Subgroups — C₄₇×#24772 #26064470

Order 12032.

840 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#473	C₂	1	2	yes	maximal
2	C₄₇×#3039	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#137×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2906	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#2064	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2047	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1908	C₂	1	2	yes	maximal
11	C₄₇×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₇	C₂²	1	2	yes	—
13	C₂×#137×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂×#131×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#473	—	2	8	no	—
20	C₄₇×#462	—	2	1	no	—
21	C₄₇×#462	—	2	1	no	—
22	C₄₇×#462	—	2	1	no	—
23	C₄₇×#462	—	2	1	no	—
24	C₄₇×#462	—	2	2	no	—
25	C₄₇×#461	—	2	1	no	—
26	C₄₇×#461	—	2	1	no	—
27	C₄₇×#441	—	2	1	no	—
28	C₄₇×#440	—	2	1	no	—
29	C₄×Q₁₆×C₄₇	—	2	1	no	—
30	C₄×SD₁₆×C₄₇	—	2	1	no	—
31	C₂×#108×C₄₇	C₂²	1	2	yes	—
32	C₄₇×#428	C₂²	1	1	yes	characteristic
33	C₄₇×#424	—	2	2	no	—
34	C₄₇×#424	C₂²	1	2	yes	—
35	C₄₇×#423	—	2	1	no	—
36	C₄₇×#423	C₂²	1	1	yes	characteristic
37	C₄₇×#423	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#419	C₂²	1	2	yes	—
41	C₄₇×#419	C₂²	1	1	yes	characteristic
42	C₄₇×#417	C₂²	1	1	yes	characteristic
43	C₂×#103×C₄₇	C₂²	1	2	yes	—
44	C₂×#101×C₄₇	C₂²	1	2	yes	—
45	C₂×#101×C₄₇	C₂²	1	2	yes	—
46	C₂×#101×C₄₇	C₂²	1	2	yes	—
47	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
48	C₄₇×#343	C₂²	1	2	yes	—
49	C₄₇×#341	C₂²	1	2	yes	—
50	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
52	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
53	#137×C₄₇	—	2	2	no	—
54	#137×C₄₇	—	2	4	no	—
55	#137×C₄₇	—	2	4	no	—
56	#137×C₄₇	D₄	1	4	yes	—
57	C₂×Q₁₆×C₄₇	—	2	1	no	—
58	C₂×Q₁₆×C₄₇	—	2	2	no	—
59	C₂×Q₁₆×C₄₇	—	2	4	no	—
60	C₂×Q₁₆×C₄₇	—	2	2	no	—
61	C₂×Q₁₆×C₄₇	—	2	2	no	—
62	C₂×Q₁₆×C₄₇	—	4	2	no	—
63	C₂×SD₁₆×C₄₇	—	2	1	no	—
64	C₂×SD₁₆×C₄₇	—	2	2	no	—
65	#131×C₄₇	—	2	4	no	—
66	#131×C₄₇	—	4	2	no	—
67	C₂×M₁₆×C₄₇	—	2	2	no	—
68	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
69	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
70	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	—	2	2	no	—
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	C₄⋊Q₈×C₄₇	—	2	1	no	—
75	C₄⋊Q₈×C₄₇	—	2	1	no	—
76	C₄⋊Q₈×C₄₇	—	2	1	no	—
77	C₄⋊Q₈×C₄₇	—	2	1	no	—
78	C₄×Q₈×C₄₇	—	2	1	no	—
79	C₄×Q₈×C₄₇	—	2	1	no	—
80	C₄×Q₈×C₄₇	—	2	1	no	—
81	C₄×Q₈×C₄₇	—	2	1	no	—
82	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
84	C₄×D₄×C₄₇	—	2	1	no	—
85	C₄×D₄×C₄₇	—	2	1	no	—
86	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
87	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
88	#117×C₄₇	—	2	1	no	—
89	#117×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	—	2	1	no	—
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	#108×C₄₇	—	2	4	no	—
98	#107×C₄₇	—	2	1	no	—
99	#106×C₄₇	—	2	1	no	—
100	C₄⋊C₈×C₄₇	—	2	2	no	—
101	C₄⋊C₈×C₄₇	—	2	2	no	—
102	C₄⋊C₈×C₄₇	—	2	1	no	—
103	C₄⋊C₈×C₄₇	—	2	1	no	—
104	C₄⋊C₈×C₄₇	—	2	1	no	—
105	C₄⋊C₈×C₄₇	—	2	1	no	—
106	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
107	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
108	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
109	#103×C₄₇	—	2	1	no	—
110	#103×C₄₇	—	2	2	no	—
111	#103×C₄₇	—	2	2	no	—
112	#103×C₄₇	—	2	2	no	—
113	#103×C₄₇	—	2	2	no	—
114	#103×C₄₇	—	2	1	no	—
115	#103×C₄₇	—	2	1	no	—
116	#102×C₄₇	—	2	1	no	—
117	#101×C₄₇	—	2	4	no	—
118	#101×C₄₇	—	2	4	no	—
119	#101×C₄₇	—	4	2	no	—
120	#97×C₄₇	—	2	1	no	—
121	C₄×C₈×C₄₇	—	2	1	no	—
122	#41×C₄₇	—	2	1	no	—
123	#41×C₄₇	—	2	1	no	—
124	#41×C₄₇	C₂×D₄	1	2	yes	—
125	#41×C₄₇	#41	1	2	yes	—
126	C₂×Q₈×C₄₇	—	2	1	no	—
127	C₂×Q₈×C₄₇	—	2	1	no	—
128	C₂×Q₈×C₄₇	—	2	1	no	—
129	C₂×Q₈×C₄₇	—	2	2	no	—
130	C₂×Q₈×C₄₇	—	2	2	no	—
131	C₂×Q₈×C₄₇	—	2	2	no	—
132	C₂×Q₈×C₄₇	—	2	1	no	—
133	C₂×Q₈×C₄₇	—	2	2	no	—
134	C₂×Q₈×C₄₇	—	2	1	no	—
135	C₂×Q₈×C₄₇	—	2	2	no	—
136	C₂×Q₈×C₄₇	—	2	2	no	—
137	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂×D₄×C₄₇	—	2	1	no	—
140	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	—	2	1	no	—
142	C₂²×C₄×C₄₇	—	2	1	no	—
143	C₂²×C₄×C₄₇	—	2	1	no	—
144	C₂²×C₄×C₄₇	—	2	1	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	1	no	—
147	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
150	Q₁₆×C₄₇	—	2	4	no	—
151	Q₁₆×C₄₇	—	4	4	no	—
152	Q₁₆×C₄₇	—	4	4	no	—
153	Q₁₆×C₄₇	—	4	4	no	—
154	SD₁₆×C₄₇	—	2	4	no	—
155	SD₁₆×C₄₇	—	4	4	no	—
156	M₁₆×C₄₇	—	2	1	no	—
157	M₁₆×C₄₇	—	2	2	no	—
158	M₁₆×C₄₇	—	2	2	no	—
159	M₁₆×C₄₇	—	2	2	no	—
160	M₁₆×C₄₇	—	2	2	no	—
161	M₁₆×C₄₇	—	2	1	no	—
162	M₁₆×C₄₇	—	2	1	no	—
163	M₁₆×C₄₇	—	4	4	no	—
164	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₄₇	—	2	1	no	—
166	C₂×C₈×C₄₇	—	2	2	no	—
167	C₂×C₈×C₄₇	—	2	2	no	—
168	C₂×C₈×C₄₇	—	2	1	no	—
169	C₂×C₈×C₄₇	—	2	2	no	—
170	C₂×C₈×C₄₇	—	2	2	no	—
171	C₂×C₈×C₄₇	—	4	4	no	—
172	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	1	no	—
176	C₄⋊C₄×C₄₇	—	2	1	no	—
177	C₄⋊C₄×C₄₇	—	2	1	no	—
178	C₄⋊C₄×C₄₇	—	4	1	no	—
179	C₄⋊C₄×C₄₇	—	4	1	no	—
180	C₄⋊C₄×C₄₇	—	4	1	no	—
181	C₄⋊C₄×C₄₇	—	4	1	no	—
182	C₄⋊C₄×C₄₇	—	4	1	no	—
183	C₄⋊C₄×C₄₇	—	4	1	no	—
184	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
186	C₂²⋊C₄×C₄₇	—	2	1	no	—
187	C₂²⋊C₄×C₄₇	—	2	1	no	—
188	C₂²⋊C₄×C₄₇	—	2	1	no	—
189	C₄²×C₄₇	—	2	1	no	—
190	C₄²×C₄₇	—	2	1	no	—
191	C₄²×C₄₇	—	2	1	no	—
192	C₄²×C₄₇	—	4	1	no	—
193	C₄²×C₄₇	—	4	1	no	—
194	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₄₇	—	2	1	no	—
199	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
200	Q₈×C₄₇	—	2	1	no	—
201	Q₈×C₄₇	—	2	2	no	—
202	Q₈×C₄₇	—	2	2	no	—
203	Q₈×C₄₇	—	4	1	no	—
204	Q₈×C₄₇	—	4	1	no	—
205	Q₈×C₄₇	—	4	2	no	—
206	Q₈×C₄₇	—	4	2	no	—
207	Q₈×C₄₇	—	4	2	no	—
208	Q₈×C₄₇	—	4	2	no	—
209	Q₈×C₄₇	#121	1	2	yes	—
210	D₄×C₄₇	—	2	2	no	—
211	D₄×C₄₇	—	2	2	no	—
212	D₄×C₄₇	—	2	1	no	—
213	D₄×C₄₇	#121	1	2	yes	—
214	C₂×C₄×C₄₇	—	2	1	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	1	no	—
219	C₂×C₄×C₄₇	—	2	1	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	4	1	no	—
222	C₂×C₄×C₄₇	—	4	1	no	—
223	C₂×C₄×C₄₇	—	4	1	no	—
224	C₂×C₄×C₄₇	—	4	2	no	—
225	C₂×C₄×C₄₇	—	4	1	no	—
226	C₂×C₄×C₄₇	—	4	2	no	—
227	C₂×C₄×C₄₇	—	4	2	no	—
228	C₂×C₄×C₄₇	—	4	2	no	—
229	C₂×C₄×C₄₇	—	8	1	no	—
230	C₂×C₄×C₄₇	—	8	1	no	—
231	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
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	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
241	C₈×C₄₇	—	2	2	no	—
242	C₈×C₄₇	—	2	2	no	—
243	C₈×C₄₇	—	2	2	no	—
244	C₈×C₄₇	—	4	2	no	—
245	C₈×C₄₇	—	4	1	no	—
246	C₈×C₄₇	—	4	2	no	—
247	#24772	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂²×C₄₇	—	2	1	no	—
249	C₂²×C₄₇	—	2	1	no	—
250	C₂²×C₄₇	—	2	2	no	—
251	C₂²×C₄₇	—	4	1	no	—
252	C₂²×C₄₇	—	4	1	no	—
253	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
254	C₂²×C₄₇	#547	1	1	yes	characteristic
255	C₂²×C₄₇	#553	1	1	yes	characteristic
256	C₄×C₄₇	—	2	2	no	—
257	C₄×C₄₇	—	2	1	no	—
258	C₄×C₄₇	—	2	1	no	—
259	C₄×C₄₇	—	2	1	no	—
260	C₄×C₄₇	—	4	2	no	—
261	C₄×C₄₇	—	4	1	no	—
262	C₄×C₄₇	—	4	1	no	—
263	C₄×C₄₇	—	8	2	no	—
264	C₄×C₄₇	—	8	1	no	—
265	C₄×C₄₇	#473	1	2	yes	complemented
266	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
267	C₄×C₄₇	#537	1	1	yes	characteristic
268	C₄×C₄₇	D₄²	1	1	yes	characteristic
269	C₄×C₄₇	#548	1	1	yes	characteristic
270	C₂×#473	C₂×C₄₇	1	2	yes	—
271	#3039	C₂×C₄₇	1	1	yes	characteristic
272	C₂×#462	C₂×C₄₇	1	1	yes	characteristic, complemented
273	C₄×#137	C₂×C₄₇	1	1	yes	characteristic
274	#2906	C₂×C₄₇	1	1	yes	characteristic
275	#2064	C₂×C₄₇	1	2	yes	complemented
276	#2047	C₂×C₄₇	1	2	yes	complemented
277	#1966	C₂×C₄₇	1	1	yes	characteristic, complemented
278	#1950	C₂×C₄₇	1	1	yes	characteristic, complemented
279	#1908	C₂×C₄₇	1	2	yes	—
280	#1801	C₂×C₄₇	1	1	yes	characteristic, complemented
281	C₂×C₄₇	—	2	1	no	—
282	C₂×C₄₇	—	2	1	no	—
283	C₂×C₄₇	—	4	2	no	—
284	C₂×C₄₇	#2416	1	1	yes	characteristic
285	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
286	C₂×C₄₇	#3069	1	1	yes	characteristic
287	C₂×#137	C₂²×C₄₇	1	2	yes	—
288	C₂×#137	C₂²×C₄₇	1	1	yes	characteristic
289	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	—
290	C₂×#131	C₂²×C₄₇	1	2	yes	—
291	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
292	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
293	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
294	#473	—	2	8	no	—
295	#462	—	2	1	no	—
296	#462	—	2	1	no	—
297	#462	—	2	1	no	—
298	#462	—	2	1	no	—
299	#462	—	2	2	no	—
300	#461	—	2	1	no	—
301	#461	—	2	1	no	—
302	#441	—	2	1	no	—
303	#440	—	2	1	no	—
304	C₄×Q₁₆	—	2	1	no	—
305	C₄×SD₁₆	—	2	1	no	—
306	C₂×#108	C₂²×C₄₇	1	2	yes	—
307	#428	C₂²×C₄₇	1	1	yes	characteristic
308	#424	—	2	2	no	—
309	#424	C₂²×C₄₇	1	2	yes	—
310	#423	—	2	1	no	—
311	#423	C₂²×C₄₇	1	1	yes	characteristic
312	#423	C₂²×C₄₇	1	1	yes	characteristic
313	C₂×C₄⋊C₈	—	2	1	no	—
314	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
315	#419	C₂²×C₄₇	1	2	yes	—
316	#419	C₂²×C₄₇	1	1	yes	characteristic
317	#417	C₂²×C₄₇	1	1	yes	characteristic
318	C₂×#103	C₂²×C₄₇	1	2	yes	—
319	C₂×#101	C₂²×C₄₇	1	2	yes	—
320	C₂×#101	C₂²×C₄₇	1	2	yes	—
321	C₂×#101	C₂²×C₄₇	1	2	yes	—
322	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
323	#343	C₂²×C₄₇	1	2	yes	—
324	#341	C₂²×C₄₇	1	2	yes	—
325	C₄₇	#24772	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
328	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
329	#137	—	2	2	no	—
330	#137	—	2	4	no	—
331	#137	—	2	4	no	—
332	#137	D₄×C₄₇	1	4	yes	—
333	C₂×Q₁₆	—	2	1	no	—
334	C₂×Q₁₆	—	2	4	no	—
335	C₂×Q₁₆	—	2	2	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×Q₁₆	—	2	2	no	—
338	C₂×Q₁₆	—	4	2	no	—
339	C₂×SD₁₆	—	2	1	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	#131	—	2	4	no	—
342	#131	—	4	2	no	—
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
345	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
346	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
347	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
348	C₂²×C₈	—	2	2	no	—
349	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
350	C₄⋊Q₈	—	2	1	no	—
351	C₄⋊Q₈	—	2	1	no	—
352	C₄⋊Q₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
359	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
363	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
364	#117	—	2	1	no	—
365	#117	C₂³×C₄₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
373	#108	—	2	4	no	—
374	#107	—	2	1	no	—
375	#106	—	2	1	no	—
376	C₄⋊C₈	—	2	2	no	—
377	C₄⋊C₈	—	2	2	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	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	1	yes	characteristic
384	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
385	#103	—	2	1	no	—
386	#103	—	2	2	no	—
387	#103	—	2	2	no	—
388	#103	—	2	1	no	—
389	#103	—	2	1	no	—
390	#103	—	2	2	no	—
391	#103	—	2	2	no	—
392	#102	—	2	1	no	—
393	#101	—	2	4	no	—
394	#101	—	2	4	no	—
395	#101	—	4	2	no	—
396	#97	—	2	1	no	—
397	C₄×C₈	—	2	1	no	—
398	#41	—	2	1	no	—
399	#41	—	2	1	no	—
400	#41	C₂×D₄×C₄₇	1	2	yes	—
401	#41	#41×C₄₇	1	2	yes	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
414	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
424	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
426	Q₁₆	—	2	4	no	—
427	Q₁₆	—	4	4	no	—
428	Q₁₆	—	4	4	no	—
429	Q₁₆	—	4	4	no	—
430	SD₁₆	—	2	4	no	—
431	SD₁₆	—	4	4	no	—
432	M₁₆	—	2	1	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	2	1	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	1	no	—
439	M₁₆	—	4	4	no	—
440	M₁₆	C₂×D₄×C₄₇	1	2	yes	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	4	4	no	—
448	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
449	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	4	1	no	—
469	C₄²	—	4	1	no	—
470	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
472	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
474	C₂³	—	2	1	no	—
475	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
476	Q₈	—	2	1	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	Q₈	#121×C₄₇	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	1	no	—
489	D₄	#121×C₄₇	1	2	yes	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	1	no	—
506	C₂×C₄	—	8	1	no	—
507	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
508	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
509	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
510	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
515	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
516	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
517	C₈	—	2	2	no	—
518	C₈	—	2	2	no	—
519	C₈	—	2	2	no	—
520	C₈	—	4	2	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
529	C₂²	C₄₇×#547	1	1	yes	characteristic
530	C₂²	C₄₇×#553	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	2	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	2	no	—
540	C₄	C₄₇×#473	1	2	yes	complemented
541	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
542	C₄	C₄₇×#537	1	1	yes	characteristic
543	C₄	D₄²×C₄₇	1	1	yes	characteristic
544	C₄	C₄₇×#548	1	1	yes	characteristic
545	C₂	—	2	1	no	—
546	C₂	—	2	1	no	—
547	C₂	—	4	2	no	—
548	C₂	C₄₇×#2416	1	1	yes	characteristic
549	C₂	C₂×C₄₇×#473	1	1	yes	characteristic
550	C₂	C₄₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×#41×C₄₇	C₂³
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
3. C₂×C₄₇×#462	C₂	semidirect
6. C₄₇×#2064	C₂	semidirect
7. C₄₇×#2047	C₂	semidirect
8. C₄₇×#1966	C₂	semidirect
9. C₄₇×#1950	C₂	semidirect
11. C₄₇×#1801	C₂	semidirect
247. #24772	C₄₇	direct (N × H)
265. C₄×C₄₇	#473	semidirect
272. C₂×#462	C₂×C₄₇	semidirect
275. #2064	C₂×C₄₇	semidirect
276. #2047	C₂×C₄₇	semidirect
277. #1966	C₂×C₄₇	semidirect
278. #1950	C₂×C₄₇	semidirect
280. #1801	C₂×C₄₇	semidirect
325. C₄₇	#24772	direct (N × H)
540. C₄	C₄₇×#473	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#473	2
C₄₇×#3039	2
C₂×C₄₇×#462	2
C₄×#137×C₄₇	2
C₄₇×#2906	2
C₄₇×#2064	2
C₄₇×#2047	2
C₄₇×#1966	2
C₄₇×#1950	2
C₄₇×#1908	2
C₄₇×#1801	2
#24772	47

Subgroups — C47×#24772 #26064470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24772 #26064470