Subgroups — #27080884

Order 12032.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256780	C₂	1	1	yes	maximal, characteristic
2	#20252394	C₂	1	2	yes	maximal, complemented
3	#20252391	C₂	1	2	yes	maximal, complemented
4	#20252381	C₂	1	2	yes	maximal, complemented
5	#20252381	C₂	1	2	yes	maximal, complemented
6	#20252372	C₂	1	2	yes	maximal, complemented
7	#20252372	C₂	1	2	yes	maximal, complemented
8	#20252365	C₂	1	2	yes	maximal, complemented
9	#20252362	C₂	1	2	yes	maximal, complemented
10	#20252337	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252134	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252131	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252116	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252116	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252112	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252112	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252038	C₂	1	1	yes	maximal, characteristic, complemented
18	#20252031	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#15689183	C₂	1	1	yes	maximal, characteristic, complemented
20	#20251815	C₂	1	1	yes	maximal, characteristic, complemented
21	#20251810	C₂	1	1	yes	maximal, characteristic, complemented
22	#20251805	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094032	C₂²	1	1	yes	characteristic
25	C₂×#13094032	C₂²	1	1	yes	characteristic
26	C₂×#13094030	C₂²	1	1	yes	characteristic
27	C₂×#13094030	C₂²	1	1	yes	characteristic
28	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
29	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
30	#15689747	C₄	1	1	yes	characteristic
31	#15689747	C₄	1	1	yes	characteristic
32	#15689747	C₄	1	1	yes	characteristic
33	#15689747	C₄	1	1	yes	characteristic
34	#15689736	C₄	1	1	yes	characteristic
35	#15689736	C₄	1	1	yes	characteristic
36	#15689729	C₄	1	1	yes	characteristic
37	#15689729	C₄	1	1	yes	characteristic
38	#15689722	C₄	1	2	yes	—
39	#15689722	C₄	1	2	yes	—
40	#15689713	C₄	1	2	yes	—
41	#15689713	C₄	1	2	yes	—
42	#15689673	C₂²	1	1	yes	characteristic
43	#15689660	C₂²	1	2	yes	—
44	#15689660	C₂²	1	2	yes	—
45	#15689660	C₂²	1	2	yes	—
46	#15689660	C₂²	1	2	yes	—
47	#15689635	C₂²	1	1	yes	characteristic
48	#15689635	C₂²	1	1	yes	characteristic
49	#15689591	C₂²	1	1	yes	characteristic
50	#15689591	C₂²	1	1	yes	characteristic
51	C₂×#13093981	C₂²	1	1	yes	characteristic
52	#15689254	C₂²	1	2	yes	complemented
53	#15689254	C₂²	1	2	yes	complemented
54	#15689254	C₂²	1	2	yes	complemented
55	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
56	#15689202	C₂²	1	2	yes	—
57	#15689202	C₂²	1	2	yes	—
58	#15689202	C₂²	1	2	yes	complemented
59	#15689200	C₂²	1	2	yes	—
60	#15689200	C₂²	1	2	yes	—
61	#15689200	C₂²	1	2	yes	complemented
62	#15689196	C₂²	1	2	yes	—
63	#15689196	C₂²	1	2	yes	—
64	#15689196	C₂²	1	2	yes	—
65	#15689196	C₂²	1	2	yes	—
66	#15689196	C₂²	1	2	yes	complemented
67	#15689196	C₂²	1	2	yes	complemented
68	#15689193	C₂²	1	2	yes	—
69	#15689193	C₂²	1	2	yes	—
70	#15689193	C₂²	1	2	yes	—
71	#15689193	C₂²	1	2	yes	—
72	#15689193	C₂²	1	2	yes	complemented
73	#15689193	C₂²	1	2	yes	complemented
74	C₈×D₁₈₈	C₂²	1	2	yes	—
75	C₈×D₁₈₈	C₂²	1	2	yes	—
76	C₈×D₁₈₈	C₂²	1	2	yes	complemented
77	#15689188	C₂²	1	2	yes	—
78	#15689188	C₂²	1	2	yes	—
79	#15689188	C₂²	1	2	yes	complemented
80	#15689183	C₂²	1	1	yes	characteristic
81	#15689183	C₂²	1	1	yes	characteristic
82	#15689183	C₂²	1	1	yes	characteristic
83	#15689183	C₂²	1	1	yes	characteristic
84	#15689183	C₂²	1	1	yes	characteristic
85	#15689183	C₂²	1	1	yes	characteristic
86	#15689183	C₂²	1	1	yes	characteristic
87	#15689183	C₂²	1	1	yes	characteristic
88	#15689183	C₂²	1	2	yes	complemented
89	#15689183	C₂²	1	2	yes	complemented
90	#15689183	C₂²	1	2	yes	complemented
91	#15689183	C₂²	1	2	yes	complemented
92	#15689179	C₂²	1	2	yes	complemented
93	#15689179	C₂²	1	2	yes	complemented
94	#15689175	C₂²	1	2	yes	complemented
95	#15689175	C₂²	1	2	yes	complemented
96	#15689150	C₂²	1	1	yes	characteristic
97	#15689150	C₂²	1	1	yes	characteristic
98	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
99	#15689091	C₂²	1	1	yes	characteristic
100	#15689091	C₂²	1	1	yes	characteristic
101	#15689089	C₂²	1	1	yes	characteristic
102	#15689089	C₂²	1	1	yes	characteristic
103	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
104	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
105	#15689080	C₂²	1	2	yes	—
106	#15689080	C₂²	1	2	yes	—
107	#15689080	C₂²	1	2	yes	complemented
108	#15689080	C₂²	1	2	yes	complemented
109	#15689079	C₂²	1	1	yes	characteristic
110	#15689079	C₂²	1	1	yes	characteristic
111	#15689077	C₂²	1	2	yes	—
112	#15689077	C₂²	1	2	yes	—
113	#15689077	C₂²	1	2	yes	complemented
114	#15689077	C₂²	1	2	yes	complemented
115	C₄×#10625329	C₂²	1	1	yes	characteristic
116	#15689075	C₂²	1	2	yes	complemented
117	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
118	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
119	C₄×#10625324	C₂²	1	2	yes	complemented
120	C₂×#13093934	C₂²	1	1	yes	characteristic
121	#97×D₄₇	C₂²	1	2	yes	complemented
122	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
123	C₄×C₈×D₄₇	C₂²	1	2	yes	complemented
124	C₄₇×#533	C₂²	1	1	yes	characteristic
125	C₄₇×#446	C₂²	1	2	yes	complemented
126	C₄₇×#446	C₂²	1	2	yes	complemented
127	C₄₇×#446	C₂²	1	2	yes	complemented
128	C₈×Q₈×C₄₇	C₂²	1	2	yes	complemented
129	C₄₇×#424	C₂²	1	1	yes	characteristic
130	C₄₇×#424	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
132	C₄₇×#405	C₂²	1	1	yes	characteristic
133	C₄₇×#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂×#10625350	C₂³	1	1	yes	characteristic
137	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
138	#13094032	—	2	4	no	—
139	#13094032	—	2	4	no	—
140	#13094030	—	2	4	no	—
141	#13094030	—	2	4	no	—
142	C₂×#10625329	C₂³	1	1	yes	characteristic
143	C₂×#10625329	C₂³	1	1	yes	characteristic
144	C₂×#10625324	C₂³	1	2	yes	—
145	C₂×#10625324	C₂³	1	2	yes	—
146	C₂×#10625324	C₂³	1	2	yes	—
147	C₂×#10625324	C₂³	1	2	yes	—
148	C₂×#10625324	C₂³	1	2	yes	—
149	C₂×#10625324	C₂³	1	2	yes	—
150	M₁₆×D₄₇	—	2	4	no	—
151	M₁₆×D₄₇	—	2	4	no	—
152	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₇	C₂³	1	2	yes	—
155	C₂×C₈×D₄₇	C₂³	1	2	yes	—
156	C₂×C₈×D₄₇	C₂³	1	2	yes	—
157	C₂×C₈×D₄₇	C₂³	1	2	yes	—
158	C₂×C₈×D₄₇	C₂³	1	2	yes	—
159	C₂×C₈×D₄₇	C₂³	1	2	yes	—
160	#13094024	C₂×C₄	1	1	yes	characteristic
161	#13094021	C₂×C₄	1	1	yes	characteristic
162	#13094019	C₂×C₄	1	2	yes	—
163	#13094019	C₂×C₄	1	2	yes	—
164	#13094019	C₂×C₄	1	2	yes	—
165	#13094019	C₂×C₄	1	2	yes	—
166	#13094019	C₂×C₄	1	2	yes	—
167	#13094019	C₂×C₄	1	2	yes	—
168	#13094019	C₂×C₄	1	2	yes	—
169	#13094019	C₂×C₄	1	2	yes	—
170	#13094015	C₂×C₄	1	2	yes	—
171	#13094015	C₂×C₄	1	2	yes	—
172	#13094015	C₂×C₄	1	2	yes	—
173	#13094015	C₂×C₄	1	2	yes	—
174	#13094013	C₂×C₄	1	2	yes	—
175	#13094013	C₂×C₄	1	2	yes	—
176	#13094013	C₂×C₄	1	2	yes	—
177	#13094013	C₂×C₄	1	2	yes	—
178	#13094012	C₂×C₄	1	1	yes	characteristic
179	#13094012	C₂×C₄	1	1	yes	characteristic
180	#13094009	C₂×C₄	1	2	yes	—
181	#13094009	C₂×C₄	1	2	yes	—
182	#13094009	C₂×C₄	1	2	yes	—
183	#13094009	C₂×C₄	1	2	yes	—
184	#13094009	C₂×C₄	1	2	yes	—
185	#13094009	C₂×C₄	1	2	yes	—
186	#13094009	C₂×C₄	1	2	yes	—
187	#13094009	C₂×C₄	1	2	yes	—
188	#13094008	C₂×C₄	1	2	yes	—
189	#13094008	C₂×C₄	1	2	yes	—
190	#13094004	C₂×C₄	1	1	yes	characteristic
191	#13094004	C₂×C₄	1	1	yes	characteristic
192	#13094004	C₂×C₄	1	1	yes	characteristic
193	#13094004	C₂×C₄	1	1	yes	characteristic
194	#13094000	C₂×C₄	1	2	yes	—
195	#13094000	C₂×C₄	1	2	yes	—
196	#13094000	C₂×C₄	1	2	yes	—
197	#13094000	C₂×C₄	1	2	yes	—
198	#13093999	C₂×C₄	1	1	yes	characteristic
199	#13093999	C₂×C₄	1	1	yes	characteristic
200	#13093999	C₂×C₄	1	1	yes	characteristic
201	#13093999	C₂×C₄	1	1	yes	characteristic
202	#13093999	C₂×C₄	1	2	yes	—
203	#13093999	C₂×C₄	1	2	yes	—
204	#13093999	C₂×C₄	1	2	yes	—
205	#13093999	C₂×C₄	1	2	yes	—
206	#13093998	C₂×C₄	1	2	yes	—
207	#13093998	C₂×C₄	1	2	yes	—
208	#13093994	C₂×C₄	1	2	yes	—
209	#13093994	C₂×C₄	1	2	yes	—
210	#13093989	C₂×C₄	1	1	yes	characteristic
211	#13093989	C₂×C₄	1	1	yes	characteristic
212	#13093989	C₂×C₄	1	1	yes	characteristic
213	#13093989	C₂×C₄	1	1	yes	characteristic
214	C₄×D₁₈₈	C₂³	1	2	yes	—
215	C₄×D₁₈₈	C₂³	1	2	yes	—
216	C₄×D₁₈₈	C₂³	1	2	yes	—
217	C₄×D₁₈₈	C₂³	1	2	yes	—
218	C₄×D₁₈₈	C₂³	1	2	yes	—
219	C₄×D₁₈₈	C₂³	1	2	yes	—
220	#13093986	C₂×C₄	1	1	yes	characteristic
221	#13093986	C₂×C₄	1	1	yes	characteristic
222	#13093986	C₂×C₄	1	1	yes	characteristic
223	#13093986	C₂×C₄	1	1	yes	characteristic
224	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
225	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
226	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
227	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
228	#13093981	C₂×C₄	1	1	yes	characteristic
229	#13093981	C₂×C₄	1	1	yes	characteristic
230	#13093981	C₂×C₄	1	1	yes	characteristic
231	#13093981	C₂×C₄	1	1	yes	characteristic
232	#13093981	C₂³	1	1	yes	characteristic
233	#13093981	C₂³	1	1	yes	characteristic
234	#13093981	C₂³	1	1	yes	characteristic
235	#13093981	C₂³	1	1	yes	characteristic
236	#13093981	C₂³	1	2	yes	—
237	#13093981	C₂³	1	2	yes	—
238	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
239	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
240	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
241	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
242	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
243	C₄²×D₄₇	C₂³	1	2	yes	—
244	C₄²×D₄₇	C₂³	1	2	yes	—
245	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
246	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
247	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
250	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
251	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
252	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
253	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
254	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
255	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
256	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
257	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
258	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
259	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
260	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
262	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
263	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
264	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
265	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
267	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
268	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
269	#13093935	C₂³	1	2	yes	—
270	#13093935	C₂³	1	2	yes	—
271	#13093935	C₂³	1	2	yes	—
272	#13093934	C₂³	1	1	yes	characteristic
273	#13093934	C₂³	1	2	yes	—
274	#13093934	C₂³	1	1	yes	characteristic
275	#13093934	C₂³	1	1	yes	characteristic
276	#13093934	C₂³	1	1	yes	characteristic
277	#13093934	C₂³	1	2	yes	—
278	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
279	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
280	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
281	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
282	C₈×Dic₄₇	C₂³	1	2	yes	—
283	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
284	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
285	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
286	C₈×Dic₄₇	C₂³	1	2	yes	—
287	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
292	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
293	#125×C₄₇	C₂×C₄	1	1	yes	characteristic
294	#125×C₄₇	C₂×C₄	1	1	yes	characteristic
295	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
296	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
297	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
298	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
299	#117×C₄₇	C₂³	1	1	yes	characteristic
300	#117×C₄₇	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
303	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
304	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
305	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
306	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
308	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
310	#97×C₄₇	C₂³	1	2	yes	—
311	#97×C₄₇	C₂³	1	2	yes	—
312	#97×C₄₇	C₂³	1	2	yes	—
313	C₄×C₈×C₄₇	C₂³	1	2	yes	—
314	C₄×C₈×C₄₇	C₂³	1	2	yes	—
315	C₄×C₈×C₄₇	C₂³	1	2	yes	—
316	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
317	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
318	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
319	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
321	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
323	C₂×C₂²⋊D₄₇	C₂²×C₄	1	2	yes	—
324	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
325	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
326	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
327	#10625350	—	2	2	no	—
328	#10625350	—	2	2	no	—
329	#10625350	—	2	2	no	—
330	#10625350	—	2	2	no	—
331	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
332	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
333	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
334	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
335	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
336	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
337	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
338	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
339	C₂×C₄×D₄₇	—	2	2	no	—
340	C₂×C₄×D₄₇	—	2	2	no	—
341	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
343	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
344	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
345	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
346	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
347	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
348	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
349	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
350	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
351	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
352	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
353	M₁₆×C₄₇	—	2	2	no	—
354	M₁₆×C₄₇	#41	1	4	yes	—
355	C₂×C₈×C₄₇	—	2	2	no	—
356	C₂×C₈×C₄₇	—	2	2	no	—
357	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
362	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
364	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
366	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
367	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
368	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
374	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
375	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
376	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
377	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
379	C₄²×C₄₇	C₂⁴	1	2	yes	—
380	C₄²×C₄₇	C₂⁴	1	2	yes	—
381	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
382	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
383	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
384	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
385	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
386	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
387	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
390	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
391	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
392	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
393	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
394	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
395	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
396	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
397	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
398	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
399	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
400	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
401	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
402	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
403	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
404	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
405	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
406	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
407	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
408	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
409	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
410	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
411	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
414	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
415	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
416	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
417	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
418	Dic₄₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
419	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
420	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
421	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
422	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
423	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
424	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
425	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
426	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
427	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
428	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
429	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
430	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
431	#10625329	—	2	2	no	—
432	#10625329	#41	1	4	yes	—
433	C₂×C₄₇⋊C₈	—	2	2	no	—
434	C₂×C₄₇⋊C₈	—	2	2	no	—
435	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
436	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
437	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
438	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
439	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
441	#10625324	—	2	4	no	—
442	#10625324	—	2	4	no	—
443	#10625324	—	2	4	no	—
444	#10625324	—	2	4	no	—
445	#10625324	—	2	4	no	—
446	#10625324	—	2	4	no	—
447	C₈×D₄₇	—	2	4	no	—
448	C₈×D₄₇	—	2	4	no	—
449	C₈×D₄₇	—	2	4	no	—
450	C₈×D₄₇	—	2	4	no	—
451	C₈×D₄₇	—	2	4	no	—
452	C₈×D₄₇	—	2	4	no	—
453	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
454	C₂²×D₄₇	—	2	2	no	—
455	C₂²×D₄₇	—	4	1	no	—
456	C₂²×D₄₇	—	4	1	no	—
457	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
458	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
459	C₂²×D₄₇	C₂³×C₄	1	2	yes	—
460	C₂²×D₄₇	C₂³×C₄	1	2	yes	—
461	Q₈×C₄₇	—	4	2	no	—
462	Q₈×C₄₇	—	4	2	no	—
463	C₂×C₄×C₄₇	—	4	1	no	—
464	C₂×C₄×C₄₇	—	4	1	no	—
465	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
467	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
468	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
469	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
470	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
471	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
472	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
473	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
475	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
476	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
477	C₂²⋊D₄₇	—	2	4	no	—
478	C₂²⋊D₄₇	—	2	4	no	—
479	C₂×Dic₄₇	—	2	2	no	—
480	C₂×Dic₄₇	—	4	1	no	—
481	C₂×Dic₄₇	—	4	1	no	—
482	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
483	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
484	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
485	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
486	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
487	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
488	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
489	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
490	D₁₈₈	—	2	2	no	—
491	D₁₈₈	—	2	2	no	—
492	D₁₈₈	—	4	2	no	—
493	D₁₈₈	—	4	2	no	—
494	D₁₈₈	—	4	2	no	—
495	D₁₈₈	—	4	2	no	—
496	D₁₈₈	—	4	2	no	—
497	D₁₈₈	—	4	2	no	—
498	C₄×D₄₇	—	2	2	no	—
499	C₄×D₄₇	—	2	2	no	—
500	C₄×D₄₇	—	2	1	no	—
501	C₄×D₄₇	—	2	1	no	—
502	C₄×D₄₇	—	2	2	no	—
503	C₄×D₄₇	—	2	2	no	—
504	C₄×D₄₇	—	2	2	no	—
505	C₄×D₄₇	—	2	2	no	—
506	C₄×D₄₇	—	2	1	no	—
507	C₄×D₄₇	—	2	1	no	—
508	C₄×D₄₇	—	4	2	no	—
509	C₄×D₄₇	—	4	2	no	—
510	C₄×D₄₇	—	4	2	no	—
511	C₄×D₄₇	—	4	2	no	—
512	Dic₉₄	—	2	2	no	—
513	Dic₉₄	—	2	2	no	—
514	C₈×C₄₇	—	2	1	no	—
515	C₈×C₄₇	—	2	1	no	—
516	C₈×C₄₇	—	2	2	no	—
517	C₈×C₄₇	—	2	1	no	—
518	C₈×C₄₇	—	2	1	no	—
519	C₈×C₄₇	C₂×#41	1	4	yes	—
520	C₄₇⋊C₈	—	2	1	no	—
521	C₄₇⋊C₈	—	2	1	no	—
522	C₄₇⋊C₈	—	2	2	no	—
523	C₄₇⋊C₈	—	2	1	no	—
524	C₄₇⋊C₈	—	2	1	no	—
525	C₄₇⋊C₈	C₂×#41	1	4	yes	—
526	#60212	—	47	1	no	maximal, Sylow
527	C₂²×C₄₇	—	2	1	no	—
528	C₂²×C₄₇	—	2	1	no	—
529	C₂²×C₄₇	C₄×#41	1	2	yes	—
530	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
531	C₂×D₄₇	—	2	1	no	—
532	C₂×D₄₇	—	2	1	no	—
533	C₂×D₄₇	—	2	2	no	—
534	C₂×D₄₇	—	2	2	no	—
535	C₂×D₄₇	—	2	2	no	—
536	C₂×D₄₇	—	2	2	no	—
537	C₂×D₄₇	—	2	2	no	—
538	C₂×D₄₇	—	2	2	no	—
539	C₂×D₄₇	—	2	1	no	—
540	C₂×D₄₇	—	2	1	no	—
541	C₂×D₄₇	—	2	1	no	—
542	C₂×D₄₇	—	2	1	no	—
543	C₂×D₄₇	—	8	2	no	—
544	C₄×C₄₇	—	2	2	no	—
545	C₄×C₄₇	—	2	2	no	—
546	C₄×C₄₇	—	2	2	no	—
547	C₄×C₄₇	—	2	2	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	2	1	no	—
550	C₄×C₄₇	—	2	1	no	—
551	C₄×C₄₇	—	2	1	no	—
552	C₄×C₄₇	C₄×#41	1	2	yes	—
553	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
554	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
555	Dic₄₇	—	2	2	no	—
556	Dic₄₇	—	2	2	no	—
557	Dic₄₇	—	2	1	no	—
558	Dic₄₇	—	2	1	no	—
559	Dic₄₇	—	2	1	no	—
560	Dic₄₇	—	2	1	no	—
561	Dic₄₇	—	2	1	no	—
562	Dic₄₇	—	2	1	no	—
563	#3455	—	47	1	no	—
564	#2969	—	47	2	no	—
565	#2969	—	47	2	no	—
566	#2968	—	47	2	no	—
567	#2968	—	47	2	no	—
568	#2967	—	47	2	no	—
569	#2967	—	47	2	no	—
570	#2966	—	47	2	no	—
571	#2966	—	47	2	no	—
572	#2962	—	47	1	no	—
573	#2962	D₄₇	1	1	yes	characteristic, complemented
574	#2935	—	47	1	no	—
575	#2935	—	47	1	no	—
576	#2933	—	47	1	no	—
577	#2933	—	47	1	no	—
578	#2933	—	47	1	no	—
579	#2933	—	47	1	no	—
580	#2923	—	47	1	no	—
581	#2922	—	47	1	no	—
582	C₂×#433	—	47	1	no	—
583	#2875	—	47	1	no	—
584	C₄×#131	—	47	1	no	—
585	#2873	—	47	1	no	—
586	C₂×C₄₇	—	2	2	no	—
587	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
588	C₂×C₄₇	#3573	1	1	yes	characteristic
589	C₂×C₄₇	#3573	1	1	yes	characteristic
590	D₄₇	—	4	2	no	—
591	D₄₇	—	4	2	no	—
592	D₄₇	—	4	1	no	—
593	D₄₇	—	4	1	no	—
594	C₂×#131	—	47	1	no	—
595	C₂×#131	—	47	1	no	—
596	C₂×#131	—	47	1	no	—
597	C₂×#131	—	47	1	no	—
598	C₂²×M₁₆	—	47	1	no	—
599	C₂²×M₁₆	—	47	1	no	—
600	#542	—	47	1	no	—
601	#542	—	47	1	no	—
602	#542	—	47	1	no	—
603	#542	—	47	1	no	—
604	#541	—	47	1	no	—
605	#541	—	47	1	no	—
606	#540	—	47	1	no	—
607	#540	—	47	1	no	—
608	#539	—	47	2	no	—
609	#539	—	47	2	no	—
610	#538	—	47	2	no	—
611	#538	—	47	2	no	—
612	#533	C₂×D₄₇	1	1	yes	characteristic
613	#532	—	47	1	no	—
614	#529	—	47	2	no	—
615	#529	—	47	2	no	—
616	#529	—	47	2	no	—
617	#529	—	47	2	no	—
618	#525	—	47	1	no	—
619	#525	—	47	1	no	—
620	C₄×#41	—	47	1	no	—
621	C₄×#41	—	47	1	no	—
622	C₂×#117	—	47	1	no	—
623	#446	—	47	2	no	—
624	#446	—	47	2	no	—
625	#446	—	47	2	no	—
626	#446	C₂×D₄₇	1	2	yes	complemented
627	#446	C₂×D₄₇	1	2	yes	complemented
628	#446	C₂×D₄₇	1	2	yes	complemented
629	C₈×Q₈	—	47	2	no	—
630	C₈×Q₈	C₂×D₄₇	1	2	yes	complemented
631	#436	—	47	2	no	—
632	#436	—	47	2	no	—
633	#436	—	47	2	no	—
634	#436	—	47	2	no	—
635	#436	—	47	2	no	—
636	#436	—	47	2	no	—
637	#435	—	47	2	no	—
638	#435	—	47	2	no	—
639	#435	—	47	2	no	—
640	#435	—	47	2	no	—
641	#435	—	47	2	no	—
642	#435	—	47	2	no	—
643	#435	—	47	2	no	—
644	#435	—	47	2	no	—
645	#435	—	47	2	no	—
646	#435	—	47	2	no	—
647	#435	—	47	2	no	—
648	#435	—	47	2	no	—
649	C₈×D₄	—	47	2	no	—
650	C₈×D₄	—	47	2	no	—
651	C₈×D₄	—	47	2	no	—
652	C₈×D₄	—	47	2	no	—
653	C₈×D₄	—	47	2	no	—
654	C₈×D₄	—	47	2	no	—
655	#433	—	47	1	no	—
656	#433	—	47	1	no	—
657	#433	—	47	1	no	—
658	#433	—	47	1	no	—
659	#433	—	47	1	no	—
660	#433	—	47	1	no	—
661	#433	—	47	1	no	—
662	#433	—	47	1	no	—
663	#433	—	47	2	no	—
664	#433	—	47	2	no	—
665	#433	—	47	2	no	—
666	#433	—	47	2	no	—
667	#432	—	47	2	no	—
668	#432	—	47	2	no	—
669	#431	—	47	2	no	—
670	#431	—	47	2	no	—
671	#424	—	47	1	no	—
672	#424	—	47	1	no	—
673	#424	C₂×D₄₇	1	1	yes	characteristic
674	#424	C₂×D₄₇	1	1	yes	characteristic
675	C₂×C₄⋊C₈	—	47	1	no	—
676	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
677	#408	—	47	1	no	—
678	#408	—	47	1	no	—
679	#408	—	47	1	no	—
680	#408	—	47	1	no	—
681	C₂×C₂²⋊C₈	—	47	1	no	—
682	C₂×C₂²⋊C₈	—	47	1	no	—
683	#405	—	47	1	no	—
684	#405	—	47	1	no	—
685	#405	—	47	2	no	—
686	#405	—	47	2	no	—
687	#405	—	47	2	no	—
688	#405	—	47	2	no	—
689	#405	—	47	2	no	—
690	#405	—	47	2	no	—
691	#405	—	47	2	no	—
692	#405	—	47	2	no	—
693	#405	C₂×D₄₇	1	1	yes	characteristic
694	#405	C₂×D₄₇	1	1	yes	characteristic
695	C₄×M₁₆	—	47	1	no	—
696	C₄×M₁₆	—	47	1	no	—
697	C₄×M₁₆	—	47	1	no	—
698	C₄×M₁₆	—	47	2	no	—
699	C₄×M₁₆	—	47	2	no	—
700	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
701	C₂×#97	—	47	1	no	—
702	C₂×#97	—	47	2	no	—
703	C₂×C₄×C₈	—	47	1	no	—
704	C₂×C₄×C₈	—	47	2	no	—
705	C₄₇	#60212	1	1	yes	characteristic, complemented, Sylow
706	C₂×#41	—	47	1	no	—
707	C₂×#41	—	47	1	no	—
708	C₂³×C₄	—	47	1	no	—
709	#131	—	94	4	no	—
710	#131	—	94	4	no	—
711	#131	—	94	4	no	—
712	#131	—	94	4	no	—
713	C₂×M₁₆	—	47	1	no	—
714	C₂×M₁₆	—	47	1	no	—
715	C₂×M₁₆	—	47	2	no	—
716	C₂×M₁₆	—	47	2	no	—
717	C₂×M₁₆	—	47	2	no	—
718	C₂×M₁₆	—	47	2	no	—
719	C₂×M₁₆	—	47	2	no	—
720	C₂×M₁₆	—	47	2	no	—
721	C₂×M₁₆	—	94	4	no	—
722	C₂×M₁₆	—	94	4	no	—
723	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
724	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
725	C₂²×C₈	—	47	1	no	—
726	C₂²×C₈	—	47	1	no	—
727	C₂²×C₈	—	47	2	no	—
728	C₂²×C₈	—	47	2	no	—
729	C₂²×C₈	—	47	2	no	—
730	C₂²×C₈	—	47	2	no	—
731	C₂²×C₈	—	47	2	no	—
732	C₂²×C₈	—	47	2	no	—
733	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
734	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
735	C₄⋊Q₈	—	47	1	no	—
736	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
737	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
738	#127	—	47	1	no	—
739	#126	—	47	2	no	—
740	#126	—	47	2	no	—
741	#126	—	47	2	no	—
742	#126	—	47	2	no	—
743	#126	—	47	2	no	—
744	#126	—	47	2	no	—
745	#126	—	47	2	no	—
746	#126	—	47	2	no	—
747	#125	—	47	2	no	—
748	#125	—	47	2	no	—
749	#125	—	47	2	no	—
750	#125	—	47	2	no	—
751	#125	C₄×D₄₇	1	1	yes	characteristic
752	#125	C₄×D₄₇	1	1	yes	characteristic
753	#124	—	47	2	no	—
754	#124	—	47	2	no	—
755	#124	—	47	2	no	—
756	#124	—	47	2	no	—
757	#124	—	47	1	no	—
758	#124	—	47	1	no	—
759	#123	—	47	2	no	—
760	#123	—	47	2	no	—
761	#123	—	47	2	no	—
762	#123	—	47	2	no	—
763	#123	—	47	2	no	—
764	#123	—	47	2	no	—
765	#123	—	47	2	no	—
766	#123	—	47	2	no	—
767	#123	—	47	2	no	—
768	#123	—	47	2	no	—
769	C₂²⋊Q₈	—	47	2	no	—
770	C₂²⋊Q₈	—	47	2	no	—
771	C₂²⋊Q₈	—	47	2	no	—
772	C₂²⋊Q₈	—	47	2	no	—
773	C₂²⋊Q₈	—	47	1	no	—
774	C₂²⋊Q₈	—	47	1	no	—
775	C₂²⋊Q₈	—	47	1	no	—
776	C₂²⋊Q₈	—	47	1	no	—
777	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
778	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
779	#121	—	47	2	no	—
780	#121	—	47	2	no	—
781	#121	—	47	1	no	—
782	#121	—	47	1	no	—
783	#121	—	47	1	no	—
784	#121	—	47	1	no	—
785	#121	—	47	2	no	—
786	#121	—	47	2	no	—
787	#121	—	47	2	no	—
788	#121	—	47	2	no	—
789	#120	—	47	2	no	—
790	#120	—	47	2	no	—
791	C₄×Q₈	—	47	1	no	—
792	C₄×Q₈	—	47	1	no	—
793	C₄×Q₈	—	47	1	no	—
794	C₄×Q₈	—	47	1	no	—
795	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
796	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
797	C₄×D₄	—	47	1	no	—
798	C₄×D₄	—	47	1	no	—
799	C₄×D₄	—	47	1	no	—
800	C₄×D₄	—	47	1	no	—
801	C₄×D₄	—	47	2	no	—
802	C₄×D₄	—	47	2	no	—
803	C₄×D₄	—	47	2	no	—
804	C₄×D₄	—	47	2	no	—
805	C₄×D₄	—	47	2	no	—
806	C₄×D₄	—	47	2	no	—
807	C₄×D₄	—	47	2	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	2	no	—
811	#117	—	47	1	no	—
812	#117	—	47	1	no	—
813	#117	—	47	1	no	—
814	#117	—	47	1	no	—
815	#117	—	47	1	no	—
816	#117	—	47	1	no	—
817	#117	—	47	1	no	—
818	#117	—	47	1	no	—
819	#117	—	47	2	no	—
820	#117	—	47	2	no	—
821	#117	C₂²×D₄₇	1	1	yes	characteristic
822	#117	C₂²×D₄₇	1	1	yes	characteristic
823	C₂×C₄⋊C₄	—	47	1	no	—
824	C₂×C₄⋊C₄	—	47	1	no	—
825	C₂×C₂²⋊C₄	—	47	1	no	—
826	C₂×C₂²⋊C₄	—	47	1	no	—
827	C₂×C₄²	—	47	1	no	—
828	C₂×C₄²	—	47	2	no	—
829	C₂×C₄²	—	47	2	no	—
830	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
831	C₄⋊C₈	—	47	1	no	—
832	C₄⋊C₈	—	47	1	no	—
833	C₄⋊C₈	—	47	1	no	—
834	C₄⋊C₈	—	47	1	no	—
835	C₄⋊C₈	—	47	2	no	—
836	C₄⋊C₈	—	47	2	no	—
837	C₄⋊C₈	—	47	2	no	—
838	C₄⋊C₈	—	47	2	no	—
839	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
840	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
841	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
842	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
843	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
844	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
845	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
846	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
847	C₂²⋊C₈	—	47	1	no	—
848	C₂²⋊C₈	—	47	1	no	—
849	C₂²⋊C₈	—	47	1	no	—
850	C₂²⋊C₈	—	47	1	no	—
851	C₂²⋊C₈	—	47	1	no	—
852	C₂²⋊C₈	—	47	1	no	—
853	C₂²⋊C₈	—	47	1	no	—
854	C₂²⋊C₈	—	47	1	no	—
855	C₂²⋊C₈	—	47	2	no	—
856	C₂²⋊C₈	—	47	2	no	—
857	C₂²⋊C₈	—	47	2	no	—
858	C₂²⋊C₈	—	47	2	no	—
859	C₂²⋊C₈	—	47	2	no	—
860	C₂²⋊C₈	—	47	2	no	—
861	C₂²⋊C₈	—	47	2	no	—
862	C₂²⋊C₈	—	47	2	no	—
863	#97	—	47	1	no	—
864	#97	—	47	2	no	—
865	#97	—	47	1	no	—
866	#97	—	47	1	no	—
867	#97	—	47	1	no	—
868	#97	—	47	2	no	—
869	#97	—	47	2	no	—
870	#97	—	47	2	no	—
871	#97	—	47	2	no	—
872	#97	C₂²×D₄₇	1	2	yes	—
873	#97	C₂²×D₄₇	1	2	yes	—
874	#97	C₂²×D₄₇	1	2	yes	—
875	C₄×C₈	—	47	1	no	—
876	C₄×C₈	—	47	2	no	—
877	C₄×C₈	—	47	1	no	—
878	C₄×C₈	—	47	1	no	—
879	C₄×C₈	—	47	1	no	—
880	C₄×C₈	—	47	2	no	—
881	C₄×C₈	—	47	2	no	—
882	C₄×C₈	—	47	2	no	—
883	C₄×C₈	—	47	2	no	—
884	C₄×C₈	C₂²×D₄₇	1	2	yes	—
885	C₄×C₈	C₂²×D₄₇	1	2	yes	—
886	C₄×C₈	C₂²×D₄₇	1	2	yes	—
887	C₂⁴	—	47	1	no	—
888	#41	—	94	2	no	—
889	#41	—	94	2	no	—
890	#41	—	94	2	no	—
891	#41	—	94	2	no	—
892	C₂×Q₈	—	47	1	no	—
893	C₂×Q₈	—	47	1	no	—
894	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
895	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
896	C₂×D₄	—	47	2	no	—
897	C₂×D₄	—	47	2	no	—
898	C₂×D₄	—	47	1	no	—
899	C₂×D₄	—	47	1	no	—
900	C₂×D₄	—	47	2	no	—
901	C₂×D₄	—	47	2	no	—
902	C₂×D₄	—	47	2	no	—
903	C₂×D₄	—	47	2	no	—
904	C₂×D₄	—	47	2	no	—
905	C₂×D₄	—	47	2	no	—
906	C₂²×C₄	—	47	1	no	—
907	C₂²×C₄	—	47	1	no	—
908	C₂²×C₄	—	47	1	no	—
909	C₂²×C₄	—	47	1	no	—
910	C₂²×C₄	—	47	1	no	—
911	C₂²×C₄	—	47	2	no	—
912	C₂²×C₄	—	47	2	no	—
913	C₂²×C₄	—	47	1	no	—
914	C₂²×C₄	—	47	1	no	—
915	C₂²×C₄	—	47	2	no	—
916	C₂²×C₄	—	47	2	no	—
917	C₂²×C₄	—	47	2	no	—
918	C₂²×C₄	—	47	2	no	—
919	C₂²×C₄	—	94	2	no	—
920	C₂²×C₄	—	94	2	no	—
921	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
922	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
923	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
924	M₁₆	—	2	2	no	—
925	M₁₆	—	47	4	no	—
926	M₁₆	—	94	4	no	—
927	M₁₆	—	94	4	no	—
928	M₁₆	—	94	4	no	—
929	M₁₆	—	94	2	no	—
930	M₁₆	—	94	4	no	—
931	M₁₆	—	94	4	no	—
932	M₁₆	—	94	4	no	—
933	M₁₆	#10625354	1	4	yes	—
934	C₂×C₈	—	2	2	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	47	2	no	—
937	C₂×C₈	—	47	1	no	—
938	C₂×C₈	—	47	1	no	—
939	C₂×C₈	—	47	2	no	—
940	C₂×C₈	—	47	1	no	—
941	C₂×C₈	—	47	1	no	—
942	C₂×C₈	—	94	4	no	—
943	C₂×C₈	—	94	4	no	—
944	C₂×C₈	—	94	4	no	—
945	C₂×C₈	—	94	2	no	—
946	C₂×C₈	—	94	2	no	—
947	C₂×C₈	—	94	4	no	—
948	C₂×C₈	—	94	4	no	—
949	C₂×C₈	—	94	4	no	—
950	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₄₇	1	2	yes	—
953	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
954	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
955	C₂×C₈	C₂³×D₄₇	1	2	yes	—
956	C₄⋊C₄	—	47	1	no	—
957	C₄⋊C₄	—	47	1	no	—
958	C₄⋊C₄	—	47	1	no	—
959	C₄⋊C₄	—	47	1	no	—
960	C₄⋊C₄	—	47	1	no	—
961	C₄⋊C₄	—	47	1	no	—
962	C₄⋊C₄	—	47	1	no	—
963	C₄⋊C₄	—	47	1	no	—
964	C₄⋊C₄	—	47	2	no	—
965	C₄⋊C₄	—	47	2	no	—
966	C₄⋊C₄	—	47	2	no	—
967	C₄⋊C₄	—	47	2	no	—
968	C₄⋊C₄	—	47	2	no	—
969	C₄⋊C₄	—	47	2	no	—
970	C₄⋊C₄	—	47	2	no	—
971	C₄⋊C₄	—	47	2	no	—
972	C₄⋊C₄	—	47	2	no	—
973	C₄⋊C₄	—	47	2	no	—
974	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
975	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
979	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
980	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
981	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
982	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
983	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
984	C₂²⋊C₄	—	47	1	no	—
985	C₂²⋊C₄	—	47	1	no	—
986	C₂²⋊C₄	—	47	1	no	—
987	C₂²⋊C₄	—	47	1	no	—
988	C₂²⋊C₄	—	47	1	no	—
989	C₂²⋊C₄	—	47	1	no	—
990	C₂²⋊C₄	—	47	1	no	—
991	C₂²⋊C₄	—	47	1	no	—
992	C₂²⋊C₄	—	47	2	no	—
993	C₂²⋊C₄	—	47	2	no	—
994	C₂²⋊C₄	—	47	2	no	—
995	C₂²⋊C₄	—	47	2	no	—
996	C₂²⋊C₄	—	47	2	no	—
997	C₂²⋊C₄	—	47	2	no	—
998	C₂²⋊C₄	—	47	2	no	—
999	C₂²⋊C₄	—	47	2	no	—
1000	C₂²⋊C₄	—	47	2	no	—
1001	C₂²⋊C₄	—	47	2	no	—
1002	C₂²⋊C₄	—	47	2	no	—
1003	C₂²⋊C₄	—	47	2	no	—
1004	C₂²⋊C₄	—	47	2	no	—
1005	C₂²⋊C₄	—	47	2	no	—
1006	C₂²⋊C₄	—	47	2	no	—
1007	C₂²⋊C₄	—	47	2	no	—
1008	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1009	C₂²⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
1010	C₄²	—	47	1	no	—
1011	C₄²	—	47	1	no	—
1012	C₄²	—	47	2	no	—
1013	C₄²	—	47	2	no	—
1014	C₄²	—	47	2	no	—
1015	C₄²	—	47	2	no	—
1016	C₄²	—	47	1	no	—
1017	C₄²	—	47	1	no	—
1018	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1019	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
1020	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1021	C₄²	C₂³×D₄₇	1	2	yes	—
1022	C₄²	C₂³×D₄₇	1	2	yes	—
1023	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1024	C₂³	—	47	1	no	—
1025	C₂³	—	47	1	no	—
1026	C₂³	—	47	2	no	—
1027	C₂³	—	47	2	no	—
1028	C₂³	—	94	2	no	—
1029	C₂³	—	188	1	no	—
1030	C₂³	—	188	1	no	—
1031	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
1032	Q₈	—	4	2	no	—
1033	Q₈	—	4	2	no	—
1034	Q₈	—	94	2	no	—
1035	Q₈	—	94	2	no	—
1036	D₄	—	94	4	no	—
1037	D₄	—	94	4	no	—
1038	D₄	—	94	2	no	—
1039	D₄	—	94	2	no	—
1040	D₄	—	188	2	no	—
1041	D₄	—	188	2	no	—
1042	D₄	—	188	2	no	—
1043	D₄	—	188	2	no	—
1044	D₄	—	188	2	no	—
1045	D₄	—	188	2	no	—
1046	C₂×C₄	—	4	1	no	—
1047	C₂×C₄	—	4	1	no	—
1048	C₂×C₄	—	47	1	no	—
1049	C₂×C₄	—	47	1	no	—
1050	C₂×C₄	—	47	1	no	—
1051	C₂×C₄	—	47	1	no	—
1052	C₂×C₄	—	47	2	no	—
1053	C₂×C₄	—	47	2	no	—
1054	C₂×C₄	—	47	1	no	—
1055	C₂×C₄	—	47	1	no	—
1056	C₂×C₄	—	94	2	no	—
1057	C₂×C₄	—	94	2	no	—
1058	C₂×C₄	—	94	2	no	—
1059	C₂×C₄	—	94	1	no	—
1060	C₂×C₄	—	94	2	no	—
1061	C₂×C₄	—	94	2	no	—
1062	C₂×C₄	—	94	1	no	—
1063	C₂×C₄	—	94	1	no	—
1064	C₂×C₄	—	94	2	no	—
1065	C₂×C₄	—	94	2	no	—
1066	C₂×C₄	—	94	1	no	—
1067	C₂×C₄	—	188	2	no	—
1068	C₂×C₄	—	188	2	no	—
1069	C₂×C₄	—	188	2	no	—
1070	C₂×C₄	—	188	2	no	—
1071	C₂×C₄	—	188	1	no	—
1072	C₂×C₄	—	188	1	no	—
1073	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1074	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1075	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1076	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
1077	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1078	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1079	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1080	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1081	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
1082	C₂×C₄	#41×D₄₇	1	2	yes	—
1083	C₂×C₄	C₂×#10625354	1	2	yes	—
1084	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1085	C₈	—	2	1	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	2	no	—
1090	C₈	—	47	4	no	—
1091	C₈	—	94	1	no	—
1092	C₈	—	94	1	no	—
1093	C₈	—	94	2	no	—
1094	C₈	—	94	1	no	—
1095	C₈	—	94	1	no	—
1096	C₈	C₂×#10625354	1	4	yes	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	94	2	no	—
1100	C₂²	—	94	2	no	—
1101	C₂²	—	94	1	no	—
1102	C₂²	—	94	1	no	—
1103	C₂²	—	94	2	no	—
1104	C₂²	—	94	2	no	—
1105	C₂²	—	94	1	no	—
1106	C₂²	—	94	1	no	—
1107	C₂²	—	94	1	no	—
1108	C₂²	—	94	1	no	—
1109	C₂²	—	94	2	no	—
1110	C₂²	—	94	2	no	—
1111	C₂²	—	376	2	no	—
1112	C₂²	C₄×#10625354	1	2	yes	—
1113	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	94	1	no	—
1123	C₄	—	94	1	no	—
1124	C₄	—	94	1	no	—
1125	C₄	—	94	1	no	—
1126	C₄	—	94	1	no	—
1127	C₄	—	94	1	no	—
1128	C₄	—	94	2	no	—
1129	C₄	—	94	2	no	—
1130	C₄	C₄×#10625354	1	2	yes	—
1131	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1132	C₄	C₂²×#10625354	1	1	yes	characteristic
1133	C₂	—	2	2	no	—
1134	C₂	—	188	1	no	—
1135	C₂	—	188	1	no	—
1136	C₂	—	188	2	no	—
1137	C₂	—	188	2	no	—
1138	C₂	C₂×C₄×#10625354	1	1	yes	characteristic
1139	C₂	#20258099	1	1	yes	characteristic
1140	C₂	#20258101	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2962	C₂
prime radical	#20256780	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2962	D₄₇
hypocenter	C₄₇	#60212
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2962

Complements

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

N	H ≅ G/N	type
2. #20252394	C₂	semidirect
3. #20252391	C₂	semidirect
4. #20252381	C₂	semidirect
5. #20252381	C₂	semidirect
6. #20252372	C₂	semidirect
7. #20252372	C₂	semidirect
8. #20252365	C₂	semidirect
9. #20252362	C₂	semidirect
10. #20252337	C₂	semidirect
11. #20252134	C₂	semidirect
12. #20252131	C₂	semidirect
13. #20252116	C₂	semidirect
14. #20252116	C₂	semidirect
15. #20252112	C₂	semidirect
16. #20252112	C₂	semidirect
17. #20252038	C₂	semidirect
18. #20252031	C₂	semidirect
19. C₂×#15689183	C₂	semidirect
20. #20251815	C₂	semidirect
21. #20251810	C₂	semidirect
22. #20251805	C₂	semidirect
23. C₄₇×#2962	C₂	semidirect
52. #15689254	C₂²	semidirect
53. #15689254	C₂²	semidirect
54. #15689254	C₂²	semidirect
55. Q₈×C₄₇⋊C₈	C₂²	semidirect
58. #15689202	C₂²	semidirect
61. #15689200	C₂²	semidirect
66. #15689196	C₂²	semidirect
67. #15689196	C₂²	semidirect
72. #15689193	C₂²	semidirect
73. #15689193	C₂²	semidirect
76. C₈×D₁₈₈	C₂²	semidirect
79. #15689188	C₂²	semidirect
88. #15689183	C₂²	semidirect
89. #15689183	C₂²	semidirect
90. #15689183	C₂²	semidirect
91. #15689183	C₂²	semidirect
92. #15689179	C₂²	semidirect
93. #15689179	C₂²	semidirect
94. #15689175	C₂²	semidirect
95. #15689175	C₂²	semidirect
107. #15689080	C₂²	semidirect
108. #15689080	C₂²	semidirect
113. #15689077	C₂²	semidirect
114. #15689077	C₂²	semidirect
116. #15689075	C₂²	semidirect
119. C₄×#10625324	C₂²	semidirect
121. #97×D₄₇	C₂²	semidirect
123. C₄×C₈×D₄₇	C₂²	semidirect
125. C₄₇×#446	C₂²	semidirect
126. C₄₇×#446	C₂²	semidirect
127. C₄₇×#446	C₂²	semidirect
128. C₈×Q₈×C₄₇	C₂²	semidirect
573. #2962	D₄₇	semidirect
626. #446	C₂×D₄₇	semidirect
627. #446	C₂×D₄₇	semidirect
628. #446	C₂×D₄₇	semidirect
630. C₈×Q₈	C₂×D₄₇	semidirect
705. C₄₇	#60212	semidirect

Maximal subgroups

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

subgroup	index
#20256780	2
#20252394	2
#20252391	2
#20252381	2
#20252372	2
#20252365	2
#20252362	2
#20252337	2
#20252134	2
#20252131	2
#20252116	2
#20252112	2
#20252038	2
#20252031	2
C₂×#15689183	2
#20251815	2
#20251810	2
#20251805	2
C₄₇×#2962	2
#60212	47