Subgroups — #26385668

Order 12032.

1848 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20248130	C₂	1	2	yes	maximal, complemented
2	#20248007	C₂	1	2	yes	maximal, complemented
3	#20247996	C₂	1	1	yes	maximal, characteristic, complemented
4	#20247926	C₂	1	1	yes	maximal, characteristic, complemented
5	#20247873	C₂	1	1	yes	maximal, characteristic, complemented
6	#20247799	C₂	1	1	yes	maximal, characteristic, complemented
7	#20247767	C₂	1	2	yes	maximal, complemented
8	#20247729	C₂	1	1	yes	maximal, characteristic, complemented
9	#20247696	C₂	1	1	yes	maximal, characteristic
10	#20247112	C₂	1	1	yes	maximal, characteristic, complemented
11	#20246859	C₂	1	2	yes	maximal
12	#20246839	C₂	1	1	yes	maximal, characteristic
13	#20246695	C₂	1	2	yes	maximal, complemented
14	#20246688	C₂	1	2	yes	maximal, complemented
15	C₄×#13094016	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#13094005	C₂	1	2	yes	maximal
19	#20245865	C₂	1	1	yes	maximal, characteristic, complemented
20	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
21	#20245782	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
24	C₂×#13094016	C₂²	1	1	yes	characteristic
25	C₂×#13094005	C₂²	1	2	yes	—
26	C₂×#13094003	C₂²	1	1	yes	characteristic
27	C₂×#13094003	C₂²	1	1	yes	characteristic
28	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
32	C₄₇⋊#401	C₂²	1	2	yes	—
33	#15689065	C₂²	1	2	yes	—
34	#15689064	C₂²	1	2	yes	—
35	#15689064	C₂²	1	2	yes	—
36	#15689064	C₂²	1	2	yes	—
37	#15689063	C₂²	1	2	yes	—
38	#15689063	C₂²	1	2	yes	—
39	#15689061	C₂²	1	2	yes	—
40	#15689057	C₂²	1	2	yes	—
41	#15689056	C₂²	1	2	yes	—
42	#15689054	C₂²	1	2	yes	—
43	#15689053	C₂²	1	2	yes	—
44	#15689051	C₂²	1	2	yes	—
45	#15689051	C₂²	1	2	yes	—
46	#15689048	C₂²	1	2	yes	—
47	#15689046	C₂²	1	2	yes	—
48	#15689029	C₂²	1	1	yes	characteristic
49	#15689029	C₂²	1	1	yes	characteristic
50	#15689029	C₂²	1	1	yes	characteristic
51	#15689029	C₂²	1	1	yes	characteristic
52	#15689021	C₂²	1	1	yes	characteristic
53	#15689021	C₂²	1	1	yes	characteristic
54	#15689021	C₂²	1	1	yes	characteristic
55	#15689021	C₂²	1	1	yes	characteristic
56	#15689021	C₂²	1	1	yes	characteristic
57	#15689021	C₂²	1	1	yes	characteristic
58	#15689011	C₂²	1	2	yes	—
59	#15689011	C₂²	1	2	yes	—
60	#15689007	C₂²	1	2	yes	—
61	#15689007	C₂²	1	2	yes	—
62	#15689007	C₂²	1	2	yes	—
63	#15689007	C₂²	1	2	yes	—
64	#15689007	C₂²	1	2	yes	—
65	#15689007	C₂²	1	2	yes	—
66	#15689004	C₂²	1	2	yes	—
67	#15689004	C₂²	1	2	yes	—
68	#15689003	C₂²	1	2	yes	—
69	#15688996	C₂²	1	2	yes	—
70	#15688996	C₂²	1	2	yes	—
71	#15688995	C₂²	1	2	yes	—
72	#15688991	C₂²	1	2	yes	—
73	#15688990	C₂²	1	2	yes	—
74	#15688990	C₂²	1	2	yes	—
75	#15688989	C₂²	1	1	yes	characteristic
76	#15688989	C₂²	1	1	yes	characteristic
77	#15688989	C₂²	1	1	yes	characteristic
78	#15688987	C₂²	1	2	yes	—
79	#15688987	C₂²	1	2	yes	—
80	#15688986	C₂²	1	2	yes	—
81	#15688984	C₂²	1	2	yes	—
82	#15688984	C₂²	1	2	yes	—
83	#15688984	C₂²	1	2	yes	—
84	#15688983	C₂²	1	1	yes	characteristic
85	#15688983	C₂²	1	1	yes	characteristic
86	#15688983	C₂²	1	1	yes	characteristic
87	#15688983	C₂²	1	1	yes	characteristic
88	#15688981	C₂²	1	2	yes	—
89	#15688981	C₂²	1	2	yes	—
90	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
91	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
92	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
93	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
94	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
95	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
98	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
100	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
105	#15688969	C₂²	1	2	yes	—
106	#15688969	C₂²	1	2	yes	—
107	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
108	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
109	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
110	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
111	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
112	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
122	C₄³×C₄₇	C₂²	1	1	yes	characteristic
123	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
124	C₂³×Dic₄₇	C₂³	1	2	yes	—
125	C₂³×Dic₄₇	C₂³	1	2	yes	—
126	#13094016	—	2	4	no	—
127	#13094005	—	2	8	no	—
128	#13094003	—	2	4	no	—
129	#13094003	—	2	4	no	—
130	C₄×Dic₉₄	—	2	4	no	—
131	C₂×C₄⋊Dic₄₇	—	2	4	no	—
132	C₂×C₄⋊Dic₄₇	—	2	4	no	—
133	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
137	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
138	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
142	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
143	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
144	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
145	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
146	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
147	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
148	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
149	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
150	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
151	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
152	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
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	8	no	—
160	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
161	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
162	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
163	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
164	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
165	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
166	C₄₇⋊#95	C₂³	1	2	yes	—
167	C₄₇⋊#95	C₂³	1	2	yes	—
168	C₄₇⋊#95	C₂³	1	2	yes	—
169	C₄₇⋊#95	C₂³	1	2	yes	—
170	C₄₇⋊#95	C₂³	1	2	yes	—
171	C₄₇⋊#95	C₂³	1	2	yes	—
172	C₄₇⋊#95	C₂³	1	2	yes	—
173	C₄₇⋊#95	C₂³	1	2	yes	—
174	C₄₇⋊#95	C₂³	1	2	yes	—
175	C₄₇⋊#95	C₂³	1	2	yes	—
176	C₄₇⋊#95	C₂³	1	2	yes	—
177	C₄₇⋊#95	C₂³	1	2	yes	—
178	C₄₇⋊#95	C₂³	1	2	yes	—
179	C₄₇⋊#95	C₂³	1	2	yes	—
180	C₄₇⋊#95	C₂³	1	2	yes	—
181	C₄₇⋊#95	C₂³	1	2	yes	—
182	C₄₇⋊#95	C₂³	1	2	yes	—
183	C₄₇⋊#95	C₂³	1	2	yes	—
184	C₄₇⋊#95	C₂³	1	2	yes	—
185	C₄₇⋊#95	C₂³	1	2	yes	—
186	C₄₇⋊#95	C₂³	1	2	yes	—
187	C₄₇⋊#95	C₂³	1	2	yes	—
188	C₄₇⋊#95	C₂³	1	2	yes	—
189	C₄₇⋊#95	C₂³	1	2	yes	—
190	C₄₇⋊#95	C₂³	1	2	yes	—
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	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
202	C₄×D₄×C₄₇	—	2	4	no	—
203	C₄×D₄×C₄₇	—	2	4	no	—
204	C₄×D₄×C₄₇	—	2	4	no	—
205	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₄₇	—	2	4	no	—
215	C₂×C₄²×C₄₇	—	2	4	no	—
216	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
229	#95×C₄₇	C₂³	1	1	yes	characteristic
230	#95×C₄₇	C₂³	1	1	yes	characteristic
231	#95×C₄₇	C₂³	1	1	yes	characteristic
232	#95×C₄₇	C₂³	1	1	yes	characteristic
233	#95×C₄₇	C₂³	1	1	yes	characteristic
234	#95×C₄₇	C₂³	1	1	yes	characteristic
235	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₄₇	—	2	2	no	—
238	C₂×D₄×C₄₇	—	2	2	no	—
239	C₂×D₄×C₄₇	#41	1	4	yes	—
240	C₂²×C₄×C₄₇	—	2	2	no	—
241	C₂²×C₄×C₄₇	—	2	2	no	—
242	C₂²×C₄×C₄₇	—	2	2	no	—
243	C₂²×C₄×C₄₇	—	2	2	no	—
244	C₂²×C₄×C₄₇	—	2	2	no	—
245	C₂²×C₄×C₄₇	—	2	2	no	—
246	C₂²×C₄×C₄₇	—	2	2	no	—
247	C₂²×C₄×C₄₇	—	2	2	no	—
248	C₂²×C₄×C₄₇	—	2	2	no	—
249	C₂²×C₄×C₄₇	—	2	2	no	—
250	C₂²×C₄×C₄₇	—	2	2	no	—
251	C₂²×C₄×C₄₇	—	2	2	no	—
252	C₂²×C₄×C₄₇	—	2	2	no	—
253	C₂²×C₄×C₄₇	—	2	2	no	—
254	C₂²×C₄×C₄₇	—	4	1	no	—
255	C₂²×C₄×C₄₇	—	4	1	no	—
256	C₂²×C₄×C₄₇	#41	1	4	yes	—
257	C₂²×C₄×C₄₇	#41	1	4	yes	—
258	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
271	C₂²×Dic₄₇	—	2	4	no	—
272	C₂²×Dic₄₇	—	2	4	no	—
273	C₂²×Dic₄₇	—	2	4	no	—
274	C₂²×Dic₄₇	—	2	4	no	—
275	C₂²×Dic₄₇	—	2	4	no	—
276	C₂²×Dic₄₇	—	4	2	no	—
277	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
278	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
279	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
280	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
281	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
282	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
283	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
284	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
285	C₂×Dic₉₄	—	2	2	no	—
286	C₂×Dic₉₄	—	2	2	no	—
287	C₂×Dic₉₄	—	2	2	no	—
288	C₄⋊C₄×C₄₇	—	2	2	no	—
289	C₄⋊C₄×C₄₇	—	2	2	no	—
290	C₄⋊C₄×C₄₇	—	2	2	no	—
291	C₂²⋊C₄×C₄₇	—	2	2	no	—
292	C₂²⋊C₄×C₄₇	—	2	2	no	—
293	C₂²⋊C₄×C₄₇	—	2	2	no	—
294	C₂²⋊C₄×C₄₇	—	2	2	no	—
295	C₂²⋊C₄×C₄₇	—	2	2	no	—
296	C₂²⋊C₄×C₄₇	—	2	2	no	—
297	C₄²×C₄₇	—	2	2	no	—
298	C₄²×C₄₇	—	2	2	no	—
299	C₄²×C₄₇	—	2	2	no	—
300	C₄²×C₄₇	—	2	2	no	—
301	C₄²×C₄₇	—	2	2	no	—
302	C₄²×C₄₇	—	2	2	no	—
303	C₄²×C₄₇	—	2	2	no	—
304	C₄²×C₄₇	—	2	2	no	—
305	C₄²×C₄₇	—	2	2	no	—
306	C₄²×C₄₇	—	2	2	no	—
307	C₄²×C₄₇	—	2	2	no	—
308	C₄²×C₄₇	—	4	1	no	—
309	C₄²×C₄₇	#41	1	4	yes	—
310	C₂²⋊Dic₄₇	—	2	4	no	—
311	C₂²⋊Dic₄₇	—	2	4	no	—
312	C₂²⋊Dic₄₇	—	2	4	no	—
313	C₂²⋊Dic₄₇	—	2	4	no	—
314	C₂²⋊Dic₄₇	—	2	4	no	—
315	C₂²⋊Dic₄₇	—	4	2	no	—
316	C₄⋊Dic₄₇	—	2	2	no	—
317	C₄⋊Dic₄₇	—	2	4	no	—
318	C₄⋊Dic₄₇	—	2	2	no	—
319	C₄⋊Dic₄₇	—	2	2	no	—
320	C₄⋊Dic₄₇	—	2	2	no	—
321	C₄⋊Dic₄₇	—	2	2	no	—
322	C₄⋊Dic₄₇	—	2	2	no	—
323	C₄⋊Dic₄₇	—	2	4	no	—
324	C₄⋊Dic₄₇	#41	1	4	yes	—
325	Dic₄₇⋊C₄	—	2	4	no	—
326	Dic₄₇⋊C₄	—	2	4	no	—
327	Dic₄₇⋊C₄	—	2	4	no	—
328	Dic₄₇⋊C₄	—	2	4	no	—
329	Dic₄₇⋊C₄	—	2	4	no	—
330	Dic₄₇⋊C₄	—	2	4	no	—
331	Dic₄₇⋊C₄	—	2	4	no	—
332	Dic₄₇⋊C₄	—	4	2	no	—
333	Dic₄₇⋊C₄	—	4	2	no	—
334	Dic₄₇⋊C₄	—	4	2	no	—
335	Dic₄₇⋊C₄	—	4	2	no	—
336	C₄×Dic₄₇	—	2	4	no	—
337	C₄×Dic₄₇	—	2	4	no	—
338	C₄×Dic₄₇	—	2	4	no	—
339	C₄×Dic₄₇	—	2	4	no	—
340	C₄×Dic₄₇	—	2	4	no	—
341	C₄×Dic₄₇	—	2	4	no	—
342	C₂³×C₄₇	—	2	1	no	—
343	C₂³×C₄₇	—	2	1	no	—
344	C₂³×C₄₇	—	2	1	no	—
345	C₂³×C₄₇	—	2	1	no	—
346	C₂³×C₄₇	—	2	1	no	—
347	C₂³×C₄₇	—	2	1	no	—
348	C₂³×C₄₇	—	2	1	no	—
349	C₂³×C₄₇	—	2	1	no	—
350	C₂³×C₄₇	—	2	1	no	—
351	C₂³×C₄₇	—	2	1	no	—
352	C₂³×C₄₇	C₂×#41	1	2	yes	—
353	C₂³×C₄₇	C₂×#41	1	2	yes	—
354	C₂³×C₄₇	C₂×#41	1	2	yes	—
355	C₂³×C₄₇	C₂×#41	1	2	yes	—
356	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
357	D₄×C₄₇	—	2	8	no	—
358	C₂×C₄×C₄₇	—	2	1	no	—
359	C₂×C₄×C₄₇	—	2	1	no	—
360	C₂×C₄×C₄₇	—	2	1	no	—
361	C₂×C₄×C₄₇	—	2	1	no	—
362	C₂×C₄×C₄₇	—	2	1	no	—
363	C₂×C₄×C₄₇	—	2	1	no	—
364	C₂×C₄×C₄₇	—	2	1	no	—
365	C₂×C₄×C₄₇	—	2	1	no	—
366	C₂×C₄×C₄₇	—	2	8	no	—
367	C₂×C₄×C₄₇	—	2	8	no	—
368	C₂×C₄×C₄₇	—	2	1	no	—
369	C₂×C₄×C₄₇	—	2	1	no	—
370	C₂×C₄×C₄₇	—	2	1	no	—
371	C₂×C₄×C₄₇	—	2	1	no	—
372	C₂×C₄×C₄₇	—	2	1	no	—
373	C₂×C₄×C₄₇	—	2	1	no	—
374	C₂×C₄×C₄₇	—	2	1	no	—
375	C₂×C₄×C₄₇	—	2	1	no	—
376	C₂×C₄×C₄₇	—	2	1	no	—
377	C₂×C₄×C₄₇	—	2	1	no	—
378	C₂×C₄×C₄₇	—	2	1	no	—
379	C₂×C₄×C₄₇	—	2	1	no	—
380	C₂×C₄×C₄₇	—	2	1	no	—
381	C₂×C₄×C₄₇	—	2	1	no	—
382	C₂×C₄×C₄₇	—	2	1	no	—
383	C₂×C₄×C₄₇	—	2	1	no	—
384	C₂×C₄×C₄₇	—	2	1	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	—	4	4	no	—
390	C₂×C₄×C₄₇	—	4	4	no	—
391	C₂×C₄×C₄₇	—	4	4	no	—
392	C₂×C₄×C₄₇	—	4	4	no	—
393	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
394	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
395	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
396	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
397	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
398	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
399	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
400	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
401	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
402	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
403	C₂×Dic₄₇	—	2	2	no	—
404	C₂×Dic₄₇	—	2	2	no	—
405	C₂×Dic₄₇	—	2	2	no	—
406	C₂×Dic₄₇	—	2	2	no	—
407	C₂×Dic₄₇	—	2	2	no	—
408	C₂×Dic₄₇	—	2	2	no	—
409	C₂×Dic₄₇	—	2	2	no	—
410	C₂×Dic₄₇	—	2	2	no	—
411	C₂×Dic₄₇	—	2	2	no	—
412	C₂×Dic₄₇	—	2	2	no	—
413	C₂×Dic₄₇	—	2	2	no	—
414	C₂×Dic₄₇	—	2	2	no	—
415	C₂×Dic₄₇	—	2	2	no	—
416	C₂×Dic₄₇	—	2	2	no	—
417	C₂×Dic₄₇	—	2	2	no	—
418	C₂×Dic₄₇	—	2	2	no	—
419	C₂×Dic₄₇	—	2	2	no	—
420	C₂×Dic₄₇	—	2	2	no	—
421	C₂×Dic₄₇	—	2	2	no	—
422	C₂×Dic₄₇	—	2	2	no	—
423	C₂×Dic₄₇	—	2	2	no	—
424	C₂×Dic₄₇	—	2	2	no	—
425	C₂×Dic₄₇	—	2	2	no	—
426	C₂×Dic₄₇	—	4	8	no	—
427	C₂×Dic₄₇	—	4	8	no	—
428	C₂×Dic₄₇	C₂×#41	1	4	yes	—
429	Dic₉₄	—	4	4	no	—
430	#34780	—	47	1	no	maximal, Sylow
431	C₂²×C₄₇	—	2	2	no	—
432	C₂²×C₄₇	—	2	2	no	—
433	C₂²×C₄₇	—	2	2	no	—
434	C₂²×C₄₇	—	2	2	no	—
435	C₂²×C₄₇	—	2	2	no	—
436	C₂²×C₄₇	—	2	2	no	—
437	C₂²×C₄₇	—	2	2	no	—
438	C₂²×C₄₇	—	2	2	no	—
439	C₂²×C₄₇	—	2	2	no	—
440	C₂²×C₄₇	—	4	1	no	—
441	C₂²×C₄₇	—	4	1	no	—
442	C₂²×C₄₇	—	4	1	no	—
443	C₂²×C₄₇	—	4	1	no	—
444	C₂²×C₄₇	#529	1	4	yes	—
445	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
446	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
447	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
449	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
450	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂²×C₄₇	#585	1	1	yes	characteristic
452	C₄×C₄₇	—	2	2	no	—
453	C₄×C₄₇	—	2	2	no	—
454	C₄×C₄₇	—	2	2	no	—
455	C₄×C₄₇	—	2	2	no	—
456	C₄×C₄₇	—	4	1	no	—
457	C₄×C₄₇	—	4	1	no	—
458	C₄×C₄₇	—	4	1	no	—
459	C₄×C₄₇	—	4	1	no	—
460	C₄×C₄₇	—	4	1	no	—
461	C₄×C₄₇	—	4	1	no	—
462	C₄×C₄₇	—	4	1	no	—
463	C₄×C₄₇	#529	1	4	yes	—
464	C₄×C₄₇	#552	1	4	yes	—
465	Dic₄₇	—	2	4	no	—
466	Dic₄₇	—	4	2	no	—
467	Dic₄₇	—	4	2	no	—
468	Dic₄₇	—	4	2	no	—
469	Dic₄₇	—	4	2	no	—
470	Dic₄₇	—	4	2	no	—
471	Dic₄₇	—	4	2	no	—
472	Dic₄₇	—	4	2	no	—
473	#2524	—	47	2	no	—
474	#2515	—	47	2	no	—
475	#2514	—	47	1	no	—
476	#2508	—	47	1	no	—
477	#2503	—	47	1	no	—
478	#2495	—	47	1	no	—
479	#2493	—	47	2	no	—
480	#2489	—	47	1	no	—
481	#2486	—	47	1	no	—
482	#2442	—	47	1	no	—
483	#2419	—	47	2	no	—
484	#2417	—	47	1	no	—
485	#2402	—	47	2	no	—
486	#2401	—	47	2	no	—
487	C₄×#125	—	47	1	no	—
488	C₄×C₂²⋊Q₈	—	47	1	no	—
489	C₄×C₂²⋊Q₈	—	47	1	no	—
490	C₄×#123	—	47	2	no	—
491	#2295	—	47	1	no	—
492	#2283	—	47	1	no	—
493	#2283	—	47	2	no	—
494	C₄²×D₄	D₄₇	1	1	yes	characteristic
495	C₂×C₄×C₄⋊C₄	—	47	1	no	—
496	C₂×C₄₇	—	2	4	no	—
497	C₂×C₄₇	—	4	2	no	—
498	C₂×C₄₇	C₂×#529	1	1	yes	characteristic
499	C₂×C₄₇	C₂×#529	1	1	yes	characteristic
500	C₂×C₄₇	#3461	1	1	yes	characteristic
501	C₂×C₄₇	C₂×#552	1	1	yes	characteristic
502	C₂×C₄₇	#3475	1	1	yes	characteristic
503	C₂×C₄₇	#3475	1	1	yes	characteristic
504	C₂×C₄₇	#3482	1	1	yes	characteristic
505	C₂×#125	—	47	1	no	—
506	C₂×#123	—	47	2	no	—
507	C₂×C₂²⋊Q₈	—	47	1	no	—
508	C₂×C₂²⋊Q₈	—	47	1	no	—
509	C₂×C₄×Q₈	—	47	1	no	—
510	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
511	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
512	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
513	C₂²×C₄⋊C₄	—	47	1	no	—
514	C₂²×C₄⋊C₄	—	47	1	no	—
515	C₂²×C₄²	—	47	2	no	—
516	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
517	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
518	#401	—	47	2	no	—
519	#400	—	47	2	no	—
520	#400	—	47	2	no	—
521	#400	—	47	2	no	—
522	#400	—	47	2	no	—
523	#400	—	47	2	no	—
524	#400	—	47	2	no	—
525	#400	—	47	2	no	—
526	#398	—	47	2	no	—
527	#398	—	47	2	no	—
528	#398	—	47	2	no	—
529	#398	—	47	2	no	—
530	#397	—	47	2	no	—
531	#397	—	47	2	no	—
532	#397	—	47	2	no	—
533	#396	—	47	2	no	—
534	#391	—	47	1	no	—
535	#391	—	47	1	no	—
536	#391	—	47	1	no	—
537	#391	—	47	1	no	—
538	#389	—	47	1	no	—
539	#389	—	47	1	no	—
540	#389	—	47	1	no	—
541	#389	—	47	1	no	—
542	#389	—	47	1	no	—
543	#389	—	47	1	no	—
544	#388	—	47	2	no	—
545	#388	—	47	2	no	—
546	#387	—	47	2	no	—
547	#387	—	47	2	no	—
548	#387	—	47	2	no	—
549	#387	—	47	2	no	—
550	#387	—	47	2	no	—
551	#387	—	47	2	no	—
552	#387	—	47	2	no	—
553	#387	—	47	2	no	—
554	#386	—	47	2	no	—
555	#385	—	47	2	no	—
556	#385	—	47	2	no	—
557	#385	—	47	2	no	—
558	#383	—	47	2	no	—
559	#383	—	47	2	no	—
560	#383	—	47	2	no	—
561	#382	—	47	1	no	—
562	#382	—	47	1	no	—
563	#382	—	47	1	no	—
564	#382	—	47	2	no	—
565	#382	—	47	2	no	—
566	#381	—	47	2	no	—
567	#381	—	47	2	no	—
568	#381	—	47	2	no	—
569	#381	—	47	2	no	—
570	#380	—	47	1	no	—
571	#380	—	47	1	no	—
572	#380	—	47	1	no	—
573	#380	—	47	1	no	—
574	#380	—	47	2	no	—
575	#380	—	47	2	no	—
576	C₄×C₄⋊C₄	—	47	1	no	—
577	C₄×C₄⋊C₄	—	47	1	no	—
578	C₄×C₄⋊C₄	—	47	2	no	—
579	C₄×C₄⋊C₄	—	47	2	no	—
580	C₄×C₄⋊C₄	—	47	2	no	—
581	C₄×C₄⋊C₄	—	47	1	no	—
582	C₄×C₄⋊C₄	—	47	1	no	—
583	C₄×C₄⋊C₄	—	47	2	no	—
584	C₄×C₄⋊C₄	—	47	1	no	—
585	C₄×C₄⋊C₄	—	47	2	no	—
586	C₄×C₄⋊C₄	—	47	2	no	—
587	C₄×C₄⋊C₄	—	47	2	no	—
588	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
590	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	—	47	2	no	—
592	C₄×C₂²⋊C₄	—	47	2	no	—
593	C₄×C₂²⋊C₄	—	47	2	no	—
594	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
595	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
596	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
597	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
598	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
599	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
600	#376	—	47	2	no	—
601	#376	—	47	2	no	—
602	C₂×#95	—	47	2	no	—
603	C₄³	C₂×D₄₇	1	1	yes	characteristic
604	C₄₇	#34780	1	1	yes	characteristic, complemented, Sylow
605	C₂²×Q₈	—	47	1	no	—
606	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
607	C₂³×C₄	—	47	2	no	—
608	C₂³×C₄	—	47	2	no	—
609	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
610	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
611	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
612	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
613	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
614	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
615	#125	—	94	4	no	—
616	#123	—	94	8	no	—
617	C₂²⋊Q₈	—	94	4	no	—
618	C₂²⋊Q₈	—	94	4	no	—
619	C₄×Q₈	—	94	4	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	4	no	—
623	C₂×C₄⋊C₄	—	47	1	no	—
624	C₂×C₄⋊C₄	—	47	1	no	—
625	C₂×C₄⋊C₄	—	47	1	no	—
626	C₂×C₄⋊C₄	—	47	1	no	—
627	C₂×C₄⋊C₄	—	47	2	no	—
628	C₂×C₄⋊C₄	—	47	2	no	—
629	C₂×C₄⋊C₄	—	47	2	no	—
630	C₂×C₄⋊C₄	—	47	1	no	—
631	C₂×C₄⋊C₄	—	47	2	no	—
632	C₂×C₄⋊C₄	—	47	2	no	—
633	C₂×C₄⋊C₄	—	47	1	no	—
634	C₂×C₄⋊C₄	—	47	2	no	—
635	C₂×C₄⋊C₄	—	47	2	no	—
636	C₂×C₄⋊C₄	—	47	2	no	—
637	C₂×C₄⋊C₄	—	47	2	no	—
638	C₂×C₄⋊C₄	—	47	1	no	—
639	C₂×C₄⋊C₄	—	47	2	no	—
640	C₂×C₄⋊C₄	—	47	2	no	—
641	C₂×C₄⋊C₄	—	47	2	no	—
642	C₂×C₄⋊C₄	—	47	2	no	—
643	C₂×C₄⋊C₄	—	94	4	no	—
644	C₂×C₄⋊C₄	—	94	4	no	—
645	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	—	47	2	no	—
649	C₂×C₂²⋊C₄	—	47	2	no	—
650	C₂×C₂²⋊C₄	—	47	2	no	—
651	C₂×C₂²⋊C₄	—	47	2	no	—
652	C₂×C₂²⋊C₄	—	47	2	no	—
653	C₂×C₂²⋊C₄	—	47	2	no	—
654	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
660	C₂×C₄²	—	2	4	no	—
661	C₂×C₄²	—	2	4	no	—
662	C₂×C₄²	—	47	2	no	—
663	C₂×C₄²	—	47	2	no	—
664	C₂×C₄²	—	47	2	no	—
665	C₂×C₄²	—	47	2	no	—
666	C₂×C₄²	—	47	2	no	—
667	C₂×C₄²	—	47	2	no	—
668	C₂×C₄²	—	94	8	no	—
669	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
670	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
671	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
672	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
673	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
674	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
675	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
676	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
677	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
678	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
679	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
680	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
681	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
682	#95	—	47	2	no	—
683	#95	—	47	2	no	—
684	#95	—	47	2	no	—
685	#95	—	47	2	no	—
686	#95	—	47	2	no	—
687	#95	—	47	2	no	—
688	#95	—	47	2	no	—
689	#95	—	47	2	no	—
690	#95	—	47	2	no	—
691	#95	—	47	2	no	—
692	#95	—	47	2	no	—
693	#95	—	47	2	no	—
694	#95	—	47	2	no	—
695	#95	—	47	2	no	—
696	#95	—	47	2	no	—
697	#95	—	47	2	no	—
698	#95	—	47	2	no	—
699	#95	—	47	2	no	—
700	#95	—	47	2	no	—
701	#95	—	47	2	no	—
702	#95	—	47	2	no	—
703	#95	—	47	2	no	—
704	#95	—	47	2	no	—
705	#95	—	47	2	no	—
706	#95	—	47	2	no	—
707	#95	—	47	2	no	—
708	#95	—	47	2	no	—
709	#95	—	47	2	no	—
710	#95	—	47	2	no	—
711	#95	C₂²×D₄₇	1	1	yes	characteristic
712	#95	C₂²×D₄₇	1	1	yes	characteristic
713	#95	C₂²×D₄₇	1	1	yes	characteristic
714	#95	C₂²×D₄₇	1	1	yes	characteristic
715	#95	C₂²×D₄₇	1	1	yes	characteristic
716	#95	C₂²×D₄₇	1	1	yes	characteristic
717	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
718	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
719	C₂×Q₈	—	94	2	no	—
720	C₂×Q₈	—	94	2	no	—
721	C₂×Q₈	—	94	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	#10625350	1	4	yes	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	47	2	no	—
742	C₂²×C₄	—	47	2	no	—
743	C₂²×C₄	—	47	2	no	—
744	C₂²×C₄	—	47	2	no	—
745	C₂²×C₄	—	47	2	no	—
746	C₂²×C₄	—	47	2	no	—
747	C₂²×C₄	—	47	2	no	—
748	C₂²×C₄	—	47	2	no	—
749	C₂²×C₄	—	94	4	no	—
750	C₂²×C₄	—	94	4	no	—
751	C₂²×C₄	—	94	4	no	—
752	C₂²×C₄	—	94	4	no	—
753	C₂²×C₄	—	94	4	no	—
754	C₂²×C₄	—	188	2	no	—
755	C₂²×C₄	#10625350	1	4	yes	—
756	C₂²×C₄	#10625350	1	4	yes	—
757	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
758	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
759	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
760	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
761	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
762	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
763	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
765	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
766	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
767	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
768	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	47	4	no	—
774	C₄⋊C₄	—	94	4	no	—
775	C₄⋊C₄	—	94	4	no	—
776	C₄⋊C₄	—	94	4	no	—
777	C₄⋊C₄	—	94	4	no	—
778	C₄⋊C₄	—	94	2	no	—
779	C₄⋊C₄	—	94	2	no	—
780	C₄⋊C₄	—	94	4	no	—
781	C₄⋊C₄	—	94	2	no	—
782	C₄⋊C₄	—	94	4	no	—
783	C₄⋊C₄	—	94	4	no	—
784	C₄⋊C₄	—	94	4	no	—
785	C₄⋊C₄	—	94	4	no	—
786	C₄⋊C₄	—	94	2	no	—
787	C₄⋊C₄	—	94	2	no	—
788	C₄⋊C₄	—	94	2	no	—
789	C₄⋊C₄	—	188	2	no	—
790	C₄⋊C₄	—	188	2	no	—
791	C₄⋊C₄	—	188	2	no	—
792	C₄⋊C₄	—	188	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	94	4	no	—
800	C₂²⋊C₄	—	94	4	no	—
801	C₂²⋊C₄	—	94	4	no	—
802	C₂²⋊C₄	—	94	4	no	—
803	C₂²⋊C₄	—	94	4	no	—
804	C₂²⋊C₄	—	188	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	4	1	no	—
817	C₄²	—	94	4	no	—
818	C₄²	—	94	4	no	—
819	C₄²	—	94	4	no	—
820	C₄²	—	94	4	no	—
821	C₄²	—	94	4	no	—
822	C₄²	—	94	4	no	—
823	C₄²	#10625352	1	4	yes	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	C₂×#10625350	1	2	yes	—
835	C₂³	C₂×#10625350	1	2	yes	—
836	C₂³	C₂×#10625350	1	2	yes	—
837	C₂³	C₂×#10625350	1	2	yes	—
838	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
839	Q₈	—	188	4	no	—
840	D₄	—	2	8	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	8	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	4	no	—
876	C₂×C₄	—	47	4	no	—
877	C₂×C₄	—	94	2	no	—
878	C₂×C₄	—	94	2	no	—
879	C₂×C₄	—	94	2	no	—
880	C₂×C₄	—	94	2	no	—
881	C₂×C₄	—	94	2	no	—
882	C₂×C₄	—	94	2	no	—
883	C₂×C₄	—	94	2	no	—
884	C₂×C₄	—	94	2	no	—
885	C₂×C₄	—	94	2	no	—
886	C₂×C₄	—	94	2	no	—
887	C₂×C₄	—	94	2	no	—
888	C₂×C₄	—	94	2	no	—
889	C₂×C₄	—	94	2	no	—
890	C₂×C₄	—	94	2	no	—
891	C₂×C₄	—	94	2	no	—
892	C₂×C₄	—	94	2	no	—
893	C₂×C₄	—	94	2	no	—
894	C₂×C₄	—	94	2	no	—
895	C₂×C₄	—	94	2	no	—
896	C₂×C₄	—	94	2	no	—
897	C₂×C₄	—	94	2	no	—
898	C₂×C₄	—	94	2	no	—
899	C₂×C₄	—	94	2	no	—
900	C₂×C₄	—	188	8	no	—
901	C₂×C₄	—	188	8	no	—
902	C₂×C₄	#41×D₄₇	1	2	yes	—
903	C₂×C₄	C₂×#10625352	1	2	yes	—
904	C₂×C₄	C₂×#10625352	1	2	yes	—
905	C₂×C₄	C₂×#10625352	1	2	yes	—
906	C₂×C₄	C₂×#10625350	1	2	yes	—
907	C₂×C₄	C₂×#10625350	1	2	yes	—
908	C₂×C₄	C₂×#10625350	1	2	yes	—
909	C₂×C₄	C₂×#10625350	1	2	yes	—
910	C₂×C₄	C₂×#10625350	1	2	yes	—
911	C₂×C₄	#13094071	1	2	yes	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	#15689657	1	4	yes	—
926	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
927	C₂²	C₂²×#10625352	1	1	yes	characteristic
928	C₂²	C₂²×#10625350	1	1	yes	characteristic
929	C₂²	C₂²×#10625350	1	1	yes	characteristic
930	C₂²	C₂²×#10625350	1	1	yes	characteristic
931	C₂²	C₂×#13094071	1	1	yes	characteristic
932	C₂²	#15689959	1	1	yes	characteristic
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	94	4	no	—
945	C₄	—	188	2	no	—
946	C₄	—	188	2	no	—
947	C₄	—	188	2	no	—
948	C₄	—	188	2	no	—
949	C₄	—	188	2	no	—
950	C₄	—	188	2	no	—
951	C₄	—	188	2	no	—
952	C₄	#15689653	1	4	yes	—
953	C₄	#15689813	1	4	yes	—
954	C₂	—	2	4	no	—
955	C₂	—	4	2	no	—
956	C₂	C₂×#15689653	1	1	yes	characteristic
957	C₂	C₂×#15689657	1	1	yes	characteristic
958	C₂	#20256815	1	1	yes	characteristic
959	C₂	C₂×#15689813	1	1	yes	characteristic
960	C₂	#20256946	1	1	yes	characteristic
961	C₂	#20256952	1	1	yes	characteristic
962	C₂	#20257003	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator, socle, cosocle	C₂³×C₄₇	C₂⁵
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₄²×D₄×C₄₇	C₂
prime radical	C₂²×D₄×C₄₇	C₂³
hypercenter	C₄²×D₄	D₄₇
hypocenter	C₄₇	#34780
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
1. #20248130	C₂	semidirect
2. #20248007	C₂	semidirect
3. #20247996	C₂	semidirect
4. #20247926	C₂	semidirect
5. #20247873	C₂	semidirect
6. #20247799	C₂	semidirect
7. #20247767	C₂	semidirect
8. #20247729	C₂	semidirect
10. #20247112	C₂	semidirect
13. #20246695	C₂	semidirect
14. #20246688	C₂	semidirect
15. C₄×#13094016	C₂	semidirect
16. C₄×#13094003	C₂	semidirect
17. C₄×#13094003	C₂	semidirect
19. #20245865	C₂	semidirect
20. #20245786	C₂	semidirect
21. #20245782	C₂	semidirect
22. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
604. C₄₇	#34780	semidirect

Maximal subgroups

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

subgroup	index
#20248130	2
#20248007	2
#20247996	2
#20247926	2
#20247873	2
#20247799	2
#20247767	2
#20247729	2
#20247696	2
#20247112	2
#20246859	2
#20246839	2
#20246695	2
#20246688	2
C₄×#13094016	2
C₄×#13094003	2
C₄×#13094005	2
#20245865	2
#20245786	2
#20245782	2
C₂×C₄×C₄⋊Dic₄₇	2
C₄²×D₄×C₄₇	2
#34780	47