Subgroups — C₄₇×#25407 #26065105

Order 12032.

936 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	C₄₇×#3151	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#471	C₂	1	2	yes	maximal, complemented
3	C₄₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2051	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2019	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1907	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₇	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
14	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
16	C₂×#131×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#532	C₂²	1	1	yes	characteristic
18	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#496	—	2	2	no	—
21	C₄₇×#493	—	2	1	no	—
22	C₄₇×#492	—	2	1	no	—
23	C₄₇×#471	—	2	8	no	—
24	C₄₇×#464	—	2	2	no	—
25	C₄₇×#462	—	2	1	no	—
26	C₄₇×#460	—	2	1	no	—
27	C₄₇×#460	—	2	1	no	—
28	C₄₇×#460	—	2	2	no	—
29	C₄₇×#460	—	2	1	no	—
30	C₄₇×#436	—	2	1	no	—
31	C₄₇×#435	—	2	2	no	—
32	C₈×D₄×C₄₇	—	2	1	no	—
33	C₂×#108×C₄₇	C₂²	1	2	yes	—
34	C₄₇×#423	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#417	C₂²	1	2	yes	—
37	C₂×#102×C₄₇	C₂²	1	2	yes	—
38	C₂×#101×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#101×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#100×C₄₇	C₂²	1	2	yes	—
41	C₂×#100×C₄₇	C₂²	1	2	yes	—
42	C₄₇×#408	C₂²	1	2	yes	—
43	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#343	C₂²	1	1	yes	characteristic
46	C₄₇×#343	C₂²	1	1	yes	characteristic
47	C₄₇×#341	C₂²	1	2	yes	—
48	C₂×#41×C₄₇	C₂³	1	2	yes	—
49	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	—	2	1	no	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
53	#137×C₄₇	—	2	4	no	—
54	#137×C₄₇	—	4	2	no	—
55	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
56	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
57	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
58	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
59	C₂×Q₁₆×C₄₇	—	2	2	no	—
60	C₂×SD₁₆×C₄₇	—	2	4	no	—
61	C₂×SD₁₆×C₄₇	—	2	2	no	—
62	C₂×SD₁₆×C₄₇	—	2	2	no	—
63	C₂×SD₁₆×C₄₇	—	2	2	no	—
64	C₂×SD₁₆×C₄₇	—	2	2	no	—
65	C₂×SD₁₆×C₄₇	—	2	2	no	—
66	C₂×SD₁₆×C₄₇	—	4	2	no	—
67	C₂×D₈×C₄₇	—	2	2	no	—
68	C₂×D₈×C₄₇	—	2	2	no	—
69	#131×C₄₇	—	2	4	no	—
70	#131×C₄₇	—	4	2	no	—
71	C₂×M₁₆×C₄₇	—	2	2	no	—
72	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
73	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	—	2	2	no	—
78	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
79	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
80	#127×C₄₇	—	2	1	no	—
81	#127×C₄₇	—	2	1	no	—
82	#127×C₄₇	—	2	1	no	—
83	#127×C₄₇	—	2	1	no	—
84	#127×C₄₇	D₄	1	1	yes	characteristic
85	#124×C₄₇	D₄	1	2	yes	—
86	#121×C₄₇	—	2	1	no	—
87	#121×C₄₇	—	2	1	no	—
88	C₄×Q₈×C₄₇	—	2	1	no	—
89	C₄×Q₈×C₄₇	—	2	1	no	—
90	C₄×Q₈×C₄₇	—	2	1	no	—
91	C₄×Q₈×C₄₇	—	2	1	no	—
92	C₄×D₄×C₄₇	—	2	1	no	—
93	C₄×D₄×C₄₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	#108×C₄₇	—	2	4	no	—
99	C₄⋊C₈×C₄₇	—	2	1	no	—
100	C₄⋊C₈×C₄₇	—	2	1	no	—
101	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
102	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
103	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
104	#103×C₄₇	—	2	2	no	—
105	#102×C₄₇	—	2	2	no	—
106	#102×C₄₇	—	2	2	no	—
107	#102×C₄₇	—	2	2	no	—
108	#101×C₄₇	—	2	2	no	—
109	#101×C₄₇	D₄	1	4	yes	complemented
110	#100×C₄₇	—	2	4	no	—
111	#100×C₄₇	—	4	2	no	—
112	C₂²⋊C₈×C₄₇	—	2	2	no	—
113	C₂²⋊C₈×C₄₇	—	2	2	no	—
114	#97×C₄₇	—	2	1	no	—
115	#97×C₄₇	—	2	1	no	—
116	C₄×C₈×C₄₇	—	2	1	no	—
117	C₄×C₈×C₄₇	—	2	1	no	—
118	C₂⁴×C₄₇	—	2	2	no	—
119	#41×C₄₇	—	2	2	no	—
120	#41×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	2	no	—
122	#41×C₄₇	—	2	2	no	—
123	C₂×Q₈×C₄₇	—	2	1	no	—
124	C₂×Q₈×C₄₇	—	2	1	no	—
125	C₂×Q₈×C₄₇	—	2	1	no	—
126	C₂×Q₈×C₄₇	—	2	1	no	—
127	C₂×Q₈×C₄₇	—	2	1	no	—
128	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	1	no	—
132	C₂×D₄×C₄₇	—	2	1	no	—
133	C₂×D₄×C₄₇	—	2	2	no	—
134	C₂×D₄×C₄₇	—	2	2	no	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	4	1	no	—
140	C₂×D₄×C₄₇	—	4	1	no	—
141	C₂×D₄×C₄₇	—	4	1	no	—
142	C₂×D₄×C₄₇	—	4	1	no	—
143	C₂×D₄×C₄₇	—	8	2	no	—
144	C₂×D₄×C₄₇	—	8	2	no	—
145	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₇	—	2	1	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	1	no	—
149	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
152	Q₁₆×C₄₇	—	4	4	no	—
153	SD₁₆×C₄₇	—	4	4	no	—
154	SD₁₆×C₄₇	—	4	4	no	—
155	SD₁₆×C₄₇	—	4	4	no	—
156	SD₁₆×C₄₇	—	4	4	no	—
157	SD₁₆×C₄₇	—	4	4	no	—
158	D₈×C₄₇	—	4	4	no	—
159	D₈×C₄₇	—	4	4	no	—
160	M₁₆×C₄₇	—	2	1	no	—
161	M₁₆×C₄₇	—	2	1	no	—
162	M₁₆×C₄₇	—	2	1	no	—
163	M₁₆×C₄₇	—	2	2	no	—
164	M₁₆×C₄₇	—	2	1	no	—
165	M₁₆×C₄₇	—	2	2	no	—
166	M₁₆×C₄₇	—	2	1	no	—
167	M₁₆×C₄₇	—	4	4	no	—
168	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
169	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
170	M₁₆×C₄₇	#41	1	2	yes	—
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	2	2	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	4	4	no	—
179	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₄₇	—	2	1	no	—
182	C₄⋊C₄×C₄₇	—	2	1	no	—
183	C₄⋊C₄×C₄₇	—	2	1	no	—
184	C₄⋊C₄×C₄₇	—	2	1	no	—
185	C₄⋊C₄×C₄₇	—	4	1	no	—
186	C₄⋊C₄×C₄₇	—	4	1	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	2	no	—
189	C₄²×C₄₇	—	4	1	no	—
190	C₄²×C₄₇	—	4	1	no	—
191	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₂³×C₄₇	—	2	2	no	—
196	C₂³×C₄₇	—	4	2	no	—
197	C₂³×C₄₇	—	4	2	no	—
198	C₂³×C₄₇	—	4	2	no	—
199	C₂³×C₄₇	—	8	2	no	—
200	C₂³×C₄₇	—	8	2	no	—
201	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
202	Q₈×C₄₇	—	2	2	no	—
203	Q₈×C₄₇	—	2	2	no	—
204	Q₈×C₄₇	—	2	2	no	—
205	Q₈×C₄₇	—	2	2	no	—
206	Q₈×C₄₇	—	4	1	no	—
207	Q₈×C₄₇	—	4	1	no	—
208	D₄×C₄₇	—	2	2	no	—
209	D₄×C₄₇	—	2	2	no	—
210	D₄×C₄₇	—	4	2	no	—
211	D₄×C₄₇	—	4	2	no	—
212	D₄×C₄₇	—	4	2	no	—
213	D₄×C₄₇	—	4	2	no	—
214	D₄×C₄₇	—	4	2	no	—
215	D₄×C₄₇	—	4	2	no	—
216	D₄×C₄₇	—	4	2	no	—
217	D₄×C₄₇	—	8	1	no	—
218	D₄×C₄₇	—	8	2	no	—
219	D₄×C₄₇	—	8	2	no	—
220	D₄×C₄₇	—	8	2	no	—
221	D₄×C₄₇	—	8	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	4	1	no	—
226	C₂×C₄×C₄₇	—	4	1	no	—
227	C₂×C₄×C₄₇	—	4	1	no	—
228	C₂×C₄×C₄₇	—	4	2	no	—
229	C₂×C₄×C₄₇	—	4	2	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	8	1	no	—
232	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
242	C₈×C₄₇	—	2	2	no	—
243	C₈×C₄₇	—	2	2	no	—
244	C₈×C₄₇	—	2	2	no	—
245	C₈×C₄₇	—	2	2	no	—
246	C₈×C₄₇	—	2	2	no	—
247	C₈×C₄₇	—	4	2	no	—
248	C₈×C₄₇	—	4	1	no	—
249	#25407	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂²×C₄₇	—	2	1	no	—
251	C₂²×C₄₇	—	2	1	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	—	8	2	no	—
258	C₂²×C₄₇	—	16	2	no	—
259	C₂²×C₄₇	—	16	2	no	—
260	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
261	C₂²×C₄₇	#532	1	1	yes	characteristic
262	C₂²×C₄₇	#540	1	1	yes	characteristic
263	C₄×C₄₇	—	2	1	no	—
264	C₄×C₄₇	—	2	1	no	—
265	C₄×C₄₇	—	2	1	no	—
266	C₄×C₄₇	—	4	2	no	—
267	C₄×C₄₇	—	4	2	no	—
268	C₄×C₄₇	—	8	1	no	—
269	C₄×C₄₇	#471	1	2	yes	complemented
270	C₄×C₄₇	D₄²	1	1	yes	characteristic
271	C₄×C₄₇	D₄²	1	1	yes	characteristic
272	C₄×C₄₇	#546	1	1	yes	characteristic
273	C₄×C₄₇	#550	1	1	yes	characteristic
274	#3151	C₂×C₄₇	1	1	yes	characteristic
275	C₂×#471	C₂×C₄₇	1	2	yes	complemented
276	#3037	C₂×C₄₇	1	1	yes	characteristic, complemented
277	C₂×#460	C₂×C₄₇	1	1	yes	characteristic, complemented
278	#2935	C₂×C₄₇	1	1	yes	characteristic, complemented
279	#2051	C₂×C₄₇	1	2	yes	complemented
280	#2019	C₂×C₄₇	1	2	yes	complemented
281	#1965	C₂×C₄₇	1	1	yes	characteristic, complemented
282	#1950	C₂×C₄₇	1	1	yes	characteristic, complemented
283	#1907	C₂×C₄₇	1	2	yes	complemented
284	C₄×#101	C₂×C₄₇	1	1	yes	characteristic, complemented
285	C₂×C₄₇	—	2	1	no	—
286	C₂×C₄₇	—	2	1	no	—
287	C₂×C₄₇	—	8	2	no	—
288	C₂×C₄₇	—	16	2	no	—
289	C₂×C₄₇	#2428	1	1	yes	characteristic
290	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
291	C₂×C₄₇	#3068	1	1	yes	characteristic
292	C₂×#137	C₂²×C₄₇	1	2	yes	—
293	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	—
294	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	—
295	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
296	C₂×#131	C₂²×C₄₇	1	2	yes	—
297	#532	C₂²×C₄₇	1	1	yes	characteristic
298	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
300	#496	—	2	2	no	—
301	#493	—	2	1	no	—
302	#492	—	2	1	no	—
303	#471	—	2	8	no	—
304	#464	—	2	2	no	—
305	#462	—	2	1	no	—
306	#460	—	2	1	no	—
307	#460	—	2	1	no	—
308	#460	—	2	2	no	—
309	#460	—	2	1	no	—
310	#436	—	2	1	no	—
311	#435	—	2	2	no	—
312	C₈×D₄	—	2	1	no	—
313	C₂×#108	C₂²×C₄₇	1	2	yes	—
314	#423	C₂²×C₄₇	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
316	#417	C₂²×C₄₇	1	2	yes	—
317	C₂×#102	C₂²×C₄₇	1	2	yes	—
318	C₂×#101	C₂²×C₄₇	1	1	yes	characteristic
319	C₂×#101	C₂²×C₄₇	1	1	yes	characteristic
320	C₂×#100	C₂²×C₄₇	1	2	yes	—
321	C₂×#100	C₂²×C₄₇	1	2	yes	—
322	#408	C₂²×C₄₇	1	2	yes	—
323	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
324	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
325	#343	C₂²×C₄₇	1	1	yes	characteristic
326	#343	C₂²×C₄₇	1	1	yes	characteristic
327	#341	C₂²×C₄₇	1	2	yes	—
328	C₄₇	#25407	1	1	yes	characteristic, direct product factor, Sylow
329	C₂×#41	C₂³×C₄₇	1	2	yes	—
330	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
334	#137	—	2	4	no	—
335	#137	—	4	2	no	—
336	AGL(1,ℤ/8)	—	2	4	no	—
337	AGL(1,ℤ/8)	—	2	4	no	—
338	AGL(1,ℤ/8)	—	4	2	no	—
339	AGL(1,ℤ/8)	—	4	2	no	—
340	C₂×Q₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×SD₁₆	—	2	2	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×SD₁₆	—	4	2	no	—
348	C₂×D₈	—	2	2	no	—
349	C₂×D₈	—	2	2	no	—
350	#131	—	2	4	no	—
351	#131	—	4	2	no	—
352	C₂×M₁₆	—	2	2	no	—
353	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
354	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
355	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
356	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
357	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
358	C₂²×C₈	—	2	2	no	—
359	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
360	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
361	#127	—	2	1	no	—
362	#127	—	2	1	no	—
363	#127	—	2	1	no	—
364	#127	—	2	1	no	—
365	#127	D₄×C₄₇	1	1	yes	characteristic
366	#124	D₄×C₄₇	1	2	yes	—
367	#121	—	2	1	no	—
368	#121	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
379	#108	—	2	4	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
383	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
384	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
385	#103	—	2	2	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	2	no	—
389	#101	—	2	2	no	—
390	#101	D₄×C₄₇	1	4	yes	complemented
391	#100	—	2	4	no	—
392	#100	—	4	2	no	—
393	C₂²⋊C₈	—	2	2	no	—
394	C₂²⋊C₈	—	2	2	no	—
395	#97	—	2	1	no	—
396	#97	—	2	1	no	—
397	C₄×C₈	—	2	1	no	—
398	C₄×C₈	—	2	1	no	—
399	C₂⁴	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
410	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	8	2	no	—
425	C₂×D₄	—	8	2	no	—
426	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
431	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
433	Q₁₆	—	4	4	no	—
434	SD₁₆	—	4	4	no	—
435	SD₁₆	—	4	4	no	—
436	SD₁₆	—	4	4	no	—
437	SD₁₆	—	4	4	no	—
438	SD₁₆	—	4	4	no	—
439	D₈	—	4	4	no	—
440	D₈	—	4	4	no	—
441	M₁₆	—	2	1	no	—
442	M₁₆	—	2	1	no	—
443	M₁₆	—	2	1	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	2	1	no	—
446	M₁₆	—	2	1	no	—
447	M₁₆	—	2	2	no	—
448	M₁₆	—	4	4	no	—
449	M₁₆	C₂×D₄×C₄₇	1	2	yes	—
450	M₁₆	C₂×D₄×C₄₇	1	2	yes	—
451	M₁₆	#41×C₄₇	1	2	yes	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	4	4	no	—
460	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
461	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₄²	—	4	1	no	—
471	C₄²	—	4	1	no	—
472	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
475	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
476	C₂³	—	2	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	8	2	no	—
481	C₂³	—	8	2	no	—
482	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	4	1	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	8	1	no	—
499	D₄	—	8	2	no	—
500	D₄	—	8	2	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	8	1	no	—
513	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
514	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
515	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
516	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
520	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
521	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
522	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
523	C₈	—	2	2	no	—
524	C₈	—	2	2	no	—
525	C₈	—	2	2	no	—
526	C₈	—	2	2	no	—
527	C₈	—	2	2	no	—
528	C₈	—	4	2	no	—
529	C₈	—	4	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	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	—	8	2	no	—
538	C₂²	—	16	2	no	—
539	C₂²	—	16	2	no	—
540	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
541	C₂²	C₄₇×#532	1	1	yes	characteristic
542	C₂²	C₄₇×#540	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	8	1	no	—
549	C₄	C₄₇×#471	1	2	yes	complemented
550	C₄	D₄²×C₄₇	1	1	yes	characteristic
551	C₄	D₄²×C₄₇	1	1	yes	characteristic
552	C₄	C₄₇×#546	1	1	yes	characteristic
553	C₄	C₄₇×#550	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	8	2	no	—
557	C₂	—	16	2	no	—
558	C₂	C₄₇×#2428	1	1	yes	characteristic
559	C₂	C₂×C₄₇×#471	1	1	yes	characteristic
560	C₂	C₄₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#3151	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#471	C₂	semidirect
3. C₄₇×#3037	C₂	semidirect
4. C₂×C₄₇×#460	C₂	semidirect
5. C₄₇×#2935	C₂	semidirect
6. C₄₇×#2051	C₂	semidirect
7. C₄₇×#2019	C₂	semidirect
8. C₄₇×#1965	C₂	semidirect
9. C₄₇×#1950	C₂	semidirect
10. C₄₇×#1907	C₂	semidirect
11. C₄×#101×C₄₇	C₂	semidirect
109. #101×C₄₇	D₄	semidirect
249. #25407	C₄₇	direct (N × H)
269. C₄×C₄₇	#471	semidirect
275. C₂×#471	C₂×C₄₇	semidirect
276. #3037	C₂×C₄₇	semidirect
277. C₂×#460	C₂×C₄₇	semidirect
278. #2935	C₂×C₄₇	semidirect
279. #2051	C₂×C₄₇	semidirect
280. #2019	C₂×C₄₇	semidirect
281. #1965	C₂×C₄₇	semidirect
282. #1950	C₂×C₄₇	semidirect
283. #1907	C₂×C₄₇	semidirect
284. C₄×#101	C₂×C₄₇	semidirect
328. C₄₇	#25407	direct (N × H)
390. #101	D₄×C₄₇	semidirect
549. C₄	C₄₇×#471	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3151	2
C₂×C₄₇×#471	2
C₄₇×#3037	2
C₂×C₄₇×#460	2
C₄₇×#2935	2
C₄₇×#2051	2
C₄₇×#2019	2
C₄₇×#1965	2
C₄₇×#1950	2
C₄₇×#1907	2
C₄×#101×C₄₇	2
#25407	47

Subgroups — C47×#25407 #26065105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25407 #26065105