Subgroups — C₄₇×#18838 #26058536

Order 12032.

1216 conjugacy classes of subgroups.

The subgroup lattice has 612 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×#3253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1635	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1629	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×#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×#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×#493	C₂²	1	1	yes	characteristic, complemented
27	C₄₇×#492	C₂²	1	1	yes	characteristic, complemented
28	C₄₇×#487	C₂²	1	1	yes	characteristic, complemented
29	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
30	C₄₇×#481	—	2	1	no	—
31	C₄₇×#476	—	2	1	no	—
32	C₄₇×#476	C₂²	1	2	yes	complemented
33	C₄₇×#476	C₂²	1	2	yes	complemented
34	C₄₇×#469	—	2	2	no	—
35	C₄₇×#463	—	2	2	no	—
36	C₄₇×#459	—	2	1	no	—
37	C₄₇×#459	C₂²	1	2	yes	complemented
38	C₄₇×#459	C₂²	1	2	yes	complemented
39	C₄₇×#449	—	2	2	no	—
40	C₄₇×#447	—	2	1	no	—
41	C₄₇×#442	—	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	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	#106×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	#102×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	#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	1	no	—
170	C₂²×C₄×C₄₇	—	8	1	no	—
171	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
174	SD₁₆×C₄₇	—	8	2	no	—
175	D₈×C₄₇	—	4	4	no	—
176	D₈×C₄₇	—	8	2	no	—
177	D₈×C₄₇	—	8	2	no	—
178	M₁₆×C₄₇	—	8	1	no	—
179	C₂×C₈×C₄₇	—	2	1	no	—
180	C₂×C₈×C₄₇	—	2	2	no	—
181	C₂×C₈×C₄₇	—	2	1	no	—
182	C₂×C₈×C₄₇	—	2	2	no	—
183	C₄⋊C₄×C₄₇	—	2	4	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	—	2	1	no	—
189	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
192	C₂²⋊C₄×C₄₇	—	2	4	no	—
193	C₂²⋊C₄×C₄₇	—	2	4	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	—	2	2	no	—
200	C₂²⋊C₄×C₄₇	—	4	1	no	—
201	C₂²⋊C₄×C₄₇	—	4	1	no	—
202	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
206	C₂³×C₄₇	—	2	4	no	—
207	C₂³×C₄₇	—	2	2	no	—
208	C₂³×C₄₇	—	2	2	no	—
209	C₂³×C₄₇	—	2	2	no	—
210	C₂³×C₄₇	—	4	8	no	—
211	C₂³×C₄₇	—	4	1	no	—
212	C₂³×C₄₇	—	8	1	no	—
213	C₂³×C₄₇	—	8	1	no	—
214	C₂³×C₄₇	—	8	4	no	—
215	C₂³×C₄₇	—	8	4	no	—
216	C₂³×C₄₇	#120	1	1	yes	characteristic
217	Q₈×C₄₇	—	4	2	no	—
218	Q₈×C₄₇	—	4	2	no	—
219	Q₈×C₄₇	—	4	2	no	—
220	D₄×C₄₇	—	2	4	no	—
221	D₄×C₄₇	—	2	2	no	—
222	D₄×C₄₇	—	2	2	no	—
223	D₄×C₄₇	—	2	2	no	—
224	D₄×C₄₇	—	4	2	no	—
225	D₄×C₄₇	—	4	2	no	—
226	D₄×C₄₇	—	4	2	no	—
227	D₄×C₄₇	—	4	4	no	—
228	D₄×C₄₇	—	4	4	no	—
229	D₄×C₄₇	—	4	8	no	—
230	D₄×C₄₇	—	4	8	no	—
231	D₄×C₄₇	—	4	2	no	—
232	D₄×C₄₇	—	4	2	no	—
233	D₄×C₄₇	—	4	1	no	—
234	D₄×C₄₇	—	4	1	no	—
235	D₄×C₄₇	—	4	1	no	—
236	D₄×C₄₇	—	4	1	no	—
237	D₄×C₄₇	—	8	1	no	—
238	D₄×C₄₇	—	8	4	no	—
239	D₄×C₄₇	—	8	2	no	—
240	D₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	2	no	—
247	C₂×C₄×C₄₇	—	4	1	no	—
248	C₂×C₄×C₄₇	—	4	4	no	—
249	C₂×C₄×C₄₇	—	4	8	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	—	4	2	no	—
252	C₂×C₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	—	4	2	no	—
254	C₂×C₄×C₄₇	—	4	1	no	—
255	C₂×C₄×C₄₇	—	8	2	no	—
256	C₂×C₄×C₄₇	—	8	2	no	—
257	C₂×C₄×C₄₇	—	8	1	no	—
258	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
259	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
260	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
264	C₈×C₄₇	—	4	1	no	—
265	C₈×C₄₇	—	4	1	no	—
266	C₈×C₄₇	—	4	2	no	—
267	C₈×C₄₇	—	4	2	no	—
268	#18838	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂²×C₄₇	—	2	1	no	—
270	C₂²×C₄₇	—	2	4	no	—
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	2	1	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	—	4	2	no	—
278	C₂²×C₄₇	—	4	2	no	—
279	C₂²×C₄₇	—	4	2	no	—
280	C₂²×C₄₇	—	4	2	no	—
281	C₂²×C₄₇	—	8	4	no	—
282	C₂²×C₄₇	—	8	1	no	—
283	C₂²×C₄₇	—	8	1	no	—
284	C₂²×C₄₇	—	8	1	no	—
285	C₂²×C₄₇	—	16	8	no	—
286	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	2	1	no	—
290	C₄×C₄₇	—	2	1	no	—
291	C₄×C₄₇	—	4	2	no	—
292	C₄×C₄₇	—	4	2	no	—
293	C₄×C₄₇	—	4	2	no	—
294	C₄×C₄₇	—	8	1	no	—
295	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
296	C₄×C₄₇	#576	1	1	yes	characteristic
297	C₄×C₄₇	#577	1	1	yes	characteristic
298	#3496	C₂×C₄₇	1	1	yes	characteristic, complemented
299	#3253	C₂×C₄₇	1	1	yes	characteristic, complemented
300	#3207	C₂×C₄₇	1	1	yes	characteristic, complemented
301	#3109	C₂×C₄₇	1	1	yes	characteristic, complemented
302	#1635	C₂×C₄₇	1	2	yes	complemented
303	#1629	C₂×C₄₇	1	2	yes	complemented
304	#1625	C₂×C₄₇	1	2	yes	complemented
305	#1619	C₂×C₄₇	1	2	yes	complemented
306	#1557	C₂×C₄₇	1	1	yes	characteristic, complemented
307	#1496	C₂×C₄₇	1	1	yes	characteristic, complemented
308	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
309	C₂×C₄₇	—	4	1	no	—
310	C₂×C₄₇	—	4	4	no	—
311	C₂×C₄₇	—	8	2	no	—
312	C₂×C₄₇	—	8	2	no	—
313	C₂×C₄₇	—	16	1	no	—
314	C₂×C₄₇	#3003	1	1	yes	characteristic
315	C₂×C₄₇	#3012	1	1	yes	characteristic
316	C₂×C₄₇	#3021	1	1	yes	characteristic
317	C₂×H(5,𝔽₂)	—	2	1	no	—
318	#547	—	2	1	no	—
319	#547	C₂²×C₄₇	1	2	yes	—
320	#546	—	2	2	no	—
321	#546	—	2	2	no	—
322	D₄²	—	2	1	no	—
323	D₄²	C₂²×C₄₇	1	2	yes	—
324	#537	—	2	1	no	—
325	#534	—	2	2	no	—
326	#532	C₂²×C₄₇	1	1	yes	characteristic
327	#532	C₂²×C₄₇	1	1	yes	characteristic
328	#532	C₂²×C₄₇	1	1	yes	characteristic, complemented
329	C₂×#121	—	2	2	no	—
330	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
331	#493	C₂²×C₄₇	1	1	yes	characteristic, complemented
332	#492	C₂²×C₄₇	1	1	yes	characteristic, complemented
333	#487	C₂²×C₄₇	1	1	yes	characteristic, complemented
334	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
335	#481	—	2	1	no	—
336	#476	—	2	1	no	—
337	#476	C₂²×C₄₇	1	2	yes	complemented
338	#476	C₂²×C₄₇	1	2	yes	complemented
339	#469	—	2	2	no	—
340	#463	—	2	2	no	—
341	#459	—	2	1	no	—
342	#459	C₂²×C₄₇	1	2	yes	complemented
343	#459	C₂²×C₄₇	1	2	yes	complemented
344	#449	—	2	2	no	—
345	#447	—	2	1	no	—
346	#442	—	2	2	no	—
347	#432	C₂²×C₄₇	1	1	yes	characteristic, complemented
348	#431	C₂²×C₄₇	1	1	yes	characteristic, complemented
349	#423	C₂²×C₄₇	1	1	yes	characteristic, complemented
350	#332	C₂²×C₄₇	1	2	yes	complemented
351	#331	C₂²×C₄₇	1	2	yes	complemented
352	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
353	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
354	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
355	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
356	C₄₇	#18838	1	1	yes	characteristic, direct product factor, Sylow
357	H(5,𝔽₂)	—	4	8	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂²×D₄	—	2	4	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
368	C₂³×C₄	—	2	1	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×D₈	—	2	2	no	—
371	C₂×D₈	—	2	2	no	—
372	C₂×D₈	—	2	2	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
377	#127	D₄×C₄₇	1	1	yes	characteristic
378	#127	C₂³×C₄₇	1	1	yes	characteristic
379	#127	C₂³×C₄₇	1	1	yes	characteristic
380	#124	—	2	1	no	—
381	#124	—	2	1	no	—
382	#124	—	2	1	no	—
383	#123	—	2	4	no	—
384	#123	—	2	4	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	#121	—	2	4	no	—
388	#121	—	2	4	no	—
389	#121	—	2	2	no	—
390	#121	—	2	2	no	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	#121	—	2	2	no	—
394	#121	—	2	2	no	—
395	#121	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	D₄×C₄₇	1	2	yes	—
398	#121	D₄×C₄₇	1	2	yes	—
399	#120	—	2	4	no	—
400	#120	—	2	4	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	D₄×C₄₇	1	2	yes	—
408	C₄×D₄	D₄×C₄₇	1	2	yes	—
409	C₄×D₄	C₂³×C₄₇	1	2	yes	—
410	C₄×D₄	C₂³×C₄₇	1	2	yes	—
411	C₂×C₄⋊C₄	—	2	2	no	—
412	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	2	4	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
416	#106	—	2	2	no	—
417	#106	—	2	2	no	—
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
421	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
422	#103	—	2	2	no	—
423	#102	—	2	2	no	—
424	#102	—	2	2	no	—
425	#102	—	2	2	no	—
426	#102	—	2	2	no	—
427	#102	—	2	2	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	#97	—	2	1	no	—
431	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
433	C₂⁴	—	2	1	no	—
434	C₂⁴	—	2	4	no	—
435	#41	—	4	4	no	—
436	#41	—	4	4	no	—
437	#41	—	4	8	no	—
438	#41	—	4	4	no	—
439	#41	—	4	4	no	—
440	#41	—	8	2	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	4	8	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	16	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	8	2	no	—
464	C₂×D₄	—	8	2	no	—
465	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
466	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
467	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	8	1	no	—
476	C₂²×C₄	—	8	1	no	—
477	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
480	SD₁₆	—	8	2	no	—
481	D₈	—	4	4	no	—
482	D₈	—	8	2	no	—
483	D₈	—	8	2	no	—
484	M₁₆	—	8	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
496	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
497	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
511	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
512	C₂³	—	2	4	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	4	8	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	8	1	no	—
519	C₂³	—	8	1	no	—
520	C₂³	—	8	4	no	—
521	C₂³	—	8	4	no	—
522	C₂³	#120×C₄₇	1	1	yes	characteristic
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	8	no	—
536	D₄	—	4	8	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	8	1	no	—
544	D₄	—	8	4	no	—
545	D₄	—	8	2	no	—
546	D₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	8	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
565	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
566	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	2	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	8	4	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	16	8	no	—
591	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	8	1	no	—
600	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
601	C₄	C₄₇×#576	1	1	yes	characteristic
602	C₄	C₄₇×#577	1	1	yes	characteristic
603	C₂	—	4	1	no	—
604	C₂	—	4	4	no	—
605	C₂	—	8	2	no	—
606	C₂	—	8	2	no	—
607	C₂	—	16	1	no	—
608	C₂	C₄₇×#3003	1	1	yes	characteristic
609	C₂	C₄₇×#3012	1	1	yes	characteristic
610	C₂	C₄₇×#3021	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×#3253	C₂	semidirect
3. C₄₇×#3207	C₂	semidirect
4. C₄₇×#3109	C₂	semidirect
5. C₄₇×#1635	C₂	semidirect
6. C₄₇×#1629	C₂	semidirect
7. C₄₇×#1625	C₂	semidirect
8. C₄₇×#1619	C₂	semidirect
9. C₄₇×#1557	C₂	semidirect
10. C₄₇×#1496	C₂	semidirect
11. C₄₇×#1486	C₂	semidirect
23. C₄₇×#532	C₂²	semidirect
26. C₄₇×#493	C₂²	semidirect
27. C₄₇×#492	C₂²	semidirect
28. C₄₇×#487	C₂²	semidirect
29. C₄₇×#486	C₂²	semidirect
32. C₄₇×#476	C₂²	semidirect
33. C₄₇×#476	C₂²	semidirect
37. C₄₇×#459	C₂²	semidirect
38. C₄₇×#459	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
268. #18838	C₄₇	direct (N × H)
298. #3496	C₂×C₄₇	semidirect
299. #3253	C₂×C₄₇	semidirect
300. #3207	C₂×C₄₇	semidirect
301. #3109	C₂×C₄₇	semidirect
302. #1635	C₂×C₄₇	semidirect
303. #1629	C₂×C₄₇	semidirect
304. #1625	C₂×C₄₇	semidirect
305. #1619	C₂×C₄₇	semidirect
306. #1557	C₂×C₄₇	semidirect
307. #1496	C₂×C₄₇	semidirect
308. #1486	C₂×C₄₇	semidirect
328. #532	C₂²×C₄₇	semidirect
331. #493	C₂²×C₄₇	semidirect
332. #492	C₂²×C₄₇	semidirect
333. #487	C₂²×C₄₇	semidirect
334. #486	C₂²×C₄₇	semidirect
337. #476	C₂²×C₄₇	semidirect
338. #476	C₂²×C₄₇	semidirect
342. #459	C₂²×C₄₇	semidirect
343. #459	C₂²×C₄₇	semidirect
347. #432	C₂²×C₄₇	semidirect
348. #431	C₂²×C₄₇	semidirect
349. #423	C₂²×C₄₇	semidirect
350. #332	C₂²×C₄₇	semidirect
351. #331	C₂²×C₄₇	semidirect
352. D₄⋊C₈	C₂²×C₄₇	semidirect
353. D₄⋊C₈	C₂²×C₄₇	semidirect
354. D₄⋊C₈	C₂²×C₄₇	semidirect
355. D₄⋊C₈	C₂²×C₄₇	semidirect
356. C₄₇	#18838	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×#3253	2
C₄₇×#3207	2
C₄₇×#3109	2
C₄₇×#1635	2
C₄₇×#1629	2
C₄₇×#1625	2
C₄₇×#1619	2
C₄₇×#1557	2
C₄₇×#1496	2
C₄₇×#1486	2
#18838	47

Subgroups — C47×#18838 #26058536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18838 #26058536