Subgroups — C₄₇×#24670 #26064368

Order 12032.

838 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×AGL(1,ℤ/8)×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2051	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2018	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1978	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×#1931	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1800	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
15	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
16	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#460	—	2	1	no	—
19	C₄₇×#460	—	2	1	no	—
20	C₄₇×#459	—	2	1	no	—
21	C₄₇×#459	—	2	1	no	—
22	C₄₇×#459	—	2	1	no	—
23	C₄₇×#459	—	2	1	no	—
24	C₄₇×#459	—	2	2	no	—
25	C₄₇×#442	—	2	1	no	—
26	C₄₇×#440	—	2	1	no	—
27	C₄×SD₁₆×C₄₇	—	2	1	no	—
28	C₄×D₈×C₄₇	—	2	1	no	—
29	C₄₇×#433	—	2	2	no	—
30	C₄₇×#432	—	2	1	no	—
31	C₄₇×#431	—	2	1	no	—
32	C₂×#108×C₄₇	C₂²	1	2	yes	—
33	C₄₇×#428	C₂²	1	1	yes	characteristic
34	C₄₇×#423	C₂²	1	1	yes	characteristic
35	C₄₇×#423	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#418	C₂²	1	2	yes	—
38	C₄₇×#418	C₂²	1	1	yes	characteristic
39	C₄₇×#417	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₇	C₂²	1	2	yes	—
41	C₂×#100×C₄₇	C₂²	1	2	yes	—
42	C₂×#100×C₄₇	C₂²	1	2	yes	—
43	C₂×#100×C₄₇	C₂²	1	2	yes	—
44	C₄₇×#408	C₂²	1	2	yes	—
45	C₄₇×#405	C₂²	1	2	yes	—
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#343	C₂²	1	2	yes	—
48	C₄₇×#341	C₂²	1	2	yes	—
49	C₂×#41×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	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	—	2	1	no	—
55	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
56	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
57	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
58	AGL(1,ℤ/8)×C₄₇	—	4	2	no	—
59	C₂×SD₁₆×C₄₇	—	2	1	no	—
60	C₂×SD₁₆×C₄₇	—	2	2	no	—
61	C₂×D₈×C₄₇	—	2	1	no	—
62	C₂×D₈×C₄₇	—	2	2	no	—
63	C₂×D₈×C₄₇	—	2	4	no	—
64	C₂×D₈×C₄₇	—	2	2	no	—
65	C₂×D₈×C₄₇	—	2	2	no	—
66	C₂×D₈×C₄₇	—	4	2	no	—
67	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
68	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
69	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
72	#127×C₄₇	—	2	1	no	—
73	#127×C₄₇	—	2	1	no	—
74	#127×C₄₇	—	2	1	no	—
75	#127×C₄₇	—	2	1	no	—
76	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
77	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
78	C₄×D₄×C₄₇	—	2	1	no	—
79	C₄×D₄×C₄₇	—	2	1	no	—
80	C₄×D₄×C₄₇	—	2	1	no	—
81	C₄×D₄×C₄₇	—	2	1	no	—
82	C₄×D₄×C₄₇	—	2	1	no	—
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
85	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
86	#117×C₄₇	—	2	1	no	—
87	#117×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	#108×C₄₇	—	4	2	no	—
93	#107×C₄₇	—	2	1	no	—
94	#106×C₄₇	—	2	1	no	—
95	C₄⋊C₈×C₄₇	—	2	1	no	—
96	C₄⋊C₈×C₄₇	—	2	1	no	—
97	C₄⋊C₈×C₄₇	—	2	1	no	—
98	C₄⋊C₈×C₄₇	—	2	1	no	—
99	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
101	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
102	#103×C₄₇	—	2	1	no	—
103	#102×C₄₇	—	2	1	no	—
104	#102×C₄₇	—	2	2	no	—
105	#102×C₄₇	—	2	2	no	—
106	#102×C₄₇	—	2	2	no	—
107	#102×C₄₇	—	2	2	no	—
108	#102×C₄₇	—	2	1	no	—
109	#102×C₄₇	—	2	1	no	—
110	#100×C₄₇	—	2	4	no	—
111	#100×C₄₇	—	4	2	no	—
112	#100×C₄₇	—	4	2	no	—
113	C₂²⋊C₈×C₄₇	—	2	2	no	—
114	C₂²⋊C₈×C₄₇	—	2	2	no	—
115	#97×C₄₇	—	2	2	no	—
116	#97×C₄₇	—	2	1	no	—
117	C₄×C₈×C₄₇	—	2	2	no	—
118	C₄×C₈×C₄₇	—	2	1	no	—
119	C₂⁴×C₄₇	—	2	1	no	—
120	C₂⁴×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	1	no	—
122	#41×C₄₇	—	2	1	no	—
123	#41×C₄₇	—	2	1	no	—
124	#41×C₄₇	—	2	1	no	—
125	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	—	2	1	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	1	no	—
132	C₂×D₄×C₄₇	—	2	2	no	—
133	C₂×D₄×C₄₇	—	2	2	no	—
134	C₂×D₄×C₄₇	—	2	1	no	—
135	C₂×D₄×C₄₇	—	2	1	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	4	1	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	—	8	2	no	—
143	C₂×D₄×C₄₇	—	8	2	no	—
144	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₄₇	#41	1	2	yes	—
146	C₂²×C₄×C₄₇	—	2	1	no	—
147	C₂²×C₄×C₄₇	—	2	1	no	—
148	C₂²×C₄×C₄₇	—	2	1	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	4	1	no	—
151	C₂²×C₄×C₄₇	—	4	1	no	—
152	C₂²×C₄×C₄₇	—	8	2	no	—
153	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₄₇	—	2	4	no	—
157	SD₁₆×C₄₇	—	4	4	no	—
158	D₈×C₄₇	—	2	4	no	—
159	D₈×C₄₇	—	4	4	no	—
160	D₈×C₄₇	—	4	4	no	—
161	D₈×C₄₇	—	4	4	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	2	no	—
167	M₁₆×C₄₇	—	2	1	no	—
168	M₁₆×C₄₇	—	2	2	no	—
169	M₁₆×C₄₇	#41	1	2	yes	—
170	C₂×C₈×C₄₇	—	2	1	no	—
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	2	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
178	C₄⋊C₄×C₄₇	—	2	1	no	—
179	C₄⋊C₄×C₄₇	—	2	1	no	—
180	C₄⋊C₄×C₄₇	—	2	1	no	—
181	C₄⋊C₄×C₄₇	—	2	1	no	—
182	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
183	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
184	C₂²⋊C₄×C₄₇	—	2	1	no	—
185	C₂²⋊C₄×C₄₇	—	2	1	no	—
186	C₂²⋊C₄×C₄₇	—	2	1	no	—
187	C₂²⋊C₄×C₄₇	—	4	1	no	—
188	C₂²⋊C₄×C₄₇	—	4	1	no	—
189	C₄²×C₄₇	—	2	1	no	—
190	C₄²×C₄₇	—	2	1	no	—
191	C₄²×C₄₇	—	2	1	no	—
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	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
196	C₂³×C₄₇	—	2	1	no	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	4	1	no	—
199	C₂³×C₄₇	—	4	1	no	—
200	C₂³×C₄₇	—	4	2	no	—
201	C₂³×C₄₇	—	4	2	no	—
202	C₂³×C₄₇	—	4	2	no	—
203	C₂³×C₄₇	—	8	1	no	—
204	C₂³×C₄₇	—	8	1	no	—
205	C₂³×C₄₇	—	8	2	no	—
206	C₂³×C₄₇	—	8	2	no	—
207	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
208	Q₈×C₄₇	—	2	1	no	—
209	Q₈×C₄₇	—	2	1	no	—
210	D₄×C₄₇	—	2	1	no	—
211	D₄×C₄₇	—	2	2	no	—
212	D₄×C₄₇	—	2	1	no	—
213	D₄×C₄₇	—	2	2	no	—
214	D₄×C₄₇	—	4	1	no	—
215	D₄×C₄₇	—	4	1	no	—
216	D₄×C₄₇	—	4	2	no	—
217	D₄×C₄₇	—	4	1	no	—
218	D₄×C₄₇	—	4	2	no	—
219	D₄×C₄₇	—	4	2	no	—
220	D₄×C₄₇	—	4	1	no	—
221	D₄×C₄₇	—	4	2	no	—
222	D₄×C₄₇	—	8	2	no	—
223	D₄×C₄₇	—	8	2	no	—
224	D₄×C₄₇	—	8	2	no	—
225	D₄×C₄₇	—	8	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	1	no	—
228	C₂×C₄×C₄₇	—	2	1	no	—
229	C₂×C₄×C₄₇	—	2	1	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	1	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	4	1	no	—
235	C₂×C₄×C₄₇	—	8	1	no	—
236	C₂×C₄×C₄₇	—	8	2	no	—
237	C₂×C₄×C₄₇	—	8	2	no	—
238	C₂×C₄×C₄₇	—	8	1	no	—
239	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
248	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
249	C₈×C₄₇	—	2	2	no	—
250	C₈×C₄₇	—	2	2	no	—
251	C₈×C₄₇	—	2	2	no	—
252	C₈×C₄₇	—	4	1	no	—
253	C₈×C₄₇	—	4	2	no	—
254	C₈×C₄₇	—	4	2	no	—
255	#24670	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₇	—	2	1	no	—
257	C₂²×C₄₇	—	2	1	no	—
258	C₂²×C₄₇	—	4	1	no	—
259	C₂²×C₄₇	—	4	2	no	—
260	C₂²×C₄₇	—	4	1	no	—
261	C₂²×C₄₇	—	4	1	no	—
262	C₂²×C₄₇	—	8	2	no	—
263	C₂²×C₄₇	—	8	2	no	—
264	C₂²×C₄₇	—	8	1	no	—
265	C₂²×C₄₇	—	8	1	no	—
266	C₂²×C₄₇	—	8	2	no	—
267	C₂²×C₄₇	—	8	2	no	—
268	C₂²×C₄₇	—	8	2	no	—
269	C₂²×C₄₇	—	16	2	no	—
270	C₂²×C₄₇	—	16	2	no	—
271	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
272	C₂²×C₄₇	#553	1	1	yes	characteristic
273	C₂²×C₄₇	#555	1	1	yes	characteristic
274	C₄×C₄₇	—	2	1	no	—
275	C₄×C₄₇	—	2	1	no	—
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	4	1	no	—
278	C₄×C₄₇	—	4	1	no	—
279	C₄×C₄₇	—	4	1	no	—
280	C₄×C₄₇	—	8	1	no	—
281	C₄×C₄₇	#472	1	2	yes	—
282	C₄×C₄₇	#525	1	1	yes	characteristic
283	C₄×C₄₇	#535	1	1	yes	characteristic
284	C₄×C₄₇	#546	1	1	yes	characteristic
285	C₄×C₄₇	#550	1	1	yes	characteristic
286	#3038	C₂×C₄₇	1	1	yes	characteristic, complemented
287	C₂×#459	C₂×C₄₇	1	1	yes	characteristic, complemented
288	C₄×AGL(1,ℤ/8)	C₂×C₄₇	1	1	yes	characteristic, complemented
289	#2925	C₂×C₄₇	1	1	yes	characteristic, complemented
290	#2051	C₂×C₄₇	1	2	yes	complemented
291	#2018	C₂×C₄₇	1	2	yes	complemented
292	#1978	C₂×C₄₇	1	2	yes	complemented
293	#1965	C₂×C₄₇	1	1	yes	characteristic, complemented
294	#1950	C₂×C₄₇	1	1	yes	characteristic, complemented
295	#1931	C₂×C₄₇	1	2	yes	complemented
296	#1800	C₂×C₄₇	1	1	yes	characteristic, complemented
297	C₂×C₄₇	—	2	1	no	—
298	C₂×C₄₇	—	2	1	no	—
299	C₂×C₄₇	—	8	1	no	—
300	C₂×C₄₇	—	8	2	no	—
301	C₂×C₄₇	—	16	2	no	—
302	C₂×C₄₇	#2414	1	1	yes	characteristic
303	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
304	C₂×C₄₇	#3068	1	1	yes	characteristic
305	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	1	yes	characteristic
306	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	—
307	C₂²×D₈	C₂²×C₄₇	1	2	yes	—
308	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
309	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
310	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
311	#460	—	2	1	no	—
312	#460	—	2	1	no	—
313	#459	—	2	1	no	—
314	#459	—	2	1	no	—
315	#459	—	2	1	no	—
316	#459	—	2	1	no	—
317	#459	—	2	2	no	—
318	#442	—	2	1	no	—
319	#440	—	2	1	no	—
320	C₄×SD₁₆	—	2	1	no	—
321	C₄×D₈	—	2	1	no	—
322	#433	—	2	2	no	—
323	#432	—	2	1	no	—
324	#431	—	2	1	no	—
325	C₂×#108	C₂²×C₄₇	1	2	yes	—
326	#428	C₂²×C₄₇	1	1	yes	characteristic
327	#423	C₂²×C₄₇	1	1	yes	characteristic
328	#423	C₂²×C₄₇	1	1	yes	characteristic
329	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
330	#418	C₂²×C₄₇	1	1	yes	characteristic
331	#418	C₂²×C₄₇	1	2	yes	—
332	#417	C₂²×C₄₇	1	1	yes	characteristic
333	C₂×#102	C₂²×C₄₇	1	2	yes	—
334	C₂×#100	C₂²×C₄₇	1	2	yes	—
335	C₂×#100	C₂²×C₄₇	1	2	yes	—
336	C₂×#100	C₂²×C₄₇	1	2	yes	—
337	#408	C₂²×C₄₇	1	2	yes	—
338	#405	C₂²×C₄₇	1	2	yes	—
339	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
340	#343	C₂²×C₄₇	1	2	yes	—
341	#341	C₂²×C₄₇	1	2	yes	—
342	C₄₇	#24670	1	1	yes	characteristic, direct product factor, Sylow
343	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
347	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	AGL(1,ℤ/8)	—	2	2	no	—
350	AGL(1,ℤ/8)	—	2	2	no	—
351	AGL(1,ℤ/8)	—	4	2	no	—
352	AGL(1,ℤ/8)	—	4	2	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	2	no	—
355	C₂×D₈	—	2	1	no	—
356	C₂×D₈	—	2	2	no	—
357	C₂×D₈	—	2	4	no	—
358	C₂×D₈	—	2	2	no	—
359	C₂×D₈	—	2	2	no	—
360	C₂×D₈	—	4	2	no	—
361	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
362	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
363	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
364	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
366	#127	—	2	1	no	—
367	#127	—	2	1	no	—
368	#127	—	2	1	no	—
369	#127	—	2	1	no	—
370	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
371	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
379	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
380	#117	—	2	1	no	—
381	#117	C₂³×C₄₇	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
386	#108	—	4	2	no	—
387	#107	—	2	1	no	—
388	#106	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
394	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
395	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
396	#103	—	2	1	no	—
397	#102	—	2	1	no	—
398	#102	—	2	2	no	—
399	#102	—	2	2	no	—
400	#102	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#100	—	2	4	no	—
405	#100	—	4	2	no	—
406	#100	—	4	2	no	—
407	C₂²⋊C₈	—	2	2	no	—
408	C₂²⋊C₈	—	2	2	no	—
409	#97	—	2	2	no	—
410	#97	—	2	1	no	—
411	C₄×C₈	—	2	2	no	—
412	C₄×C₈	—	2	1	no	—
413	C₂⁴	—	2	1	no	—
414	C₂⁴	—	2	2	no	—
415	#41	—	2	1	no	—
416	#41	—	2	1	no	—
417	#41	—	2	1	no	—
418	#41	—	2	1	no	—
419	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂×D₄	—	8	2	no	—
437	C₂×D₄	—	8	2	no	—
438	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
439	C₂×D₄	#41×C₄₇	1	2	yes	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	8	2	no	—
447	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
448	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
450	SD₁₆	—	2	4	no	—
451	SD₁₆	—	4	4	no	—
452	D₈	—	2	4	no	—
453	D₈	—	4	4	no	—
454	D₈	—	4	4	no	—
455	D₈	—	4	4	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	1	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	1	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	#41×C₄₇	1	2	yes	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
471	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
477	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
487	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
488	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
489	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
490	C₂³	—	2	1	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	8	1	no	—
498	C₂³	—	8	1	no	—
499	C₂³	—	8	2	no	—
500	C₂³	—	8	2	no	—
501	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	D₄	—	2	1	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	2	no	—
516	D₄	—	8	2	no	—
517	D₄	—	8	2	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	8	1	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	1	no	—
533	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
534	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
535	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
536	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
540	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
541	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
542	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	2	no	—
548	C₈	—	4	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	16	2	no	—
563	C₂²	—	16	2	no	—
564	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
565	C₂²	C₄₇×#553	1	1	yes	characteristic
566	C₂²	C₄₇×#555	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	8	1	no	—
574	C₄	C₄₇×#472	1	2	yes	—
575	C₄	C₄₇×#525	1	1	yes	characteristic
576	C₄	C₄₇×#535	1	1	yes	characteristic
577	C₄	C₄₇×#546	1	1	yes	characteristic
578	C₄	C₄₇×#550	1	1	yes	characteristic
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	8	1	no	—
582	C₂	—	8	2	no	—
583	C₂	—	16	2	no	—
584	C₂	C₄₇×#2414	1	1	yes	characteristic
585	C₂	C₂×C₄₇×#472	1	1	yes	characteristic
586	C₂	C₄₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
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
1. C₄₇×#3038	C₂	semidirect
2. C₂×C₄₇×#459	C₂	semidirect
3. C₄×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
4. C₄₇×#2925	C₂	semidirect
5. C₄₇×#2051	C₂	semidirect
6. C₄₇×#2018	C₂	semidirect
7. C₄₇×#1978	C₂	semidirect
8. C₄₇×#1965	C₂	semidirect
9. C₄₇×#1950	C₂	semidirect
10. C₄₇×#1931	C₂	semidirect
11. C₄₇×#1800	C₂	semidirect
255. #24670	C₄₇	direct (N × H)
286. #3038	C₂×C₄₇	semidirect
287. C₂×#459	C₂×C₄₇	semidirect
288. C₄×AGL(1,ℤ/8)	C₂×C₄₇	semidirect
289. #2925	C₂×C₄₇	semidirect
290. #2051	C₂×C₄₇	semidirect
291. #2018	C₂×C₄₇	semidirect
292. #1978	C₂×C₄₇	semidirect
293. #1965	C₂×C₄₇	semidirect
294. #1950	C₂×C₄₇	semidirect
295. #1931	C₂×C₄₇	semidirect
296. #1800	C₂×C₄₇	semidirect
342. C₄₇	#24670	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3038	2
C₂×C₄₇×#459	2
C₄×AGL(1,ℤ/8)×C₄₇	2
C₄₇×#2925	2
C₄₇×#2051	2
C₄₇×#2018	2
C₄₇×#1978	2
C₄₇×#1965	2
C₄₇×#1950	2
C₄₇×#1931	2
C₄₇×#1800	2
#24670	47

Subgroups — C47×#24670 #26064368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24670 #26064368