Subgroups — #27081121

Order 12032.

2094 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252464	C₂	1	4	yes	maximal, complemented
2	#20252459	C₂	1	2	yes	maximal, complemented
3	#20252455	C₂	1	2	yes	maximal, complemented
4	#20252450	C₂	1	2	yes	maximal, complemented
5	#20252444	C₂	1	2	yes	maximal, complemented
6	#20252436	C₂	1	4	yes	maximal, complemented
7	#20252115	C₂	1	2	yes	maximal, complemented
8	#20252115	C₂	1	2	yes	maximal, complemented
9	#20252092	C₂	1	2	yes	maximal, complemented
10	#20252083	C₂	1	2	yes	maximal, complemented
11	#20252046	C₂	1	2	yes	maximal, complemented
12	#20251837	C₂	1	2	yes	maximal, complemented
13	#20251833	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15689090	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#3449	C₂	1	1	yes	maximal, characteristic
16	C₂×#13094031	C₂²	1	2	yes	—
17	C₂×#13094031	C₂²	1	2	yes	—
18	C₂²×#10625329	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#10625329	C₂²	1	1	yes	characteristic, complemented
20	C₂²×#10625329	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
22	#15689201	C₂²	1	4	yes	complemented
23	#15689201	C₂²	1	4	yes	complemented
24	#15689201	C₂²	1	4	yes	complemented
25	#15689201	C₂²	1	4	yes	complemented
26	#15689195	C₂²	1	4	yes	complemented
27	#15689195	C₂²	1	4	yes	complemented
28	#15689195	C₂²	1	4	yes	complemented
29	#15689195	C₂²	1	4	yes	complemented
30	#15689195	C₂²	1	4	yes	complemented
31	#15689195	C₂²	1	4	yes	complemented
32	#15689195	C₂²	1	4	yes	complemented
33	#15689195	C₂²	1	4	yes	complemented
34	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
35	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
36	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
37	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
38	#15689184	C₂²	1	4	yes	complemented
39	#15689184	C₂²	1	4	yes	complemented
40	#15689180	C₂²	1	4	yes	complemented
41	#15689176	C₂²	1	4	yes	complemented
42	#15689150	C₂²	1	2	yes	complemented
43	#15689150	C₂²	1	2	yes	complemented
44	#15689090	C₂²	1	2	yes	—
45	#15689090	C₂²	1	2	yes	—
46	#15689090	C₂²	1	1	yes	characteristic
47	#15689090	C₂²	1	2	yes	—
48	#15689090	C₂²	1	1	yes	characteristic
49	#15689090	C₂²	1	2	yes	—
50	#15689090	C₂²	1	2	yes	—
51	#15689090	C₂²	1	1	yes	characteristic, complemented
52	#15689090	C₂²	1	2	yes	complemented
53	#15689090	C₂²	1	4	yes	complemented
54	#15689090	C₂²	1	1	yes	characteristic, complemented
55	#15689090	C₂²	1	4	yes	complemented
56	#15689090	C₂²	1	2	yes	complemented
57	#15689090	C₂²	1	2	yes	complemented
58	#15689087	C₂²	1	2	yes	—
59	#15689087	C₂²	1	4	yes	complemented
60	#15689087	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
62	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
63	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
64	#15689079	C₂²	1	2	yes	complemented
65	#15689079	C₂²	1	2	yes	complemented
66	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
67	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
68	C₄₇×#537	C₄	1	2	yes	—
69	C₄₇×#537	C₄	1	2	yes	—
70	C₄₇×#536	C₄	1	1	yes	characteristic
71	C₄₇×#536	C₄	1	1	yes	characteristic
72	C₄₇×#536	C₄	1	2	yes	—
73	C₄₇×#535	C₄	1	2	yes	—
74	C₄₇×#535	C₄	1	1	yes	characteristic
75	C₄₇×#535	C₄	1	1	yes	characteristic
76	C₄₇×#534	C₄	1	2	yes	—
77	C₄₇×#534	C₄	1	2	yes	—
78	C₄₇×#532	C₂²	1	2	yes	—
79	C₄₇×#532	C₂²	1	2	yes	—
80	C₄₇×#525	C₂²	1	2	yes	—
81	C₄₇×#525	C₂²	1	2	yes	—
82	C₄₇×#525	C₂²	1	2	yes	—
83	C₄₇×#525	C₂²	1	2	yes	—
84	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
85	#13094031	—	4	4	no	—
86	#13094031	—	4	4	no	—
87	C₂×#10625329	—	4	2	no	—
88	C₂×#10625329	—	4	2	no	—
89	C₂×#10625329	—	4	2	no	—
90	C₂×#10625329	C₂³	1	2	yes	—
91	C₂×#10625329	C₂³	1	2	yes	—
92	C₂×#10625329	C₂³	1	4	yes	—
93	C₂×#10625329	C₂³	1	4	yes	—
94	C₂×#10625329	C₂³	1	1	yes	characteristic
95	C₂×#10625329	C₂³	1	2	yes	—
96	C₂×#10625329	C₂³	1	2	yes	—
97	C₂×#10625329	C₂³	1	2	yes	—
98	C₂×#10625329	C₂³	1	1	yes	characteristic
99	C₂²×C₄₇⋊C₈	—	4	2	no	—
100	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
101	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
102	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
103	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
104	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
106	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
108	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
109	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
110	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
111	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
112	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
113	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
114	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
115	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
116	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
117	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
118	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
119	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
120	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
121	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
122	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
123	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
124	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
125	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
126	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
127	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
128	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
129	#13093935	C₂³	1	4	yes	—
130	#13093935	C₂³	1	4	yes	—
131	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
132	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
133	C₂×#41×C₄₇	—	4	2	no	—
134	C₂×#41×C₄₇	—	4	2	no	—
135	C₂×#41×C₄₇	—	4	2	no	—
136	C₂×#41×C₄₇	—	4	2	no	—
137	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
138	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
139	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
140	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
141	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
142	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
143	C₂×#41×C₄₇	C₂³	1	2	yes	—
144	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
145	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
147	C₂×#41×C₄₇	C₂³	1	2	yes	—
148	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
150	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
151	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
152	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
153	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
154	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
155	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
156	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
161	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
162	#127×C₄₇	C₂×C₄	1	2	yes	—
163	#127×C₄₇	C₂×C₄	1	2	yes	—
164	#124×C₄₇	C₂×C₄	1	2	yes	—
165	#124×C₄₇	C₂×C₄	1	2	yes	—
166	#124×C₄₇	C₂×C₄	1	2	yes	—
167	#124×C₄₇	C₂×C₄	1	2	yes	—
168	#123×C₄₇	C₂×C₄	1	4	yes	—
169	#123×C₄₇	C₂×C₄	1	4	yes	—
170	#123×C₄₇	C₂×C₄	1	2	yes	—
171	#123×C₄₇	C₂×C₄	1	2	yes	—
172	#123×C₄₇	C₂×C₄	1	2	yes	—
173	#123×C₄₇	C₂×C₄	1	2	yes	—
174	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
175	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
176	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
177	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
178	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
179	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
180	#121×C₄₇	C₂×C₄	1	2	yes	—
181	#121×C₄₇	C₂×C₄	1	2	yes	—
182	#121×C₄₇	C₂×C₄	1	2	yes	—
183	#121×C₄₇	C₂×C₄	1	2	yes	—
184	#121×C₄₇	C₂×C₄	1	4	yes	—
185	#121×C₄₇	C₂×C₄	1	4	yes	—
186	#121×C₄₇	C₂×C₄	1	4	yes	—
187	#121×C₄₇	C₂×C₄	1	4	yes	—
188	#121×C₄₇	C₂×C₄	1	4	yes	—
189	#121×C₄₇	C₂×C₄	1	4	yes	—
190	#120×C₄₇	C₂×C₄	1	4	yes	—
191	#120×C₄₇	C₂×C₄	1	4	yes	—
192	#120×C₄₇	C₂×C₄	1	2	yes	—
193	#120×C₄₇	C₂×C₄	1	2	yes	—
194	#120×C₄₇	C₂×C₄	1	2	yes	—
195	#120×C₄₇	C₂×C₄	1	2	yes	—
196	C₄×D₄×C₄₇	C₂³	1	4	yes	—
197	C₄×D₄×C₄₇	C₂³	1	4	yes	—
198	C₄×D₄×C₄₇	C₂³	1	4	yes	—
199	C₄×D₄×C₄₇	C₂³	1	4	yes	—
200	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
201	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
202	#117×C₄₇	C₂×C₄	1	2	yes	—
203	#117×C₄₇	C₂³	1	2	yes	—
204	#117×C₄₇	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
206	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
207	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
208	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
209	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
210	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
211	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
212	#41×C₄₇	—	2	4	no	—
213	#41×C₄₇	—	2	4	no	—
214	#41×C₄₇	—	4	2	no	—
215	#41×C₄₇	—	4	2	no	—
216	#41×C₄₇	—	4	2	no	—
217	#41×C₄₇	—	4	2	no	—
218	#41×C₄₇	—	4	1	no	—
219	#41×C₄₇	—	4	1	no	—
220	#41×C₄₇	—	4	1	no	—
221	#41×C₄₇	—	4	1	no	—
222	#41×C₄₇	—	4	1	no	—
223	#41×C₄₇	—	4	1	no	—
224	#41×C₄₇	—	4	2	no	—
225	#41×C₄₇	—	4	2	no	—
226	#41×C₄₇	—	4	1	no	—
227	#41×C₄₇	—	4	1	no	—
228	#41×C₄₇	—	4	4	no	—
229	#41×C₄₇	—	4	4	no	—
230	C₂×Q₈×C₄₇	—	4	2	no	—
231	C₂×Q₈×C₄₇	—	4	2	no	—
232	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
233	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
234	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
235	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
236	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
237	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
238	C₂×D₄×C₄₇	—	4	2	no	—
239	C₂×D₄×C₄₇	—	4	2	no	—
240	C₂×D₄×C₄₇	—	4	2	no	—
241	C₂×D₄×C₄₇	—	4	2	no	—
242	C₂×D₄×C₄₇	—	4	4	no	—
243	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
244	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
245	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
246	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
247	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
248	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
249	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
250	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
251	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
252	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
253	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
254	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
255	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
256	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
257	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
258	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
259	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
260	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
261	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
262	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
263	C₂²×C₄×C₄₇	—	2	2	no	—
264	C₂²×C₄×C₄₇	—	2	2	no	—
265	C₂²×C₄×C₄₇	—	2	2	no	—
266	C₂²×C₄×C₄₇	—	2	2	no	—
267	C₂²×C₄×C₄₇	—	2	2	no	—
268	C₂²×C₄×C₄₇	—	2	2	no	—
269	C₂²×C₄×C₄₇	—	4	2	no	—
270	C₂²×C₄×C₄₇	—	4	2	no	—
271	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
272	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
273	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
274	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
275	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
276	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
277	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
278	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
279	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
280	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
281	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
282	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
283	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
291	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
292	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
293	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
294	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
295	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
296	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
297	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
298	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
299	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
300	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
301	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
302	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
303	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
304	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
305	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
306	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
307	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
308	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
309	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
310	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
311	C₄²×C₄₇	C₂⁴	1	4	yes	—
312	#10625329	—	2	4	no	—
313	#10625329	—	2	4	no	—
314	#10625329	—	4	1	no	—
315	#10625329	—	4	2	no	—
316	#10625329	—	4	1	no	—
317	#10625329	—	4	2	no	—
318	#10625329	—	4	2	no	—
319	#10625329	—	4	4	no	—
320	#10625329	—	4	4	no	—
321	C₂×C₄₇⋊C₈	—	2	4	no	—
322	C₂×C₄₇⋊C₈	—	2	4	no	—
323	C₂×C₄₇⋊C₈	—	4	1	no	—
324	C₂×C₄₇⋊C₈	—	4	2	no	—
325	C₂×C₄₇⋊C₈	—	4	1	no	—
326	C₂×C₄₇⋊C₈	—	4	2	no	—
327	C₂×C₄₇⋊C₈	—	4	2	no	—
328	C₂×C₄₇⋊C₈	—	4	4	no	—
329	C₂×C₄₇⋊C₈	—	4	4	no	—
330	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
331	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
332	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
333	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
334	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
335	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
336	C₂³×C₄₇	—	2	2	no	—
337	C₂³×C₄₇	—	2	2	no	—
338	C₂³×C₄₇	—	2	2	no	—
339	C₂³×C₄₇	—	4	2	no	—
340	C₂³×C₄₇	—	4	2	no	—
341	C₂³×C₄₇	—	4	2	no	—
342	C₂³×C₄₇	—	4	2	no	—
343	C₂³×C₄₇	—	4	4	no	—
344	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
345	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
346	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
347	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
348	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
349	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
350	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
351	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
352	Q₈×C₄₇	—	2	4	no	—
353	Q₈×C₄₇	—	4	1	no	—
354	Q₈×C₄₇	—	4	1	no	—
355	Q₈×C₄₇	—	4	1	no	—
356	Q₈×C₄₇	—	4	1	no	—
357	Q₈×C₄₇	—	4	2	no	—
358	D₄×C₄₇	—	2	8	no	—
359	D₄×C₄₇	—	2	4	no	—
360	D₄×C₄₇	—	4	1	no	—
361	D₄×C₄₇	—	4	1	no	—
362	D₄×C₄₇	—	4	1	no	—
363	D₄×C₄₇	—	4	1	no	—
364	D₄×C₄₇	—	4	2	no	—
365	D₄×C₄₇	—	4	1	no	—
366	D₄×C₄₇	—	4	1	no	—
367	D₄×C₄₇	—	4	1	no	—
368	D₄×C₄₇	—	4	1	no	—
369	D₄×C₄₇	—	4	1	no	—
370	D₄×C₄₇	—	4	1	no	—
371	D₄×C₄₇	—	4	1	no	—
372	D₄×C₄₇	—	4	1	no	—
373	D₄×C₄₇	—	4	4	no	—
374	D₄×C₄₇	—	4	4	no	—
375	D₄×C₄₇	—	4	4	no	—
376	D₄×C₄₇	—	4	4	no	—
377	D₄×C₄₇	—	4	4	no	—
378	C₂×C₄×C₄₇	—	2	2	no	—
379	C₂×C₄×C₄₇	—	2	2	no	—
380	C₂×C₄×C₄₇	—	2	2	no	—
381	C₂×C₄×C₄₇	—	2	2	no	—
382	C₂×C₄×C₄₇	—	2	2	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	1	no	—
391	C₂×C₄×C₄₇	—	2	4	no	—
392	C₂×C₄×C₄₇	—	2	4	no	—
393	C₂×C₄×C₄₇	—	2	1	no	—
394	C₂×C₄×C₄₇	—	2	1	no	—
395	C₂×C₄×C₄₇	—	2	1	no	—
396	C₂×C₄×C₄₇	—	2	1	no	—
397	C₂×C₄×C₄₇	—	2	1	no	—
398	C₂×C₄×C₄₇	—	2	1	no	—
399	C₂×C₄×C₄₇	—	2	1	no	—
400	C₂×C₄×C₄₇	—	2	1	no	—
401	C₂×C₄×C₄₇	—	4	2	no	—
402	C₂×C₄×C₄₇	—	4	4	no	—
403	C₂×C₄×C₄₇	—	4	4	no	—
404	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
405	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
406	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
407	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
408	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
409	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
410	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
411	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
412	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
413	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
414	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
415	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
416	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
417	C₄₇⋊C₈	—	2	2	no	—
418	C₄₇⋊C₈	—	2	2	no	—
419	C₄₇⋊C₈	—	2	2	no	—
420	C₄₇⋊C₈	—	2	2	no	—
421	C₄₇⋊C₈	—	2	4	no	—
422	C₄₇⋊C₈	—	2	4	no	—
423	#60235	—	47	1	no	maximal, Sylow
424	C₂²×C₄₇	—	2	2	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	—	2	1	no	—
431	C₂²×C₄₇	—	2	4	no	—
432	C₂²×C₄₇	—	2	2	no	—
433	C₂²×C₄₇	—	2	2	no	—
434	C₂²×C₄₇	—	2	2	no	—
435	C₂²×C₄₇	—	2	2	no	—
436	C₂²×C₄₇	—	2	2	no	—
437	C₂²×C₄₇	—	2	4	no	—
438	C₂²×C₄₇	—	2	4	no	—
439	C₂²×C₄₇	—	2	2	no	—
440	C₂²×C₄₇	—	4	4	no	—
441	C₂²×C₄₇	—	8	2	no	—
442	C₂²×C₄₇	—	8	2	no	—
443	C₂²×C₄₇	—	8	4	no	—
444	C₂²×C₄₇	#518	1	2	yes	—
445	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
446	C₄×C₄₇	—	2	1	no	—
447	C₄×C₄₇	—	2	1	no	—
448	C₄×C₄₇	—	2	1	no	—
449	C₄×C₄₇	—	2	1	no	—
450	C₄×C₄₇	—	2	1	no	—
451	C₄×C₄₇	—	2	1	no	—
452	C₄×C₄₇	—	2	4	no	—
453	C₄×C₄₇	—	2	4	no	—
454	C₄×C₄₇	—	2	4	no	—
455	C₄×C₄₇	#518	1	2	yes	—
456	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	#3449	D₄₇	1	1	yes	characteristic
459	#2981	—	47	4	no	—
460	#2980	—	47	2	no	—
461	#2979	—	47	2	no	—
462	#2978	—	47	2	no	—
463	#2977	—	47	2	no	—
464	#2976	—	47	4	no	—
465	#2933	—	47	2	no	—
466	#2933	—	47	2	no	—
467	#2930	—	47	2	no	—
468	#2929	—	47	2	no	—
469	#2924	—	47	2	no	—
470	#2880	—	47	2	no	—
471	#2879	—	47	1	no	—
472	C₂×#408	—	47	1	no	—
473	C₂×C₄₇	—	2	2	no	—
474	C₂×C₄₇	—	4	1	no	—
475	C₂×C₄₇	—	4	1	no	—
476	C₂×C₄₇	—	4	1	no	—
477	C₂×C₄₇	—	4	1	no	—
478	C₂×C₄₇	—	4	1	no	—
479	C₂×C₄₇	—	4	4	no	—
480	C₂×C₄₇	—	4	1	no	—
481	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
482	C₂×C₄₇	#3573	1	2	yes	—
483	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
484	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
485	C₂×#131	—	47	2	no	—
486	C₂×#131	—	47	2	no	—
487	C₂²×M₁₆	—	47	1	no	—
488	C₂²×M₁₆	—	47	1	no	—
489	C₂²×M₁₆	—	47	1	no	—
490	C₂³×C₈	—	47	1	no	—
491	#537	Dic₄₇	1	2	yes	—
492	#537	Dic₄₇	1	2	yes	—
493	#536	Dic₄₇	1	1	yes	characteristic
494	#536	Dic₄₇	1	1	yes	characteristic
495	#536	Dic₄₇	1	2	yes	—
496	#535	Dic₄₇	1	2	yes	—
497	#535	Dic₄₇	1	1	yes	characteristic
498	#535	Dic₄₇	1	1	yes	characteristic
499	#534	Dic₄₇	1	2	yes	—
500	#534	Dic₄₇	1	2	yes	—
501	#532	C₂×D₄₇	1	2	yes	—
502	#532	C₂×D₄₇	1	2	yes	—
503	#525	C₂×D₄₇	1	2	yes	—
504	#525	C₂×D₄₇	1	2	yes	—
505	#525	C₂×D₄₇	1	2	yes	—
506	#525	C₂×D₄₇	1	2	yes	—
507	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
508	#436	—	47	4	no	—
509	#436	—	47	4	no	—
510	#436	—	47	4	no	—
511	#436	—	47	4	no	—
512	#435	—	47	4	no	—
513	#435	—	47	4	no	—
514	#435	—	47	4	no	—
515	#435	—	47	4	no	—
516	#435	—	47	4	no	—
517	#435	—	47	4	no	—
518	#435	—	47	4	no	—
519	#435	—	47	4	no	—
520	C₈×D₄	—	47	4	no	—
521	C₈×D₄	—	47	4	no	—
522	C₈×D₄	—	47	4	no	—
523	C₈×D₄	—	47	4	no	—
524	#433	—	47	4	no	—
525	#433	—	47	4	no	—
526	#432	—	47	4	no	—
527	#431	—	47	4	no	—
528	#424	—	47	2	no	—
529	#424	—	47	2	no	—
530	#408	—	47	2	no	—
531	#408	—	47	1	no	—
532	#408	—	47	1	no	—
533	#408	—	47	1	no	—
534	#408	—	47	1	no	—
535	#408	—	47	2	no	—
536	#408	—	47	2	no	—
537	#408	—	47	2	no	—
538	#408	—	47	2	no	—
539	#408	—	47	2	no	—
540	#408	—	47	2	no	—
541	#408	—	47	2	no	—
542	#408	—	47	4	no	—
543	#408	—	47	4	no	—
544	#407	—	47	2	no	—
545	#407	—	47	2	no	—
546	#407	—	47	4	no	—
547	C₂×C₂²⋊C₈	—	47	2	no	—
548	C₂×C₂²⋊C₈	—	47	2	no	—
549	C₂×C₂²⋊C₈	—	47	4	no	—
550	#405	—	47	2	no	—
551	#405	—	47	2	no	—
552	C₄₇	#60235	1	1	yes	characteristic, complemented, Sylow
553	C₂×#41	—	4	2	no	—
554	C₂×#41	—	4	2	no	—
555	C₂×#41	—	4	2	no	—
556	C₂×#41	—	4	2	no	—
557	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
558	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
559	C₂×#41	C₂×Dic₄₇	1	2	yes	—
560	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
561	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
562	C₂×#41	C₂×Dic₄₇	1	2	yes	—
563	C₂×#41	C₂²×D₄₇	1	2	yes	—
564	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
565	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
566	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
567	C₂×#41	C₂²×D₄₇	1	2	yes	—
568	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
569	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
570	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
571	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
572	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
573	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
574	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
575	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
576	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
577	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
578	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
579	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
580	#131	—	188	4	no	—
581	#131	—	188	4	no	—
582	C₂×M₁₆	—	47	2	no	—
583	C₂×M₁₆	—	47	2	no	—
584	C₂×M₁₆	—	47	1	no	—
585	C₂×M₁₆	—	47	2	no	—
586	C₂×M₁₆	—	47	2	no	—
587	C₂×M₁₆	—	47	2	no	—
588	C₂×M₁₆	—	47	1	no	—
589	C₂×M₁₆	—	47	4	no	—
590	C₂×M₁₆	—	47	4	no	—
591	C₂×M₁₆	—	188	2	no	—
592	C₂×M₁₆	—	188	2	no	—
593	C₂×M₁₆	—	188	2	no	—
594	C₂²×C₈	—	47	2	no	—
595	C₂²×C₈	—	47	2	no	—
596	C₂²×C₈	—	47	1	no	—
597	C₂²×C₈	—	47	2	no	—
598	C₂²×C₈	—	47	1	no	—
599	C₂²×C₈	—	47	2	no	—
600	C₂²×C₈	—	47	2	no	—
601	C₂²×C₈	—	47	4	no	—
602	C₂²×C₈	—	47	4	no	—
603	C₂²×C₈	—	188	2	no	—
604	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
605	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
606	#127	C₂×Dic₄₇	1	2	yes	—
607	#127	C₂×Dic₄₇	1	2	yes	—
608	#124	C₂×Dic₄₇	1	2	yes	—
609	#124	C₂×Dic₄₇	1	2	yes	—
610	#124	C₂×Dic₄₇	1	2	yes	—
611	#124	C₂×Dic₄₇	1	2	yes	—
612	#123	C₂×Dic₄₇	1	4	yes	—
613	#123	C₂×Dic₄₇	1	4	yes	—
614	#123	C₂×Dic₄₇	1	2	yes	—
615	#123	C₂×Dic₄₇	1	2	yes	—
616	#123	C₂×Dic₄₇	1	2	yes	—
617	#123	C₂×Dic₄₇	1	2	yes	—
618	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
619	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
620	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
621	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
622	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
623	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
624	#121	C₂×Dic₄₇	1	2	yes	—
625	#121	C₂×Dic₄₇	1	2	yes	—
626	#121	C₂×Dic₄₇	1	2	yes	—
627	#121	C₂×Dic₄₇	1	2	yes	—
628	#121	C₂×Dic₄₇	1	4	yes	—
629	#121	C₂×Dic₄₇	1	4	yes	—
630	#121	C₂×Dic₄₇	1	4	yes	—
631	#121	C₂×Dic₄₇	1	4	yes	—
632	#121	C₂×Dic₄₇	1	4	yes	—
633	#121	C₂×Dic₄₇	1	4	yes	—
634	#120	C₂×Dic₄₇	1	4	yes	—
635	#120	C₂×Dic₄₇	1	4	yes	—
636	#120	C₂×Dic₄₇	1	2	yes	—
637	#120	C₂×Dic₄₇	1	2	yes	—
638	#120	C₂×Dic₄₇	1	2	yes	—
639	#120	C₂×Dic₄₇	1	2	yes	—
640	C₄×D₄	C₂²×D₄₇	1	4	yes	—
641	C₄×D₄	C₂²×D₄₇	1	4	yes	—
642	C₄×D₄	C₂²×D₄₇	1	4	yes	—
643	C₄×D₄	C₂²×D₄₇	1	4	yes	—
644	#117	C₂×Dic₄₇	1	1	yes	characteristic
645	#117	C₂×Dic₄₇	1	1	yes	characteristic
646	#117	C₂×Dic₄₇	1	2	yes	—
647	#117	C₂²×D₄₇	1	2	yes	—
648	#117	C₂²×D₄₇	1	2	yes	—
649	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
651	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
652	C₄⋊C₈	—	47	4	no	—
653	C₄⋊C₈	—	47	4	no	—
654	C₄⋊C₈	—	47	4	no	—
655	C₄⋊C₈	—	47	4	no	—
656	C₂²⋊C₈	—	47	2	no	—
657	C₂²⋊C₈	—	47	2	no	—
658	C₂²⋊C₈	—	47	4	no	—
659	C₂²⋊C₈	—	47	2	no	—
660	C₂²⋊C₈	—	47	2	no	—
661	C₂²⋊C₈	—	47	2	no	—
662	C₂²⋊C₈	—	47	4	no	—
663	C₂²⋊C₈	—	47	2	no	—
664	C₂²⋊C₈	—	47	2	no	—
665	C₂²⋊C₈	—	47	4	no	—
666	C₂²⋊C₈	—	47	2	no	—
667	C₂²⋊C₈	—	47	4	no	—
668	C₂²⋊C₈	—	47	4	no	—
669	C₂²⋊C₈	—	47	4	no	—
670	C₂²⋊C₈	—	47	4	no	—
671	C₂²⋊C₈	—	47	4	no	—
672	#97	—	47	4	no	—
673	#97	—	47	4	no	—
674	C₄×C₈	—	47	4	no	—
675	C₄×C₈	—	47	4	no	—
676	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
677	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
678	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
679	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
680	#41	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	4	2	no	—
683	#41	—	4	2	no	—
684	#41	—	4	2	no	—
685	#41	—	4	2	no	—
686	#41	—	4	1	no	—
687	#41	—	4	1	no	—
688	#41	—	4	1	no	—
689	#41	—	4	1	no	—
690	#41	—	4	1	no	—
691	#41	—	4	1	no	—
692	#41	—	4	2	no	—
693	#41	—	4	2	no	—
694	#41	—	4	1	no	—
695	#41	—	4	1	no	—
696	#41	—	4	4	no	—
697	#41	—	4	4	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
701	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
702	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
703	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
704	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
705	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
712	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
713	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
714	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
715	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
716	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
717	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
718	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
719	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
720	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
721	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
722	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
723	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
724	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
725	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
726	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
727	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
728	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
729	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
730	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
740	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
741	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
742	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
743	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
744	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
745	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
746	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
747	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
748	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
749	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
750	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
751	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
752	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
753	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
754	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
755	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
756	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
757	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
758	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
759	M₁₆	—	94	4	no	—
760	M₁₆	—	94	4	no	—
761	M₁₆	—	188	1	no	—
762	M₁₆	—	188	2	no	—
763	M₁₆	—	188	1	no	—
764	M₁₆	—	188	2	no	—
765	M₁₆	—	188	2	no	—
766	M₁₆	—	188	4	no	—
767	M₁₆	—	188	4	no	—
768	C₂×C₈	—	47	2	no	—
769	C₂×C₈	—	47	2	no	—
770	C₂×C₈	—	47	4	no	—
771	C₂×C₈	—	47	4	no	—
772	C₂×C₈	—	47	2	no	—
773	C₂×C₈	—	47	2	no	—
774	C₂×C₈	—	94	4	no	—
775	C₂×C₈	—	94	4	no	—
776	C₂×C₈	—	188	1	no	—
777	C₂×C₈	—	188	2	no	—
778	C₂×C₈	—	188	1	no	—
779	C₂×C₈	—	188	2	no	—
780	C₂×C₈	—	188	2	no	—
781	C₂×C₈	—	188	4	no	—
782	C₂×C₈	—	188	4	no	—
783	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
784	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
785	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
786	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
787	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
788	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
789	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
790	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
791	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
792	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
793	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
794	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
795	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
796	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
797	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
798	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
799	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
800	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
801	C₄²	C₂²×Dic₄₇	1	2	yes	—
802	C₄²	C₂²×Dic₄₇	1	2	yes	—
803	C₄²	C₂³×D₄₇	1	4	yes	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	4	no	—
812	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
813	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
814	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
815	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
816	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
817	C₂³	C₂³×Dic₄₇	1	4	yes	—
818	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
819	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
820	Q₈	—	2	4	no	—
821	Q₈	—	4	1	no	—
822	Q₈	—	4	1	no	—
823	Q₈	—	4	1	no	—
824	Q₈	—	4	1	no	—
825	Q₈	—	4	2	no	—
826	D₄	—	2	8	no	—
827	D₄	—	2	4	no	—
828	D₄	—	4	1	no	—
829	D₄	—	4	1	no	—
830	D₄	—	4	1	no	—
831	D₄	—	4	1	no	—
832	D₄	—	4	2	no	—
833	D₄	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	4	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
873	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
874	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
875	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
876	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
877	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
878	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
879	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
880	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
881	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
882	C₂×C₄	#13094069	1	2	yes	—
883	C₂×C₄	#13094069	1	2	yes	—
884	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
885	C₈	—	94	2	no	—
886	C₈	—	94	2	no	—
887	C₈	—	94	2	no	—
888	C₈	—	94	2	no	—
889	C₈	—	94	4	no	—
890	C₈	—	94	4	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	4	no	—
907	C₂²	—	4	4	no	—
908	C₂²	—	8	2	no	—
909	C₂²	—	8	2	no	—
910	C₂²	—	8	4	no	—
911	C₂²	#15689598	1	2	yes	—
912	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
913	C₄	—	2	4	no	—
914	C₄	—	2	4	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	4	no	—
922	C₄	#15689598	1	2	yes	—
923	C₄	C₂×#13094069	1	1	yes	characteristic
924	C₄	C₂×#13094069	1	1	yes	characteristic
925	C₂	—	2	2	no	—
926	C₂	—	4	1	no	—
927	C₂	—	4	1	no	—
928	C₂	—	4	1	no	—
929	C₂	—	4	1	no	—
930	C₂	—	4	1	no	—
931	C₂	—	4	1	no	—
932	C₂	—	4	4	no	—
933	C₂	C₂×#15689598	1	1	yes	characteristic
934	C₂	#20258100	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₄₇×#3449	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#3449	D₄₇
hypocenter	C₄₇	#60235
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #3449

Complements

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

N	H ≅ G/N	type
1. #20252464	C₂	semidirect
2. #20252459	C₂	semidirect
3. #20252455	C₂	semidirect
4. #20252450	C₂	semidirect
5. #20252444	C₂	semidirect
6. #20252436	C₂	semidirect
7. #20252115	C₂	semidirect
8. #20252115	C₂	semidirect
9. #20252092	C₂	semidirect
10. #20252083	C₂	semidirect
11. #20252046	C₂	semidirect
12. #20251837	C₂	semidirect
13. #20251833	C₂	semidirect
14. C₂×#15689090	C₂	semidirect
18. C₂²×#10625329	C₂²	semidirect
19. C₂²×#10625329	C₂²	semidirect
20. C₂²×#10625329	C₂²	semidirect
21. C₂³×C₄₇⋊C₈	C₂²	semidirect
22. #15689201	C₂²	semidirect
23. #15689201	C₂²	semidirect
24. #15689201	C₂²	semidirect
25. #15689201	C₂²	semidirect
26. #15689195	C₂²	semidirect
27. #15689195	C₂²	semidirect
28. #15689195	C₂²	semidirect
29. #15689195	C₂²	semidirect
30. #15689195	C₂²	semidirect
31. #15689195	C₂²	semidirect
32. #15689195	C₂²	semidirect
33. #15689195	C₂²	semidirect
34. D₄×C₄₇⋊C₈	C₂²	semidirect
35. D₄×C₄₇⋊C₈	C₂²	semidirect
36. D₄×C₄₇⋊C₈	C₂²	semidirect
37. D₄×C₄₇⋊C₈	C₂²	semidirect
38. #15689184	C₂²	semidirect
39. #15689184	C₂²	semidirect
40. #15689180	C₂²	semidirect
41. #15689176	C₂²	semidirect
42. #15689150	C₂²	semidirect
43. #15689150	C₂²	semidirect
51. #15689090	C₂²	semidirect
52. #15689090	C₂²	semidirect
53. #15689090	C₂²	semidirect
54. #15689090	C₂²	semidirect
55. #15689090	C₂²	semidirect
56. #15689090	C₂²	semidirect
57. #15689090	C₂²	semidirect
59. #15689087	C₂²	semidirect
60. #15689087	C₂²	semidirect
62. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
63. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
64. #15689079	C₂²	semidirect
65. #15689079	C₂²	semidirect
552. C₄₇	#60235	semidirect

Maximal subgroups

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

subgroup	index
#20252464	2
#20252459	2
#20252455	2
#20252450	2
#20252444	2
#20252436	2
#20252115	2
#20252092	2
#20252083	2
#20252046	2
#20251837	2
#20251833	2
C₂×#15689090	2
C₄₇×#3449	2
#60235	47