Subgroups — #27094791

Order 12032.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256942	C₂	1	2	yes	maximal, complemented
2	#20255816	C₂	1	1	yes	maximal, characteristic, complemented
3	#20255808	C₂	1	1	yes	maximal, characteristic, complemented
4	#20255797	C₂	1	2	yes	maximal, complemented
5	#20255790	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255786	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255778	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255768	C₂	1	2	yes	maximal, complemented
9	#20255763	C₂	1	2	yes	maximal, complemented
10	#20255756	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255752	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255741	C₂	1	2	yes	maximal, complemented
13	#20255733	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253900	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253305	C₂	1	2	yes	maximal, complemented
16	#20253301	C₂	1	2	yes	maximal, complemented
17	#20253174	C₂	1	2	yes	maximal, complemented
18	#20252970	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252969	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252159	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#427×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094046	C₂²	1	1	yes	characteristic
25	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
26	#15689841	C₂²	1	2	yes	—
27	#15689836	C₂²	1	2	yes	—
28	#15689828	C₂²	1	2	yes	—
29	#15689821	C₂²	1	2	yes	—
30	#15689817	C₂²	1	2	yes	—
31	#15689812	C₂²	1	2	yes	—
32	#15689808	C₂²	1	2	yes	—
33	#15689806	—	2	2	no	—
34	#15689799	—	2	2	no	—
35	#15689797	—	2	2	no	—
36	#15689774	C₂²	1	2	yes	—
37	#15689763	—	2	2	no	—
38	#15689676	C₂²	1	2	yes	—
39	#15689657	—	2	2	no	—
40	#15689651	—	2	2	no	—
41	#15689651	—	2	2	no	—
42	#15689635	C₂²	1	2	yes	—
43	#15689634	C₂²	1	2	yes	—
44	C₄×#10625350	—	2	2	no	—
45	#15689591	C₂²	1	2	yes	—
46	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
47	#117×D₄₇	C₂²	1	2	yes	—
48	#15689527	C₂²	1	1	yes	characteristic, complemented
49	#15689527	C₂²	1	1	yes	characteristic, complemented
50	#15689524	C₂²	1	1	yes	characteristic, complemented
51	#15689524	C₂²	1	1	yes	characteristic, complemented
52	#15689523	C₂²	1	2	yes	complemented
53	#15689520	C₂²	1	2	yes	complemented
54	#15689467	C₂²	1	2	yes	complemented
55	#15689466	C₂²	1	2	yes	complemented
56	#15689464	C₂²	1	2	yes	complemented
57	#15689464	C₂²	1	2	yes	complemented
58	#15689460	C₂²	1	2	yes	complemented
59	#15689458	C₂²	1	2	yes	complemented
60	#15689455	C₂²	1	2	yes	complemented
61	#15689453	C₂²	1	2	yes	complemented
62	#15689450	C₂²	1	2	yes	complemented
63	#15689449	C₂²	1	2	yes	complemented
64	#15689447	C₂²	1	2	yes	complemented
65	#15689447	C₂²	1	2	yes	complemented
66	#15689443	C₂²	1	2	yes	complemented
67	#15689441	C₂²	1	2	yes	complemented
68	#15689438	C₂²	1	2	yes	complemented
69	#15689436	C₂²	1	2	yes	complemented
70	#15689433	C₂²	1	2	yes	complemented
71	#15689429	C₂²	1	2	yes	complemented
72	#15689426	C₂²	1	2	yes	complemented
73	#15689422	C₂²	1	2	yes	complemented
74	#15689417	C₂²	1	2	yes	complemented
75	#15689412	C₂²	1	2	yes	complemented
76	#15689407	C₂²	1	2	yes	complemented
77	#15689402	C₂²	1	2	yes	complemented
78	#15689365	C₂²	1	1	yes	characteristic, complemented
79	#15689365	C₂²	1	1	yes	characteristic, complemented
80	#15689364	C₂²	1	1	yes	characteristic, complemented
81	#15689364	C₂²	1	1	yes	characteristic, complemented
82	#15689360	C₂²	1	1	yes	characteristic, complemented
83	#15689360	C₂²	1	1	yes	characteristic, complemented
84	#15689359	C₂²	1	1	yes	characteristic, complemented
85	#15689359	C₂²	1	1	yes	characteristic, complemented
86	#15689353	C₂²	1	2	yes	complemented
87	#15689353	C₂²	1	2	yes	complemented
88	#15689352	C₂²	1	2	yes	complemented
89	#15689352	C₂²	1	2	yes	complemented
90	#15689217	C₂²	1	1	yes	characteristic, complemented
91	#15689217	C₂²	1	1	yes	characteristic, complemented
92	#15689210	C₂²	1	2	yes	complemented
93	#15689210	C₂²	1	2	yes	complemented
94	#15689205	C₂²	1	1	yes	characteristic, complemented
95	#15689205	C₂²	1	1	yes	characteristic, complemented
96	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
97	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
98	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
99	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
100	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
101	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
102	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
103	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
104	#15689161	C₂²	1	1	yes	characteristic
105	#15689160	C₂²	1	1	yes	characteristic, complemented
106	#15689160	C₂²	1	1	yes	characteristic, complemented
107	#15689159	C₂²	1	2	yes	—
108	#15689159	C₂²	1	2	yes	—
109	#15689158	C₂²	1	2	yes	complemented
110	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
111	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
112	#106×D₄₇	C₂²	1	2	yes	complemented
113	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
114	#15689120	C₂²	1	2	yes	—
115	#15689117	C₂²	1	2	yes	—
116	#15689117	C₂²	1	2	yes	—
117	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
118	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
119	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
120	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
121	C₂×#117×C₄₇	C₂²	1	2	yes	—
122	C₄₇×#427	C₂²	1	1	yes	characteristic
123	C₄₇×#427	C₂²	1	1	yes	characteristic
124	C₄₇×#427	C₂²	1	2	yes	—
125	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#427	C₂²	1	2	yes	complemented
127	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
128	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×#106×C₄₇	C₂²	1	2	yes	complemented
131	C₂×#10625350	—	2	2	no	—
132	C₂×#10625350	C₂³	1	2	yes	—
133	C₂²×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
134	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
135	#13094046	—	2	4	no	—
136	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
137	C₂×#10625325	C₂³	1	2	yes	—
138	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
139	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
140	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
141	C₂×C₈×D₄₇	—	2	4	no	—
142	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
144	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
145	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
146	#13094023	C₂³	1	2	yes	—
147	#13094023	C₂³	1	2	yes	—
148	#13094019	—	2	2	no	—
149	#13094019	—	2	2	no	—
150	#13094018	—	2	2	no	—
151	#13094018	—	2	2	no	—
152	#13094017	—	2	2	no	—
153	#13094017	—	2	2	no	—
154	#13094016	—	2	2	no	—
155	#13094015	C₂³	1	2	yes	—
156	#13094015	C₂³	1	2	yes	—
157	#13094014	—	2	2	no	—
158	#13094014	—	2	2	no	—
159	#13094012	—	2	2	no	—
160	#13094010	—	2	2	no	—
161	#13094010	—	2	2	no	—
162	#13094009	—	2	2	no	—
163	#13094009	—	2	2	no	—
164	#13094008	—	2	2	no	—
165	#13094007	—	2	2	no	—
166	#13094007	—	2	2	no	—
167	#13094007	—	2	2	no	—
168	#13094006	—	2	2	no	—
169	#13094006	—	2	2	no	—
170	#13094004	C₂³	1	2	yes	—
171	#13094004	C₂³	1	2	yes	—
172	#13094003	—	2	2	no	—
173	#13094003	C₂³	1	2	yes	—
174	#13094003	C₂³	1	2	yes	—
175	#13094002	—	2	2	no	—
176	#13094002	—	2	2	no	—
177	#13094001	—	2	2	no	—
178	#13094001	—	2	2	no	—
179	#13093999	C₂³	1	2	yes	—
180	#13093999	C₂³	1	2	yes	—
181	#13093998	—	2	2	no	—
182	#13093998	C₂³	1	2	yes	—
183	#13093998	C₂³	1	2	yes	—
184	#13093997	—	2	2	no	—
185	#13093997	—	2	2	no	—
186	#13093994	—	2	2	no	—
187	#13093993	—	2	2	no	—
188	C₄×Dic₉₄	—	2	2	no	—
189	C₄×Dic₉₄	—	2	2	no	—
190	C₄×Dic₉₄	—	2	2	no	—
191	#13093989	C₂³	1	2	yes	—
192	#13093989	C₂³	1	2	yes	—
193	C₄×D₁₈₈	—	2	2	no	—
194	C₄×D₁₈₈	—	2	2	no	—
195	C₄×D₁₈₈	—	2	2	no	—
196	#13093986	C₂³	1	2	yes	—
197	#13093986	C₂³	1	2	yes	—
198	C₄×C₂²⋊D₄₇	—	2	2	no	—
199	C₄×C₂²⋊D₄₇	—	2	2	no	—
200	C₄×C₂²⋊D₄₇	—	2	2	no	—
201	C₄×C₂²⋊D₄₇	—	2	2	no	—
202	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
203	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
204	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
205	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
206	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
207	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
208	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
209	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
210	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
211	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
212	#13093983	—	2	2	no	—
213	#13093983	C₂³	1	2	yes	—
214	#13093982	C₂³	1	2	yes	—
215	#13093982	C₂³	1	2	yes	—
216	#13093981	—	2	2	no	—
217	#13093981	—	2	2	no	—
218	#13093981	—	2	2	no	—
219	#13093981	—	2	2	no	—
220	#13093980	—	2	2	no	—
221	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
222	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
223	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
225	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
226	C₂²⋊C₄×D₄₇	—	2	2	no	—
227	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
228	C₄²×D₄₇	—	2	2	no	—
229	C₄²×D₄₇	—	2	2	no	—
230	#13093958	C₂³	1	1	yes	characteristic
231	#13093958	C₂³	1	1	yes	characteristic
232	#13093957	C₂³	1	2	yes	—
233	#13093957	C₂³	1	2	yes	—
234	#13093957	C₂³	1	2	yes	—
235	#13093957	C₂³	1	2	yes	—
236	#13093956	C₂³	1	2	yes	—
237	#13093955	C₂³	1	2	yes	—
238	#13093955	C₂³	1	2	yes	—
239	#13093955	C₂³	1	2	yes	—
240	#13093955	C₂³	1	2	yes	—
241	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
242	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	#13093949	C₂³	1	2	yes	—
246	#13093949	C₂³	1	2	yes	—
247	#13093947	C₂³	1	2	yes	—
248	#13093947	C₂³	1	2	yes	—
249	#13093947	C₂³	1	2	yes	—
250	#13093947	C₂³	1	2	yes	—
251	#13093946	C₂³	1	2	yes	—
252	#13093946	C₂³	1	2	yes	—
253	#13093944	C₂³	1	2	yes	—
254	#13093944	C₂³	1	2	yes	—
255	#13093944	C₂³	1	2	yes	—
256	#13093944	C₂³	1	2	yes	—
257	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
258	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
259	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
260	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
261	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
263	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
264	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
269	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₄₇	—	2	4	no	—
271	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
277	#117×C₄₇	—	2	2	no	—
278	#117×C₄₇	—	2	2	no	—
279	#117×C₄₇	C₂³	1	2	yes	—
280	#117×C₄₇	C₂³	1	2	yes	—
281	#117×C₄₇	C₂³	1	2	yes	—
282	#117×C₄₇	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
284	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
285	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
286	C₂×C₄²×C₄₇	—	2	2	no	—
287	#107×C₄₇	C₂³	1	1	yes	characteristic
288	#107×C₄₇	C₂³	1	1	yes	characteristic
289	#107×C₄₇	C₂³	1	1	yes	characteristic
290	#107×C₄₇	C₂³	1	1	yes	characteristic
291	#107×C₄₇	C₂³	1	2	yes	—
292	#107×C₄₇	C₂³	1	2	yes	—
293	#106×C₄₇	C₂³	1	2	yes	—
294	#106×C₄₇	C₂³	1	2	yes	—
295	#106×C₄₇	C₂³	1	2	yes	—
296	#106×C₄₇	C₂³	1	2	yes	—
297	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
298	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₄₇	—	2	2	no	—
300	C₂²×C₄×C₄₇	—	2	2	no	—
301	C₂²×C₄×C₄₇	—	2	2	no	—
302	C₂²×C₄×C₄₇	—	2	2	no	—
303	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
309	C₂×C₂²⋊D₄₇	—	2	4	no	—
310	C₂×C₂²⋊D₄₇	—	2	2	no	—
311	C₂×C₂²⋊D₄₇	—	2	2	no	—
312	C₂×C₂²⋊D₄₇	—	2	2	no	—
313	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
314	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
315	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
316	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
317	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
318	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
319	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
320	#10625350	—	2	4	no	—
321	#10625350	—	2	4	no	—
322	#10625350	—	4	8	no	—
323	C₂×D₁₈₈	—	2	2	no	—
324	C₂×D₁₈₈	—	2	2	no	—
325	C₂×D₁₈₈	C₂⁴	1	2	yes	—
326	C₂×C₄×D₄₇	—	2	2	no	—
327	C₂×C₄×D₄₇	—	2	2	no	—
328	C₂×C₄×D₄₇	—	2	2	no	—
329	C₂×C₄×D₄₇	—	2	2	no	—
330	C₂×C₄×D₄₇	—	2	2	no	—
331	C₂×C₄×D₄₇	—	2	2	no	—
332	C₂×C₄×D₄₇	—	2	2	no	—
333	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
336	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
337	C₂×Dic₉₄	—	2	2	no	—
338	C₂×Dic₉₄	—	2	2	no	—
339	C₂×Dic₉₄	C₂⁴	1	2	yes	—
340	C₂×C₈×C₄₇	—	2	2	no	—
341	C₂×C₈×C₄₇	—	2	2	no	—
342	C₂×C₈×C₄₇	—	2	2	no	—
343	C₂×C₈×C₄₇	—	2	2	no	—
344	C₂×C₈×C₄₇	—	2	2	no	—
345	C₂×C₈×C₄₇	#41	1	4	yes	complemented
346	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
350	C₄⋊C₄×C₄₇	—	2	2	no	—
351	C₄⋊C₄×C₄₇	—	2	2	no	—
352	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
353	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
356	C₂²⋊C₄×C₄₇	—	2	2	no	—
357	C₂²⋊C₄×C₄₇	—	2	2	no	—
358	C₂²⋊C₄×C₄₇	—	2	2	no	—
359	C₂²⋊C₄×C₄₇	—	2	2	no	—
360	C₄²×C₄₇	—	2	2	no	—
361	C₄²×C₄₇	—	2	2	no	—
362	C₄²×C₄₇	—	2	2	no	—
363	C₄²×C₄₇	—	2	2	no	—
364	C₂²⋊Dic₄₇	—	2	2	no	—
365	C₂²⋊Dic₄₇	—	2	2	no	—
366	C₂²⋊Dic₄₇	—	2	2	no	—
367	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
368	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
369	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
370	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
371	(C₂×D₄₇)⋊C₄	—	2	2	no	—
372	(C₂×D₄₇)⋊C₄	—	2	2	no	—
373	(C₂×D₄₇)⋊C₄	—	2	2	no	—
374	(C₂×D₄₇)⋊C₄	—	2	2	no	—
375	(C₂×D₄₇)⋊C₄	—	2	2	no	—
376	(C₂×D₄₇)⋊C₄	—	2	2	no	—
377	(C₂×D₄₇)⋊C₄	—	2	2	no	—
378	(C₂×D₄₇)⋊C₄	—	2	2	no	—
379	(C₂×D₄₇)⋊C₄	—	2	2	no	—
380	(C₂×D₄₇)⋊C₄	—	2	2	no	—
381	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
382	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	C₄⋊Dic₄₇	—	2	2	no	—
386	C₄⋊Dic₄₇	—	2	2	no	—
387	C₄⋊Dic₄₇	—	2	2	no	—
388	C₄⋊Dic₄₇	—	2	2	no	—
389	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
390	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
391	Dic₄₇⋊C₄	—	2	2	no	—
392	Dic₄₇⋊C₄	—	2	2	no	—
393	Dic₄₇⋊C₄	—	2	2	no	—
394	Dic₄₇⋊C₄	—	2	2	no	—
395	Dic₄₇⋊C₄	—	2	2	no	—
396	Dic₄₇⋊C₄	—	2	2	no	—
397	Dic₄₇⋊C₄	—	2	2	no	—
398	Dic₄₇⋊C₄	—	2	2	no	—
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
402	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
403	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄×Dic₄₇	—	2	2	no	—
406	C₄×Dic₄₇	—	2	2	no	—
407	C₄×Dic₄₇	—	2	2	no	—
408	C₄×Dic₄₇	—	2	2	no	—
409	C₄×Dic₄₇	—	2	2	no	—
410	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
413	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₄₇⋊C₈	—	2	2	no	—
415	C₂×C₄₇⋊C₈	—	2	2	no	—
416	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
419	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
420	Dic₁₈₈	—	2	2	no	—
421	D₃₇₆	—	2	2	no	—
422	#10625325	—	2	4	no	—
423	C₈×D₄₇	—	2	2	no	—
424	C₈×D₄₇	—	2	2	no	—
425	C₈×D₄₇	—	2	2	no	—
426	C₈×D₄₇	—	2	2	no	—
427	C₂³×C₄₇	—	2	2	no	—
428	C₂³×C₄₇	—	2	2	no	—
429	C₂³×C₄₇	—	4	1	no	—
430	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
431	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
432	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
433	C₂²×D₄₇	—	2	2	no	—
434	C₂²×D₄₇	—	2	2	no	—
435	C₂²×D₄₇	—	2	2	no	—
436	C₂²×D₄₇	—	4	1	no	—
437	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
438	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₄₇	—	2	2	no	—
440	C₂×C₄×C₄₇	—	2	2	no	—
441	C₂×C₄×C₄₇	—	2	2	no	—
442	C₂×C₄×C₄₇	—	2	1	no	—
443	C₂×C₄×C₄₇	—	2	1	no	—
444	C₂×C₄×C₄₇	—	2	1	no	—
445	C₂×C₄×C₄₇	—	2	1	no	—
446	C₂×C₄×C₄₇	—	2	2	no	—
447	C₂×C₄×C₄₇	—	2	2	no	—
448	C₂×C₄×C₄₇	—	2	2	no	—
449	C₂×C₄×C₄₇	—	2	2	no	—
450	C₂×C₄×C₄₇	—	4	4	no	—
451	C₂×C₄×C₄₇	—	8	2	no	—
452	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
456	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
457	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
458	C₂²⋊D₄₇	—	2	2	no	—
459	C₂²⋊D₄₇	—	2	2	no	—
460	C₂²⋊D₄₇	—	2	2	no	—
461	C₂²⋊D₄₇	—	4	4	no	—
462	C₂²⋊D₄₇	—	4	4	no	—
463	C₂²⋊D₄₇	—	8	2	no	—
464	C₂²⋊D₄₇	#135	1	4	yes	complemented
465	C₂×Dic₄₇	—	2	2	no	—
466	C₂×Dic₄₇	—	2	2	no	—
467	C₂×Dic₄₇	—	2	2	no	—
468	C₂×Dic₄₇	—	2	2	no	—
469	C₂×Dic₄₇	—	2	2	no	—
470	C₂×Dic₄₇	—	4	1	no	—
471	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
477	D₁₈₈	—	2	2	no	—
478	D₁₈₈	—	2	2	no	—
479	D₁₈₈	—	4	4	no	—
480	D₁₈₈	—	8	2	no	—
481	C₄×D₄₇	—	2	2	no	—
482	C₄×D₄₇	—	2	2	no	—
483	C₄×D₄₇	—	2	1	no	—
484	C₄×D₄₇	—	2	1	no	—
485	C₄×D₄₇	—	2	1	no	—
486	C₄×D₄₇	—	2	1	no	—
487	C₄×D₄₇	—	4	4	no	—
488	C₄×D₄₇	—	4	4	no	—
489	C₄×D₄₇	—	4	4	no	—
490	C₄×D₄₇	—	8	2	no	—
491	C₄×D₄₇	—	8	2	no	—
492	Dic₉₄	—	2	2	no	—
493	Dic₉₄	—	2	2	no	—
494	Dic₉₄	—	4	4	no	—
495	Dic₉₄	—	8	2	no	—
496	C₈×C₄₇	—	2	1	no	—
497	C₈×C₄₇	—	2	1	no	—
498	C₈×C₄₇	C₂×#41	1	2	yes	—
499	C₈×C₄₇	C₂×#41	1	2	yes	—
500	C₄₇⋊C₈	—	2	1	no	—
501	C₄₇⋊C₈	—	2	1	no	—
502	C₄₇⋊C₈	—	2	1	no	—
503	C₄₇⋊C₈	—	2	1	no	—
504	#61234	—	47	1	no	maximal, Sylow
505	C₂²×C₄₇	—	2	1	no	—
506	C₂²×C₄₇	—	2	1	no	—
507	C₂²×C₄₇	—	2	1	no	—
508	C₂²×C₄₇	—	2	1	no	—
509	C₂²×C₄₇	—	2	1	no	—
510	C₂²×C₄₇	—	2	1	no	—
511	C₂²×C₄₇	—	2	1	no	—
512	C₂²×C₄₇	—	4	4	no	—
513	C₂²×C₄₇	#547	1	2	yes	—
514	C₂²×C₄₇	C₂×#135	1	2	yes	—
515	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
516	C₂×D₄₇	—	2	1	no	—
517	C₂×D₄₇	—	2	1	no	—
518	C₂×D₄₇	—	2	1	no	—
519	C₂×D₄₇	—	2	1	no	—
520	C₂×D₄₇	—	2	1	no	—
521	C₂×D₄₇	—	4	4	no	—
522	C₂×D₄₇	—	4	2	no	—
523	C₂×D₄₇	—	4	2	no	—
524	C₂×D₄₇	—	4	2	no	—
525	C₂×D₄₇	C₂×#135	1	2	yes	—
526	C₄×C₄₇	—	2	1	no	—
527	C₄×C₄₇	—	2	1	no	—
528	C₄×C₄₇	—	4	2	no	—
529	C₄×C₄₇	—	4	2	no	—
530	C₄×C₄₇	—	4	2	no	—
531	C₄×C₄₇	—	4	2	no	—
532	C₄×C₄₇	#547	1	2	yes	—
533	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
534	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	Dic₄₇	—	2	1	no	—
536	Dic₄₇	—	2	1	no	—
537	Dic₄₇	—	2	1	no	—
538	Dic₄₇	—	2	1	no	—
539	Dic₄₇	—	2	1	no	—
540	Dic₄₇	—	4	2	no	—
541	Dic₄₇	—	4	2	no	—
542	Dic₄₇	—	4	2	no	—
543	Dic₄₇	C₂×#135	1	2	yes	—
544	#3475	—	47	2	no	—
545	#3342	—	47	1	no	—
546	#3341	—	47	1	no	—
547	#3340	—	47	2	no	—
548	#3339	—	47	1	no	—
549	#3339	—	47	1	no	—
550	#3338	—	47	1	no	—
551	#3337	—	47	2	no	—
552	#3337	—	47	2	no	—
553	#3336	—	47	1	no	—
554	#3336	—	47	1	no	—
555	#3335	—	47	2	no	—
556	#3334	—	47	1	no	—
557	#3160	—	47	1	no	—
558	#3091	—	47	2	no	—
559	#3091	—	47	2	no	—
560	#3076	—	47	2	no	—
561	#3050	—	47	1	no	—
562	#3050	—	47	1	no	—
563	C₄×#135	—	47	1	no	—
564	C₂×C₈×D₄	—	47	1	no	—
565	C₂×#427	—	47	1	no	—
566	C₂×#427	D₄₇	1	1	yes	characteristic, complemented
567	C₂×C₄₇	—	2	2	no	—
568	C₂×C₄₇	—	2	2	no	—
569	C₂×C₄₇	—	4	1	no	—
570	C₂×C₄₇	C₂×#547	1	1	yes	characteristic
571	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
572	C₂×C₄₇	#3584	1	1	yes	characteristic
573	D₄₇	—	2	2	no	—
574	D₄₇	—	4	1	no	—
575	D₄₇	—	8	2	no	—
576	C₂×#135	—	47	1	no	—
577	C₂³×C₈	—	47	1	no	—
578	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
579	#556	—	47	2	no	—
580	#555	—	47	2	no	—
581	#554	—	47	2	no	—
582	#553	—	47	2	no	—
583	#553	—	47	2	no	—
584	#552	—	47	2	no	—
585	#552	—	47	2	no	—
586	#552	—	94	2	no	—
587	#551	—	94	2	no	—
588	#551	—	94	2	no	—
589	#547	—	47	2	no	—
590	#546	—	94	2	no	—
591	#533	—	47	2	no	—
592	#529	—	94	2	no	—
593	#529	—	94	2	no	—
594	#529	—	94	2	no	—
595	#525	—	47	2	no	—
596	#525	—	47	2	no	—
597	C₄×#41	—	47	2	no	—
598	C₄×#41	—	94	2	no	—
599	C₂×C₄×D₄	—	47	1	no	—
600	C₂×#117	—	47	2	no	—
601	C₂×#117	C₂×D₄₇	1	2	yes	—
602	#500	—	47	1	no	—
603	#500	—	47	1	no	—
604	#499	—	47	1	no	—
605	#499	—	47	1	no	—
606	#499	—	47	2	no	—
607	#498	—	47	2	no	—
608	#485	—	47	2	no	—
609	#485	—	47	2	no	—
610	#485	—	47	2	no	—
611	#485	—	47	2	no	—
612	#484	—	47	2	no	—
613	#484	—	47	2	no	—
614	#483	—	47	2	no	—
615	#483	—	47	2	no	—
616	#482	—	47	2	no	—
617	#482	—	47	2	no	—
618	#482	—	47	2	no	—
619	#482	—	47	2	no	—
620	#481	—	47	2	no	—
621	#481	—	47	2	no	—
622	#480	—	47	2	no	—
623	#480	—	47	2	no	—
624	#479	—	47	2	no	—
625	#479	—	47	2	no	—
626	#478	—	47	2	no	—
627	#478	—	47	2	no	—
628	#477	—	47	2	no	—
629	#476	—	47	2	no	—
630	#475	—	47	2	no	—
631	#474	—	47	2	no	—
632	#467	—	47	1	no	—
633	#467	—	47	1	no	—
634	#467	—	47	1	no	—
635	#467	—	47	1	no	—
636	#466	—	47	1	no	—
637	#466	—	47	1	no	—
638	#466	—	47	1	no	—
639	#466	—	47	1	no	—
640	#465	—	47	2	no	—
641	#465	—	47	2	no	—
642	#465	—	47	2	no	—
643	#465	—	47	2	no	—
644	C₄×Q₁₆	—	47	1	no	—
645	C₄×Q₁₆	—	47	1	no	—
646	C₄×SD₁₆	—	47	2	no	—
647	C₄×SD₁₆	—	47	2	no	—
648	C₄×D₈	—	47	1	no	—
649	C₄×D₈	—	47	1	no	—
650	C₈×D₄	—	47	1	no	—
651	C₈×D₄	—	47	1	no	—
652	C₈×D₄	—	47	1	no	—
653	C₈×D₄	—	47	1	no	—
654	C₈×D₄	—	47	1	no	—
655	C₈×D₄	—	47	1	no	—
656	C₈×D₄	—	47	1	no	—
657	C₈×D₄	—	47	1	no	—
658	#427	—	47	1	no	—
659	#427	—	47	2	no	—
660	#427	—	47	2	no	—
661	#427	—	47	1	no	—
662	#427	—	47	1	no	—
663	#427	—	47	2	no	—
664	#427	C₂×D₄₇	1	2	yes	—
665	#427	C₂×D₄₇	1	1	yes	characteristic
666	#427	C₂×D₄₇	1	1	yes	characteristic
667	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
668	#427	C₂×D₄₇	1	2	yes	complemented
669	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
670	C₂×#107	—	47	1	no	—
671	C₂×#107	—	47	1	no	—
672	C₂×#107	C₂×D₄₇	1	1	yes	characteristic, complemented
673	C₂×#107	C₂×D₄₇	1	1	yes	characteristic, complemented
674	C₂×#106	—	47	2	no	—
675	C₂×#106	C₂×D₄₇	1	2	yes	complemented
676	C₂×C₄⋊C₈	—	47	1	no	—
677	#416	—	47	2	no	—
678	#416	—	47	2	no	—
679	#416	—	47	2	no	—
680	C₂×C₂²⋊C₈	—	47	1	no	—
681	C₂×C₂²⋊C₈	—	47	1	no	—
682	C₂×C₄×C₈	—	47	1	no	—
683	C₄₇	#61234	1	1	yes	characteristic, complemented, Sylow
684	C₂×#41	—	47	2	no	—
685	C₂×#41	—	94	2	no	—
686	C₂²×D₄	—	47	1	no	—
687	C₂³×C₄	—	47	1	no	—
688	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
689	#135	—	94	4	no	—
690	C₂×Q₁₆	—	47	1	no	—
691	C₂×SD₁₆	—	47	2	no	—
692	C₂×D₈	—	47	1	no	—
693	C₂²×C₈	—	2	4	no	—
694	C₂²×C₈	—	47	1	no	—
695	C₂²×C₈	—	47	1	no	—
696	C₂²×C₈	—	47	1	no	—
697	C₂²×C₈	—	47	1	no	—
698	C₂²×C₈	—	47	1	no	—
699	C₂²×C₈	—	47	1	no	—
700	C₂²×C₈	—	94	4	no	—
701	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
702	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
703	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
704	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
705	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
706	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
707	C₄⋊Q₈	—	47	2	no	—
708	C₄⋊Q₈	—	47	2	no	—
709	#126	—	94	2	no	—
710	#126	—	94	2	no	—
711	#126	—	94	2	no	—
712	#126	—	94	2	no	—
713	#126	—	94	2	no	—
714	#126	—	94	2	no	—
715	#125	—	47	2	no	—
716	#125	—	47	2	no	—
717	#125	—	94	2	no	—
718	#125	—	94	2	no	—
719	#125	—	94	2	no	—
720	#124	—	94	2	no	—
721	#124	—	94	2	no	—
722	#124	—	94	2	no	—
723	#123	—	94	2	no	—
724	#123	—	94	2	no	—
725	#123	—	94	2	no	—
726	#123	—	94	2	no	—
727	#123	—	94	2	no	—
728	#123	—	94	2	no	—
729	#123	—	94	2	no	—
730	#123	—	94	2	no	—
731	C₂²⋊Q₈	—	47	2	no	—
732	C₂²⋊Q₈	—	47	2	no	—
733	C₂²⋊Q₈	—	47	2	no	—
734	C₂²⋊Q₈	—	47	2	no	—
735	C₂²⋊Q₈	—	94	2	no	—
736	C₂²⋊Q₈	—	94	2	no	—
737	C₂²⋊Q₈	—	94	2	no	—
738	C₂²⋊Q₈	—	94	2	no	—
739	C₂²⋊Q₈	—	94	2	no	—
740	#121	—	47	2	no	—
741	#121	—	47	2	no	—
742	#121	—	47	2	no	—
743	#121	—	47	2	no	—
744	#121	—	94	2	no	—
745	#121	—	94	2	no	—
746	#121	—	94	2	no	—
747	#120	—	94	2	no	—
748	#120	—	94	2	no	—
749	C₄×Q₈	—	47	2	no	—
750	C₄×Q₈	—	47	2	no	—
751	C₄×Q₈	—	94	2	no	—
752	C₄×Q₈	—	94	2	no	—
753	C₄×Q₈	—	94	2	no	—
754	C₄×D₄	—	47	1	no	—
755	C₄×D₄	—	47	1	no	—
756	C₄×D₄	—	47	1	no	—
757	C₄×D₄	—	47	1	no	—
758	C₄×D₄	—	47	1	no	—
759	C₄×D₄	—	47	1	no	—
760	C₄×D₄	—	47	1	no	—
761	C₄×D₄	—	47	1	no	—
762	C₄×D₄	—	47	2	no	—
763	C₄×D₄	—	47	2	no	—
764	C₄×D₄	—	94	2	no	—
765	C₄×D₄	—	94	2	no	—
766	C₄×D₄	—	94	2	no	—
767	C₄×D₄	—	94	2	no	—
768	C₄×D₄	—	94	2	no	—
769	C₄×D₄	—	94	2	no	—
770	C₄×D₄	—	94	2	no	—
771	C₄×D₄	—	94	2	no	—
772	C₄×D₄	—	94	2	no	—
773	#117	—	2	2	no	—
774	#117	—	2	2	no	—
775	#117	—	47	2	no	—
776	#117	—	47	2	no	—
777	#117	—	47	2	no	—
778	#117	—	94	2	no	—
779	#117	—	94	2	no	—
780	#117	—	94	2	no	—
781	#117	—	94	2	no	—
782	#117	—	94	2	no	—
783	#117	—	94	2	no	—
784	#117	C₂²×D₄₇	1	2	yes	—
785	#117	C₂²×D₄₇	1	2	yes	—
786	#117	C₂²×D₄₇	1	2	yes	—
787	#117	C₂²×D₄₇	1	2	yes	—
788	C₂×C₄⋊C₄	—	47	1	no	—
789	C₂×C₄⋊C₄	—	47	2	no	—
790	C₂×C₄⋊C₄	—	47	2	no	—
791	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
792	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
793	C₂×C₂²⋊C₄	—	2	2	no	—
794	C₂×C₂²⋊C₄	—	47	1	no	—
795	C₂×C₂²⋊C₄	—	47	1	no	—
796	C₂×C₂²⋊C₄	—	94	2	no	—
797	C₂×C₄²	—	2	2	no	—
798	C₂×C₄²	—	47	1	no	—
799	C₂×C₄²	—	94	2	no	—
800	C₂×C₄²	—	94	2	no	—
801	#107	—	47	1	no	—
802	#107	—	47	1	no	—
803	#107	—	47	2	no	—
804	#107	—	47	2	no	—
805	#107	—	47	2	no	—
806	#107	—	47	2	no	—
807	#107	C₂²×D₄₇	1	1	yes	characteristic
808	#107	C₂²×D₄₇	1	1	yes	characteristic
809	#107	C₂²×D₄₇	1	1	yes	characteristic
810	#107	C₂²×D₄₇	1	1	yes	characteristic
811	#107	C₂²×D₄₇	1	2	yes	—
812	#107	C₂²×D₄₇	1	2	yes	—
813	#106	—	47	2	no	—
814	#106	—	47	2	no	—
815	#106	—	47	2	no	—
816	#106	—	47	2	no	—
817	#106	—	47	2	no	—
818	#106	C₂²×D₄₇	1	2	yes	—
819	#106	C₂²×D₄₇	1	2	yes	—
820	#106	C₂²×D₄₇	1	2	yes	—
821	#106	C₂²×D₄₇	1	2	yes	—
822	C₄⋊C₈	—	47	1	no	—
823	C₄⋊C₈	—	47	1	no	—
824	C₄⋊C₈	—	47	1	no	—
825	C₄⋊C₈	—	47	1	no	—
826	#103	—	47	2	no	—
827	#103	—	47	2	no	—
828	#103	—	47	2	no	—
829	#103	—	47	2	no	—
830	#103	—	47	2	no	—
831	#103	—	47	2	no	—
832	#102	—	47	2	no	—
833	#102	—	47	2	no	—
834	#102	—	47	2	no	—
835	#102	—	47	2	no	—
836	#102	—	47	2	no	—
837	#102	—	47	2	no	—
838	C₂²⋊C₈	—	47	1	no	—
839	C₂²⋊C₈	—	47	1	no	—
840	C₂²⋊C₈	—	47	1	no	—
841	C₂²⋊C₈	—	47	1	no	—
842	C₂²⋊C₈	—	47	1	no	—
843	C₂²⋊C₈	—	47	1	no	—
844	C₂²⋊C₈	—	47	1	no	—
845	C₂²⋊C₈	—	47	1	no	—
846	C₄×C₈	—	47	1	no	—
847	C₄×C₈	—	47	1	no	—
848	C₄×C₈	—	47	1	no	—
849	C₄×C₈	—	47	1	no	—
850	C₂⁴	—	47	1	no	—
851	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
852	#41	—	94	4	no	—
853	#41	—	94	4	no	—
854	#41	—	188	8	no	—
855	C₂×Q₈	—	47	2	no	—
856	C₂×Q₈	—	94	2	no	—
857	C₂×Q₈	—	94	2	no	—
858	C₂×D₄	—	47	1	no	—
859	C₂×D₄	—	47	1	no	—
860	C₂×D₄	—	47	1	no	—
861	C₂×D₄	—	47	1	no	—
862	C₂×D₄	—	47	2	no	—
863	C₂×D₄	—	94	2	no	—
864	C₂×D₄	—	94	2	no	—
865	C₂×D₄	—	94	4	no	—
866	C₂×D₄	—	94	2	no	—
867	C₂×D₄	—	94	2	no	—
868	C₂×D₄	—	94	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	47	1	no	—
874	C₂²×C₄	—	47	1	no	—
875	C₂²×C₄	—	47	1	no	—
876	C₂²×C₄	—	47	1	no	—
877	C₂²×C₄	—	47	1	no	—
878	C₂²×C₄	—	47	1	no	—
879	C₂²×C₄	—	47	1	no	—
880	C₂²×C₄	—	94	2	no	—
881	C₂²×C₄	—	94	2	no	—
882	C₂²×C₄	—	94	2	no	—
883	C₂²×C₄	—	94	2	no	—
884	C₂²×C₄	—	94	2	no	—
885	C₂²×C₄	—	94	2	no	—
886	C₂²×C₄	—	94	2	no	—
887	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
888	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
889	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
890	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
891	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
892	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
893	Q₁₆	—	94	2	no	—
894	SD₁₆	—	94	4	no	—
895	D₈	—	94	2	no	—
896	C₂×C₈	—	2	2	no	—
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	2	2	no	—
900	C₂×C₈	—	2	2	no	—
901	C₂×C₈	—	47	1	no	—
902	C₂×C₈	—	47	1	no	—
903	C₂×C₈	—	47	1	no	—
904	C₂×C₈	—	47	1	no	—
905	C₂×C₈	—	94	2	no	—
906	C₂×C₈	—	94	2	no	—
907	C₂×C₈	—	94	2	no	—
908	C₂×C₈	—	94	2	no	—
909	C₂×C₈	—	94	2	no	—
910	C₂×C₈	—	94	2	no	—
911	C₂×C₈	#10625350	1	4	yes	complemented
912	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	47	1	no	—
919	C₄⋊C₄	—	47	1	no	—
920	C₄⋊C₄	—	47	1	no	—
921	C₄⋊C₄	—	47	1	no	—
922	C₄⋊C₄	—	47	2	no	—
923	C₄⋊C₄	—	47	2	no	—
924	C₄⋊C₄	—	94	2	no	—
925	C₄⋊C₄	—	94	2	no	—
926	C₄⋊C₄	—	94	2	no	—
927	C₄⋊C₄	—	94	2	no	—
928	C₄⋊C₄	—	94	2	no	—
929	C₄⋊C₄	—	94	2	no	—
930	C₄⋊C₄	—	94	2	no	—
931	C₄⋊C₄	—	94	2	no	—
932	C₄⋊C₄	—	94	2	no	—
933	C₄⋊C₄	—	94	2	no	—
934	C₄⋊C₄	—	94	2	no	—
935	C₄⋊C₄	—	94	2	no	—
936	C₄⋊C₄	—	94	2	no	—
937	C₄⋊C₄	—	94	2	no	—
938	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
939	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
940	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
941	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	47	1	no	—
947	C₂²⋊C₄	—	47	1	no	—
948	C₂²⋊C₄	—	47	1	no	—
949	C₂²⋊C₄	—	47	1	no	—
950	C₂²⋊C₄	—	47	1	no	—
951	C₂²⋊C₄	—	47	1	no	—
952	C₂²⋊C₄	—	47	1	no	—
953	C₂²⋊C₄	—	47	1	no	—
954	C₂²⋊C₄	—	94	2	no	—
955	C₂²⋊C₄	—	94	2	no	—
956	C₂²⋊C₄	—	94	2	no	—
957	C₂²⋊C₄	—	94	2	no	—
958	C₂²⋊C₄	—	94	2	no	—
959	C₂²⋊C₄	—	94	2	no	—
960	C₂²⋊C₄	—	94	2	no	—
961	C₂²⋊C₄	—	94	2	no	—
962	C₂²⋊C₄	—	94	2	no	—
963	C₂²⋊C₄	—	94	2	no	—
964	C₂²⋊C₄	—	94	2	no	—
965	C₂²⋊C₄	—	94	2	no	—
966	C₂²⋊C₄	—	94	2	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	47	1	no	—
972	C₄²	—	47	1	no	—
973	C₄²	—	47	1	no	—
974	C₄²	—	47	1	no	—
975	C₄²	—	94	2	no	—
976	C₄²	—	94	2	no	—
977	C₄²	—	94	2	no	—
978	C₄²	—	94	2	no	—
979	C₄²	—	94	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	4	1	no	—
983	C₂³	—	47	1	no	—
984	C₂³	—	47	1	no	—
985	C₂³	—	94	2	no	—
986	C₂³	—	94	2	no	—
987	C₂³	—	94	2	no	—
988	C₂³	—	188	1	no	—
989	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
990	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
991	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
992	Q₈	—	94	2	no	—
993	Q₈	—	94	2	no	—
994	Q₈	—	376	2	no	—
995	Q₈	—	188	4	no	—
996	D₄	—	47	4	no	—
997	D₄	—	94	2	no	—
998	D₄	—	94	2	no	—
999	D₄	—	94	2	no	—
1000	D₄	—	94	2	no	—
1001	D₄	—	94	2	no	—
1002	D₄	—	376	2	no	—
1003	D₄	—	376	2	no	—
1004	D₄	—	188	4	no	—
1005	D₄	—	188	4	no	—
1006	D₄	—	188	4	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	47	1	no	—
1021	C₂×C₄	—	47	1	no	—
1022	C₂×C₄	—	47	1	no	—
1023	C₂×C₄	—	47	1	no	—
1024	C₂×C₄	—	47	1	no	—
1025	C₂×C₄	—	47	1	no	—
1026	C₂×C₄	—	94	2	no	—
1027	C₂×C₄	—	94	2	no	—
1028	C₂×C₄	—	94	2	no	—
1029	C₂×C₄	—	94	2	no	—
1030	C₂×C₄	—	94	1	no	—
1031	C₂×C₄	—	94	1	no	—
1032	C₂×C₄	—	94	1	no	—
1033	C₂×C₄	—	94	1	no	—
1034	C₂×C₄	—	94	2	no	—
1035	C₂×C₄	—	94	2	no	—
1036	C₂×C₄	—	94	2	no	—
1037	C₂×C₄	—	376	2	no	—
1038	C₂×C₄	—	376	2	no	—
1039	C₂×C₄	—	188	4	no	—
1040	C₂×C₄	—	188	4	no	—
1041	C₂×C₄	—	188	1	no	—
1042	C₂×C₄	—	188	4	no	—
1043	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1044	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1045	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1046	C₂×C₄	C₂×#10625350	1	2	yes	—
1047	C₂×C₄	#13094072	1	2	yes	—
1048	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1049	C₈	—	2	1	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	94	1	no	—
1052	C₈	—	94	1	no	—
1053	C₈	—	94	1	no	—
1054	C₈	—	94	1	no	—
1055	C₈	C₂×#10625350	1	2	yes	—
1056	C₈	C₂×#10625350	1	2	yes	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	4	4	no	—
1065	C₂²	—	47	2	no	—
1066	C₂²	—	94	1	no	—
1067	C₂²	—	94	1	no	—
1068	C₂²	—	94	1	no	—
1069	C₂²	—	94	1	no	—
1070	C₂²	—	94	1	no	—
1071	C₂²	—	188	4	no	—
1072	C₂²	—	188	2	no	—
1073	C₂²	—	188	2	no	—
1074	C₂²	—	188	2	no	—
1075	C₂²	#15689774	1	2	yes	—
1076	C₂²	#135×D₄₇	1	2	yes	—
1077	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1078	C₄	—	2	1	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	47	2	no	—
1085	C₄	—	94	1	no	—
1086	C₄	—	94	1	no	—
1087	C₄	—	94	1	no	—
1088	C₄	—	94	1	no	—
1089	C₄	—	94	1	no	—
1090	C₄	—	188	2	no	—
1091	C₄	—	188	2	no	—
1092	C₄	—	188	2	no	—
1093	C₄	#15689774	1	2	yes	—
1094	C₄	C₂²×#10625350	1	1	yes	characteristic
1095	C₄	C₂×#13094072	1	1	yes	characteristic
1096	C₂	—	2	2	no	—
1097	C₂	—	2	2	no	—
1098	C₂	—	4	1	no	—
1099	C₂	—	94	2	no	—
1100	C₂	—	376	2	no	—
1101	C₂	—	188	1	no	—
1102	C₂	C₂×#15689774	1	1	yes	characteristic
1103	C₂	C₂×#135×D₄₇	1	1	yes	characteristic
1104	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#427	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₂×#427	D₄₇
hypocenter	C₄₇	#61234
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
1. #20256942	C₂	semidirect
2. #20255816	C₂	semidirect
3. #20255808	C₂	semidirect
4. #20255797	C₂	semidirect
5. #20255790	C₂	semidirect
6. #20255786	C₂	semidirect
7. #20255778	C₂	semidirect
8. #20255768	C₂	semidirect
9. #20255763	C₂	semidirect
10. #20255756	C₂	semidirect
11. #20255752	C₂	semidirect
12. #20255741	C₂	semidirect
13. #20255733	C₂	semidirect
14. #20253900	C₂	semidirect
15. #20253305	C₂	semidirect
16. #20253301	C₂	semidirect
17. #20253174	C₂	semidirect
18. #20252970	C₂	semidirect
19. #20252969	C₂	semidirect
20. #20252159	C₂	semidirect
21. C₂×C₈×C₂²⋊D₄₇	C₂	semidirect
22. #427×D₄₇	C₂	semidirect
23. C₂×C₄₇×#427	C₂	semidirect
48. #15689527	C₂²	semidirect
49. #15689527	C₂²	semidirect
50. #15689524	C₂²	semidirect
51. #15689524	C₂²	semidirect
52. #15689523	C₂²	semidirect
53. #15689520	C₂²	semidirect
54. #15689467	C₂²	semidirect
55. #15689466	C₂²	semidirect
56. #15689464	C₂²	semidirect
57. #15689464	C₂²	semidirect
58. #15689460	C₂²	semidirect
59. #15689458	C₂²	semidirect
60. #15689455	C₂²	semidirect
61. #15689453	C₂²	semidirect
62. #15689450	C₂²	semidirect
63. #15689449	C₂²	semidirect
64. #15689447	C₂²	semidirect
65. #15689447	C₂²	semidirect
66. #15689443	C₂²	semidirect
67. #15689441	C₂²	semidirect
68. #15689438	C₂²	semidirect
69. #15689436	C₂²	semidirect
70. #15689433	C₂²	semidirect
71. #15689429	C₂²	semidirect
72. #15689426	C₂²	semidirect
73. #15689422	C₂²	semidirect
74. #15689417	C₂²	semidirect
75. #15689412	C₂²	semidirect
76. #15689407	C₂²	semidirect
77. #15689402	C₂²	semidirect
78. #15689365	C₂²	semidirect
79. #15689365	C₂²	semidirect
80. #15689364	C₂²	semidirect
81. #15689364	C₂²	semidirect
82. #15689360	C₂²	semidirect
83. #15689360	C₂²	semidirect
84. #15689359	C₂²	semidirect
85. #15689359	C₂²	semidirect
86. #15689353	C₂²	semidirect
87. #15689353	C₂²	semidirect
88. #15689352	C₂²	semidirect
89. #15689352	C₂²	semidirect
90. #15689217	C₂²	semidirect
91. #15689217	C₂²	semidirect
92. #15689210	C₂²	semidirect
93. #15689210	C₂²	semidirect
94. #15689205	C₂²	semidirect
95. #15689205	C₂²	semidirect
105. #15689160	C₂²	semidirect
106. #15689160	C₂²	semidirect
109. #15689158	C₂²	semidirect
110. #107×D₄₇	C₂²	semidirect
111. #107×D₄₇	C₂²	semidirect
112. #106×D₄₇	C₂²	semidirect
125. C₄₇×#427	C₂²	semidirect
126. C₄₇×#427	C₂²	semidirect
127. C₄₇×#427	C₂²	semidirect
128. C₂×#107×C₄₇	C₂²	semidirect
129. C₂×#107×C₄₇	C₂²	semidirect
130. C₂×#106×C₄₇	C₂²	semidirect
345. C₂×C₈×C₄₇	#41	semidirect
464. C₂²⋊D₄₇	#135	semidirect
566. C₂×#427	D₄₇	semidirect
667. #427	C₂×D₄₇	semidirect
668. #427	C₂×D₄₇	semidirect
669. #427	C₂×D₄₇	semidirect
672. C₂×#107	C₂×D₄₇	semidirect
673. C₂×#107	C₂×D₄₇	semidirect
675. C₂×#106	C₂×D₄₇	semidirect
683. C₄₇	#61234	semidirect
911. C₂×C₈	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20256942	2
#20255816	2
#20255808	2
#20255797	2
#20255790	2
#20255786	2
#20255778	2
#20255768	2
#20255763	2
#20255756	2
#20255752	2
#20255741	2
#20255733	2
#20253900	2
#20253305	2
#20253301	2
#20253174	2
#20252970	2
#20252969	2
#20252159	2
C₂×C₈×C₂²⋊D₄₇	2
#427×D₄₇	2
C₂×C₄₇×#427	2
#61234	47