Subgroups — #27080922

Order 12032.

1970 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252402	C₂	1	2	yes	maximal, complemented
2	#20252393	C₂	1	2	yes	maximal, complemented
3	#20252384	C₂	1	4	yes	maximal, complemented
4	#20252364	C₂	1	4	yes	maximal, complemented
5	#20252364	C₂	1	2	yes	maximal, complemented
6	#41×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
7	#20252337	C₂	1	1	yes	maximal, characteristic, complemented
8	#20252323	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252115	C₂	1	2	yes	maximal, complemented
11	#20252083	C₂	1	2	yes	maximal, complemented
12	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252054	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252046	C₂	1	2	yes	maximal, complemented
15	C₄×#13094031	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15689079	C₂	1	2	yes	maximal, complemented
17	C₄₇×#3475	C₂	1	1	yes	maximal, characteristic
18	C₂×#13094031	C₂²	1	1	yes	characteristic
19	C₂×#13094031	C₂²	1	1	yes	characteristic
20	C₂²×#10625329	C₂²	1	2	yes	—
21	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
22	#15689254	C₂²	1	2	yes	complemented
23	#15689254	C₂²	1	2	yes	complemented
24	#15689254	C₂²	1	4	yes	complemented
25	#15689254	C₂²	1	2	yes	complemented
26	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
27	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
28	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
29	#15689201	C₂²	1	2	yes	—
30	#15689201	C₂²	1	4	yes	complemented
31	#15689195	C₂²	1	4	yes	—
32	#15689195	C₂²	1	4	yes	complemented
33	#15689195	C₂²	1	4	yes	complemented
34	#15689195	C₂²	1	4	yes	complemented
35	#15689195	C₂²	1	4	yes	complemented
36	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
38	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
39	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
40	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
41	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
42	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
43	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
44	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
45	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
46	#15689184	C₂²	1	4	yes	complemented
47	#15689184	C₂²	1	4	yes	complemented
48	#15689184	C₂²	1	4	yes	complemented
49	#15689180	C₂²	1	4	yes	complemented
50	#15689180	C₂²	1	2	yes	complemented
51	#15689176	C₂²	1	4	yes	complemented
52	#15689176	C₂²	1	2	yes	complemented
53	#15689150	C₂²	1	2	yes	—
54	#15689150	C₂²	1	2	yes	—
55	#15689147	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
57	#15689090	C₂²	1	2	yes	—
58	#15689087	C₂²	1	2	yes	—
59	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
60	#15689079	C₂²	1	1	yes	characteristic
61	#15689079	C₂²	1	2	yes	—
62	#15689079	C₂²	1	1	yes	characteristic
63	#15689079	C₂²	1	2	yes	—
64	#15689079	C₂²	1	2	yes	—
65	#15689079	C₂²	1	4	yes	complemented
66	#15689079	C₂²	1	4	yes	complemented
67	#15689079	C₂²	1	2	yes	complemented
68	#15689079	C₂²	1	2	yes	complemented
69	C₄×#10625329	C₂²	1	1	yes	characteristic
70	C₄×#10625329	C₂²	1	2	yes	complemented
71	C₂×#13093935	C₂²	1	4	yes	complemented
72	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
73	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
74	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
75	C₄₇×#556	C₄	1	1	yes	characteristic
76	C₄₇×#555	C₄	1	1	yes	characteristic
77	C₄₇×#554	C₄	1	1	yes	characteristic
78	C₄₇×#553	C₄	1	2	yes	—
79	C₄₇×#552	C₄	1	2	yes	—
80	C₄₇×#552	C₄	1	2	yes	—
81	C₄₇×#551	C₄	1	4	yes	—
82	C₄₇×#547	C₄	1	1	yes	characteristic
83	C₄₇×#546	C₄	1	2	yes	—
84	C₄₇×#533	C₂²	1	1	yes	characteristic
85	C₄₇×#529	C₂²	1	4	yes	—
86	C₄₇×#529	C₂²	1	2	yes	—
87	C₄₇×#525	C₂²	1	2	yes	—
88	C₄×#41×C₄₇	C₂²	1	2	yes	—
89	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
91	C₂×#117×C₄₇	C₂²	1	2	yes	—
92	#13094031	—	2	4	no	—
93	#13094031	—	2	4	no	—
94	C₂×#10625329	—	2	8	no	—
95	C₂×#10625329	C₂³	1	1	yes	characteristic
96	C₂×#10625329	C₂³	1	2	yes	—
97	C₂×#10625329	C₂³	1	2	yes	—
98	C₂×#10625329	C₂³	1	2	yes	—
99	C₂×#10625329	C₂³	1	4	yes	—
100	C₂×#10625329	C₂³	1	1	yes	characteristic
101	C₂²×C₄₇⋊C₈	—	2	8	no	—
102	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
104	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
105	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
106	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
107	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
108	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
109	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
110	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
111	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
112	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
113	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
114	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
115	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
116	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
117	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
118	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
119	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
120	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
121	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
122	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
123	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
124	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	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	#13093935	C₂³	1	2	yes	—
132	#13093935	C₂³	1	2	yes	—
133	#13093935	C₂³	1	4	yes	—
134	#13093935	C₂³	1	2	yes	—
135	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
136	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
137	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
138	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
139	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
140	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
141	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
142	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
143	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
144	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
145	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
146	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
148	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
150	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
151	#126×C₄₇	C₂×C₄	1	4	yes	—
152	#126×C₄₇	C₂×C₄	1	4	yes	—
153	#126×C₄₇	C₂×C₄	1	4	yes	—
154	#125×C₄₇	C₂×C₄	1	4	yes	—
155	#125×C₄₇	C₂×C₄	1	2	yes	—
156	#125×C₄₇	C₂×C₄	1	2	yes	—
157	#124×C₄₇	C₂×C₄	1	2	yes	—
158	#124×C₄₇	C₂×C₄	1	4	yes	—
159	#123×C₄₇	C₂×C₄	1	4	yes	—
160	#123×C₄₇	C₂×C₄	1	4	yes	—
161	#123×C₄₇	C₂×C₄	1	4	yes	—
162	#123×C₄₇	C₂×C₄	1	4	yes	—
163	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
164	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
165	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
166	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
167	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
168	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
169	#121×C₄₇	C₂×C₄	1	2	yes	—
170	#121×C₄₇	C₂×C₄	1	2	yes	—
171	#121×C₄₇	C₂×C₄	1	4	yes	—
172	#121×C₄₇	C₂×C₄	1	2	yes	—
173	#120×C₄₇	C₂×C₄	1	4	yes	—
174	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
175	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
176	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
177	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
178	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
179	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
180	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
181	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
182	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
183	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
184	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
185	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
186	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
187	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
188	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₄₇	C₂³	1	2	yes	—
190	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₄₇	C₂³	1	4	yes	—
192	C₄×D₄×C₄₇	C₂³	1	4	yes	—
193	#117×C₄₇	C₂×C₄	1	4	yes	—
194	#117×C₄₇	C₂×C₄	1	2	yes	—
195	#117×C₄₇	C₂×C₄	1	2	yes	—
196	#117×C₄₇	C₂×C₄	1	4	yes	—
197	#117×C₄₇	C₂×C₄	1	2	yes	—
198	#117×C₄₇	C₂³	1	1	yes	characteristic
199	#117×C₄₇	C₂³	1	2	yes	—
200	#117×C₄₇	C₂³	1	4	yes	—
201	#117×C₄₇	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
203	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
204	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
206	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
207	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
208	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
210	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
211	#41×C₄₇	—	2	8	no	—
212	#41×C₄₇	—	2	2	no	—
213	#41×C₄₇	—	2	2	no	—
214	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
215	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
216	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
217	C₂×D₄×C₄₇	—	2	4	no	—
218	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
219	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
220	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
221	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
222	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
223	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
224	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₄×C₄₇	—	2	4	no	—
226	C₂²×C₄×C₄₇	—	2	4	no	—
227	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
228	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
230	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
231	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
232	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
235	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
236	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
241	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
242	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
243	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
244	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
245	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
246	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
247	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
248	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
249	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
250	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
251	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
252	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
253	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
254	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
255	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
256	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
257	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
258	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
259	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
260	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
261	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
262	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
263	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
264	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
265	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
266	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
267	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
268	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
269	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
270	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
271	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
272	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
273	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
274	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
275	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
276	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
277	C₄²×C₄₇	C₂⁴	1	2	yes	—
278	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
279	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
280	C₄²×C₄₇	C₂⁴	1	4	yes	—
281	#10625329	—	2	4	no	—
282	#10625329	—	2	2	no	—
283	#10625329	—	2	8	no	—
284	#10625329	—	2	4	no	—
285	#10625329	—	2	4	no	—
286	#10625329	#41	1	4	yes	complemented
287	C₂×C₄₇⋊C₈	—	2	4	no	—
288	C₂×C₄₇⋊C₈	—	2	2	no	—
289	C₂×C₄₇⋊C₈	—	2	4	no	—
290	C₂×C₄₇⋊C₈	—	2	4	no	—
291	C₂×C₄₇⋊C₈	—	2	4	no	—
292	C₂×C₄₇⋊C₈	—	2	4	no	—
293	C₂×C₄₇⋊C₈	—	2	8	no	—
294	C₂×C₄₇⋊C₈	—	2	4	no	—
295	C₂×C₄₇⋊C₈	—	2	4	no	—
296	C₂×C₄₇⋊C₈	#41	1	4	yes	complemented
297	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
298	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
299	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
300	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
301	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
302	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
303	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
304	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
305	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
306	C₂³×C₄₇	—	2	4	no	—
307	C₂³×C₄₇	—	2	4	no	—
308	C₂³×C₄₇	—	4	2	no	—
309	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
310	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
311	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
312	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
313	Q₈×C₄₇	—	2	2	no	—
314	Q₈×C₄₇	—	2	4	no	—
315	Q₈×C₄₇	—	4	2	no	—
316	D₄×C₄₇	—	2	4	no	—
317	D₄×C₄₇	—	2	4	no	—
318	D₄×C₄₇	—	2	8	no	—
319	D₄×C₄₇	—	2	2	no	—
320	D₄×C₄₇	—	2	2	no	—
321	D₄×C₄₇	—	4	4	no	—
322	D₄×C₄₇	#131	1	4	yes	complemented
323	C₂×C₄×C₄₇	—	2	4	no	—
324	C₂×C₄×C₄₇	—	2	8	no	—
325	C₂×C₄×C₄₇	—	2	4	no	—
326	C₂×C₄×C₄₇	—	2	4	no	—
327	C₂×C₄×C₄₇	—	2	2	no	—
328	C₂×C₄×C₄₇	—	2	4	no	—
329	C₂×C₄×C₄₇	—	2	2	no	—
330	C₂×C₄×C₄₇	—	2	2	no	—
331	C₂×C₄×C₄₇	—	2	2	no	—
332	C₂×C₄×C₄₇	—	2	2	no	—
333	C₂×C₄×C₄₇	—	2	2	no	—
334	C₂×C₄×C₄₇	—	2	2	no	—
335	C₂×C₄×C₄₇	—	4	2	no	—
336	C₂×C₄×C₄₇	—	4	4	no	—
337	C₂×C₄×C₄₇	—	4	1	no	—
338	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
339	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
340	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
342	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
343	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
345	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
346	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
348	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
349	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
350	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
351	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
352	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
353	C₄₇⋊C₈	—	2	2	no	—
354	C₄₇⋊C₈	—	2	2	no	—
355	C₄₇⋊C₈	—	2	1	no	—
356	C₄₇⋊C₈	—	2	1	no	—
357	C₄₇⋊C₈	—	2	4	no	—
358	C₄₇⋊C₈	—	2	2	no	—
359	C₄₇⋊C₈	C₂×#41	1	2	yes	—
360	C₄₇⋊C₈	C₂×#41	1	2	yes	—
361	C₄₇⋊C₈	C₂×#41	1	4	yes	—
362	#60215	—	47	1	no	maximal, Sylow
363	C₂²×C₄₇	—	2	2	no	—
364	C₂²×C₄₇	—	2	1	no	—
365	C₂²×C₄₇	—	2	2	no	—
366	C₂²×C₄₇	—	2	1	no	—
367	C₂²×C₄₇	—	2	2	no	—
368	C₂²×C₄₇	—	2	2	no	—
369	C₂²×C₄₇	—	2	2	no	—
370	C₂²×C₄₇	—	2	2	no	—
371	C₂²×C₄₇	—	2	2	no	—
372	C₂²×C₄₇	—	2	2	no	—
373	C₂²×C₄₇	—	4	8	no	—
374	C₂²×C₄₇	C₄×#41	1	2	yes	—
375	C₂²×C₄₇	C₂×#131	1	4	yes	—
376	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
377	C₄×C₄₇	—	2	2	no	—
378	C₄×C₄₇	—	2	2	no	—
379	C₄×C₄₇	—	2	2	no	—
380	C₄×C₄₇	—	2	2	no	—
381	C₄×C₄₇	—	2	1	no	—
382	C₄×C₄₇	—	2	4	no	—
383	C₄×C₄₇	—	2	1	no	—
384	C₄×C₄₇	—	2	2	no	—
385	C₄×C₄₇	—	2	4	no	—
386	C₄×C₄₇	—	2	1	no	—
387	C₄×C₄₇	C₄×#41	1	2	yes	—
388	C₄×C₄₇	C₂×#131	1	2	yes	—
389	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
390	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
391	#3475	D₄₇	1	1	yes	characteristic
392	#2970	—	47	2	no	—
393	#2969	—	47	2	no	—
394	#2968	—	47	4	no	—
395	#2966	—	47	4	no	—
396	#2966	—	47	2	no	—
397	C₈×#41	—	47	2	no	—
398	#2962	—	47	1	no	—
399	#2960	—	47	1	no	—
400	D₄×M₁₆	—	47	1	no	—
401	#2933	—	47	2	no	—
402	#2929	—	47	2	no	—
403	C₂×C₈×D₄	—	47	1	no	—
404	#2925	—	47	1	no	—
405	#2924	—	47	2	no	—
406	C₄×#131	—	47	1	no	—
407	C₂×#405	—	47	2	no	—
408	C₂×C₄₇	—	2	2	no	—
409	C₂×C₄₇	—	2	4	no	—
410	C₂×C₄₇	—	4	2	no	—
411	C₂×C₄₇	—	4	2	no	—
412	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
413	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
414	C₂×C₄₇	#3573	1	1	yes	characteristic
415	C₂×#131	—	47	1	no	—
416	C₂×#131	—	47	1	no	—
417	C₂²×M₁₆	—	47	2	no	—
418	C₂³×C₈	—	47	2	no	—
419	#556	Dic₄₇	1	1	yes	characteristic
420	#555	Dic₄₇	1	1	yes	characteristic
421	#554	Dic₄₇	1	1	yes	characteristic
422	#553	Dic₄₇	1	2	yes	—
423	#552	Dic₄₇	1	2	yes	—
424	#552	Dic₄₇	1	2	yes	—
425	#551	Dic₄₇	1	4	yes	—
426	#547	Dic₄₇	1	1	yes	characteristic
427	#546	Dic₄₇	1	2	yes	—
428	#533	C₂×D₄₇	1	1	yes	characteristic
429	#529	C₂×D₄₇	1	4	yes	—
430	#529	C₂×D₄₇	1	2	yes	—
431	#525	C₂×D₄₇	1	2	yes	—
432	C₄×#41	C₂×D₄₇	1	2	yes	—
433	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
435	C₂×#117	C₂×D₄₇	1	2	yes	—
436	#446	—	47	2	no	—
437	#446	—	47	2	no	—
438	#446	—	47	4	no	—
439	#446	—	47	2	no	—
440	C₈×Q₈	—	47	2	no	—
441	C₈×Q₈	—	47	2	no	—
442	C₈×Q₈	—	47	2	no	—
443	#436	—	47	4	no	—
444	#436	—	47	2	no	—
445	#435	—	47	4	no	—
446	#435	—	47	4	no	—
447	#435	—	47	4	no	—
448	#435	—	47	4	no	—
449	#435	—	47	4	no	—
450	C₈×D₄	—	47	1	no	—
451	C₈×D₄	—	47	1	no	—
452	C₈×D₄	—	47	2	no	—
453	C₈×D₄	—	47	2	no	—
454	C₈×D₄	—	47	1	no	—
455	C₈×D₄	—	47	1	no	—
456	C₈×D₄	—	47	4	no	—
457	C₈×D₄	—	47	4	no	—
458	C₈×D₄	—	47	4	no	—
459	C₈×D₄	—	47	2	no	—
460	#433	—	47	4	no	—
461	#433	—	47	4	no	—
462	#433	—	47	4	no	—
463	#432	—	47	4	no	—
464	#432	—	47	2	no	—
465	#431	—	47	4	no	—
466	#431	—	47	2	no	—
467	#424	—	47	2	no	—
468	#424	—	47	2	no	—
469	#423	—	47	1	no	—
470	C₂×C₄⋊C₈	—	47	1	no	—
471	#408	—	47	2	no	—
472	#407	—	47	2	no	—
473	C₂×C₂²⋊C₈	—	47	2	no	—
474	#405	—	47	1	no	—
475	#405	—	47	2	no	—
476	#405	—	47	2	no	—
477	#405	—	47	2	no	—
478	#405	—	47	4	no	—
479	#405	—	47	4	no	—
480	#405	—	47	1	no	—
481	#405	—	47	2	no	—
482	#405	—	47	2	no	—
483	C₄×M₁₆	—	47	1	no	—
484	C₄×M₁₆	—	47	2	no	—
485	C₂×#97	—	47	4	no	—
486	C₂×C₄×C₈	—	47	4	no	—
487	C₂×C₄×C₈	—	47	1	no	—
488	C₂×C₄×C₈	—	47	2	no	—
489	C₄₇	#60215	1	1	yes	characteristic, complemented, Sylow
490	C₂×#41	C₂×Dic₄₇	1	2	yes	—
491	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
492	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
493	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
494	#131	—	94	4	no	—
495	#131	—	94	4	no	—
496	C₂×M₁₆	—	47	1	no	—
497	C₂×M₁₆	—	47	2	no	—
498	C₂×M₁₆	—	47	4	no	—
499	C₂×M₁₆	—	47	1	no	—
500	C₂×M₁₆	—	47	2	no	—
501	C₂×M₁₆	—	47	2	no	—
502	C₂×M₁₆	—	94	8	no	—
503	C₂²×C₈	—	47	1	no	—
504	C₂²×C₈	—	47	2	no	—
505	C₂²×C₈	—	47	2	no	—
506	C₂²×C₈	—	47	2	no	—
507	C₂²×C₈	—	47	2	no	—
508	C₂²×C₈	—	47	2	no	—
509	C₂²×C₈	—	47	4	no	—
510	C₂²×C₈	—	47	1	no	—
511	C₂²×C₈	—	47	2	no	—
512	C₂²×C₈	—	47	2	no	—
513	C₂²×C₈	—	94	8	no	—
514	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
515	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
516	#126	C₂×Dic₄₇	1	4	yes	—
517	#126	C₂×Dic₄₇	1	4	yes	—
518	#126	C₂×Dic₄₇	1	4	yes	—
519	#125	C₂×Dic₄₇	1	4	yes	—
520	#125	C₂×Dic₄₇	1	2	yes	—
521	#125	C₂×Dic₄₇	1	2	yes	—
522	#124	C₂×Dic₄₇	1	2	yes	—
523	#124	C₂×Dic₄₇	1	4	yes	—
524	#123	C₂×Dic₄₇	1	4	yes	—
525	#123	C₂×Dic₄₇	1	4	yes	—
526	#123	C₂×Dic₄₇	1	4	yes	—
527	#123	C₂×Dic₄₇	1	4	yes	—
528	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
529	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
530	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
531	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
532	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
533	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
534	#121	C₂×Dic₄₇	1	2	yes	—
535	#121	C₂×Dic₄₇	1	2	yes	—
536	#121	C₂×Dic₄₇	1	4	yes	—
537	#121	C₂×Dic₄₇	1	2	yes	—
538	#120	C₂×Dic₄₇	1	4	yes	—
539	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
540	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
541	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
542	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
543	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
544	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
545	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
546	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
547	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
548	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
549	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
550	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
551	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
552	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
553	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
554	C₄×D₄	C₂²×D₄₇	1	2	yes	—
555	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
556	C₄×D₄	C₂²×D₄₇	1	4	yes	—
557	C₄×D₄	C₂²×D₄₇	1	4	yes	—
558	#117	C₂×Dic₄₇	1	4	yes	—
559	#117	C₂×Dic₄₇	1	2	yes	—
560	#117	C₂×Dic₄₇	1	2	yes	—
561	#117	C₂×Dic₄₇	1	4	yes	—
562	#117	C₂×Dic₄₇	1	2	yes	—
563	#117	C₂²×D₄₇	1	1	yes	characteristic
564	#117	C₂²×D₄₇	1	2	yes	—
565	#117	C₂²×D₄₇	1	4	yes	—
566	#117	C₂²×D₄₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
572	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
573	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
574	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
575	C₄⋊C₈	—	47	1	no	—
576	C₄⋊C₈	—	47	1	no	—
577	C₄⋊C₈	—	47	2	no	—
578	C₄⋊C₈	—	47	2	no	—
579	C₄⋊C₈	—	47	2	no	—
580	C₄⋊C₈	—	47	4	no	—
581	C₄⋊C₈	—	47	4	no	—
582	C₄⋊C₈	—	47	4	no	—
583	C₄⋊C₈	—	47	4	no	—
584	C₂²⋊C₈	—	47	2	no	—
585	C₂²⋊C₈	—	47	2	no	—
586	C₂²⋊C₈	—	47	2	no	—
587	C₂²⋊C₈	—	47	2	no	—
588	C₂²⋊C₈	—	47	4	no	—
589	C₂²⋊C₈	—	47	4	no	—
590	C₂²⋊C₈	—	47	4	no	—
591	C₂²⋊C₈	—	47	4	no	—
592	#97	—	47	2	no	—
593	#97	—	47	4	no	—
594	#97	—	47	4	no	—
595	#97	—	47	4	no	—
596	#97	—	47	2	no	—
597	#97	—	47	2	no	—
598	C₄×C₈	—	47	2	no	—
599	C₄×C₈	—	47	1	no	—
600	C₄×C₈	—	47	1	no	—
601	C₄×C₈	—	47	2	no	—
602	C₄×C₈	—	47	4	no	—
603	C₄×C₈	—	47	2	no	—
604	C₄×C₈	—	47	1	no	—
605	C₄×C₈	—	47	4	no	—
606	C₄×C₈	—	47	1	no	—
607	C₄×C₈	—	47	4	no	—
608	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
609	#41	—	2	8	no	—
610	#41	—	2	2	no	—
611	#41	—	2	2	no	—
612	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
613	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
614	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
617	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
618	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
619	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
620	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
621	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
622	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
626	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
627	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
628	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
629	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
630	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
631	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
632	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
633	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
634	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
635	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
636	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
637	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
638	M₁₆	—	47	4	no	—
639	M₁₆	—	94	8	no	—
640	M₁₆	—	94	4	no	—
641	M₁₆	—	94	4	no	—
642	M₁₆	—	94	4	no	—
643	M₁₆	—	94	2	no	—
644	C₂×C₈	—	47	4	no	—
645	C₂×C₈	—	47	1	no	—
646	C₂×C₈	—	47	2	no	—
647	C₂×C₈	—	47	1	no	—
648	C₂×C₈	—	47	1	no	—
649	C₂×C₈	—	47	2	no	—
650	C₂×C₈	—	47	1	no	—
651	C₂×C₈	—	47	2	no	—
652	C₂×C₈	—	47	4	no	—
653	C₂×C₈	—	47	2	no	—
654	C₂×C₈	—	94	4	no	—
655	C₂×C₈	—	94	4	no	—
656	C₂×C₈	—	94	4	no	—
657	C₂×C₈	—	94	4	no	—
658	C₂×C₈	—	94	8	no	—
659	C₂×C₈	—	94	4	no	—
660	C₂×C₈	—	94	4	no	—
661	C₂×C₈	—	94	4	no	—
662	C₂×C₈	—	94	2	no	—
663	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
664	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
665	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
666	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
667	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
668	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
669	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
670	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
671	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
672	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
673	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
674	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
675	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
676	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
677	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
678	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
679	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
680	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
681	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
682	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
683	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
684	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
685	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
686	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
687	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
688	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
689	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
690	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
691	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
692	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
693	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
694	C₄²	C₂²×Dic₄₇	1	4	yes	—
695	C₄²	C₂²×Dic₄₇	1	4	yes	—
696	C₄²	C₂²×Dic₄₇	1	2	yes	—
697	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
698	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
699	C₄²	C₂²×Dic₄₇	1	2	yes	—
700	C₄²	C₂³×D₄₇	1	2	yes	—
701	C₄²	C₂³×D₄₇	1	1	yes	characteristic
702	C₄²	C₂³×D₄₇	1	1	yes	characteristic
703	C₄²	C₂³×D₄₇	1	4	yes	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	4	2	no	—
707	C₂³	C₂³×Dic₄₇	1	2	yes	—
708	C₂³	C₂³×Dic₄₇	1	2	yes	—
709	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
710	C₂³	C₂³×Dic₄₇	1	2	yes	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	4	no	—
713	Q₈	—	4	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	8	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	4	4	no	—
720	D₄	#13094031	1	4	yes	complemented
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	8	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
737	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
738	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
739	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
740	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
741	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
742	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
743	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
744	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
745	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
746	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
747	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
748	C₂×C₄	#41×D₄₇	1	2	yes	—
749	C₂×C₄	#41×D₄₇	1	2	yes	—
750	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
751	C₈	—	47	2	no	—
752	C₈	—	47	2	no	—
753	C₈	—	47	4	no	—
754	C₈	—	94	2	no	—
755	C₈	—	94	1	no	—
756	C₈	—	94	2	no	—
757	C₈	—	94	4	no	—
758	C₈	—	94	2	no	—
759	C₈	—	94	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	4	8	no	—
771	C₂²	#41×Dic₄₇	1	2	yes	—
772	C₂²	C₂×#13094031	1	4	yes	—
773	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	#41×Dic₄₇	1	2	yes	—
785	C₄	C₂×#13094031	1	2	yes	—
786	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
787	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
788	C₂	—	2	2	no	—
789	C₂	—	2	4	no	—
790	C₂	—	4	2	no	—
791	C₂	—	4	2	no	—
792	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
793	C₂	C₂²×#13094031	1	1	yes	characteristic
794	C₂	#20258100	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₄₇×#3475	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#3475	D₄₇
hypocenter	C₄₇	#60215
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #3475

Complements

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

N	H ≅ G/N	type
1. #20252402	C₂	semidirect
2. #20252393	C₂	semidirect
3. #20252384	C₂	semidirect
4. #20252364	C₂	semidirect
5. #20252364	C₂	semidirect
6. #41×C₄₇⋊C₈	C₂	semidirect
7. #20252337	C₂	semidirect
8. #20252323	C₂	semidirect
9. D₄×#10625329	C₂	semidirect
10. #20252115	C₂	semidirect
11. #20252083	C₂	semidirect
12. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
13. #20252054	C₂	semidirect
14. #20252046	C₂	semidirect
15. C₄×#13094031	C₂	semidirect
16. C₂×#15689079	C₂	semidirect
22. #15689254	C₂²	semidirect
23. #15689254	C₂²	semidirect
24. #15689254	C₂²	semidirect
25. #15689254	C₂²	semidirect
26. Q₈×C₄₇⋊C₈	C₂²	semidirect
27. Q₈×C₄₇⋊C₈	C₂²	semidirect
28. Q₈×C₄₇⋊C₈	C₂²	semidirect
30. #15689201	C₂²	semidirect
32. #15689195	C₂²	semidirect
33. #15689195	C₂²	semidirect
34. #15689195	C₂²	semidirect
35. #15689195	C₂²	semidirect
43. D₄×C₄₇⋊C₈	C₂²	semidirect
44. D₄×C₄₇⋊C₈	C₂²	semidirect
45. D₄×C₄₇⋊C₈	C₂²	semidirect
46. #15689184	C₂²	semidirect
47. #15689184	C₂²	semidirect
48. #15689184	C₂²	semidirect
49. #15689180	C₂²	semidirect
50. #15689180	C₂²	semidirect
51. #15689176	C₂²	semidirect
52. #15689176	C₂²	semidirect
65. #15689079	C₂²	semidirect
66. #15689079	C₂²	semidirect
67. #15689079	C₂²	semidirect
68. #15689079	C₂²	semidirect
70. C₄×#10625329	C₂²	semidirect
71. C₂×#13093935	C₂²	semidirect
73. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
74. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
286. #10625329	#41	semidirect
296. C₂×C₄₇⋊C₈	#41	semidirect
322. D₄×C₄₇	#131	semidirect
489. C₄₇	#60215	semidirect
720. D₄	#13094031	semidirect

Maximal subgroups

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

subgroup	index
#20252402	2
#20252393	2
#20252384	2
#20252364	2
#41×C₄₇⋊C₈	2
#20252337	2
#20252323	2
D₄×#10625329	2
#20252115	2
#20252083	2
C₂×D₄×C₄₇⋊C₈	2
#20252054	2
#20252046	2
C₄×#13094031	2
C₂×#15689079	2
C₄₇×#3475	2
#60215	47