Subgroups — C₄₇×#61983 #26101681

Order 12032.

2164 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3397	C₂	1	2	yes	maximal, complemented
4	C₄₇×#3368	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3310	C₂	1	4	yes	maximal, complemented
6	C₄₇×#3294	C₂	1	2	yes	maximal, complemented
7	D₄×SD₁₆×C₄₇	C₂	1	2	yes	maximal, complemented
8	C₄₇×#3265	C₂	1	4	yes	maximal, complemented
9	C₄₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#3247	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3217	C₂	1	2	yes	maximal, complemented
12	C₄₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₇×#3112	C₂	1	2	yes	maximal, complemented
14	C₄₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₇×#460	C₂	1	2	yes	maximal, complemented
17	C₄₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₄₇	—	2	1	no	—
19	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₄₇	C₂²	1	4	yes	complemented
21	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
22	C₄₇×#556	—	2	1	no	—
23	C₄₇×#556	C₂²	1	1	yes	characteristic, complemented
24	C₄₇×#552	—	2	2	no	—
25	C₄₇×#552	C₂²	1	2	yes	complemented
26	C₄₇×#550	—	2	1	no	—
27	C₄₇×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
29	C₄₇×#548	C₂²	1	2	yes	complemented
30	C₄₇×#547	—	2	1	no	—
31	C₄₇×#547	C₂²	1	1	yes	characteristic, complemented
32	D₄²×C₄₇	—	2	1	no	—
33	D₄²×C₄₇	—	2	2	no	—
34	D₄²×C₄₇	C₂²	1	2	yes	—
35	D₄²×C₄₇	C₂²	1	4	yes	—
36	C₄₇×#535	—	2	2	no	—
37	C₄₇×#535	—	2	1	no	—
38	C₄₇×#533	—	2	1	no	—
39	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×#532	C₂²	1	1	yes	characteristic
41	C₄₇×#532	C₂²	1	2	yes	—
42	C₂×#127×C₄₇	C₂²	1	2	yes	—
43	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#529	—	2	2	no	—
45	C₄₇×#529	C₂²	1	2	yes	complemented
46	C₄×#41×C₄₇	—	2	1	no	—
47	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
48	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
50	C₄₇×#496	C₂²	1	4	yes	complemented
51	C₄₇×#492	C₂²	1	2	yes	complemented
52	C₄₇×#490	C₂²	1	4	yes	complemented
53	C₄₇×#486	C₂²	1	2	yes	complemented
54	C₄₇×#482	C₂²	1	2	yes	complemented
55	C₄₇×#480	C₂²	1	4	yes	complemented
56	C₄₇×#478	C₂²	1	4	yes	complemented
57	C₄₇×#477	C₂²	1	1	yes	characteristic, complemented
58	C₄₇×#477	C₂²	1	2	yes	complemented
59	C₄₇×#476	C₂²	1	1	yes	characteristic, complemented
60	C₄₇×#474	C₂²	1	2	yes	complemented
61	C₄₇×#468	C₂²	1	4	yes	complemented
62	C₄₇×#466	C₂²	1	4	yes	complemented
63	C₄₇×#465	C₂²	1	4	yes	complemented
64	C₄₇×#463	C₂²	1	4	yes	complemented
65	C₄₇×#461	C₂²	1	2	yes	complemented
66	C₄₇×#460	C₂²	1	1	yes	characteristic, complemented
67	C₄₇×#460	C₂²	1	2	yes	complemented
68	C₄₇×#460	C₂²	1	4	yes	complemented
69	C₄₇×#460	C₂²	1	4	yes	complemented
70	C₄₇×#460	C₂²	1	2	yes	complemented
71	C₄₇×#460	C₂²	1	2	yes	complemented
72	C₄₇×#460	C₂²	1	2	yes	complemented
73	C₄₇×#460	C₂²	1	2	yes	complemented
74	C₄₇×#459	C₂²	1	2	yes	complemented
75	C₄₇×#459	C₂²	1	2	yes	complemented
76	C₄₇×#459	C₂²	1	1	yes	characteristic, complemented
77	C₄₇×#450	C₂²	1	4	yes	complemented
78	C₄₇×#450	C₂²	1	4	yes	complemented
79	C₄₇×#449	C₂²	1	2	yes	complemented
80	C₄₇×#448	C₂²	1	4	yes	complemented
81	C₄₇×#447	C₂²	1	4	yes	complemented
82	C₄₇×#446	C₂²	1	2	yes	complemented
83	C₄₇×#440	C₂²	1	4	yes	complemented
84	C₄₇×#440	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
86	C₄×D₈×C₄₇	C₂²	1	2	yes	complemented
87	C₄₇×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
89	C₄₇×#432	C₂²	1	2	yes	complemented
90	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
91	C₄₇×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
93	C₄₇×#418	C₂²	1	2	yes	complemented
94	C₂×#102×C₄₇	C₂²	1	4	yes	complemented
95	H(5,𝔽₂)×C₄₇	—	4	8	no	—
96	C₂×#41×C₄₇	—	2	2	no	—
97	C₂×#41×C₄₇	—	2	1	no	—
98	C₂×#41×C₄₇	—	2	2	no	—
99	C₂×#41×C₄₇	—	2	1	no	—
100	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
101	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
103	C₂²×D₄×C₄₇	—	2	4	no	—
104	C₂²×D₄×C₄₇	—	2	2	no	—
105	C₂²×D₄×C₄₇	—	2	2	no	—
106	C₂²×D₄×C₄₇	—	2	1	no	—
107	C₂²×D₄×C₄₇	—	2	2	no	—
108	C₂²×D₄×C₄₇	—	2	1	no	—
109	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
111	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
112	C₂×SD₁₆×C₄₇	—	4	8	no	—
113	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	—
118	C₂×D₈×C₄₇	C₂³	1	2	yes	—
119	C₂×D₈×C₄₇	C₂³	1	4	yes	—
120	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
121	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₄₇	—	2	1	no	—
123	C₄⋊Q₈×C₄₇	—	2	1	no	—
124	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
127	#127×C₄₇	—	2	1	no	—
128	#127×C₄₇	—	2	2	no	—
129	#127×C₄₇	—	2	1	no	—
130	#127×C₄₇	—	2	2	no	—
131	#127×C₄₇	C₂³	1	2	yes	—
132	#127×C₄₇	C₂³	1	1	yes	characteristic
133	#127×C₄₇	C₂³	1	2	yes	—
134	#127×C₄₇	C₂³	1	4	yes	—
135	#126×C₄₇	—	2	2	no	—
136	#126×C₄₇	—	2	2	no	—
137	#126×C₄₇	—	2	2	no	—
138	#125×C₄₇	—	2	2	no	—
139	#125×C₄₇	—	2	2	no	—
140	#125×C₄₇	—	2	1	no	—
141	#125×C₄₇	C₂³	1	2	yes	—
142	#124×C₄₇	—	2	2	no	—
143	#124×C₄₇	—	2	1	no	—
144	#124×C₄₇	—	2	2	no	—
145	#124×C₄₇	C₂³	1	2	yes	—
146	#123×C₄₇	—	2	2	no	—
147	#123×C₄₇	—	2	2	no	—
148	#123×C₄₇	—	2	2	no	—
149	C₂²⋊Q₈×C₄₇	—	2	1	no	—
150	C₂²⋊Q₈×C₄₇	—	2	1	no	—
151	C₂²⋊Q₈×C₄₇	—	2	1	no	—
152	C₂²⋊Q₈×C₄₇	—	2	2	no	—
153	C₂²⋊Q₈×C₄₇	—	2	2	no	—
154	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
155	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
156	#121×C₄₇	—	2	2	no	—
157	#121×C₄₇	—	2	2	no	—
158	#121×C₄₇	—	2	1	no	—
159	#121×C₄₇	—	2	2	no	—
160	#121×C₄₇	—	2	4	no	—
161	#121×C₄₇	—	2	4	no	—
162	#121×C₄₇	—	2	2	no	—
163	#121×C₄₇	C₂³	1	2	yes	—
164	#121×C₄₇	C₂³	1	4	yes	—
165	#121×C₄₇	C₂³	1	2	yes	—
166	#120×C₄₇	—	2	4	no	—
167	#120×C₄₇	—	2	4	no	—
168	#120×C₄₇	—	2	4	no	—
169	C₄×Q₈×C₄₇	—	2	1	no	—
170	C₄×Q₈×C₄₇	—	2	2	no	—
171	C₄×Q₈×C₄₇	—	2	2	no	—
172	C₄×Q₈×C₄₇	—	2	1	no	—
173	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
176	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
177	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
178	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
179	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₄₇	—	2	1	no	—
181	C₄×D₄×C₄₇	—	2	2	no	—
182	C₄×D₄×C₄₇	—	2	1	no	—
183	C₄×D₄×C₄₇	—	2	1	no	—
184	C₄×D₄×C₄₇	—	2	2	no	—
185	C₄×D₄×C₄₇	—	2	1	no	—
186	C₄×D₄×C₄₇	—	2	2	no	—
187	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
188	C₄×D₄×C₄₇	D₄	1	2	yes	—
189	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₄₇	C₂³	1	2	yes	—
192	C₄×D₄×C₄₇	C₂³	1	4	yes	—
193	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₄₇	C₂³	1	2	yes	—
195	#117×C₄₇	—	2	1	no	—
196	#117×C₄₇	—	2	1	no	—
197	#117×C₄₇	—	2	2	no	—
198	#117×C₄₇	—	2	1	no	—
199	#117×C₄₇	—	2	2	no	—
200	#117×C₄₇	D₄	1	2	yes	—
201	#117×C₄₇	D₄	1	1	yes	characteristic
202	#117×C₄₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
204	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₄₇	—	2	2	no	—
206	C₂×C₄²×C₄₇	—	2	1	no	—
207	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
208	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
209	#107×C₄₇	C₂³	1	4	yes	—
210	#107×C₄₇	C₂³	1	2	yes	—
211	#106×C₄₇	C₂³	1	2	yes	—
212	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
213	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
215	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
217	#103×C₄₇	C₂³	1	2	yes	—
218	#103×C₄₇	C₂³	1	4	yes	—
219	#102×C₄₇	C₂³	1	2	yes	—
220	#102×C₄₇	C₂³	1	2	yes	—
221	#102×C₄₇	C₂³	1	4	yes	—
222	#102×C₄₇	C₂³	1	4	yes	—
223	#102×C₄₇	C₂³	1	4	yes	—
224	#102×C₄₇	C₂³	1	4	yes	—
225	#102×C₄₇	C₂³	1	2	yes	—
226	#102×C₄₇	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
228	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
229	#97×C₄₇	C₂³	1	4	yes	—
230	C₄×C₈×C₄₇	C₂³	1	2	yes	—
231	C₂⁴×C₄₇	—	2	2	no	—
232	C₂⁴×C₄₇	—	2	4	no	—
233	#41×C₄₇	—	2	4	no	—
234	#41×C₄₇	—	2	2	no	—
235	#41×C₄₇	—	4	1	no	—
236	#41×C₄₇	—	4	8	no	—
237	#41×C₄₇	—	4	4	no	—
238	#41×C₄₇	—	4	8	no	—
239	#41×C₄₇	—	4	4	no	—
240	C₂×Q₈×C₄₇	—	2	2	no	—
241	C₂×Q₈×C₄₇	—	2	1	no	—
242	C₂×Q₈×C₄₇	—	2	1	no	—
243	C₂×Q₈×C₄₇	—	2	4	no	—
244	C₂×Q₈×C₄₇	—	4	2	no	—
245	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₄₇	—	2	1	no	—
249	C₂×D₄×C₄₇	—	2	2	no	—
250	C₂×D₄×C₄₇	—	2	2	no	—
251	C₂×D₄×C₄₇	—	2	4	no	—
252	C₂×D₄×C₄₇	—	2	1	no	—
253	C₂×D₄×C₄₇	—	2	2	no	—
254	C₂×D₄×C₄₇	—	2	4	no	—
255	C₂×D₄×C₄₇	—	2	2	no	—
256	C₂×D₄×C₄₇	—	2	1	no	—
257	C₂×D₄×C₄₇	—	2	2	no	—
258	C₂×D₄×C₄₇	—	2	2	no	—
259	C₂×D₄×C₄₇	—	2	4	no	—
260	C₂×D₄×C₄₇	—	2	4	no	—
261	C₂×D₄×C₄₇	—	2	2	no	—
262	C₂×D₄×C₄₇	—	4	4	no	—
263	C₂×D₄×C₄₇	—	4	2	no	—
264	C₂×D₄×C₄₇	—	4	4	no	—
265	C₂×D₄×C₄₇	—	4	2	no	—
266	C₂×D₄×C₄₇	—	4	8	no	—
267	C₂×D₄×C₄₇	—	4	4	no	—
268	C₂×D₄×C₄₇	—	4	16	no	—
269	C₂×D₄×C₄₇	—	4	8	no	—
270	C₂×D₄×C₄₇	—	8	4	no	—
271	C₂×D₄×C₄₇	—	8	2	no	—
272	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
275	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
276	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₄₇	—	2	2	no	—
278	C₂²×C₄×C₄₇	—	2	2	no	—
279	C₂²×C₄×C₄₇	—	2	1	no	—
280	C₂²×C₄×C₄₇	—	2	1	no	—
281	C₂²×C₄×C₄₇	—	2	1	no	—
282	C₂²×C₄×C₄₇	—	2	4	no	—
283	C₂²×C₄×C₄₇	—	2	2	no	—
284	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
290	SD₁₆×C₄₇	—	2	4	no	—
291	SD₁₆×C₄₇	—	2	8	no	—
292	SD₁₆×C₄₇	—	4	4	no	—
293	SD₁₆×C₄₇	—	4	4	no	—
294	SD₁₆×C₄₇	—	4	4	no	—
295	D₈×C₄₇	—	4	2	no	—
296	D₈×C₄₇	—	4	4	no	—
297	M₁₆×C₄₇	—	4	2	no	—
298	C₂×C₈×C₄₇	—	4	4	no	—
299	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
300	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
301	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₄₇	—	2	1	no	—
303	C₄⋊C₄×C₄₇	—	2	2	no	—
304	C₄⋊C₄×C₄₇	—	2	2	no	—
305	C₄⋊C₄×C₄₇	—	2	2	no	—
306	C₄⋊C₄×C₄₇	—	2	2	no	—
307	C₄⋊C₄×C₄₇	—	2	1	no	—
308	C₄⋊C₄×C₄₇	—	2	2	no	—
309	C₄⋊C₄×C₄₇	—	2	2	no	—
310	C₄⋊C₄×C₄₇	—	2	1	no	—
311	C₄⋊C₄×C₄₇	—	2	1	no	—
312	C₄⋊C₄×C₄₇	—	2	2	no	—
313	C₄⋊C₄×C₄₇	—	2	1	no	—
314	C₄⋊C₄×C₄₇	—	2	2	no	—
315	C₄⋊C₄×C₄₇	—	2	1	no	—
316	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
318	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
319	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
320	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
324	C₂²⋊C₄×C₄₇	—	2	2	no	—
325	C₂²⋊C₄×C₄₇	—	2	2	no	—
326	C₂²⋊C₄×C₄₇	—	2	1	no	—
327	C₂²⋊C₄×C₄₇	—	2	2	no	—
328	C₂²⋊C₄×C₄₇	—	2	1	no	—
329	C₂²⋊C₄×C₄₇	—	2	1	no	—
330	C₂²⋊C₄×C₄₇	—	2	2	no	—
331	C₂²⋊C₄×C₄₇	—	2	2	no	—
332	C₂²⋊C₄×C₄₇	—	2	2	no	—
333	C₂²⋊C₄×C₄₇	—	2	4	no	—
334	C₂²⋊C₄×C₄₇	—	2	4	no	—
335	C₂²⋊C₄×C₄₇	—	2	2	no	—
336	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
339	C₄²×C₄₇	—	2	1	no	—
340	C₄²×C₄₇	—	2	1	no	—
341	C₄²×C₄₇	—	2	2	no	—
342	C₄²×C₄₇	—	2	2	no	—
343	C₄²×C₄₇	—	2	1	no	—
344	C₄²×C₄₇	—	2	2	no	—
345	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₄₇	C₂×D₄	1	2	yes	—
348	C₄²×C₄₇	C₂×D₄	1	2	yes	—
349	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
350	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
351	C₄²×C₄₇	C₂⁴	1	2	yes	—
352	C₂³×C₄₇	—	2	1	no	—
353	C₂³×C₄₇	—	2	4	no	—
354	C₂³×C₄₇	—	2	2	no	—
355	C₂³×C₄₇	—	4	4	no	—
356	C₂³×C₄₇	—	4	8	no	—
357	C₂³×C₄₇	—	8	4	no	—
358	C₂³×C₄₇	—	8	2	no	—
359	C₂³×C₄₇	—	8	4	no	—
360	C₂³×C₄₇	—	8	2	no	—
361	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
362	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
363	Q₈×C₄₇	—	2	2	no	—
364	Q₈×C₄₇	—	2	1	no	—
365	Q₈×C₄₇	—	2	2	no	—
366	Q₈×C₄₇	—	2	2	no	—
367	Q₈×C₄₇	—	4	4	no	—
368	Q₈×C₄₇	—	4	2	no	—
369	Q₈×C₄₇	—	4	2	no	—
370	Q₈×C₄₇	H(5,𝔽₂)	1	2	yes	complemented
371	D₄×C₄₇	—	2	4	no	—
372	D₄×C₄₇	—	2	1	no	—
373	D₄×C₄₇	—	2	4	no	—
374	D₄×C₄₇	—	2	2	no	—
375	D₄×C₄₇	—	2	1	no	—
376	D₄×C₄₇	—	2	2	no	—
377	D₄×C₄₇	—	2	4	no	—
378	D₄×C₄₇	—	4	2	no	—
379	D₄×C₄₇	—	4	4	no	—
380	D₄×C₄₇	—	4	2	no	—
381	D₄×C₄₇	—	4	8	no	—
382	D₄×C₄₇	—	4	4	no	—
383	D₄×C₄₇	—	4	8	no	—
384	D₄×C₄₇	—	4	4	no	—
385	D₄×C₄₇	—	4	4	no	—
386	D₄×C₄₇	—	4	2	no	—
387	D₄×C₄₇	—	4	4	no	—
388	D₄×C₄₇	—	8	2	no	—
389	D₄×C₄₇	—	8	4	no	—
390	D₄×C₄₇	—	8	4	no	—
391	D₄×C₄₇	—	8	2	no	—
392	D₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	complemented
393	C₂×C₄×C₄₇	—	2	4	no	—
394	C₂×C₄×C₄₇	—	2	1	no	—
395	C₂×C₄×C₄₇	—	2	2	no	—
396	C₂×C₄×C₄₇	—	2	4	no	—
397	C₂×C₄×C₄₇	—	2	2	no	—
398	C₂×C₄×C₄₇	—	2	2	no	—
399	C₂×C₄×C₄₇	—	2	1	no	—
400	C₂×C₄×C₄₇	—	2	2	no	—
401	C₂×C₄×C₄₇	—	2	1	no	—
402	C₂×C₄×C₄₇	—	2	1	no	—
403	C₂×C₄×C₄₇	—	2	1	no	—
404	C₂×C₄×C₄₇	—	2	2	no	—
405	C₂×C₄×C₄₇	—	2	2	no	—
406	C₂×C₄×C₄₇	—	2	2	no	—
407	C₂×C₄×C₄₇	—	4	2	no	—
408	C₂×C₄×C₄₇	—	4	4	no	—
409	C₂×C₄×C₄₇	—	4	8	no	—
410	C₂×C₄×C₄₇	—	4	4	no	—
411	C₂×C₄×C₄₇	—	4	4	no	—
412	C₂×C₄×C₄₇	—	4	2	no	—
413	C₂×C₄×C₄₇	—	4	2	no	—
414	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
423	C₈×C₄₇	—	2	2	no	—
424	C₈×C₄₇	—	2	4	no	—
425	C₈×C₄₇	—	2	2	no	—
426	#61983	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂²×C₄₇	—	2	2	no	—
428	C₂²×C₄₇	—	2	2	no	—
429	C₂²×C₄₇	—	2	1	no	—
430	C₂²×C₄₇	—	2	1	no	—
431	C₂²×C₄₇	—	2	1	no	—
432	C₂²×C₄₇	—	4	1	no	—
433	C₂²×C₄₇	—	4	4	no	—
434	C₂²×C₄₇	—	4	2	no	—
435	C₂²×C₄₇	—	4	4	no	—
436	C₂²×C₄₇	—	4	2	no	—
437	C₂²×C₄₇	—	4	1	no	—
438	C₂²×C₄₇	—	4	1	no	—
439	C₂²×C₄₇	—	4	2	no	—
440	C₂²×C₄₇	—	4	4	no	—
441	C₂²×C₄₇	—	16	8	no	—
442	C₂²×C₄₇	—	16	4	no	—
443	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
444	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₄₇	—	2	1	no	—
446	C₄×C₄₇	—	2	2	no	—
447	C₄×C₄₇	—	2	2	no	—
448	C₄×C₄₇	—	2	1	no	—
449	C₄×C₄₇	—	2	2	no	—
450	C₄×C₄₇	—	2	2	no	—
451	C₄×C₄₇	—	2	1	no	—
452	C₄×C₄₇	—	4	2	no	—
453	C₄×C₄₇	—	4	1	no	—
454	C₄×C₄₇	—	4	2	no	—
455	C₄×C₄₇	—	4	2	no	—
456	C₄×C₄₇	—	4	1	no	—
457	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
458	C₄×C₄₇	#577	1	2	yes	—
459	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₄×C₄₇	#585	1	1	yes	characteristic
461	#3498	C₂×C₄₇	1	1	yes	characteristic, complemented
462	#3482	C₂×C₄₇	1	1	yes	characteristic, complemented
463	#3397	C₂×C₄₇	1	2	yes	complemented
464	#3368	C₂×C₄₇	1	2	yes	complemented
465	#3310	C₂×C₄₇	1	4	yes	complemented
466	#3294	C₂×C₄₇	1	2	yes	complemented
467	D₄×SD₁₆	C₂×C₄₇	1	2	yes	complemented
468	#3265	C₂×C₄₇	1	4	yes	complemented
469	#3254	C₂×C₄₇	1	1	yes	characteristic, complemented
470	#3247	C₂×C₄₇	1	2	yes	complemented
471	#3217	C₂×C₄₇	1	2	yes	complemented
472	#3208	C₂×C₄₇	1	1	yes	characteristic, complemented
473	#3112	C₂×C₄₇	1	2	yes	complemented
474	#3106	C₂×C₄₇	1	1	yes	characteristic, complemented
475	#3038	C₂×C₄₇	1	1	yes	characteristic, complemented
476	C₂×#460	C₂×C₄₇	1	2	yes	complemented
477	#2990	C₂×C₄₇	1	1	yes	characteristic, complemented
478	C₂×C₄₇	—	2	4	no	—
479	C₂×C₄₇	—	4	1	no	—
480	C₂×C₄₇	—	8	1	no	—
481	C₂×C₄₇	—	8	2	no	—
482	C₂×C₄₇	—	8	4	no	—
483	C₂×C₄₇	#3488	1	1	yes	characteristic
484	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
485	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
486	C₂×H(5,𝔽₂)	—	2	1	no	—
487	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	complemented
488	C₂²×SD₁₆	C₂²×C₄₇	1	4	yes	complemented
489	#557	C₂²×C₄₇	1	1	yes	characteristic, complemented
490	#556	—	2	1	no	—
491	#556	C₂²×C₄₇	1	1	yes	characteristic, complemented
492	#552	—	2	2	no	—
493	#552	C₂²×C₄₇	1	2	yes	complemented
494	#550	—	2	1	no	—
495	#550	C₂²×C₄₇	1	2	yes	—
496	D₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
497	#548	C₂²×C₄₇	1	2	yes	complemented
498	#547	—	2	1	no	—
499	#547	C₂²×C₄₇	1	1	yes	characteristic, complemented
500	D₄²	—	2	1	no	—
501	D₄²	—	2	2	no	—
502	D₄²	C₂²×C₄₇	1	4	yes	—
503	D₄²	C₂²×C₄₇	1	2	yes	—
504	#535	—	2	2	no	—
505	#535	—	2	1	no	—
506	#533	—	2	1	no	—
507	#533	C₂²×C₄₇	1	1	yes	characteristic, complemented
508	#532	C₂²×C₄₇	1	1	yes	characteristic
509	#532	C₂²×C₄₇	1	2	yes	—
510	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
511	C₂×#127	C₂²×C₄₇	1	2	yes	—
512	#529	—	2	2	no	—
513	#529	C₂²×C₄₇	1	2	yes	complemented
514	C₄×#41	—	2	1	no	—
515	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
516	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic, complemented
517	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	complemented
518	#496	C₂²×C₄₇	1	4	yes	complemented
519	#492	C₂²×C₄₇	1	2	yes	complemented
520	#490	C₂²×C₄₇	1	4	yes	complemented
521	#486	C₂²×C₄₇	1	2	yes	complemented
522	#482	C₂²×C₄₇	1	2	yes	complemented
523	#480	C₂²×C₄₇	1	4	yes	complemented
524	#478	C₂²×C₄₇	1	4	yes	complemented
525	#477	C₂²×C₄₇	1	1	yes	characteristic, complemented
526	#477	C₂²×C₄₇	1	2	yes	complemented
527	#476	C₂²×C₄₇	1	1	yes	characteristic, complemented
528	#474	C₂²×C₄₇	1	2	yes	complemented
529	#468	C₂²×C₄₇	1	4	yes	complemented
530	#466	C₂²×C₄₇	1	4	yes	complemented
531	#465	C₂²×C₄₇	1	4	yes	complemented
532	#463	C₂²×C₄₇	1	4	yes	complemented
533	#461	C₂²×C₄₇	1	2	yes	complemented
534	#460	C₂²×C₄₇	1	1	yes	characteristic, complemented
535	#460	C₂²×C₄₇	1	2	yes	complemented
536	#460	C₂²×C₄₇	1	2	yes	complemented
537	#460	C₂²×C₄₇	1	4	yes	complemented
538	#460	C₂²×C₄₇	1	2	yes	complemented
539	#460	C₂²×C₄₇	1	4	yes	complemented
540	#460	C₂²×C₄₇	1	2	yes	complemented
541	#460	C₂²×C₄₇	1	2	yes	complemented
542	#459	C₂²×C₄₇	1	1	yes	characteristic, complemented
543	#459	C₂²×C₄₇	1	2	yes	complemented
544	#459	C₂²×C₄₇	1	2	yes	complemented
545	#450	C₂²×C₄₇	1	4	yes	complemented
546	#450	C₂²×C₄₇	1	4	yes	complemented
547	#449	C₂²×C₄₇	1	2	yes	complemented
548	#448	C₂²×C₄₇	1	4	yes	complemented
549	#447	C₂²×C₄₇	1	4	yes	complemented
550	#446	C₂²×C₄₇	1	2	yes	complemented
551	#440	C₂²×C₄₇	1	4	yes	complemented
552	#440	C₂²×C₄₇	1	4	yes	complemented
553	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	complemented
554	C₄×D₈	C₂²×C₄₇	1	2	yes	complemented
555	#435	C₂²×C₄₇	1	4	yes	complemented
556	C₈×D₄	C₂²×C₄₇	1	2	yes	complemented
557	#432	C₂²×C₄₇	1	2	yes	complemented
558	#431	C₂²×C₄₇	1	1	yes	characteristic, complemented
559	#423	C₂²×C₄₇	1	1	yes	characteristic, complemented
560	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
561	#418	C₂²×C₄₇	1	2	yes	complemented
562	C₂×#102	C₂²×C₄₇	1	4	yes	complemented
563	C₄₇	#61983	1	1	yes	characteristic, direct product factor, Sylow
564	H(5,𝔽₂)	—	4	8	no	—
565	C₂×#41	—	2	2	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	2	2	no	—
568	C₂×#41	—	2	1	no	—
569	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
570	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
572	C₂²×D₄	—	2	4	no	—
573	C₂²×D₄	—	2	2	no	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	2	no	—
577	C₂²×D₄	—	2	1	no	—
578	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
579	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
580	AGL(1,ℤ/8)	—	4	4	no	—
581	C₂×SD₁₆	—	4	8	no	—
582	C₂×SD₁₆	C₂³×C₄₇	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₄₇	1	4	yes	—
584	C₂×SD₁₆	C₂³×C₄₇	1	4	yes	—
585	C₂×SD₁₆	C₂³×C₄₇	1	4	yes	—
586	C₂×SD₁₆	C₂³×C₄₇	1	4	yes	—
587	C₂×D₈	C₂³×C₄₇	1	4	yes	—
588	C₂×D₈	C₂³×C₄₇	1	2	yes	—
589	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
590	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
591	C₄⋊Q₈	—	2	1	no	—
592	C₄⋊Q₈	—	2	1	no	—
593	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
594	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
595	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
596	#127	—	2	1	no	—
597	#127	—	2	2	no	—
598	#127	—	2	1	no	—
599	#127	—	2	2	no	—
600	#127	C₂³×C₄₇	1	2	yes	—
601	#127	C₂³×C₄₇	1	1	yes	characteristic
602	#127	C₂³×C₄₇	1	2	yes	—
603	#127	C₂³×C₄₇	1	4	yes	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	—	2	2	no	—
609	#125	—	2	1	no	—
610	#125	C₂³×C₄₇	1	2	yes	—
611	#124	—	2	2	no	—
612	#124	—	2	1	no	—
613	#124	—	2	2	no	—
614	#124	C₂³×C₄₇	1	2	yes	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₄₇	1	2	yes	—
625	#121	—	2	2	no	—
626	#121	—	2	2	no	—
627	#121	—	2	1	no	—
628	#121	—	2	2	no	—
629	#121	—	2	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	2	no	—
632	#121	C₂³×C₄₇	1	2	yes	—
633	#121	C₂³×C₄₇	1	4	yes	—
634	#121	C₂³×C₄₇	1	2	yes	—
635	#120	—	2	4	no	—
636	#120	—	2	4	no	—
637	#120	—	2	4	no	—
638	C₄×Q₈	—	2	1	no	—
639	C₄×Q₈	—	2	2	no	—
640	C₄×Q₈	—	2	2	no	—
641	C₄×Q₈	—	2	1	no	—
642	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
643	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
644	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
645	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
646	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
647	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
648	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	—	2	1	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
657	C₄×D₄	D₄×C₄₇	1	2	yes	—
658	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
659	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
660	C₄×D₄	C₂³×C₄₇	1	2	yes	—
661	C₄×D₄	C₂³×C₄₇	1	4	yes	—
662	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
663	C₄×D₄	C₂³×C₄₇	1	2	yes	—
664	#117	—	2	1	no	—
665	#117	—	2	1	no	—
666	#117	—	2	2	no	—
667	#117	—	2	1	no	—
668	#117	—	2	2	no	—
669	#117	D₄×C₄₇	1	2	yes	—
670	#117	D₄×C₄₇	1	1	yes	characteristic
671	#117	C₂³×C₄₇	1	1	yes	characteristic
672	C₂×C₄⋊C₄	—	2	2	no	—
673	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
674	C₂×C₄²	—	2	2	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
677	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
678	#107	C₂³×C₄₇	1	2	yes	—
679	#107	C₂³×C₄₇	1	4	yes	—
680	#106	C₂³×C₄₇	1	2	yes	—
681	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
682	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
683	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
684	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
685	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
686	#103	C₂³×C₄₇	1	2	yes	—
687	#103	C₂³×C₄₇	1	4	yes	—
688	#102	C₂³×C₄₇	1	2	yes	—
689	#102	C₂³×C₄₇	1	4	yes	—
690	#102	C₂³×C₄₇	1	4	yes	—
691	#102	C₂³×C₄₇	1	4	yes	—
692	#102	C₂³×C₄₇	1	4	yes	—
693	#102	C₂³×C₄₇	1	2	yes	—
694	#102	C₂³×C₄₇	1	2	yes	—
695	#102	C₂³×C₄₇	1	4	yes	—
696	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
697	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
698	#97	C₂³×C₄₇	1	4	yes	—
699	C₄×C₈	C₂³×C₄₇	1	2	yes	—
700	C₂⁴	—	2	2	no	—
701	C₂⁴	—	2	4	no	—
702	#41	—	2	4	no	—
703	#41	—	2	2	no	—
704	#41	—	4	1	no	—
705	#41	—	4	8	no	—
706	#41	—	4	4	no	—
707	#41	—	4	8	no	—
708	#41	—	4	4	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	4	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
715	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
716	C₂×Q₈	C₂⁴×C₄₇	1	1	yes	characteristic
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	4	4	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	8	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	16	no	—
738	C₂×D₄	—	4	8	no	—
739	C₂×D₄	—	8	4	no	—
740	C₂×D₄	—	8	2	no	—
741	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
742	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
743	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
744	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
745	C₂×D₄	C₂⁴×C₄₇	1	1	yes	characteristic
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
754	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	4	4	no	—
762	SD₁₆	—	4	4	no	—
763	SD₁₆	—	4	4	no	—
764	D₈	—	4	2	no	—
765	D₈	—	4	4	no	—
766	M₁₆	—	4	2	no	—
767	C₂×C₈	—	4	4	no	—
768	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
769	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
770	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
786	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
787	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
788	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
789	C₄⋊C₄	C₂⁴×C₄₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₄₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
807	C₂²⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	1	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	2	no	—
814	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
815	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
816	C₄²	C₂×D₄×C₄₇	1	2	yes	—
817	C₄²	C₂×D₄×C₄₇	1	2	yes	—
818	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
819	C₄²	C₂⁴×C₄₇	1	2	yes	—
820	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
821	C₂³	—	2	1	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	4	4	no	—
825	C₂³	—	4	8	no	—
826	C₂³	—	8	4	no	—
827	C₂³	—	8	2	no	—
828	C₂³	—	8	4	no	—
829	C₂³	—	8	2	no	—
830	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
831	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
832	Q₈	—	2	2	no	—
833	Q₈	—	2	1	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	4	4	no	—
837	Q₈	—	4	2	no	—
838	Q₈	—	4	2	no	—
839	Q₈	H(5,𝔽₂)×C₄₇	1	2	yes	complemented
840	D₄	—	2	4	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	1	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	4	no	—
847	D₄	—	4	2	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	8	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	8	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	4	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	4	no	—
859	D₄	—	8	4	no	—
860	D₄	—	8	2	no	—
861	D₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	complemented
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	4	8	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
884	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
885	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
887	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
889	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
891	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	4	no	—
894	C₈	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	4	4	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	4	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	4	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	16	8	no	—
910	C₂²	—	16	4	no	—
911	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	4	yes	—
912	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
926	C₄	C₄₇×#577	1	2	yes	—
927	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
928	C₄	C₄₇×#585	1	1	yes	characteristic
929	C₂	—	2	4	no	—
930	C₂	—	4	1	no	—
931	C₂	—	8	2	no	—
932	C₂	—	8	4	no	—
933	C₂	—	8	1	no	—
934	C₂	C₄₇×#3488	1	1	yes	characteristic
935	C₂	C₂²×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
936	C₂	C₂×C₄₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄×#41×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3498	C₂	semidirect
2. C₄₇×#3482	C₂	semidirect
3. C₄₇×#3397	C₂	semidirect
4. C₄₇×#3368	C₂	semidirect
5. C₄₇×#3310	C₂	semidirect
6. C₄₇×#3294	C₂	semidirect
7. D₄×SD₁₆×C₄₇	C₂	semidirect
8. C₄₇×#3265	C₂	semidirect
9. C₄₇×#3254	C₂	semidirect
10. C₄₇×#3247	C₂	semidirect
11. C₄₇×#3217	C₂	semidirect
12. C₄₇×#3208	C₂	semidirect
13. C₄₇×#3112	C₂	semidirect
14. C₄₇×#3106	C₂	semidirect
15. C₄₇×#3038	C₂	semidirect
16. C₂×C₄₇×#460	C₂	semidirect
17. C₄₇×#2990	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₄₇	C₂²	semidirect
20. C₂²×SD₁₆×C₄₇	C₂²	semidirect
21. C₄₇×#557	C₂²	semidirect
23. C₄₇×#556	C₂²	semidirect
25. C₄₇×#552	C₂²	semidirect
28. D₄×Q₈×C₄₇	C₂²	semidirect
29. C₄₇×#548	C₂²	semidirect
31. C₄₇×#547	C₂²	semidirect
39. C₄₇×#533	C₂²	semidirect
45. C₄₇×#529	C₂²	semidirect
48. C₄×#41×C₄₇	C₂²	semidirect
49. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
50. C₄₇×#496	C₂²	semidirect
51. C₄₇×#492	C₂²	semidirect
52. C₄₇×#490	C₂²	semidirect
53. C₄₇×#486	C₂²	semidirect
54. C₄₇×#482	C₂²	semidirect
55. C₄₇×#480	C₂²	semidirect
56. C₄₇×#478	C₂²	semidirect
57. C₄₇×#477	C₂²	semidirect
58. C₄₇×#477	C₂²	semidirect
59. C₄₇×#476	C₂²	semidirect
60. C₄₇×#474	C₂²	semidirect
61. C₄₇×#468	C₂²	semidirect
62. C₄₇×#466	C₂²	semidirect
63. C₄₇×#465	C₂²	semidirect
64. C₄₇×#463	C₂²	semidirect
65. C₄₇×#461	C₂²	semidirect
66. C₄₇×#460	C₂²	semidirect
67. C₄₇×#460	C₂²	semidirect
68. C₄₇×#460	C₂²	semidirect
69. C₄₇×#460	C₂²	semidirect
70. C₄₇×#460	C₂²	semidirect
71. C₄₇×#460	C₂²	semidirect
72. C₄₇×#460	C₂²	semidirect
73. C₄₇×#460	C₂²	semidirect
74. C₄₇×#459	C₂²	semidirect
75. C₄₇×#459	C₂²	semidirect
76. C₄₇×#459	C₂²	semidirect
77. C₄₇×#450	C₂²	semidirect
78. C₄₇×#450	C₂²	semidirect
79. C₄₇×#449	C₂²	semidirect
80. C₄₇×#448	C₂²	semidirect
81. C₄₇×#447	C₂²	semidirect
82. C₄₇×#446	C₂²	semidirect
83. C₄₇×#440	C₂²	semidirect
84. C₄₇×#440	C₂²	semidirect
85. C₄×SD₁₆×C₄₇	C₂²	semidirect
86. C₄×D₈×C₄₇	C₂²	semidirect
87. C₄₇×#435	C₂²	semidirect
88. C₈×D₄×C₄₇	C₂²	semidirect
89. C₄₇×#432	C₂²	semidirect
90. C₄₇×#431	C₂²	semidirect
91. C₄₇×#423	C₂²	semidirect
92. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
93. C₄₇×#418	C₂²	semidirect
94. C₂×#102×C₄₇	C₂²	semidirect
370. Q₈×C₄₇	H(5,𝔽₂)	semidirect
392. D₄×C₄₇	AGL(1,ℤ/8)	semidirect
426. #61983	C₄₇	direct (N × H)
461. #3498	C₂×C₄₇	semidirect
462. #3482	C₂×C₄₇	semidirect
463. #3397	C₂×C₄₇	semidirect
464. #3368	C₂×C₄₇	semidirect
465. #3310	C₂×C₄₇	semidirect
466. #3294	C₂×C₄₇	semidirect
467. D₄×SD₁₆	C₂×C₄₇	semidirect
468. #3265	C₂×C₄₇	semidirect
469. #3254	C₂×C₄₇	semidirect
470. #3247	C₂×C₄₇	semidirect
471. #3217	C₂×C₄₇	semidirect
472. #3208	C₂×C₄₇	semidirect
473. #3112	C₂×C₄₇	semidirect
474. #3106	C₂×C₄₇	semidirect
475. #3038	C₂×C₄₇	semidirect
476. C₂×#460	C₂×C₄₇	semidirect
477. #2990	C₂×C₄₇	semidirect
487. C₂×AGL(1,ℤ/8)	C₂²×C₄₇	semidirect
488. C₂²×SD₁₆	C₂²×C₄₇	semidirect
489. #557	C₂²×C₄₇	semidirect
491. #556	C₂²×C₄₇	semidirect
493. #552	C₂²×C₄₇	semidirect
496. D₄×Q₈	C₂²×C₄₇	semidirect
497. #548	C₂²×C₄₇	semidirect
499. #547	C₂²×C₄₇	semidirect
507. #533	C₂²×C₄₇	semidirect
513. #529	C₂²×C₄₇	semidirect
516. C₄×#41	C₂²×C₄₇	semidirect
517. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
518. #496	C₂²×C₄₇	semidirect
519. #492	C₂²×C₄₇	semidirect
520. #490	C₂²×C₄₇	semidirect
521. #486	C₂²×C₄₇	semidirect
522. #482	C₂²×C₄₇	semidirect
523. #480	C₂²×C₄₇	semidirect
524. #478	C₂²×C₄₇	semidirect
525. #477	C₂²×C₄₇	semidirect
526. #477	C₂²×C₄₇	semidirect
527. #476	C₂²×C₄₇	semidirect
528. #474	C₂²×C₄₇	semidirect
529. #468	C₂²×C₄₇	semidirect
530. #466	C₂²×C₄₇	semidirect
531. #465	C₂²×C₄₇	semidirect
532. #463	C₂²×C₄₇	semidirect
533. #461	C₂²×C₄₇	semidirect
534. #460	C₂²×C₄₇	semidirect
535. #460	C₂²×C₄₇	semidirect
536. #460	C₂²×C₄₇	semidirect
537. #460	C₂²×C₄₇	semidirect
538. #460	C₂²×C₄₇	semidirect
539. #460	C₂²×C₄₇	semidirect
540. #460	C₂²×C₄₇	semidirect
541. #460	C₂²×C₄₇	semidirect
542. #459	C₂²×C₄₇	semidirect
543. #459	C₂²×C₄₇	semidirect
544. #459	C₂²×C₄₇	semidirect
545. #450	C₂²×C₄₇	semidirect
546. #450	C₂²×C₄₇	semidirect
547. #449	C₂²×C₄₇	semidirect
548. #448	C₂²×C₄₇	semidirect
549. #447	C₂²×C₄₇	semidirect
550. #446	C₂²×C₄₇	semidirect
551. #440	C₂²×C₄₇	semidirect
552. #440	C₂²×C₄₇	semidirect
553. C₄×SD₁₆	C₂²×C₄₇	semidirect
554. C₄×D₈	C₂²×C₄₇	semidirect
555. #435	C₂²×C₄₇	semidirect
556. C₈×D₄	C₂²×C₄₇	semidirect
557. #432	C₂²×C₄₇	semidirect
558. #431	C₂²×C₄₇	semidirect
559. #423	C₂²×C₄₇	semidirect
560. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
561. #418	C₂²×C₄₇	semidirect
562. C₂×#102	C₂²×C₄₇	semidirect
563. C₄₇	#61983	direct (N × H)
839. Q₈	H(5,𝔽₂)×C₄₇	semidirect
861. D₄	AGL(1,ℤ/8)×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3498	2
C₄₇×#3482	2
C₄₇×#3397	2
C₄₇×#3368	2
C₄₇×#3310	2
C₄₇×#3294	2
D₄×SD₁₆×C₄₇	2
C₄₇×#3265	2
C₄₇×#3254	2
C₄₇×#3247	2
C₄₇×#3217	2
C₄₇×#3208	2
C₄₇×#3112	2
C₄₇×#3106	2
C₄₇×#3038	2
C₂×C₄₇×#460	2
C₄₇×#2990	2
#61983	47

Subgroups — C47×#61983 #26101681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#61983 #26101681