C₄₇	—	2	1	no	—
60	C₂×#41×C₄₇	—	2	2	no	—
61	C₂×#41×C₄₇	—	2	4	no	—
62	C₂×#41×C₄₇	—	2	2	no	—
63	C₂×#41×C₄₇	—	4	2	no	—
64	C₂×#41×C₄₇	—	4	2	no	—
65	C₂×#41×C₄₇	D₄	1	2	yes	complemented
66	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×#41×C₄₇	C₂³	1	2	yes	—
68	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₄₇	—	2	1	no	—
71	C₂²×D₄×C₄₇	—	2	2	no	—
72	C₂²×D₄×C₄₇	—	2	1	no	—
73	C₂²×D₄×C₄₇	D₄	1	2	yes	complemented
74	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	—	2	1	no	—
76	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
77	#137×C₄₇	—	2	4	no	—
78	#137×C₄₇	—	2	2	no	—
79	#137×C₄₇	—	2	2	no	—
80	#137×C₄₇	—	2	4	no	—
81	#137×C₄₇	—	4	2	no	—
82	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
83	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
84	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
85	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
86	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
87	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
88	#135×C₄₇	—	2	8	no	—
89	#135×C₄₇	—	2	4	no	—
90	C₂×Q₁₆×C₄₇	—	2	2	no	—
91	C₂×SD₁₆×C₄₇	—	2	4	no	—
92	C₂×SD₁₆×C₄₇	—	2	2	no	—
93	C₂×SD₁₆×C₄₇	D₄	1	4	yes	complemented
94	C₂×D₈×C₄₇	—	2	4	no	—
95	C₂×D₈×C₄₇	D₄	1	4	yes	complemented
96	#131×C₄₇	—	2	4	no	—
97	C₂×M₁₆×C₄₇	—	2	2	no	—
98	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
99	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
100	C₄⋊Q₈×C₄₇	—	2	1	no	—
101	C₄⋊Q₈×C₄₇	D₄	1	2	yes	complemented
102	#124×C₄₇	—	2	1	no	—
103	#124×C₄₇	D₄	1	2	yes	complemented
104	#123×C₄₇	—	2	4	no	—
105	#123×C₄₇	—	2	4	no	—
106	#123×C₄₇	—	2	4	no	—
107	#123×C₄₇	—	2	2	no	—
108	#123×C₄₇	—	2	1	no	—
109	#123×C₄₇	—	2	2	no	—
110	#123×C₄₇	—	2	2	no	—
111	#123×C₄₇	D₄	1	2	yes	—
112	C₂²⋊Q₈×C₄₇	—	2	1	no	—
113	C₂²⋊Q₈×C₄₇	—	2	1	no	—
114	C₂²⋊Q₈×C₄₇	—	2	2	no	—
115	C₂²⋊Q₈×C₄₇	—	2	2	no	—
116	C₂²⋊Q₈×C₄₇	—	2	2	no	—
117	#121×C₄₇	—	2	4	no	—
118	#121×C₄₇	—	2	4	no	—
119	#121×C₄₇	—	2	1	no	—
120	#121×C₄₇	—	2	1	no	—
121	#121×C₄₇	—	2	2	no	—
122	#120×C₄₇	—	2	4	no	—
123	#120×C₄₇	—	2	1	no	—
124	#120×C₄₇	—	2	2	no	—
125	#120×C₄₇	D₄	1	2	yes	—
126	C₄×D₄×C₄₇	—	2	2	no	—
127	C₄×D₄×C₄₇	—	2	2	no	—
128	C₄×D₄×C₄₇	—	2	2	no	—
129	C₄×D₄×C₄₇	—	2	2	no	—
130	C₄×D₄×C₄₇	—	4	2	no	—
131	#117×C₄₇	C₂³	1	2	yes	—
132	#117×C₄₇	C₂³	1	1	yes	characteristic
133	#117×C₄₇	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
137	#104×C₄₇	—	2	4	no	—
138	#104×C₄₇	—	4	2	no	—
139	#103×C₄₇	—	2	4	no	—
140	#102×C₄₇	—	2	4	no	—
141	#101×C₄₇	—	2	1	no	—
142	#100×C₄₇	—	2	1	no	—
143	#99×C₄₇	—	2	2	no	—
144	#99×C₄₇	—	2	4	no	—
145	C₂²⋊C₈×C₄₇	—	2	4	no	—
146	C₂⁴×C₄₇	—	2	1	no	—
147	C₂⁴×C₄₇	—	2	2	no	—
148	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
149	#41×C₄₇	—	2	2	no	—
150	#41×C₄₇	—	2	2	no	—
151	#41×C₄₇	—	2	4	no	—
152	#41×C₄₇	—	2	4	no	—
153	#41×C₄₇	—	2	2	no	—
154	#41×C₄₇	—	2	2	no	—
155	#41×C₄₇	—	2	2	no	—
156	#41×C₄₇	—	2	2	no	—
157	#41×C₄₇	—	2	2	no	—
158	#41×C₄₇	—	2	2	no	—
159	#41×C₄₇	—	4	2	no	—
160	#41×C₄₇	—	4	4	no	—
161	#41×C₄₇	—	4	2	no	—
162	#41×C₄₇	—	4	8	no	—
163	#41×C₄₇	—	4	4	no	—
164	#41×C₄₇	—	4	2	no	—
165	#41×C₄₇	—	4	2	no	—
166	#41×C₄₇	—	4	4	no	—
167	#41×C₄₇	—	4	4	no	—
168	#41×C₄₇	—	4	2	no	—
169	C₂×Q₈×C₄₇	—	2	1	no	—
170	C₂×Q₈×C₄₇	—	2	2	no	—
171	C₂×Q₈×C₄₇	—	2	2	no	—
172	C₂×Q₈×C₄₇	—	2	2	no	—
173	C₂×Q₈×C₄₇	—	4	2	no	—
174	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
175	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
177	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₄₇	—	2	2	no	—
179	C₂×D₄×C₄₇	—	2	4	no	—
180	C₂×D₄×C₄₇	—	2	4	no	—
181	C₂×D₄×C₄₇	—	2	2	no	—
182	C₂×D₄×C₄₇	—	2	1	no	—
183	C₂×D₄×C₄₇	—	2	2	no	—
184	C₂×D₄×C₄₇	—	2	2	no	—
185	C₂×D₄×C₄₇	—	2	2	no	—
186	C₂×D₄×C₄₇	—	2	2	no	—
187	C₂×D₄×C₄₇	—	2	1	no	—
188	C₂×D₄×C₄₇	—	2	2	no	—
189	C₂×D₄×C₄₇	—	4	2	no	—
190	C₂×D₄×C₄₇	—	4	4	no	—
191	C₂×D₄×C₄₇	—	4	2	no	—
192	C₂×D₄×C₄₇	—	4	8	no	—
193	C₂×D₄×C₄₇	—	4	4	no	—
194	C₂×D₄×C₄₇	—	4	4	no	—
195	C₂×D₄×C₄₇	—	4	2	no	—
196	C₂×D₄×C₄₇	—	4	2	no	—
197	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
200	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₄₇	—	2	4	no	—
204	C₂²×C₄×C₄₇	—	2	1	no	—
205	C₂²×C₄×C₄₇	—	2	4	no	—
206	C₂²×C₄×C₄₇	—	2	2	no	—
207	C₂²×C₄×C₄₇	—	2	1	no	—
208	C₂²×C₄×C₄₇	—	2	1	no	—
209	C₂²×C₄×C₄₇	—	2	1	no	—
210	C₂²×C₄×C₄₇	—	2	2	no	—
211	C₂²×C₄×C₄₇	—	2	2	no	—
212	C₂²×C₄×C₄₇	—	2	2	no	—
213	C₂²×C₄×C₄₇	—	4	4	no	—
214	C₂²×C₄×C₄₇	—	4	2	no	—
215	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
218	Q₁₆×C₄₇	—	2	4	no	—
219	Q₁₆×C₄₇	—	4	4	no	—
220	SD₁₆×C₄₇	—	2	4	no	—
221	SD₁₆×C₄₇	—	2	4	no	—
222	SD₁₆×C₄₇	—	2	8	no	—
223	SD₁₆×C₄₇	—	4	4	no	—
224	D₈×C₄₇	—	2	4	no	—
225	D₈×C₄₇	—	2	8	no	—
226	M₁₆×C₄₇	—	2	4	no	—
227	M₁₆×C₄₇	—	2	2	no	—
228	M₁₆×C₄₇	—	2	2	no	—
229	M₁₆×C₄₇	—	2	2	no	—
230	M₁₆×C₄₇	—	2	2	no	—
231	C₂×C₈×C₄₇	—	2	4	no	—
232	C₂×C₈×C₄₇	—	2	2	no	—
233	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
234	C₄⋊C₄×C₄₇	—	2	2	no	—
235	C₄⋊C₄×C₄₇	—	2	4	no	—
236	C₄⋊C₄×C₄₇	—	2	2	no	—
237	C₄⋊C₄×C₄₇	—	2	4	no	—
238	C₄⋊C₄×C₄₇	—	2	1	no	—
239	C₄⋊C₄×C₄₇	—	2	1	no	—
240	C₄⋊C₄×C₄₇	—	2	2	no	—
241	C₄⋊C₄×C₄₇	—	4	2	no	—
242	C₂²⋊C₄×C₄₇	—	2	2	no	—
243	C₂²⋊C₄×C₄₇	—	2	4	no	—
244	C₂²⋊C₄×C₄₇	—	2	4	no	—
245	C₂²⋊C₄×C₄₇	—	2	2	no	—
246	C₂²⋊C₄×C₄₇	—	2	2	no	—
247	C₂²⋊C₄×C₄₇	—	2	4	no	—
248	C₂²⋊C₄×C₄₇	—	2	1	no	—
249	C₂²⋊C₄×C₄₇	—	2	2	no	—
250	C₂²⋊C₄×C₄₇	—	2	2	no	—
251	C₂²⋊C₄×C₄₇	—	4	2	no	—
252	C₂²⋊C₄×C₄₇	—	4	2	no	—
253	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
254	C₄²×C₄₇	—	2	1	no	—
255	C₄²×C₄₇	—	2	2	no	—
256	C₄²×C₄₇	C₂×D₄	1	2	yes	—
257	C₂³×C₄₇	—	2	2	no	—
258	C₂³×C₄₇	—	2	4	no	—
259	C₂³×C₄₇	—	2	1	no	—
260	C₂³×C₄₇	—	2	1	no	—
261	C₂³×C₄₇	—	2	2	no	—
262	C₂³×C₄₇	—	2	2	no	—
263	C₂³×C₄₇	—	4	4	no	—
264	C₂³×C₄₇	—	4	2	no	—
265	C₂³×C₄₇	—	8	1	no	—
266	C₂³×C₄₇	—	8	2	no	—
267	C₂³×C₄₇	—	8	4	no	—
268	C₂³×C₄₇	#120	1	2	yes	—
269	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
270	Q₈×C₄₇	—	2	2	no	—
271	Q₈×C₄₇	—	2	2	no	—
272	Q₈×C₄₇	—	2	1	no	—
273	Q₈×C₄₇	—	2	1	no	—
274	Q₈×C₄₇	—	2	4	no	—
275	Q₈×C₄₇	—	2	2	no	—
276	Q₈×C₄₇	—	4	2	no	—
277	Q₈×C₄₇	—	4	1	no	—
278	Q₈×C₄₇	—	4	1	no	—
279	D₄×C₄₇	—	2	4	no	—
280	D₄×C₄₇	—	2	2	no	—
281	D₄×C₄₇	—	2	1	no	—
282	D₄×C₄₇	—	2	2	no	—
283	D₄×C₄₇	—	2	1	no	—
284	D₄×C₄₇	—	2	4	no	—
285	D₄×C₄₇	—	2	2	no	—
286	D₄×C₄₇	—	2	2	no	—
287	D₄×C₄₇	—	4	4	no	—
288	D₄×C₄₇	—	4	2	no	—
289	D₄×C₄₇	—	4	4	no	—
290	D₄×C₄₇	—	4	8	no	—
291	D₄×C₄₇	—	4	4	no	—
292	D₄×C₄₇	—	4	2	no	—
293	D₄×C₄₇	—	4	2	no	—
294	D₄×C₄₇	—	4	2	no	—
295	D₄×C₄₇	—	8	2	no	—
296	D₄×C₄₇	—	8	2	no	—
297	D₄×C₄₇	—	8	4	no	—
298	D₄×C₄₇	#120	1	4	yes	—
299	C₂×C₄×C₄₇	—	2	2	no	—
300	C₂×C₄×C₄₇	—	2	2	no	—
301	C₂×C₄×C₄₇	—	2	2	no	—
302	C₂×C₄×C₄₇	—	2	2	no	—
303	C₂×C₄×C₄₇	—	2	1	no	—
304	C₂×C₄×C₄₇	—	2	2	no	—
305	C₂×C₄×C₄₇	—	2	1	no	—
306	C₂×C₄×C₄₇	—	2	2	no	—
307	C₂×C₄×C₄₇	—	2	2	no	—
308	C₂×C₄×C₄₇	—	4	4	no	—
309	C₂×C₄×C₄₇	—	4	4	no	—
310	C₂×C₄×C₄₇	—	4	8	no	—
311	C₂×C₄×C₄₇	—	4	2	no	—
312	C₂×C₄×C₄₇	—	4	2	no	—
313	C₂×C₄×C₄₇	—	4	1	no	—
314	C₂×C₄×C₄₇	—	4	1	no	—
315	C₂×C₄×C₄₇	—	4	2	no	—
316	C₂×C₄×C₄₇	—	4	2	no	—
317	C₂×C₄×C₄₇	—	4	2	no	—
318	C₂×C₄×C₄₇	—	4	2	no	—
319	C₂×C₄×C₄₇	—	4	2	no	—
320	C₂×C₄×C₄₇	—	8	4	no	—
321	C₂×C₄×C₄₇	#120	1	2	yes	—
322	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
326	C₈×C₄₇	—	2	4	no	—
327	C₈×C₄₇	—	4	2	no	—
328	#23883	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂²×C₄₇	—	2	2	no	—
330	C₂²×C₄₇	—	2	4	no	—
331	C₂²×C₄₇	—	4	1	no	—
332	C₂²×C₄₇	—	4	2	no	—
333	C₂²×C₄₇	—	4	4	no	—
334	C₂²×C₄₇	—	4	1	no	—
335	C₂²×C₄₇	—	4	1	no	—
336	C₂²×C₄₇	—	4	2	no	—
337	C₂²×C₄₇	—	4	2	no	—
338	C₂²×C₄₇	—	4	2	no	—
339	C₂²×C₄₇	—	4	2	no	—
340	C₂²×C₄₇	—	4	1	no	—
341	C₂²×C₄₇	—	4	1	no	—
342	C₂²×C₄₇	—	8	4	no	—
343	C₂²×C₄₇	—	8	2	no	—
344	C₂²×C₄₇	—	16	4	no	—
345	C₂²×C₄₇	—	16	2	no	—
346	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
347	C₂²×C₄₇	D₄²	1	2	yes	—
348	C₄×C₄₇	—	2	2	no	—
349	C₄×C₄₇	—	4	2	no	—
350	C₄×C₄₇	—	4	2	no	—
351	C₄×C₄₇	—	4	1	no	—
352	C₄×C₄₇	—	4	1	no	—
353	C₄×C₄₇	—	4	2	no	—
354	C₄×C₄₇	—	4	2	no	—
355	C₄×C₄₇	—	8	2	no	—
356	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
357	C₄×C₄₇	#534	1	1	yes	characteristic
358	C₄×C₄₇	D₄²	1	2	yes	—
359	#3585	C₂×C₄₇	1	1	yes	characteristic, complemented
360	#3485	C₂×C₄₇	1	1	yes	characteristic, complemented
361	#3025	C₂×C₄₇	1	1	yes	characteristic, complemented
362	#3022	C₂×C₄₇	1	1	yes	characteristic, complemented
363	#3005	C₂×C₄₇	1	2	yes	complemented
364	#2010	C₂×C₄₇	1	2	yes	complemented
365	#2009	C₂×C₄₇	1	2	yes	complemented
366	#1909	C₂×C₄₇	1	1	yes	characteristic, complemented
367	#1904	C₂×C₄₇	1	2	yes	complemented
368	#1891	C₂×C₄₇	1	1	yes	characteristic, complemented
369	#1795	C₂×C₄₇	1	1	yes	characteristic, complemented
370	C₂×C₄₇	—	2	1	no	—
371	C₂×C₄₇	—	2	2	no	—
372	C₂×C₄₇	—	4	4	no	—
373	C₂×C₄₇	—	4	2	no	—
374	C₂×C₄₇	—	8	1	no	—
375	C₂×C₄₇	—	8	1	no	—
376	C₂×C₄₇	—	8	2	no	—
377	C₂×C₄₇	#2403	1	1	yes	characteristic
378	#585	C₂²×C₄₇	1	1	yes	characteristic
379	C₂×H(5,𝔽₂)	C₂²×C₄₇	1	1	yes	characteristic
380	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic, complemented
381	#577	—	2	4	no	—
382	#576	—	2	4	no	—
383	#575	—	2	2	no	—
384	#575	C₂²×C₄₇	1	2	yes	—
385	C₂×#137	C₂²×C₄₇	1	2	yes	complemented
386	C₂×AGL(1,ℤ/8)	—	2	2	no	—
387	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	—
388	#568	C₂²×C₄₇	1	1	yes	characteristic
389	#547	—	2	2	no	—
390	#547	—	2	2	no	—
391	#546	—	2	2	no	—
392	#546	—	2	2	no	—
393	#536	C₂²×C₄₇	1	1	yes	characteristic
394	#536	C₂²×C₄₇	1	1	yes	characteristic, complemented
395	#534	—	2	2	no	—
396	#525	C₂²×C₄₇	1	1	yes	characteristic
397	#525	C₂²×C₄₇	1	1	yes	characteristic, complemented
398	#525	C₂²×C₄₇	1	2	yes	complemented
399	C₂×#123	—	2	2	no	—
400	#518	C₂²×C₄₇	1	1	yes	characteristic, complemented
401	#458	—	2	2	no	—
402	B(4,𝔽₂)	—	2	2	no	—
403	#456	—	2	2	no	—
404	#455	—	2	2	no	—
405	#452	—	2	4	no	—
406	#449	—	2	4	no	—
407	#421	C₂²×C₄₇	1	2	yes	complemented
408	#421	C₂²×C₄₇	1	2	yes	complemented
409	#419	C₂²×C₄₇	1	2	yes	complemented
410	#418	C₂²×C₄₇	1	2	yes	complemented
411	#413	C₂²×C₄₇	1	1	yes	characteristic
412	#410	C₂²×C₄₇	1	1	yes	characteristic
413	#410	C₂²×C₄₇	1	2	yes	complemented
414	#407	C₂²×C₄₇	1	2	yes	complemented
415	#344	C₂²×C₄₇	1	2	yes	complemented
416	H(3,ℤ/4)	C₂²×C₄₇	1	2	yes	complemented
417	C₄₇	#23883	1	1	yes	characteristic, direct product factor, Sylow
418	2₋¹⁺⁴	—	2	2	no	—
419	2₋¹⁺⁴	—	2	1	no	—
420	H(5,𝔽₂)	—	2	2	no	—
421	H(5,𝔽₂)	—	2	4	no	—
422	H(5,𝔽₂)	—	2	2	no	—
423	H(5,𝔽₂)	—	2	1	no	—
424	H(5,𝔽₂)	—	4	2	no	—
425	C₂×#41	—	2	2	no	—
426	C₂×#41	—	2	1	no	—
427	C₂×#41	—	2	2	no	—
428	C₂×#41	—	2	4	no	—
429	C₂×#41	—	2	2	no	—
430	C₂×#41	—	4	2	no	—
431	C₂×#41	—	4	2	no	—
432	C₂×#41	D₄×C₄₇	1	2	yes	complemented
433	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
434	C₂×#41	C₂³×C₄₇	1	2	yes	—
435	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
436	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
437	C₂²×D₄	—	2	1	no	—
438	C₂²×D₄	—	2	2	no	—
439	C₂²×D₄	—	2	1	no	—
440	C₂²×D₄	D₄×C₄₇	1	2	yes	complemented
441	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
444	#137	—	2	4	no	—
445	#137	—	2	2	no	—
446	#137	—	2	2	no	—
447	#137	—	2	4	no	—
448	#137	—	4	2	no	—
449	AGL(1,ℤ/8)	—	2	8	no	—
450	AGL(1,ℤ/8)	—	2	4	no	—
451	AGL(1,ℤ/8)	—	2	2	no	—
452	AGL(1,ℤ/8)	—	2	4	no	—
453	AGL(1,ℤ/8)	—	2	4	no	—
454	AGL(1,ℤ/8)	—	2	2	no	—
455	#135	—	2	8	no	—
456	#135	—	2	4	no	—
457	C₂×Q₁₆	—	2	2	no	—
458	C₂×SD₁₆	—	2	4	no	—
459	C₂×SD₁₆	—	2	2	no	—
460	C₂×SD₁₆	D₄×C₄₇	1	4	yes	complemented
461	C₂×D₈	—	2	4	no	—
462	C₂×D₈	D₄×C₄₇	1	4	yes	complemented
463	#131	—	2	4	no	—
464	C₂×M₁₆	—	2	2	no	—
465	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
466	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
467	C₄⋊Q₈	—	2	1	no	—
468	C₄⋊Q₈	D₄×C₄₇	1	2	yes	complemented
469	#124	—	2	1	no	—
470	#124	D₄×C₄₇	1	2	yes	complemented
471	#123	—	2	4	no	—
472	#123	—	2	4	no	—
473	#123	—	2	4	no	—
474	#123	—	2	2	no	—
475	#123	—	2	1	no	—
476	#123	—	2	2	no	—
477	#123	—	2	2	no	—
478	#123	D₄×C₄₇	1	2	yes	—
479	C₂²⋊Q₈	—	2	1	no	—
480	C₂²⋊Q₈	—	2	1	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	#121	—	2	4	no	—
485	#121	—	2	4	no	—
486	#121	—	2	1	no	—
487	#121	—	2	1	no	—
488	#121	—	2	2	no	—
489	#120	—	2	4	no	—
490	#120	—	2	1	no	—
491	#120	—	2	2	no	—
492	#120	D₄×C₄₇	1	2	yes	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	4	2	no	—
498	#117	C₂³×C₄₇	1	2	yes	—
499	#117	C₂³×C₄₇	1	1	yes	characteristic
500	#117	C₂³×C₄₇	1	1	yes	characteristic
501	C₂×C₄⋊C₄	—	2	4	no	—
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₂²⋊C₄	—	2	2	no	—
504	#104	—	2	4	no	—
505	#104	—	4	2	no	—
506	#103	—	2	4	no	—
507	#102	—	2	4	no	—
508	#101	—	2	1	no	—
509	#100	—	2	1	no	—
510	#99	—	2	2	no	—
511	#99	—	2	4	no	—
512	C₂²⋊C₈	—	2	4	no	—
513	C₂⁴	—	2	1	no	—
514	C₂⁴	—	2	2	no	—
515	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
516	#41	—	2	2	no	—
517	#41	—	2	2	no	—
518	#41	—	2	4	no	—
519	#41	—	2	4	no	—
520	#41	—	2	2	no	—
521	#41	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	—	4	2	no	—
527	#41	—	4	4	no	—
528	#41	—	4	2	no	—
529	#41	—	4	8	no	—
530	#41	—	4	4	no	—
531	#41	—	4	2	no	—
532	#41	—	4	2	no	—
533	#41	—	4	4	no	—
534	#41	—	4	4	no	—
535	#41	—	4	2	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	2	no	—
540	C₂×Q₈	—	4	2	no	—
541	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
542	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
543	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
544	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	8	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
565	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
566	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
567	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
568	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
569	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	4	4	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
585	Q₁₆	—	2	4	no	—
586	Q₁₆	—	4	4	no	—
587	SD₁₆	—	2	4	no	—
588	SD₁₆	—	2	4	no	—
589	SD₁₆	—	2	8	no	—
590	SD₁₆	—	4	4	no	—
591	D₈	—	2	4	no	—
592	D₈	—	2	8	no	—
593	M₁₆	—	2	4	no	—
594	M₁₆	—	2	2	no	—
595	M₁₆	—	2	2	no	—
596	M₁₆	—	2	2	no	—
597	M₁₆	—	2	2	no	—
598	C₂×C₈	—	2	4	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	2	no	—
623	C₄²	C₂×D₄×C₄₇	1	2	yes	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	4	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	4	4	no	—
631	C₂³	—	4	2	no	—
632	C₂³	—	8	1	no	—
633	C₂³	—	8	2	no	—
634	C₂³	—	8	4	no	—
635	C₂³	#120×C₄₇	1	2	yes	—
636	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
637	Q₈	—	2	2	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	2	1	no	—
640	Q₈	—	2	1	no	—
641	Q₈	—	2	4	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	4	2	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	D₄	—	2	4	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	1	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	1	no	—
651	D₄	—	2	4	no	—
652	D₄	—	2	2	no	—
653	D₄	—	2	2	no	—
654	D₄	—	4	4	no	—
655	D₄	—	4	2	no	—
656	D₄	—	4	4	no	—
657	D₄	—	4	8	no	—
658	D₄	—	4	4	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	2	no	—
661	D₄	—	4	2	no	—
662	D₄	—	8	2	no	—
663	D₄	—	8	2	no	—
664	D₄	—	8	4	no	—
665	D₄	#120×C₄₇	1	4	yes	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	8	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	8	4	no	—
688	C₂×C₄	#120×C₄₇	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
692	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
693	C₈	—	2	4	no	—
694	C₈	—	4	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	8	4	no	—
709	C₂²	—	8	2	no	—
710	C₂²	—	16	4	no	—
711	C₂²	—	16	2	no	—
712	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
713	C₂²	D₄²×C₄₇	1	2	yes	—
714	C₄	—	2	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	8	2	no	—
722	C₄	C₂×#120×C₄₇	1	1	yes	characteristic
723	C₄	C₄₇×#534	1	1	yes	characteristic
724	C₄	D₄²×C₄₇	1	2	yes	—
725	C₂	—	2	1	no	—
726	C₂	—	2	2	no	—
727	C₂	—	4	4	no	—
728	C₂	—	4	2	no	—
729	C₂	—	8	1	no	—
730	C₂	—	8	1	no	—
731	C₂	—	8	2	no	—
732	C₂	C₄₇×#2403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₇	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₇ ◁ C₂²×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3585	C₂	semidirect
2. C₄₇×#3485	C₂	semidirect
3. C₄₇×#3025	C₂	semidirect
4. C₄₇×#3022	C₂	semidirect
5. C₄₇×#3005	C₂	semidirect
6. C₄₇×#2010	C₂	semidirect
7. C₄₇×#2009	C₂	semidirect
8. C₄₇×#1909	C₂	semidirect
9. C₄₇×#1904	C₂	semidirect
10. C₄₇×#1891	C₂	semidirect
11. C₄₇×#1795	C₂	semidirect
14. C₂²×#41×C₄₇	C₂²	semidirect
19. C₂×#137×C₄₇	C₂²	semidirect
28. C₄₇×#536	C₂²	semidirect
31. C₄₇×#525	C₂²	semidirect
32. C₄₇×#525	C₂²	semidirect
34. C₄₇×#518	C₂²	semidirect
41. C₄₇×#421	C₂²	semidirect
42. C₄₇×#421	C₂²	semidirect
43. C₄₇×#419	C₂²	semidirect
44. C₄₇×#418	C₂²	semidirect
47. C₄₇×#410	C₂²	semidirect
48. C₄₇×#407	C₂²	semidirect
49. C₄₇×#344	C₂²	semidirect
50. C₄₇×H(3,ℤ/4)	C₂²	semidirect
65. C₂×#41×C₄₇	D₄	semidirect
73. C₂²×D₄×C₄₇	D₄	semidirect
93. C₂×SD₁₆×C₄₇	D₄	semidirect
95. C₂×D₈×C₄₇	D₄	semidirect
101. C₄⋊Q₈×C₄₇	D₄	semidirect
103. #124×C₄₇	D₄	semidirect
328. #23883	C₄₇	direct (N × H)
359. #3585	C₂×C₄₇	semidirect
360. #3485	C₂×C₄₇	semidirect
361. #3025	C₂×C₄₇	semidirect
362. #3022	C₂×C₄₇	semidirect
363. #3005	C₂×C₄₇	semidirect
364. #2010	C₂×C₄₇	semidirect
365. #2009	C₂×C₄₇	semidirect
366. #1909	C₂×C₄₇	semidirect
367. #1904	C₂×C₄₇	semidirect
368. #1891	C₂×C₄₇	semidirect
369. #1795	C₂×C₄₇	semidirect
380. C₂²×#41	C₂²×C₄₇	semidirect
385. C₂×#137	C₂²×C₄₇	semidirect
394. #536	C₂²×C₄₇	semidirect
397. #525	C₂²×C₄₇	semidirect
398. #525	C₂²×C₄₇	semidirect
400. #518	C₂²×C₄₇	semidirect
407. #421	C₂²×C₄₇	semidirect
408. #421	C₂²×C₄₇	semidirect
409. #419	C₂²×C₄₇	semidirect
410. #418	C₂²×C₄₇	semidirect
413. #410	C₂²×C₄₇	semidirect
414. #407	C₂²×C₄₇	semidirect
415. #344	C₂²×C₄₇	semidirect
416. H(3,ℤ/4)	C₂²×C₄₇	semidirect
417. C₄₇	#23883	direct (N × H)
432. C₂×#41	D₄×C₄₇	semidirect
440. C₂²×D₄	D₄×C₄₇	semidirect
460. C₂×SD₁₆	D₄×C₄₇	semidirect
462. C₂×D₈	D₄×C₄₇	semidirect
468. C₄⋊Q₈	D₄×C₄₇	semidirect
470. #124	D₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3585	2
C₄₇×#3485	2
C₄₇×#3025	2
C₄₇×#3022	2
C₄₇×#3005	2
C₄₇×#2010	2
C₄₇×#2009	2
C₄₇×#1909	2
C₄₇×#1904	2
C₄₇×#1891	2
C₄₇×#1795	2
#23883	47

Subgroups — C47×#23883 #26063581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#23883 #26063581