Subgroups — #27085024

Order 12032.

2214 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689597	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253635	C₂	1	4	yes	maximal, complemented
3	#20253566	C₂	1	4	yes	maximal, complemented
4	#20253522	C₂	1	2	yes	maximal, complemented
5	#20253483	C₂	1	2	yes	maximal, complemented
6	#20253431	C₂	1	2	yes	maximal, complemented
7	#20253392	C₂	1	2	yes	maximal, complemented
8	#20253332	C₂	1	1	yes	maximal, characteristic, complemented
9	#20253297	C₂	1	1	yes	maximal, characteristic, complemented
10	#20253213	C₂	1	2	yes	maximal, complemented
11	#20252896	C₂	1	2	yes	maximal, complemented
12	#20252614	C₂	1	1	yes	maximal, characteristic
13	C₂×#15689273	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252247	C₂	1	2	yes	maximal, complemented
15	#20252216	C₂	1	2	yes	maximal, complemented
16	#20252046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
19	C₂×#13094049	C₂²	1	2	yes	—
20	C₂²×#10625336	C₂²	1	2	yes	—
21	#15689597	—	2	1	no	—
22	#15689597	—	2	2	no	—
23	#15689597	—	2	1	no	—
24	#15689597	C₂²	1	2	yes	—
25	#15689597	C₂²	1	2	yes	—
26	#15689597	C₂²	1	4	yes	—
27	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
28	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
29	C₂×#13093986	—	2	1	no	—
30	C₂×#13093986	—	2	1	no	—
31	C₂×#13093983	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×D₄₇	—	2	2	no	—
33	#15689461	C₂²	1	2	yes	complemented
34	#15689461	C₂²	1	4	yes	complemented
35	#15689456	C₂²	1	1	yes	characteristic, complemented
36	#15689456	C₂²	1	2	yes	complemented
37	#15689451	C₂²	1	2	yes	complemented
38	#15689451	C₂²	1	1	yes	characteristic, complemented
39	#15689444	C₂²	1	2	yes	complemented
40	#15689439	C₂²	1	1	yes	characteristic, complemented
41	#15689434	C₂²	1	1	yes	characteristic, complemented
42	#15689420	C₂²	1	4	yes	complemented
43	#15689420	C₂²	1	4	yes	complemented
44	#15689410	C₂²	1	4	yes	complemented
45	#15689400	C₂²	1	4	yes	complemented
46	#15689335	C₂²	1	4	yes	complemented
47	#15689335	C₂²	1	4	yes	complemented
48	#15689325	C₂²	1	4	yes	complemented
49	#15689325	C₂²	1	4	yes	complemented
50	#15689273	C₂²	1	2	yes	—
51	#15689273	C₂²	1	2	yes	—
52	#15689273	C₂²	1	4	yes	—
53	#15689273	C₂²	1	2	yes	—
54	#15689273	C₂²	1	2	yes	—
55	#15689256	C₂²	1	2	yes	—
56	#15689256	C₂²	1	2	yes	—
57	#15689233	C₂²	1	4	yes	complemented
58	#15689221	C₂²	1	4	yes	complemented
59	#15689221	C₂²	1	4	yes	complemented
60	#15689221	C₂²	1	4	yes	complemented
61	C₄×#10625336	C₂²	1	4	yes	complemented
62	C₄×#10625336	C₂²	1	4	yes	complemented
63	C₄×#10625336	C₂²	1	4	yes	complemented
64	C₄×#10625334	C₂²	1	4	yes	complemented
65	#15689184	C₂²	1	4	yes	complemented
66	#15689180	C₂²	1	2	yes	complemented
67	#15689176	C₂²	1	2	yes	complemented
68	#15689163	C₂²	1	2	yes	complemented
69	#15689159	C₂²	1	2	yes	complemented
70	#15689150	C₂²	1	2	yes	complemented
71	#15689132	C₂²	1	2	yes	complemented
72	#15689127	C₂²	1	2	yes	—
73	#15689119	C₂²	1	2	yes	complemented
74	C₂×#13093944	C₂²	1	2	yes	—
75	#15689087	C₂²	1	1	yes	characteristic
76	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
77	#15689079	C₂²	1	2	yes	complemented
78	C₄₇×#556	—	2	1	no	—
79	C₄₇×#554	—	2	1	no	—
80	C₄₇×#552	—	2	2	no	—
81	C₄₇×#552	—	2	1	no	—
82	C₄₇×#552	—	2	1	no	—
83	C₄₇×#551	—	2	2	no	—
84	C₄₇×#544	C₂²	1	1	yes	characteristic, complemented
85	C₄₇×#542	C₂²	1	2	yes	complemented
86	C₄₇×#541	C₂²	1	2	yes	complemented
87	C₄₇×#536	C₂²	1	1	yes	characteristic, complemented
88	C₄₇×#533	C₂²	1	2	yes	complemented
89	C₄₇×#529	C₂²	1	2	yes	complemented
90	C₄₇×#525	C₂²	1	1	yes	characteristic
91	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
92	C₄₇×#520	C₂²	1	1	yes	characteristic, complemented
93	C₄₇×#519	C₂²	1	1	yes	characteristic, complemented
94	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
95	C₂⁴×D₄₇	—	2	1	no	—
96	C₂²×D₁₈₈	—	2	1	no	—
97	C₂²×D₁₈₈	—	2	1	no	—
98	C₂²×D₁₈₈	—	2	1	no	—
99	C₂²×D₁₈₈	—	2	8	no	—
100	C₂²×D₁₈₈	C₂³	1	2	yes	—
101	C₂²×D₁₈₈	C₂³	1	2	yes	—
102	C₂²×D₁₈₈	C₂³	1	2	yes	—
103	C₂²×C₄×D₄₇	—	2	2	no	—
104	C₂²×C₄×D₄₇	—	2	2	no	—
105	#13094049	—	2	8	no	—
106	C₂×#10625336	—	2	8	no	—
107	C₂×#10625336	C₂³	1	4	yes	—
108	C₂×#10625336	C₂³	1	4	yes	—
109	C₂×#10625336	C₂³	1	4	yes	—
110	C₂×#10625334	C₂³	1	4	yes	—
111	C₂×#10625329	C₂³	1	2	yes	—
112	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
113	C₄×D₁₈₈	—	2	2	no	—
114	C₄×D₁₈₈	—	2	2	no	—
115	C₄×D₁₈₈	—	2	2	no	—
116	C₄×D₁₈₈	—	2	2	no	—
117	C₄×D₁₈₈	C₂³	1	4	yes	—
118	C₄×D₁₈₈	C₂³	1	4	yes	—
119	C₄×D₁₈₈	C₂³	1	4	yes	—
120	C₄×D₁₈₈	C₂³	1	4	yes	—
121	#13093986	—	2	2	no	—
122	#13093986	—	2	2	no	—
123	#13093986	—	2	2	no	—
124	#13093986	—	2	4	no	—
125	#13093986	—	2	2	no	—
126	#13093986	—	2	4	no	—
127	#13093983	—	2	1	no	—
128	#13093983	—	2	1	no	—
129	#13093983	C₂³	1	2	yes	—
130	#13093983	C₂³	1	2	yes	—
131	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
134	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
136	C₂²⋊C₄×D₄₇	—	2	4	no	—
137	C₂²⋊C₄×D₄₇	—	2	4	no	—
138	C₂²⋊C₄×D₄₇	—	2	4	no	—
139	C₂²⋊C₄×D₄₇	—	2	4	no	—
140	C₂×C₄×Dic₄₇	—	2	1	no	—
141	#13093957	C₂³	1	2	yes	complemented
142	#13093957	C₂³	1	2	yes	complemented
143	#13093957	C₂³	1	4	yes	complemented
144	#13093955	C₂³	1	4	yes	complemented
145	#13093955	C₂³	1	2	yes	complemented
146	#13093955	C₂³	1	2	yes	complemented
147	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	complemented
148	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	complemented
149	#13093948	C₂³	1	2	yes	complemented
150	#13093948	C₂³	1	4	yes	complemented
151	#13093948	C₂³	1	4	yes	complemented
152	#13093948	C₂³	1	2	yes	complemented
153	#13093945	C₂³	1	2	yes	complemented
154	#13093945	C₂³	1	2	yes	complemented
155	#13093944	C₂³	1	4	yes	—
156	#13093944	C₂³	1	4	yes	—
157	#13093944	C₂³	1	4	yes	—
158	#13093944	C₂³	1	4	yes	—
159	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
160	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
161	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
162	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
163	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
164	#13093935	C₂³	1	4	yes	complemented
165	C₄×C₄₇⋊C₈	C₂³	1	4	yes	complemented
166	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
167	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₄₇	—	2	1	no	—
170	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	complemented
171	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	complemented
172	#126×C₄₇	—	2	2	no	—
173	#126×C₄₇	—	2	2	no	—
174	#126×C₄₇	—	2	2	no	—
175	#126×C₄₇	—	2	2	no	—
176	#125×C₄₇	—	2	2	no	—
177	#125×C₄₇	—	2	2	no	—
178	#125×C₄₇	—	2	1	no	—
179	#125×C₄₇	—	2	2	no	—
180	#125×C₄₇	C₂³	1	2	yes	complemented
181	#124×C₄₇	—	2	2	no	—
182	#124×C₄₇	C₂³	1	2	yes	complemented
183	#123×C₄₇	—	2	1	no	—
184	#123×C₄₇	—	2	2	no	—
185	#123×C₄₇	—	2	2	no	—
186	#123×C₄₇	—	2	2	no	—
187	C₂²⋊Q₈×C₄₇	—	2	1	no	—
188	C₂²⋊Q₈×C₄₇	—	2	1	no	—
189	C₂²⋊Q₈×C₄₇	—	2	2	no	—
190	C₂²⋊Q₈×C₄₇	—	2	1	no	—
191	C₂²⋊Q₈×C₄₇	—	2	1	no	—
192	C₂²⋊Q₈×C₄₇	—	2	2	no	—
193	C₂²⋊Q₈×C₄₇	—	2	2	no	—
194	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
197	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
198	#121×C₄₇	C₂³	1	1	yes	characteristic
199	#121×C₄₇	C₂³	1	1	yes	characteristic
200	#120×C₄₇	—	2	1	no	—
201	C₄×Q₈×C₄₇	—	2	1	no	—
202	C₄×Q₈×C₄₇	—	2	1	no	—
203	C₄×Q₈×C₄₇	—	2	2	no	—
204	C₄×Q₈×C₄₇	C₂³	1	2	yes	complemented
205	C₄×Q₈×C₄₇	C₂³	1	2	yes	complemented
206	C₄×Q₈×C₄₇	C₂³	1	2	yes	complemented
207	C₄×D₄×C₄₇	—	2	1	no	—
208	C₄×D₄×C₄₇	—	2	1	no	—
209	C₄×D₄×C₄₇	—	2	2	no	—
210	C₄×D₄×C₄₇	—	2	2	no	—
211	C₄×D₄×C₄₇	C₂³	1	2	yes	complemented
212	#117×C₄₇	—	2	2	no	—
213	#117×C₄₇	—	2	1	no	—
214	#117×C₄₇	—	2	2	no	—
215	#117×C₄₇	—	2	2	no	—
216	#117×C₄₇	D₄	1	1	yes	characteristic
217	#117×C₄₇	D₄	1	2	yes	—
218	#117×C₄₇	D₄	1	1	yes	characteristic
219	#117×C₄₇	C₂³	1	1	yes	characteristic
220	#117×C₄₇	C₂³	1	1	yes	characteristic
221	#117×C₄₇	C₂³	1	1	yes	characteristic
222	#117×C₄₇	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
224	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
225	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
229	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
230	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
231	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
232	C₂³×D₄₇	—	2	2	no	—
233	C₂³×D₄₇	—	2	8	no	—
234	C₂³×D₄₇	—	2	2	no	—
235	C₂³×D₄₇	—	2	2	no	—
236	C₂³×D₄₇	—	8	2	no	—
237	C₂³×D₄₇	—	8	2	no	—
238	#41×C₄₇	—	2	4	no	—
239	C₂×Q₈×C₄₇	—	2	1	no	—
240	C₂×Q₈×C₄₇	—	2	2	no	—
241	C₂×Q₈×C₄₇	—	2	4	no	—
242	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₄₇	—	2	1	no	—
245	C₂×D₄×C₄₇	—	2	1	no	—
246	C₂×D₄×C₄₇	—	2	1	no	—
247	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₄₇	—	2	4	no	—
249	C₂²×C₄×C₄₇	—	2	1	no	—
250	C₂²×C₄×C₄₇	—	2	1	no	—
251	C₂²×C₄×C₄₇	—	2	1	no	—
252	C₂²×C₄×C₄₇	—	2	2	no	—
253	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₄₇	C₂×D₄	1	2	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×Dic₄₇	—	2	1	no	—
262	C₂²×Dic₄₇	—	2	1	no	—
263	C₂×D₁₈₈	—	2	8	no	—
264	C₂×D₁₈₈	—	2	8	no	—
265	C₂×D₁₈₈	—	2	8	no	—
266	C₂×D₁₈₈	—	2	2	no	—
267	C₂×D₁₈₈	—	2	2	no	—
268	C₂×D₁₈₈	—	2	2	no	—
269	C₂×D₁₈₈	—	2	4	no	—
270	C₂×D₁₈₈	—	2	8	no	—
271	C₂×D₁₈₈	—	2	8	no	—
272	C₂×D₁₈₈	#41	1	8	yes	—
273	C₂×D₁₈₈	C₂⁴	1	4	yes	—
274	C₂×C₄×D₄₇	—	2	4	no	—
275	C₂×C₄×D₄₇	—	2	4	no	—
276	C₂×C₄×D₄₇	—	2	4	no	—
277	C₂×C₄×D₄₇	—	2	4	no	—
278	C₂×C₄×D₄₇	—	8	4	no	—
279	C₂×C₄×D₄₇	—	8	4	no	—
280	C₄⋊C₄×C₄₇	—	2	1	no	—
281	C₄⋊C₄×C₄₇	—	2	2	no	—
282	C₄⋊C₄×C₄₇	—	2	2	no	—
283	C₄⋊C₄×C₄₇	—	2	2	no	—
284	C₄⋊C₄×C₄₇	—	2	2	no	—
285	C₄⋊C₄×C₄₇	—	2	2	no	—
286	C₄⋊C₄×C₄₇	—	2	2	no	—
287	C₄⋊C₄×C₄₇	—	2	2	no	—
288	C₄⋊C₄×C₄₇	—	2	2	no	—
289	C₄⋊C₄×C₄₇	—	2	1	no	—
290	C₄⋊C₄×C₄₇	—	2	2	no	—
291	C₄⋊C₄×C₄₇	—	2	1	no	—
292	C₄⋊C₄×C₄₇	—	2	2	no	—
293	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
302	C₂²⋊C₄×C₄₇	—	2	2	no	—
303	C₂²⋊C₄×C₄₇	—	2	2	no	—
304	C₂²⋊C₄×C₄₇	—	2	1	no	—
305	C₂²⋊C₄×C₄₇	—	2	1	no	—
306	C₂²⋊C₄×C₄₇	—	2	1	no	—
307	C₂²⋊C₄×C₄₇	—	2	1	no	—
308	C₂²⋊C₄×C₄₇	—	2	2	no	—
309	C₂²⋊C₄×C₄₇	—	2	2	no	—
310	C₂²⋊C₄×C₄₇	—	2	1	no	—
311	C₂²⋊C₄×C₄₇	—	2	2	no	—
312	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
316	C₄²×C₄₇	—	2	2	no	—
317	C₄²×C₄₇	—	2	2	no	—
318	C₄²×C₄₇	—	2	2	no	—
319	C₄²×C₄₇	—	2	1	no	—
320	C₄²×C₄₇	C₂×D₄	1	2	yes	—
321	C₄²×C₄₇	C₂×D₄	1	2	yes	—
322	C₄²×C₄₇	C₂⁴	1	2	yes	—
323	C₄²×C₄₇	C₂⁴	1	2	yes	—
324	C₂²⋊Dic₄₇	—	2	2	no	—
325	C₂²⋊Dic₄₇	—	2	2	no	—
326	#10625336	—	2	8	no	—
327	#10625336	—	2	8	no	—
328	#10625336	—	2	8	no	—
329	#10625334	—	2	8	no	—
330	(C₂×D₄₇)⋊C₄	—	2	4	no	—
331	(C₂×D₄₇)⋊C₄	—	2	4	no	—
332	(C₂×D₄₇)⋊C₄	—	2	4	no	—
333	(C₂×D₄₇)⋊C₄	—	2	4	no	—
334	C₄⋊Dic₄₇	—	2	1	no	—
335	C₄⋊Dic₄₇	—	2	1	no	—
336	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
337	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
338	C₄×Dic₄₇	—	2	2	no	—
339	C₄×Dic₄₇	—	2	2	no	—
340	#10625329	—	2	4	no	—
341	C₂×C₄₇⋊C₈	—	2	4	no	—
342	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
343	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
344	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
345	C₂³×C₄₇	—	2	2	no	—
346	C₂³×C₄₇	—	2	2	no	—
347	C₂³×C₄₇	—	2	1	no	—
348	C₂³×C₄₇	—	4	1	no	—
349	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
350	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
352	C₂²×D₄₇	—	2	8	no	—
353	C₂²×D₄₇	—	2	4	no	—
354	C₂²×D₄₇	—	2	8	no	—
355	C₂²×D₄₇	—	2	8	no	—
356	C₂²×D₄₇	—	4	4	no	—
357	C₂²×D₄₇	—	4	4	no	—
358	C₂²×D₄₇	—	8	2	no	—
359	C₂²×D₄₇	—	8	2	no	—
360	C₂²×D₄₇	—	8	2	no	—
361	C₂²×D₄₇	—	8	2	no	—
362	C₂²×D₄₇	—	8	16	no	—
363	Q₈×C₄₇	—	2	4	no	—
364	Q₈×C₄₇	—	2	2	no	—
365	Q₈×C₄₇	—	4	2	no	—
366	Q₈×C₄₇	—	8	2	no	—
367	D₄×C₄₇	—	2	2	no	—
368	D₄×C₄₇	—	4	2	no	—
369	D₄×C₄₇	—	4	2	no	—
370	D₄×C₄₇	—	8	1	no	—
371	C₂×C₄×C₄₇	—	2	2	no	—
372	C₂×C₄×C₄₇	—	2	4	no	—
373	C₂×C₄×C₄₇	—	2	2	no	—
374	C₂×C₄×C₄₇	—	2	2	no	—
375	C₂×C₄×C₄₇	—	2	2	no	—
376	C₂×C₄×C₄₇	—	2	2	no	—
377	C₂×C₄×C₄₇	—	2	1	no	—
378	C₂×C₄×C₄₇	—	2	1	no	—
379	C₂×C₄×C₄₇	—	2	2	no	—
380	C₂×C₄×C₄₇	—	2	1	no	—
381	C₂×C₄×C₄₇	—	2	2	no	—
382	C₂×C₄×C₄₇	—	4	2	no	—
383	C₂×C₄×C₄₇	—	4	2	no	—
384	C₂×C₄×C₄₇	—	4	2	no	—
385	C₂×C₄×C₄₇	—	8	2	no	—
386	C₂×C₄×C₄₇	—	8	1	no	—
387	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
395	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
396	C₂×Dic₄₇	—	2	2	no	—
397	C₂×Dic₄₇	—	2	2	no	—
398	C₂×Dic₄₇	—	4	2	no	—
399	C₂×Dic₄₇	—	4	2	no	—
400	D₁₈₈	—	2	8	no	—
401	D₁₈₈	—	2	8	no	—
402	D₁₈₈	—	2	8	no	—
403	D₁₈₈	—	2	4	no	—
404	D₁₈₈	C₂×#41	1	8	yes	—
405	C₄×D₄₇	—	8	4	no	—
406	C₄×D₄₇	—	8	4	no	—
407	C₄×D₄₇	—	8	4	no	—
408	C₄×D₄₇	—	8	4	no	—
409	C₄₇⋊C₈	—	2	2	no	—
410	C₄₇⋊C₈	—	2	2	no	—
411	C₄₇⋊C₈	—	2	4	no	—
412	#60579	—	47	1	no	maximal, Sylow
413	C₂²×C₄₇	—	2	1	no	—
414	C₂²×C₄₇	—	2	1	no	—
415	C₂²×C₄₇	—	2	1	no	—
416	C₂²×C₄₇	—	2	1	no	—
417	C₂²×C₄₇	—	2	1	no	—
418	C₂²×C₄₇	—	2	1	no	—
419	C₂²×C₄₇	—	2	1	no	—
420	C₂²×C₄₇	—	4	4	no	—
421	C₂²×C₄₇	—	4	1	no	—
422	C₂²×C₄₇	—	4	1	no	—
423	C₂²×C₄₇	—	4	1	no	—
424	C₂²×C₄₇	#525	1	2	yes	—
425	C₂²×C₄₇	#577	1	2	yes	—
426	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
427	C₂×D₄₇	—	2	8	no	—
428	C₂×D₄₇	—	4	16	no	—
429	C₂×D₄₇	—	4	4	no	—
430	C₂×D₄₇	—	4	4	no	—
431	C₂×D₄₇	—	8	8	no	—
432	C₂×D₄₇	—	8	8	no	—
433	C₄×C₄₇	—	2	2	no	—
434	C₄×C₄₇	—	2	2	no	—
435	C₄×C₄₇	—	2	1	no	—
436	C₄×C₄₇	—	2	1	no	—
437	C₄×C₄₇	—	2	2	no	—
438	C₄×C₄₇	—	2	2	no	—
439	C₄×C₄₇	—	4	2	no	—
440	C₄×C₄₇	—	4	1	no	—
441	C₄×C₄₇	—	4	1	no	—
442	C₄×C₄₇	—	4	2	no	—
443	C₄×C₄₇	—	4	1	no	—
444	C₄×C₄₇	#525	1	2	yes	—
445	C₄×C₄₇	C₂²×#41	1	2	yes	—
446	Dic₄₇	—	4	2	no	—
447	Dic₄₇	—	4	2	no	—
448	#3495	D₄₇	1	1	yes	characteristic, complemented
449	C₂×#518	—	47	1	no	—
450	#3123	—	47	4	no	—
451	#3118	—	47	4	no	—
452	#3114	—	47	2	no	—
453	#3110	—	47	2	no	—
454	#3105	—	47	2	no	—
455	#3101	—	47	2	no	—
456	#3095	—	47	1	no	—
457	#3091	—	47	1	no	—
458	#3081	—	47	2	no	—
459	#3042	—	47	2	no	—
460	#3003	—	47	1	no	—
461	C₂×#450	—	47	1	no	—
462	#2949	—	47	2	no	—
463	#2946	—	47	2	no	—
464	#2924	—	47	1	no	—
465	C₂×C₄₇	—	2	2	no	—
466	C₂×C₄₇	—	2	2	no	—
467	C₂×C₄₇	—	4	1	no	—
468	C₂×C₄₇	—	8	1	no	—
469	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
470	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
471	C₂×C₄₇	#3585	1	1	yes	characteristic
472	D₄₇	—	4	8	no	—
473	C₂³×D₄	—	47	1	no	—
474	C₂×AGL(1,ℤ/8)	—	47	2	no	—
475	C₂²×SD₁₆	—	47	2	no	—
476	#556	—	2	1	no	—
477	#554	—	2	1	no	—
478	#552	—	2	2	no	—
479	#552	—	2	1	no	—
480	#552	—	2	1	no	—
481	#551	—	2	2	no	—
482	#544	C₂×D₄₇	1	1	yes	characteristic, complemented
483	#542	C₂×D₄₇	1	2	yes	complemented
484	#541	C₂×D₄₇	1	2	yes	complemented
485	#536	C₂×D₄₇	1	1	yes	characteristic, complemented
486	#533	C₂×D₄₇	1	2	yes	complemented
487	#529	C₂×D₄₇	1	2	yes	complemented
488	#525	C₂×D₄₇	1	1	yes	characteristic
489	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
490	#520	C₂×D₄₇	1	1	yes	characteristic, complemented
491	#519	C₂×D₄₇	1	1	yes	characteristic, complemented
492	#518	—	47	2	no	—
493	#518	—	47	4	no	—
494	#518	—	47	2	no	—
495	#518	—	94	2	no	—
496	#518	—	94	1	no	—
497	#518	—	94	1	no	—
498	C₂×C₄×D₄	—	47	2	no	—
499	C₂×C₄×D₄	—	47	2	no	—
500	C₂×C₄×D₄	—	94	1	no	—
501	C₂×C₄×D₄	—	94	1	no	—
502	C₂×#117	—	47	1	no	—
503	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
504	C₂²×C₂²⋊C₄	—	94	2	no	—
505	#485	—	47	2	no	—
506	#485	—	47	4	no	—
507	#484	—	47	1	no	—
508	#484	—	47	2	no	—
509	#483	—	47	1	no	—
510	#483	—	47	2	no	—
511	#482	—	47	2	no	—
512	#481	—	47	1	no	—
513	#480	—	47	1	no	—
514	#478	—	47	4	no	—
515	#478	—	47	4	no	—
516	#476	—	47	4	no	—
517	#474	—	47	4	no	—
518	#463	—	47	4	no	—
519	#463	—	47	4	no	—
520	#461	—	47	4	no	—
521	#461	—	47	4	no	—
522	#450	—	47	2	no	—
523	#450	—	47	2	no	—
524	#450	—	47	2	no	—
525	#450	—	47	4	no	—
526	#450	—	47	2	no	—
527	#447	—	47	2	no	—
528	#447	—	47	2	no	—
529	#442	—	47	4	no	—
530	#440	—	47	4	no	—
531	#440	—	47	4	no	—
532	#440	—	47	4	no	—
533	C₄×SD₁₆	—	47	4	no	—
534	C₄×SD₁₆	—	47	4	no	—
535	C₄×SD₁₆	—	47	4	no	—
536	C₄×D₈	—	47	4	no	—
537	#433	—	47	4	no	—
538	#432	—	47	2	no	—
539	#431	—	47	2	no	—
540	#428	—	47	2	no	—
541	#427	—	47	2	no	—
542	#424	—	47	2	no	—
543	#419	—	47	2	no	—
544	#418	—	47	2	no	—
545	#416	—	47	2	no	—
546	C₂×#102	—	47	2	no	—
547	#407	—	47	1	no	—
548	C₂×C₂²⋊C₈	—	47	1	no	—
549	#405	—	47	2	no	—
550	C₄₇	#60579	1	1	yes	characteristic, complemented, Sylow
551	C₂⁵	—	94	1	no	—
552	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
553	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
554	C₂²×D₄	—	47	2	no	—
555	C₂²×D₄	—	47	2	no	—
556	C₂²×D₄	—	47	2	no	—
557	C₂²×D₄	—	94	8	no	—
558	C₂²×D₄	—	94	1	no	—
559	C₂²×D₄	—	94	1	no	—
560	C₂²×D₄	—	94	1	no	—
561	C₂³×C₄	—	94	2	no	—
562	C₂³×C₄	—	94	2	no	—
563	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
564	AGL(1,ℤ/8)	—	94	8	no	—
565	C₂×SD₁₆	—	47	4	no	—
566	C₂×SD₁₆	—	47	4	no	—
567	C₂×SD₁₆	—	47	4	no	—
568	C₂×SD₁₆	—	94	8	no	—
569	C₂×D₈	—	47	4	no	—
570	C₂×M₁₆	—	47	2	no	—
571	C₂²×C₈	—	47	2	no	—
572	C₄⋊Q₈	—	2	1	no	—
573	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	complemented
574	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	complemented
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#125	—	2	2	no	—
580	#125	—	2	2	no	—
581	#125	—	2	1	no	—
582	#125	—	2	2	no	—
583	#125	C₂²×D₄₇	1	2	yes	complemented
584	#124	—	2	2	no	—
585	#124	C₂²×D₄₇	1	2	yes	complemented
586	#123	—	2	1	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
598	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
599	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
600	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
601	#121	C₂²×D₄₇	1	1	yes	characteristic
602	#121	C₂²×D₄₇	1	1	yes	characteristic
603	#120	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	C₂²×D₄₇	1	2	yes	complemented
608	C₄×Q₈	C₂²×D₄₇	1	2	yes	complemented
609	C₄×Q₈	C₂²×D₄₇	1	2	yes	complemented
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	47	4	no	—
615	C₄×D₄	—	47	4	no	—
616	C₄×D₄	—	47	4	no	—
617	C₄×D₄	—	47	4	no	—
618	C₄×D₄	—	94	2	no	—
619	C₄×D₄	—	94	2	no	—
620	C₄×D₄	—	94	2	no	—
621	C₄×D₄	—	94	4	no	—
622	C₄×D₄	—	94	2	no	—
623	C₄×D₄	—	94	4	no	—
624	C₄×D₄	—	94	2	no	—
625	C₄×D₄	—	94	2	no	—
626	C₄×D₄	—	94	2	no	—
627	C₄×D₄	—	94	2	no	—
628	C₄×D₄	C₂²×D₄₇	1	2	yes	complemented
629	#117	—	2	2	no	—
630	#117	—	2	1	no	—
631	#117	—	2	2	no	—
632	#117	—	2	2	no	—
633	#117	—	47	2	no	—
634	#117	—	47	2	no	—
635	#117	—	94	1	no	—
636	#117	—	94	1	no	—
637	#117	C₂²⋊D₄₇	1	1	yes	characteristic
638	#117	C₂²⋊D₄₇	1	2	yes	—
639	#117	C₂²⋊D₄₇	1	1	yes	characteristic
640	#117	C₂²×D₄₇	1	1	yes	characteristic
641	#117	C₂²×D₄₇	1	1	yes	characteristic
642	#117	C₂²×D₄₇	1	1	yes	characteristic
643	#117	C₂²×D₄₇	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	47	1	no	—
647	C₂×C₄⋊C₄	—	47	1	no	—
648	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	94	1	no	—
653	C₂×C₂²⋊C₄	—	94	2	no	—
654	C₂×C₂²⋊C₄	—	94	2	no	—
655	C₂×C₂²⋊C₄	—	94	4	no	—
656	C₂×C₂²⋊C₄	—	94	4	no	—
657	C₂×C₂²⋊C₄	—	94	4	no	—
658	C₂×C₂²⋊C₄	—	94	4	no	—
659	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
660	C₂×C₄²	—	94	1	no	—
661	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
662	#107	—	47	2	no	—
663	#107	—	47	2	no	—
664	#107	—	47	4	no	—
665	#106	—	47	2	no	—
666	#106	—	47	2	no	—
667	#106	—	47	4	no	—
668	C₄⋊C₈	—	47	4	no	—
669	C₄⋊C₈	—	47	4	no	—
670	#103	—	47	2	no	—
671	#103	—	47	2	no	—
672	#103	—	47	4	no	—
673	#103	—	47	4	no	—
674	#102	—	47	2	no	—
675	#102	—	47	2	no	—
676	#102	—	47	4	no	—
677	#102	—	47	4	no	—
678	#102	—	47	4	no	—
679	#102	—	47	4	no	—
680	C₂²⋊C₈	—	47	1	no	—
681	C₂²⋊C₈	—	47	1	no	—
682	C₂²⋊C₈	—	47	2	no	—
683	C₂²⋊C₈	—	47	2	no	—
684	C₂²⋊C₈	—	47	2	no	—
685	#97	—	47	4	no	—
686	C₄×C₈	—	47	4	no	—
687	C₂⁴	—	94	8	no	—
688	C₂⁴	—	94	2	no	—
689	C₂⁴	—	94	2	no	—
690	C₂⁴	—	94	2	no	—
691	C₂⁴	—	376	2	no	—
692	C₂⁴	—	376	2	no	—
693	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
694	#41	—	2	4	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
699	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	47	8	no	—
704	C₂×D₄	—	47	4	no	—
705	C₂×D₄	—	94	8	no	—
706	C₂×D₄	—	94	8	no	—
707	C₂×D₄	—	94	8	no	—
708	C₂×D₄	—	94	8	no	—
709	C₂×D₄	—	94	8	no	—
710	C₂×D₄	—	94	2	no	—
711	C₂×D₄	—	94	2	no	—
712	C₂×D₄	—	94	2	no	—
713	C₂×D₄	—	94	4	no	—
714	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	94	1	no	—
721	C₂²×C₄	—	94	1	no	—
722	C₂²×C₄	—	94	4	no	—
723	C₂²×C₄	—	94	4	no	—
724	C₂²×C₄	—	94	4	no	—
725	C₂²×C₄	—	94	4	no	—
726	C₂²×C₄	—	376	4	no	—
727	C₂²×C₄	—	376	4	no	—
728	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
729	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
730	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
731	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
732	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
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	SD₁₆	—	94	8	no	—
737	SD₁₆	—	94	8	no	—
738	SD₁₆	—	94	8	no	—
739	D₈	—	94	8	no	—
740	M₁₆	—	94	4	no	—
741	C₂×C₈	—	47	2	no	—
742	C₂×C₈	—	47	4	no	—
743	C₂×C₈	—	47	2	no	—
744	C₂×C₈	—	94	4	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	47	2	no	—
759	C₄⋊C₄	—	47	2	no	—
760	C₄⋊C₄	—	94	1	no	—
761	C₄⋊C₄	—	94	1	no	—
762	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
763	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
764	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
765	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
766	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
767	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
768	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
769	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
770	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	94	2	no	—
782	C₂²⋊C₄	—	94	2	no	—
783	C₂²⋊C₄	—	94	4	no	—
784	C₂²⋊C₄	—	94	4	no	—
785	C₂²⋊C₄	—	94	4	no	—
786	C₂²⋊C₄	—	94	4	no	—
787	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
788	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
789	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
790	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	1	no	—
795	C₄²	—	94	2	no	—
796	C₄²	—	94	2	no	—
797	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
798	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
799	C₄²	C₂³×D₄₇	1	2	yes	—
800	C₄²	C₂³×D₄₇	1	2	yes	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	94	8	no	—
806	C₂³	—	94	8	no	—
807	C₂³	—	94	8	no	—
808	C₂³	—	94	4	no	—
809	C₂³	—	376	2	no	—
810	C₂³	—	376	2	no	—
811	C₂³	—	376	2	no	—
812	C₂³	—	376	2	no	—
813	C₂³	—	376	16	no	—
814	C₂³	—	188	4	no	—
815	C₂³	—	188	4	no	—
816	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
817	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
818	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
819	Q₈	—	2	4	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	—	8	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	2	no	—
826	D₄	—	8	1	no	—
827	D₄	—	47	8	no	—
828	D₄	—	94	8	no	—
829	D₄	—	94	8	no	—
830	D₄	—	94	8	no	—
831	D₄	—	94	4	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	—	8	1	no	—
848	C₂×C₄	—	94	2	no	—
849	C₂×C₄	—	94	2	no	—
850	C₂×C₄	—	376	4	no	—
851	C₂×C₄	—	376	4	no	—
852	C₂×C₄	—	376	4	no	—
853	C₂×C₄	—	376	4	no	—
854	C₂×C₄	—	188	2	no	—
855	C₂×C₄	—	188	2	no	—
856	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
857	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
858	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
859	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
860	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
861	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
862	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
863	C₂×C₄	#41×D₄₇	1	4	yes	—
864	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
865	C₈	—	94	2	no	—
866	C₈	—	94	2	no	—
867	C₈	—	94	4	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	4	4	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	94	8	no	—
880	C₂²	—	376	8	no	—
881	C₂²	—	376	8	no	—
882	C₂²	—	188	16	no	—
883	C₂²	—	188	4	no	—
884	C₂²	—	188	4	no	—
885	C₂²	#15689630	1	2	yes	—
886	C₂²	#15689931	1	2	yes	—
887	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	1	no	—
899	C₄	—	188	2	no	—
900	C₄	—	188	2	no	—
901	C₄	#15689630	1	2	yes	—
902	C₄	C₂×#41×D₄₇	1	2	yes	—
903	C₂	—	2	2	no	—
904	C₂	—	2	2	no	—
905	C₂	—	4	1	no	—
906	C₂	—	8	1	no	—
907	C₂	—	188	8	no	—
908	C₂	C₂×#15689630	1	1	yes	characteristic
909	C₂	C₂×#15689931	1	1	yes	characteristic
910	C₂	#20258167	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3495	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20252614	C₂
hypercenter	#3495	D₄₇
hypocenter	C₄₇	#60579
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ #3495

Complements

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

N	H ≅ G/N	type
1. C₂×#15689597	C₂	semidirect
2. #20253635	C₂	semidirect
3. #20253566	C₂	semidirect
4. #20253522	C₂	semidirect
5. #20253483	C₂	semidirect
6. #20253431	C₂	semidirect
7. #20253392	C₂	semidirect
8. #20253332	C₂	semidirect
9. #20253297	C₂	semidirect
10. #20253213	C₂	semidirect
11. #20252896	C₂	semidirect
13. C₂×#15689273	C₂	semidirect
14. #20252247	C₂	semidirect
15. #20252216	C₂	semidirect
16. #20252046	C₂	semidirect
17. C₄₇×#3495	C₂	semidirect
33. #15689461	C₂²	semidirect
34. #15689461	C₂²	semidirect
35. #15689456	C₂²	semidirect
36. #15689456	C₂²	semidirect
37. #15689451	C₂²	semidirect
38. #15689451	C₂²	semidirect
39. #15689444	C₂²	semidirect
40. #15689439	C₂²	semidirect
41. #15689434	C₂²	semidirect
42. #15689420	C₂²	semidirect
43. #15689420	C₂²	semidirect
44. #15689410	C₂²	semidirect
45. #15689400	C₂²	semidirect
46. #15689335	C₂²	semidirect
47. #15689335	C₂²	semidirect
48. #15689325	C₂²	semidirect
49. #15689325	C₂²	semidirect
57. #15689233	C₂²	semidirect
58. #15689221	C₂²	semidirect
59. #15689221	C₂²	semidirect
60. #15689221	C₂²	semidirect
61. C₄×#10625336	C₂²	semidirect
62. C₄×#10625336	C₂²	semidirect
63. C₄×#10625336	C₂²	semidirect
64. C₄×#10625334	C₂²	semidirect
65. #15689184	C₂²	semidirect
66. #15689180	C₂²	semidirect
67. #15689176	C₂²	semidirect
68. #15689163	C₂²	semidirect
69. #15689159	C₂²	semidirect
70. #15689150	C₂²	semidirect
71. #15689132	C₂²	semidirect
73. #15689119	C₂²	semidirect
77. #15689079	C₂²	semidirect
84. C₄₇×#544	C₂²	semidirect
85. C₄₇×#542	C₂²	semidirect
86. C₄₇×#541	C₂²	semidirect
87. C₄₇×#536	C₂²	semidirect
88. C₄₇×#533	C₂²	semidirect
89. C₄₇×#529	C₂²	semidirect
92. C₄₇×#520	C₂²	semidirect
93. C₄₇×#519	C₂²	semidirect
141. #13093957	C₂³	semidirect
142. #13093957	C₂³	semidirect
143. #13093957	C₂³	semidirect
144. #13093955	C₂³	semidirect
145. #13093955	C₂³	semidirect
146. #13093955	C₂³	semidirect
147. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
148. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
149. #13093948	C₂³	semidirect
150. #13093948	C₂³	semidirect
151. #13093948	C₂³	semidirect
152. #13093948	C₂³	semidirect
153. #13093945	C₂³	semidirect
154. #13093945	C₂³	semidirect
164. #13093935	C₂³	semidirect
165. C₄×C₄₇⋊C₈	C₂³	semidirect
170. C₄⋊Q₈×C₄₇	C₂³	semidirect
171. C₄⋊Q₈×C₄₇	C₂³	semidirect
180. #125×C₄₇	C₂³	semidirect
182. #124×C₄₇	C₂³	semidirect
204. C₄×Q₈×C₄₇	C₂³	semidirect
205. C₄×Q₈×C₄₇	C₂³	semidirect
206. C₄×Q₈×C₄₇	C₂³	semidirect
211. C₄×D₄×C₄₇	C₂³	semidirect
448. #3495	D₄₇	semidirect
482. #544	C₂×D₄₇	semidirect
483. #542	C₂×D₄₇	semidirect
484. #541	C₂×D₄₇	semidirect
485. #536	C₂×D₄₇	semidirect
486. #533	C₂×D₄₇	semidirect
487. #529	C₂×D₄₇	semidirect
490. #520	C₂×D₄₇	semidirect
491. #519	C₂×D₄₇	semidirect
550. C₄₇	#60579	semidirect
573. C₄⋊Q₈	C₂²×D₄₇	semidirect
574. C₄⋊Q₈	C₂²×D₄₇	semidirect
583. #125	C₂²×D₄₇	semidirect
585. #124	C₂²×D₄₇	semidirect
607. C₄×Q₈	C₂²×D₄₇	semidirect
608. C₄×Q₈	C₂²×D₄₇	semidirect
609. C₄×Q₈	C₂²×D₄₇	semidirect
628. C₄×D₄	C₂²×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689597	2
#20253635	2
#20253566	2
#20253522	2
#20253483	2
#20253431	2
#20253392	2
#20253332	2
#20253297	2
#20253213	2
#20252896	2
#20252614	2
C₂×#15689273	2
#20252247	2
#20252216	2
#20252046	2
C₄₇×#3495	2
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