Subgroups — #542×Dic₄₇ #26375407

Order 12032.

2294 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246203	C₂	1	2	yes	maximal, complemented
2	#20246182	C₂	1	2	yes	maximal, complemented
3	#20246167	C₂	1	2	yes	maximal, complemented
4	#20246146	C₂	1	2	yes	maximal, complemented
5	#20246137	C₂	1	1	yes	maximal, characteristic, complemented
6	#20246101	C₂	1	1	yes	maximal, characteristic, complemented
7	#20246083	C₂	1	1	yes	maximal, characteristic
8	#20246072	C₂	1	1	yes	maximal, characteristic, complemented
9	#20246039	C₂	1	1	yes	maximal, characteristic, complemented
10	#20246031	C₂	1	1	yes	maximal, characteristic, complemented
11	#20245997	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#126×Dic₄₇	C₂	1	2	yes	maximal, complemented
14	#124×Dic₄₇	C₂	1	2	yes	maximal, complemented
15	#124×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²⋊Q₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
17	C₂²⋊Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#123×Dic₄₇	C₂	1	2	yes	maximal, complemented
19	#121×Dic₄₇	C₂	1	1	yes	maximal, characteristic
20	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄₇×#542	C₂	1	1	yes	maximal, characteristic
24	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
27	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
29	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
30	C₂×#13093983	C₂²	1	1	yes	characteristic
31	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
33	#15689030	C₂²	1	1	yes	characteristic
34	#15689030	C₂²	1	1	yes	characteristic
35	#15689030	C₂²	1	2	yes	—
36	#15689030	C₂²	1	2	yes	—
37	#15689030	C₂²	1	2	yes	—
38	#15689026	C₂²	1	1	yes	characteristic
39	#15689026	C₂²	1	1	yes	characteristic
40	#15689026	C₂²	1	2	yes	—
41	#15689022	C₂²	1	1	yes	characteristic
42	#15689022	C₂²	1	1	yes	characteristic
43	#15689022	C₂²	1	1	yes	characteristic
44	#15689022	C₂²	1	1	yes	characteristic
45	#15689022	C₂²	1	2	yes	—
46	#15689022	C₂²	1	2	yes	—
47	#15689016	C₂²	1	2	yes	—
48	#15689016	C₂²	1	2	yes	—
49	#15689016	C₂²	1	2	yes	—
50	#15689016	C₂²	1	2	yes	—
51	#15689016	C₂²	1	2	yes	—
52	#15689016	C₂²	1	2	yes	—
53	#15689016	C₂²	1	2	yes	—
54	#15689016	C₂²	1	2	yes	—
55	#15689016	C₂²	1	2	yes	—
56	#15689016	C₂²	1	2	yes	—
57	#15689016	C₂²	1	2	yes	—
58	#15689016	C₂²	1	2	yes	—
59	#15689009	C₂²	1	2	yes	—
60	#15689009	C₂²	1	2	yes	—
61	#15689009	C₂²	1	2	yes	—
62	#15689009	C₂²	1	2	yes	—
63	#15689009	C₂²	1	2	yes	—
64	#15689009	C₂²	1	2	yes	—
65	#15689009	C₂²	1	2	yes	—
66	#15689009	C₂²	1	2	yes	—
67	#15689003	C₂²	1	2	yes	—
68	#15689003	C₂²	1	2	yes	—
69	#15688998	C₂²	1	2	yes	—
70	#15688998	C₂²	1	2	yes	—
71	#15688998	C₂²	1	2	yes	—
72	#15688998	C₂²	1	2	yes	—
73	#15688993	C₂²	1	1	yes	characteristic
74	#15688991	C₂²	1	2	yes	—
75	#15688989	C₂²	1	2	yes	—
76	#15688989	C₂²	1	1	yes	characteristic
77	#15688986	C₂²	1	2	yes	—
78	#15688983	C₂²	1	2	yes	—
79	#15688983	C₂²	1	1	yes	characteristic
80	#15688983	C₂²	1	1	yes	characteristic
81	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
82	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
83	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
84	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
85	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
87	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
88	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
89	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
90	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
91	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
92	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
96	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
97	C₂²⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
98	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
99	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
100	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
101	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
102	C₂²⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
103	C₂²⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
104	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	—
105	C₂²⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
107	#15688969	C₂²	1	1	yes	characteristic
108	#15688969	C₂²	1	1	yes	characteristic
109	C₄²×Dic₄₇	C₂²	1	2	yes	—
110	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
111	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
112	C₄₇×#542	C₄	1	16	yes	complemented
113	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
114	C₂×#126×C₄₇	C₂²	1	2	yes	—
115	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
116	C₂×#124×C₄₇	C₂²	1	2	yes	—
117	C₂×#123×C₄₇	C₂²	1	2	yes	—
118	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
119	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
120	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
122	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
123	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
124	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
125	C₂³×Dic₄₇	C₂³	1	2	yes	—
126	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
127	C₂³×Dic₄₇	C₂³	1	2	yes	—
128	Q₈×Dic₄₇	—	2	4	no	—
129	Q₈×Dic₄₇	—	2	4	no	—
130	Q₈×Dic₄₇	—	4	4	no	—
131	D₄×Dic₄₇	—	2	4	no	—
132	D₄×Dic₄₇	—	2	4	no	—
133	D₄×Dic₄₇	—	4	4	no	—
134	#13093983	—	2	4	no	—
135	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
140	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
141	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
144	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
145	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
146	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
147	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
148	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
159	C₂×C₄×Dic₄₇	—	2	4	no	—
160	C₂×C₄×Dic₄₇	—	4	4	no	—
161	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
163	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
164	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
165	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
166	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
167	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
168	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
169	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
170	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
171	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
172	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
173	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
175	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
176	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
177	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
178	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
179	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
180	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
181	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
182	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
183	C₄₇⋊#95	C₂³	1	1	yes	characteristic
184	C₄₇⋊#95	C₂³	1	1	yes	characteristic
185	C₄₇⋊#95	C₂³	1	1	yes	characteristic
186	C₄₇⋊#95	C₂³	1	1	yes	characteristic
187	C₄₇⋊#95	C₂³	1	1	yes	characteristic
188	C₄₇⋊#95	C₂³	1	1	yes	characteristic
189	C₄₇⋊#95	C₂³	1	1	yes	characteristic
190	C₄₇⋊#95	C₂³	1	1	yes	characteristic
191	C₄₇⋊#95	C₂³	1	2	yes	—
192	C₄₇⋊#95	C₂³	1	2	yes	—
193	C₄₇⋊#95	C₂³	1	2	yes	—
194	C₄₇⋊#95	C₂³	1	2	yes	—
195	C₄₇⋊#95	C₂³	1	2	yes	—
196	C₄₇⋊#95	C₂³	1	2	yes	—
197	C₄₇⋊#95	C₂³	1	2	yes	—
198	C₄₇⋊#95	C₂³	1	2	yes	—
199	C₄₇⋊#95	C₂³	1	2	yes	—
200	C₄₇⋊#95	C₂³	1	2	yes	—
201	C₄₇⋊#95	C₂³	1	2	yes	—
202	C₄₇⋊#95	C₂³	1	2	yes	—
203	C₄₇⋊#95	C₂³	1	2	yes	—
204	C₄₇⋊#95	C₂³	1	2	yes	—
205	C₄₇⋊#95	C₂³	1	2	yes	—
206	C₄₇⋊#95	C₂³	1	2	yes	—
207	C₄₇⋊#95	C₂³	1	2	yes	—
208	C₄₇⋊#95	C₂³	1	2	yes	—
209	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
210	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
211	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
213	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
215	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
216	#126×C₄₇	C₂×C₄	1	16	yes	complemented
217	#124×C₄₇	C₂×C₄	1	8	yes	complemented
218	#124×C₄₇	C₂×C₄	1	16	yes	complemented
219	#123×C₄₇	C₂×C₄	1	16	yes	complemented
220	C₂²⋊Q₈×C₄₇	C₂×C₄	1	16	yes	complemented
221	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
222	#121×C₄₇	C₂×C₄	1	8	yes	—
223	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
224	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
225	#117×C₄₇	C₂×C₄	1	8	yes	complemented
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
238	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
239	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
240	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
243	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₄₇	—	2	2	no	—
246	C₂×Q₈×C₄₇	—	2	2	no	—
247	C₂×Q₈×C₄₇	—	4	2	no	—
248	C₂×Q₈×C₄₇	—	4	2	no	—
249	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
250	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
251	C₂×D₄×C₄₇	—	2	2	no	—
252	C₂×D₄×C₄₇	—	2	2	no	—
253	C₂×D₄×C₄₇	—	4	2	no	—
254	C₂×D₄×C₄₇	—	4	2	no	—
255	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
256	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
257	C₂²×C₄×C₄₇	—	2	2	no	—
258	C₂²×C₄×C₄₇	—	2	2	no	—
259	C₂²×C₄×C₄₇	—	4	2	no	—
260	C₂²×C₄×C₄₇	—	4	2	no	—
261	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
262	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
263	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
272	C₂²×Dic₄₇	—	2	2	no	—
273	C₂²×Dic₄₇	—	2	2	no	—
274	C₂²×Dic₄₇	—	2	4	no	—
275	C₂²×Dic₄₇	—	2	4	no	—
276	C₂²×Dic₄₇	—	2	4	no	—
277	C₂²×Dic₄₇	—	2	2	no	—
278	C₂²×Dic₄₇	—	2	2	no	—
279	C₂²×Dic₄₇	—	2	4	no	—
280	C₂²×Dic₄₇	—	4	2	no	—
281	C₂²×Dic₄₇	—	4	1	no	—
282	C₂²×Dic₄₇	—	4	1	no	—
283	C₂²×Dic₄₇	—	4	2	no	—
284	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
285	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
286	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
287	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
288	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
289	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
290	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
291	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
292	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
293	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
294	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
295	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
296	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
297	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
298	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
299	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
300	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
301	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
302	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
303	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
304	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
305	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
306	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
307	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
308	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
309	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
310	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
311	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
312	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
313	C₂²⋊Dic₄₇	—	2	2	no	—
314	C₂²⋊Dic₄₇	—	2	2	no	—
315	C₂²⋊Dic₄₇	—	2	4	no	—
316	C₂²⋊Dic₄₇	—	2	4	no	—
317	C₂²⋊Dic₄₇	—	4	2	no	—
318	C₂²⋊Dic₄₇	—	4	2	no	—
319	C₂²⋊Dic₄₇	—	4	2	no	—
320	C₂²⋊Dic₄₇	—	4	2	no	—
321	C₂²⋊Dic₄₇	—	4	2	no	—
322	C₂²⋊Dic₄₇	—	4	2	no	—
323	C₄⋊Dic₄₇	—	2	2	no	—
324	C₄⋊Dic₄₇	—	2	2	no	—
325	C₄⋊Dic₄₇	—	2	2	no	—
326	C₄⋊Dic₄₇	—	2	2	no	—
327	C₄⋊Dic₄₇	—	2	2	no	—
328	C₄⋊Dic₄₇	—	2	2	no	—
329	C₄⋊Dic₄₇	—	2	4	no	—
330	C₄⋊Dic₄₇	—	2	4	no	—
331	C₄⋊Dic₄₇	—	4	2	no	—
332	C₄⋊Dic₄₇	—	4	2	no	—
333	C₄⋊Dic₄₇	—	4	2	no	—
334	C₄⋊Dic₄₇	—	4	2	no	—
335	C₄⋊Dic₄₇	—	4	2	no	—
336	C₄⋊Dic₄₇	—	4	2	no	—
337	C₄×Dic₄₇	—	2	2	no	—
338	C₄×Dic₄₇	—	2	2	no	—
339	C₄×Dic₄₇	—	2	2	no	—
340	C₄×Dic₄₇	—	2	2	no	—
341	C₄×Dic₄₇	—	2	4	no	—
342	C₄×Dic₄₇	—	2	4	no	—
343	C₄×Dic₄₇	—	2	2	no	—
344	C₄×Dic₄₇	—	2	4	no	—
345	C₄×Dic₄₇	—	2	4	no	—
346	C₄×Dic₄₇	—	2	2	no	—
347	C₄×Dic₄₇	—	2	2	no	—
348	C₄×Dic₄₇	—	2	2	no	—
349	C₄×Dic₄₇	—	4	2	no	—
350	C₄×Dic₄₇	—	4	2	no	—
351	C₄×Dic₄₇	—	4	1	no	—
352	C₄×Dic₄₇	—	4	2	no	—
353	C₄×Dic₄₇	—	4	1	no	—
354	C₄×Dic₄₇	—	4	1	no	—
355	C₄×Dic₄₇	—	4	1	no	—
356	C₄×Dic₄₇	—	4	2	no	—
357	C₄×Dic₄₇	#41	1	4	yes	—
358	C₄×Dic₄₇	#41	1	4	yes	—
359	C₂³×C₄₇	—	2	1	no	—
360	C₂³×C₄₇	—	2	2	no	—
361	C₂³×C₄₇	—	2	2	no	—
362	C₂³×C₄₇	—	2	1	no	—
363	C₂³×C₄₇	—	2	1	no	—
364	C₂³×C₄₇	—	2	2	no	—
365	C₂³×C₄₇	—	2	2	no	—
366	C₂³×C₄₇	—	2	1	no	—
367	C₂³×C₄₇	—	2	1	no	—
368	C₂³×C₄₇	—	2	2	no	—
369	C₂³×C₄₇	—	2	2	no	—
370	C₂³×C₄₇	—	2	1	no	—
371	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
372	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
373	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
374	Q₈×C₄₇	—	2	8	no	—
375	Q₈×C₄₇	—	4	8	no	—
376	D₄×C₄₇	—	2	8	no	—
377	D₄×C₄₇	—	4	8	no	—
378	C₂×C₄×C₄₇	—	2	1	no	—
379	C₂×C₄×C₄₇	—	2	2	no	—
380	C₂×C₄×C₄₇	—	2	2	no	—
381	C₂×C₄×C₄₇	—	2	1	no	—
382	C₂×C₄×C₄₇	—	2	1	no	—
383	C₂×C₄×C₄₇	—	2	2	no	—
384	C₂×C₄×C₄₇	—	2	2	no	—
385	C₂×C₄×C₄₇	—	2	1	no	—
386	C₂×C₄×C₄₇	—	2	1	no	—
387	C₂×C₄×C₄₇	—	2	1	no	—
388	C₂×C₄×C₄₇	—	2	1	no	—
389	C₂×C₄×C₄₇	—	2	1	no	—
390	C₂×C₄×C₄₇	—	2	1	no	—
391	C₂×C₄×C₄₇	—	2	2	no	—
392	C₂×C₄×C₄₇	—	2	1	no	—
393	C₂×C₄×C₄₇	—	2	2	no	—
394	C₂×C₄×C₄₇	—	2	8	no	—
395	C₂×C₄×C₄₇	—	4	8	no	—
396	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
397	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
398	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
399	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
400	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
401	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
402	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
403	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
404	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
405	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
406	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
407	C₂×Dic₄₇	—	2	1	no	—
408	C₂×Dic₄₇	—	2	1	no	—
409	C₂×Dic₄₇	—	2	1	no	—
410	C₂×Dic₄₇	—	2	1	no	—
411	C₂×Dic₄₇	—	2	1	no	—
412	C₂×Dic₄₇	—	2	1	no	—
413	C₂×Dic₄₇	—	2	1	no	—
414	C₂×Dic₄₇	—	2	1	no	—
415	C₂×Dic₄₇	—	2	2	no	—
416	C₂×Dic₄₇	—	2	2	no	—
417	C₂×Dic₄₇	—	2	1	no	—
418	C₂×Dic₄₇	—	2	1	no	—
419	C₂×Dic₄₇	—	2	2	no	—
420	C₂×Dic₄₇	—	2	2	no	—
421	C₂×Dic₄₇	—	2	2	no	—
422	C₂×Dic₄₇	—	2	1	no	—
423	C₂×Dic₄₇	—	2	2	no	—
424	C₂×Dic₄₇	—	2	2	no	—
425	C₂×Dic₄₇	—	2	1	no	—
426	C₂×Dic₄₇	—	2	1	no	—
427	C₂×Dic₄₇	—	2	1	no	—
428	C₂×Dic₄₇	—	2	2	no	—
429	C₂×Dic₄₇	—	2	2	no	—
430	C₂×Dic₄₇	—	2	2	no	—
431	C₂×Dic₄₇	—	2	1	no	—
432	C₂×Dic₄₇	—	2	2	no	—
433	C₂×Dic₄₇	—	2	1	no	—
434	C₂×Dic₄₇	—	2	1	no	—
435	C₂×Dic₄₇	—	2	2	no	—
436	C₂×Dic₄₇	—	2	1	no	—
437	C₂×Dic₄₇	—	4	4	no	—
438	C₂×Dic₄₇	—	4	8	no	—
439	C₂×Dic₄₇	—	4	4	no	—
440	C₂×Dic₄₇	—	4	8	no	—
441	C₂×Dic₄₇	C₂×#41	1	2	yes	—
442	C₂×Dic₄₇	C₂×#41	1	2	yes	—
443	C₂×Dic₄₇	C₂×#41	1	2	yes	—
444	C₂×Dic₄₇	C₂×#41	1	2	yes	—
445	C₂×Dic₄₇	H(5,𝔽₂)	1	2	yes	—
446	C₂×Dic₄₇	2₋¹⁺⁴	1	2	yes	—
447	C₄×#542	—	47	1	no	maximal, Sylow
448	C₂²×C₄₇	—	2	2	no	—
449	C₂²×C₄₇	—	2	4	no	—
450	C₂²×C₄₇	—	2	4	no	—
451	C₂²×C₄₇	—	2	2	no	—
452	C₂²×C₄₇	—	2	2	no	—
453	C₂²×C₄₇	—	2	4	no	—
454	C₂²×C₄₇	—	4	2	no	—
455	C₂²×C₄₇	—	4	1	no	—
456	C₂²×C₄₇	—	4	1	no	—
457	C₂²×C₄₇	—	4	2	no	—
458	C₂²×C₄₇	—	4	2	no	—
459	C₂²×C₄₇	—	4	1	no	—
460	C₂²×C₄₇	—	4	1	no	—
461	C₂²×C₄₇	—	4	2	no	—
462	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
463	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
464	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
465	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
467	C₂²×C₄₇	#585	1	1	yes	characteristic
468	C₂²×C₄₇	#585	1	1	yes	characteristic
469	C₄×C₄₇	—	2	2	no	—
470	C₄×C₄₇	—	2	4	no	—
471	C₄×C₄₇	—	2	2	no	—
472	C₄×C₄₇	—	2	4	no	—
473	C₄×C₄₇	—	2	4	no	—
474	C₄×C₄₇	—	2	2	no	—
475	C₄×C₄₇	—	2	2	no	—
476	C₄×C₄₇	—	2	2	no	—
477	C₄×C₄₇	C₄×#41	1	4	yes	—
478	Dic₄₇	—	2	2	no	—
479	Dic₄₇	—	2	2	no	—
480	Dic₄₇	—	2	2	no	—
481	Dic₄₇	—	4	1	no	—
482	Dic₄₇	—	4	2	no	—
483	Dic₄₇	—	4	2	no	—
484	Dic₄₇	—	4	1	no	—
485	Dic₄₇	—	4	2	no	—
486	Dic₄₇	—	4	1	no	—
487	Dic₄₇	—	4	2	no	—
488	Dic₄₇	—	4	1	no	—
489	Dic₄₇	#542	1	4	yes	direct product factor
490	C₂×#542	D₄₇	1	1	yes	characteristic
491	#2337	—	47	2	no	—
492	#2335	—	47	2	no	—
493	#2334	—	47	2	no	—
494	#2332	—	47	2	no	—
495	#2331	—	47	1	no	—
496	#2326	—	47	1	no	—
497	#2324	—	47	1	no	—
498	#2323	—	47	1	no	—
499	#2320	—	47	1	no	—
500	#2319	—	47	1	no	—
501	#2314	—	47	1	no	—
502	C₄×C₄⋊Q₈	—	47	1	no	—
503	C₄×#126	—	47	2	no	—
504	C₄×#124	—	47	1	no	—
505	C₄×#124	—	47	2	no	—
506	C₄×C₂²⋊Q₈	—	47	1	no	—
507	C₄×C₂²⋊Q₈	—	47	2	no	—
508	C₄×#123	—	47	2	no	—
509	C₄×#121	—	47	1	no	—
510	C₄²×Q₈	—	47	1	no	—
511	C₄²×D₄	—	47	1	no	—
512	C₄×#117	—	47	1	no	—
513	C₂×C₄₇	—	4	2	no	—
514	C₂×C₄₇	—	4	4	no	—
515	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
516	C₂×C₄₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂×C₄₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂×C₄₇	C₂×#542	1	1	yes	characteristic
519	C₂×C₄₇	#3455	1	1	yes	characteristic
520	C₂×C₄₇	#3460	1	1	yes	characteristic
521	C₂×C₄₇	#3461	1	1	yes	characteristic
522	#542	Dic₄₇	1	16	yes	direct product factor
523	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
524	C₂×#126	C₂×D₄₇	1	2	yes	—
525	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
526	C₂×#124	C₂×D₄₇	1	2	yes	—
527	C₂×#123	C₂×D₄₇	1	2	yes	—
528	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
529	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
530	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
531	C₂×C₄×Q₈	—	47	1	no	—
532	C₂×C₄×Q₈	—	47	1	no	—
533	C₂×C₄×Q₈	—	47	2	no	—
534	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
535	C₂×C₄×D₄	—	47	1	no	—
536	C₂×C₄×D₄	—	47	1	no	—
537	C₂×C₄×D₄	—	47	2	no	—
538	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
539	C₂×#117	—	47	1	no	—
540	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
541	C₂²×C₄²	—	47	1	no	—
542	C₂²×C₄²	—	47	2	no	—
543	#391	—	47	2	no	—
544	#391	—	47	1	no	—
545	#391	—	47	1	no	—
546	#391	—	47	2	no	—
547	#391	—	47	2	no	—
548	#390	—	47	1	no	—
549	#390	—	47	1	no	—
550	#390	—	47	2	no	—
551	#389	—	47	1	no	—
552	#389	—	47	1	no	—
553	#389	—	47	2	no	—
554	#389	—	47	1	no	—
555	#389	—	47	1	no	—
556	#389	—	47	2	no	—
557	#388	—	47	2	no	—
558	#388	—	47	2	no	—
559	#388	—	47	2	no	—
560	#388	—	47	2	no	—
561	#388	—	47	2	no	—
562	#388	—	47	2	no	—
563	#388	—	47	2	no	—
564	#388	—	47	2	no	—
565	#388	—	47	2	no	—
566	#388	—	47	2	no	—
567	#388	—	47	2	no	—
568	#388	—	47	2	no	—
569	#387	—	47	2	no	—
570	#387	—	47	2	no	—
571	#387	—	47	2	no	—
572	#387	—	47	2	no	—
573	#387	—	47	2	no	—
574	#387	—	47	2	no	—
575	#387	—	47	2	no	—
576	#387	—	47	2	no	—
577	#386	—	47	2	no	—
578	#386	—	47	2	no	—
579	#385	—	47	2	no	—
580	#385	—	47	2	no	—
581	#385	—	47	2	no	—
582	#385	—	47	2	no	—
583	#384	—	47	1	no	—
584	#383	—	47	2	no	—
585	#382	—	47	1	no	—
586	#382	—	47	2	no	—
587	#381	—	47	2	no	—
588	#380	—	47	1	no	—
589	#380	—	47	1	no	—
590	#380	—	47	2	no	—
591	C₄×C₄⋊C₄	—	47	1	no	—
592	C₄×C₄⋊C₄	—	47	2	no	—
593	C₄×C₄⋊C₄	—	47	2	no	—
594	C₄×C₄⋊C₄	—	47	1	no	—
595	C₄×C₄⋊C₄	—	47	1	no	—
596	C₄×C₄⋊C₄	—	47	1	no	—
597	C₄×C₄⋊C₄	—	47	1	no	—
598	C₄×C₄⋊C₄	—	47	1	no	—
599	C₄×C₄⋊C₄	—	47	2	no	—
600	C₄×C₄⋊C₄	—	47	1	no	—
601	C₄×C₄⋊C₄	—	47	1	no	—
602	C₄×C₄⋊C₄	—	47	2	no	—
603	C₄×C₄⋊C₄	—	47	1	no	—
604	C₄×C₄⋊C₄	—	47	1	no	—
605	C₄×C₄⋊C₄	—	47	2	no	—
606	C₄×C₂²⋊C₄	—	47	2	no	—
607	C₄×C₂²⋊C₄	—	47	2	no	—
608	C₄×C₂²⋊C₄	—	47	2	no	—
609	C₄×C₂²⋊C₄	—	47	2	no	—
610	C₄×C₂²⋊C₄	—	47	2	no	—
611	C₄×C₂²⋊C₄	—	47	1	no	—
612	C₄×C₂²⋊C₄	—	47	1	no	—
613	C₄×C₂²⋊C₄	—	47	1	no	—
614	C₄×C₂²⋊C₄	—	47	1	no	—
615	C₄×C₂²⋊C₄	—	47	2	no	—
616	C₄×C₂²⋊C₄	—	47	2	no	—
617	#376	—	47	1	no	—
618	#376	—	47	1	no	—
619	C₄³	—	47	2	no	—
620	C₄³	—	47	1	no	—
621	C₄³	—	47	1	no	—
622	C₄₇	C₄×#542	1	1	yes	characteristic, complemented, Sylow
623	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
624	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
625	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
626	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
627	C₂³×C₄	—	47	1	no	—
628	C₂³×C₄	—	47	2	no	—
629	C₂³×C₄	—	47	2	no	—
630	C₂³×C₄	—	47	1	no	—
631	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
632	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
633	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
634	#126	C₂×Dic₄₇	1	16	yes	complemented
635	#124	C₂×Dic₄₇	1	8	yes	complemented
636	#124	C₂×Dic₄₇	1	16	yes	complemented
637	#123	C₂×Dic₄₇	1	16	yes	complemented
638	C₂²⋊Q₈	C₂×Dic₄₇	1	16	yes	complemented
639	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
640	#121	C₂×Dic₄₇	1	8	yes	—
641	C₄×Q₈	—	94	4	no	—
642	C₄×Q₈	—	94	4	no	—
643	C₄×Q₈	—	188	4	no	—
644	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
645	C₄×D₄	—	94	4	no	—
646	C₄×D₄	—	94	4	no	—
647	C₄×D₄	—	188	4	no	—
648	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
649	#117	—	94	4	no	—
650	#117	C₂×Dic₄₇	1	8	yes	complemented
651	C₂×C₄⋊C₄	—	47	1	no	—
652	C₂×C₄⋊C₄	—	47	1	no	—
653	C₂×C₄⋊C₄	—	47	1	no	—
654	C₂×C₄⋊C₄	—	47	1	no	—
655	C₂×C₄⋊C₄	—	47	1	no	—
656	C₂×C₄⋊C₄	—	47	1	no	—
657	C₂×C₄⋊C₄	—	47	2	no	—
658	C₂×C₄⋊C₄	—	47	2	no	—
659	C₂×C₄⋊C₄	—	47	2	no	—
660	C₂×C₄⋊C₄	—	47	2	no	—
661	C₂×C₄⋊C₄	—	47	2	no	—
662	C₂×C₄⋊C₄	—	47	2	no	—
663	C₂×C₄⋊C₄	—	47	2	no	—
664	C₂×C₄⋊C₄	—	47	2	no	—
665	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
671	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
672	C₂×C₂²⋊C₄	—	47	1	no	—
673	C₂×C₂²⋊C₄	—	47	1	no	—
674	C₂×C₂²⋊C₄	—	47	2	no	—
675	C₂×C₂²⋊C₄	—	47	2	no	—
676	C₂×C₂²⋊C₄	—	47	2	no	—
677	C₂×C₂²⋊C₄	—	47	2	no	—
678	C₂×C₂²⋊C₄	—	47	2	no	—
679	C₂×C₂²⋊C₄	—	47	2	no	—
680	C₂×C₂²⋊C₄	—	47	2	no	—
681	C₂×C₂²⋊C₄	—	47	2	no	—
682	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
689	C₂×C₄²	—	47	1	no	—
690	C₂×C₄²	—	47	1	no	—
691	C₂×C₄²	—	47	1	no	—
692	C₂×C₄²	—	47	2	no	—
693	C₂×C₄²	—	47	1	no	—
694	C₂×C₄²	—	47	2	no	—
695	C₂×C₄²	—	47	2	no	—
696	C₂×C₄²	—	47	2	no	—
697	C₂×C₄²	—	47	1	no	—
698	C₂×C₄²	—	47	1	no	—
699	C₂×C₄²	—	47	1	no	—
700	C₂×C₄²	—	47	1	no	—
701	C₂×C₄²	—	47	1	no	—
702	C₂×C₄²	—	47	1	no	—
703	C₂×C₄²	—	47	1	no	—
704	C₂×C₄²	—	47	1	no	—
705	C₂×C₄²	—	47	1	no	—
706	C₂×C₄²	—	47	1	no	—
707	C₂×C₄²	—	47	2	no	—
708	C₂×C₄²	—	47	2	no	—
709	C₂×C₄²	—	47	2	no	—
710	C₂×C₄²	—	47	2	no	—
711	C₂×C₄²	—	94	4	no	—
712	C₂×C₄²	—	188	4	no	—
713	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
714	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
715	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
716	#95	—	47	1	no	—
717	#95	—	47	1	no	—
718	#95	—	47	1	no	—
719	#95	—	47	1	no	—
720	#95	—	47	1	no	—
721	#95	—	47	1	no	—
722	#95	—	47	1	no	—
723	#95	—	47	1	no	—
724	#95	—	47	2	no	—
725	#95	—	47	2	no	—
726	#95	—	47	2	no	—
727	#95	—	47	2	no	—
728	#95	—	47	2	no	—
729	#95	—	47	2	no	—
730	#95	—	47	2	no	—
731	#95	—	47	2	no	—
732	#95	—	47	2	no	—
733	#95	—	47	2	no	—
734	#95	—	47	2	no	—
735	#95	—	47	2	no	—
736	#95	—	47	2	no	—
737	#95	—	47	2	no	—
738	#95	—	47	2	no	—
739	#95	—	47	2	no	—
740	#95	—	47	2	no	—
741	#95	—	47	2	no	—
742	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
743	C₂⁴	C₂³×D₄₇	1	2	yes	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	4	2	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
749	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
755	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	47	1	no	—
761	C₂²×C₄	—	47	1	no	—
762	C₂²×C₄	—	47	1	no	—
763	C₂²×C₄	—	47	1	no	—
764	C₂²×C₄	—	47	1	no	—
765	C₂²×C₄	—	47	1	no	—
766	C₂²×C₄	—	47	1	no	—
767	C₂²×C₄	—	47	2	no	—
768	C₂²×C₄	—	47	2	no	—
769	C₂²×C₄	—	47	2	no	—
770	C₂²×C₄	—	47	1	no	—
771	C₂²×C₄	—	47	2	no	—
772	C₂²×C₄	—	94	2	no	—
773	C₂²×C₄	—	94	2	no	—
774	C₂²×C₄	—	94	4	no	—
775	C₂²×C₄	—	94	4	no	—
776	C₂²×C₄	—	94	4	no	—
777	C₂²×C₄	—	94	2	no	—
778	C₂²×C₄	—	94	2	no	—
779	C₂²×C₄	—	94	4	no	—
780	C₂²×C₄	—	188	2	no	—
781	C₂²×C₄	—	188	1	no	—
782	C₂²×C₄	—	188	1	no	—
783	C₂²×C₄	—	188	2	no	—
784	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
785	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
786	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
787	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
788	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
789	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
790	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
791	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
792	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
793	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
794	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
795	C₄⋊C₄	—	94	2	no	—
796	C₄⋊C₄	—	94	2	no	—
797	C₄⋊C₄	—	94	4	no	—
798	C₄⋊C₄	—	94	4	no	—
799	C₄⋊C₄	—	94	2	no	—
800	C₄⋊C₄	—	94	2	no	—
801	C₄⋊C₄	—	94	2	no	—
802	C₄⋊C₄	—	94	2	no	—
803	C₄⋊C₄	—	188	2	no	—
804	C₄⋊C₄	—	188	2	no	—
805	C₄⋊C₄	—	188	2	no	—
806	C₄⋊C₄	—	188	2	no	—
807	C₄⋊C₄	—	188	2	no	—
808	C₄⋊C₄	—	188	2	no	—
809	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
810	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
811	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
812	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
813	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
814	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
815	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
816	C₂²⋊C₄	—	94	2	no	—
817	C₂²⋊C₄	—	94	2	no	—
818	C₂²⋊C₄	—	94	4	no	—
819	C₂²⋊C₄	—	94	4	no	—
820	C₂²⋊C₄	—	188	2	no	—
821	C₂²⋊C₄	—	188	2	no	—
822	C₂²⋊C₄	—	188	2	no	—
823	C₂²⋊C₄	—	188	2	no	—
824	C₂²⋊C₄	—	188	2	no	—
825	C₂²⋊C₄	—	188	2	no	—
826	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
827	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
828	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
829	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
830	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
831	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
832	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
833	C₄²	—	47	4	no	—
834	C₄²	—	47	4	no	—
835	C₄²	—	94	2	no	—
836	C₄²	—	94	2	no	—
837	C₄²	—	94	2	no	—
838	C₄²	—	94	2	no	—
839	C₄²	—	94	2	no	—
840	C₄²	—	94	4	no	—
841	C₄²	—	94	4	no	—
842	C₄²	—	94	4	no	—
843	C₄²	—	94	4	no	—
844	C₄²	—	94	2	no	—
845	C₄²	—	94	2	no	—
846	C₄²	—	94	2	no	—
847	C₄²	—	188	1	no	—
848	C₄²	—	188	2	no	—
849	C₄²	—	188	1	no	—
850	C₄²	—	188	1	no	—
851	C₄²	—	188	2	no	—
852	C₄²	—	188	1	no	—
853	C₄²	—	188	2	no	—
854	C₄²	—	188	2	no	—
855	C₄²	C₂²×Dic₄₇	1	4	yes	—
856	C₄²	C₂²×Dic₄₇	1	4	yes	—
857	C₄²	C₂²×Dic₄₇	1	8	yes	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	2	no	—
870	C₂³	C₂³×Dic₄₇	1	2	yes	—
871	C₂³	C₂³×Dic₄₇	1	4	yes	—
872	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
873	Q₈	—	2	8	no	—
874	Q₈	—	4	8	no	—
875	D₄	—	2	8	no	—
876	D₄	—	4	8	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	8	no	—
894	C₂×C₄	—	4	8	no	—
895	C₂×C₄	—	47	2	no	—
896	C₂×C₄	—	47	2	no	—
897	C₂×C₄	—	47	2	no	—
898	C₂×C₄	—	47	2	no	—
899	C₂×C₄	—	47	2	no	—
900	C₂×C₄	—	47	2	no	—
901	C₂×C₄	—	94	1	no	—
902	C₂×C₄	—	94	1	no	—
903	C₂×C₄	—	94	1	no	—
904	C₂×C₄	—	94	1	no	—
905	C₂×C₄	—	94	1	no	—
906	C₂×C₄	—	94	1	no	—
907	C₂×C₄	—	94	1	no	—
908	C₂×C₄	—	94	1	no	—
909	C₂×C₄	—	94	1	no	—
910	C₂×C₄	—	94	1	no	—
911	C₂×C₄	—	94	2	no	—
912	C₂×C₄	—	94	2	no	—
913	C₂×C₄	—	94	2	no	—
914	C₂×C₄	—	94	2	no	—
915	C₂×C₄	—	94	2	no	—
916	C₂×C₄	—	94	2	no	—
917	C₂×C₄	—	94	1	no	—
918	C₂×C₄	—	94	2	no	—
919	C₂×C₄	—	94	1	no	—
920	C₂×C₄	—	94	1	no	—
921	C₂×C₄	—	94	1	no	—
922	C₂×C₄	—	94	2	no	—
923	C₂×C₄	—	94	1	no	—
924	C₂×C₄	—	94	2	no	—
925	C₂×C₄	—	94	1	no	—
926	C₂×C₄	—	94	2	no	—
927	C₂×C₄	—	94	1	no	—
928	C₂×C₄	—	94	2	no	—
929	C₂×C₄	—	94	1	no	—
930	C₂×C₄	—	94	2	no	—
931	C₂×C₄	—	188	4	no	—
932	C₂×C₄	—	188	8	no	—
933	C₂×C₄	—	188	4	no	—
934	C₂×C₄	—	188	8	no	—
935	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
936	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
937	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
938	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
939	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
940	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
941	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
942	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
943	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
944	C₂×C₄	#41×D₄₇	1	2	yes	—
945	C₂×C₄	#41×D₄₇	1	2	yes	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	4	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	4	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	1	no	—
960	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
961	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
962	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
963	C₂²	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
964	C₂²	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
965	C₂²	#15689958	1	1	yes	characteristic
966	C₂²	#15689960	1	1	yes	characteristic
967	C₄	—	2	2	no	—
968	C₄	—	2	4	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	4	no	—
971	C₄	—	2	4	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	47	4	no	—
976	C₄	—	94	2	no	—
977	C₄	—	94	2	no	—
978	C₄	—	94	2	no	—
979	C₄	—	188	1	no	—
980	C₄	—	188	2	no	—
981	C₄	—	188	2	no	—
982	C₄	—	188	1	no	—
983	C₄	—	188	2	no	—
984	C₄	—	188	1	no	—
985	C₄	—	188	1	no	—
986	C₄	—	188	2	no	—
987	C₄	#41×Dic₄₇	1	4	yes	—
988	C₂	—	4	2	no	—
989	C₂	—	4	4	no	—
990	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
991	C₂	H(5,𝔽₂)×Dic₄₇	1	1	yes	characteristic
992	C₂	2₋¹⁺⁴×Dic₄₇	1	1	yes	characteristic
993	C₂	#542×D₄₇	1	1	yes	characteristic
994	C₂	#20256775	1	1	yes	characteristic
995	C₂	#20256808	1	1	yes	characteristic
996	C₂	#20256814	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂×C₄₇×#542	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂×#121×C₄₇	C₂²
hypercenter	C₂×#542	D₄₇
hypocenter	C₄₇	C₄×#542
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. #20246203	C₂	semidirect
2. #20246182	C₂	semidirect
3. #20246167	C₂	semidirect
4. #20246146	C₂	semidirect
5. #20246137	C₂	semidirect
6. #20246101	C₂	semidirect
8. #20246072	C₂	semidirect
9. #20246039	C₂	semidirect
10. #20246031	C₂	semidirect
11. #20245997	C₂	semidirect
12. C₄⋊Q₈×Dic₄₇	C₂	semidirect
13. #126×Dic₄₇	C₂	semidirect
14. #124×Dic₄₇	C₂	semidirect
15. #124×Dic₄₇	C₂	semidirect
16. C₂²⋊Q₈×Dic₄₇	C₂	semidirect
17. C₂²⋊Q₈×Dic₄₇	C₂	semidirect
18. #123×Dic₄₇	C₂	semidirect
20. C₄×Q₈×Dic₄₇	C₂	semidirect
21. C₄×D₄×Dic₄₇	C₂	semidirect
22. #117×Dic₄₇	C₂	semidirect
112. C₄₇×#542	C₄	semidirect
215. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
216. #126×C₄₇	C₂×C₄	semidirect
217. #124×C₄₇	C₂×C₄	semidirect
218. #124×C₄₇	C₂×C₄	semidirect
219. #123×C₄₇	C₂×C₄	semidirect
220. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
221. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
223. C₄×Q₈×C₄₇	C₂×C₄	semidirect
224. C₄×D₄×C₄₇	C₂×C₄	semidirect
225. #117×C₄₇	C₂×C₄	semidirect
489. Dic₄₇	#542	direct (N × H)
522. #542	Dic₄₇	direct (N × H)
622. C₄₇	C₄×#542	semidirect
633. C₄⋊Q₈	C₂×Dic₄₇	semidirect
634. #126	C₂×Dic₄₇	semidirect
635. #124	C₂×Dic₄₇	semidirect
636. #124	C₂×Dic₄₇	semidirect
637. #123	C₂×Dic₄₇	semidirect
638. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
639. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
644. C₄×Q₈	C₂×Dic₄₇	semidirect
648. C₄×D₄	C₂×Dic₄₇	semidirect
650. #117	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246203	2
#20246182	2
#20246167	2
#20246146	2
#20246137	2
#20246101	2
#20246083	2
#20246072	2
#20246039	2
#20246031	2
#20245997	2
C₄⋊Q₈×Dic₄₇	2
#126×Dic₄₇	2
#124×Dic₄₇	2
C₂²⋊Q₈×Dic₄₇	2
#123×Dic₄₇	2
#121×Dic₄₇	2
C₄×Q₈×Dic₄₇	2
C₄×D₄×Dic₄₇	2
#117×Dic₄₇	2
C₂×C₄₇×#542	2
C₄×#542	47

Subgroups — #542×Dic47 #26375407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #542×Dic₄₇ #26375407