Subgroups — C₄₇×#61622 #26101320

Order 12032.

2028 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3489	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₄₇×#3315	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3312	C₂	1	2	yes	maximal, complemented
6	C₄₇×#3296	C₂	1	2	yes	maximal, complemented
7	D₄×Q₁₆×C₄₇	C₂	1	2	yes	maximal, complemented
8	C₄₇×#3276	C₂	1	2	yes	maximal, complemented
9	C₄₇×#3270	C₂	1	2	yes	maximal, complemented
10	C₄₇×#3266	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3223	C₂	1	2	yes	maximal, complemented
12	C₄₇×#3201	C₂	1	2	yes	maximal, complemented
13	C₄₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#3120	C₂	1	2	yes	maximal, complemented
16	C₄₇×#3011	C₂	1	2	yes	maximal, complemented
17	C₄₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#137×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#137×C₄₇	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	complemented
27	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#563	—	2	2	no	—
29	C₄₇×#552	C₂²	1	2	yes	—
30	C₄₇×#552	C₂²	1	2	yes	complemented
31	C₄₇×#551	—	2	2	no	—
32	D₄×Q₈×C₄₇	C₂²	1	2	yes	—
33	D₄×Q₈×C₄₇	C₂²	1	2	yes	—
34	D₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
35	C₄₇×#548	C₂²	1	2	yes	—
36	C₄₇×#547	—	2	2	no	—
37	C₄₇×#547	C₂²	1	2	yes	—
38	C₄₇×#546	—	2	2	no	—
39	C₄₇×#546	C₂²	1	2	yes	—
40	C₄₇×#544	—	2	1	no	—
41	C₄₇×#544	—	2	1	no	—
42	C₄₇×#541	C₂²	1	2	yes	complemented
43	C₄₇×#539	—	2	1	no	—
44	C₄₇×#539	—	2	1	no	—
45	C₄₇×#537	—	2	1	no	—
46	C₄₇×#537	C₂²	1	1	yes	characteristic
47	C₄₇×#536	—	2	1	no	—
48	C₄₇×#536	C₂²	1	1	yes	characteristic
49	C₄₇×#536	C₂²	1	2	yes	complemented
50	C₄₇×#525	—	2	1	no	—
51	C₄₇×#525	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
53	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₄₇×#520	C₂²	1	1	yes	characteristic
57	C₄₇×#497	C₂²	1	2	yes	complemented
58	C₄₇×#494	C₂²	1	2	yes	complemented
59	C₄₇×#491	C₂²	1	2	yes	complemented
60	C₄₇×#488	C₂²	1	2	yes	complemented
61	C₄₇×#485	C₂²	1	2	yes	complemented
62	C₄₇×#484	C₂²	1	2	yes	complemented
63	C₄₇×#484	C₂²	1	2	yes	complemented
64	C₄₇×#483	C₂²	1	2	yes	—
65	C₄₇×#483	C₂²	1	2	yes	complemented
66	C₄₇×#482	C₂²	1	2	yes	complemented
67	C₄₇×#479	C₂²	1	2	yes	complemented
68	C₄₇×#478	C₂²	1	2	yes	complemented
69	C₄₇×#470	C₂²	1	2	yes	complemented
70	C₄₇×#470	C₂²	1	2	yes	complemented
71	C₄₇×#470	C₂²	1	2	yes	complemented
72	C₄₇×#468	C₂²	1	2	yes	complemented
73	C₄₇×#467	C₂²	1	2	yes	—
74	C₄₇×#467	C₂²	1	2	yes	—
75	C₄₇×#467	C₂²	1	2	yes	complemented
76	C₄₇×#465	C₂²	1	2	yes	complemented
77	C₄₇×#464	C₂²	1	2	yes	complemented
78	C₄₇×#464	C₂²	1	2	yes	complemented
79	C₄₇×#462	C₂²	1	2	yes	complemented
80	C₄₇×#462	C₂²	1	2	yes	complemented
81	C₄₇×#462	C₂²	1	2	yes	complemented
82	C₄₇×#461	C₂²	1	2	yes	complemented
83	C₄₇×#452	C₂²	1	2	yes	—
84	C₄₇×#452	C₂²	1	2	yes	—
85	C₄₇×#452	C₂²	1	2	yes	—
86	C₄₇×#452	C₂²	1	2	yes	—
87	C₄₇×#452	C₂²	1	2	yes	—
88	C₄₇×#452	C₂²	1	2	yes	—
89	C₄₇×#452	C₂²	1	2	yes	complemented
90	C₄₇×#452	C₂²	1	2	yes	complemented
91	C₄₇×#451	C₂²	1	2	yes	—
92	C₄₇×#451	C₂²	1	2	yes	—
93	C₄₇×#451	C₂²	1	2	yes	complemented
94	C₄₇×#451	C₂²	1	2	yes	complemented
95	C₄₇×#451	C₂²	1	2	yes	complemented
96	C₄₇×#451	C₂²	1	2	yes	complemented
97	C₄₇×#451	C₂²	1	2	yes	complemented
98	C₄₇×#451	C₂²	1	2	yes	complemented
99	C₄₇×#450	C₂²	1	2	yes	—
100	C₄₇×#448	C₂²	1	2	yes	complemented
101	C₄₇×#441	C₂²	1	2	yes	complemented
102	C₄₇×#440	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₄₇	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
105	C₄₇×#436	C₂²	1	2	yes	complemented
106	C₄₇×#435	C₂²	1	2	yes	—
107	C₄₇×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₄₇	C₂²	1	2	yes	—
109	C₄₇×#433	C₂²	1	2	yes	complemented
110	C₄₇×#419	C₂²	1	2	yes	complemented
111	C₄₇×#417	C₂²	1	1	yes	characteristic
112	C₄₇×#417	C₂²	1	1	yes	characteristic
113	C₄₇×#416	C₂²	1	2	yes	complemented
114	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
115	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
116	C₄₇×#408	C₂²	1	2	yes	complemented
117	C₄₇×#407	C₂²	1	1	yes	characteristic
118	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
119	2₋¹⁺⁴×C₄₇	—	4	2	no	—
120	2₋¹⁺⁴×C₄₇	—	4	2	no	—
121	C₂×#41×C₄₇	—	2	1	no	—
122	C₂×#41×C₄₇	—	2	2	no	—
123	C₂×#41×C₄₇	—	2	1	no	—
124	C₂×#41×C₄₇	—	2	1	no	—
125	C₂×#41×C₄₇	—	4	2	no	—
126	C₂×#41×C₄₇	—	4	2	no	—
127	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
130	C₂×#41×C₄₇	C₂³	1	2	yes	—
131	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
132	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₄₇	—	2	1	no	—
134	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
136	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
140	C₂²×D₄×C₄₇	—	2	1	no	—
141	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₄₇	—	2	1	no	—
143	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
144	#137×C₄₇	—	4	2	no	—
145	#137×C₄₇	—	4	4	no	—
146	#137×C₄₇	—	4	2	no	—
147	C₂×Q₁₆×C₄₇	—	4	2	no	—
148	C₂×Q₁₆×C₄₇	—	4	4	no	—
149	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₄₇	—	4	2	no	—
158	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
162	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
163	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
166	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₄₇	—	2	2	no	—
169	C₄⋊Q₈×C₄₇	—	2	2	no	—
170	C₄⋊Q₈×C₄₇	—	2	2	no	—
171	C₄⋊Q₈×C₄₇	—	2	2	no	—
172	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
174	#126×C₄₇	—	2	2	no	—
175	#126×C₄₇	—	2	2	no	—
176	#126×C₄₇	—	2	2	no	—
177	#126×C₄₇	—	2	2	no	—
178	#125×C₄₇	—	2	2	no	—
179	#125×C₄₇	—	2	2	no	—
180	#125×C₄₇	—	2	2	no	—
181	#125×C₄₇	—	2	2	no	—
182	#125×C₄₇	C₂³	1	2	yes	—
183	#124×C₄₇	—	2	2	no	—
184	#124×C₄₇	—	2	2	no	—
185	#124×C₄₇	C₂³	1	2	yes	—
186	#123×C₄₇	—	2	2	no	—
187	#123×C₄₇	—	2	2	no	—
188	#123×C₄₇	—	2	2	no	—
189	#123×C₄₇	—	2	2	no	—
190	#123×C₄₇	—	2	2	no	—
191	#123×C₄₇	—	2	2	no	—
192	#123×C₄₇	—	2	2	no	—
193	#123×C₄₇	—	2	2	no	—
194	#123×C₄₇	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₄₇	—	2	1	no	—
196	C₂²⋊Q₈×C₄₇	—	2	1	no	—
197	C₂²⋊Q₈×C₄₇	—	2	1	no	—
198	C₂²⋊Q₈×C₄₇	—	2	1	no	—
199	C₂²⋊Q₈×C₄₇	—	2	1	no	—
200	C₂²⋊Q₈×C₄₇	—	2	1	no	—
201	C₂²⋊Q₈×C₄₇	—	2	1	no	—
202	C₂²⋊Q₈×C₄₇	—	2	1	no	—
203	C₂²⋊Q₈×C₄₇	—	2	2	no	—
204	C₂²⋊Q₈×C₄₇	—	2	1	no	—
205	C₂²⋊Q₈×C₄₇	—	2	2	no	—
206	C₂²⋊Q₈×C₄₇	—	2	2	no	—
207	C₂²⋊Q₈×C₄₇	—	2	2	no	—
208	C₂²⋊Q₈×C₄₇	—	2	2	no	—
209	C₂²⋊Q₈×C₄₇	—	2	2	no	—
210	C₂²⋊Q₈×C₄₇	—	2	2	no	—
211	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
212	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
213	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
222	#121×C₄₇	—	2	1	no	—
223	#121×C₄₇	—	2	2	no	—
224	#121×C₄₇	—	2	2	no	—
225	#121×C₄₇	—	2	2	no	—
226	#121×C₄₇	—	2	2	no	—
227	#121×C₄₇	D₄	1	1	yes	characteristic
228	#121×C₄₇	D₄	1	1	yes	characteristic
229	#121×C₄₇	C₂³	1	2	yes	—
230	#120×C₄₇	—	2	2	no	—
231	#120×C₄₇	D₄	1	2	yes	—
232	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
233	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
234	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
235	C₄×D₄×C₄₇	—	2	2	no	—
236	C₄×D₄×C₄₇	—	2	2	no	—
237	C₄×D₄×C₄₇	—	2	2	no	—
238	C₄×D₄×C₄₇	—	2	2	no	—
239	C₄×D₄×C₄₇	—	2	2	no	—
240	C₄×D₄×C₄₇	C₂³	1	2	yes	—
241	C₄×D₄×C₄₇	C₂³	1	2	yes	—
242	C₄×D₄×C₄₇	C₂³	1	2	yes	—
243	#117×C₄₇	—	2	1	no	—
244	#117×C₄₇	—	2	2	no	—
245	#117×C₄₇	—	2	2	no	—
246	#117×C₄₇	C₂³	1	2	yes	—
247	#117×C₄₇	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
249	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
250	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
251	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
252	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
253	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
258	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
260	#107×C₄₇	C₂³	1	2	yes	—
261	#107×C₄₇	C₂³	1	2	yes	—
262	#106×C₄₇	C₂³	1	2	yes	—
263	#106×C₄₇	C₂³	1	2	yes	—
264	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
265	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
266	#103×C₄₇	C₂³	1	2	yes	—
267	#103×C₄₇	C₂³	1	2	yes	—
268	#103×C₄₇	C₂³	1	2	yes	—
269	#103×C₄₇	C₂³	1	2	yes	—
270	#103×C₄₇	C₂³	1	2	yes	—
271	#103×C₄₇	C₂³	1	2	yes	—
272	#103×C₄₇	C₂³	1	2	yes	—
273	#103×C₄₇	C₂³	1	2	yes	—
274	#103×C₄₇	C₂³	1	2	yes	—
275	#103×C₄₇	C₂³	1	2	yes	—
276	#103×C₄₇	C₂³	1	2	yes	—
277	#103×C₄₇	C₂³	1	2	yes	—
278	#102×C₄₇	C₂³	1	2	yes	—
279	#102×C₄₇	C₂³	1	2	yes	—
280	#102×C₄₇	C₂³	1	2	yes	—
281	#102×C₄₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
288	#97×C₄₇	C₂³	1	2	yes	—
289	C₄×C₈×C₄₇	C₂³	1	2	yes	—
290	C₂⁴×C₄₇	—	2	1	no	—
291	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
292	#41×C₄₇	—	2	2	no	—
293	#41×C₄₇	—	2	2	no	—
294	#41×C₄₇	—	2	2	no	—
295	#41×C₄₇	—	2	2	no	—
296	#41×C₄₇	—	2	4	no	—
297	#41×C₄₇	—	4	1	no	—
298	#41×C₄₇	—	4	1	no	—
299	#41×C₄₇	—	4	1	no	—
300	#41×C₄₇	—	4	1	no	—
301	#41×C₄₇	—	4	1	no	—
302	#41×C₄₇	—	4	1	no	—
303	#41×C₄₇	—	4	2	no	—
304	#41×C₄₇	—	4	4	no	—
305	#41×C₄₇	—	4	4	no	—
306	#41×C₄₇	—	4	4	no	—
307	#41×C₄₇	—	4	8	no	—
308	C₂×Q₈×C₄₇	—	2	1	no	—
309	C₂×Q₈×C₄₇	—	2	2	no	—
310	C₂×Q₈×C₄₇	—	2	1	no	—
311	C₂×Q₈×C₄₇	—	2	1	no	—
312	C₂×Q₈×C₄₇	—	2	1	no	—
313	C₂×Q₈×C₄₇	—	2	2	no	—
314	C₂×Q₈×C₄₇	—	2	2	no	—
315	C₂×Q₈×C₄₇	—	2	4	no	—
316	C₂×Q₈×C₄₇	—	4	1	no	—
317	C₂×Q₈×C₄₇	—	4	2	no	—
318	C₂×Q₈×C₄₇	—	4	1	no	—
319	C₂×Q₈×C₄₇	—	4	1	no	—
320	C₂×Q₈×C₄₇	—	4	4	no	—
321	C₂×Q₈×C₄₇	—	4	1	no	—
322	C₂×Q₈×C₄₇	—	4	1	no	—
323	C₂×Q₈×C₄₇	—	4	2	no	—
324	C₂×Q₈×C₄₇	—	4	1	no	—
325	C₂×Q₈×C₄₇	—	4	1	no	—
326	C₂×Q₈×C₄₇	—	4	2	no	—
327	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₄₇	—	2	1	no	—
334	C₂×D₄×C₄₇	—	2	2	no	—
335	C₂×D₄×C₄₇	—	2	2	no	—
336	C₂×D₄×C₄₇	—	2	1	no	—
337	C₂×D₄×C₄₇	—	2	1	no	—
338	C₂×D₄×C₄₇	—	2	1	no	—
339	C₂×D₄×C₄₇	—	2	2	no	—
340	C₂×D₄×C₄₇	—	2	1	no	—
341	C₂×D₄×C₄₇	—	4	1	no	—
342	C₂×D₄×C₄₇	—	4	4	no	—
343	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₄₇	—	2	1	no	—
350	C₂²×C₄×C₄₇	—	2	1	no	—
351	C₂²×C₄×C₄₇	—	2	1	no	—
352	C₂²×C₄×C₄₇	—	2	1	no	—
353	C₂²×C₄×C₄₇	—	2	2	no	—
354	C₂²×C₄×C₄₇	—	2	1	no	—
355	C₂²×C₄×C₄₇	—	2	1	no	—
356	C₂²×C₄×C₄₇	—	2	1	no	—
357	C₂²×C₄×C₄₇	—	2	1	no	—
358	C₂²×C₄×C₄₇	—	2	2	no	—
359	C₂²×C₄×C₄₇	—	2	2	no	—
360	C₂²×C₄×C₄₇	—	2	1	no	—
361	C₂²×C₄×C₄₇	—	2	1	no	—
362	C₂²×C₄×C₄₇	—	2	1	no	—
363	C₂²×C₄×C₄₇	—	2	2	no	—
364	C₂²×C₄×C₄₇	—	4	1	no	—
365	C₂²×C₄×C₄₇	—	4	1	no	—
366	C₂²×C₄×C₄₇	—	4	4	no	—
367	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
374	Q₁₆×C₄₇	—	2	4	no	—
375	Q₁₆×C₄₇	—	2	4	no	—
376	Q₁₆×C₄₇	—	4	2	no	—
377	Q₁₆×C₄₇	—	4	2	no	—
378	Q₁₆×C₄₇	—	4	2	no	—
379	Q₁₆×C₄₇	—	4	2	no	—
380	Q₁₆×C₄₇	—	4	2	no	—
381	Q₁₆×C₄₇	—	4	2	no	—
382	SD₁₆×C₄₇	—	2	4	no	—
383	SD₁₆×C₄₇	—	2	4	no	—
384	SD₁₆×C₄₇	—	4	2	no	—
385	SD₁₆×C₄₇	—	4	2	no	—
386	M₁₆×C₄₇	—	4	2	no	—
387	M₁₆×C₄₇	—	4	1	no	—
388	M₁₆×C₄₇	—	4	1	no	—
389	C₂×C₈×C₄₇	—	4	1	no	—
390	C₂×C₈×C₄₇	—	4	1	no	—
391	C₂×C₈×C₄₇	—	4	2	no	—
392	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
393	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
394	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
395	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₄₇	—	2	2	no	—
397	C₄⋊C₄×C₄₇	—	2	1	no	—
398	C₄⋊C₄×C₄₇	—	2	2	no	—
399	C₄⋊C₄×C₄₇	—	2	2	no	—
400	C₄⋊C₄×C₄₇	—	2	2	no	—
401	C₄⋊C₄×C₄₇	—	2	2	no	—
402	C₄⋊C₄×C₄₇	—	2	2	no	—
403	C₄⋊C₄×C₄₇	—	2	2	no	—
404	C₄⋊C₄×C₄₇	—	2	2	no	—
405	C₄⋊C₄×C₄₇	—	2	2	no	—
406	C₄⋊C₄×C₄₇	—	2	1	no	—
407	C₄⋊C₄×C₄₇	—	2	1	no	—
408	C₄⋊C₄×C₄₇	—	2	2	no	—
409	C₄⋊C₄×C₄₇	—	2	2	no	—
410	C₄⋊C₄×C₄₇	—	2	2	no	—
411	C₄⋊C₄×C₄₇	—	2	2	no	—
412	C₄⋊C₄×C₄₇	—	2	2	no	—
413	C₄⋊C₄×C₄₇	—	2	2	no	—
414	C₄⋊C₄×C₄₇	—	2	2	no	—
415	C₄⋊C₄×C₄₇	—	2	2	no	—
416	C₄⋊C₄×C₄₇	—	2	2	no	—
417	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
424	C₂²⋊C₄×C₄₇	—	2	2	no	—
425	C₂²⋊C₄×C₄₇	—	2	2	no	—
426	C₂²⋊C₄×C₄₇	—	2	2	no	—
427	C₂²⋊C₄×C₄₇	—	2	2	no	—
428	C₂²⋊C₄×C₄₇	—	2	2	no	—
429	C₂²⋊C₄×C₄₇	—	2	2	no	—
430	C₂²⋊C₄×C₄₇	—	2	2	no	—
431	C₂²⋊C₄×C₄₇	—	2	2	no	—
432	C₂²⋊C₄×C₄₇	—	2	2	no	—
433	C₂²⋊C₄×C₄₇	—	2	2	no	—
434	C₂²⋊C₄×C₄₇	—	2	2	no	—
435	C₂²⋊C₄×C₄₇	—	2	2	no	—
436	C₂²⋊C₄×C₄₇	—	2	2	no	—
437	C₂²⋊C₄×C₄₇	—	2	2	no	—
438	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
443	C₄²×C₄₇	—	2	2	no	—
444	C₄²×C₄₇	—	2	2	no	—
445	C₄²×C₄₇	—	2	2	no	—
446	C₄²×C₄₇	—	2	2	no	—
447	C₄²×C₄₇	C₂⁴	1	2	yes	—
448	C₂³×C₄₇	—	2	1	no	—
449	C₂³×C₄₇	—	2	2	no	—
450	C₂³×C₄₇	—	2	1	no	—
451	C₂³×C₄₇	—	4	1	no	—
452	C₂³×C₄₇	—	4	1	no	—
453	C₂³×C₄₇	—	4	2	no	—
454	C₂³×C₄₇	—	4	2	no	—
455	C₂³×C₄₇	—	8	1	no	—
456	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
457	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
459	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₄₇	—	2	1	no	—
461	Q₈×C₄₇	—	2	2	no	—
462	Q₈×C₄₇	—	2	2	no	—
463	Q₈×C₄₇	—	2	2	no	—
464	Q₈×C₄₇	—	2	2	no	—
465	Q₈×C₄₇	—	2	2	no	—
466	Q₈×C₄₇	—	2	1	no	—
467	Q₈×C₄₇	—	2	2	no	—
468	Q₈×C₄₇	—	2	1	no	—
469	Q₈×C₄₇	—	4	1	no	—
470	Q₈×C₄₇	—	4	4	no	—
471	Q₈×C₄₇	—	4	2	no	—
472	Q₈×C₄₇	—	4	2	no	—
473	Q₈×C₄₇	—	8	1	no	—
474	Q₈×C₄₇	—	8	1	no	—
475	Q₈×C₄₇	—	8	2	no	—
476	Q₈×C₄₇	H(5,𝔽₂)	1	2	yes	—
477	D₄×C₄₇	—	2	4	no	—
478	D₄×C₄₇	—	2	4	no	—
479	D₄×C₄₇	—	2	1	no	—
480	D₄×C₄₇	—	2	1	no	—
481	D₄×C₄₇	—	2	1	no	—
482	D₄×C₄₇	—	4	2	no	—
483	D₄×C₄₇	—	4	1	no	—
484	D₄×C₄₇	—	4	2	no	—
485	D₄×C₄₇	—	4	2	no	—
486	D₄×C₄₇	—	4	2	no	—
487	D₄×C₄₇	—	4	2	no	—
488	D₄×C₄₇	—	4	4	no	—
489	D₄×C₄₇	—	4	2	no	—
490	D₄×C₄₇	—	8	2	no	—
491	D₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
492	C₂×C₄×C₄₇	—	2	4	no	—
493	C₂×C₄×C₄₇	—	2	1	no	—
494	C₂×C₄×C₄₇	—	2	1	no	—
495	C₂×C₄×C₄₇	—	2	1	no	—
496	C₂×C₄×C₄₇	—	2	2	no	—
497	C₂×C₄×C₄₇	—	2	1	no	—
498	C₂×C₄×C₄₇	—	2	1	no	—
499	C₂×C₄×C₄₇	—	2	2	no	—
500	C₂×C₄×C₄₇	—	2	1	no	—
501	C₂×C₄×C₄₇	—	2	1	no	—
502	C₂×C₄×C₄₇	—	2	2	no	—
503	C₂×C₄×C₄₇	—	2	2	no	—
504	C₂×C₄×C₄₇	—	2	2	no	—
505	C₂×C₄×C₄₇	—	2	2	no	—
506	C₂×C₄×C₄₇	—	2	2	no	—
507	C₂×C₄×C₄₇	—	2	2	no	—
508	C₂×C₄×C₄₇	—	2	1	no	—
509	C₂×C₄×C₄₇	—	4	1	no	—
510	C₂×C₄×C₄₇	—	4	1	no	—
511	C₂×C₄×C₄₇	—	4	1	no	—
512	C₂×C₄×C₄₇	—	4	2	no	—
513	C₂×C₄×C₄₇	—	4	2	no	—
514	C₂×C₄×C₄₇	—	4	2	no	—
515	C₂×C₄×C₄₇	—	4	4	no	—
516	C₂×C₄×C₄₇	—	4	4	no	—
517	C₂×C₄×C₄₇	—	4	2	no	—
518	C₂×C₄×C₄₇	—	4	2	no	—
519	C₂×C₄×C₄₇	—	4	2	no	—
520	C₂×C₄×C₄₇	—	4	2	no	—
521	C₂×C₄×C₄₇	—	8	2	no	—
522	C₂×C₄×C₄₇	—	8	1	no	—
523	C₂×C₄×C₄₇	—	8	1	no	—
524	C₂×C₄×C₄₇	—	8	2	no	—
525	C₂×C₄×C₄₇	—	8	1	no	—
526	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
533	C₈×C₄₇	—	2	2	no	—
534	C₈×C₄₇	—	2	2	no	—
535	C₈×C₄₇	—	2	2	no	—
536	C₈×C₄₇	—	2	2	no	—
537	#61622	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂²×C₄₇	—	2	1	no	—
539	C₂²×C₄₇	—	2	1	no	—
540	C₂²×C₄₇	—	2	1	no	—
541	C₂²×C₄₇	—	2	1	no	—
542	C₂²×C₄₇	—	2	2	no	—
543	C₂²×C₄₇	—	2	1	no	—
544	C₂²×C₄₇	—	2	2	no	—
545	C₂²×C₄₇	—	2	2	no	—
546	C₂²×C₄₇	—	2	1	no	—
547	C₂²×C₄₇	—	2	2	no	—
548	C₂²×C₄₇	—	2	1	no	—
549	C₂²×C₄₇	—	2	1	no	—
550	C₂²×C₄₇	—	4	1	no	—
551	C₂²×C₄₇	—	4	1	no	—
552	C₂²×C₄₇	—	4	1	no	—
553	C₂²×C₄₇	—	4	1	no	—
554	C₂²×C₄₇	—	4	1	no	—
555	C₂²×C₄₇	—	8	2	no	—
556	C₂²×C₄₇	—	8	4	no	—
557	C₂²×C₄₇	#578	1	2	yes	—
558	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₄₇	—	2	2	no	—
560	C₄×C₄₇	—	2	1	no	—
561	C₄×C₄₇	—	2	2	no	—
562	C₄×C₄₇	—	2	1	no	—
563	C₄×C₄₇	—	2	1	no	—
564	C₄×C₄₇	—	2	2	no	—
565	C₄×C₄₇	—	2	2	no	—
566	C₄×C₄₇	—	4	2	no	—
567	C₄×C₄₇	—	4	2	no	—
568	C₄×C₄₇	—	4	1	no	—
569	C₄×C₄₇	—	4	2	no	—
570	C₄×C₄₇	—	4	2	no	—
571	C₄×C₄₇	—	4	2	no	—
572	C₄×C₄₇	—	4	2	no	—
573	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
575	#3538	C₂×C₄₇	1	1	yes	characteristic, complemented
576	#3489	C₂×C₄₇	1	1	yes	characteristic
577	#3327	C₂×C₄₇	1	2	yes	complemented
578	#3315	C₂×C₄₇	1	2	yes	complemented
579	#3312	C₂×C₄₇	1	2	yes	complemented
580	#3296	C₂×C₄₇	1	2	yes	complemented
581	D₄×Q₁₆	C₂×C₄₇	1	2	yes	complemented
582	#3276	C₂×C₄₇	1	2	yes	complemented
583	#3270	C₂×C₄₇	1	2	yes	complemented
584	#3266	C₂×C₄₇	1	2	yes	complemented
585	#3223	C₂×C₄₇	1	2	yes	complemented
586	#3201	C₂×C₄₇	1	2	yes	complemented
587	#3195	C₂×C₄₇	1	1	yes	characteristic, complemented
588	#3189	C₂×C₄₇	1	1	yes	characteristic, complemented
589	#3120	C₂×C₄₇	1	2	yes	complemented
590	#3011	C₂×C₄₇	1	2	yes	complemented
591	#3007	C₂×C₄₇	1	1	yes	characteristic, complemented
592	C₂×#452	C₂×C₄₇	1	1	yes	characteristic, complemented
593	#2976	C₂×C₄₇	1	1	yes	characteristic, complemented
594	C₂×C₄₇	—	2	2	no	—
595	C₂×C₄₇	—	4	2	no	—
596	C₂×C₄₇	—	4	1	no	—
597	C₂×C₄₇	—	4	1	no	—
598	C₂×C₄₇	—	4	2	no	—
599	C₂×C₄₇	—	8	1	no	—
600	C₂×C₄₇	#3484	1	1	yes	characteristic
601	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
602	C₂×C₄₇	#3586	1	1	yes	characteristic
603	C₂×2₋¹⁺⁴	C₂²×C₄₇	1	1	yes	characteristic
604	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
605	C₂×#137	C₂²×C₄₇	1	1	yes	characteristic
606	C₂×#137	C₂²×C₄₇	1	1	yes	characteristic
607	C₂×#137	C₂²×C₄₇	1	2	yes	complemented
608	C₂²×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
609	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	complemented
610	C₂²×SD₁₆	C₂²×C₄₇	1	1	yes	characteristic
611	#563	—	2	2	no	—
612	#552	C₂²×C₄₇	1	2	yes	—
613	#552	C₂²×C₄₇	1	2	yes	complemented
614	#551	—	2	2	no	—
615	D₄×Q₈	C₂²×C₄₇	1	2	yes	—
616	D₄×Q₈	C₂²×C₄₇	1	2	yes	—
617	D₄×Q₈	C₂²×C₄₇	1	2	yes	complemented
618	#548	C₂²×C₄₇	1	2	yes	—
619	#547	—	2	2	no	—
620	#547	C₂²×C₄₇	1	2	yes	—
621	#546	—	2	2	no	—
622	#546	C₂²×C₄₇	1	2	yes	—
623	#544	—	2	1	no	—
624	#544	—	2	1	no	—
625	#541	C₂²×C₄₇	1	2	yes	complemented
626	#539	—	2	1	no	—
627	#539	—	2	1	no	—
628	#537	—	2	1	no	—
629	#537	C₂²×C₄₇	1	1	yes	characteristic
630	#536	—	2	1	no	—
631	#536	C₂²×C₄₇	1	1	yes	characteristic
632	#536	C₂²×C₄₇	1	2	yes	complemented
633	#525	—	2	1	no	—
634	#525	C₂²×C₄₇	1	1	yes	characteristic
635	C₂×C₂²⋊Q₈	—	2	1	no	—
636	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
637	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
638	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
639	#520	C₂²×C₄₇	1	1	yes	characteristic
640	#497	C₂²×C₄₇	1	2	yes	complemented
641	#494	C₂²×C₄₇	1	2	yes	complemented
642	#491	C₂²×C₄₇	1	2	yes	complemented
643	#488	C₂²×C₄₇	1	2	yes	complemented
644	#485	C₂²×C₄₇	1	2	yes	complemented
645	#484	C₂²×C₄₇	1	2	yes	complemented
646	#484	C₂²×C₄₇	1	2	yes	complemented
647	#483	C₂²×C₄₇	1	2	yes	—
648	#483	C₂²×C₄₇	1	2	yes	complemented
649	#482	C₂²×C₄₇	1	2	yes	complemented
650	#479	C₂²×C₄₇	1	2	yes	complemented
651	#478	C₂²×C₄₇	1	2	yes	complemented
652	#470	C₂²×C₄₇	1	2	yes	complemented
653	#470	C₂²×C₄₇	1	2	yes	complemented
654	#470	C₂²×C₄₇	1	2	yes	complemented
655	#468	C₂²×C₄₇	1	2	yes	complemented
656	#467	C₂²×C₄₇	1	2	yes	—
657	#467	C₂²×C₄₇	1	2	yes	—
658	#467	C₂²×C₄₇	1	2	yes	complemented
659	#465	C₂²×C₄₇	1	2	yes	complemented
660	#464	C₂²×C₄₇	1	2	yes	complemented
661	#464	C₂²×C₄₇	1	2	yes	complemented
662	#462	C₂²×C₄₇	1	2	yes	complemented
663	#462	C₂²×C₄₇	1	2	yes	complemented
664	#462	C₂²×C₄₇	1	2	yes	complemented
665	#461	C₂²×C₄₇	1	2	yes	complemented
666	#452	C₂²×C₄₇	1	2	yes	—
667	#452	C₂²×C₄₇	1	2	yes	—
668	#452	C₂²×C₄₇	1	2	yes	—
669	#452	C₂²×C₄₇	1	2	yes	—
670	#452	C₂²×C₄₇	1	2	yes	—
671	#452	C₂²×C₄₇	1	2	yes	—
672	#452	C₂²×C₄₇	1	2	yes	complemented
673	#452	C₂²×C₄₇	1	2	yes	complemented
674	#451	C₂²×C₄₇	1	2	yes	—
675	#451	C₂²×C₄₇	1	2	yes	—
676	#451	C₂²×C₄₇	1	2	yes	complemented
677	#451	C₂²×C₄₇	1	2	yes	complemented
678	#451	C₂²×C₄₇	1	2	yes	complemented
679	#451	C₂²×C₄₇	1	2	yes	complemented
680	#451	C₂²×C₄₇	1	2	yes	complemented
681	#451	C₂²×C₄₇	1	2	yes	complemented
682	#450	C₂²×C₄₇	1	2	yes	—
683	#448	C₂²×C₄₇	1	2	yes	complemented
684	#441	C₂²×C₄₇	1	2	yes	complemented
685	#440	C₂²×C₄₇	1	2	yes	complemented
686	C₄×Q₁₆	C₂²×C₄₇	1	2	yes	complemented
687	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	complemented
688	#436	C₂²×C₄₇	1	2	yes	complemented
689	#435	C₂²×C₄₇	1	2	yes	—
690	#435	C₂²×C₄₇	1	2	yes	complemented
691	C₈×D₄	C₂²×C₄₇	1	2	yes	—
692	#433	C₂²×C₄₇	1	2	yes	complemented
693	#419	C₂²×C₄₇	1	2	yes	complemented
694	#417	C₂²×C₄₇	1	1	yes	characteristic
695	#417	C₂²×C₄₇	1	1	yes	characteristic
696	#416	C₂²×C₄₇	1	2	yes	complemented
697	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
698	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
699	#408	C₂²×C₄₇	1	2	yes	complemented
700	#407	C₂²×C₄₇	1	1	yes	characteristic
701	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
702	C₄₇	#61622	1	1	yes	characteristic, direct product factor, Sylow
703	2₋¹⁺⁴	—	4	2	no	—
704	2₋¹⁺⁴	—	4	2	no	—
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	2	no	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	4	2	no	—
710	C₂×#41	—	4	2	no	—
711	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
712	C₂×#41	C₂³×C₄₇	1	2	yes	—
713	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
714	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
715	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
716	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
719	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
720	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
721	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
726	C₂³×C₄	—	2	1	no	—
727	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
728	#137	—	4	2	no	—
729	#137	—	4	4	no	—
730	#137	—	4	2	no	—
731	C₂×Q₁₆	—	4	2	no	—
732	C₂×Q₁₆	—	4	4	no	—
733	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
734	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
736	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
737	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
738	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
739	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
740	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
741	C₂×SD₁₆	—	4	2	no	—
742	C₂×SD₁₆	C₂³×C₄₇	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₄₇	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₄₇	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₄₇	1	2	yes	—
746	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
749	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
752	C₄⋊Q₈	—	2	2	no	—
753	C₄⋊Q₈	—	2	2	no	—
754	C₄⋊Q₈	—	2	2	no	—
755	C₄⋊Q₈	—	2	2	no	—
756	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
757	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	C₂³×C₄₇	1	2	yes	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	C₂³×C₄₇	1	2	yes	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	D₄×C₄₇	1	2	yes	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
796	C₂²⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	D₄×C₄₇	1	1	yes	characteristic
812	#121	D₄×C₄₇	1	1	yes	characteristic
813	#121	C₂³×C₄₇	1	2	yes	—
814	#120	—	2	2	no	—
815	#120	D₄×C₄₇	1	2	yes	—
816	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
817	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
818	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	C₂³×C₄₇	1	2	yes	—
825	C₄×D₄	C₂³×C₄₇	1	2	yes	—
826	C₄×D₄	C₂³×C₄₇	1	2	yes	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	—	2	2	no	—
830	#117	C₂³×C₄₇	1	2	yes	—
831	#117	C₂³×C₄₇	1	1	yes	characteristic
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
840	C₂×C₂²⋊C₄	—	2	1	no	—
841	C₂×C₂²⋊C₄	—	2	1	no	—
842	C₂×C₂²⋊C₄	—	2	1	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	#107	C₂³×C₄₇	1	2	yes	—
845	#107	C₂³×C₄₇	1	2	yes	—
846	#106	C₂³×C₄₇	1	2	yes	—
847	#106	C₂³×C₄₇	1	2	yes	—
848	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
849	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
850	#103	C₂³×C₄₇	1	2	yes	—
851	#103	C₂³×C₄₇	1	2	yes	—
852	#103	C₂³×C₄₇	1	2	yes	—
853	#103	C₂³×C₄₇	1	2	yes	—
854	#103	C₂³×C₄₇	1	2	yes	—
855	#103	C₂³×C₄₇	1	2	yes	—
856	#103	C₂³×C₄₇	1	2	yes	—
857	#103	C₂³×C₄₇	1	2	yes	—
858	#103	C₂³×C₄₇	1	2	yes	—
859	#103	C₂³×C₄₇	1	2	yes	—
860	#103	C₂³×C₄₇	1	2	yes	—
861	#103	C₂³×C₄₇	1	2	yes	—
862	#102	C₂³×C₄₇	1	2	yes	—
863	#102	C₂³×C₄₇	1	2	yes	—
864	#102	C₂³×C₄₇	1	2	yes	—
865	#102	C₂³×C₄₇	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
872	#97	C₂³×C₄₇	1	2	yes	—
873	C₄×C₈	C₂³×C₄₇	1	2	yes	—
874	C₂⁴	—	2	1	no	—
875	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
876	#41	—	2	2	no	—
877	#41	—	2	2	no	—
878	#41	—	2	2	no	—
879	#41	—	2	2	no	—
880	#41	—	2	4	no	—
881	#41	—	4	1	no	—
882	#41	—	4	1	no	—
883	#41	—	4	1	no	—
884	#41	—	4	1	no	—
885	#41	—	4	1	no	—
886	#41	—	4	1	no	—
887	#41	—	4	2	no	—
888	#41	—	4	4	no	—
889	#41	—	4	4	no	—
890	#41	—	4	4	no	—
891	#41	—	4	8	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	4	no	—
900	C₂×Q₈	—	4	1	no	—
901	C₂×Q₈	—	4	2	no	—
902	C₂×Q₈	—	4	1	no	—
903	C₂×Q₈	—	4	1	no	—
904	C₂×Q₈	—	4	4	no	—
905	C₂×Q₈	—	4	1	no	—
906	C₂×Q₈	—	4	1	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	1	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₄₇	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
916	C₂×Q₈	C₂⁴×C₄₇	1	1	yes	characteristic
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	4	1	no	—
926	C₂×D₄	—	4	4	no	—
927	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
928	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
929	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
930	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
931	C₂×D₄	C₂⁴×C₄₇	1	1	yes	characteristic
932	C₂×D₄	C₂⁴×C₄₇	1	1	yes	characteristic
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	4	1	no	—
949	C₂²×C₄	—	4	1	no	—
950	C₂²×C₄	—	4	4	no	—
951	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
958	Q₁₆	—	2	4	no	—
959	Q₁₆	—	2	4	no	—
960	Q₁₆	—	4	2	no	—
961	Q₁₆	—	4	2	no	—
962	Q₁₆	—	4	2	no	—
963	Q₁₆	—	4	2	no	—
964	Q₁₆	—	4	2	no	—
965	Q₁₆	—	4	2	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	2	4	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	M₁₆	—	4	2	no	—
971	M₁₆	—	4	1	no	—
972	M₁₆	—	4	1	no	—
973	C₂×C₈	—	4	1	no	—
974	C₂×C₈	—	4	1	no	—
975	C₂×C₈	—	4	2	no	—
976	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
977	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
978	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
979	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
1003	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
1004	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
1006	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
1007	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	C₂⁴×C₄₇	1	2	yes	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	—	4	2	no	—
1038	C₂³	—	4	2	no	—
1039	C₂³	—	8	1	no	—
1040	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
1041	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
1042	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
1043	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	4	1	no	—
1054	Q₈	—	4	4	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	8	1	no	—
1058	Q₈	—	8	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	H(5,𝔽₂)×C₄₇	1	2	yes	—
1061	D₄	—	2	4	no	—
1062	D₄	—	2	4	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	4	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
1076	C₂×C₄	—	2	4	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	4	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	1	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	1	no	—
1110	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
1116	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
1117	C₈	—	2	2	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	8	2	no	—
1139	C₂²	—	8	4	no	—
1140	C₂²	C₄₇×#578	1	2	yes	—
1141	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	2	no	—
1156	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
1157	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
1158	C₂	—	2	2	no	—
1159	C₂	—	4	1	no	—
1160	C₂	—	4	1	no	—
1161	C₂	—	4	2	no	—
1162	C₂	—	4	2	no	—
1163	C₂	—	8	1	no	—
1164	C₂	C₄₇×#3484	1	1	yes	characteristic
1165	C₂	C₂×C₄₇×#578	1	1	yes	characteristic
1166	C₂	C₄₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
prime radical	C₄₇×#3489	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄₇×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₄₇×#3538	C₂	semidirect
3. C₄₇×#3327	C₂	semidirect
4. C₄₇×#3315	C₂	semidirect
5. C₄₇×#3312	C₂	semidirect
6. C₄₇×#3296	C₂	semidirect
7. D₄×Q₁₆×C₄₇	C₂	semidirect
8. C₄₇×#3276	C₂	semidirect
9. C₄₇×#3270	C₂	semidirect
10. C₄₇×#3266	C₂	semidirect
11. C₄₇×#3223	C₂	semidirect
12. C₄₇×#3201	C₂	semidirect
13. C₄₇×#3195	C₂	semidirect
14. C₄₇×#3189	C₂	semidirect
15. C₄₇×#3120	C₂	semidirect
16. C₄₇×#3011	C₂	semidirect
17. C₄₇×#3007	C₂	semidirect
18. C₂×C₄₇×#452	C₂	semidirect
19. C₄₇×#2976	C₂	semidirect
24. C₂×#137×C₄₇	C₂²	semidirect
26. C₂²×Q₁₆×C₄₇	C₂²	semidirect
30. C₄₇×#552	C₂²	semidirect
34. D₄×Q₈×C₄₇	C₂²	semidirect
42. C₄₇×#541	C₂²	semidirect
49. C₄₇×#536	C₂²	semidirect
57. C₄₇×#497	C₂²	semidirect
58. C₄₇×#494	C₂²	semidirect
59. C₄₇×#491	C₂²	semidirect
60. C₄₇×#488	C₂²	semidirect
61. C₄₇×#485	C₂²	semidirect
62. C₄₇×#484	C₂²	semidirect
63. C₄₇×#484	C₂²	semidirect
65. C₄₇×#483	C₂²	semidirect
66. C₄₇×#482	C₂²	semidirect
67. C₄₇×#479	C₂²	semidirect
68. C₄₇×#478	C₂²	semidirect
69. C₄₇×#470	C₂²	semidirect
70. C₄₇×#470	C₂²	semidirect
71. C₄₇×#470	C₂²	semidirect
72. C₄₇×#468	C₂²	semidirect
75. C₄₇×#467	C₂²	semidirect
76. C₄₇×#465	C₂²	semidirect
77. C₄₇×#464	C₂²	semidirect
78. C₄₇×#464	C₂²	semidirect
79. C₄₇×#462	C₂²	semidirect
80. C₄₇×#462	C₂²	semidirect
81. C₄₇×#462	C₂²	semidirect
82. C₄₇×#461	C₂²	semidirect
89. C₄₇×#452	C₂²	semidirect
90. C₄₇×#452	C₂²	semidirect
93. C₄₇×#451	C₂²	semidirect
94. C₄₇×#451	C₂²	semidirect
95. C₄₇×#451	C₂²	semidirect
96. C₄₇×#451	C₂²	semidirect
97. C₄₇×#451	C₂²	semidirect
98. C₄₇×#451	C₂²	semidirect
100. C₄₇×#448	C₂²	semidirect
101. C₄₇×#441	C₂²	semidirect
102. C₄₇×#440	C₂²	semidirect
103. C₄×Q₁₆×C₄₇	C₂²	semidirect
104. C₄×SD₁₆×C₄₇	C₂²	semidirect
105. C₄₇×#436	C₂²	semidirect
107. C₄₇×#435	C₂²	semidirect
109. C₄₇×#433	C₂²	semidirect
110. C₄₇×#419	C₂²	semidirect
113. C₄₇×#416	C₂²	semidirect
116. C₄₇×#408	C₂²	semidirect
537. #61622	C₄₇	direct (N × H)
575. #3538	C₂×C₄₇	semidirect
577. #3327	C₂×C₄₇	semidirect
578. #3315	C₂×C₄₇	semidirect
579. #3312	C₂×C₄₇	semidirect
580. #3296	C₂×C₄₇	semidirect
581. D₄×Q₁₆	C₂×C₄₇	semidirect
582. #3276	C₂×C₄₇	semidirect
583. #3270	C₂×C₄₇	semidirect
584. #3266	C₂×C₄₇	semidirect
585. #3223	C₂×C₄₇	semidirect
586. #3201	C₂×C₄₇	semidirect
587. #3195	C₂×C₄₇	semidirect
588. #3189	C₂×C₄₇	semidirect
589. #3120	C₂×C₄₇	semidirect
590. #3011	C₂×C₄₇	semidirect
591. #3007	C₂×C₄₇	semidirect
592. C₂×#452	C₂×C₄₇	semidirect
593. #2976	C₂×C₄₇	semidirect
607. C₂×#137	C₂²×C₄₇	semidirect
609. C₂²×Q₁₆	C₂²×C₄₇	semidirect
613. #552	C₂²×C₄₇	semidirect
617. D₄×Q₈	C₂²×C₄₇	semidirect
625. #541	C₂²×C₄₇	semidirect
632. #536	C₂²×C₄₇	semidirect
640. #497	C₂²×C₄₇	semidirect
641. #494	C₂²×C₄₇	semidirect
642. #491	C₂²×C₄₇	semidirect
643. #488	C₂²×C₄₇	semidirect
644. #485	C₂²×C₄₇	semidirect
645. #484	C₂²×C₄₇	semidirect
646. #484	C₂²×C₄₇	semidirect
648. #483	C₂²×C₄₇	semidirect
649. #482	C₂²×C₄₇	semidirect
650. #479	C₂²×C₄₇	semidirect
651. #478	C₂²×C₄₇	semidirect
652. #470	C₂²×C₄₇	semidirect
653. #470	C₂²×C₄₇	semidirect
654. #470	C₂²×C₄₇	semidirect
655. #468	C₂²×C₄₇	semidirect
658. #467	C₂²×C₄₇	semidirect
659. #465	C₂²×C₄₇	semidirect
660. #464	C₂²×C₄₇	semidirect
661. #464	C₂²×C₄₇	semidirect
662. #462	C₂²×C₄₇	semidirect
663. #462	C₂²×C₄₇	semidirect
664. #462	C₂²×C₄₇	semidirect
665. #461	C₂²×C₄₇	semidirect
672. #452	C₂²×C₄₇	semidirect
673. #452	C₂²×C₄₇	semidirect
676. #451	C₂²×C₄₇	semidirect
677. #451	C₂²×C₄₇	semidirect
678. #451	C₂²×C₄₇	semidirect
679. #451	C₂²×C₄₇	semidirect
680. #451	C₂²×C₄₇	semidirect
681. #451	C₂²×C₄₇	semidirect
683. #448	C₂²×C₄₇	semidirect
684. #441	C₂²×C₄₇	semidirect
685. #440	C₂²×C₄₇	semidirect
686. C₄×Q₁₆	C₂²×C₄₇	semidirect
687. C₄×SD₁₆	C₂²×C₄₇	semidirect
688. #436	C₂²×C₄₇	semidirect
690. #435	C₂²×C₄₇	semidirect
692. #433	C₂²×C₄₇	semidirect
693. #419	C₂²×C₄₇	semidirect
696. #416	C₂²×C₄₇	semidirect
699. #408	C₂²×C₄₇	semidirect
702. C₄₇	#61622	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×#3538	2
C₄₇×#3489	2
C₄₇×#3327	2
C₄₇×#3315	2
C₄₇×#3312	2
C₄₇×#3296	2
D₄×Q₁₆×C₄₇	2
C₄₇×#3276	2
C₄₇×#3270	2
C₄₇×#3266	2
C₄₇×#3223	2
C₄₇×#3201	2
C₄₇×#3195	2
C₄₇×#3189	2
C₄₇×#3120	2
C₄₇×#3011	2
C₄₇×#3007	2
C₂×C₄₇×#452	2
C₄₇×#2976	2
#61622	47

Subgroups — C47×#61622 #26101320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#61622 #26101320