Subgroups — C₄₇×#23875 #26063573

Order 12032.

1642 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3028	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3020	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3018	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2009	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2005	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1915	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1906	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1884	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1796	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#585	C₂²	1	1	yes	characteristic
13	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic, complemented
15	C₄₇×#578	—	2	4	no	—
16	C₄₇×#577	—	2	4	no	—
17	C₄₇×#575	—	2	2	no	—
18	C₄₇×#575	C₂²	1	2	yes	—
19	C₄₇×#575	C₂²	1	2	yes	—
20	C₂×#137×C₄₇	—	2	2	no	—
21	C₂×#137×C₄₇	C₂²	1	2	yes	—
22	C₄₇×#568	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₄₇	—	2	2	no	—
24	C₄₇×#547	—	2	2	no	—
25	C₄₇×#547	—	2	4	no	—
26	C₄₇×#536	—	2	1	no	—
27	C₄₇×#536	—	2	1	no	—
28	C₄₇×#536	C₂²	1	1	yes	characteristic
29	C₄₇×#536	C₂²	1	2	yes	—
30	C₄₇×#536	C₂²	1	1	yes	characteristic, complemented
31	C₄₇×#532	—	2	1	no	—
32	C₄₇×#532	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
34	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
35	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
36	C₄₇×#458	—	2	4	no	—
37	C₄₇×#456	—	2	4	no	—
38	C₄₇×#456	—	2	1	no	—
39	C₄₇×#455	—	2	1	no	—
40	C₄₇×#454	—	2	4	no	—
41	C₄₇×#454	—	2	1	no	—
42	C₄₇×#453	—	2	1	no	—
43	C₄₇×#421	C₂²	1	2	yes	complemented
44	C₄₇×#421	C₂²	1	2	yes	complemented
45	C₂×#104×C₄₇	C₂²	1	2	yes	—
46	C₄₇×#419	C₂²	1	2	yes	complemented
47	C₄₇×#413	C₂²	1	1	yes	characteristic
48	C₂×#101×C₄₇	C₂²	1	2	yes	complemented
49	C₄₇×#410	C₂²	1	2	yes	—
50	C₄₇×#410	C₂²	1	1	yes	characteristic
51	C₄₇×#344	C₂²	1	2	yes	complemented
52	C₄₇×#339	C₂²	1	2	yes	complemented
53	2₋¹⁺⁴×C₄₇	—	2	4	no	—
54	2₋¹⁺⁴×C₄₇	—	2	2	no	—
55	2₋¹⁺⁴×C₄₇	—	2	4	no	—
56	2₋¹⁺⁴×C₄₇	—	2	1	no	—
57	2₋¹⁺⁴×C₄₇	—	4	2	no	—
58	2₋¹⁺⁴×C₄₇	—	4	2	no	—
59	H(5,𝔽₂)×C₄₇	—	2	2	no	—
60	H(5,𝔽₂)×C₄₇	—	2	2	no	—
61	H(5,𝔽₂)×C₄₇	—	2	1	no	—
62	C₂×#41×C₄₇	—	2	1	no	—
63	C₂×#41×C₄₇	—	2	1	no	—
64	C₂×#41×C₄₇	—	2	2	no	—
65	C₂×#41×C₄₇	—	2	1	no	—
66	C₂×#41×C₄₇	—	2	2	no	—
67	C₂×#41×C₄₇	—	2	2	no	—
68	C₂×#41×C₄₇	—	4	2	no	—
69	C₂×#41×C₄₇	D₄	1	2	yes	—
70	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×#41×C₄₇	C₂³	1	2	yes	—
72	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₄₇	—	2	1	no	—
75	C₂²×Q₈×C₄₇	—	2	1	no	—
76	C₂²×Q₈×C₄₇	—	2	1	no	—
77	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
78	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	#137×C₄₇	—	2	8	no	—
81	#137×C₄₇	—	2	4	no	—
82	#137×C₄₇	—	2	2	no	—
83	#137×C₄₇	—	2	4	no	—
84	#137×C₄₇	—	2	2	no	—
85	#137×C₄₇	—	2	2	no	—
86	#137×C₄₇	—	2	4	no	—
87	#137×C₄₇	D₄	1	4	yes	complemented
88	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
89	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
90	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
91	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
92	AGL(1,ℤ/8)×C₄₇	D₄	1	4	yes	complemented
93	#135×C₄₇	—	2	8	no	—
94	#135×C₄₇	—	2	4	no	—
95	#135×C₄₇	—	4	2	no	—
96	C₂×Q₁₆×C₄₇	—	2	4	no	—
97	C₂×Q₁₆×C₄₇	—	2	2	no	—
98	C₂×SD₁₆×C₄₇	—	2	4	no	—
99	C₂×SD₁₆×C₄₇	—	2	2	no	—
100	#131×C₄₇	—	2	4	no	—
101	C₂×M₁₆×C₄₇	—	2	2	no	—
102	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
103	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₄₇	—	2	4	no	—
105	C₄⋊Q₈×C₄₇	—	2	1	no	—
106	C₄⋊Q₈×C₄₇	—	2	1	no	—
107	C₄⋊Q₈×C₄₇	—	2	2	no	—
108	C₄⋊Q₈×C₄₇	—	2	2	no	—
109	C₄⋊Q₈×C₄₇	—	2	1	no	—
110	C₄⋊Q₈×C₄₇	—	2	1	no	—
111	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
112	#127×C₄₇	D₄	1	1	yes	characteristic
113	#124×C₄₇	—	2	1	no	—
114	#124×C₄₇	—	2	1	no	—
115	#124×C₄₇	—	2	2	no	—
116	#124×C₄₇	D₄	1	1	yes	characteristic
117	#124×C₄₇	D₄	1	1	yes	characteristic
118	#123×C₄₇	—	2	4	no	—
119	#123×C₄₇	—	2	4	no	—
120	#123×C₄₇	—	2	2	no	—
121	#123×C₄₇	—	2	4	no	—
122	#123×C₄₇	D₄	1	4	yes	—
123	C₂²⋊Q₈×C₄₇	—	2	4	no	—
124	C₂²⋊Q₈×C₄₇	—	2	4	no	—
125	C₂²⋊Q₈×C₄₇	—	2	2	no	—
126	C₂²⋊Q₈×C₄₇	—	2	2	no	—
127	C₂²⋊Q₈×C₄₇	—	4	2	no	—
128	#121×C₄₇	—	2	4	no	—
129	#121×C₄₇	—	2	2	no	—
130	C₄×Q₈×C₄₇	—	2	1	no	—
131	C₄×D₄×C₄₇	—	2	4	no	—
132	C₄×D₄×C₄₇	—	2	1	no	—
133	C₄×D₄×C₄₇	—	2	2	no	—
134	C₄×D₄×C₄₇	—	2	2	no	—
135	#117×C₄₇	—	2	1	no	—
136	#117×C₄₇	C₂³	1	2	yes	—
137	#117×C₄₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
139	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₂×C₄²×C₄₇	—	2	1	no	—
141	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
142	#104×C₄₇	—	2	4	no	—
143	#104×C₄₇	—	2	4	no	—
144	#104×C₄₇	—	2	2	no	—
145	#104×C₄₇	—	2	2	no	—
146	#103×C₄₇	—	4	2	no	—
147	#101×C₄₇	—	2	1	no	—
148	#101×C₄₇	—	2	4	no	—
149	#100×C₄₇	—	2	1	no	—
150	#99×C₄₇	—	2	2	no	—
151	#99×C₄₇	—	2	4	no	—
152	#41×C₄₇	—	2	2	no	—
153	#41×C₄₇	—	2	2	no	—
154	#41×C₄₇	—	2	2	no	—
155	#41×C₄₇	—	2	4	no	—
156	#41×C₄₇	—	2	4	no	—
157	#41×C₄₇	—	2	2	no	—
158	#41×C₄₇	—	2	2	no	—
159	#41×C₄₇	—	2	2	no	—
160	#41×C₄₇	—	2	2	no	—
161	#41×C₄₇	—	2	2	no	—
162	#41×C₄₇	—	2	2	no	—
163	#41×C₄₇	—	4	2	no	—
164	#41×C₄₇	—	4	4	no	—
165	#41×C₄₇	—	4	4	no	—
166	#41×C₄₇	—	4	8	no	—
167	#41×C₄₇	—	4	4	no	—
168	#41×C₄₇	—	4	2	no	—
169	#41×C₄₇	—	4	8	no	—
170	#41×C₄₇	—	4	2	no	—
171	#41×C₄₇	—	4	2	no	—
172	#41×C₄₇	—	4	2	no	—
173	#41×C₄₇	—	4	2	no	—
174	#41×C₄₇	—	4	2	no	—
175	#41×C₄₇	C₂×D₄	1	4	yes	—
176	C₂×Q₈×C₄₇	—	2	2	no	—
177	C₂×Q₈×C₄₇	—	2	2	no	—
178	C₂×Q₈×C₄₇	—	2	1	no	—
179	C₂×Q₈×C₄₇	—	2	1	no	—
180	C₂×Q₈×C₄₇	—	2	1	no	—
181	C₂×Q₈×C₄₇	—	2	2	no	—
182	C₂×Q₈×C₄₇	—	2	2	no	—
183	C₂×Q₈×C₄₇	—	2	2	no	—
184	C₂×Q₈×C₄₇	—	2	4	no	—
185	C₂×Q₈×C₄₇	—	2	2	no	—
186	C₂×Q₈×C₄₇	—	2	2	no	—
187	C₂×Q₈×C₄₇	—	4	2	no	—
188	C₂×Q₈×C₄₇	—	4	4	no	—
189	C₂×Q₈×C₄₇	—	4	4	no	—
190	C₂×Q₈×C₄₇	—	4	2	no	—
191	C₂×Q₈×C₄₇	—	4	2	no	—
192	C₂×Q₈×C₄₇	—	4	2	no	—
193	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
194	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
196	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
197	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₄₇	—	2	1	no	—
199	C₂×D₄×C₄₇	—	2	2	no	—
200	C₂×D₄×C₄₇	—	2	2	no	—
201	C₂×D₄×C₄₇	—	2	2	no	—
202	C₂×D₄×C₄₇	—	2	2	no	—
203	C₂×D₄×C₄₇	—	2	1	no	—
204	C₂×D₄×C₄₇	—	2	2	no	—
205	C₂×D₄×C₄₇	—	4	2	no	—
206	C₂×D₄×C₄₇	—	4	4	no	—
207	C₂×D₄×C₄₇	—	4	2	no	—
208	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
209	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
210	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
211	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₄₇	—	2	1	no	—
214	C₂²×C₄×C₄₇	—	2	2	no	—
215	C₂²×C₄×C₄₇	—	2	2	no	—
216	C₂²×C₄×C₄₇	—	2	2	no	—
217	C₂²×C₄×C₄₇	—	2	2	no	—
218	C₂²×C₄×C₄₇	—	2	1	no	—
219	C₂²×C₄×C₄₇	—	2	1	no	—
220	C₂²×C₄×C₄₇	—	2	2	no	—
221	C₂²×C₄×C₄₇	—	2	1	no	—
222	C₂²×C₄×C₄₇	—	2	2	no	—
223	C₂²×C₄×C₄₇	—	4	2	no	—
224	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
227	Q₁₆×C₄₇	—	2	8	no	—
228	Q₁₆×C₄₇	—	2	4	no	—
229	Q₁₆×C₄₇	—	4	2	no	—
230	SD₁₆×C₄₇	—	2	8	no	—
231	SD₁₆×C₄₇	—	2	4	no	—
232	SD₁₆×C₄₇	—	2	4	no	—
233	SD₁₆×C₄₇	—	4	2	no	—
234	SD₁₆×C₄₇	—	4	2	no	—
235	D₈×C₄₇	—	2	4	no	—
236	D₈×C₄₇	—	4	2	no	—
237	M₁₆×C₄₇	—	2	4	no	—
238	M₁₆×C₄₇	—	2	2	no	—
239	M₁₆×C₄₇	—	2	2	no	—
240	M₁₆×C₄₇	—	2	2	no	—
241	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
242	C₂×C₈×C₄₇	—	2	4	no	—
243	C₂×C₈×C₄₇	—	2	2	no	—
244	C₂×C₈×C₄₇	—	2	2	no	—
245	C₄⋊C₄×C₄₇	—	2	4	no	—
246	C₄⋊C₄×C₄₇	—	2	4	no	—
247	C₄⋊C₄×C₄₇	—	2	4	no	—
248	C₄⋊C₄×C₄₇	—	2	2	no	—
249	C₄⋊C₄×C₄₇	—	2	2	no	—
250	C₄⋊C₄×C₄₇	—	2	4	no	—
251	C₄⋊C₄×C₄₇	—	2	1	no	—
252	C₄⋊C₄×C₄₇	—	2	2	no	—
253	C₄⋊C₄×C₄₇	—	4	4	no	—
254	C₂²⋊C₄×C₄₇	—	2	2	no	—
255	C₂²⋊C₄×C₄₇	—	2	4	no	—
256	C₂²⋊C₄×C₄₇	—	2	2	no	—
257	C₂²⋊C₄×C₄₇	—	2	4	no	—
258	C₂²⋊C₄×C₄₇	—	2	2	no	—
259	C₂²⋊C₄×C₄₇	—	2	2	no	—
260	C₂²⋊C₄×C₄₇	—	4	4	no	—
261	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
262	C₄²×C₄₇	—	2	2	no	—
263	C₄²×C₄₇	—	2	1	no	—
264	C₄²×C₄₇	—	2	1	no	—
265	C₄²×C₄₇	—	2	2	no	—
266	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
268	C₂³×C₄₇	—	2	1	no	—
269	C₂³×C₄₇	—	2	1	no	—
270	C₂³×C₄₇	—	2	2	no	—
271	C₂³×C₄₇	—	4	2	no	—
272	C₂³×C₄₇	#120	1	2	yes	—
273	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₄₇	—	2	1	no	—
275	Q₈×C₄₇	—	2	2	no	—
276	Q₈×C₄₇	—	2	2	no	—
277	Q₈×C₄₇	—	2	2	no	—
278	Q₈×C₄₇	—	2	2	no	—
279	Q₈×C₄₇	—	2	2	no	—
280	Q₈×C₄₇	—	2	2	no	—
281	Q₈×C₄₇	—	4	4	no	—
282	Q₈×C₄₇	—	4	4	no	—
283	Q₈×C₄₇	—	4	2	no	—
284	Q₈×C₄₇	—	4	1	no	—
285	Q₈×C₄₇	—	4	1	no	—
286	Q₈×C₄₇	—	4	2	no	—
287	Q₈×C₄₇	—	4	2	no	—
288	Q₈×C₄₇	#120	1	2	yes	—
289	D₄×C₄₇	—	2	4	no	—
290	D₄×C₄₇	—	2	4	no	—
291	D₄×C₄₇	—	2	2	no	—
292	D₄×C₄₇	—	2	1	no	—
293	D₄×C₄₇	—	2	2	no	—
294	D₄×C₄₇	—	2	2	no	—
295	D₄×C₄₇	—	2	2	no	—
296	D₄×C₄₇	—	4	4	no	—
297	D₄×C₄₇	—	4	2	no	—
298	D₄×C₄₇	—	4	4	no	—
299	D₄×C₄₇	—	4	4	no	—
300	D₄×C₄₇	—	4	4	no	—
301	D₄×C₄₇	—	4	2	no	—
302	D₄×C₄₇	—	4	2	no	—
303	D₄×C₄₇	—	4	2	no	—
304	D₄×C₄₇	#120	1	2	yes	—
305	C₂×C₄×C₄₇	—	2	1	no	—
306	C₂×C₄×C₄₇	—	2	1	no	—
307	C₂×C₄×C₄₇	—	2	2	no	—
308	C₂×C₄×C₄₇	—	2	2	no	—
309	C₂×C₄×C₄₇	—	2	4	no	—
310	C₂×C₄×C₄₇	—	2	2	no	—
311	C₂×C₄×C₄₇	—	2	1	no	—
312	C₂×C₄×C₄₇	—	2	2	no	—
313	C₂×C₄×C₄₇	—	2	1	no	—
314	C₂×C₄×C₄₇	—	2	2	no	—
315	C₂×C₄×C₄₇	—	2	4	no	—
316	C₂×C₄×C₄₇	—	2	2	no	—
317	C₂×C₄×C₄₇	—	4	4	no	—
318	C₂×C₄×C₄₇	—	4	4	no	—
319	C₂×C₄×C₄₇	—	4	2	no	—
320	C₂×C₄×C₄₇	—	4	4	no	—
321	C₂×C₄×C₄₇	—	4	4	no	—
322	C₂×C₄×C₄₇	—	4	4	no	—
323	C₂×C₄×C₄₇	—	4	4	no	—
324	C₂×C₄×C₄₇	—	4	2	no	—
325	C₂×C₄×C₄₇	—	4	2	no	—
326	C₂×C₄×C₄₇	—	4	1	no	—
327	C₂×C₄×C₄₇	—	4	2	no	—
328	C₂×C₄×C₄₇	—	4	1	no	—
329	C₂×C₄×C₄₇	—	4	2	no	—
330	C₂×C₄×C₄₇	—	4	2	no	—
331	C₂×C₄×C₄₇	#120	1	2	yes	—
332	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
336	C₈×C₄₇	—	2	4	no	—
337	C₈×C₄₇	—	4	2	no	—
338	#23875	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂²×C₄₇	—	2	2	no	—
340	C₂²×C₄₇	—	2	2	no	—
341	C₂²×C₄₇	—	4	1	no	—
342	C₂²×C₄₇	—	4	2	no	—
343	C₂²×C₄₇	—	4	2	no	—
344	C₂²×C₄₇	—	4	2	no	—
345	C₂²×C₄₇	—	4	1	no	—
346	C₂²×C₄₇	—	4	2	no	—
347	C₂²×C₄₇	—	8	2	no	—
348	C₂²×C₄₇	—	16	2	no	—
349	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
350	C₂²×C₄₇	D₄²	1	2	yes	—
351	C₄×C₄₇	—	2	2	no	—
352	C₄×C₄₇	—	2	2	no	—
353	C₄×C₄₇	—	2	2	no	—
354	C₄×C₄₇	—	4	2	no	—
355	C₄×C₄₇	—	4	1	no	—
356	C₄×C₄₇	—	4	2	no	—
357	C₄×C₄₇	—	4	2	no	—
358	C₄×C₄₇	—	4	2	no	—
359	C₄×C₄₇	—	4	1	no	—
360	C₄×C₄₇	—	8	2	no	—
361	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
362	C₄×C₄₇	#534	1	1	yes	characteristic
363	C₄×C₄₇	D₄²	1	2	yes	—
364	#3586	C₂×C₄₇	1	1	yes	characteristic, complemented
365	#3499	C₂×C₄₇	1	1	yes	characteristic, complemented
366	#3028	C₂×C₄₇	1	1	yes	characteristic, complemented
367	#3020	C₂×C₄₇	1	2	yes	complemented
368	#3018	C₂×C₄₇	1	1	yes	characteristic, complemented
369	#2009	C₂×C₄₇	1	2	yes	complemented
370	#2005	C₂×C₄₇	1	2	yes	complemented
371	#1915	C₂×C₄₇	1	1	yes	characteristic, complemented
372	#1906	C₂×C₄₇	1	2	yes	complemented
373	#1884	C₂×C₄₇	1	1	yes	characteristic, complemented
374	#1796	C₂×C₄₇	1	1	yes	characteristic, complemented
375	C₂×C₄₇	—	2	1	no	—
376	C₂×C₄₇	—	2	2	no	—
377	C₂×C₄₇	—	4	2	no	—
378	C₂×C₄₇	—	4	2	no	—
379	C₂×C₄₇	—	8	1	no	—
380	C₂×C₄₇	—	8	2	no	—
381	C₂×C₄₇	#2403	1	1	yes	characteristic
382	#585	C₂²×C₄₇	1	1	yes	characteristic
383	C₂×2₋¹⁺⁴	C₂²×C₄₇	1	1	yes	characteristic
384	C₂×2₋¹⁺⁴	C₂²×C₄₇	1	1	yes	characteristic, complemented
385	#578	—	2	4	no	—
386	#577	—	2	4	no	—
387	#575	—	2	2	no	—
388	#575	C₂²×C₄₇	1	2	yes	—
389	#575	C₂²×C₄₇	1	2	yes	—
390	C₂×#137	—	2	2	no	—
391	C₂×#137	C₂²×C₄₇	1	2	yes	—
392	#568	C₂²×C₄₇	1	1	yes	characteristic
393	D₄×Q₈	—	2	2	no	—
394	#547	—	2	2	no	—
395	#547	—	2	4	no	—
396	#536	—	2	1	no	—
397	#536	—	2	1	no	—
398	#536	C₂²×C₄₇	1	1	yes	characteristic
399	#536	C₂²×C₄₇	1	2	yes	—
400	#536	C₂²×C₄₇	1	1	yes	characteristic, complemented
401	#532	—	2	1	no	—
402	#532	C₂²×C₄₇	1	1	yes	characteristic
403	C₂×C₄⋊Q₈	—	2	1	no	—
404	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
405	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic, complemented
406	#458	—	2	4	no	—
407	#456	—	2	4	no	—
408	#456	—	2	1	no	—
409	#455	—	2	1	no	—
410	#454	—	2	4	no	—
411	#454	—	2	1	no	—
412	#453	—	2	1	no	—
413	#421	C₂²×C₄₇	1	2	yes	complemented
414	#421	C₂²×C₄₇	1	2	yes	complemented
415	C₂×#104	C₂²×C₄₇	1	2	yes	—
416	#419	C₂²×C₄₇	1	2	yes	complemented
417	#413	C₂²×C₄₇	1	1	yes	characteristic
418	C₂×#101	C₂²×C₄₇	1	2	yes	complemented
419	#410	C₂²×C₄₇	1	1	yes	characteristic
420	#410	C₂²×C₄₇	1	2	yes	—
421	#344	C₂²×C₄₇	1	2	yes	complemented
422	#339	C₂²×C₄₇	1	2	yes	complemented
423	C₄₇	#23875	1	1	yes	characteristic, direct product factor, Sylow
424	2₋¹⁺⁴	—	2	4	no	—
425	2₋¹⁺⁴	—	2	2	no	—
426	2₋¹⁺⁴	—	2	4	no	—
427	2₋¹⁺⁴	—	2	1	no	—
428	2₋¹⁺⁴	—	4	2	no	—
429	2₋¹⁺⁴	—	4	2	no	—
430	H(5,𝔽₂)	—	2	2	no	—
431	H(5,𝔽₂)	—	2	2	no	—
432	H(5,𝔽₂)	—	2	1	no	—
433	C₂×#41	—	2	1	no	—
434	C₂×#41	—	2	1	no	—
435	C₂×#41	—	2	2	no	—
436	C₂×#41	—	2	1	no	—
437	C₂×#41	—	2	2	no	—
438	C₂×#41	—	2	2	no	—
439	C₂×#41	—	4	2	no	—
440	C₂×#41	D₄×C₄₇	1	2	yes	—
441	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
442	C₂×#41	C₂³×C₄₇	1	2	yes	—
443	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
444	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
445	C₂²×Q₈	—	2	1	no	—
446	C₂²×Q₈	—	2	1	no	—
447	C₂²×Q₈	—	2	1	no	—
448	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
449	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
450	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
451	#137	—	2	8	no	—
452	#137	—	2	4	no	—
453	#137	—	2	2	no	—
454	#137	—	2	4	no	—
455	#137	—	2	2	no	—
456	#137	—	2	2	no	—
457	#137	—	2	4	no	—
458	#137	D₄×C₄₇	1	4	yes	complemented
459	AGL(1,ℤ/8)	—	2	4	no	—
460	AGL(1,ℤ/8)	—	2	2	no	—
461	AGL(1,ℤ/8)	—	2	2	no	—
462	AGL(1,ℤ/8)	—	2	2	no	—
463	AGL(1,ℤ/8)	D₄×C₄₇	1	4	yes	complemented
464	#135	—	2	8	no	—
465	#135	—	2	4	no	—
466	#135	—	4	2	no	—
467	C₂×Q₁₆	—	2	4	no	—
468	C₂×Q₁₆	—	2	2	no	—
469	C₂×SD₁₆	—	2	4	no	—
470	C₂×SD₁₆	—	2	2	no	—
471	#131	—	2	4	no	—
472	C₂×M₁₆	—	2	2	no	—
473	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
474	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
475	C₄⋊Q₈	—	2	4	no	—
476	C₄⋊Q₈	—	2	1	no	—
477	C₄⋊Q₈	—	2	1	no	—
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	—	2	1	no	—
481	C₄⋊Q₈	—	2	1	no	—
482	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
483	#127	D₄×C₄₇	1	1	yes	characteristic
484	#124	—	2	1	no	—
485	#124	—	2	1	no	—
486	#124	—	2	2	no	—
487	#124	D₄×C₄₇	1	1	yes	characteristic
488	#124	D₄×C₄₇	1	1	yes	characteristic
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	—	2	2	no	—
492	#123	—	2	4	no	—
493	#123	D₄×C₄₇	1	4	yes	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	4	2	no	—
499	#121	—	2	4	no	—
500	#121	—	2	2	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×D₄	—	2	4	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	#117	—	2	1	no	—
507	#117	C₂³×C₄₇	1	2	yes	—
508	#117	C₂³×C₄₇	1	1	yes	characteristic
509	C₂×C₄⋊C₄	—	2	4	no	—
510	C₂×C₄⋊C₄	—	2	2	no	—
511	C₂×C₄²	—	2	1	no	—
512	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
513	#104	—	2	4	no	—
514	#104	—	2	4	no	—
515	#104	—	2	2	no	—
516	#104	—	2	2	no	—
517	#103	—	4	2	no	—
518	#101	—	2	1	no	—
519	#101	—	2	4	no	—
520	#100	—	2	1	no	—
521	#99	—	2	2	no	—
522	#99	—	2	4	no	—
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	—	2	4	no	—
527	#41	—	2	4	no	—
528	#41	—	2	2	no	—
529	#41	—	2	2	no	—
530	#41	—	2	2	no	—
531	#41	—	2	2	no	—
532	#41	—	2	2	no	—
533	#41	—	2	2	no	—
534	#41	—	4	2	no	—
535	#41	—	4	4	no	—
536	#41	—	4	4	no	—
537	#41	—	4	8	no	—
538	#41	—	4	4	no	—
539	#41	—	4	2	no	—
540	#41	—	4	8	no	—
541	#41	—	4	2	no	—
542	#41	—	4	2	no	—
543	#41	—	4	2	no	—
544	#41	—	4	2	no	—
545	#41	—	4	2	no	—
546	#41	C₂×D₄×C₄₇	1	4	yes	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	4	2	no	—
559	C₂×Q₈	—	4	4	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	—	4	2	no	—
563	C₂×Q₈	—	4	2	no	—
564	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
565	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
566	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
567	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
568	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
580	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
581	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
582	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
583	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
596	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
598	Q₁₆	—	2	8	no	—
599	Q₁₆	—	2	4	no	—
600	Q₁₆	—	4	2	no	—
601	SD₁₆	—	2	8	no	—
602	SD₁₆	—	2	4	no	—
603	SD₁₆	—	2	4	no	—
604	SD₁₆	—	4	2	no	—
605	SD₁₆	—	4	2	no	—
606	D₈	—	2	4	no	—
607	D₈	—	4	2	no	—
608	M₁₆	—	2	4	no	—
609	M₁₆	—	2	2	no	—
610	M₁₆	—	2	2	no	—
611	M₁₆	—	2	2	no	—
612	M₁₆	C₂×D₄×C₄₇	1	4	yes	—
613	C₂×C₈	—	2	4	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	4	4	no	—
632	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	2	no	—
637	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	4	2	no	—
643	C₂³	#120×C₄₇	1	2	yes	—
644	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
645	Q₈	—	2	1	no	—
646	Q₈	—	2	2	no	—
647	Q₈	—	2	2	no	—
648	Q₈	—	2	2	no	—
649	Q₈	—	2	2	no	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	4	4	no	—
653	Q₈	—	4	4	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	#120×C₄₇	1	2	yes	—
660	D₄	—	2	4	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	2	no	—
663	D₄	—	2	1	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	4	4	no	—
668	D₄	—	4	2	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	2	no	—
673	D₄	—	4	2	no	—
674	D₄	—	4	2	no	—
675	D₄	#120×C₄₇	1	2	yes	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	2	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	#120×C₄₇	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
706	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
707	C₈	—	2	4	no	—
708	C₈	—	4	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	8	2	no	—
718	C₂²	—	16	2	no	—
719	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
720	C₂²	D₄²×C₄₇	1	2	yes	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	8	2	no	—
731	C₄	C₂×#120×C₄₇	1	1	yes	characteristic
732	C₄	C₄₇×#534	1	1	yes	characteristic
733	C₄	D₄²×C₄₇	1	2	yes	—
734	C₂	—	2	1	no	—
735	C₂	—	2	2	no	—
736	C₂	—	4	2	no	—
737	C₂	—	4	2	no	—
738	C₂	—	8	1	no	—
739	C₂	—	8	2	no	—
740	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×#3586	C₂	semidirect
2. C₄₇×#3499	C₂	semidirect
3. C₄₇×#3028	C₂	semidirect
4. C₄₇×#3020	C₂	semidirect
5. C₄₇×#3018	C₂	semidirect
6. C₄₇×#2009	C₂	semidirect
7. C₄₇×#2005	C₂	semidirect
8. C₄₇×#1915	C₂	semidirect
9. C₄₇×#1906	C₂	semidirect
10. C₄₇×#1884	C₂	semidirect
11. C₄₇×#1796	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₄₇	C₂²	semidirect
30. C₄₇×#536	C₂²	semidirect
34. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
35. C₄×#41×C₄₇	C₂²	semidirect
43. C₄₇×#421	C₂²	semidirect
44. C₄₇×#421	C₂²	semidirect
46. C₄₇×#419	C₂²	semidirect
48. C₂×#101×C₄₇	C₂²	semidirect
51. C₄₇×#344	C₂²	semidirect
52. C₄₇×#339	C₂²	semidirect
87. #137×C₄₇	D₄	semidirect
92. AGL(1,ℤ/8)×C₄₇	D₄	semidirect
338. #23875	C₄₇	direct (N × H)
364. #3586	C₂×C₄₇	semidirect
365. #3499	C₂×C₄₇	semidirect
366. #3028	C₂×C₄₇	semidirect
367. #3020	C₂×C₄₇	semidirect
368. #3018	C₂×C₄₇	semidirect
369. #2009	C₂×C₄₇	semidirect
370. #2005	C₂×C₄₇	semidirect
371. #1915	C₂×C₄₇	semidirect
372. #1906	C₂×C₄₇	semidirect
373. #1884	C₂×C₄₇	semidirect
374. #1796	C₂×C₄₇	semidirect
384. C₂×2₋¹⁺⁴	C₂²×C₄₇	semidirect
400. #536	C₂²×C₄₇	semidirect
404. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
405. C₄×#41	C₂²×C₄₇	semidirect
413. #421	C₂²×C₄₇	semidirect
414. #421	C₂²×C₄₇	semidirect
416. #419	C₂²×C₄₇	semidirect
418. C₂×#101	C₂²×C₄₇	semidirect
421. #344	C₂²×C₄₇	semidirect
422. #339	C₂²×C₄₇	semidirect
423. C₄₇	#23875	direct (N × H)
458. #137	D₄×C₄₇	semidirect
463. AGL(1,ℤ/8)	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×#3586	2
C₄₇×#3499	2
C₄₇×#3028	2
C₄₇×#3020	2
C₄₇×#3018	2
C₄₇×#2009	2
C₄₇×#2005	2
C₄₇×#1915	2
C₄₇×#1906	2
C₄₇×#1884	2
C₄₇×#1796	2
#23875	47

Subgroups — C47×#23875 #26063573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#23875 #26063573