Subgroups — #26381577

Order 12032.

2032 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689833	C₂	1	1	yes	maximal, characteristic
2	#20246550	C₂	1	2	yes	maximal, complemented
3	#20246549	C₂	1	2	yes	maximal, complemented
4	#20246482	C₂	1	1	yes	maximal, characteristic, complemented
5	#20246482	C₂	1	1	yes	maximal, characteristic, complemented
6	#20246446	C₂	1	1	yes	maximal, characteristic, complemented
7	#20246410	C₂	1	2	yes	maximal, complemented
8	#20246359	C₂	1	1	yes	maximal, characteristic
9	#20246359	C₂	1	1	yes	maximal, characteristic
10	#20246345	C₂	1	1	yes	maximal, characteristic, complemented
11	#20246335	C₂	1	1	yes	maximal, characteristic
12	#20246254	C₂	1	2	yes	maximal, complemented
13	#20246143	C₂	1	2	yes	maximal, complemented
14	#20246142	C₂	1	2	yes	maximal, complemented
15	#20246136	C₂	1	1	yes	maximal, characteristic, complemented
16	#20246129	C₂	1	1	yes	maximal, characteristic, complemented
17	#20246065	C₂	1	2	yes	maximal, complemented
18	#20246032	C₂	1	1	yes	maximal, characteristic
19	#20246032	C₂	1	1	yes	maximal, characteristic
20	#20245987	C₂	1	2	yes	maximal, complemented
21	C₄×#13094016	C₂	1	1	yes	maximal, characteristic, complemented
22	#20245852	C₂	1	1	yes	maximal, characteristic
23	C₄₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689833	C₄	1	16	yes	complemented
25	C₂×#13094024	C₂²	1	1	yes	characteristic
26	C₂×#13094016	C₂²	1	1	yes	characteristic
27	C₂×#13094016	C₂²	1	1	yes	characteristic
28	C₂×#13094002	C₂²	1	2	yes	—
29	C₂×#13094002	C₂²	1	2	yes	—
30	C₂×#13094000	C₂²	1	2	yes	—
31	C₂×#13093989	C₂²	1	2	yes	—
32	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
35	C₂×#13093982	C₂²	1	2	yes	—
36	C₂×#13093981	C₂²	1	2	yes	—
37	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
38	#15689030	C₂²	1	2	yes	—
39	#15689028	C₂²	1	2	yes	—
40	#15689027	C₂²	1	2	yes	—
41	#15689027	C₂²	1	2	yes	—
42	#15689025	C₂²	1	1	yes	characteristic
43	#15689025	C₂²	1	1	yes	characteristic
44	#15689025	C₂²	1	1	yes	characteristic
45	#15689025	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	#15689021	C₂²	1	1	yes	characteristic
51	#15689021	C₂²	1	1	yes	characteristic
52	#15689020	C₂²	1	2	yes	—
53	#15689020	C₂²	1	2	yes	—
54	#15689018	C₂²	1	2	yes	—
55	#15689018	C₂²	1	2	yes	—
56	#15689015	C₂²	1	2	yes	—
57	#15689015	C₂²	1	2	yes	—
58	#15689014	C₂²	1	2	yes	—
59	#15689014	C₂²	1	2	yes	—
60	#15689013	C₂²	1	2	yes	—
61	#15689013	C₂²	1	2	yes	—
62	#15689013	C₂²	1	2	yes	—
63	#15689013	C₂²	1	2	yes	—
64	#15689012	C₂²	1	2	yes	—
65	#15689012	C₂²	1	2	yes	—
66	#15689012	C₂²	1	2	yes	—
67	#15689012	C₂²	1	2	yes	—
68	#15689010	C₂²	1	2	yes	—
69	#15689010	C₂²	1	2	yes	—
70	#15689009	C₂²	1	2	yes	—
71	#15689009	C₂²	1	2	yes	—
72	#15689008	C₂²	1	2	yes	—
73	#15689008	C₂²	1	2	yes	—
74	#15689007	C₂²	1	2	yes	—
75	#15689007	C₂²	1	2	yes	—
76	#15689006	C₂²	1	2	yes	—
77	#15689006	C₂²	1	2	yes	—
78	#15689005	C₂²	1	2	yes	—
79	#15689005	C₂²	1	2	yes	—
80	#15689004	C₂²	1	2	yes	—
81	#15689004	C₂²	1	2	yes	—
82	#15688993	C₂²	1	1	yes	characteristic
83	#15688989	C₂²	1	1	yes	characteristic
84	#15688989	C₂²	1	1	yes	characteristic
85	#15688985	C₂²	1	2	yes	—
86	#15688985	C₂²	1	2	yes	—
87	#15688985	C₂²	1	2	yes	—
88	#15688985	C₂²	1	2	yes	—
89	#15688982	C₂²	1	2	yes	—
90	#15688982	C₂²	1	2	yes	—
91	#15688980	C₂²	1	2	yes	—
92	C₄⋊C₄×Dic₄₇	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	1	yes	characteristic
98	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
104	#15688974	C₂²	1	2	yes	—
105	#15688974	C₂²	1	2	yes	—
106	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
107	#15688970	C₂²	1	2	yes	—
108	#15688970	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×D₁₈₈	C₂³	1	1	yes	characteristic
126	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
127	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
128	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
129	#13094024	C₂×C₄	1	8	yes	—
130	#13094016	C₂×C₄	1	8	yes	—
131	#13094016	C₂×C₄	1	8	yes	—
132	#13094002	C₂×C₄	1	16	yes	—
133	#13094002	C₂×C₄	1	16	yes	—
134	#13094000	C₂×C₄	1	16	yes	—
135	#13093989	—	4	4	no	—
136	C₄×D₁₈₈	C₂×C₄	1	8	yes	—
137	C₄×D₁₈₈	C₂×C₄	1	8	yes	—
138	C₄×D₁₈₈	C₂×C₄	1	8	yes	—
139	#13093982	—	4	4	no	—
140	#13093981	—	4	4	no	—
141	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
146	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
147	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊Dic₄₇	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	C₄⋊C₄×D₄₇	C₂×C₄	1	16	yes	—
162	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
163	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
164	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
165	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
166	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
167	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
168	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
169	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
170	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
171	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
172	C₂×(C₂×D₄₇)⋊C₄	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	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	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	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
203	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
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×C₄²×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	#95×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	C₂³×D₄₇	C₂⁴	1	2	yes	—
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	C₂×D₁₈₈	—	2	2	no	—
264	C₂×D₁₈₈	—	2	2	no	—
265	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
266	C₂×C₄×D₄₇	—	4	2	no	—
267	C₂×C₄×D₄₇	—	4	2	no	—
268	C₂×C₄×D₄₇	—	4	2	no	—
269	C₂×C₄×D₄₇	—	4	2	no	—
270	C₂×C₄×D₄₇	—	4	2	no	—
271	C₂×C₄×D₄₇	—	4	2	no	—
272	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
273	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
274	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
275	C₂×Dic₉₄	—	4	2	no	—
276	C₂×Dic₉₄	—	4	2	no	—
277	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
278	C₄⋊C₄×C₄₇	—	2	2	no	—
279	C₄⋊C₄×C₄₇	—	2	2	no	—
280	C₄⋊C₄×C₄₇	—	4	1	no	—
281	C₄⋊C₄×C₄₇	—	4	1	no	—
282	C₄⋊C₄×C₄₇	—	4	1	no	—
283	C₄⋊C₄×C₄₇	—	4	1	no	—
284	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
285	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
286	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
287	C₄²×C₄₇	—	2	2	no	—
288	C₄²×C₄₇	—	2	2	no	—
289	C₄²×C₄₇	—	2	2	no	—
290	C₄²×C₄₇	—	2	2	no	—
291	C₄²×C₄₇	—	2	2	no	—
292	C₄²×C₄₇	—	4	1	no	—
293	C₄²×C₄₇	—	4	1	no	—
294	C₄²×C₄₇	—	4	1	no	—
295	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
296	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
297	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
298	(C₂×D₄₇)⋊C₄	—	2	4	no	—
299	(C₂×D₄₇)⋊C₄	—	4	2	no	—
300	(C₂×D₄₇)⋊C₄	—	4	2	no	—
301	(C₂×D₄₇)⋊C₄	—	4	2	no	—
302	(C₂×D₄₇)⋊C₄	—	4	2	no	—
303	(C₂×D₄₇)⋊C₄	—	4	2	no	—
304	(C₂×D₄₇)⋊C₄	—	4	2	no	—
305	(C₂×D₄₇)⋊C₄	—	4	2	no	—
306	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	8	yes	—
307	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	8	yes	—
308	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	8	yes	—
309	C₄⋊Dic₄₇	—	2	2	no	—
310	C₄⋊Dic₄₇	—	2	2	no	—
311	C₄⋊Dic₄₇	—	2	2	no	—
312	C₄⋊Dic₄₇	—	2	2	no	—
313	C₄⋊Dic₄₇	—	4	2	no	—
314	C₄⋊Dic₄₇	—	4	2	no	—
315	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
316	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
317	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
318	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
319	Dic₄₇⋊C₄	—	2	4	no	—
320	Dic₄₇⋊C₄	—	4	2	no	—
321	Dic₄₇⋊C₄	—	4	2	no	—
322	Dic₄₇⋊C₄	—	4	2	no	—
323	Dic₄₇⋊C₄	—	4	2	no	—
324	Dic₄₇⋊C₄	—	4	2	no	—
325	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
326	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
327	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
328	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
329	C₄×Dic₄₇	—	2	4	no	—
330	C₄×Dic₄₇	—	4	2	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	—	4	2	no	—
338	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
339	C₂²×D₄₇	—	2	2	no	—
340	C₂²×D₄₇	—	2	2	no	—
341	C₂²×D₄₇	—	2	2	no	—
342	C₂²×D₄₇	—	2	2	no	—
343	C₂²×D₄₇	—	2	2	no	—
344	C₂²×D₄₇	—	2	2	no	—
345	C₂²×D₄₇	C₂³×C₄	1	4	yes	—
346	Q₈×C₄₇	—	4	4	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	—	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	C₂³×C₄	1	2	yes	—
383	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
384	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
385	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
386	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
387	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
388	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
389	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
390	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
391	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
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	—	2	2	no	—
398	C₂×Dic₄₇	—	2	2	no	—
399	C₂×Dic₄₇	—	2	2	no	—
400	C₂×Dic₄₇	—	2	2	no	—
401	C₂×Dic₄₇	—	2	2	no	—
402	C₂×Dic₄₇	—	2	2	no	—
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	C₂³×C₄	1	4	yes	—
411	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
412	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
413	D₁₈₈	—	2	8	no	—
414	C₄×D₄₇	—	4	8	no	—
415	C₄×D₄₇	—	4	8	no	—
416	C₄×D₄₇	—	4	8	no	—
417	Dic₉₄	—	4	8	no	—
418	#34489	—	47	1	no	maximal, Sylow
419	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
420	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂²×C₄₇	#585	1	1	yes	characteristic
424	C₂²×C₄₇	#585	1	1	yes	characteristic
425	C₂²×C₄₇	#585	1	1	yes	characteristic
426	C₂×D₄₇	—	2	4	no	—
427	C₂×D₄₇	—	2	4	no	—
428	C₂×D₄₇	—	2	4	no	—
429	C₂×D₄₇	—	4	2	no	—
430	C₂×D₄₇	—	4	2	no	—
431	C₂×D₄₇	—	4	2	no	—
432	C₂×D₄₇	—	4	2	no	—
433	C₄×C₄₇	—	2	2	no	—
434	C₄×C₄₇	—	2	2	no	—
435	C₄×C₄₇	—	2	2	no	—
436	C₄×C₄₇	—	2	2	no	—
437	C₄×C₄₇	—	2	2	no	—
438	C₄×C₄₇	—	2	2	no	—
439	C₄×C₄₇	—	2	2	no	—
440	C₄×C₄₇	—	4	1	no	—
441	C₄×C₄₇	—	4	1	no	—
442	C₄×C₄₇	—	4	1	no	—
443	C₄×C₄₇	—	4	1	no	—
444	C₄×C₄₇	—	4	1	no	—
445	C₄×C₄₇	—	4	1	no	—
446	C₄×C₄₇	—	4	1	no	—
447	C₄×C₄₇	#519	1	4	yes	—
448	Dic₄₇	—	2	4	no	—
449	Dic₄₇	—	2	4	no	—
450	Dic₄₇	—	2	4	no	—
451	Dic₄₇	—	4	2	no	—
452	Dic₄₇	—	4	2	no	—
453	Dic₄₇	—	4	2	no	—
454	Dic₄₇	—	4	2	no	—
455	C₂×#554	—	47	1	no	—
456	#2378	—	47	2	no	—
457	#2378	—	47	2	no	—
458	#2370	—	47	1	no	—
459	#2370	—	47	1	no	—
460	#2365	—	47	1	no	—
461	#2362	—	47	2	no	—
462	#2357	—	47	1	no	—
463	#2357	—	47	1	no	—
464	#2355	—	47	1	no	—
465	#2354	—	47	1	no	—
466	#2344	—	47	2	no	—
467	#2332	—	47	2	no	—
468	#2332	—	47	2	no	—
469	#2331	—	47	1	no	—
470	#2330	—	47	1	no	—
471	#2323	—	47	2	no	—
472	#2319	—	47	1	no	—
473	#2319	—	47	1	no	—
474	#2313	—	47	2	no	—
475	C₄×#125	—	47	1	no	—
476	#2295	D₄₇	1	1	yes	characteristic, complemented
477	#2293	—	47	1	no	—
478	C₂×C₄₇	C₂×#519	1	1	yes	characteristic
479	C₂×C₄₇	#3428	1	1	yes	characteristic
480	C₂×C₄₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂×C₄₇	#3554	1	1	yes	characteristic
482	C₂×C₄₇	#3557	1	1	yes	characteristic
483	C₂×C₄₇	#3559	1	1	yes	characteristic
484	C₂×C₄₇	#3565	1	1	yes	characteristic
485	D₄₇	—	4	4	no	—
486	#554	—	47	16	no	—
487	C₂×C₄⋊Q₈	—	47	1	no	—
488	C₂×#125	—	47	1	no	—
489	C₂×#125	—	47	1	no	—
490	C₂×C₂²⋊Q₈	—	47	2	no	—
491	C₂×C₂²⋊Q₈	—	47	2	no	—
492	C₂×C₂²⋊Q₈	—	47	2	no	—
493	C₂×C₄×Q₈	—	47	2	no	—
494	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
495	C₂×C₄×D₄	—	47	1	no	—
496	C₂×C₄×D₄	—	47	1	no	—
497	C₂×C₄×D₄	—	47	1	no	—
498	C₂×#117	—	47	2	no	—
499	C₂×#117	—	47	2	no	—
500	C₂²×C₄⋊C₄	—	47	2	no	—
501	#391	—	47	2	no	—
502	#391	—	47	2	no	—
503	#391	—	47	2	no	—
504	#391	—	47	2	no	—
505	#391	C₂×D₄₇	1	1	yes	characteristic
506	#391	C₂×D₄₇	1	1	yes	characteristic
507	#390	—	47	1	no	—
508	#390	—	47	1	no	—
509	#390	—	47	1	no	—
510	#390	—	47	1	no	—
511	#389	—	47	2	no	—
512	#389	—	47	2	no	—
513	#389	—	47	1	no	—
514	#389	—	47	1	no	—
515	#389	—	47	1	no	—
516	#389	—	47	1	no	—
517	#389	—	47	1	no	—
518	#389	—	47	1	no	—
519	#389	—	47	2	no	—
520	#389	—	47	2	no	—
521	#389	C₂×D₄₇	1	1	yes	characteristic
522	#389	C₂×D₄₇	1	1	yes	characteristic
523	#388	—	47	2	no	—
524	#388	—	47	2	no	—
525	#388	—	47	2	no	—
526	#388	—	47	2	no	—
527	#388	—	47	2	no	—
528	#388	—	47	2	no	—
529	#388	—	47	2	no	—
530	#388	—	47	2	no	—
531	#388	—	47	2	no	—
532	#388	—	47	2	no	—
533	#388	—	47	2	no	—
534	#388	—	47	2	no	—
535	#387	—	47	2	no	—
536	#387	—	47	2	no	—
537	#387	—	47	2	no	—
538	#387	—	47	2	no	—
539	#387	—	47	2	no	—
540	#387	—	47	2	no	—
541	#387	—	47	2	no	—
542	#387	—	47	2	no	—
543	#387	—	47	2	no	—
544	#387	—	47	2	no	—
545	#387	—	47	2	no	—
546	#387	—	47	2	no	—
547	#387	—	47	2	no	—
548	#387	—	47	2	no	—
549	#387	C₂×D₄₇	1	1	yes	characteristic
550	#387	C₂×D₄₇	1	1	yes	characteristic
551	#387	C₂×D₄₇	1	1	yes	characteristic
552	#387	C₂×D₄₇	1	1	yes	characteristic
553	#384	—	47	1	no	—
554	#382	—	47	1	no	—
555	#382	—	47	1	no	—
556	#381	—	47	2	no	—
557	#381	—	47	2	no	—
558	#381	—	47	2	no	—
559	#381	—	47	2	no	—
560	#380	—	47	2	no	—
561	#380	—	47	2	no	—
562	#380	—	47	2	no	—
563	C₄×C₄⋊C₄	—	47	2	no	—
564	C₄×C₄⋊C₄	—	47	1	no	—
565	C₄×C₄⋊C₄	—	47	1	no	—
566	C₄×C₄⋊C₄	—	47	2	no	—
567	C₄×C₄⋊C₄	—	47	2	no	—
568	C₄×C₄⋊C₄	—	47	1	no	—
569	C₄×C₄⋊C₄	—	47	1	no	—
570	C₄×C₄⋊C₄	—	47	1	no	—
571	C₄×C₄⋊C₄	—	47	1	no	—
572	C₄×C₄⋊C₄	—	47	1	no	—
573	C₄×C₄⋊C₄	—	47	1	no	—
574	C₄×C₄⋊C₄	—	47	1	no	—
575	C₄×C₄⋊C₄	—	47	2	no	—
576	C₄×C₄⋊C₄	—	47	2	no	—
577	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	—	47	2	no	—
581	C₄×C₂²⋊C₄	—	47	2	no	—
582	C₄×C₂²⋊C₄	—	47	2	no	—
583	#376	C₂×D₄₇	1	1	yes	characteristic
584	#376	C₂×D₄₇	1	1	yes	characteristic
585	C₄³	C₂×D₄₇	1	1	yes	characteristic
586	C₄₇	#34489	1	1	yes	characteristic, complemented, Sylow
587	C₂²×Q₈	—	47	2	no	—
588	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
589	C₂²×D₄	—	47	1	no	—
590	C₂³×C₄	—	47	2	no	—
591	C₂³×C₄	—	47	2	no	—
592	C₂³×C₄	—	47	2	no	—
593	C₄⋊Q₈	—	47	8	no	—
594	#125	—	47	8	no	—
595	#125	—	47	8	no	—
596	C₂²⋊Q₈	—	47	16	no	—
597	C₂²⋊Q₈	—	47	16	no	—
598	C₂²⋊Q₈	—	47	16	no	—
599	C₄×Q₈	—	188	4	no	—
600	C₄×Q₈	C₄×D₄₇	1	8	yes	—
601	C₄×D₄	—	47	8	no	—
602	C₄×D₄	—	47	8	no	—
603	C₄×D₄	—	47	8	no	—
604	#117	—	188	4	no	—
605	#117	—	188	4	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	1	no	—
610	C₂×C₄⋊C₄	—	47	1	no	—
611	C₂×C₄⋊C₄	—	47	1	no	—
612	C₂×C₄⋊C₄	—	47	2	no	—
613	C₂×C₄⋊C₄	—	47	2	no	—
614	C₂×C₄⋊C₄	—	47	16	no	—
615	C₂×C₄⋊C₄	—	47	2	no	—
616	C₂×C₄⋊C₄	—	47	1	no	—
617	C₂×C₄⋊C₄	—	47	1	no	—
618	C₂×C₄⋊C₄	—	47	1	no	—
619	C₂×C₄⋊C₄	—	47	1	no	—
620	C₂×C₄⋊C₄	—	47	2	no	—
621	C₂×C₄⋊C₄	—	47	2	no	—
622	C₂×C₄⋊C₄	—	47	2	no	—
623	C₂×C₄⋊C₄	—	47	2	no	—
624	C₂×C₄⋊C₄	—	47	2	no	—
625	C₂×C₄⋊C₄	—	47	2	no	—
626	C₂×C₄⋊C₄	—	47	2	no	—
627	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	—	47	2	no	—
637	C₂×C₂²⋊C₄	—	47	2	no	—
638	C₂×C₂²⋊C₄	—	47	2	no	—
639	C₂×C₂²⋊C₄	—	47	2	no	—
640	C₂×C₂²⋊C₄	—	47	2	no	—
641	C₂×C₂²⋊C₄	—	47	2	no	—
642	C₂×C₂²⋊C₄	—	47	2	no	—
643	C₂×C₂²⋊C₄	—	47	2	no	—
644	C₂×C₂²⋊C₄	—	47	2	no	—
645	C₂×C₂²⋊C₄	—	47	2	no	—
646	C₂×C₂²⋊C₄	—	47	2	no	—
647	C₂×C₄²	—	47	2	no	—
648	C₂×C₄²	—	47	2	no	—
649	C₂×C₄²	—	47	2	no	—
650	C₂×C₄²	—	47	2	no	—
651	C₂×C₄²	—	47	2	no	—
652	C₂×C₄²	—	47	2	no	—
653	C₂×C₄²	—	47	2	no	—
654	C₂×C₄²	—	47	2	no	—
655	C₂×C₄²	—	47	2	no	—
656	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
657	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
658	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
659	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
660	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
661	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
662	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
663	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
664	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
665	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
666	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
667	#95	—	47	2	no	—
668	#95	—	47	2	no	—
669	#95	—	47	2	no	—
670	#95	—	47	2	no	—
671	#95	—	47	2	no	—
672	#95	—	47	2	no	—
673	#95	—	47	2	no	—
674	#95	—	47	2	no	—
675	#95	—	47	2	no	—
676	#95	—	47	2	no	—
677	#95	—	47	2	no	—
678	#95	—	47	2	no	—
679	#95	—	47	2	no	—
680	#95	—	47	2	no	—
681	#95	—	47	2	no	—
682	#95	—	47	2	no	—
683	#95	—	47	2	no	—
684	#95	—	47	2	no	—
685	#95	—	47	2	no	—
686	#95	C₂²×D₄₇	1	1	yes	characteristic
687	#95	C₂²×D₄₇	1	1	yes	characteristic
688	#95	C₂²×D₄₇	1	1	yes	characteristic
689	#95	C₂²×D₄₇	1	1	yes	characteristic
690	#95	C₂²×D₄₇	1	1	yes	characteristic
691	#95	C₂²×D₄₇	1	1	yes	characteristic
692	#95	C₂²×D₄₇	1	1	yes	characteristic
693	#95	C₂²×D₄₇	1	1	yes	characteristic
694	#95	C₂²×D₄₇	1	1	yes	characteristic
695	#95	C₂²×D₄₇	1	1	yes	characteristic
696	#95	C₂²×D₄₇	1	1	yes	characteristic
697	#95	C₂²×D₄₇	1	1	yes	characteristic
698	#95	C₂²×D₄₇	1	1	yes	characteristic
699	#95	C₂²×D₄₇	1	1	yes	characteristic
700	C₂⁴	—	47	2	no	—
701	C₂×Q₈	—	4	1	no	—
702	C₂×Q₈	—	4	1	no	—
703	C₂×Q₈	—	47	8	no	—
704	C₂×Q₈	—	188	2	no	—
705	C₂×Q₈	—	188	2	no	—
706	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
707	C₂×D₄	—	47	4	no	—
708	C₂×D₄	—	94	2	no	—
709	C₂×D₄	—	94	2	no	—
710	C₂²×C₄	—	47	2	no	—
711	C₂²×C₄	—	47	2	no	—
712	C₂²×C₄	—	47	2	no	—
713	C₂²×C₄	—	47	8	no	—
714	C₂²×C₄	—	47	8	no	—
715	C₂²×C₄	—	47	8	no	—
716	C₂²×C₄	—	47	2	no	—
717	C₂²×C₄	—	47	2	no	—
718	C₂²×C₄	—	47	2	no	—
719	C₂²×C₄	—	47	2	no	—
720	C₂²×C₄	—	188	2	no	—
721	C₂²×C₄	—	188	2	no	—
722	C₂²×C₄	—	188	2	no	—
723	C₂²×C₄	—	188	2	no	—
724	C₂²×C₄	—	188	2	no	—
725	C₂²×C₄	—	188	2	no	—
726	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
727	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
728	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
729	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
730	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
731	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
732	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
733	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
734	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
735	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
736	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
737	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
738	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
739	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
740	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	4	1	no	—
744	C₄⋊C₄	—	4	1	no	—
745	C₄⋊C₄	—	4	1	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	47	8	no	—
748	C₄⋊C₄	—	47	8	no	—
749	C₄⋊C₄	—	47	8	no	—
750	C₄⋊C₄	—	47	8	no	—
751	C₄⋊C₄	—	47	8	no	—
752	C₄⋊C₄	—	47	4	no	—
753	C₄⋊C₄	—	47	4	no	—
754	C₄⋊C₄	—	47	4	no	—
755	C₄⋊C₄	—	94	4	no	—
756	C₄⋊C₄	—	94	2	no	—
757	C₄⋊C₄	—	94	2	no	—
758	C₄⋊C₄	—	94	2	no	—
759	C₄⋊C₄	—	94	2	no	—
760	C₄⋊C₄	—	188	2	no	—
761	C₄⋊C₄	—	188	2	no	—
762	C₄⋊C₄	—	188	2	no	—
763	C₄⋊C₄	—	188	2	no	—
764	C₄⋊C₄	—	188	2	no	—
765	C₄⋊C₄	—	188	2	no	—
766	C₄⋊C₄	—	188	2	no	—
767	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
768	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
769	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
770	C₂²⋊C₄	—	47	8	no	—
771	C₂²⋊C₄	—	47	8	no	—
772	C₂²⋊C₄	—	47	8	no	—
773	C₂²⋊C₄	—	94	4	no	—
774	C₂²⋊C₄	—	188	2	no	—
775	C₂²⋊C₄	—	188	2	no	—
776	C₂²⋊C₄	—	188	2	no	—
777	C₂²⋊C₄	—	188	2	no	—
778	C₂²⋊C₄	—	188	2	no	—
779	C₂²⋊C₄	—	188	2	no	—
780	C₂²⋊C₄	—	188	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	4	1	no	—
787	C₄²	—	4	1	no	—
788	C₄²	—	4	1	no	—
789	C₄²	—	94	4	no	—
790	C₄²	—	188	2	no	—
791	C₄²	—	188	2	no	—
792	C₄²	—	188	2	no	—
793	C₄²	—	188	2	no	—
794	C₄²	—	188	2	no	—
795	C₄²	—	188	2	no	—
796	C₄²	—	188	2	no	—
797	C₄²	—	188	2	no	—
798	C₄²	C₂×C₄×D₄₇	1	4	yes	—
799	C₄²	C₂×C₄×D₄₇	1	4	yes	—
800	C₄²	C₂×C₄×D₄₇	1	4	yes	—
801	C₂³	—	47	4	no	—
802	C₂³	—	94	2	no	—
803	C₂³	—	94	2	no	—
804	C₂³	—	94	2	no	—
805	C₂³	—	94	2	no	—
806	C₂³	—	94	2	no	—
807	C₂³	—	94	2	no	—
808	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
809	Q₈	—	4	4	no	—
810	Q₈	—	188	8	no	—
811	D₄	—	94	8	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	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	—	47	4	no	—
848	C₂×C₄	—	47	4	no	—
849	C₂×C₄	—	47	4	no	—
850	C₂×C₄	—	94	2	no	—
851	C₂×C₄	—	94	2	no	—
852	C₂×C₄	—	94	2	no	—
853	C₂×C₄	—	94	2	no	—
854	C₂×C₄	—	94	2	no	—
855	C₂×C₄	—	94	2	no	—
856	C₂×C₄	—	94	2	no	—
857	C₂×C₄	—	94	2	no	—
858	C₂×C₄	—	94	2	no	—
859	C₂×C₄	—	94	2	no	—
860	C₂×C₄	—	94	2	no	—
861	C₂×C₄	—	94	2	no	—
862	C₂×C₄	—	94	2	no	—
863	C₂×C₄	—	94	2	no	—
864	C₂×C₄	—	94	2	no	—
865	C₂×C₄	—	94	2	no	—
866	C₂×C₄	—	94	2	no	—
867	C₂×C₄	—	94	2	no	—
868	C₂×C₄	—	188	8	no	—
869	C₂×C₄	—	188	8	no	—
870	C₂×C₄	—	188	8	no	—
871	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
872	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
873	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
874	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
875	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
876	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
877	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
878	C₂×C₄	#13094070	1	2	yes	—
879	C₂×C₄	#13094071	1	2	yes	—
880	C₂×C₄	#13094072	1	2	yes	—
881	C₂²	—	94	4	no	—
882	C₂²	—	94	4	no	—
883	C₂²	—	94	4	no	—
884	C₂²	—	188	2	no	—
885	C₂²	—	188	2	no	—
886	C₂²	—	188	2	no	—
887	C₂²	—	188	2	no	—
888	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
889	C₂²	C₂×#13094070	1	1	yes	characteristic
890	C₂²	C₂×#13094071	1	1	yes	characteristic
891	C₂²	C₂×#13094072	1	1	yes	characteristic
892	C₂²	#15689959	1	1	yes	characteristic
893	C₂²	#15689959	1	1	yes	characteristic
894	C₂²	#15689959	1	1	yes	characteristic
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	94	4	no	—
910	C₄	—	94	4	no	—
911	C₄	—	94	4	no	—
912	C₄	—	188	2	no	—
913	C₄	—	188	2	no	—
914	C₄	—	188	2	no	—
915	C₄	—	188	2	no	—
916	C₄	#15689599	1	4	yes	—
917	C₂	—	188	4	no	—
918	C₂	C₂×#15689599	1	1	yes	characteristic
919	C₂	#20256589	1	1	yes	characteristic
920	C₂	C₄×#13094070	1	1	yes	characteristic
921	C₂	#20257859	1	1	yes	characteristic
922	C₂	#20257894	1	1	yes	characteristic
923	C₂	#20257919	1	1	yes	characteristic
924	C₂	#20258033	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2295	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂²×D₁₈₈	C₂³
hypercenter	#2295	D₄₇
hypocenter	C₄₇	#34489
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
2. #20246550	C₂	semidirect
3. #20246549	C₂	semidirect
4. #20246482	C₂	semidirect
5. #20246482	C₂	semidirect
6. #20246446	C₂	semidirect
7. #20246410	C₂	semidirect
10. #20246345	C₂	semidirect
12. #20246254	C₂	semidirect
13. #20246143	C₂	semidirect
14. #20246142	C₂	semidirect
15. #20246136	C₂	semidirect
16. #20246129	C₂	semidirect
17. #20246065	C₂	semidirect
20. #20245987	C₂	semidirect
21. C₄×#13094016	C₂	semidirect
23. C₄₇×#2295	C₂	semidirect
24. #15689833	C₄	semidirect
476. #2295	D₄₇	semidirect
586. C₄₇	#34489	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689833	2
#20246550	2
#20246549	2
#20246482	2
#20246446	2
#20246410	2
#20246359	2
#20246345	2
#20246335	2
#20246254	2
#20246143	2
#20246142	2
#20246136	2
#20246129	2
#20246065	2
#20246032	2
#20245987	2
C₄×#13094016	2
#20245852	2
C₄₇×#2295	2
#34489	47