Subgroups — C₄₇×#18846 #26058544

Order 12032.

1182 conjugacy classes of subgroups.

The subgroup lattice has 592 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
2	C₄₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1654	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1647	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1639	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1639	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1557	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1486	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×#533	C₂²	1	1	yes	characteristic, complemented
22	C₄₇×#532	C₂²	1	1	yes	characteristic
23	C₄₇×#532	C₂²	1	1	yes	characteristic
24	C₂×#121×C₄₇	—	2	2	no	—
25	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
27	C₄₇×#498	C₂²	1	1	yes	characteristic, complemented
28	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
29	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
30	C₄₇×#484	—	2	1	no	—
31	C₄₇×#482	—	2	2	no	—
32	C₄₇×#478	—	2	2	no	—
33	C₄₇×#477	—	2	1	no	—
34	C₄₇×#474	C₂²	1	2	yes	complemented
35	C₄₇×#474	C₂²	1	2	yes	complemented
36	C₄₇×#468	—	2	2	no	—
37	C₄₇×#461	C₂²	1	2	yes	complemented
38	C₄₇×#461	C₂²	1	2	yes	complemented
39	C₄₇×#460	—	2	1	no	—
40	C₄₇×#450	—	2	1	no	—
41	C₄₇×#440	—	2	2	no	—
42	C₄₇×#432	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
44	C₄₇×#423	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	C₂²×D₄×C₄₇	—	2	4	no	—
57	C₂²×D₄×C₄₇	—	2	2	no	—
58	C₂²×D₄×C₄₇	—	2	2	no	—
59	C₂²×D₄×C₄₇	—	2	2	no	—
60	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	—	2	1	no	—
62	C₂×SD₁₆×C₄₇	—	2	2	no	—
63	C₂×SD₁₆×C₄₇	—	2	2	no	—
64	C₂×M₁₆×C₄₇	—	2	1	no	—
65	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
69	#127×C₄₇	D₄	1	1	yes	characteristic
70	#127×C₄₇	C₂³	1	1	yes	characteristic
71	#125×C₄₇	—	2	1	no	—
72	#124×C₄₇	—	2	1	no	—
73	#124×C₄₇	—	2	1	no	—
74	#123×C₄₇	—	2	4	no	—
75	#123×C₄₇	—	2	4	no	—
76	C₂²⋊Q₈×C₄₇	—	2	2	no	—
77	C₂²⋊Q₈×C₄₇	—	2	2	no	—
78	C₂²⋊Q₈×C₄₇	—	2	1	no	—
79	C₂²⋊Q₈×C₄₇	—	2	1	no	—
80	#121×C₄₇	—	2	4	no	—
81	#121×C₄₇	—	2	4	no	—
82	#121×C₄₇	—	2	2	no	—
83	#121×C₄₇	—	2	2	no	—
84	#121×C₄₇	—	2	1	no	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	—	2	2	no	—
87	#121×C₄₇	—	2	2	no	—
88	#121×C₄₇	D₄	1	2	yes	—
89	#121×C₄₇	D₄	1	2	yes	—
90	#120×C₄₇	—	2	4	no	—
91	#120×C₄₇	—	2	4	no	—
92	C₄×Q₈×C₄₇	—	2	1	no	—
93	C₄×Q₈×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	—	2	1	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	D₄	1	2	yes	—
99	C₄×D₄×C₄₇	D₄	1	2	yes	—
100	C₄×D₄×C₄₇	C₂³	1	2	yes	—
101	C₄×D₄×C₄₇	C₂³	1	2	yes	—
102	#117×C₄₇	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
106	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	#107×C₄₇	—	2	2	no	—
109	#107×C₄₇	—	2	2	no	—
110	#107×C₄₇	—	2	2	no	—
111	#106×C₄₇	—	2	2	no	—
112	C₄⋊C₈×C₄₇	—	2	1	no	—
113	C₄⋊C₈×C₄₇	—	2	1	no	—
114	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
115	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
116	#103×C₄₇	—	2	2	no	—
117	#103×C₄₇	—	2	2	no	—
118	#102×C₄₇	—	2	2	no	—
119	#102×C₄₇	—	2	2	no	—
120	#102×C₄₇	—	2	2	no	—
121	#102×C₄₇	—	2	2	no	—
122	C₂²⋊C₈×C₄₇	—	2	1	no	—
123	C₂²⋊C₈×C₄₇	—	2	1	no	—
124	#97×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	C₂×Q₈×C₄₇	—	2	1	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	—	4	8	no	—
150	C₂×D₄×C₄₇	—	4	4	no	—
151	C₂×D₄×C₄₇	—	4	16	no	—
152	C₂×D₄×C₄₇	—	4	4	no	—
153	C₂×D₄×C₄₇	—	8	2	no	—
154	C₂×D₄×C₄₇	—	8	2	no	—
155	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₇	—	2	4	no	—
159	C₂²×C₄×C₄₇	—	2	1	no	—
160	C₂²×C₄×C₄₇	—	2	2	no	—
161	C₂²×C₄×C₄₇	—	2	2	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	8	1	no	—
165	C₂²×C₄×C₄₇	—	8	1	no	—
166	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
169	SD₁₆×C₄₇	—	4	4	no	—
170	SD₁₆×C₄₇	—	8	2	no	—
171	M₁₆×C₄₇	—	8	1	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	1	no	—
176	C₄⋊C₄×C₄₇	—	2	4	no	—
177	C₄⋊C₄×C₄₇	—	2	1	no	—
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	—	2	1	no	—
183	C₄⋊C₄×C₄₇	—	2	1	no	—
184	C₄⋊C₄×C₄₇	—	4	1	no	—
185	C₄⋊C₄×C₄₇	—	4	1	no	—
186	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
187	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
189	C₂²⋊C₄×C₄₇	—	2	4	no	—
190	C₂²⋊C₄×C₄₇	—	2	4	no	—
191	C₂²⋊C₄×C₄₇	—	2	2	no	—
192	C₂²⋊C₄×C₄₇	—	2	2	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	—	4	1	no	—
198	C₄²×C₄₇	—	4	1	no	—
199	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
203	C₂³×C₄₇	—	2	4	no	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	4	8	no	—
208	C₂³×C₄₇	—	8	1	no	—
209	C₂³×C₄₇	—	8	1	no	—
210	C₂³×C₄₇	—	8	4	no	—
211	C₂³×C₄₇	—	8	4	no	—
212	C₂³×C₄₇	#120	1	1	yes	characteristic
213	Q₈×C₄₇	—	4	2	no	—
214	Q₈×C₄₇	—	4	2	no	—
215	Q₈×C₄₇	—	4	2	no	—
216	Q₈×C₄₇	—	4	1	no	—
217	Q₈×C₄₇	—	4	1	no	—
218	D₄×C₄₇	—	2	4	no	—
219	D₄×C₄₇	—	2	2	no	—
220	D₄×C₄₇	—	2	2	no	—
221	D₄×C₄₇	—	2	2	no	—
222	D₄×C₄₇	—	4	2	no	—
223	D₄×C₄₇	—	4	2	no	—
224	D₄×C₄₇	—	4	4	no	—
225	D₄×C₄₇	—	4	4	no	—
226	D₄×C₄₇	—	4	8	no	—
227	D₄×C₄₇	—	4	8	no	—
228	D₄×C₄₇	—	4	2	no	—
229	D₄×C₄₇	—	4	1	no	—
230	D₄×C₄₇	—	4	1	no	—
231	D₄×C₄₇	—	8	1	no	—
232	D₄×C₄₇	—	8	4	no	—
233	D₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	2	no	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	4	1	no	—
241	C₂×C₄×C₄₇	—	4	4	no	—
242	C₂×C₄×C₄₇	—	4	8	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	4	2	no	—
246	C₂×C₄×C₄₇	—	4	2	no	—
247	C₂×C₄×C₄₇	—	4	1	no	—
248	C₂×C₄×C₄₇	—	4	1	no	—
249	C₂×C₄×C₄₇	—	8	2	no	—
250	C₂×C₄×C₄₇	—	8	1	no	—
251	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
252	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
253	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
257	C₈×C₄₇	—	4	1	no	—
258	C₈×C₄₇	—	4	1	no	—
259	C₈×C₄₇	—	4	2	no	—
260	C₈×C₄₇	—	4	2	no	—
261	#18846	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	4	no	—
264	C₂²×C₄₇	—	2	1	no	—
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	4	2	no	—
267	C₂²×C₄₇	—	4	2	no	—
268	C₂²×C₄₇	—	4	2	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	—	8	4	no	—
275	C₂²×C₄₇	—	16	8	no	—
276	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	2	1	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	—	4	2	no	—
282	C₄×C₄₇	—	4	2	no	—
283	C₄×C₄₇	—	4	2	no	—
284	C₄×C₄₇	—	8	1	no	—
285	C₄×C₄₇	—	8	1	no	—
286	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
287	C₄×C₄₇	#576	1	1	yes	characteristic
288	C₄×C₄₇	#577	1	1	yes	characteristic
289	#3496	C₂×C₄₇	1	1	yes	characteristic
290	#3254	C₂×C₄₇	1	1	yes	characteristic, complemented
291	#3228	C₂×C₄₇	1	1	yes	characteristic, complemented
292	#3110	C₂×C₄₇	1	1	yes	characteristic, complemented
293	#1654	C₂×C₄₇	1	2	yes	complemented
294	#1647	C₂×C₄₇	1	2	yes	complemented
295	#1639	C₂×C₄₇	1	2	yes	complemented
296	#1639	C₂×C₄₇	1	2	yes	complemented
297	#1557	C₂×C₄₇	1	1	yes	characteristic, complemented
298	#1496	C₂×C₄₇	1	1	yes	characteristic, complemented
299	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
300	C₂×C₄₇	—	4	1	no	—
301	C₂×C₄₇	—	4	4	no	—
302	C₂×C₄₇	—	8	2	no	—
303	C₂×C₄₇	—	8	2	no	—
304	C₂×C₄₇	#3003	1	1	yes	characteristic
305	C₂×C₄₇	#3012	1	1	yes	characteristic
306	C₂×C₄₇	#3022	1	1	yes	characteristic
307	C₂×H(5,𝔽₂)	—	2	1	no	—
308	#547	—	2	1	no	—
309	#547	C₂²×C₄₇	1	2	yes	—
310	#546	—	2	2	no	—
311	#546	—	2	2	no	—
312	D₄²	—	2	1	no	—
313	D₄²	C₂²×C₄₇	1	2	yes	—
314	#537	—	2	1	no	—
315	#534	—	2	2	no	—
316	#533	C₂²×C₄₇	1	1	yes	characteristic, complemented
317	#532	C₂²×C₄₇	1	1	yes	characteristic
318	#532	C₂²×C₄₇	1	1	yes	characteristic
319	C₂×#121	—	2	2	no	—
320	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
321	#500	C₂²×C₄₇	1	1	yes	characteristic, complemented
322	#498	C₂²×C₄₇	1	1	yes	characteristic, complemented
323	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
324	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
325	#484	—	2	1	no	—
326	#482	—	2	2	no	—
327	#478	—	2	2	no	—
328	#477	—	2	1	no	—
329	#474	C₂²×C₄₇	1	2	yes	complemented
330	#474	C₂²×C₄₇	1	2	yes	complemented
331	#468	—	2	2	no	—
332	#461	C₂²×C₄₇	1	2	yes	complemented
333	#461	C₂²×C₄₇	1	2	yes	complemented
334	#460	—	2	1	no	—
335	#450	—	2	1	no	—
336	#440	—	2	2	no	—
337	#432	C₂²×C₄₇	1	1	yes	characteristic, complemented
338	#431	C₂²×C₄₇	1	1	yes	characteristic, complemented
339	#423	C₂²×C₄₇	1	1	yes	characteristic, complemented
340	#332	C₂²×C₄₇	1	2	yes	complemented
341	#331	C₂²×C₄₇	1	2	yes	complemented
342	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
343	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
344	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
345	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
346	C₄₇	#18846	1	1	yes	characteristic, direct product factor, Sylow
347	H(5,𝔽₂)	—	4	8	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂²×D₄	—	2	4	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂×SD₁₆	—	2	2	no	—
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
363	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
365	#127	D₄×C₄₇	1	1	yes	characteristic
366	#127	C₂³×C₄₇	1	1	yes	characteristic
367	#125	—	2	1	no	—
368	#124	—	2	1	no	—
369	#124	—	2	1	no	—
370	#123	—	2	4	no	—
371	#123	—	2	4	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	#121	—	2	4	no	—
377	#121	—	2	4	no	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	—	2	2	no	—
383	#121	—	2	2	no	—
384	#121	D₄×C₄₇	1	2	yes	—
385	#121	D₄×C₄₇	1	2	yes	—
386	#120	—	2	4	no	—
387	#120	—	2	4	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	D₄×C₄₇	1	2	yes	—
395	C₄×D₄	D₄×C₄₇	1	2	yes	—
396	C₄×D₄	C₂³×C₄₇	1	2	yes	—
397	C₄×D₄	C₂³×C₄₇	1	2	yes	—
398	#117	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	4	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
404	#107	—	2	2	no	—
405	#107	—	2	2	no	—
406	#107	—	2	2	no	—
407	#106	—	2	2	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
411	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
412	#103	—	2	2	no	—
413	#103	—	2	2	no	—
414	#102	—	2	2	no	—
415	#102	—	2	2	no	—
416	#102	—	2	2	no	—
417	#102	—	2	2	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	#97	—	2	1	no	—
421	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
423	C₂⁴	—	2	1	no	—
424	C₂⁴	—	2	4	no	—
425	#41	—	4	4	no	—
426	#41	—	4	4	no	—
427	#41	—	4	8	no	—
428	#41	—	4	4	no	—
429	#41	—	4	4	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	16	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	8	2	no	—
450	C₂×D₄	—	8	2	no	—
451	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
452	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
453	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	8	1	no	—
461	C₂²×C₄	—	8	1	no	—
462	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
465	SD₁₆	—	4	4	no	—
466	SD₁₆	—	8	2	no	—
467	M₁₆	—	8	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
483	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
484	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₄²	—	4	1	no	—
495	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
498	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	8	no	—
504	C₂³	—	8	1	no	—
505	C₂³	—	8	1	no	—
506	C₂³	—	8	4	no	—
507	C₂³	—	8	4	no	—
508	C₂³	#120×C₄₇	1	1	yes	characteristic
509	Q₈	—	4	2	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	4	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	8	no	—
523	D₄	—	4	8	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	8	1	no	—
528	D₄	—	8	4	no	—
529	D₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	—	8	1	no	—
547	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
548	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
549	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	2	no	—
556	C₈	—	4	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	8	4	no	—
570	C₂²	—	16	8	no	—
571	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	2	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
582	C₄	C₄₇×#576	1	1	yes	characteristic
583	C₄	C₄₇×#577	1	1	yes	characteristic
584	C₂	—	4	1	no	—
585	C₂	—	4	4	no	—
586	C₂	—	8	2	no	—
587	C₂	—	8	2	no	—
588	C₂	C₄₇×#3003	1	1	yes	characteristic
589	C₂	C₄₇×#3012	1	1	yes	characteristic
590	C₂	C₄₇×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	C₄₇×#3496	C₂
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
2. C₄₇×#3254	C₂	semidirect
3. C₄₇×#3228	C₂	semidirect
4. C₄₇×#3110	C₂	semidirect
5. C₄₇×#1654	C₂	semidirect
6. C₄₇×#1647	C₂	semidirect
7. C₄₇×#1639	C₂	semidirect
8. C₄₇×#1639	C₂	semidirect
9. C₄₇×#1557	C₂	semidirect
10. C₄₇×#1496	C₂	semidirect
11. C₄₇×#1486	C₂	semidirect
21. C₄₇×#533	C₂²	semidirect
26. C₄₇×#500	C₂²	semidirect
27. C₄₇×#498	C₂²	semidirect
28. C₄₇×#486	C₂²	semidirect
29. C₄₇×#486	C₂²	semidirect
34. C₄₇×#474	C₂²	semidirect
35. C₄₇×#474	C₂²	semidirect
37. C₄₇×#461	C₂²	semidirect
38. C₄₇×#461	C₂²	semidirect
42. C₄₇×#432	C₂²	semidirect
43. C₄₇×#431	C₂²	semidirect
44. C₄₇×#423	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
261. #18846	C₄₇	direct (N × H)
290. #3254	C₂×C₄₇	semidirect
291. #3228	C₂×C₄₇	semidirect
292. #3110	C₂×C₄₇	semidirect
293. #1654	C₂×C₄₇	semidirect
294. #1647	C₂×C₄₇	semidirect
295. #1639	C₂×C₄₇	semidirect
296. #1639	C₂×C₄₇	semidirect
297. #1557	C₂×C₄₇	semidirect
298. #1496	C₂×C₄₇	semidirect
299. #1486	C₂×C₄₇	semidirect
316. #533	C₂²×C₄₇	semidirect
321. #500	C₂²×C₄₇	semidirect
322. #498	C₂²×C₄₇	semidirect
323. #486	C₂²×C₄₇	semidirect
324. #486	C₂²×C₄₇	semidirect
329. #474	C₂²×C₄₇	semidirect
330. #474	C₂²×C₄₇	semidirect
332. #461	C₂²×C₄₇	semidirect
333. #461	C₂²×C₄₇	semidirect
337. #432	C₂²×C₄₇	semidirect
338. #431	C₂²×C₄₇	semidirect
339. #423	C₂²×C₄₇	semidirect
340. #332	C₂²×C₄₇	semidirect
341. #331	C₂²×C₄₇	semidirect
342. D₄⋊C₈	C₂²×C₄₇	semidirect
343. D₄⋊C₈	C₂²×C₄₇	semidirect
344. D₄⋊C₈	C₂²×C₄₇	semidirect
345. D₄⋊C₈	C₂²×C₄₇	semidirect
346. C₄₇	#18846	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×#3254	2
C₄₇×#3228	2
C₄₇×#3110	2
C₄₇×#1654	2
C₄₇×#1647	2
C₄₇×#1639	2
C₄₇×#1557	2
C₄₇×#1496	2
C₄₇×#1486	2
#18846	47

Subgroups — C47×#18846 #26058544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18846 #26058544