Subgroups — #27085007

Order 12032.

2274 conjugacy classes of subgroups.

The subgroup lattice has 940 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	#20253626	C₂	1	4	yes	maximal, complemented
3	#20253566	C₂	1	4	yes	maximal, complemented
4	#20253522	C₂	1	2	yes	maximal, complemented
5	#20253475	C₂	1	2	yes	maximal, complemented
6	#20253431	C₂	1	2	yes	maximal, complemented
7	#20253384	C₂	1	2	yes	maximal, complemented
8	#20253324	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	#20252887	C₂	1	2	yes	maximal, complemented
12	#20252614	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15689256	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252238	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×#3494	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
19	C₂×#13094049	C₂²	1	2	yes	—
20	C₂²×#10625334	C₂²	1	2	yes	—
21	#15689597	—	2	2	no	—
22	#15689597	—	2	1	no	—
23	#15689597	—	2	1	no	—
24	#15689597	C₂²	1	2	yes	—
25	#15689597	C₂²	1	2	yes	—
26	#15689597	C₂²	1	4	yes	complemented
27	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
28	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
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	#15689456	C₂²	1	1	yes	characteristic, complemented
35	#15689451	C₂²	1	1	yes	characteristic, complemented
36	#15689444	C₂²	1	2	yes	complemented
37	#15689444	C₂²	1	4	yes	complemented
38	#15689439	C₂²	1	1	yes	characteristic, complemented
39	#15689439	C₂²	1	2	yes	complemented
40	#15689434	C₂²	1	2	yes	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	#15689315	C₂²	1	4	yes	complemented
49	#15689315	C₂²	1	4	yes	complemented
50	#15689273	C₂²	1	2	yes	complemented
51	#15689273	C₂²	1	2	yes	complemented
52	#15689256	C₂²	1	2	yes	—
53	#15689256	C₂²	1	4	yes	—
54	#15689256	C₂²	1	2	yes	—
55	#15689256	C₂²	1	2	yes	complemented
56	#15689256	C₂²	1	2	yes	complemented
57	#15689233	C₂²	1	4	yes	complemented
58	#15689233	C₂²	1	4	yes	complemented
59	#15689233	C₂²	1	4	yes	complemented
60	#15689221	C₂²	1	4	yes	complemented
61	C₄×#10625336	C₂²	1	4	yes	complemented
62	C₄×#10625334	C₂²	1	4	yes	complemented
63	C₄×#10625334	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	#15689128	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×#555	—	2	1	no	—
79	C₄₇×#553	—	2	1	no	—
80	C₄₇×#553	—	2	1	no	—
81	C₄₇×#551	—	2	2	no	—
82	C₄₇×#547	—	2	1	no	—
83	C₄₇×#546	—	2	2	no	—
84	C₄₇×#544	C₂²	1	1	yes	characteristic, complemented
85	C₄₇×#542	C₂²	1	2	yes	complemented
86	C₄₇×#540	C₂²	1	2	yes	complemented
87	C₄₇×#535	C₂²	1	1	yes	characteristic, complemented
88	C₄₇×#532	C₂²	1	2	yes	complemented
89	C₄₇×#529	C₂²	1	2	yes	complemented
90	C₄₇×#525	C₂²	1	1	yes	characteristic
91	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
92	C₄₇×#520	C₂²	1	1	yes	characteristic, complemented
93	C₄₇×#518	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	C₂³	1	4	yes	—
107	C₂×#10625334	—	2	8	no	—
108	C₂×#10625334	C₂³	1	4	yes	—
109	C₂×#10625334	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	2	no	—
125	#13093986	—	2	4	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	4	yes	complemented
142	#13093957	C₂³	1	2	yes	complemented
143	#13093957	C₂³	1	2	yes	complemented
144	#13093955	C₂³	1	2	yes	complemented
145	#13093955	C₂³	1	2	yes	complemented
146	#13093955	C₂³	1	4	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	2	yes	complemented
151	#13093945	C₂³	1	2	yes	complemented
152	#13093945	C₂³	1	4	yes	complemented
153	#13093945	C₂³	1	4	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	1	yes	characteristic
160	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
161	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
162	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
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	—	2	2	no	—
167	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
168	C₂²×D₄×C₄₇	—	2	1	no	—
169	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
170	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₄₇	—	2	1	no	—
172	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	complemented
173	#127×C₄₇	C₂³	1	2	yes	complemented
174	#126×C₄₇	—	2	2	no	—
175	#126×C₄₇	—	2	2	no	—
176	#125×C₄₇	—	2	1	no	—
177	#125×C₄₇	C₂³	1	2	yes	complemented
178	#124×C₄₇	—	2	2	no	—
179	#124×C₄₇	—	2	2	no	—
180	#124×C₄₇	C₂³	1	2	yes	complemented
181	#123×C₄₇	—	2	1	no	—
182	#123×C₄₇	—	2	2	no	—
183	#123×C₄₇	—	2	2	no	—
184	#123×C₄₇	—	2	2	no	—
185	#123×C₄₇	—	2	2	no	—
186	C₂²⋊Q₈×C₄₇	—	2	2	no	—
187	C₂²⋊Q₈×C₄₇	—	2	2	no	—
188	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
189	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
190	#121×C₄₇	—	2	1	no	—
191	#121×C₄₇	—	2	1	no	—
192	#121×C₄₇	—	2	2	no	—
193	#121×C₄₇	—	2	1	no	—
194	#121×C₄₇	—	2	1	no	—
195	#121×C₄₇	—	2	2	no	—
196	#121×C₄₇	—	2	2	no	—
197	#121×C₄₇	C₂³	1	2	yes	—
198	#121×C₄₇	C₂³	1	2	yes	—
199	#121×C₄₇	C₂³	1	1	yes	characteristic
200	#121×C₄₇	C₂³	1	1	yes	characteristic
201	#120×C₄₇	—	2	1	no	—
202	#120×C₄₇	—	2	2	no	—
203	C₄×Q₈×C₄₇	C₂³	1	2	yes	complemented
204	C₄×D₄×C₄₇	—	2	1	no	—
205	C₄×D₄×C₄₇	—	2	1	no	—
206	C₄×D₄×C₄₇	—	2	2	no	—
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	C₄×D₄×C₄₇	C₂³	1	2	yes	complemented
213	C₄×D₄×C₄₇	C₂³	1	2	yes	complemented
214	#117×C₄₇	—	2	1	no	—
215	#117×C₄₇	—	2	2	no	—
216	#117×C₄₇	D₄	1	2	yes	—
217	#117×C₄₇	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
228	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
229	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
230	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
231	C₂⁴×C₄₇	—	2	1	no	—
232	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
233	C₂³×D₄₇	—	2	2	no	—
234	C₂³×D₄₇	—	2	8	no	—
235	C₂³×D₄₇	—	2	2	no	—
236	C₂³×D₄₇	—	2	2	no	—
237	C₂³×D₄₇	—	8	2	no	—
238	C₂³×D₄₇	—	8	2	no	—
239	#41×C₄₇	—	2	4	no	—
240	#41×C₄₇	—	8	4	no	—
241	C₂×Q₈×C₄₇	—	2	2	no	—
242	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₄₇	—	2	1	no	—
244	C₂×D₄×C₄₇	—	2	1	no	—
245	C₂×D₄×C₄₇	—	2	2	no	—
246	C₂×D₄×C₄₇	—	2	1	no	—
247	C₂×D₄×C₄₇	—	2	2	no	—
248	C₂×D₄×C₄₇	—	2	1	no	—
249	C₂×D₄×C₄₇	—	2	2	no	—
250	C₂×D₄×C₄₇	—	2	2	no	—
251	C₂×D₄×C₄₇	—	2	4	no	—
252	C₂×D₄×C₄₇	—	8	2	no	—
253	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
254	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₄₇	—	2	4	no	—
256	C₂²×C₄×C₄₇	—	2	1	no	—
257	C₂²×C₄×C₄₇	—	2	1	no	—
258	C₂²×C₄×C₄₇	—	2	2	no	—
259	C₂²×C₄×C₄₇	—	2	2	no	—
260	C₂²×C₄×C₄₇	—	2	2	no	—
261	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
269	C₂²×Dic₄₇	—	2	1	no	—
270	C₂²×Dic₄₇	—	2	1	no	—
271	C₂×D₁₈₈	—	2	8	no	—
272	C₂×D₁₈₈	—	2	8	no	—
273	C₂×D₁₈₈	—	2	8	no	—
274	C₂×D₁₈₈	—	2	2	no	—
275	C₂×D₁₈₈	—	2	2	no	—
276	C₂×D₁₈₈	—	2	2	no	—
277	C₂×D₁₈₈	—	2	4	no	—
278	C₂×D₁₈₈	—	2	8	no	—
279	C₂×D₁₈₈	—	2	8	no	—
280	C₂×D₁₈₈	#41	1	8	yes	complemented
281	C₂×D₁₈₈	C₂⁴	1	4	yes	—
282	C₂×C₄×D₄₇	—	2	4	no	—
283	C₂×C₄×D₄₇	—	2	4	no	—
284	C₂×C₄×D₄₇	—	2	4	no	—
285	C₂×C₄×D₄₇	—	2	4	no	—
286	C₂×C₄×D₄₇	—	8	4	no	—
287	C₂×C₄×D₄₇	—	8	4	no	—
288	C₄⋊C₄×C₄₇	—	2	1	no	—
289	C₄⋊C₄×C₄₇	—	2	2	no	—
290	C₄⋊C₄×C₄₇	—	2	1	no	—
291	C₄⋊C₄×C₄₇	—	2	2	no	—
292	C₄⋊C₄×C₄₇	—	2	2	no	—
293	C₄⋊C₄×C₄₇	—	2	2	no	—
294	C₄⋊C₄×C₄₇	—	2	1	no	—
295	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
299	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
308	C₂²⋊C₄×C₄₇	—	2	2	no	—
309	C₂²⋊C₄×C₄₇	—	2	2	no	—
310	C₂²⋊C₄×C₄₇	—	2	2	no	—
311	C₂²⋊C₄×C₄₇	—	2	2	no	—
312	C₂²⋊C₄×C₄₇	—	2	2	no	—
313	C₂²⋊C₄×C₄₇	—	2	1	no	—
314	C₂²⋊C₄×C₄₇	—	2	2	no	—
315	C₂²⋊C₄×C₄₇	—	2	1	no	—
316	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
317	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
318	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
320	C₄²×C₄₇	—	2	2	no	—
321	C₄²×C₄₇	—	2	1	no	—
322	C₄²×C₄₇	C₂×D₄	1	2	yes	—
323	C₄²×C₄₇	C₂×D₄	1	2	yes	—
324	C₄²×C₄₇	C₂⁴	1	2	yes	—
325	C₄²×C₄₇	C₂⁴	1	2	yes	—
326	C₂²⋊Dic₄₇	—	2	2	no	—
327	C₂²⋊Dic₄₇	—	2	2	no	—
328	#10625336	—	2	8	no	—
329	#10625334	—	2	8	no	—
330	#10625334	—	2	8	no	—
331	#10625334	—	2	8	no	—
332	(C₂×D₄₇)⋊C₄	—	2	4	no	—
333	(C₂×D₄₇)⋊C₄	—	2	4	no	—
334	(C₂×D₄₇)⋊C₄	—	2	4	no	—
335	(C₂×D₄₇)⋊C₄	—	2	4	no	—
336	C₄⋊Dic₄₇	—	2	1	no	—
337	C₄⋊Dic₄₇	—	2	1	no	—
338	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
339	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
340	C₄×Dic₄₇	—	2	2	no	—
341	C₄×Dic₄₇	—	2	2	no	—
342	#10625329	—	2	4	no	—
343	C₂×C₄₇⋊C₈	—	2	4	no	—
344	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
345	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
346	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
347	C₂³×C₄₇	—	2	2	no	—
348	C₂³×C₄₇	—	2	2	no	—
349	C₂³×C₄₇	—	2	2	no	—
350	C₂³×C₄₇	—	2	1	no	—
351	C₂³×C₄₇	—	4	1	no	—
352	C₂³×C₄₇	—	4	2	no	—
353	C₂³×C₄₇	—	8	1	no	—
354	C₂³×C₄₇	—	8	1	no	—
355	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
357	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
358	C₂²×D₄₇	—	2	8	no	—
359	C₂²×D₄₇	—	2	4	no	—
360	C₂²×D₄₇	—	2	8	no	—
361	C₂²×D₄₇	—	2	8	no	—
362	C₂²×D₄₇	—	4	4	no	—
363	C₂²×D₄₇	—	4	4	no	—
364	C₂²×D₄₇	—	8	2	no	—
365	C₂²×D₄₇	—	8	2	no	—
366	C₂²×D₄₇	—	8	2	no	—
367	C₂²×D₄₇	—	8	2	no	—
368	C₂²×D₄₇	—	8	16	no	—
369	Q₈×C₄₇	—	2	2	no	—
370	Q₈×C₄₇	—	8	2	no	—
371	D₄×C₄₇	—	2	4	no	—
372	D₄×C₄₇	—	2	2	no	—
373	D₄×C₄₇	—	4	2	no	—
374	D₄×C₄₇	—	4	4	no	—
375	D₄×C₄₇	—	4	2	no	—
376	D₄×C₄₇	—	4	2	no	—
377	D₄×C₄₇	—	8	2	no	—
378	D₄×C₄₇	—	8	2	no	—
379	D₄×C₄₇	—	8	1	no	—
380	D₄×C₄₇	—	8	2	no	—
381	C₂×C₄×C₄₇	—	2	2	no	—
382	C₂×C₄×C₄₇	—	2	4	no	—
383	C₂×C₄×C₄₇	—	2	2	no	—
384	C₂×C₄×C₄₇	—	2	2	no	—
385	C₂×C₄×C₄₇	—	2	2	no	—
386	C₂×C₄×C₄₇	—	2	2	no	—
387	C₂×C₄×C₄₇	—	2	1	no	—
388	C₂×C₄×C₄₇	—	2	1	no	—
389	C₂×C₄×C₄₇	—	2	1	no	—
390	C₂×C₄×C₄₇	—	2	2	no	—
391	C₂×C₄×C₄₇	—	4	2	no	—
392	C₂×C₄×C₄₇	—	4	2	no	—
393	C₂×C₄×C₄₇	—	8	2	no	—
394	C₂×C₄×C₄₇	—	8	2	no	—
395	C₂×C₄×C₄₇	—	8	2	no	—
396	C₂×C₄×C₄₇	—	8	1	no	—
397	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
405	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
406	C₂×Dic₄₇	—	2	2	no	—
407	C₂×Dic₄₇	—	2	2	no	—
408	C₂×Dic₄₇	—	4	2	no	—
409	C₂×Dic₄₇	—	4	2	no	—
410	D₁₈₈	—	2	8	no	—
411	D₁₈₈	—	2	8	no	—
412	D₁₈₈	—	2	8	no	—
413	D₁₈₈	—	2	4	no	—
414	D₁₈₈	C₂×#41	1	8	yes	—
415	C₄×D₄₇	—	8	4	no	—
416	C₄×D₄₇	—	8	4	no	—
417	C₄×D₄₇	—	8	4	no	—
418	C₄×D₄₇	—	8	4	no	—
419	C₄₇⋊C₈	—	2	2	no	—
420	C₄₇⋊C₈	—	2	2	no	—
421	C₄₇⋊C₈	—	2	4	no	—
422	#60578	—	47	1	no	maximal, Sylow
423	C₂²×C₄₇	—	2	1	no	—
424	C₂²×C₄₇	—	2	1	no	—
425	C₂²×C₄₇	—	2	1	no	—
426	C₂²×C₄₇	—	2	1	no	—
427	C₂²×C₄₇	—	2	1	no	—
428	C₂²×C₄₇	—	2	1	no	—
429	C₂²×C₄₇	—	2	1	no	—
430	C₂²×C₄₇	—	4	4	no	—
431	C₂²×C₄₇	—	4	2	no	—
432	C₂²×C₄₇	—	4	1	no	—
433	C₂²×C₄₇	—	4	1	no	—
434	C₂²×C₄₇	—	4	2	no	—
435	C₂²×C₄₇	—	4	1	no	—
436	C₂²×C₄₇	—	4	2	no	—
437	C₂²×C₄₇	—	16	2	no	—
438	C₂²×C₄₇	#525	1	2	yes	—
439	C₂²×C₄₇	#576	1	2	yes	—
440	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
441	C₂×D₄₇	—	2	8	no	—
442	C₂×D₄₇	—	4	16	no	—
443	C₂×D₄₇	—	4	4	no	—
444	C₂×D₄₇	—	4	4	no	—
445	C₂×D₄₇	—	8	8	no	—
446	C₂×D₄₇	—	8	8	no	—
447	C₄×C₄₇	—	2	2	no	—
448	C₄×C₄₇	—	2	2	no	—
449	C₄×C₄₇	—	2	1	no	—
450	C₄×C₄₇	—	2	1	no	—
451	C₄×C₄₇	—	2	2	no	—
452	C₄×C₄₇	—	2	2	no	—
453	C₄×C₄₇	—	4	1	no	—
454	C₄×C₄₇	—	4	1	no	—
455	C₄×C₄₇	—	4	2	no	—
456	C₄×C₄₇	—	4	1	no	—
457	C₄×C₄₇	#525	1	2	yes	—
458	C₄×C₄₇	C₂²×#41	1	2	yes	—
459	Dic₄₇	—	4	2	no	—
460	Dic₄₇	—	4	2	no	—
461	#3494	D₄₇	1	1	yes	characteristic, complemented
462	C₂×#518	—	47	1	no	—
463	#3122	—	47	4	no	—
464	#3118	—	47	4	no	—
465	#3114	—	47	2	no	—
466	#3109	—	47	2	no	—
467	#3105	—	47	2	no	—
468	#3100	—	47	2	no	—
469	#3094	—	47	1	no	—
470	#3091	—	47	1	no	—
471	#3081	—	47	2	no	—
472	#3041	—	47	2	no	—
473	#3003	—	47	1	no	—
474	C₂×#447	—	47	1	no	—
475	#2948	—	47	2	no	—
476	#2946	—	47	2	no	—
477	#2924	—	47	1	no	—
478	C₂×C₄₇	—	2	2	no	—
479	C₂×C₄₇	—	2	2	no	—
480	C₂×C₄₇	—	4	1	no	—
481	C₂×C₄₇	—	8	1	no	—
482	C₂×C₄₇	—	8	2	no	—
483	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
484	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
485	C₂×C₄₇	#3585	1	1	yes	characteristic
486	D₄₇	—	4	8	no	—
487	C₂³×D₄	—	47	1	no	—
488	C₂×AGL(1,ℤ/8)	—	47	2	no	—
489	C₂²×D₈	—	47	2	no	—
490	#555	—	2	1	no	—
491	#553	—	2	1	no	—
492	#553	—	2	1	no	—
493	#551	—	2	2	no	—
494	#547	—	2	1	no	—
495	#546	—	2	2	no	—
496	#544	C₂×D₄₇	1	1	yes	characteristic, complemented
497	#542	C₂×D₄₇	1	2	yes	complemented
498	#540	C₂×D₄₇	1	2	yes	complemented
499	#535	C₂×D₄₇	1	1	yes	characteristic, complemented
500	#532	C₂×D₄₇	1	2	yes	complemented
501	#529	C₂×D₄₇	1	2	yes	complemented
502	#525	C₂×D₄₇	1	1	yes	characteristic
503	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
504	#520	C₂×D₄₇	1	1	yes	characteristic, complemented
505	#518	—	47	2	no	—
506	#518	—	47	4	no	—
507	#518	—	47	2	no	—
508	#518	—	94	2	no	—
509	#518	—	94	1	no	—
510	#518	—	94	1	no	—
511	#518	C₂×D₄₇	1	1	yes	characteristic, complemented
512	C₂×C₄×D₄	—	47	2	no	—
513	C₂×C₄×D₄	—	47	2	no	—
514	C₂×C₄×D₄	—	94	1	no	—
515	C₂×C₄×D₄	—	94	1	no	—
516	C₂×#117	—	47	1	no	—
517	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
518	C₂²×C₂²⋊C₄	—	94	2	no	—
519	#485	—	47	2	no	—
520	#484	—	47	1	no	—
521	#483	—	47	1	no	—
522	#482	—	47	2	no	—
523	#482	—	47	4	no	—
524	#481	—	47	1	no	—
525	#481	—	47	2	no	—
526	#480	—	47	1	no	—
527	#480	—	47	2	no	—
528	#478	—	47	4	no	—
529	#478	—	47	4	no	—
530	#476	—	47	4	no	—
531	#474	—	47	4	no	—
532	#463	—	47	4	no	—
533	#463	—	47	4	no	—
534	#459	—	47	4	no	—
535	#459	—	47	4	no	—
536	#450	—	47	2	no	—
537	#450	—	47	2	no	—
538	#447	—	47	2	no	—
539	#447	—	47	2	no	—
540	#447	—	47	2	no	—
541	#447	—	47	4	no	—
542	#447	—	47	2	no	—
543	#442	—	47	4	no	—
544	#442	—	47	4	no	—
545	#442	—	47	4	no	—
546	#440	—	47	4	no	—
547	C₄×SD₁₆	—	47	4	no	—
548	C₄×D₈	—	47	4	no	—
549	C₄×D₈	—	47	4	no	—
550	C₄×D₈	—	47	4	no	—
551	#433	—	47	4	no	—
552	#432	—	47	2	no	—
553	#431	—	47	2	no	—
554	#428	—	47	2	no	—
555	#427	—	47	2	no	—
556	#424	—	47	2	no	—
557	#418	—	47	2	no	—
558	#418	—	47	2	no	—
559	#416	—	47	2	no	—
560	C₂×#102	—	47	2	no	—
561	#407	—	47	1	no	—
562	C₂×C₂²⋊C₈	—	47	1	no	—
563	#405	—	47	2	no	—
564	C₄₇	#60578	1	1	yes	characteristic, complemented, Sylow
565	C₂⁵	—	94	1	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
568	C₂²×D₄	—	2	1	no	—
569	C₂²×D₄	—	47	2	no	—
570	C₂²×D₄	—	47	2	no	—
571	C₂²×D₄	—	47	2	no	—
572	C₂²×D₄	—	94	8	no	—
573	C₂²×D₄	—	94	1	no	—
574	C₂²×D₄	—	94	1	no	—
575	C₂²×D₄	—	94	1	no	—
576	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
577	C₂³×C₄	—	94	2	no	—
578	C₂³×C₄	—	94	2	no	—
579	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
580	AGL(1,ℤ/8)	—	94	8	no	—
581	C₂×SD₁₆	—	47	4	no	—
582	C₂×D₈	—	47	4	no	—
583	C₂×D₈	—	47	4	no	—
584	C₂×D₈	—	47	4	no	—
585	C₂×D₈	—	94	8	no	—
586	C₂×M₁₆	—	47	2	no	—
587	C₂²×C₈	—	47	2	no	—
588	C₄⋊Q₈	—	2	1	no	—
589	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	complemented
590	#127	C₂²×D₄₇	1	2	yes	complemented
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#125	—	2	1	no	—
594	#125	C₂²×D₄₇	1	2	yes	complemented
595	#124	—	2	2	no	—
596	#124	—	2	2	no	—
597	#124	C₂²×D₄₇	1	2	yes	complemented
598	#123	—	2	1	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
606	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	1	no	—
611	#121	—	2	1	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	C₂²×D₄₇	1	2	yes	—
615	#121	C₂²×D₄₇	1	2	yes	—
616	#121	C₂²×D₄₇	1	1	yes	characteristic
617	#121	C₂²×D₄₇	1	1	yes	characteristic
618	#120	—	2	1	no	—
619	#120	—	2	2	no	—
620	C₄×Q₈	C₂²×D₄₇	1	2	yes	complemented
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	47	4	no	—
629	C₄×D₄	—	47	4	no	—
630	C₄×D₄	—	47	4	no	—
631	C₄×D₄	—	47	4	no	—
632	C₄×D₄	—	94	2	no	—
633	C₄×D₄	—	94	2	no	—
634	C₄×D₄	—	94	2	no	—
635	C₄×D₄	—	94	2	no	—
636	C₄×D₄	—	94	4	no	—
637	C₄×D₄	—	94	4	no	—
638	C₄×D₄	—	94	2	no	—
639	C₄×D₄	—	94	2	no	—
640	C₄×D₄	—	94	2	no	—
641	C₄×D₄	—	94	2	no	—
642	C₄×D₄	C₂²×D₄₇	1	2	yes	complemented
643	C₄×D₄	C₂²×D₄₇	1	2	yes	complemented
644	C₄×D₄	C₂²×D₄₇	1	2	yes	complemented
645	#117	—	2	1	no	—
646	#117	—	2	2	no	—
647	#117	—	47	2	no	—
648	#117	—	47	2	no	—
649	#117	—	94	1	no	—
650	#117	—	94	1	no	—
651	#117	C₂²⋊D₄₇	1	2	yes	—
652	#117	C₂²⋊D₄₇	1	1	yes	characteristic
653	#117	C₂²⋊D₄₇	1	1	yes	characteristic
654	#117	C₂²×D₄₇	1	1	yes	characteristic
655	#117	C₂²×D₄₇	1	1	yes	characteristic
656	#117	C₂²×D₄₇	1	1	yes	characteristic
657	#117	C₂²×D₄₇	1	2	yes	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	47	1	no	—
660	C₂×C₄⋊C₄	—	47	1	no	—
661	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	94	1	no	—
667	C₂×C₂²⋊C₄	—	94	2	no	—
668	C₂×C₂²⋊C₄	—	94	2	no	—
669	C₂×C₂²⋊C₄	—	94	4	no	—
670	C₂×C₂²⋊C₄	—	94	4	no	—
671	C₂×C₂²⋊C₄	—	94	4	no	—
672	C₂×C₂²⋊C₄	—	94	4	no	—
673	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
674	C₂×C₄²	—	94	1	no	—
675	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
676	#107	—	47	2	no	—
677	#107	—	47	2	no	—
678	#107	—	47	4	no	—
679	#106	—	47	2	no	—
680	#106	—	47	2	no	—
681	#106	—	47	4	no	—
682	C₄⋊C₈	—	47	4	no	—
683	C₄⋊C₈	—	47	4	no	—
684	#103	—	47	2	no	—
685	#103	—	47	2	no	—
686	#102	—	47	2	no	—
687	#102	—	47	2	no	—
688	#102	—	47	4	no	—
689	#102	—	47	4	no	—
690	#102	—	47	4	no	—
691	#102	—	47	4	no	—
692	#102	—	47	4	no	—
693	#102	—	47	4	no	—
694	C₂²⋊C₈	—	47	1	no	—
695	C₂²⋊C₈	—	47	1	no	—
696	C₂²⋊C₈	—	47	2	no	—
697	C₂²⋊C₈	—	47	2	no	—
698	C₂²⋊C₈	—	47	2	no	—
699	#97	—	47	4	no	—
700	C₄×C₈	—	47	4	no	—
701	C₂⁴	—	2	1	no	—
702	C₂⁴	—	94	8	no	—
703	C₂⁴	—	94	2	no	—
704	C₂⁴	—	94	2	no	—
705	C₂⁴	—	94	2	no	—
706	C₂⁴	—	376	2	no	—
707	C₂⁴	—	376	2	no	—
708	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
709	#41	—	2	4	no	—
710	#41	—	8	4	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	8	2	no	—
723	C₂×D₄	—	47	8	no	—
724	C₂×D₄	—	47	4	no	—
725	C₂×D₄	—	94	8	no	—
726	C₂×D₄	—	94	8	no	—
727	C₂×D₄	—	94	8	no	—
728	C₂×D₄	—	94	8	no	—
729	C₂×D₄	—	94	8	no	—
730	C₂×D₄	—	94	2	no	—
731	C₂×D₄	—	94	2	no	—
732	C₂×D₄	—	94	2	no	—
733	C₂×D₄	—	94	4	no	—
734	C₂×D₄	C₂³×D₄₇	1	2	yes	—
735	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	94	1	no	—
743	C₂²×C₄	—	94	1	no	—
744	C₂²×C₄	—	94	4	no	—
745	C₂²×C₄	—	94	4	no	—
746	C₂²×C₄	—	94	4	no	—
747	C₂²×C₄	—	94	4	no	—
748	C₂²×C₄	—	376	4	no	—
749	C₂²×C₄	—	376	4	no	—
750	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
751	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
752	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
753	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
754	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
755	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
756	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
757	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
758	SD₁₆	—	94	8	no	—
759	D₈	—	94	8	no	—
760	D₈	—	94	8	no	—
761	D₈	—	94	8	no	—
762	M₁₆	—	94	4	no	—
763	C₂×C₈	—	47	2	no	—
764	C₂×C₈	—	47	4	no	—
765	C₂×C₈	—	47	2	no	—
766	C₂×C₈	—	94	4	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	47	2	no	—
775	C₄⋊C₄	—	47	2	no	—
776	C₄⋊C₄	—	94	1	no	—
777	C₄⋊C₄	—	94	1	no	—
778	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
780	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
783	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
784	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
785	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
786	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
787	C₂²⋊C₄	—	2	1	no	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	94	2	no	—
800	C₂²⋊C₄	—	94	2	no	—
801	C₂²⋊C₄	—	94	4	no	—
802	C₂²⋊C₄	—	94	4	no	—
803	C₂²⋊C₄	—	94	4	no	—
804	C₂²⋊C₄	—	94	4	no	—
805	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
806	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
807	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
808	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	1	no	—
811	C₄²	—	94	2	no	—
812	C₄²	—	94	2	no	—
813	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
814	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
815	C₄²	C₂³×D₄₇	1	2	yes	—
816	C₄²	C₂³×D₄₇	1	2	yes	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	4	1	no	—
822	C₂³	—	4	2	no	—
823	C₂³	—	8	1	no	—
824	C₂³	—	8	1	no	—
825	C₂³	—	94	8	no	—
826	C₂³	—	94	8	no	—
827	C₂³	—	94	8	no	—
828	C₂³	—	94	4	no	—
829	C₂³	—	376	2	no	—
830	C₂³	—	376	2	no	—
831	C₂³	—	376	2	no	—
832	C₂³	—	376	2	no	—
833	C₂³	—	376	16	no	—
834	C₂³	—	188	4	no	—
835	C₂³	—	188	4	no	—
836	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
837	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
838	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
839	Q₈	—	2	2	no	—
840	Q₈	—	8	2	no	—
841	D₄	—	2	4	no	—
842	D₄	—	2	2	no	—
843	D₄	—	4	2	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	1	no	—
850	D₄	—	8	2	no	—
851	D₄	—	47	8	no	—
852	D₄	—	94	8	no	—
853	D₄	—	94	8	no	—
854	D₄	—	94	8	no	—
855	D₄	—	94	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	—	8	1	no	—
872	C₂×C₄	—	94	2	no	—
873	C₂×C₄	—	94	2	no	—
874	C₂×C₄	—	376	4	no	—
875	C₂×C₄	—	376	4	no	—
876	C₂×C₄	—	376	4	no	—
877	C₂×C₄	—	376	4	no	—
878	C₂×C₄	—	188	2	no	—
879	C₂×C₄	—	188	2	no	—
880	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
881	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
882	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
883	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
884	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
885	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
886	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
887	C₂×C₄	#41×D₄₇	1	4	yes	—
888	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
889	C₈	—	94	2	no	—
890	C₈	—	94	2	no	—
891	C₈	—	94	4	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	4	4	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	16	2	no	—
907	C₂²	—	94	8	no	—
908	C₂²	—	376	8	no	—
909	C₂²	—	376	8	no	—
910	C₂²	—	188	16	no	—
911	C₂²	—	188	4	no	—
912	C₂²	—	188	4	no	—
913	C₂²	#15689630	1	2	yes	—
914	C₂²	#15689926	1	2	yes	—
915	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	188	2	no	—
927	C₄	—	188	2	no	—
928	C₄	#15689630	1	2	yes	—
929	C₄	C₂×#41×D₄₇	1	2	yes	—
930	C₂	—	2	2	no	—
931	C₂	—	2	2	no	—
932	C₂	—	4	1	no	—
933	C₂	—	8	2	no	—
934	C₂	—	8	1	no	—
935	C₂	—	188	8	no	—
936	C₂	C₂×#15689630	1	1	yes	characteristic
937	C₂	C₂×#15689926	1	1	yes	characteristic
938	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×#3494	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3494	D₄₇
hypocenter	C₄₇	#60578
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ #3494

Complements

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

N	H ≅ G/N	type
1. C₂×#15689597	C₂	semidirect
2. #20253626	C₂	semidirect
3. #20253566	C₂	semidirect
4. #20253522	C₂	semidirect
5. #20253475	C₂	semidirect
6. #20253431	C₂	semidirect
7. #20253384	C₂	semidirect
8. #20253324	C₂	semidirect
9. #20253297	C₂	semidirect
10. #20253213	C₂	semidirect
11. #20252887	C₂	semidirect
12. #20252614	C₂	semidirect
13. C₂×#15689256	C₂	semidirect
14. #20252238	C₂	semidirect
15. #20252216	C₂	semidirect
16. #20252046	C₂	semidirect
17. C₄₇×#3494	C₂	semidirect
26. #15689597	C₂²	semidirect
27. C₂×C₄×D₁₈₈	C₂²	semidirect
28. C₂×C₄×D₁₈₈	C₂²	semidirect
33. #15689461	C₂²	semidirect
34. #15689456	C₂²	semidirect
35. #15689451	C₂²	semidirect
36. #15689444	C₂²	semidirect
37. #15689444	C₂²	semidirect
38. #15689439	C₂²	semidirect
39. #15689439	C₂²	semidirect
40. #15689434	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. #15689315	C₂²	semidirect
49. #15689315	C₂²	semidirect
50. #15689273	C₂²	semidirect
51. #15689273	C₂²	semidirect
55. #15689256	C₂²	semidirect
56. #15689256	C₂²	semidirect
57. #15689233	C₂²	semidirect
58. #15689233	C₂²	semidirect
59. #15689233	C₂²	semidirect
60. #15689221	C₂²	semidirect
61. C₄×#10625336	C₂²	semidirect
62. C₄×#10625334	C₂²	semidirect
63. C₄×#10625334	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. #15689128	C₂²	semidirect
73. #15689119	C₂²	semidirect
77. #15689079	C₂²	semidirect
84. C₄₇×#544	C₂²	semidirect
85. C₄₇×#542	C₂²	semidirect
86. C₄₇×#540	C₂²	semidirect
87. C₄₇×#535	C₂²	semidirect
88. C₄₇×#532	C₂²	semidirect
89. C₄₇×#529	C₂²	semidirect
92. C₄₇×#520	C₂²	semidirect
93. C₄₇×#518	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. #13093945	C₂³	semidirect
152. #13093945	C₂³	semidirect
153. #13093945	C₂³	semidirect
154. #13093945	C₂³	semidirect
164. #13093935	C₂³	semidirect
165. C₄×C₄₇⋊C₈	C₂³	semidirect
172. C₄⋊Q₈×C₄₇	C₂³	semidirect
173. #127×C₄₇	C₂³	semidirect
177. #125×C₄₇	C₂³	semidirect
180. #124×C₄₇	C₂³	semidirect
203. C₄×Q₈×C₄₇	C₂³	semidirect
211. C₄×D₄×C₄₇	C₂³	semidirect
212. C₄×D₄×C₄₇	C₂³	semidirect
213. C₄×D₄×C₄₇	C₂³	semidirect
280. C₂×D₁₈₈	#41	semidirect
461. #3494	D₄₇	semidirect
496. #544	C₂×D₄₇	semidirect
497. #542	C₂×D₄₇	semidirect
498. #540	C₂×D₄₇	semidirect
499. #535	C₂×D₄₇	semidirect
500. #532	C₂×D₄₇	semidirect
501. #529	C₂×D₄₇	semidirect
504. #520	C₂×D₄₇	semidirect
511. #518	C₂×D₄₇	semidirect
564. C₄₇	#60578	semidirect
589. C₄⋊Q₈	C₂²×D₄₇	semidirect
590. #127	C₂²×D₄₇	semidirect
594. #125	C₂²×D₄₇	semidirect
597. #124	C₂²×D₄₇	semidirect
620. C₄×Q₈	C₂²×D₄₇	semidirect
642. C₄×D₄	C₂²×D₄₇	semidirect
643. C₄×D₄	C₂²×D₄₇	semidirect
644. 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
#20253626	2
#20253566	2
#20253522	2
#20253475	2
#20253431	2
#20253384	2
#20253324	2
#20253297	2
#20253213	2
#20252887	2
#20252614	2
C₂×#15689256	2
#20252238	2
#20252216	2
#20252046	2
C₄₇×#3494	2
#60578	47