Subgroups — C₄₇×#18598 #26058296

Order 12032.

1224 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3184	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1654	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1639	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1625	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1619	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₄₇	—	2	1	no	—
13	C₄₇×#547	—	2	1	no	—
14	C₄₇×#547	C₂²	1	2	yes	—
15	C₄₇×#546	—	2	2	no	—
16	C₄₇×#546	—	2	2	no	—
17	D₄²×C₄₇	—	2	1	no	—
18	D₄²×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#537	—	2	1	no	—
20	C₄₇×#534	—	2	2	no	—
21	C₄₇×#532	C₂²	1	1	yes	characteristic
22	C₄₇×#532	C₂²	1	1	yes	characteristic
23	C₄₇×#532	C₂²	1	1	yes	characteristic, complemented
24	C₂×#121×C₄₇	—	2	2	no	—
25	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#498	C₂²	1	1	yes	characteristic, complemented
27	C₄₇×#496	—	2	1	no	—
28	C₄₇×#493	C₂²	1	1	yes	characteristic, complemented
29	C₄₇×#489	—	2	1	no	—
30	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
31	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
32	C₄₇×#480	—	2	1	no	—
33	C₄₇×#474	C₂²	1	2	yes	complemented
34	C₄₇×#469	—	2	2	no	—
35	C₄₇×#461	C₂²	1	2	yes	complemented
36	C₄₇×#459	C₂²	1	2	yes	complemented
37	C₄₇×#459	C₂²	1	2	yes	complemented
38	C₄₇×#449	—	2	2	no	—
39	C₄₇×#447	—	2	1	no	—
40	C₄₇×#442	—	2	2	no	—
41	C₄×D₈×C₄₇	—	2	2	no	—
42	C₄₇×#432	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
44	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	C₄₇×#332	C₂²	1	2	yes	complemented
46	C₄₇×#331	C₂²	1	2	yes	complemented
47	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
48	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
49	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
50	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
51	H(5,𝔽₂)×C₄₇	—	4	8	no	—
52	C₂×#41×C₄₇	—	2	2	no	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	—	2	1	no	—
55	C₂×#41×C₄₇	—	2	1	no	—
56	C₂×#41×C₄₇	—	2	1	no	—
57	C₂²×D₄×C₄₇	—	2	4	no	—
58	C₂²×D₄×C₄₇	—	2	2	no	—
59	C₂²×D₄×C₄₇	—	2	2	no	—
60	C₂²×D₄×C₄₇	—	2	2	no	—
61	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	—	2	1	no	—
63	C₂×SD₁₆×C₄₇	—	2	2	no	—
64	C₂×D₈×C₄₇	—	2	2	no	—
65	C₂×D₈×C₄₇	—	2	2	no	—
66	C₂×D₈×C₄₇	—	2	2	no	—
67	C₂×M₁₆×C₄₇	—	2	1	no	—
68	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
71	#127×C₄₇	D₄	1	1	yes	characteristic
72	#127×C₄₇	C₂³	1	1	yes	characteristic
73	#127×C₄₇	C₂³	1	1	yes	characteristic
74	#124×C₄₇	—	2	1	no	—
75	#124×C₄₇	—	2	1	no	—
76	#124×C₄₇	—	2	1	no	—
77	#123×C₄₇	—	2	4	no	—
78	#123×C₄₇	—	2	4	no	—
79	C₂²⋊Q₈×C₄₇	—	2	2	no	—
80	C₂²⋊Q₈×C₄₇	—	2	2	no	—
81	#121×C₄₇	—	2	4	no	—
82	#121×C₄₇	—	2	4	no	—
83	#121×C₄₇	—	2	2	no	—
84	#121×C₄₇	—	2	2	no	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	—	2	1	no	—
87	#121×C₄₇	—	2	2	no	—
88	#121×C₄₇	—	2	2	no	—
89	#121×C₄₇	—	2	1	no	—
90	#121×C₄₇	—	2	1	no	—
91	#121×C₄₇	D₄	1	2	yes	—
92	#121×C₄₇	D₄	1	2	yes	—
93	#120×C₄₇	—	2	4	no	—
94	#120×C₄₇	—	2	4	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	—	2	1	no	—
97	C₄×D₄×C₄₇	—	2	1	no	—
98	C₄×D₄×C₄₇	—	2	1	no	—
99	C₄×D₄×C₄₇	—	2	1	no	—
100	C₄×D₄×C₄₇	—	2	1	no	—
101	C₄×D₄×C₄₇	D₄	1	2	yes	—
102	C₄×D₄×C₄₇	D₄	1	2	yes	—
103	C₄×D₄×C₄₇	C₂³	1	2	yes	—
104	C₄×D₄×C₄₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
108	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	#107×C₄₇	—	2	2	no	—
111	#106×C₄₇	—	2	2	no	—
112	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
113	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
114	#103×C₄₇	—	2	2	no	—
115	#102×C₄₇	—	2	2	no	—
116	#102×C₄₇	—	2	2	no	—
117	#102×C₄₇	—	2	2	no	—
118	#102×C₄₇	—	2	2	no	—
119	#102×C₄₇	—	2	2	no	—
120	C₂²⋊C₈×C₄₇	—	2	1	no	—
121	C₂²⋊C₈×C₄₇	—	2	1	no	—
122	#97×C₄₇	—	2	1	no	—
123	#97×C₄₇	—	2	1	no	—
124	C₄×C₈×C₄₇	—	2	1	no	—
125	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂⁴×C₄₇	—	2	1	no	—
128	C₂⁴×C₄₇	—	2	4	no	—
129	#41×C₄₇	—	4	4	no	—
130	#41×C₄₇	—	4	4	no	—
131	#41×C₄₇	—	4	8	no	—
132	#41×C₄₇	—	4	4	no	—
133	#41×C₄₇	—	4	4	no	—
134	#41×C₄₇	—	8	2	no	—
135	C₂×Q₈×C₄₇	—	2	1	no	—
136	C₂×Q₈×C₄₇	—	2	1	no	—
137	C₂×Q₈×C₄₇	—	2	1	no	—
138	C₂×D₄×C₄₇	—	2	4	no	—
139	C₂×D₄×C₄₇	—	2	4	no	—
140	C₂×D₄×C₄₇	—	2	4	no	—
141	C₂×D₄×C₄₇	—	2	2	no	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	2	4	no	—
144	C₂×D₄×C₄₇	—	2	1	no	—
145	C₂×D₄×C₄₇	—	2	1	no	—
146	C₂×D₄×C₄₇	—	2	1	no	—
147	C₂×D₄×C₄₇	—	2	1	no	—
148	C₂×D₄×C₄₇	—	2	1	no	—
149	C₂×D₄×C₄₇	—	2	1	no	—
150	C₂×D₄×C₄₇	—	2	1	no	—
151	C₂×D₄×C₄₇	—	2	1	no	—
152	C₂×D₄×C₄₇	—	4	8	no	—
153	C₂×D₄×C₄₇	—	4	4	no	—
154	C₂×D₄×C₄₇	—	4	16	no	—
155	C₂×D₄×C₄₇	—	4	4	no	—
156	C₂×D₄×C₄₇	—	4	1	no	—
157	C₂×D₄×C₄₇	—	8	2	no	—
158	C₂×D₄×C₄₇	—	8	2	no	—
159	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₇	—	2	4	no	—
163	C₂²×C₄×C₄₇	—	2	1	no	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	2	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	4	1	no	—
169	C₂²×C₄×C₄₇	—	8	2	no	—
170	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
173	SD₁₆×C₄₇	—	8	2	no	—
174	D₈×C₄₇	—	4	4	no	—
175	D₈×C₄₇	—	4	4	no	—
176	D₈×C₄₇	—	8	2	no	—
177	M₁₆×C₄₇	—	4	2	no	—
178	C₂×C₈×C₄₇	—	2	1	no	—
179	C₂×C₈×C₄₇	—	2	2	no	—
180	C₂×C₈×C₄₇	—	2	2	no	—
181	C₂×C₈×C₄₇	—	2	1	no	—
182	C₄⋊C₄×C₄₇	—	2	4	no	—
183	C₄⋊C₄×C₄₇	—	2	1	no	—
184	C₄⋊C₄×C₄₇	—	2	1	no	—
185	C₄⋊C₄×C₄₇	—	2	1	no	—
186	C₄⋊C₄×C₄₇	—	2	1	no	—
187	C₄⋊C₄×C₄₇	—	2	1	no	—
188	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
191	C₂²⋊C₄×C₄₇	—	2	4	no	—
192	C₂²⋊C₄×C₄₇	—	2	4	no	—
193	C₂²⋊C₄×C₄₇	—	2	2	no	—
194	C₂²⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	2	2	no	—
196	C₂²⋊C₄×C₄₇	—	2	2	no	—
197	C₂²⋊C₄×C₄₇	—	2	2	no	—
198	C₂²⋊C₄×C₄₇	—	2	2	no	—
199	C₂²⋊C₄×C₄₇	—	4	1	no	—
200	C₂²⋊C₄×C₄₇	—	4	1	no	—
201	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
205	C₂³×C₄₇	—	2	4	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	2	2	no	—
208	C₂³×C₄₇	—	2	2	no	—
209	C₂³×C₄₇	—	4	8	no	—
210	C₂³×C₄₇	—	4	1	no	—
211	C₂³×C₄₇	—	8	1	no	—
212	C₂³×C₄₇	—	8	1	no	—
213	C₂³×C₄₇	—	8	4	no	—
214	C₂³×C₄₇	—	8	4	no	—
215	C₂³×C₄₇	#120	1	1	yes	characteristic
216	Q₈×C₄₇	—	4	2	no	—
217	Q₈×C₄₇	—	4	2	no	—
218	Q₈×C₄₇	—	4	2	no	—
219	D₄×C₄₇	—	2	4	no	—
220	D₄×C₄₇	—	2	2	no	—
221	D₄×C₄₇	—	2	2	no	—
222	D₄×C₄₇	—	2	2	no	—
223	D₄×C₄₇	—	4	2	no	—
224	D₄×C₄₇	—	4	2	no	—
225	D₄×C₄₇	—	4	2	no	—
226	D₄×C₄₇	—	4	4	no	—
227	D₄×C₄₇	—	4	4	no	—
228	D₄×C₄₇	—	4	8	no	—
229	D₄×C₄₇	—	4	8	no	—
230	D₄×C₄₇	—	4	2	no	—
231	D₄×C₄₇	—	4	2	no	—
232	D₄×C₄₇	—	4	2	no	—
233	D₄×C₄₇	—	4	2	no	—
234	D₄×C₄₇	—	8	1	no	—
235	D₄×C₄₇	—	8	4	no	—
236	D₄×C₄₇	—	8	2	no	—
237	D₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	4	1	no	—
244	C₂×C₄×C₄₇	—	4	4	no	—
245	C₂×C₄×C₄₇	—	4	8	no	—
246	C₂×C₄×C₄₇	—	4	2	no	—
247	C₂×C₄×C₄₇	—	4	2	no	—
248	C₂×C₄×C₄₇	—	4	2	no	—
249	C₂×C₄×C₄₇	—	4	2	no	—
250	C₂×C₄×C₄₇	—	4	1	no	—
251	C₂×C₄×C₄₇	—	8	2	no	—
252	C₂×C₄×C₄₇	—	8	2	no	—
253	C₂×C₄×C₄₇	—	8	1	no	—
254	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
255	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
256	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
260	C₈×C₄₇	—	2	2	no	—
261	C₈×C₄₇	—	4	1	no	—
262	C₈×C₄₇	—	4	2	no	—
263	C₈×C₄₇	—	4	2	no	—
264	#18598	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	2	4	no	—
267	C₂²×C₄₇	—	2	1	no	—
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	4	2	no	—
270	C₂²×C₄₇	—	4	2	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	—	4	2	no	—
273	C₂²×C₄₇	—	4	2	no	—
274	C₂²×C₄₇	—	4	2	no	—
275	C₂²×C₄₇	—	4	2	no	—
276	C₂²×C₄₇	—	4	2	no	—
277	C₂²×C₄₇	—	8	4	no	—
278	C₂²×C₄₇	—	8	1	no	—
279	C₂²×C₄₇	—	8	1	no	—
280	C₂²×C₄₇	—	8	1	no	—
281	C₂²×C₄₇	—	16	8	no	—
282	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
283	C₄×C₄₇	—	2	1	no	—
284	C₄×C₄₇	—	2	1	no	—
285	C₄×C₄₇	—	2	1	no	—
286	C₄×C₄₇	—	2	1	no	—
287	C₄×C₄₇	—	4	2	no	—
288	C₄×C₄₇	—	4	2	no	—
289	C₄×C₄₇	—	4	2	no	—
290	C₄×C₄₇	—	8	1	no	—
291	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
292	C₄×C₄₇	#576	1	2	yes	—
293	#3496	C₂×C₄₇	1	1	yes	characteristic, complemented
294	#3214	C₂×C₄₇	1	1	yes	characteristic, complemented
295	#3184	C₂×C₄₇	1	1	yes	characteristic, complemented
296	#3100	C₂×C₄₇	1	1	yes	characteristic, complemented
297	#1654	C₂×C₄₇	1	2	yes	complemented
298	#1639	C₂×C₄₇	1	2	yes	complemented
299	#1625	C₂×C₄₇	1	2	yes	complemented
300	#1619	C₂×C₄₇	1	2	yes	complemented
301	#1553	C₂×C₄₇	1	1	yes	characteristic, complemented
302	#1490	C₂×C₄₇	1	1	yes	characteristic, complemented
303	#1484	C₂×C₄₇	1	1	yes	characteristic, complemented
304	C₂×C₄₇	—	4	1	no	—
305	C₂×C₄₇	—	4	4	no	—
306	C₂×C₄₇	—	8	2	no	—
307	C₂×C₄₇	—	8	2	no	—
308	C₂×C₄₇	—	16	1	no	—
309	C₂×C₄₇	#3003	1	1	yes	characteristic
310	C₂×C₄₇	#3008	1	1	yes	characteristic
311	C₂×C₄₇	#3018	1	1	yes	characteristic
312	C₂×H(5,𝔽₂)	—	2	1	no	—
313	#547	—	2	1	no	—
314	#547	C₂²×C₄₇	1	2	yes	—
315	#546	—	2	2	no	—
316	#546	—	2	2	no	—
317	D₄²	—	2	1	no	—
318	D₄²	C₂²×C₄₇	1	2	yes	—
319	#537	—	2	1	no	—
320	#534	—	2	2	no	—
321	#532	C₂²×C₄₇	1	1	yes	characteristic
322	#532	C₂²×C₄₇	1	1	yes	characteristic
323	#532	C₂²×C₄₇	1	1	yes	characteristic, complemented
324	C₂×#121	—	2	2	no	—
325	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
326	#498	C₂²×C₄₇	1	1	yes	characteristic, complemented
327	#496	—	2	1	no	—
328	#493	C₂²×C₄₇	1	1	yes	characteristic, complemented
329	#489	—	2	1	no	—
330	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
331	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
332	#480	—	2	1	no	—
333	#474	C₂²×C₄₇	1	2	yes	complemented
334	#469	—	2	2	no	—
335	#461	C₂²×C₄₇	1	2	yes	complemented
336	#459	C₂²×C₄₇	1	2	yes	complemented
337	#459	C₂²×C₄₇	1	2	yes	complemented
338	#449	—	2	2	no	—
339	#447	—	2	1	no	—
340	#442	—	2	2	no	—
341	C₄×D₈	—	2	2	no	—
342	#432	C₂²×C₄₇	1	1	yes	characteristic, complemented
343	#431	C₂²×C₄₇	1	1	yes	characteristic, complemented
344	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic, complemented
345	#332	C₂²×C₄₇	1	2	yes	complemented
346	#331	C₂²×C₄₇	1	2	yes	complemented
347	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
348	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
349	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
350	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
351	C₄₇	#18598	1	1	yes	characteristic, direct product factor, Sylow
352	H(5,𝔽₂)	—	4	8	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	2	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂²×D₄	—	2	4	no	—
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
363	C₂³×C₄	—	2	1	no	—
364	C₂×SD₁₆	—	2	2	no	—
365	C₂×D₈	—	2	2	no	—
366	C₂×D₈	—	2	2	no	—
367	C₂×D₈	—	2	2	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
372	#127	D₄×C₄₇	1	1	yes	characteristic
373	#127	C₂³×C₄₇	1	1	yes	characteristic
374	#127	C₂³×C₄₇	1	1	yes	characteristic
375	#124	—	2	1	no	—
376	#124	—	2	1	no	—
377	#124	—	2	1	no	—
378	#123	—	2	4	no	—
379	#123	—	2	4	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	#121	—	2	4	no	—
383	#121	—	2	4	no	—
384	#121	—	2	2	no	—
385	#121	—	2	2	no	—
386	#121	—	2	1	no	—
387	#121	—	2	1	no	—
388	#121	—	2	2	no	—
389	#121	—	2	2	no	—
390	#121	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	D₄×C₄₇	1	2	yes	—
393	#121	D₄×C₄₇	1	2	yes	—
394	#120	—	2	4	no	—
395	#120	—	2	4	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	D₄×C₄₇	1	2	yes	—
403	C₄×D₄	D₄×C₄₇	1	2	yes	—
404	C₄×D₄	C₂³×C₄₇	1	2	yes	—
405	C₄×D₄	C₂³×C₄₇	1	2	yes	—
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	4	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
411	#107	—	2	2	no	—
412	#106	—	2	2	no	—
413	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
414	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
415	#103	—	2	2	no	—
416	#102	—	2	2	no	—
417	#102	—	2	2	no	—
418	#102	—	2	2	no	—
419	#102	—	2	2	no	—
420	#102	—	2	2	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	#97	—	2	1	no	—
424	#97	—	2	1	no	—
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
427	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
428	C₂⁴	—	2	1	no	—
429	C₂⁴	—	2	4	no	—
430	#41	—	4	4	no	—
431	#41	—	4	4	no	—
432	#41	—	4	8	no	—
433	#41	—	4	4	no	—
434	#41	—	4	4	no	—
435	#41	—	8	2	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	—	4	4	no	—
455	C₂×D₄	—	4	16	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	8	2	no	—
459	C₂×D₄	—	8	2	no	—
460	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
461	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
462	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	8	2	no	—
471	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
474	SD₁₆	—	8	2	no	—
475	D₈	—	4	4	no	—
476	D₈	—	4	4	no	—
477	D₈	—	8	2	no	—
478	M₁₆	—	4	2	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	2	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
490	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
491	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
503	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
504	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
505	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
506	C₂³	—	2	4	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	8	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	8	1	no	—
513	C₂³	—	8	1	no	—
514	C₂³	—	8	4	no	—
515	C₂³	—	8	4	no	—
516	C₂³	#120×C₄₇	1	1	yes	characteristic
517	Q₈	—	4	2	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	4	2	no	—
520	D₄	—	2	4	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	8	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	4	no	—
537	D₄	—	8	2	no	—
538	D₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	8	2	no	—
554	C₂×C₄	—	8	1	no	—
555	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
556	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
557	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
561	C₈	—	2	2	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	2	no	—
564	C₈	—	4	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	8	4	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	16	8	no	—
582	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	2	no	—
590	C₄	—	8	1	no	—
591	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
592	C₄	C₄₇×#576	1	2	yes	—
593	C₂	—	4	1	no	—
594	C₂	—	4	4	no	—
595	C₂	—	8	2	no	—
596	C₂	—	8	2	no	—
597	C₂	—	16	1	no	—
598	C₂	C₄₇×#3003	1	1	yes	characteristic
599	C₂	C₄₇×#3008	1	1	yes	characteristic
600	C₂	C₄₇×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#3496	C₂	semidirect
2. C₄₇×#3214	C₂	semidirect
3. C₄₇×#3184	C₂	semidirect
4. C₄₇×#3100	C₂	semidirect
5. C₄₇×#1654	C₂	semidirect
6. C₄₇×#1639	C₂	semidirect
7. C₄₇×#1625	C₂	semidirect
8. C₄₇×#1619	C₂	semidirect
9. C₄₇×#1553	C₂	semidirect
10. C₄₇×#1490	C₂	semidirect
11. C₄₇×#1484	C₂	semidirect
23. C₄₇×#532	C₂²	semidirect
26. C₄₇×#498	C₂²	semidirect
28. C₄₇×#493	C₂²	semidirect
30. C₄₇×#486	C₂²	semidirect
31. C₄₇×#486	C₂²	semidirect
33. C₄₇×#474	C₂²	semidirect
35. C₄₇×#461	C₂²	semidirect
36. C₄₇×#459	C₂²	semidirect
37. C₄₇×#459	C₂²	semidirect
42. C₄₇×#432	C₂²	semidirect
43. C₄₇×#431	C₂²	semidirect
44. C₄×M₁₆×C₄₇	C₂²	semidirect
45. C₄₇×#332	C₂²	semidirect
46. C₄₇×#331	C₂²	semidirect
47. C₄₇×D₄⋊C₈	C₂²	semidirect
48. C₄₇×D₄⋊C₈	C₂²	semidirect
49. C₄₇×D₄⋊C₈	C₂²	semidirect
50. C₄₇×D₄⋊C₈	C₂²	semidirect
264. #18598	C₄₇	direct (N × H)
293. #3496	C₂×C₄₇	semidirect
294. #3214	C₂×C₄₇	semidirect
295. #3184	C₂×C₄₇	semidirect
296. #3100	C₂×C₄₇	semidirect
297. #1654	C₂×C₄₇	semidirect
298. #1639	C₂×C₄₇	semidirect
299. #1625	C₂×C₄₇	semidirect
300. #1619	C₂×C₄₇	semidirect
301. #1553	C₂×C₄₇	semidirect
302. #1490	C₂×C₄₇	semidirect
303. #1484	C₂×C₄₇	semidirect
323. #532	C₂²×C₄₇	semidirect
326. #498	C₂²×C₄₇	semidirect
328. #493	C₂²×C₄₇	semidirect
330. #486	C₂²×C₄₇	semidirect
331. #486	C₂²×C₄₇	semidirect
333. #474	C₂²×C₄₇	semidirect
335. #461	C₂²×C₄₇	semidirect
336. #459	C₂²×C₄₇	semidirect
337. #459	C₂²×C₄₇	semidirect
342. #432	C₂²×C₄₇	semidirect
343. #431	C₂²×C₄₇	semidirect
344. C₄×M₁₆	C₂²×C₄₇	semidirect
345. #332	C₂²×C₄₇	semidirect
346. #331	C₂²×C₄₇	semidirect
347. D₄⋊C₈	C₂²×C₄₇	semidirect
348. D₄⋊C₈	C₂²×C₄₇	semidirect
349. D₄⋊C₈	C₂²×C₄₇	semidirect
350. D₄⋊C₈	C₂²×C₄₇	semidirect
351. C₄₇	#18598	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×#3496	2
C₄₇×#3214	2
C₄₇×#3184	2
C₄₇×#3100	2
C₄₇×#1654	2
C₄₇×#1639	2
C₄₇×#1625	2
C₄₇×#1619	2
C₄₇×#1553	2
C₄₇×#1490	2
C₄₇×#1484	2
#18598	47

Subgroups — C47×#18598 #26058296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18598 #26058296