Subgroups — C₄₇×#15179 #26054877

Order 12032.

1946 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#1442	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1441	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1440	C₂	1	2	yes	maximal
10	C₄₇×#1439	C₂	1	2	yes	maximal
11	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₇	—	2	4	no	—
15	C₂×C₂²⋊Q₈×C₄₇	—	2	4	no	—
16	C₂×C₂²⋊Q₈×C₄₇	—	2	4	no	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#391	—	2	4	no	—
29	C₄₇×#391	—	2	4	no	—
30	C₄₇×#389	—	2	4	no	—
31	C₄₇×#380	—	2	4	no	—
32	C₄×C₂²⋊C₄×C₄₇	—	2	4	no	—
33	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#95×C₄₇	C₂²	1	2	yes	—
36	C₂×#95×C₄₇	C₂²	1	2	yes	—
37	C₂×#95×C₄₇	C₂²	1	2	yes	—
38	C₂×#95×C₄₇	C₂²	1	2	yes	—
39	C₂×#95×C₄₇	C₂²	1	2	yes	—
40	C₂×#95×C₄₇	C₂²	1	2	yes	—
41	C₂×#95×C₄₇	C₂²	1	2	yes	—
42	C₂×#95×C₄₇	C₂²	1	2	yes	—
43	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₄₇	—	2	2	no	—
45	C₂²×Q₈×C₄₇	—	2	2	no	—
46	C₂²×Q₈×C₄₇	—	2	2	no	—
47	C₂²×Q₈×C₄₇	—	2	2	no	—
48	C₂²×Q₈×C₄₇	—	2	2	no	—
49	C₂²×Q₈×C₄₇	—	2	2	no	—
50	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
51	C₂³×C₄×C₄₇	—	2	2	no	—
52	C₂³×C₄×C₄₇	—	2	2	no	—
53	C₂³×C₄×C₄₇	—	2	2	no	—
54	C₂³×C₄×C₄₇	—	2	2	no	—
55	C₂³×C₄×C₄₇	—	2	2	no	—
56	C₂³×C₄×C₄₇	—	2	2	no	—
57	C₂³×C₄×C₄₇	D₄	1	4	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂²⋊Q₈×C₄₇	—	2	32	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
82	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
95	C₂×C₂²⋊C₄×C₄₇	Q₈	1	4	yes	complemented
96	C₂×C₄²×C₄₇	—	2	2	no	—
97	C₂×C₄²×C₄₇	—	2	2	no	—
98	C₂×C₄²×C₄₇	—	2	2	no	—
99	C₂×C₄²×C₄₇	—	2	2	no	—
100	C₂×C₄²×C₄₇	—	2	2	no	—
101	C₂×C₄²×C₄₇	—	2	2	no	—
102	#95×C₄₇	—	2	2	no	—
103	#95×C₄₇	—	2	2	no	—
104	#95×C₄₇	—	2	4	no	—
105	#95×C₄₇	—	2	4	no	—
106	#95×C₄₇	—	2	4	no	—
107	#95×C₄₇	—	2	4	no	—
108	#95×C₄₇	—	2	4	no	—
109	#95×C₄₇	—	2	4	no	—
110	#95×C₄₇	—	2	4	no	—
111	#95×C₄₇	—	4	2	no	—
112	C₂⁴×C₄₇	—	2	1	no	—
113	C₂⁴×C₄₇	—	2	1	no	—
114	C₂⁴×C₄₇	—	2	1	no	—
115	C₂⁴×C₄₇	—	2	1	no	—
116	C₂⁴×C₄₇	—	2	1	no	—
117	C₂⁴×C₄₇	—	2	1	no	—
118	C₂⁴×C₄₇	—	2	1	no	—
119	C₂⁴×C₄₇	—	2	1	no	—
120	C₂⁴×C₄₇	—	2	1	no	—
121	C₂⁴×C₄₇	—	2	1	no	—
122	C₂⁴×C₄₇	—	2	1	no	—
123	C₂⁴×C₄₇	—	2	1	no	—
124	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
125	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
126	C₂⁴×C₄₇	#41	1	2	yes	—
127	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂×Q₈×C₄₇	—	2	8	no	—
129	C₂×Q₈×C₄₇	—	2	8	no	—
130	C₂×Q₈×C₄₇	—	2	8	no	—
131	C₂×Q₈×C₄₇	—	4	4	no	—
132	C₂×Q₈×C₄₇	—	4	4	no	—
133	C₂×Q₈×C₄₇	—	4	4	no	—
134	C₂×Q₈×C₄₇	—	4	4	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	—	2	1	no	—
140	C₂²×C₄×C₄₇	—	2	1	no	—
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	2	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	2	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	—	2	1	no	—
156	C₂²×C₄×C₄₇	—	2	1	no	—
157	C₂²×C₄×C₄₇	—	2	1	no	—
158	C₂²×C₄×C₄₇	—	2	1	no	—
159	C₂²×C₄×C₄₇	—	2	1	no	—
160	C₂²×C₄×C₄₇	—	2	2	no	—
161	C₂²×C₄×C₄₇	—	2	2	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	1	no	—
165	C₂²×C₄×C₄₇	—	2	1	no	—
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	2	2	no	—
170	C₂²×C₄×C₄₇	—	2	2	no	—
171	C₂²×C₄×C₄₇	—	2	2	no	—
172	C₂²×C₄×C₄₇	—	2	1	no	—
173	C₂²×C₄×C₄₇	—	2	2	no	—
174	C₂²×C₄×C₄₇	—	2	1	no	—
175	C₂²×C₄×C₄₇	—	2	2	no	—
176	C₂²×C₄×C₄₇	—	2	2	no	—
177	C₂²×C₄×C₄₇	—	2	1	no	—
178	C₂²×C₄×C₄₇	—	2	1	no	—
179	C₂²×C₄×C₄₇	—	2	1	no	—
180	C₂²×C₄×C₄₇	—	2	1	no	—
181	C₂²×C₄×C₄₇	—	2	1	no	—
182	C₂²×C₄×C₄₇	—	2	1	no	—
183	C₂²×C₄×C₄₇	—	2	8	no	—
184	C₂²×C₄×C₄₇	—	2	8	no	—
185	C₂²×C₄×C₄₇	—	2	8	no	—
186	C₂²×C₄×C₄₇	—	2	2	no	—
187	C₂²×C₄×C₄₇	—	2	2	no	—
188	C₂²×C₄×C₄₇	—	2	2	no	—
189	C₂²×C₄×C₄₇	—	2	2	no	—
190	C₂²×C₄×C₄₇	—	2	2	no	—
191	C₂²×C₄×C₄₇	—	2	2	no	—
192	C₂²×C₄×C₄₇	—	2	2	no	—
193	C₂²×C₄×C₄₇	—	4	4	no	—
194	C₂²×C₄×C₄₇	—	4	4	no	—
195	C₂²×C₄×C₄₇	—	4	4	no	—
196	C₂²×C₄×C₄₇	—	4	4	no	—
197	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
206	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
207	C₂²×C₄×C₄₇	#41	1	2	yes	—
208	C₂²×C₄×C₄₇	#41	1	2	yes	—
209	C₂²×C₄×C₄₇	#41	1	2	yes	—
210	C₂²×C₄×C₄₇	#41	1	2	yes	—
211	C₂²×C₄×C₄₇	#41	1	2	yes	—
212	C₄⋊C₄×C₄₇	—	2	16	no	—
213	C₄⋊C₄×C₄₇	—	2	8	no	—
214	C₄⋊C₄×C₄₇	—	2	8	no	—
215	C₄⋊C₄×C₄₇	—	4	8	no	—
216	C₄⋊C₄×C₄₇	—	4	4	no	—
217	C₂²⋊C₄×C₄₇	—	2	8	no	—
218	C₂²⋊C₄×C₄₇	—	2	16	no	—
219	C₂²⋊C₄×C₄₇	—	2	8	no	—
220	C₂²⋊C₄×C₄₇	—	4	8	no	—
221	C₄²×C₄₇	—	4	4	no	—
222	C₄²×C₄₇	—	4	4	no	—
223	C₂³×C₄₇	—	2	2	no	—
224	C₂³×C₄₇	—	2	2	no	—
225	C₂³×C₄₇	—	2	2	no	—
226	C₂³×C₄₇	—	2	2	no	—
227	C₂³×C₄₇	—	2	2	no	—
228	C₂³×C₄₇	—	2	2	no	—
229	C₂³×C₄₇	—	2	2	no	—
230	C₂³×C₄₇	—	2	2	no	—
231	C₂³×C₄₇	—	2	2	no	—
232	C₂³×C₄₇	—	2	2	no	—
233	C₂³×C₄₇	—	2	2	no	—
234	C₂³×C₄₇	—	2	2	no	—
235	C₂³×C₄₇	—	2	2	no	—
236	C₂³×C₄₇	—	2	2	no	—
237	C₂³×C₄₇	—	2	2	no	—
238	C₂³×C₄₇	—	2	2	no	—
239	C₂³×C₄₇	—	2	2	no	—
240	C₂³×C₄₇	—	2	2	no	—
241	C₂³×C₄₇	—	4	1	no	—
242	C₂³×C₄₇	—	4	1	no	—
243	C₂³×C₄₇	—	4	1	no	—
244	C₂³×C₄₇	—	4	1	no	—
245	C₂³×C₄₇	—	4	1	no	—
246	C₂³×C₄₇	—	4	1	no	—
247	C₂³×C₄₇	—	4	1	no	—
248	C₂³×C₄₇	—	4	1	no	—
249	C₂³×C₄₇	—	4	1	no	—
250	C₂³×C₄₇	—	4	1	no	—
251	C₂³×C₄₇	—	4	1	no	—
252	C₂³×C₄₇	—	4	1	no	—
253	C₂³×C₄₇	—	4	1	no	—
254	C₂³×C₄₇	—	4	1	no	—
255	C₂³×C₄₇	—	4	1	no	—
256	C₂³×C₄₇	—	4	1	no	—
257	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
258	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
259	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
260	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
261	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
262	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
263	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
264	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
265	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
266	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
267	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
268	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
269	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
270	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
271	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
272	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
273	Q₈×C₄₇	—	4	16	no	—
274	C₂×C₄×C₄₇	—	2	4	no	—
275	C₂×C₄×C₄₇	—	2	4	no	—
276	C₂×C₄×C₄₇	—	2	2	no	—
277	C₂×C₄×C₄₇	—	2	4	no	—
278	C₂×C₄×C₄₇	—	2	2	no	—
279	C₂×C₄×C₄₇	—	2	4	no	—
280	C₂×C₄×C₄₇	—	2	2	no	—
281	C₂×C₄×C₄₇	—	2	2	no	—
282	C₂×C₄×C₄₇	—	2	2	no	—
283	C₂×C₄×C₄₇	—	2	4	no	—
284	C₂×C₄×C₄₇	—	2	2	no	—
285	C₂×C₄×C₄₇	—	2	2	no	—
286	C₂×C₄×C₄₇	—	2	4	no	—
287	C₂×C₄×C₄₇	—	2	2	no	—
288	C₂×C₄×C₄₇	—	2	4	no	—
289	C₂×C₄×C₄₇	—	2	4	no	—
290	C₂×C₄×C₄₇	—	2	4	no	—
291	C₂×C₄×C₄₇	—	2	2	no	—
292	C₂×C₄×C₄₇	—	2	2	no	—
293	C₂×C₄×C₄₇	—	2	2	no	—
294	C₂×C₄×C₄₇	—	2	2	no	—
295	C₂×C₄×C₄₇	—	2	2	no	—
296	C₂×C₄×C₄₇	—	2	2	no	—
297	C₂×C₄×C₄₇	—	2	2	no	—
298	C₂×C₄×C₄₇	—	4	1	no	—
299	C₂×C₄×C₄₇	—	4	1	no	—
300	C₂×C₄×C₄₇	—	4	1	no	—
301	C₂×C₄×C₄₇	—	4	1	no	—
302	C₂×C₄×C₄₇	—	4	1	no	—
303	C₂×C₄×C₄₇	—	4	1	no	—
304	C₂×C₄×C₄₇	—	4	2	no	—
305	C₂×C₄×C₄₇	—	4	2	no	—
306	C₂×C₄×C₄₇	—	4	1	no	—
307	C₂×C₄×C₄₇	—	4	2	no	—
308	C₂×C₄×C₄₇	—	4	2	no	—
309	C₂×C₄×C₄₇	—	4	1	no	—
310	C₂×C₄×C₄₇	—	4	2	no	—
311	C₂×C₄×C₄₇	—	4	2	no	—
312	C₂×C₄×C₄₇	—	4	1	no	—
313	C₂×C₄×C₄₇	—	4	1	no	—
314	C₂×C₄×C₄₇	—	4	1	no	—
315	C₂×C₄×C₄₇	—	4	2	no	—
316	C₂×C₄×C₄₇	—	4	1	no	—
317	C₂×C₄×C₄₇	—	4	2	no	—
318	C₂×C₄×C₄₇	—	4	2	no	—
319	C₂×C₄×C₄₇	—	4	1	no	—
320	C₂×C₄×C₄₇	—	4	1	no	—
321	C₂×C₄×C₄₇	—	4	1	no	—
322	C₂×C₄×C₄₇	—	4	2	no	—
323	C₂×C₄×C₄₇	—	4	1	no	—
324	C₂×C₄×C₄₇	—	4	1	no	—
325	C₂×C₄×C₄₇	—	4	2	no	—
326	C₂×C₄×C₄₇	—	4	1	no	—
327	C₂×C₄×C₄₇	—	4	2	no	—
328	C₂×C₄×C₄₇	—	4	1	no	—
329	C₂×C₄×C₄₇	—	4	1	no	—
330	C₂×C₄×C₄₇	—	4	16	no	—
331	C₂×C₄×C₄₇	—	4	2	no	—
332	C₂×C₄×C₄₇	—	4	2	no	—
333	C₂×C₄×C₄₇	—	4	2	no	—
334	C₂×C₄×C₄₇	—	4	2	no	—
335	C₂×C₄×C₄₇	—	4	2	no	—
336	C₂×C₄×C₄₇	—	4	2	no	—
337	C₂×C₄×C₄₇	—	4	2	no	—
338	C₂×C₄×C₄₇	#120	1	4	yes	—
339	C₂×C₄×C₄₇	#121	1	4	yes	—
340	C₂×C₄×C₄₇	#121	1	4	yes	—
341	C₂×C₄×C₄₇	#121	1	4	yes	—
342	C₂×C₄×C₄₇	#123	1	4	yes	—
343	C₂×C₄×C₄₇	#123	1	4	yes	—
344	C₂×C₄×C₄₇	#124	1	4	yes	—
345	#15179	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂²×C₄₇	—	2	4	no	—
347	C₂²×C₄₇	—	2	4	no	—
348	C₂²×C₄₇	—	2	4	no	—
349	C₂²×C₄₇	—	4	2	no	—
350	C₂²×C₄₇	—	4	2	no	—
351	C₂²×C₄₇	—	4	2	no	—
352	C₂²×C₄₇	—	4	2	no	—
353	C₂²×C₄₇	—	4	2	no	—
354	C₂²×C₄₇	—	4	2	no	—
355	C₂²×C₄₇	—	4	2	no	—
356	C₂²×C₄₇	—	4	2	no	—
357	C₂²×C₄₇	—	4	2	no	—
358	C₂²×C₄₇	—	4	2	no	—
359	C₂²×C₄₇	—	4	2	no	—
360	C₂²×C₄₇	—	4	2	no	—
361	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
362	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
363	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
364	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
365	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
366	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
367	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
368	C₂²×C₄₇	#525	1	1	yes	characteristic
369	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
370	C₂²×C₄₇	#529	1	1	yes	characteristic
371	C₂²×C₄₇	#529	1	1	yes	characteristic
372	C₂²×C₄₇	#533	1	1	yes	characteristic
373	C₂²×C₄₇	#533	1	1	yes	characteristic
374	C₂²×C₄₇	#536	1	1	yes	characteristic
375	C₂²×C₄₇	#537	1	1	yes	characteristic
376	C₂²×C₄₇	#541	1	1	yes	characteristic
377	C₂²×C₄₇	#541	1	1	yes	characteristic
378	C₂²×C₄₇	#542	1	1	yes	characteristic
379	C₂²×C₄₇	#542	1	1	yes	characteristic
380	C₂²×C₄₇	#546	1	1	yes	characteristic
381	C₂²×C₄₇	#546	1	1	yes	characteristic
382	C₂²×C₄₇	#547	1	1	yes	characteristic
383	C₂²×C₄₇	#547	1	1	yes	characteristic
384	C₂²×C₄₇	#548	1	1	yes	characteristic
385	C₂²×C₄₇	#548	1	1	yes	characteristic
386	C₂²×C₄₇	#548	1	1	yes	characteristic
387	C₂²×C₄₇	#548	1	1	yes	characteristic
388	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
389	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
390	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
391	C₂²×C₄₇	#550	1	1	yes	characteristic
392	C₂²×C₄₇	#552	1	1	yes	characteristic
393	C₂²×C₄₇	#552	1	1	yes	characteristic
394	C₂²×C₄₇	#554	1	1	yes	characteristic
395	C₂²×C₄₇	#556	1	1	yes	characteristic
396	C₄×C₄₇	—	4	2	no	—
397	C₄×C₄₇	—	4	4	no	—
398	C₄×C₄₇	—	4	4	no	—
399	C₄×C₄₇	—	4	2	no	—
400	C₄×C₄₇	—	4	2	no	—
401	C₄×C₄₇	—	4	2	no	—
402	C₄×C₄₇	—	4	2	no	—
403	C₄×C₄₇	—	4	4	no	—
404	C₄×C₄₇	—	8	2	no	—
405	C₄×C₄₇	#394	1	8	yes	—
406	C₂²×C₂²⋊Q₈	C₂×C₄₇	1	1	yes	characteristic
407	C₂×#391	C₂×C₄₇	1	1	yes	characteristic, complemented
408	C₂×#391	C₂×C₄₇	1	1	yes	characteristic, complemented
409	C₂×#389	C₂×C₄₇	1	1	yes	characteristic, complemented
410	C₂×#380	C₂×C₄₇	1	1	yes	characteristic
411	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
412	#1442	C₂×C₄₇	1	2	yes	complemented
413	#1441	C₂×C₄₇	1	2	yes	complemented
414	#1440	C₂×C₄₇	1	2	yes	—
415	#1439	C₂×C₄₇	1	2	yes	—
416	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic, complemented
417	C₂×C₄₇	—	4	4	no	—
418	C₂×C₄₇	C₂×#394	1	1	yes	characteristic
419	C₂×C₄₇	#2407	1	1	yes	characteristic
420	C₂×C₄₇	#2409	1	1	yes	characteristic
421	C₂×C₄₇	#2415	1	1	yes	characteristic
422	C₂×C₄₇	#2417	1	1	yes	characteristic
423	C₂×C₄₇	#2421	1	1	yes	characteristic
424	C₂×C₄₇	#2423	1	1	yes	characteristic
425	C₂×C₄₇	#2426	1	1	yes	characteristic
426	C₂×C₄₇	#2427	1	1	yes	characteristic
427	C₂×C₄₇	#2429	1	1	yes	characteristic
428	C₂×C₄₇	#2429	1	1	yes	characteristic
429	C₂×C₄₇	#2489	1	1	yes	characteristic
430	C₂×C₄₇	#2492	1	1	yes	characteristic
431	C₂×C₄₇	#2625	1	1	yes	characteristic
432	C₂×C₄₇	#2855	1	1	yes	characteristic
433	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
434	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
435	C₂×C₂²⋊Q₈	—	2	4	no	—
436	C₂×C₂²⋊Q₈	—	2	4	no	—
437	C₂×C₂²⋊Q₈	—	2	4	no	—
438	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
439	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
440	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
441	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
442	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
443	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
444	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
445	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
446	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
447	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
448	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
449	#391	—	2	4	no	—
450	#391	—	2	4	no	—
451	#389	—	2	4	no	—
452	#380	—	2	4	no	—
453	C₄×C₂²⋊C₄	—	2	4	no	—
454	C₂×#95	C₂²×C₄₇	1	2	yes	—
455	C₂×#95	C₂²×C₄₇	1	2	yes	—
456	C₂×#95	C₂²×C₄₇	1	2	yes	—
457	C₂×#95	C₂²×C₄₇	1	2	yes	—
458	C₂×#95	C₂²×C₄₇	1	2	yes	—
459	C₂×#95	C₂²×C₄₇	1	2	yes	—
460	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
461	C₂×#95	C₂²×C₄₇	1	2	yes	—
462	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
463	C₂×#95	C₂²×C₄₇	1	2	yes	—
464	C₄₇	#15179	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×Q₈	—	2	2	no	—
470	C₂²×Q₈	—	2	2	no	—
471	C₂²×Q₈	—	2	2	no	—
472	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
473	C₂³×C₄	—	2	2	no	—
474	C₂³×C₄	—	2	2	no	—
475	C₂³×C₄	—	2	2	no	—
476	C₂³×C₄	—	2	2	no	—
477	C₂³×C₄	—	2	2	no	—
478	C₂³×C₄	—	2	2	no	—
479	C₂³×C₄	D₄×C₄₇	1	4	yes	—
480	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
481	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
482	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
483	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
484	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
490	C₂²⋊Q₈	—	2	32	no	—
491	C₂×C₄⋊C₄	—	2	4	no	—
492	C₂×C₄⋊C₄	—	2	4	no	—
493	C₂×C₄⋊C₄	—	2	4	no	—
494	C₂×C₄⋊C₄	—	2	2	no	—
495	C₂×C₄⋊C₄	—	2	2	no	—
496	C₂×C₄⋊C₄	—	2	2	no	—
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	2	no	—
499	C₂×C₄⋊C₄	—	2	4	no	—
500	C₂×C₄⋊C₄	—	2	2	no	—
501	C₂×C₄⋊C₄	—	2	4	no	—
502	C₂×C₄⋊C₄	—	2	2	no	—
503	C₂×C₄⋊C₄	—	4	2	no	—
504	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
505	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
506	C₂×C₂²⋊C₄	—	2	4	no	—
507	C₂×C₂²⋊C₄	—	2	2	no	—
508	C₂×C₂²⋊C₄	—	2	2	no	—
509	C₂×C₂²⋊C₄	—	2	2	no	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	2	4	no	—
512	C₂×C₂²⋊C₄	—	2	2	no	—
513	C₂×C₂²⋊C₄	—	2	2	no	—
514	C₂×C₂²⋊C₄	—	2	4	no	—
515	C₂×C₂²⋊C₄	—	2	4	no	—
516	C₂×C₂²⋊C₄	—	4	2	no	—
517	C₂×C₂²⋊C₄	Q₈×C₄₇	1	4	yes	complemented
518	C₂×C₄²	—	2	2	no	—
519	C₂×C₄²	—	2	2	no	—
520	C₂×C₄²	—	2	2	no	—
521	C₂×C₄²	—	2	2	no	—
522	C₂×C₄²	—	2	2	no	—
523	C₂×C₄²	—	2	2	no	—
524	#95	—	2	2	no	—
525	#95	—	2	2	no	—
526	#95	—	2	4	no	—
527	#95	—	2	4	no	—
528	#95	—	2	4	no	—
529	#95	—	2	4	no	—
530	#95	—	2	4	no	—
531	#95	—	2	4	no	—
532	#95	—	2	4	no	—
533	#95	—	4	2	no	—
534	C₂⁴	—	2	1	no	—
535	C₂⁴	—	2	1	no	—
536	C₂⁴	—	2	1	no	—
537	C₂⁴	—	2	1	no	—
538	C₂⁴	—	2	1	no	—
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	2	1	no	—
541	C₂⁴	—	2	1	no	—
542	C₂⁴	—	2	1	no	—
543	C₂⁴	—	2	1	no	—
544	C₂⁴	—	2	1	no	—
545	C₂⁴	—	2	1	no	—
546	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
547	C₂⁴	C₂×Q₈×C₄₇	1	2	yes	—
548	C₂⁴	#41×C₄₇	1	2	yes	—
549	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
550	C₂×Q₈	—	2	8	no	—
551	C₂×Q₈	—	2	8	no	—
552	C₂×Q₈	—	2	8	no	—
553	C₂×Q₈	—	4	4	no	—
554	C₂×Q₈	—	4	4	no	—
555	C₂×Q₈	—	4	4	no	—
556	C₂×Q₈	—	4	4	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	8	no	—
606	C₂²×C₄	—	2	8	no	—
607	C₂²×C₄	—	2	8	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	4	4	no	—
616	C₂²×C₄	—	4	4	no	—
617	C₂²×C₄	—	4	4	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
620	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
621	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
622	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
623	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
624	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
625	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
626	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
627	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
628	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
629	C₂²×C₄	#41×C₄₇	1	2	yes	—
630	C₂²×C₄	#41×C₄₇	1	2	yes	—
631	C₂²×C₄	#41×C₄₇	1	2	yes	—
632	C₂²×C₄	#41×C₄₇	1	2	yes	—
633	C₂²×C₄	#41×C₄₇	1	2	yes	—
634	C₄⋊C₄	—	2	16	no	—
635	C₄⋊C₄	—	2	8	no	—
636	C₄⋊C₄	—	2	8	no	—
637	C₄⋊C₄	—	4	8	no	—
638	C₄⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	2	16	no	—
641	C₂²⋊C₄	—	2	8	no	—
642	C₂²⋊C₄	—	4	8	no	—
643	C₄²	—	4	4	no	—
644	C₄²	—	4	4	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	C₂²⋊Q₈×C₄₇	1	4	yes	—
680	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
681	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
682	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
683	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
684	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
685	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
686	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
687	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
688	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
689	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
690	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
691	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
692	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
693	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
694	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
695	Q₈	—	4	16	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	16	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	#120×C₄₇	1	4	yes	—
761	C₂×C₄	#121×C₄₇	1	4	yes	—
762	C₂×C₄	#121×C₄₇	1	4	yes	—
763	C₂×C₄	#121×C₄₇	1	4	yes	—
764	C₂×C₄	#123×C₄₇	1	4	yes	—
765	C₂×C₄	#123×C₄₇	1	4	yes	—
766	C₂×C₄	#124×C₄₇	1	4	yes	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
783	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
784	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
785	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
786	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
787	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
788	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
789	C₂²	C₄₇×#525	1	1	yes	characteristic
790	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
791	C₂²	C₄₇×#529	1	1	yes	characteristic
792	C₂²	C₄₇×#529	1	1	yes	characteristic
793	C₂²	C₄₇×#533	1	1	yes	characteristic
794	C₂²	C₄₇×#533	1	1	yes	characteristic
795	C₂²	C₄₇×#536	1	1	yes	characteristic
796	C₂²	C₄₇×#537	1	1	yes	characteristic
797	C₂²	C₄₇×#541	1	1	yes	characteristic
798	C₂²	C₄₇×#541	1	1	yes	characteristic
799	C₂²	C₄₇×#542	1	1	yes	characteristic
800	C₂²	C₄₇×#542	1	1	yes	characteristic
801	C₂²	C₄₇×#546	1	1	yes	characteristic
802	C₂²	C₄₇×#546	1	1	yes	characteristic
803	C₂²	C₄₇×#547	1	1	yes	characteristic
804	C₂²	C₄₇×#547	1	1	yes	characteristic
805	C₂²	C₄₇×#548	1	1	yes	characteristic
806	C₂²	C₄₇×#548	1	1	yes	characteristic
807	C₂²	C₄₇×#548	1	1	yes	characteristic
808	C₂²	C₄₇×#548	1	1	yes	characteristic
809	C₂²	D₄×Q₈×C₄₇	1	1	yes	characteristic
810	C₂²	D₄×Q₈×C₄₇	1	1	yes	characteristic
811	C₂²	D₄×Q₈×C₄₇	1	1	yes	characteristic
812	C₂²	C₄₇×#550	1	1	yes	characteristic
813	C₂²	C₄₇×#552	1	1	yes	characteristic
814	C₂²	C₄₇×#552	1	1	yes	characteristic
815	C₂²	C₄₇×#554	1	1	yes	characteristic
816	C₂²	C₄₇×#556	1	1	yes	characteristic
817	C₄	—	4	2	no	—
818	C₄	—	4	4	no	—
819	C₄	—	4	4	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	4	no	—
825	C₄	—	8	2	no	—
826	C₄	C₄₇×#394	1	8	yes	—
827	C₂	—	4	4	no	—
828	C₂	C₂×C₄₇×#394	1	1	yes	characteristic
829	C₂	C₄₇×#2407	1	1	yes	characteristic
830	C₂	C₄₇×#2409	1	1	yes	characteristic
831	C₂	C₄₇×#2415	1	1	yes	characteristic
832	C₂	C₄₇×#2417	1	1	yes	characteristic
833	C₂	C₄₇×#2421	1	1	yes	characteristic
834	C₂	C₄₇×#2423	1	1	yes	characteristic
835	C₂	C₄₇×#2426	1	1	yes	characteristic
836	C₂	C₄₇×#2427	1	1	yes	characteristic
837	C₂	C₄₇×#2429	1	1	yes	characteristic
838	C₂	C₄₇×#2429	1	1	yes	characteristic
839	C₂	C₄₇×#2489	1	1	yes	characteristic
840	C₂	C₄₇×#2492	1	1	yes	characteristic
841	C₂	C₄₇×#2625	1	1	yes	characteristic
842	C₂	C₄₇×#2855	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂⁵×C₄₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#391	C₂	semidirect
3. C₂×C₄₇×#391	C₂	semidirect
4. C₂×C₄₇×#389	C₂	semidirect
7. C₄₇×#1442	C₂	semidirect
8. C₄₇×#1441	C₂	semidirect
11. C₄₇×C₄⋊#95	C₂	semidirect
95. C₂×C₂²⋊C₄×C₄₇	Q₈	semidirect
345. #15179	C₄₇	direct (N × H)
407. C₂×#391	C₂×C₄₇	semidirect
408. C₂×#391	C₂×C₄₇	semidirect
409. C₂×#389	C₂×C₄₇	semidirect
412. #1442	C₂×C₄₇	semidirect
413. #1441	C₂×C₄₇	semidirect
416. C₄⋊#95	C₂×C₄₇	semidirect
464. C₄₇	#15179	direct (N × H)
517. C₂×C₂²⋊C₄	Q₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₄₇	2
C₂×C₄₇×#391	2
C₂×C₄₇×#389	2
C₂×C₄₇×#380	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₄₇×#1442	2
C₄₇×#1441	2
C₄₇×#1440	2
C₄₇×#1439	2
C₄₇×C₄⋊#95	2
#15179	47

Subgroups — C47×#15179 #26054877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15179 #26054877