Subgroups — #27092529

Order 12032.

2656 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258168	C₂	1	2	yes	maximal, complemented
2	#20258157	C₂	1	1	yes	maximal, characteristic, complemented
3	#20255185	C₂	1	4	yes	maximal, complemented
4	#20255170	C₂	1	4	yes	maximal, complemented
5	#20255152	C₂	1	8	yes	maximal, complemented
6	#20253869	C₂	1	1	yes	maximal, characteristic, complemented
7	#20253113	C₂	1	2	yes	maximal, complemented
8	#20253108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689390	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252757	C₂	1	2	yes	maximal, complemented
11	#20252745	C₂	1	2	yes	maximal, complemented
12	#20252305	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252289	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₇×#576	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689959	C₂²	1	2	yes	complemented
16	#15689937	C₂²	1	2	yes	complemented
17	#15689936	—	2	1	no	—
18	#15689934	—	2	4	no	—
19	#15689934	C₂²	1	8	yes	complemented
20	#15689930	C₂²	1	4	yes	complemented
21	#15689929	—	2	2	no	—
22	#15689926	—	2	4	no	—
23	#15689926	C₂²	1	8	yes	complemented
24	#15689925	C₂²	1	2	yes	complemented
25	#15689924	—	2	1	no	—
26	#15689921	—	2	4	no	—
27	#15689921	C₂²	1	1	yes	characteristic
28	#15689921	C₂²	1	2	yes	complemented
29	#15689921	C₂²	1	2	yes	complemented
30	#15689920	—	2	2	no	—
31	C₂×#13094050	—	2	4	no	—
32	C₂×#13094050	C₂²	1	2	yes	complemented
33	C₂×#13094050	C₂²	1	2	yes	complemented
34	C₂×#13094046	C₂²	1	1	yes	characteristic, complemented
35	#135×D₄₇	—	2	2	no	—
36	#15689890	C₂²	1	2	yes	complemented
37	C₂×#13094030	C₂²	1	1	yes	characteristic, complemented
38	#15689690	C₂²	1	2	yes	complemented
39	#15689511	C₂²	1	4	yes	complemented
40	#15689506	C₂²	1	2	yes	complemented
41	#15689498	C₂²	1	2	yes	complemented
42	#15689398	C₂²	1	2	yes	complemented
43	#15689393	C₂²	1	2	yes	complemented
44	#15689391	C₂²	1	8	yes	complemented
45	#15689390	C₂²	1	4	yes	complemented
46	#15689390	C₂²	1	4	yes	complemented
47	#15689386	C₂²	1	4	yes	complemented
48	#15689384	C₂²	1	8	yes	complemented
49	#15689301	C₂²	1	8	yes	complemented
50	#15689294	C₂²	1	8	yes	complemented
51	#15689291	C₂²	1	8	yes	complemented
52	#15689289	C₂²	1	8	yes	complemented
53	#15689245	C₂²	1	4	yes	complemented
54	#15689243	C₂²	1	4	yes	complemented
55	#15689240	C₂²	1	4	yes	complemented
56	#15689238	C₂²	1	4	yes	complemented
57	#15689171	C₂²	1	1	yes	characteristic, complemented
58	C₂×#13093960	C₂²	1	1	yes	characteristic, complemented
59	#15689140	C₂²	1	1	yes	characteristic, complemented
60	#15689140	C₂²	1	2	yes	complemented
61	#15689139	C₂²	1	1	yes	characteristic, complemented
62	#15689105	C₂²	1	2	yes	complemented
63	C₂×#13093941	C₂²	1	2	yes	complemented
64	#15689078	C₂²	1	1	yes	characteristic, complemented
65	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	2	yes	complemented
66	C₄₇×#576	—	2	2	no	—
67	C₄₇×#576	—	2	2	no	—
68	C₄₇×#576	C₂²	1	4	yes	complemented
69	C₄₇×#576	C₂²	1	4	yes	complemented
70	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
71	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	complemented
72	C₂×#135×C₄₇	—	2	1	no	—
73	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
74	C₂²×D₈×C₄₇	—	2	1	no	—
75	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
76	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic, complemented
77	#13094072	—	2	2	no	—
78	#13094071	—	2	2	no	—
79	#13094071	C₂³	1	4	yes	complemented
80	#13094070	—	2	2	no	—
81	#13094070	C₂³	1	4	yes	complemented
82	#13094069	—	2	2	no	—
83	#13094069	—	4	2	no	—
84	C₂×#10625350	—	2	4	no	—
85	C₂×#10625350	C₂³	1	1	yes	characteristic
86	C₂×#10625350	C₂³	1	2	yes	—
87	#41×D₄₇	—	2	4	no	—
88	#41×D₄₇	—	4	2	no	—
89	#13094056	—	2	4	no	—
90	#13094055	—	2	2	no	—
91	#13094055	—	2	2	no	—
92	#13094055	D₄	1	2	yes	complemented
93	#13094054	—	2	8	no	—
94	#13094054	D₄	1	2	yes	complemented
95	#13094054	C₂³	1	4	yes	—
96	#13094054	C₂³	1	4	yes	complemented
97	#13094053	—	2	4	no	—
98	#13094051	—	2	4	no	—
99	#13094050	—	2	2	no	—
100	#13094050	—	2	2	no	—
101	#13094050	—	2	4	no	—
102	#13094050	—	2	8	no	—
103	#13094050	—	2	8	no	—
104	#13094050	—	2	4	no	—
105	#13094050	—	2	4	no	—
106	#13094050	D₄	1	2	yes	complemented
107	#13094050	C₂³	1	8	yes	complemented
108	#13094049	—	2	8	no	—
109	#13094049	D₄	1	2	yes	complemented
110	#13094049	C₂³	1	4	yes	—
111	#13094049	C₂³	1	4	yes	complemented
112	#13094048	—	2	4	no	—
113	#13094047	—	2	2	no	—
114	#13094046	—	2	1	no	—
115	#13094046	—	2	1	no	—
116	#13094046	—	2	1	no	—
117	#13094046	—	2	1	no	—
118	#13094045	—	2	4	no	—
119	#13094044	—	2	4	no	—
120	#13094044	—	2	4	no	—
121	#13094044	—	2	8	no	—
122	#13094044	—	2	8	no	—
123	#13094044	C₂³	1	4	yes	—
124	#13094043	—	2	2	no	—
125	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic, complemented
126	Q₁₆×D₄₇	—	2	2	no	—
127	C₂×#10625325	C₂³	1	2	yes	complemented
128	C₂×#10625335	—	2	2	no	—
129	C₂×#10625335	—	2	8	no	—
130	C₂×#10625335	C₂³	1	4	yes	complemented
131	SD₁₆×D₄₇	—	2	4	no	—
132	C₂×D₃₇₆	C₂³	1	1	yes	characteristic, complemented
133	C₂×#10625334	—	2	2	no	—
134	C₂×#10625334	—	2	8	no	—
135	C₂×#10625334	C₂³	1	4	yes	complemented
136	D₈×D₄₇	—	2	2	no	—
137	#13094031	—	2	4	no	—
138	#13094031	C₂³	1	8	yes	complemented
139	#13094030	—	2	1	no	—
140	#13094030	—	2	1	no	—
141	#13094030	C₂³	1	2	yes	complemented
142	#13094030	C₂³	1	2	yes	complemented
143	C₂×#10625329	—	2	4	no	—
144	C₂×#10625329	C₂³	1	1	yes	characteristic
145	C₂×#10625329	C₂³	1	2	yes	—
146	C₂×#10625329	C₂³	1	1	yes	characteristic
147	C₂×#10625324	—	2	1	no	—
148	C₂×C₈×D₄₇	—	2	1	no	—
149	#13094020	C₂³	1	4	yes	complemented
150	#13094011	C₂³	1	4	yes	complemented
151	#13093995	—	4	2	no	—
152	#13093993	—	4	2	no	—
153	#13093983	C₂³	1	1	yes	characteristic
154	#13093960	C₂³	1	2	yes	complemented
155	#13093960	C₂³	1	2	yes	complemented
156	#13093959	C₂³	1	4	yes	complemented
157	#13093951	C₂³	1	4	yes	—
158	#13093951	C₂³	1	8	yes	complemented
159	#13093950	C₂³	1	4	yes	complemented
160	#13093942	C₂³	1	4	yes	complemented
161	#13093941	C₂³	1	8	yes	complemented
162	#13093940	C₂³	1	4	yes	complemented
163	#13093934	C₂³	1	2	yes	complemented
164	C₈×Dic₄₇	C₂³	1	2	yes	complemented
165	H(5,𝔽₂)×C₄₇	—	2	4	no	—
166	H(5,𝔽₂)×C₄₇	—	2	4	no	—
167	H(5,𝔽₂)×C₄₇	—	4	2	no	—
168	H(5,𝔽₂)×C₄₇	C₂³	1	8	yes	—
169	C₂×#41×C₄₇	—	2	2	no	—
170	C₂×#41×C₄₇	—	2	2	no	—
171	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
172	C₂×#41×C₄₇	C₂³	1	2	yes	—
173	C₂²×D₄×C₄₇	—	2	2	no	—
174	C₂²×D₄×C₄₇	—	2	2	no	—
175	C₂²×D₄×C₄₇	—	4	2	no	—
176	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
177	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
178	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
179	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
180	AGL(1,ℤ/8)×C₄₇	C₂³	1	8	yes	—
181	#135×C₄₇	—	2	4	no	—
182	#135×C₄₇	—	2	4	no	—
183	#135×C₄₇	D₄	1	2	yes	complemented
184	#135×C₄₇	D₄	1	2	yes	complemented
185	#135×C₄₇	C₂³	1	2	yes	—
186	#135×C₄₇	C₂³	1	2	yes	—
187	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic, complemented
188	C₂×SD₁₆×C₄₇	—	2	2	no	—
189	C₂×SD₁₆×C₄₇	D₄	1	2	yes	complemented
190	C₂×D₈×C₄₇	—	2	2	no	—
191	C₂×D₈×C₄₇	—	2	4	no	—
192	C₂×D₈×C₄₇	—	2	4	no	—
193	C₂×D₈×C₄₇	—	2	1	no	—
194	C₂×D₈×C₄₇	—	2	1	no	—
195	C₂×D₈×C₄₇	—	2	1	no	—
196	C₂×D₈×C₄₇	—	2	1	no	—
197	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic, complemented
198	C₂×D₈×C₄₇	C₂³	1	2	yes	—
199	C₂×D₈×C₄₇	C₂³	1	2	yes	—
200	#131×C₄₇	—	2	1	no	—
201	#131×C₄₇	—	2	1	no	—
202	#131×C₄₇	C₂³	1	2	yes	—
203	#131×C₄₇	C₂³	1	2	yes	—
204	C₂×M₁₆×C₄₇	—	2	1	no	—
205	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
206	C₂²×C₈×C₄₇	—	2	1	no	—
207	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
208	C₂⁴×C₄₇	—	2	2	no	—
209	C₂⁴×C₄₇	—	4	2	no	—
210	#41×C₄₇	—	2	1	no	—
211	#41×C₄₇	—	2	2	no	—
212	#41×C₄₇	—	2	1	no	—
213	#41×C₄₇	—	2	2	no	—
214	#41×C₄₇	—	2	8	no	—
215	#41×C₄₇	—	2	8	no	—
216	#41×C₄₇	—	4	4	no	—
217	#41×C₄₇	—	4	4	no	—
218	#41×C₄₇	C₂×D₄	1	2	yes	—
219	#41×C₄₇	C₂×D₄	1	4	yes	—
220	#41×C₄₇	C₂⁴	1	2	yes	—
221	#41×C₄₇	C₂⁴	1	4	yes	—
222	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
223	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₄₇	—	2	1	no	—
225	C₂×D₄×C₄₇	—	2	2	no	—
226	C₂×D₄×C₄₇	—	2	8	no	—
227	C₂×D₄×C₄₇	—	2	8	no	—
228	C₂×D₄×C₄₇	—	2	2	no	—
229	C₂×D₄×C₄₇	—	2	2	no	—
230	C₂×D₄×C₄₇	—	2	2	no	—
231	C₂×D₄×C₄₇	—	2	2	no	—
232	C₂×D₄×C₄₇	—	2	2	no	—
233	C₂×D₄×C₄₇	—	4	4	no	—
234	C₂×D₄×C₄₇	—	4	4	no	—
235	C₂×D₄×C₄₇	—	4	2	no	—
236	C₂×D₄×C₄₇	—	4	2	no	—
237	C₂×D₄×C₄₇	—	4	8	no	—
238	C₂×D₄×C₄₇	—	4	8	no	—
239	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
240	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₄₇	—	2	1	no	—
243	C₂²×C₄×C₄₇	—	2	2	no	—
244	C₂²×C₄×C₄₇	—	4	2	no	—
245	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₂²⋊D₄₇	—	2	1	no	—
247	C₂×C₂²⋊D₄₇	—	2	2	no	—
248	C₂×C₂²⋊D₄₇	—	4	4	no	—
249	C₂×C₂²⋊D₄₇	—	4	4	no	—
250	#10625354	—	2	4	no	—
251	#10625354	—	4	2	no	—
252	Q₈×D₄₇	—	2	4	no	—
253	Q₈×D₄₇	—	4	2	no	—
254	#10625352	—	2	4	no	—
255	#10625352	—	4	2	no	—
256	#10625352	—	4	4	no	—
257	#10625352	—	4	4	no	—
258	D₄×D₄₇	—	2	4	no	—
259	D₄×D₄₇	—	4	2	no	—
260	D₄×D₄₇	—	4	4	no	—
261	D₄×D₄₇	—	4	4	no	—
262	#10625350	—	2	1	no	—
263	#10625350	—	2	1	no	—
264	#10625350	—	2	2	no	—
265	#10625350	—	2	2	no	—
266	#10625350	—	2	2	no	—
267	#10625350	—	2	2	no	—
268	#10625350	—	2	4	no	—
269	#10625350	—	2	4	no	—
270	#10625350	—	4	4	no	—
271	#10625350	—	4	4	no	—
272	#10625350	C₂×D₄	1	2	yes	—
273	#10625350	C₂⁴	1	2	yes	—
274	C₂×D₁₈₈	—	2	4	no	—
275	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
276	C₂×D₁₈₈	C₂⁴	1	2	yes	—
277	C₂×C₄×D₄₇	—	2	1	no	—
278	C₂×C₄×D₄₇	—	2	2	no	—
279	C₂×C₄×D₄₇	—	4	4	no	—
280	C₂×Dic₉₄	—	2	4	no	—
281	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
282	C₂×Dic₉₄	C₂⁴	1	2	yes	—
283	Q₁₆×C₄₇	C₂×D₄	1	2	yes	—
284	Q₁₆×C₄₇	C₂×D₄	1	2	yes	—
285	SD₁₆×C₄₇	—	2	8	no	—
286	SD₁₆×C₄₇	C₂×D₄	1	4	yes	—
287	SD₁₆×C₄₇	C₂×D₄	1	4	yes	—
288	D₈×C₄₇	—	2	8	no	—
289	D₈×C₄₇	—	2	2	no	—
290	D₈×C₄₇	—	2	2	no	—
291	D₈×C₄₇	—	2	2	no	—
292	D₈×C₄₇	—	2	2	no	—
293	D₈×C₄₇	C₂×D₄	1	2	yes	—
294	D₈×C₄₇	C₂×D₄	1	2	yes	—
295	M₁₆×C₄₇	—	2	1	no	—
296	M₁₆×C₄₇	—	2	2	no	—
297	M₁₆×C₄₇	—	2	2	no	—
298	M₁₆×C₄₇	C₂⁴	1	2	yes	—
299	C₂×C₈×C₄₇	—	2	1	no	—
300	C₂×C₈×C₄₇	—	2	2	no	—
301	C₂×C₈×C₄₇	—	2	2	no	—
302	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
303	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
304	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
305	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
306	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
307	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
308	C₂²⋊Dic₄₇	—	2	1	no	—
309	C₂²⋊Dic₄₇	—	4	4	no	—
310	#10625337	—	2	4	no	—
311	#10625337	—	2	4	no	—
312	#10625337	C₂×D₄	1	4	yes	—
313	#10625336	—	2	4	no	—
314	#10625336	—	2	4	no	—
315	#10625336	C₂×D₄	1	4	yes	—
316	#10625335	—	2	4	no	—
317	#10625335	—	2	4	no	—
318	#10625335	—	2	8	no	—
319	#10625335	—	2	8	no	—
320	#10625335	C₂×D₄	1	4	yes	—
321	#10625334	—	2	4	no	—
322	#10625334	—	2	4	no	—
323	#10625334	—	2	8	no	—
324	#10625334	—	2	8	no	—
325	#10625334	C₂×D₄	1	4	yes	—
326	C₄⋊Dic₄₇	—	2	1	no	—
327	C₄×Dic₄₇	C₂⁴	1	2	yes	—
328	#10625329	—	2	2	no	—
329	#10625329	—	2	1	no	—
330	#10625329	—	2	8	no	—
331	#10625329	C₂×D₄	1	2	yes	—
332	#10625329	C₂×D₄	1	2	yes	—
333	#10625329	C₂⁴	1	4	yes	—
334	#10625329	C₂⁴	1	2	yes	—
335	C₂×C₄₇⋊C₈	—	2	1	no	—
336	C₂×C₄₇⋊C₈	—	2	2	no	—
337	C₂×C₄₇⋊C₈	—	2	8	no	—
338	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
339	Dic₁₈₈	—	2	1	no	—
340	Dic₁₈₈	—	2	1	no	—
341	D₃₇₆	—	2	1	no	—
342	D₃₇₆	—	2	1	no	—
343	#10625325	—	2	2	no	—
344	#10625325	—	2	2	no	—
345	#10625324	—	2	2	no	—
346	#10625324	—	2	2	no	—
347	C₈×D₄₇	—	2	2	no	—
348	C₈×D₄₇	—	2	2	no	—
349	C₂³×C₄₇	—	2	1	no	—
350	C₂³×C₄₇	—	2	2	no	—
351	C₂³×C₄₇	—	2	4	no	—
352	C₂³×C₄₇	—	4	8	no	—
353	C₂³×C₄₇	—	4	2	no	—
354	C₂³×C₄₇	—	4	2	no	—
355	C₂³×C₄₇	—	16	2	no	—
356	C₂³×C₄₇	—	16	4	no	—
357	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
358	C₂²×D₄₇	—	2	1	no	—
359	C₂²×D₄₇	—	2	2	no	—
360	C₂²×D₄₇	—	4	4	no	—
361	Q₈×C₄₇	—	2	2	no	—
362	Q₈×C₄₇	—	2	1	no	—
363	Q₈×C₄₇	C₂²×D₄	1	2	yes	—
364	Q₈×C₄₇	C₂²×D₄	1	4	yes	—
365	D₄×C₄₇	—	2	4	no	—
366	D₄×C₄₇	—	2	2	no	—
367	D₄×C₄₇	—	2	4	no	—
368	D₄×C₄₇	—	2	2	no	—
369	D₄×C₄₇	—	2	2	no	—
370	D₄×C₄₇	—	2	1	no	—
371	D₄×C₄₇	—	2	4	no	—
372	D₄×C₄₇	—	2	4	no	—
373	D₄×C₄₇	—	4	8	no	—
374	D₄×C₄₇	—	4	8	no	—
375	D₄×C₄₇	—	4	2	no	—
376	D₄×C₄₇	—	4	2	no	—
377	D₄×C₄₇	C₂²×D₄	1	2	yes	—
378	D₄×C₄₇	C₂²×D₄	1	4	yes	—
379	C₂×C₄×C₄₇	—	2	2	no	—
380	C₂×C₄×C₄₇	—	2	1	no	—
381	C₂×C₄×C₄₇	—	2	4	no	—
382	C₂×C₄×C₄₇	—	2	2	no	—
383	C₂×C₄×C₄₇	—	2	4	no	—
384	C₂×C₄×C₄₇	—	2	2	no	—
385	C₂×C₄×C₄₇	—	4	8	no	—
386	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
390	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
391	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
392	C₂²⋊D₄₇	—	2	2	no	—
393	C₂²⋊D₄₇	—	2	2	no	—
394	C₂²⋊D₄₇	—	4	4	no	—
395	C₂²⋊D₄₇	—	4	4	no	—
396	C₂²⋊D₄₇	—	4	2	no	—
397	C₂²⋊D₄₇	—	4	2	no	—
398	C₂²⋊D₄₇	—	16	4	no	—
399	C₂×Dic₄₇	—	2	1	no	—
400	C₂×Dic₄₇	—	2	2	no	—
401	C₂×Dic₄₇	—	2	2	no	—
402	C₂×Dic₄₇	—	4	4	no	—
403	D₁₈₈	—	2	1	no	—
404	D₁₈₈	—	2	2	no	—
405	D₁₈₈	—	2	2	no	—
406	D₁₈₈	—	4	4	no	—
407	D₁₈₈	C₂²×D₄	1	2	yes	—
408	C₄×D₄₇	—	2	2	no	—
409	C₄×D₄₇	—	2	2	no	—
410	C₄×D₄₇	—	4	4	no	—
411	C₄×D₄₇	—	4	4	no	—
412	C₄×D₄₇	—	4	2	no	—
413	C₄×D₄₇	—	4	2	no	—
414	Dic₉₄	—	2	1	no	—
415	Dic₉₄	—	2	2	no	—
416	Dic₉₄	—	2	2	no	—
417	Dic₉₄	—	4	4	no	—
418	Dic₉₄	C₂²×D₄	1	2	yes	—
419	C₈×C₄₇	—	2	2	no	—
420	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
421	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
422	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
423	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
424	C₄₇⋊C₈	—	2	2	no	—
425	C₄₇⋊C₈	—	2	4	no	—
426	C₄₇⋊C₈	C₂²×D₄	1	4	yes	—
427	#61106	—	47	1	no	maximal, Sylow
428	C₂²×C₄₇	—	2	4	no	—
429	C₂²×C₄₇	—	2	2	no	—
430	C₂²×C₄₇	—	4	1	no	—
431	C₂²×C₄₇	—	4	2	no	—
432	C₂²×C₄₇	—	4	4	no	—
433	C₂²×C₄₇	—	8	2	no	—
434	C₂²×C₄₇	—	8	4	no	—
435	C₂²×C₄₇	—	8	4	no	—
436	C₂²×C₄₇	—	16	2	no	—
437	C₂²×C₄₇	—	16	8	no	—
438	C₂²×C₄₇	D₄²	1	1	yes	characteristic
439	C₂²×C₄₇	D₄²	1	1	yes	characteristic
440	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂×D₄₇	—	2	2	no	—
442	C₂×D₄₇	—	4	2	no	—
443	C₂×D₄₇	—	8	1	no	—
444	C₂×D₄₇	—	8	2	no	—
445	C₂×D₄₇	—	16	4	no	—
446	C₄×C₄₇	—	2	4	no	—
447	C₄×C₄₇	—	2	2	no	—
448	C₄×C₄₇	D₄²	1	1	yes	characteristic
449	C₄×C₄₇	D₄²	1	1	yes	characteristic
450	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
451	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
452	Dic₄₇	—	2	2	no	—
453	Dic₄₇	—	4	2	no	—
454	Dic₄₇	—	4	2	no	—
455	#3585	—	47	2	no	—
456	#3584	—	47	1	no	—
457	C₂×#576	D₄₇	1	1	yes	characteristic, complemented
458	#3292	—	47	4	no	—
459	#3290	—	47	4	no	—
460	#3288	—	47	8	no	—
461	#3155	—	47	1	no	—
462	#3068	—	47	2	no	—
463	#3067	—	47	1	no	—
464	C₂×#472	—	47	1	no	—
465	#3021	—	47	2	no	—
466	#3019	—	47	2	no	—
467	#2957	—	47	1	no	—
468	#2955	—	47	1	no	—
469	C₂×C₄₇	—	2	1	no	—
470	C₂×C₄₇	—	2	1	no	—
471	C₂×C₄₇	—	2	1	no	—
472	C₂×C₄₇	—	4	4	no	—
473	C₂×C₄₇	—	4	2	no	—
474	C₂×C₄₇	—	8	4	no	—
475	C₂×C₄₇	C₂×D₄²	1	1	yes	characteristic
476	D₄₇	—	4	2	no	—
477	D₄₇	—	8	2	no	—
478	#585	—	47	2	no	—
479	C₂×H(5,𝔽₂)	C₂×D₄₇	1	2	yes	complemented
480	#578	—	47	2	no	—
481	#578	—	94	1	no	—
482	#577	—	47	8	no	—
483	#577	—	47	4	no	—
484	#577	—	94	4	no	—
485	#577	—	94	2	no	—
486	#576	—	2	2	no	—
487	#576	—	2	2	no	—
488	#576	—	47	8	no	—
489	#576	—	47	2	no	—
490	#576	—	94	4	no	—
491	#576	—	94	1	no	—
492	#576	C₂×D₄₇	1	4	yes	complemented
493	#576	C₂×D₄₇	1	4	yes	complemented
494	#575	—	47	1	no	—
495	#575	—	47	2	no	—
496	#575	—	47	2	no	—
497	#575	—	94	4	no	—
498	#575	—	94	2	no	—
499	C₂×AGL(1,ℤ/8)	—	2	2	no	—
500	C₂×AGL(1,ℤ/8)	—	47	2	no	—
501	C₂×AGL(1,ℤ/8)	—	47	2	no	—
502	C₂×AGL(1,ℤ/8)	—	94	4	no	—
503	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	2	yes	complemented
504	C₂×#135	—	2	1	no	—
505	C₂×#135	—	47	1	no	—
506	C₂×#135	—	94	2	no	—
507	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
508	C₂²×D₈	—	2	1	no	—
509	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
510	#568	—	47	2	no	—
511	C₂×#131	—	47	1	no	—
512	C₂×#131	C₂×D₄₇	1	1	yes	characteristic, complemented
513	#535	—	47	2	no	—
514	#496	—	47	4	no	—
515	#495	—	47	2	no	—
516	#493	—	47	2	no	—
517	#473	—	47	2	no	—
518	#472	—	47	8	no	—
519	#472	—	47	4	no	—
520	#472	—	47	4	no	—
521	#472	—	47	2	no	—
522	#471	—	47	8	no	—
523	#471	—	47	4	no	—
524	#455	—	47	8	no	—
525	#454	—	47	8	no	—
526	#453	—	47	8	no	—
527	#453	—	47	8	no	—
528	#444	—	47	4	no	—
529	#444	—	47	4	no	—
530	#443	—	47	4	no	—
531	#443	—	47	4	no	—
532	#430	—	47	1	no	—
533	C₂×#108	—	47	1	no	—
534	#421	—	47	1	no	—
535	#421	—	47	2	no	—
536	#421	—	47	1	no	—
537	#413	—	47	2	no	—
538	C₂×#100	—	47	2	no	—
539	#405	—	47	1	no	—
540	C₄₇	#61106	1	1	yes	characteristic, complemented, Sylow
541	2₋¹⁺⁴	—	47	4	no	—
542	2₋¹⁺⁴	—	94	2	no	—
543	2₋¹⁺⁴	—	94	2	no	—
544	H(5,𝔽₂)	—	2	4	no	—
545	H(5,𝔽₂)	—	2	4	no	—
546	H(5,𝔽₂)	—	4	2	no	—
547	H(5,𝔽₂)	—	47	4	no	—
548	H(5,𝔽₂)	—	94	2	no	—
549	H(5,𝔽₂)	—	94	2	no	—
550	H(5,𝔽₂)	—	188	2	no	—
551	H(5,𝔽₂)	C₂²×D₄₇	1	8	yes	—
552	C₂×#41	—	2	2	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	47	1	no	—
555	C₂×#41	—	47	2	no	—
556	C₂×#41	—	94	4	no	—
557	C₂×#41	—	94	4	no	—
558	C₂×#41	—	188	2	no	—
559	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
560	C₂×#41	C₂²×D₄₇	1	2	yes	—
561	C₂²×D₄	—	2	2	no	—
562	C₂²×D₄	—	2	2	no	—
563	C₂²×D₄	—	4	2	no	—
564	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
565	#137	—	47	2	no	—
566	#137	—	47	2	no	—
567	#137	—	47	4	no	—
568	#137	—	47	4	no	—
569	#137	—	94	8	no	—
570	#137	—	94	2	no	—
571	#137	—	94	2	no	—
572	#137	—	94	4	no	—
573	#137	—	94	4	no	—
574	AGL(1,ℤ/8)	—	2	4	no	—
575	AGL(1,ℤ/8)	—	2	8	no	—
576	AGL(1,ℤ/8)	—	2	8	no	—
577	AGL(1,ℤ/8)	—	47	2	no	—
578	AGL(1,ℤ/8)	—	47	2	no	—
579	AGL(1,ℤ/8)	—	47	4	no	—
580	AGL(1,ℤ/8)	—	47	4	no	—
581	AGL(1,ℤ/8)	—	47	8	no	—
582	AGL(1,ℤ/8)	—	94	4	no	—
583	AGL(1,ℤ/8)	—	94	4	no	—
584	AGL(1,ℤ/8)	—	94	8	no	—
585	AGL(1,ℤ/8)	—	94	8	no	—
586	AGL(1,ℤ/8)	—	94	8	no	—
587	AGL(1,ℤ/8)	—	94	4	no	—
588	AGL(1,ℤ/8)	—	94	2	no	—
589	AGL(1,ℤ/8)	—	94	2	no	—
590	AGL(1,ℤ/8)	—	94	4	no	—
591	AGL(1,ℤ/8)	—	94	4	no	—
592	AGL(1,ℤ/8)	C₂²×D₄₇	1	8	yes	—
593	#135	—	2	4	no	—
594	#135	—	2	4	no	—
595	#135	—	47	4	no	—
596	#135	—	94	8	no	—
597	#135	—	94	8	no	—
598	#135	—	94	4	no	—
599	#135	—	94	4	no	—
600	#135	—	94	2	no	—
601	#135	—	94	4	no	—
602	#135	—	94	2	no	—
603	#135	—	94	1	no	—
604	#135	—	94	1	no	—
605	#135	—	94	1	no	—
606	#135	—	94	1	no	—
607	#135	C₂²⋊D₄₇	1	2	yes	complemented
608	#135	C₂²⋊D₄₇	1	2	yes	complemented
609	#135	C₂²×D₄₇	1	2	yes	—
610	#135	C₂²×D₄₇	1	2	yes	—
611	C₂×Q₁₆	—	47	1	no	—
612	C₂×Q₁₆	—	94	2	no	—
613	C₂×Q₁₆	C₂²⋊D₄₇	1	1	yes	characteristic, complemented
614	C₂×SD₁₆	—	2	2	no	—
615	C₂×SD₁₆	—	47	4	no	—
616	C₂×SD₁₆	—	47	2	no	—
617	C₂×SD₁₆	—	94	8	no	—
618	C₂×SD₁₆	—	94	2	no	—
619	C₂×SD₁₆	—	94	4	no	—
620	C₂×SD₁₆	C₂²⋊D₄₇	1	2	yes	complemented
621	C₂×D₈	—	2	2	no	—
622	C₂×D₈	—	2	4	no	—
623	C₂×D₈	—	2	4	no	—
624	C₂×D₈	—	2	1	no	—
625	C₂×D₈	—	2	1	no	—
626	C₂×D₈	—	2	1	no	—
627	C₂×D₈	—	2	1	no	—
628	C₂×D₈	—	47	4	no	—
629	C₂×D₈	—	47	1	no	—
630	C₂×D₈	—	94	8	no	—
631	C₂×D₈	—	94	2	no	—
632	C₂×D₈	—	94	2	no	—
633	C₂×D₈	C₂²⋊D₄₇	1	1	yes	characteristic, complemented
634	C₂×D₈	C₂²×D₄₇	1	2	yes	—
635	C₂×D₈	C₂²×D₄₇	1	2	yes	—
636	#131	—	2	1	no	—
637	#131	—	2	1	no	—
638	#131	—	47	8	no	—
639	#131	—	47	2	no	—
640	#131	—	47	2	no	—
641	#131	—	94	4	no	—
642	#131	—	94	1	no	—
643	#131	—	94	1	no	—
644	#131	C₂²×D₄₇	1	2	yes	—
645	#131	C₂²×D₄₇	1	2	yes	—
646	C₂×M₁₆	—	2	1	no	—
647	C₂×M₁₆	—	47	1	no	—
648	C₂×M₁₆	—	47	1	no	—
649	C₂×M₁₆	—	47	2	no	—
650	C₂×M₁₆	—	94	4	no	—
651	C₂×M₁₆	—	94	1	no	—
652	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
653	C₂²×C₈	—	2	1	no	—
654	C₂²×C₈	—	94	1	no	—
655	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
656	#127	—	47	4	no	—
657	#124	—	47	4	no	—
658	#121	—	188	2	no	—
659	#120	—	188	2	no	—
660	#117	—	47	1	no	—
661	#108	—	47	4	no	—
662	#108	—	47	2	no	—
663	#108	—	47	2	no	—
664	#104	—	47	4	no	—
665	#104	—	47	8	no	—
666	#104	—	47	4	no	—
667	#101	—	47	4	no	—
668	#100	—	47	8	no	—
669	#100	—	47	4	no	—
670	#97	—	47	2	no	—
671	C₄×C₈	—	47	2	no	—
672	C₂⁴	—	2	2	no	—
673	C₂⁴	—	4	2	no	—
674	#41	—	2	2	no	—
675	#41	—	2	1	no	—
676	#41	—	2	2	no	—
677	#41	—	2	1	no	—
678	#41	—	2	8	no	—
679	#41	—	2	8	no	—
680	#41	—	4	4	no	—
681	#41	—	4	4	no	—
682	#41	—	47	2	no	—
683	#41	—	47	2	no	—
684	#41	—	94	4	no	—
685	#41	—	94	4	no	—
686	#41	—	94	1	no	—
687	#41	—	94	1	no	—
688	#41	—	94	4	no	—
689	#41	—	94	4	no	—
690	#41	—	94	2	no	—
691	#41	—	94	2	no	—
692	#41	—	94	2	no	—
693	#41	—	94	2	no	—
694	#41	—	188	4	no	—
695	#41	—	188	4	no	—
696	#41	—	188	4	no	—
697	#41	—	188	4	no	—
698	#41	—	188	2	no	—
699	#41	—	188	2	no	—
700	#41	D₄×D₄₇	1	2	yes	—
701	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
702	#41	C₂³×D₄₇	1	2	yes	—
703	#41	C₂³×D₄₇	1	4	yes	—
704	C₂×Q₈	—	47	1	no	—
705	C₂×Q₈	—	47	2	no	—
706	C₂×Q₈	—	94	4	no	—
707	C₂×Q₈	—	94	4	no	—
708	C₂×Q₈	—	188	2	no	—
709	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
710	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	8	no	—
714	C₂×D₄	—	2	8	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	8	no	—
725	C₂×D₄	—	4	8	no	—
726	C₂×D₄	—	47	1	no	—
727	C₂×D₄	—	47	2	no	—
728	C₂×D₄	—	94	4	no	—
729	C₂×D₄	—	94	1	no	—
730	C₂×D₄	—	94	4	no	—
731	C₂×D₄	—	94	2	no	—
732	C₂×D₄	—	188	4	no	—
733	C₂×D₄	—	188	4	no	—
734	C₂×D₄	—	188	2	no	—
735	C₂×D₄	—	188	4	no	—
736	C₂×D₄	—	188	4	no	—
737	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
738	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
739	C₂×D₄	C₂³×D₄₇	1	4	yes	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	94	1	no	—
744	C₂²×C₄	—	94	2	no	—
745	C₂²×C₄	—	188	4	no	—
746	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
747	Q₁₆	—	47	4	no	—
748	Q₁₆	—	94	4	no	—
749	Q₁₆	—	94	4	no	—
750	Q₁₆	—	94	1	no	—
751	Q₁₆	—	94	1	no	—
752	Q₁₆	C₂×C₂²⋊D₄₇	1	2	yes	—
753	Q₁₆	C₂×C₂²⋊D₄₇	1	2	yes	—
754	SD₁₆	—	2	8	no	—
755	SD₁₆	—	47	4	no	—
756	SD₁₆	—	47	4	no	—
757	SD₁₆	—	94	8	no	—
758	SD₁₆	—	94	8	no	—
759	SD₁₆	—	94	4	no	—
760	SD₁₆	—	94	4	no	—
761	SD₁₆	—	94	4	no	—
762	SD₁₆	—	94	4	no	—
763	SD₁₆	—	94	2	no	—
764	SD₁₆	—	94	2	no	—
765	SD₁₆	C₂×C₂²⋊D₄₇	1	4	yes	—
766	SD₁₆	C₂×C₂²⋊D₄₇	1	4	yes	—
767	D₈	—	2	8	no	—
768	D₈	—	2	2	no	—
769	D₈	—	2	2	no	—
770	D₈	—	2	2	no	—
771	D₈	—	2	2	no	—
772	D₈	—	47	4	no	—
773	D₈	—	94	8	no	—
774	D₈	—	94	8	no	—
775	D₈	—	94	4	no	—
776	D₈	—	94	4	no	—
777	D₈	—	94	1	no	—
778	D₈	—	94	1	no	—
779	D₈	C₂×C₂²⋊D₄₇	1	2	yes	—
780	D₈	C₂×C₂²⋊D₄₇	1	2	yes	—
781	M₁₆	—	2	1	no	—
782	M₁₆	—	2	2	no	—
783	M₁₆	—	2	2	no	—
784	M₁₆	—	47	2	no	—
785	M₁₆	—	47	2	no	—
786	M₁₆	—	47	2	no	—
787	M₁₆	—	47	4	no	—
788	M₁₆	—	94	8	no	—
789	M₁₆	—	94	2	no	—
790	M₁₆	—	94	1	no	—
791	M₁₆	—	94	2	no	—
792	M₁₆	—	94	2	no	—
793	M₁₆	C₂³×D₄₇	1	2	yes	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	2	2	no	—
796	C₂×C₈	—	2	2	no	—
797	C₂×C₈	—	47	2	no	—
798	C₂×C₈	—	94	8	no	—
799	C₂×C₈	—	94	2	no	—
800	C₂×C₈	—	94	1	no	—
801	C₂×C₈	—	94	2	no	—
802	C₂×C₈	—	94	2	no	—
803	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
804	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
805	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
806	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
807	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
808	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
809	C₄⋊C₄	—	94	1	no	—
810	C₂²⋊C₄	—	94	1	no	—
811	C₂²⋊C₄	—	188	4	no	—
812	C₄²	—	47	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	4	8	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	16	2	no	—
820	C₂³	—	16	4	no	—
821	C₂³	—	94	1	no	—
822	C₂³	—	94	2	no	—
823	C₂³	—	188	4	no	—
824	C₂³	#13094069	1	1	yes	characteristic
825	Q₈	—	2	2	no	—
826	Q₈	—	2	1	no	—
827	Q₈	—	47	2	no	—
828	Q₈	—	94	1	no	—
829	Q₈	—	94	2	no	—
830	Q₈	—	94	2	no	—
831	Q₈	—	188	4	no	—
832	Q₈	C₂×D₄×D₄₇	1	2	yes	—
833	Q₈	C₂²×C₂²⋊D₄₇	1	4	yes	—
834	D₄	—	2	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	4	no	—
838	D₄	—	2	1	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	4	no	—
842	D₄	—	4	8	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	2	no	—
846	D₄	—	47	2	no	—
847	D₄	—	94	2	no	—
848	D₄	—	94	2	no	—
849	D₄	—	94	1	no	—
850	D₄	—	94	2	no	—
851	D₄	—	94	2	no	—
852	D₄	—	188	4	no	—
853	D₄	—	188	4	no	—
854	D₄	—	188	4	no	—
855	D₄	—	188	2	no	—
856	D₄	—	188	2	no	—
857	D₄	—	752	4	no	—
858	D₄	C₂×D₄×D₄₇	1	2	yes	—
859	D₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	94	1	no	—
868	C₂×C₄	—	94	2	no	—
869	C₂×C₄	—	94	2	no	—
870	C₂×C₄	—	94	2	no	—
871	C₂×C₄	—	94	2	no	—
872	C₂×C₄	—	188	4	no	—
873	C₂×C₄	—	188	4	no	—
874	C₂×C₄	—	188	4	no	—
875	C₂×C₄	—	188	2	no	—
876	C₂×C₄	—	188	2	no	—
877	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
878	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
879	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
880	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
881	C₂×C₄	#13094069	1	1	yes	characteristic
882	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
883	C₈	—	2	2	no	—
884	C₈	—	47	4	no	—
885	C₈	—	94	4	no	—
886	C₈	—	94	2	no	—
887	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
888	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
889	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
890	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
891	C₂²	—	2	4	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	8	2	no	—
897	C₂²	—	8	4	no	—
898	C₂²	—	8	4	no	—
899	C₂²	—	16	2	no	—
900	C₂²	—	16	8	no	—
901	C₂²	—	94	2	no	—
902	C₂²	—	376	2	no	—
903	C₂²	—	376	1	no	—
904	C₂²	—	188	2	no	—
905	C₂²	—	752	4	no	—
906	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
907	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
908	C₂²	C₂×#13094069	1	1	yes	characteristic
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	94	2	no	—
912	C₄	—	188	2	no	—
913	C₄	—	188	2	no	—
914	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
915	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
916	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
917	C₄	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
918	C₂	—	2	1	no	—
919	C₂	—	2	1	no	—
920	C₂	—	2	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	4	4	no	—
923	C₂	—	8	4	no	—
924	C₂	—	376	2	no	—
925	C₂	—	188	2	no	—
926	C₂	C₂×D₄×C₂²⋊D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#576	C₂
socle	C₂×C₄₇	C₂×D₄²
hypercenter	C₂×#576	D₄₇
hypocenter	C₄₇	#61106
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #20258168	C₂	semidirect
2. #20258157	C₂	semidirect
3. #20255185	C₂	semidirect
4. #20255170	C₂	semidirect
5. #20255152	C₂	semidirect
6. #20253869	C₂	semidirect
7. #20253113	C₂	semidirect
8. #20253108	C₂	semidirect
9. C₂×#15689390	C₂	semidirect
10. #20252757	C₂	semidirect
11. #20252745	C₂	semidirect
12. #20252305	C₂	semidirect
13. #20252289	C₂	semidirect
14. C₂×C₄₇×#576	C₂	semidirect
15. #15689959	C₂²	semidirect
16. #15689937	C₂²	semidirect
19. #15689934	C₂²	semidirect
20. #15689930	C₂²	semidirect
23. #15689926	C₂²	semidirect
24. #15689925	C₂²	semidirect
28. #15689921	C₂²	semidirect
29. #15689921	C₂²	semidirect
32. C₂×#13094050	C₂²	semidirect
33. C₂×#13094050	C₂²	semidirect
34. C₂×#13094046	C₂²	semidirect
36. #15689890	C₂²	semidirect
37. C₂×#13094030	C₂²	semidirect
38. #15689690	C₂²	semidirect
39. #15689511	C₂²	semidirect
40. #15689506	C₂²	semidirect
41. #15689498	C₂²	semidirect
42. #15689398	C₂²	semidirect
43. #15689393	C₂²	semidirect
44. #15689391	C₂²	semidirect
45. #15689390	C₂²	semidirect
46. #15689390	C₂²	semidirect
47. #15689386	C₂²	semidirect
48. #15689384	C₂²	semidirect
49. #15689301	C₂²	semidirect
50. #15689294	C₂²	semidirect
51. #15689291	C₂²	semidirect
52. #15689289	C₂²	semidirect
53. #15689245	C₂²	semidirect
54. #15689243	C₂²	semidirect
55. #15689240	C₂²	semidirect
56. #15689238	C₂²	semidirect
57. #15689171	C₂²	semidirect
58. C₂×#13093960	C₂²	semidirect
59. #15689140	C₂²	semidirect
60. #15689140	C₂²	semidirect
61. #15689139	C₂²	semidirect
62. #15689105	C₂²	semidirect
63. C₂×#13093941	C₂²	semidirect
64. #15689078	C₂²	semidirect
65. C₂×H(5,𝔽₂)×C₄₇	C₂²	semidirect
68. C₄₇×#576	C₂²	semidirect
69. C₄₇×#576	C₂²	semidirect
71. C₂×AGL(1,ℤ/8)×C₄₇	C₂²	semidirect
75. C₂²×D₈×C₄₇	C₂²	semidirect
76. C₂×#131×C₄₇	C₂²	semidirect
79. #13094071	C₂³	semidirect
81. #13094070	C₂³	semidirect
92. #13094055	D₄	semidirect
94. #13094054	D₄	semidirect
96. #13094054	C₂³	semidirect
106. #13094050	D₄	semidirect
107. #13094050	C₂³	semidirect
109. #13094049	D₄	semidirect
111. #13094049	C₂³	semidirect
125. C₂×Dic₁₈₈	C₂³	semidirect
127. C₂×#10625325	C₂³	semidirect
130. C₂×#10625335	C₂³	semidirect
132. C₂×D₃₇₆	C₂³	semidirect
135. C₂×#10625334	C₂³	semidirect
138. #13094031	C₂³	semidirect
141. #13094030	C₂³	semidirect
142. #13094030	C₂³	semidirect
149. #13094020	C₂³	semidirect
150. #13094011	C₂³	semidirect
154. #13093960	C₂³	semidirect
155. #13093960	C₂³	semidirect
156. #13093959	C₂³	semidirect
158. #13093951	C₂³	semidirect
159. #13093950	C₂³	semidirect
160. #13093942	C₂³	semidirect
161. #13093941	C₂³	semidirect
162. #13093940	C₂³	semidirect
163. #13093934	C₂³	semidirect
164. C₈×Dic₄₇	C₂³	semidirect
183. #135×C₄₇	D₄	semidirect
184. #135×C₄₇	D₄	semidirect
187. C₂×Q₁₆×C₄₇	D₄	semidirect
189. C₂×SD₁₆×C₄₇	D₄	semidirect
197. C₂×D₈×C₄₇	D₄	semidirect
457. C₂×#576	D₄₇	semidirect
479. C₂×H(5,𝔽₂)	C₂×D₄₇	semidirect
492. #576	C₂×D₄₇	semidirect
493. #576	C₂×D₄₇	semidirect
503. C₂×AGL(1,ℤ/8)	C₂×D₄₇	semidirect
509. C₂²×D₈	C₂×D₄₇	semidirect
512. C₂×#131	C₂×D₄₇	semidirect
540. C₄₇	#61106	semidirect
607. #135	C₂²⋊D₄₇	semidirect
608. #135	C₂²⋊D₄₇	semidirect
613. C₂×Q₁₆	C₂²⋊D₄₇	semidirect
620. C₂×SD₁₆	C₂²⋊D₄₇	semidirect
633. C₂×D₈	C₂²⋊D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20258168	2
#20258157	2
#20255185	2
#20255170	2
#20255152	2
#20253869	2
#20253113	2
#20253108	2
C₂×#15689390	2
#20252757	2
#20252745	2
#20252305	2
#20252289	2
C₂×C₄₇×#576	2
#61106	47