Subgroups — #26378833

Order 12032.

2024 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689851	C₂	1	1	yes	maximal, characteristic
2	#20246487	C₂	1	2	yes	maximal
3	#20246482	C₂	1	1	yes	maximal, characteristic
4	#20246482	C₂	1	1	yes	maximal, characteristic
5	#20246479	C₂	1	2	yes	maximal
6	#20246477	C₂	1	1	yes	maximal, characteristic
7	#20246476	C₂	1	2	yes	maximal
8	#20246345	C₂	1	1	yes	maximal, characteristic
9	#20246342	C₂	1	2	yes	maximal
10	#20246308	C₂	1	1	yes	maximal, characteristic
11	#20246308	C₂	1	1	yes	maximal, characteristic
12	C₄⋊C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic
13	#20246136	C₂	1	1	yes	maximal, characteristic
14	#20246131	C₂	1	2	yes	maximal
15	#20246129	C₂	1	1	yes	maximal, characteristic
16	#20246126	C₂	1	2	yes	maximal
17	C₄×#13094016	C₂	1	1	yes	maximal, characteristic
18	#20245945	C₂	1	2	yes	maximal
19	#20245861	C₂	1	2	yes	maximal
20	#20245751	C₂	1	1	yes	maximal, characteristic
21	#20245751	C₂	1	1	yes	maximal, characteristic
22	C₄²×Dic₉₄	C₂	1	1	yes	maximal, characteristic
23	C₄₇×#2295	C₂	1	1	yes	maximal, characteristic
24	#15689851	C₄	1	16	yes	complemented
25	C₂×#13094024	C₂²	1	1	yes	characteristic
26	C₂×#13094022	C₂²	1	2	yes	—
27	C₂×#13094016	C₂²	1	1	yes	characteristic
28	C₂×#13094016	C₂²	1	1	yes	characteristic
29	C₂×#13094014	C₂²	1	2	yes	—
30	C₂×#13094014	C₂²	1	2	yes	—
31	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
38	C₂×#13093989	C₂²	1	2	yes	—
39	#15689030	C₂²	1	2	yes	—
40	#15689027	C₂²	1	2	yes	—
41	#15689027	C₂²	1	2	yes	—
42	#15689027	C₂²	1	2	yes	—
43	#15689027	C₂²	1	2	yes	—
44	#15689021	C₂²	1	1	yes	characteristic
45	#15689021	C₂²	1	1	yes	characteristic
46	#15689021	C₂²	1	1	yes	characteristic
47	#15689021	C₂²	1	1	yes	characteristic
48	#15689021	C₂²	1	1	yes	characteristic
49	#15689021	C₂²	1	1	yes	characteristic
50	#15689020	C₂²	1	2	yes	—
51	#15689020	C₂²	1	2	yes	—
52	#15689020	C₂²	1	2	yes	—
53	#15689020	C₂²	1	2	yes	—
54	#15689019	C₂²	1	2	yes	—
55	#15689018	C₂²	1	2	yes	—
56	#15689018	C₂²	1	2	yes	—
57	#15689018	C₂²	1	2	yes	—
58	#15689018	C₂²	1	2	yes	—
59	#15689018	C₂²	1	2	yes	—
60	#15689018	C₂²	1	2	yes	—
61	#15689010	C₂²	1	2	yes	—
62	#15689010	C₂²	1	2	yes	—
63	#15689009	C₂²	1	2	yes	—
64	#15689009	C₂²	1	2	yes	—
65	#15689007	C₂²	1	2	yes	—
66	#15689007	C₂²	1	2	yes	—
67	#15689006	C₂²	1	2	yes	—
68	#15689006	C₂²	1	2	yes	—
69	#15689005	C₂²	1	2	yes	—
70	#15689005	C₂²	1	2	yes	—
71	#15689004	C₂²	1	2	yes	—
72	#15689004	C₂²	1	2	yes	—
73	#15688993	C₂²	1	1	yes	characteristic
74	#15688992	C₂²	1	2	yes	—
75	#15688989	C₂²	1	1	yes	characteristic
76	#15688989	C₂²	1	1	yes	characteristic
77	#15688987	C₂²	1	2	yes	—
78	#15688987	C₂²	1	2	yes	—
79	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
80	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
81	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
82	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
83	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
84	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
85	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
86	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
87	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
88	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
89	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
96	#15688974	C₂²	1	2	yes	—
97	#15688974	C₂²	1	2	yes	—
98	#15688974	C₂²	1	2	yes	—
99	#15688974	C₂²	1	2	yes	—
100	#15688974	C₂²	1	2	yes	—
101	#15688974	C₂²	1	2	yes	—
102	#15688974	C₂²	1	2	yes	—
103	#15688974	C₂²	1	2	yes	—
104	#15688974	C₂²	1	2	yes	—
105	#15688974	C₂²	1	2	yes	—
106	#15688968	C₂²	1	2	yes	—
107	#15688968	C₂²	1	2	yes	—
108	C₄²×Dic₄₇	C₂²	1	2	yes	—
109	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
110	C₄₇×#391	C₂²	1	1	yes	characteristic
111	C₄₇×#391	C₂²	1	1	yes	characteristic
112	C₄₇×#389	C₂²	1	1	yes	characteristic
113	C₄₇×#389	C₂²	1	1	yes	characteristic
114	C₄₇×#387	C₂²	1	1	yes	characteristic
115	C₄₇×#387	C₂²	1	1	yes	characteristic
116	C₄₇×#387	C₂²	1	1	yes	characteristic
117	C₄₇×#387	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
120	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
121	C₄₇×#376	C₂²	1	1	yes	characteristic
122	C₄₇×#376	C₂²	1	1	yes	characteristic
123	C₄³×C₄₇	C₂²	1	1	yes	characteristic
124	C₂²×Dic₉₄	C₂³	1	2	yes	—
125	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
126	#13094024	C₂×C₄	1	8	yes	—
127	#13094022	C₂×C₄	1	16	yes	—
128	#13094016	C₂×C₄	1	8	yes	—
129	#13094016	C₂×C₄	1	8	yes	—
130	#13094014	C₂×C₄	1	16	yes	—
131	#13094014	C₂×C₄	1	16	yes	—
132	C₄×Dic₉₄	—	2	4	no	—
133	C₄×Dic₉₄	—	2	4	no	—
134	C₄×Dic₉₄	—	2	4	no	—
135	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
136	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
137	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
138	C₄×Dic₉₄	Q₈	1	8	yes	complemented
139	#13093989	C₂×C₄	1	16	yes	—
140	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
146	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
149	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
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×Dic₄₇⋊C₄	C₂³	1	2	yes	—
154	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
155	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
156	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
157	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
158	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
159	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
160	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
161	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
162	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
163	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
164	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
165	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
166	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
167	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
168	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
169	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
170	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
171	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
172	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
173	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
174	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
175	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
176	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
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	2	yes	—
182	C₂×C₄×Dic₄₇	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	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	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
204	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
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	#95×C₄₇	C₂³	1	1	yes	characteristic
225	#95×C₄₇	C₂³	1	1	yes	characteristic
226	#95×C₄₇	C₂³	1	1	yes	characteristic
227	#95×C₄₇	C₂³	1	1	yes	characteristic
228	#95×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	#95×C₄₇	C₂³	1	1	yes	characteristic
236	#95×C₄₇	C₂³	1	1	yes	characteristic
237	#95×C₄₇	C₂³	1	1	yes	characteristic
238	C₂×Q₈×C₄₇	—	4	1	no	—
239	C₂×Q₈×C₄₇	—	4	1	no	—
240	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
241	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
256	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
257	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
258	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
259	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
260	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
261	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
262	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
263	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
264	C₂×Dic₉₄	—	4	2	no	—
265	C₂×Dic₉₄	—	4	2	no	—
266	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
267	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
268	C₂×Dic₉₄	C₂×Q₈	1	4	yes	—
269	C₂×Dic₉₄	#41	1	4	yes	—
270	C₄⋊C₄×C₄₇	—	2	2	no	—
271	C₄⋊C₄×C₄₇	—	2	2	no	—
272	C₄⋊C₄×C₄₇	—	4	1	no	—
273	C₄⋊C₄×C₄₇	—	4	1	no	—
274	C₄⋊C₄×C₄₇	—	4	1	no	—
275	C₄⋊C₄×C₄₇	—	4	1	no	—
276	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
277	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
278	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
279	C₄²×C₄₇	—	2	2	no	—
280	C₄²×C₄₇	—	2	2	no	—
281	C₄²×C₄₇	—	2	2	no	—
282	C₄²×C₄₇	—	2	2	no	—
283	C₄²×C₄₇	—	4	1	no	—
284	C₄²×C₄₇	—	4	1	no	—
285	C₄²×C₄₇	—	4	1	no	—
286	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
287	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
288	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
289	C₄²×C₄₇	C₂×Q₈	1	4	yes	—
290	C₄⋊Dic₄₇	—	2	2	no	—
291	C₄⋊Dic₄₇	—	2	2	no	—
292	C₄⋊Dic₄₇	—	2	2	no	—
293	C₄⋊Dic₄₇	—	4	2	no	—
294	C₄⋊Dic₄₇	—	4	2	no	—
295	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
296	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
297	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
298	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
299	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
300	Dic₄₇⋊C₄	—	2	4	no	—
301	Dic₄₇⋊C₄	—	2	4	no	—
302	Dic₄₇⋊C₄	—	2	4	no	—
303	Dic₄₇⋊C₄	—	2	4	no	—
304	Dic₄₇⋊C₄	—	4	2	no	—
305	Dic₄₇⋊C₄	—	4	2	no	—
306	Dic₄₇⋊C₄	—	4	2	no	—
307	Dic₄₇⋊C₄	—	4	2	no	—
308	Dic₄₇⋊C₄	—	4	2	no	—
309	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
310	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
311	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
312	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
313	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
314	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
315	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
316	Dic₄₇⋊C₄	C₂×Q₈	1	8	yes	—
317	C₄×Dic₄₇	—	2	4	no	—
318	C₄×Dic₄₇	—	2	4	no	—
319	C₄×Dic₄₇	—	2	4	no	—
320	C₄×Dic₄₇	—	4	2	no	—
321	C₄×Dic₄₇	—	4	2	no	—
322	C₄×Dic₄₇	—	4	2	no	—
323	C₄×Dic₄₇	—	4	2	no	—
324	C₄×Dic₄₇	—	4	2	no	—
325	C₄×Dic₄₇	—	4	2	no	—
326	C₄×Dic₄₇	—	4	2	no	—
327	C₄×Dic₄₇	—	4	2	no	—
328	C₄×Dic₄₇	—	4	2	no	—
329	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
330	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
331	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
332	C₄×Dic₄₇	C₂×Q₈	1	8	yes	—
333	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
334	Q₈×C₄₇	—	4	4	no	—
335	C₂×C₄×C₄₇	—	2	1	no	—
336	C₂×C₄×C₄₇	—	2	1	no	—
337	C₂×C₄×C₄₇	—	2	1	no	—
338	C₂×C₄×C₄₇	—	2	1	no	—
339	C₂×C₄×C₄₇	—	2	1	no	—
340	C₂×C₄×C₄₇	—	2	1	no	—
341	C₂×C₄×C₄₇	—	2	1	no	—
342	C₂×C₄×C₄₇	—	2	1	no	—
343	C₂×C₄×C₄₇	—	2	1	no	—
344	C₂×C₄×C₄₇	—	2	1	no	—
345	C₂×C₄×C₄₇	—	2	1	no	—
346	C₂×C₄×C₄₇	—	2	1	no	—
347	C₂×C₄×C₄₇	—	2	1	no	—
348	C₂×C₄×C₄₇	—	2	1	no	—
349	C₂×C₄×C₄₇	—	2	1	no	—
350	C₂×C₄×C₄₇	—	2	1	no	—
351	C₂×C₄×C₄₇	—	2	1	no	—
352	C₂×C₄×C₄₇	—	2	1	no	—
353	C₂×C₄×C₄₇	—	2	1	no	—
354	C₂×C₄×C₄₇	—	2	1	no	—
355	C₂×C₄×C₄₇	—	2	1	no	—
356	C₂×C₄×C₄₇	—	2	1	no	—
357	C₂×C₄×C₄₇	—	2	1	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	1	no	—
367	C₂×C₄×C₄₇	—	2	1	no	—
368	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
369	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
370	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
371	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
372	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
373	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
374	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
375	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
376	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
377	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
378	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
379	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
380	C₂×Dic₄₇	—	2	2	no	—
381	C₂×Dic₄₇	—	2	2	no	—
382	C₂×Dic₄₇	—	2	2	no	—
383	C₂×Dic₄₇	—	2	2	no	—
384	C₂×Dic₄₇	—	2	2	no	—
385	C₂×Dic₄₇	—	2	2	no	—
386	C₂×Dic₄₇	—	2	2	no	—
387	C₂×Dic₄₇	—	2	2	no	—
388	C₂×Dic₄₇	—	2	2	no	—
389	C₂×Dic₄₇	—	2	2	no	—
390	C₂×Dic₄₇	—	2	2	no	—
391	C₂×Dic₄₇	—	2	2	no	—
392	C₂×Dic₄₇	—	2	2	no	—
393	C₂×Dic₄₇	—	2	2	no	—
394	C₂×Dic₄₇	—	2	2	no	—
395	C₂×Dic₄₇	—	2	2	no	—
396	C₂×Dic₄₇	—	2	2	no	—
397	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
398	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
399	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
400	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
401	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
402	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
403	C₂×Dic₄₇	C₂×#41	1	4	yes	—
404	Dic₉₄	—	4	8	no	—
405	Dic₉₄	C₄×Q₈	1	16	yes	—
406	#34336	—	47	1	no	maximal, Sylow
407	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
408	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
409	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂²×C₄₇	#585	1	1	yes	characteristic
412	C₂²×C₄₇	#585	1	1	yes	characteristic
413	C₂²×C₄₇	#585	1	1	yes	characteristic
414	C₄×C₄₇	—	2	2	no	—
415	C₄×C₄₇	—	2	2	no	—
416	C₄×C₄₇	—	2	2	no	—
417	C₄×C₄₇	—	2	2	no	—
418	C₄×C₄₇	—	2	2	no	—
419	C₄×C₄₇	—	2	2	no	—
420	C₄×C₄₇	—	2	2	no	—
421	C₄×C₄₇	—	2	2	no	—
422	C₄×C₄₇	—	2	2	no	—
423	C₄×C₄₇	—	4	1	no	—
424	C₄×C₄₇	—	4	1	no	—
425	C₄×C₄₇	—	4	1	no	—
426	C₄×C₄₇	—	4	1	no	—
427	C₄×C₄₇	—	4	1	no	—
428	C₄×C₄₇	C₂×C₄×Q₈	1	4	yes	—
429	Dic₄₇	—	2	4	no	—
430	Dic₄₇	—	2	4	no	—
431	Dic₄₇	—	2	4	no	—
432	Dic₄₇	—	2	4	no	—
433	Dic₄₇	—	4	2	no	—
434	Dic₄₇	—	4	2	no	—
435	Dic₄₇	—	4	2	no	—
436	Dic₄₇	C₂×C₄×Q₈	1	8	yes	—
437	C₂×#557	—	47	1	no	—
438	#2370	—	47	2	no	—
439	#2370	—	47	2	no	—
440	#2370	—	47	1	no	—
441	#2370	—	47	1	no	—
442	#2369	—	47	2	no	—
443	#2369	—	47	1	no	—
444	#2355	—	47	2	no	—
445	#2355	—	47	1	no	—
446	#2351	—	47	1	no	—
447	#2351	—	47	1	no	—
448	Q₈×C₄⋊C₄	—	47	1	no	—
449	#2331	—	47	2	no	—
450	#2331	—	47	1	no	—
451	#2330	—	47	2	no	—
452	#2330	—	47	1	no	—
453	C₄×#125	—	47	2	no	—
454	C₄×#125	—	47	1	no	—
455	#2295	—	47	2	no	—
456	#2295	D₄₇	1	1	yes	characteristic
457	#2276	—	47	1	no	—
458	#2276	—	47	1	no	—
459	C₄²×Q₈	—	47	1	no	—
460	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
461	C₂×C₄₇	#3428	1	1	yes	characteristic
462	C₂×C₄₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂×C₄₇	#3502	1	1	yes	characteristic
464	C₂×C₄₇	#3504	1	1	yes	characteristic
465	C₂×C₄₇	#3516	1	1	yes	characteristic
466	C₂×C₄₇	#3524	1	1	yes	characteristic
467	#557	—	47	16	no	—
468	C₂×C₄⋊Q₈	—	47	2	no	—
469	C₂×C₄⋊Q₈	—	47	1	no	—
470	C₂×#125	—	47	2	no	—
471	C₂×#125	—	47	2	no	—
472	C₂×#125	—	47	1	no	—
473	C₂×#125	—	47	1	no	—
474	C₂×C₄×Q₈	—	47	2	no	—
475	C₂×C₄×Q₈	—	47	1	no	—
476	C₂×C₄×Q₈	—	47	1	no	—
477	C₂×C₄×Q₈	—	47	1	no	—
478	C₂×C₄×Q₈	—	47	1	no	—
479	C₂×C₄×Q₈	—	47	1	no	—
480	C₂×C₄×Q₈	—	47	1	no	—
481	C₂×C₄×Q₈	—	47	1	no	—
482	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
483	#391	—	47	2	no	—
484	#391	—	47	2	no	—
485	#391	—	47	2	no	—
486	#391	—	47	2	no	—
487	#391	—	47	2	no	—
488	#391	C₂×D₄₇	1	1	yes	characteristic
489	#391	C₂×D₄₇	1	1	yes	characteristic
490	#389	—	47	2	no	—
491	#389	—	47	2	no	—
492	#389	—	47	2	no	—
493	#389	—	47	2	no	—
494	#389	—	47	2	no	—
495	#389	—	47	2	no	—
496	#389	—	47	2	no	—
497	#389	—	47	1	no	—
498	#389	—	47	1	no	—
499	#389	—	47	1	no	—
500	#389	—	47	1	no	—
501	#389	—	47	1	no	—
502	#389	—	47	1	no	—
503	#389	—	47	2	no	—
504	#389	—	47	2	no	—
505	#389	—	47	2	no	—
506	#389	—	47	2	no	—
507	#389	C₂×D₄₇	1	1	yes	characteristic
508	#389	C₂×D₄₇	1	1	yes	characteristic
509	#387	—	47	2	no	—
510	#387	—	47	2	no	—
511	#387	—	47	2	no	—
512	#387	—	47	2	no	—
513	#387	—	47	2	no	—
514	#387	—	47	2	no	—
515	#387	—	47	2	no	—
516	#387	—	47	2	no	—
517	#387	—	47	2	no	—
518	#387	—	47	2	no	—
519	#387	—	47	2	no	—
520	#387	—	47	2	no	—
521	#387	C₂×D₄₇	1	1	yes	characteristic
522	#387	C₂×D₄₇	1	1	yes	characteristic
523	#387	C₂×D₄₇	1	1	yes	characteristic
524	#387	C₂×D₄₇	1	1	yes	characteristic
525	#384	—	47	2	no	—
526	#384	—	47	1	no	—
527	#382	—	47	1	no	—
528	#382	—	47	1	no	—
529	#382	—	47	2	no	—
530	#382	—	47	2	no	—
531	C₄×C₄⋊C₄	—	47	2	no	—
532	C₄×C₄⋊C₄	—	47	2	no	—
533	C₄×C₄⋊C₄	—	47	2	no	—
534	C₄×C₄⋊C₄	—	47	1	no	—
535	C₄×C₄⋊C₄	—	47	1	no	—
536	C₄×C₄⋊C₄	—	47	2	no	—
537	C₄×C₄⋊C₄	—	47	2	no	—
538	C₄×C₄⋊C₄	—	47	1	no	—
539	C₄×C₄⋊C₄	—	47	1	no	—
540	C₄×C₄⋊C₄	—	47	1	no	—
541	C₄×C₄⋊C₄	—	47	1	no	—
542	C₄×C₄⋊C₄	—	47	1	no	—
543	C₄×C₄⋊C₄	—	47	1	no	—
544	C₄×C₄⋊C₄	—	47	1	no	—
545	C₄×C₄⋊C₄	—	47	2	no	—
546	C₄×C₄⋊C₄	—	47	2	no	—
547	C₄×C₄⋊C₄	—	47	2	no	—
548	C₄×C₄⋊C₄	—	47	2	no	—
549	C₄×C₄⋊C₄	—	47	2	no	—
550	C₄×C₄⋊C₄	—	47	2	no	—
551	C₄×C₄⋊C₄	—	47	2	no	—
552	C₄×C₄⋊C₄	—	47	2	no	—
553	C₄×C₄⋊C₄	—	47	2	no	—
554	C₄×C₄⋊C₄	—	47	2	no	—
555	C₄×C₄⋊C₄	—	47	2	no	—
556	C₄×C₄⋊C₄	—	47	2	no	—
557	C₄×C₄⋊C₄	—	47	2	no	—
558	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
560	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
561	#376	—	47	2	no	—
562	#376	—	47	2	no	—
563	#376	C₂×D₄₇	1	1	yes	characteristic
564	#376	C₂×D₄₇	1	1	yes	characteristic
565	C₄³	—	47	2	no	—
566	C₄³	C₂×D₄₇	1	1	yes	characteristic
567	C₄₇	#34336	1	1	yes	characteristic, complemented, Sylow
568	C₂²×Q₈	—	47	1	no	—
569	C₂²×Q₈	—	47	2	no	—
570	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
571	C₄⋊Q₈	—	47	16	no	—
572	C₄⋊Q₈	—	47	8	no	—
573	#125	—	47	16	no	—
574	#125	—	47	16	no	—
575	#125	—	47	8	no	—
576	#125	—	47	8	no	—
577	C₄×Q₈	—	47	16	no	—
578	C₄×Q₈	—	47	8	no	—
579	C₄×Q₈	—	47	8	no	—
580	C₄×Q₈	—	47	8	no	—
581	C₄×Q₈	—	47	8	no	—
582	C₄×Q₈	—	94	4	no	—
583	C₄×Q₈	—	94	4	no	—
584	C₄×Q₈	—	94	4	no	—
585	C₄×Q₈	C₄×D₄₇	1	8	yes	—
586	C₂×C₄⋊C₄	—	47	2	no	—
587	C₂×C₄⋊C₄	—	47	2	no	—
588	C₂×C₄⋊C₄	—	47	2	no	—
589	C₂×C₄⋊C₄	—	47	1	no	—
590	C₂×C₄⋊C₄	—	47	2	no	—
591	C₂×C₄⋊C₄	—	47	2	no	—
592	C₂×C₄⋊C₄	—	47	1	no	—
593	C₂×C₄⋊C₄	—	47	1	no	—
594	C₂×C₄⋊C₄	—	47	2	no	—
595	C₂×C₄⋊C₄	—	47	1	no	—
596	C₂×C₄⋊C₄	—	47	2	no	—
597	C₂×C₄⋊C₄	—	47	2	no	—
598	C₂×C₄⋊C₄	—	47	2	no	—
599	C₂×C₄⋊C₄	—	47	2	no	—
600	C₂×C₄⋊C₄	—	47	2	no	—
601	C₂×C₄⋊C₄	—	47	2	no	—
602	C₂×C₄⋊C₄	—	47	1	no	—
603	C₂×C₄⋊C₄	—	47	1	no	—
604	C₂×C₄⋊C₄	—	47	1	no	—
605	C₂×C₄⋊C₄	—	47	2	no	—
606	C₂×C₄⋊C₄	—	47	2	no	—
607	C₂×C₄⋊C₄	—	47	2	no	—
608	C₂×C₄⋊C₄	—	47	2	no	—
609	C₂×C₄⋊C₄	—	47	2	no	—
610	C₂×C₄⋊C₄	—	47	2	no	—
611	C₂×C₄⋊C₄	—	47	2	no	—
612	C₂×C₄⋊C₄	—	47	2	no	—
613	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
622	C₂×C₄²	—	47	2	no	—
623	C₂×C₄²	—	47	2	no	—
624	C₂×C₄²	—	47	2	no	—
625	C₂×C₄²	—	47	2	no	—
626	C₂×C₄²	—	47	2	no	—
627	C₂×C₄²	—	47	2	no	—
628	C₂×C₄²	—	47	2	no	—
629	C₂×C₄²	—	47	2	no	—
630	C₂×C₄²	—	47	2	no	—
631	C₂×C₄²	—	47	2	no	—
632	C₂×C₄²	—	47	2	no	—
633	C₂×C₄²	—	47	2	no	—
634	C₂×C₄²	—	47	2	no	—
635	C₂×C₄²	—	47	2	no	—
636	C₂×C₄²	—	47	2	no	—
637	C₂×C₄²	—	47	2	no	—
638	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
639	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
640	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
641	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
642	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
643	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
644	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
645	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
646	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
647	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
648	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
649	#95	—	47	2	no	—
650	#95	—	47	2	no	—
651	#95	—	47	2	no	—
652	#95	—	47	2	no	—
653	#95	—	47	2	no	—
654	#95	—	47	2	no	—
655	#95	—	47	2	no	—
656	#95	—	47	2	no	—
657	#95	—	47	2	no	—
658	#95	—	47	2	no	—
659	#95	—	47	2	no	—
660	#95	—	47	2	no	—
661	#95	—	47	2	no	—
662	#95	—	47	2	no	—
663	#95	—	47	2	no	—
664	#95	—	47	2	no	—
665	#95	—	47	2	no	—
666	#95	—	47	2	no	—
667	#95	—	47	2	no	—
668	#95	C₂²×D₄₇	1	1	yes	characteristic
669	#95	C₂²×D₄₇	1	1	yes	characteristic
670	#95	C₂²×D₄₇	1	1	yes	characteristic
671	#95	C₂²×D₄₇	1	1	yes	characteristic
672	#95	C₂²×D₄₇	1	1	yes	characteristic
673	#95	C₂²×D₄₇	1	1	yes	characteristic
674	#95	C₂²×D₄₇	1	1	yes	characteristic
675	#95	C₂²×D₄₇	1	1	yes	characteristic
676	#95	C₂²×D₄₇	1	1	yes	characteristic
677	#95	C₂²×D₄₇	1	1	yes	characteristic
678	#95	C₂²×D₄₇	1	1	yes	characteristic
679	#95	C₂²×D₄₇	1	1	yes	characteristic
680	#95	C₂²×D₄₇	1	1	yes	characteristic
681	#95	C₂²×D₄₇	1	1	yes	characteristic
682	C₂×Q₈	—	4	1	no	—
683	C₂×Q₈	—	4	1	no	—
684	C₂×Q₈	—	47	4	no	—
685	C₂×Q₈	—	47	8	no	—
686	C₂×Q₈	—	47	4	no	—
687	C₂×Q₈	—	47	4	no	—
688	C₂×Q₈	—	188	2	no	—
689	C₂×Q₈	—	188	2	no	—
690	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
691	C₂²×C₄	—	47	2	no	—
692	C₂²×C₄	—	47	2	no	—
693	C₂²×C₄	—	47	2	no	—
694	C₂²×C₄	—	47	2	no	—
695	C₂²×C₄	—	47	2	no	—
696	C₂²×C₄	—	47	2	no	—
697	C₂²×C₄	—	47	2	no	—
698	C₂²×C₄	—	47	2	no	—
699	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
700	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
701	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
702	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
703	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
704	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
705	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
706	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
707	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
708	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
709	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
710	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
711	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
712	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
713	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	4	1	no	—
717	C₄⋊C₄	—	4	1	no	—
718	C₄⋊C₄	—	4	1	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	47	8	no	—
721	C₄⋊C₄	—	47	8	no	—
722	C₄⋊C₄	—	47	8	no	—
723	C₄⋊C₄	—	47	8	no	—
724	C₄⋊C₄	—	47	8	no	—
725	C₄⋊C₄	—	47	8	no	—
726	C₄⋊C₄	—	47	8	no	—
727	C₄⋊C₄	—	47	4	no	—
728	C₄⋊C₄	—	47	4	no	—
729	C₄⋊C₄	—	47	4	no	—
730	C₄⋊C₄	—	47	8	no	—
731	C₄⋊C₄	—	47	8	no	—
732	C₄⋊C₄	—	47	4	no	—
733	C₄⋊C₄	—	94	4	no	—
734	C₄⋊C₄	—	94	4	no	—
735	C₄⋊C₄	—	94	4	no	—
736	C₄⋊C₄	—	94	2	no	—
737	C₄⋊C₄	—	94	2	no	—
738	C₄⋊C₄	—	94	2	no	—
739	C₄⋊C₄	—	94	4	no	—
740	C₄⋊C₄	—	188	2	no	—
741	C₄⋊C₄	—	188	2	no	—
742	C₄⋊C₄	—	188	2	no	—
743	C₄⋊C₄	—	188	2	no	—
744	C₄⋊C₄	—	188	2	no	—
745	C₄⋊C₄	—	188	2	no	—
746	C₄⋊C₄	—	188	2	no	—
747	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
748	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
749	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	4	1	no	—
755	C₄²	—	4	1	no	—
756	C₄²	—	4	1	no	—
757	C₄²	—	47	8	no	—
758	C₄²	—	47	8	no	—
759	C₄²	—	47	8	no	—
760	C₄²	—	47	8	no	—
761	C₄²	—	94	4	no	—
762	C₄²	—	94	4	no	—
763	C₄²	—	94	4	no	—
764	C₄²	—	188	2	no	—
765	C₄²	—	188	2	no	—
766	C₄²	—	188	2	no	—
767	C₄²	—	188	2	no	—
768	C₄²	—	188	2	no	—
769	C₄²	—	188	2	no	—
770	C₄²	—	188	2	no	—
771	C₄²	—	188	2	no	—
772	C₄²	—	188	2	no	—
773	C₄²	C₂×C₄×D₄₇	1	4	yes	—
774	C₄²	C₂×C₄×D₄₇	1	4	yes	—
775	C₄²	C₂×C₄×D₄₇	1	4	yes	—
776	C₄²	Q₈×D₄₇	1	4	yes	—
777	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
778	Q₈	—	4	4	no	—
779	Q₈	—	47	16	no	—
780	Q₈	—	188	8	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	47	4	no	—
815	C₂×C₄	—	47	4	no	—
816	C₂×C₄	—	47	4	no	—
817	C₂×C₄	—	47	4	no	—
818	C₂×C₄	—	47	4	no	—
819	C₂×C₄	—	47	4	no	—
820	C₂×C₄	—	47	4	no	—
821	C₂×C₄	—	94	2	no	—
822	C₂×C₄	—	94	2	no	—
823	C₂×C₄	—	94	2	no	—
824	C₂×C₄	—	94	2	no	—
825	C₂×C₄	—	94	2	no	—
826	C₂×C₄	—	94	2	no	—
827	C₂×C₄	—	94	2	no	—
828	C₂×C₄	—	94	2	no	—
829	C₂×C₄	—	94	2	no	—
830	C₂×C₄	—	94	2	no	—
831	C₂×C₄	—	94	2	no	—
832	C₂×C₄	—	94	2	no	—
833	C₂×C₄	—	94	2	no	—
834	C₂×C₄	—	94	2	no	—
835	C₂×C₄	—	94	2	no	—
836	C₂×C₄	—	94	2	no	—
837	C₂×C₄	—	94	2	no	—
838	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
839	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
840	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
841	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
842	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
843	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
844	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
845	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
846	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
847	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
848	C₂×C₄	#41×D₄₇	1	2	yes	—
849	C₂×C₄	#13094071	1	2	yes	—
850	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
851	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
852	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
853	C₂²	C₂×#13094071	1	1	yes	characteristic
854	C₂²	#15689959	1	1	yes	characteristic
855	C₂²	#15689959	1	1	yes	characteristic
856	C₂²	#15689959	1	1	yes	characteristic
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	47	8	no	—
872	C₄	—	94	4	no	—
873	C₄	—	94	4	no	—
874	C₄	—	94	4	no	—
875	C₄	—	94	4	no	—
876	C₄	—	188	2	no	—
877	C₄	—	188	2	no	—
878	C₄	—	188	2	no	—
879	C₄	C₄×Q₈×D₄₇	1	4	yes	—
880	C₂	C₂×C₄×Q₈×D₄₇	1	1	yes	characteristic
881	C₂	#20256589	1	1	yes	characteristic
882	C₂	C₄×#13094071	1	1	yes	characteristic
883	C₂	#20257193	1	1	yes	characteristic
884	C₂	#20257209	1	1	yes	characteristic
885	C₂	#20257377	1	1	yes	characteristic
886	C₂	#20257493	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2295	C₂
socle, prime radical, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	#2295	D₄₇
hypocenter	C₄₇	#34336
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #2295

Complements

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

N	H ≅ G/N	type
24. #15689851	C₄	semidirect
138. C₄×Dic₉₄	Q₈	semidirect
567. C₄₇	#34336	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689851	2
#20246487	2
#20246482	2
#20246479	2
#20246477	2
#20246476	2
#20246345	2
#20246342	2
#20246308	2
C₄⋊C₄×Dic₉₄	2
#20246136	2
#20246131	2
#20246129	2
#20246126	2
C₄×#13094016	2
#20245945	2
#20245861	2
#20245751	2
C₄²×Dic₉₄	2
C₄₇×#2295	2
#34336	47