Subgroups — #27080993

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 778 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	#20252375	C₂	1	4	yes	maximal, complemented
5	#20252364	C₂	1	2	yes	maximal, complemented
6	#20252355	C₂	1	2	yes	maximal, complemented
7	Q₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689254	C₂	1	1	yes	maximal, characteristic, complemented
9	#20252132	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252132	C₂	1	2	yes	maximal, complemented
11	#20252106	C₂	1	2	yes	maximal, complemented
12	#20252100	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252054	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252054	C₂	1	2	yes	maximal, complemented
15	#20251816	C₂	1	2	yes	maximal, complemented
16	C₄×#13094031	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#3480	C₂	1	1	yes	maximal, characteristic
18	C₂×#13094031	C₂²	1	1	yes	characteristic
19	C₂×#13094031	C₂²	1	1	yes	characteristic
20	C₂×#13094031	C₂²	1	2	yes	—
21	C₂×#13094031	C₂²	1	2	yes	—
22	#15689254	C₂²	1	1	yes	characteristic
23	#15689254	C₂²	1	1	yes	characteristic
24	#15689254	C₂²	1	2	yes	—
25	#15689254	C₂²	1	2	yes	—
26	#15689254	C₂²	1	1	yes	characteristic
27	#15689254	C₂²	1	1	yes	characteristic
28	#15689254	C₂²	1	2	yes	—
29	#15689254	C₂²	1	4	yes	—
30	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
31	#15689201	C₂²	1	2	yes	—
32	#15689201	C₂²	1	2	yes	—
33	#15689201	C₂²	1	2	yes	—
34	#15689201	C₂²	1	4	yes	—
35	#15689195	C₂²	1	4	yes	—
36	#15689195	C₂²	1	4	yes	—
37	#15689195	C₂²	1	4	yes	—
38	#15689195	C₂²	1	4	yes	—
39	#15689195	C₂²	1	4	yes	—
40	#15689195	C₂²	1	4	yes	—
41	#15689195	C₂²	1	4	yes	—
42	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
43	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
44	D₄×C₄₇⋊C₈	C₂²	1	4	yes	—
45	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
46	#15689184	C₂²	1	4	yes	—
47	#15689184	C₂²	1	4	yes	—
48	#15689184	C₂²	1	4	yes	—
49	#15689180	C₂²	1	2	yes	—
50	#15689180	C₂²	1	4	yes	—
51	#15689176	C₂²	1	4	yes	—
52	#15689176	C₂²	1	2	yes	—
53	#15689147	C₂²	1	1	yes	characteristic
54	#15689147	C₂²	1	2	yes	—
55	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
57	#15689090	C₂²	1	2	yes	—
58	#15689090	C₂²	1	2	yes	—
59	#15689090	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	—
66	#15689079	C₂²	1	4	yes	—
67	C₄×#10625329	C₂²	1	1	yes	characteristic
68	C₄×#10625329	C₂²	1	2	yes	—
69	C₄×#10625329	C₂²	1	2	yes	—
70	C₄×#10625329	C₂²	1	4	yes	—
71	C₂×#13093935	C₂²	1	2	yes	—
72	C₂×#13093935	C₂²	1	4	yes	—
73	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
75	C₄₇×#559	C₄	1	1	yes	characteristic
76	C₄₇×#559	C₄	1	2	yes	—
77	C₄₇×#557	C₄	1	1	yes	characteristic
78	C₄₇×#556	C₄	1	1	yes	characteristic
79	C₄₇×#556	C₄	1	2	yes	—
80	C₄₇×#553	C₄	1	2	yes	—
81	C₄₇×#553	C₄	1	4	yes	—
82	C₄₇×#550	C₄	1	1	yes	characteristic
83	C₄₇×#548	C₄	1	2	yes	—
84	C₄₇×#532	C₂²	1	1	yes	characteristic
85	C₄₇×#532	C₂²	1	2	yes	—
86	C₄₇×#529	C₂²	1	2	yes	—
87	C₄₇×#529	C₂²	1	4	yes	—
88	C₄×#41×C₄₇	C₂²	1	2	yes	—
89	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
90	C₄×#41×C₄₇	C₂²	1	2	yes	—
91	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
92	#13094031	—	2	4	no	—
93	#13094031	—	2	8	no	—
94	#13094031	—	2	4	no	—
95	#13094031	—	2	8	no	—
96	C₂×#10625329	C₂³	1	1	yes	characteristic
97	C₂×#10625329	C₂³	1	2	yes	—
98	C₂×#10625329	C₂³	1	2	yes	—
99	C₂×#10625329	C₂³	1	2	yes	—
100	C₂×#10625329	C₂³	1	4	yes	—
101	C₂×#10625329	C₂³	1	4	yes	—
102	C₂×#10625329	C₂³	1	1	yes	characteristic
103	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
105	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
106	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
107	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
108	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
109	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
110	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
111	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
112	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
113	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
114	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
115	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
116	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
117	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
118	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
119	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
120	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
121	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
122	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
123	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	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	#13093935	C₂³	1	2	yes	—
128	#13093935	C₂³	1	2	yes	—
129	#13093935	C₂³	1	4	yes	—
130	#13093935	C₂³	1	2	yes	—
131	#13093935	C₂³	1	2	yes	—
132	#13093935	C₂³	1	2	yes	—
133	#13093935	C₂³	1	2	yes	—
134	#13093935	C₂³	1	4	yes	—
135	#13093935	C₂³	1	2	yes	—
136	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
137	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
138	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
139	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
144	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
145	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
146	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
147	C₂×#41×C₄₇	C₂³	1	2	yes	—
148	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
149	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
150	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
151	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
152	#127×C₄₇	C₂×C₄	1	2	yes	—
153	#126×C₄₇	C₂×C₄	1	4	yes	—
154	#126×C₄₇	C₂×C₄	1	4	yes	—
155	#126×C₄₇	C₂×C₄	1	4	yes	—
156	#125×C₄₇	C₂×C₄	1	2	yes	—
157	#125×C₄₇	C₂×C₄	1	4	yes	—
158	#124×C₄₇	C₂×C₄	1	2	yes	—
159	#124×C₄₇	C₂×C₄	1	4	yes	—
160	#124×C₄₇	C₂×C₄	1	2	yes	—
161	#124×C₄₇	C₂×C₄	1	2	yes	—
162	#124×C₄₇	C₂×C₄	1	2	yes	—
163	#123×C₄₇	C₂×C₄	1	4	yes	—
164	#123×C₄₇	C₂×C₄	1	4	yes	—
165	#123×C₄₇	C₂×C₄	1	4	yes	—
166	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
167	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
168	#121×C₄₇	C₂×C₄	1	2	yes	—
169	#121×C₄₇	C₂×C₄	1	4	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	#121×C₄₇	C₂×C₄	1	4	yes	—
174	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
175	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
176	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
177	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
178	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
179	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
180	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
181	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
182	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
183	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
184	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
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	C₂×C₄	1	2	yes	—
189	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
190	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
191	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
192	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
193	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
194	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
195	C₄×D₄×C₄₇	C₂³	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	2	yes	—
199	#117×C₄₇	C₂×C₄	1	2	yes	—
200	#117×C₄₇	C₂×C₄	1	4	yes	—
201	#117×C₄₇	C₂³	1	1	yes	characteristic
202	#117×C₄₇	C₂³	1	2	yes	—
203	#117×C₄₇	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
206	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
208	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
209	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
210	#41×C₄₇	—	2	2	no	—
211	#41×C₄₇	—	2	4	no	—
212	#41×C₄₇	—	2	2	no	—
213	#41×C₄₇	—	2	4	no	—
214	#41×C₄₇	—	4	4	no	—
215	C₂×Q₈×C₄₇	—	4	2	no	—
216	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
217	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
218	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
219	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
220	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
221	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
222	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
223	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
224	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
225	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
226	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
228	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
229	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
231	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
234	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
235	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
236	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
237	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
241	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
242	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
243	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
244	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
245	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
246	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
247	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
248	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
249	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
250	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
251	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
252	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	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	4	yes	—
258	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
259	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
260	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
261	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
262	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
263	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
264	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	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	4	yes	—
268	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
269	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
270	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
271	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
272	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
273	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
274	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
275	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
276	C₄²×C₄₇	C₂⁴	1	2	yes	—
277	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
278	C₄²×C₄₇	C₂⁴	1	2	yes	—
279	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
280	C₄²×C₄₇	C₂⁴	1	2	yes	—
281	#10625329	—	2	2	no	—
282	#10625329	—	2	4	no	—
283	#10625329	—	2	4	no	—
284	#10625329	—	2	4	no	—
285	#10625329	—	2	8	no	—
286	#10625329	—	2	8	no	—
287	#10625329	#41	1	4	yes	complemented
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	8	no	—
292	C₂×C₄₇⋊C₈	—	2	8	no	—
293	C₂×C₄₇⋊C₈	—	2	4	no	—
294	C₂×C₄₇⋊C₈	#41	1	4	yes	complemented
295	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
296	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
297	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
298	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
299	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
300	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
301	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
302	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
303	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
304	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
305	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
306	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
307	Q₈×C₄₇	—	2	2	no	—
308	Q₈×C₄₇	—	2	4	no	—
309	Q₈×C₄₇	—	2	2	no	—
310	Q₈×C₄₇	—	2	2	no	—
311	Q₈×C₄₇	—	4	2	no	—
312	D₄×C₄₇	—	2	4	no	—
313	D₄×C₄₇	—	2	8	no	—
314	D₄×C₄₇	—	2	2	no	—
315	D₄×C₄₇	—	2	4	no	—
316	D₄×C₄₇	—	2	4	no	—
317	D₄×C₄₇	—	4	4	no	—
318	D₄×C₄₇	—	4	2	no	—
319	D₄×C₄₇	—	4	4	no	—
320	C₂×C₄×C₄₇	—	2	2	no	—
321	C₂×C₄×C₄₇	—	2	4	no	—
322	C₂×C₄×C₄₇	—	2	2	no	—
323	C₂×C₄×C₄₇	—	2	4	no	—
324	C₂×C₄×C₄₇	—	2	4	no	—
325	C₂×C₄×C₄₇	—	2	2	no	—
326	C₂×C₄×C₄₇	—	4	2	no	—
327	C₂×C₄×C₄₇	—	4	4	no	—
328	C₂×C₄×C₄₇	—	4	1	no	—
329	C₂×C₄×C₄₇	—	4	2	no	—
330	C₂×C₄×C₄₇	—	4	2	no	—
331	C₂×C₄×C₄₇	—	4	4	no	—
332	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
333	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
334	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
335	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
336	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
337	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
338	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
339	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
340	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
341	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
342	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
343	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
345	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
346	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
347	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
348	C₄₇⋊C₈	—	2	1	no	—
349	C₄₇⋊C₈	—	2	2	no	—
350	C₄₇⋊C₈	—	2	1	no	—
351	C₄₇⋊C₈	—	2	2	no	—
352	C₄₇⋊C₈	—	2	4	no	—
353	C₄₇⋊C₈	—	2	2	no	—
354	C₄₇⋊C₈	C₂×#41	1	2	yes	—
355	C₄₇⋊C₈	C₂×#41	1	4	yes	—
356	C₄₇⋊C₈	C₂×#41	1	2	yes	—
357	#60219	—	47	1	no	maximal, Sylow
358	C₂²×C₄₇	—	2	1	no	—
359	C₂²×C₄₇	—	2	1	no	—
360	C₂²×C₄₇	—	2	2	no	—
361	C₂²×C₄₇	—	2	4	no	—
362	C₂²×C₄₇	—	2	2	no	—
363	C₂²×C₄₇	—	2	4	no	—
364	C₂²×C₄₇	—	2	2	no	—
365	C₂²×C₄₇	—	2	4	no	—
366	C₂²×C₄₇	C₄×#41	1	2	yes	—
367	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
368	C₄×C₄₇	—	2	2	no	—
369	C₄×C₄₇	—	2	4	no	—
370	C₄×C₄₇	—	2	2	no	—
371	C₄×C₄₇	—	2	1	no	—
372	C₄×C₄₇	—	2	2	no	—
373	C₄×C₄₇	—	2	2	no	—
374	C₄×C₄₇	—	2	2	no	—
375	C₄×C₄₇	—	2	1	no	—
376	C₄×C₄₇	—	2	2	no	—
377	C₄×C₄₇	—	2	1	no	—
378	C₄×C₄₇	—	2	2	no	—
379	C₄×C₄₇	C₄×#41	1	2	yes	—
380	C₄×C₄₇	#568	1	2	yes	—
381	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
382	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
383	#3480	D₄₇	1	1	yes	characteristic
384	#2970	—	47	2	no	—
385	#2969	—	47	2	no	—
386	#2968	—	47	4	no	—
387	#2967	—	47	4	no	—
388	#2966	—	47	2	no	—
389	#2965	—	47	2	no	—
390	Q₈×M₁₆	—	47	1	no	—
391	C₂×#446	—	47	1	no	—
392	#2935	—	47	1	no	—
393	#2935	—	47	2	no	—
394	#2932	—	47	2	no	—
395	#2931	—	47	1	no	—
396	#2925	—	47	1	no	—
397	#2925	—	47	2	no	—
398	#2875	—	47	2	no	—
399	C₄×#131	—	47	1	no	—
400	C₂×C₄₇	—	2	2	no	—
401	C₂×C₄₇	—	4	2	no	—
402	C₂×C₄₇	—	4	4	no	—
403	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
404	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
405	C₂×C₄₇	#3573	1	1	yes	characteristic
406	C₂×#131	—	47	1	no	—
407	C₂×#131	—	47	1	no	—
408	C₂×#131	—	47	2	no	—
409	C₂×#131	—	47	2	no	—
410	#559	Dic₄₇	1	1	yes	characteristic
411	#559	Dic₄₇	1	2	yes	—
412	#557	Dic₄₇	1	1	yes	characteristic
413	#556	Dic₄₇	1	1	yes	characteristic
414	#556	Dic₄₇	1	2	yes	—
415	#553	Dic₄₇	1	2	yes	—
416	#553	Dic₄₇	1	4	yes	—
417	#550	Dic₄₇	1	1	yes	characteristic
418	#548	Dic₄₇	1	2	yes	—
419	#532	C₂×D₄₇	1	1	yes	characteristic
420	#532	C₂×D₄₇	1	2	yes	—
421	#529	C₂×D₄₇	1	2	yes	—
422	#529	C₂×D₄₇	1	4	yes	—
423	C₄×#41	C₂×D₄₇	1	2	yes	—
424	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
425	C₄×#41	C₂×D₄₇	1	2	yes	—
426	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
427	#446	—	47	1	no	—
428	#446	—	47	1	no	—
429	#446	—	47	2	no	—
430	#446	—	47	2	no	—
431	#446	—	47	1	no	—
432	#446	—	47	1	no	—
433	#446	—	47	2	no	—
434	#446	—	47	4	no	—
435	C₈×Q₈	—	47	2	no	—
436	#436	—	47	2	no	—
437	#436	—	47	2	no	—
438	#436	—	47	2	no	—
439	#436	—	47	4	no	—
440	#435	—	47	4	no	—
441	#435	—	47	4	no	—
442	#435	—	47	4	no	—
443	#435	—	47	4	no	—
444	#435	—	47	4	no	—
445	#435	—	47	4	no	—
446	#435	—	47	4	no	—
447	C₈×D₄	—	47	2	no	—
448	C₈×D₄	—	47	2	no	—
449	C₈×D₄	—	47	4	no	—
450	C₈×D₄	—	47	2	no	—
451	#433	—	47	4	no	—
452	#433	—	47	4	no	—
453	#433	—	47	4	no	—
454	#432	—	47	2	no	—
455	#432	—	47	4	no	—
456	#431	—	47	4	no	—
457	#431	—	47	2	no	—
458	#423	—	47	1	no	—
459	#423	—	47	2	no	—
460	C₂×C₄⋊C₈	—	47	2	no	—
461	C₂×C₄⋊C₈	—	47	1	no	—
462	#408	—	47	2	no	—
463	#408	—	47	2	no	—
464	#408	—	47	2	no	—
465	#405	—	47	1	no	—
466	#405	—	47	1	no	—
467	#405	—	47	2	no	—
468	#405	—	47	2	no	—
469	#405	—	47	2	no	—
470	#405	—	47	4	no	—
471	#405	—	47	4	no	—
472	C₄×M₁₆	—	47	1	no	—
473	C₄×M₁₆	—	47	2	no	—
474	C₄×M₁₆	—	47	2	no	—
475	C₄×M₁₆	—	47	4	no	—
476	C₂×#97	—	47	2	no	—
477	C₂×#97	—	47	4	no	—
478	C₂×C₄×C₈	—	47	1	no	—
479	C₂×C₄×C₈	—	47	2	no	—
480	C₄₇	#60219	1	1	yes	characteristic, complemented, Sylow
481	C₂×#41	C₂×Dic₄₇	1	2	yes	—
482	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
483	C₂×#41	C₂²×D₄₇	1	2	yes	—
484	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
485	#131	—	94	4	no	—
486	#131	—	94	8	no	—
487	#131	—	94	4	no	—
488	#131	—	94	8	no	—
489	C₂×M₁₆	—	47	1	no	—
490	C₂×M₁₆	—	47	1	no	—
491	C₂×M₁₆	—	47	2	no	—
492	C₂×M₁₆	—	47	2	no	—
493	C₂×M₁₆	—	47	2	no	—
494	C₂×M₁₆	—	47	4	no	—
495	C₂×M₁₆	—	47	4	no	—
496	C₂²×C₈	—	47	1	no	—
497	C₂²×C₈	—	47	1	no	—
498	C₂²×C₈	—	47	2	no	—
499	C₂²×C₈	—	47	2	no	—
500	C₂²×C₈	—	47	2	no	—
501	C₂²×C₈	—	47	4	no	—
502	C₂²×C₈	—	47	4	no	—
503	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
504	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
505	#127	C₂×Dic₄₇	1	1	yes	characteristic
506	#127	C₂×Dic₄₇	1	2	yes	—
507	#126	C₂×Dic₄₇	1	4	yes	—
508	#126	C₂×Dic₄₇	1	4	yes	—
509	#126	C₂×Dic₄₇	1	4	yes	—
510	#125	C₂×Dic₄₇	1	2	yes	—
511	#125	C₂×Dic₄₇	1	4	yes	—
512	#124	C₂×Dic₄₇	1	2	yes	—
513	#124	C₂×Dic₄₇	1	4	yes	—
514	#124	C₂×Dic₄₇	1	2	yes	—
515	#124	C₂×Dic₄₇	1	2	yes	—
516	#124	C₂×Dic₄₇	1	2	yes	—
517	#123	C₂×Dic₄₇	1	4	yes	—
518	#123	C₂×Dic₄₇	1	4	yes	—
519	#123	C₂×Dic₄₇	1	4	yes	—
520	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
521	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
522	#121	C₂×Dic₄₇	1	2	yes	—
523	#121	C₂×Dic₄₇	1	4	yes	—
524	#121	C₂×Dic₄₇	1	2	yes	—
525	#121	C₂×Dic₄₇	1	4	yes	—
526	#121	C₂×Dic₄₇	1	2	yes	—
527	#121	C₂×Dic₄₇	1	4	yes	—
528	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
529	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
530	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
531	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
532	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
533	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
534	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
535	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
536	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
537	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
538	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
539	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
540	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
541	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
542	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
543	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
544	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
545	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
546	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
547	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
548	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
549	C₄×D₄	C₂²×D₄₇	1	2	yes	—
550	C₄×D₄	C₂²×D₄₇	1	4	yes	—
551	C₄×D₄	C₂²×D₄₇	1	4	yes	—
552	C₄×D₄	C₂²×D₄₇	1	2	yes	—
553	#117	C₂×Dic₄₇	1	2	yes	—
554	#117	C₂×Dic₄₇	1	4	yes	—
555	#117	C₂²×D₄₇	1	1	yes	characteristic
556	#117	C₂²×D₄₇	1	2	yes	—
557	#117	C₂²×D₄₇	1	4	yes	—
558	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
560	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
561	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
562	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
563	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
564	C₄⋊C₈	—	47	2	no	—
565	C₄⋊C₈	—	47	1	no	—
566	C₄⋊C₈	—	47	1	no	—
567	C₄⋊C₈	—	47	2	no	—
568	C₄⋊C₈	—	47	2	no	—
569	C₄⋊C₈	—	47	2	no	—
570	C₄⋊C₈	—	47	2	no	—
571	C₄⋊C₈	—	47	2	no	—
572	C₄⋊C₈	—	47	4	no	—
573	C₄⋊C₈	—	47	2	no	—
574	C₄⋊C₈	—	47	4	no	—
575	C₂²⋊C₈	—	47	4	no	—
576	C₂²⋊C₈	—	47	4	no	—
577	C₂²⋊C₈	—	47	4	no	—
578	C₂²⋊C₈	—	47	4	no	—
579	C₂²⋊C₈	—	47	4	no	—
580	C₂²⋊C₈	—	47	4	no	—
581	#97	—	47	2	no	—
582	#97	—	47	2	no	—
583	#97	—	47	2	no	—
584	#97	—	47	4	no	—
585	#97	—	47	4	no	—
586	#97	—	47	2	no	—
587	#97	—	47	2	no	—
588	#97	—	47	2	no	—
589	#97	—	47	2	no	—
590	C₄×C₈	—	47	1	no	—
591	C₄×C₈	—	47	2	no	—
592	C₄×C₈	—	47	1	no	—
593	C₄×C₈	—	47	2	no	—
594	C₄×C₈	—	47	2	no	—
595	C₄×C₈	—	47	1	no	—
596	C₄×C₈	—	47	1	no	—
597	C₄×C₈	—	47	4	no	—
598	C₄×C₈	—	47	4	no	—
599	#41	—	2	2	no	—
600	#41	—	2	4	no	—
601	#41	—	2	2	no	—
602	#41	—	2	4	no	—
603	#41	—	4	4	no	—
604	C₂×Q₈	—	4	2	no	—
605	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
606	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
607	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
608	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
609	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
610	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
611	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
612	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
613	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
614	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
615	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
616	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
617	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
618	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
619	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
620	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
621	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
622	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
623	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
624	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
625	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
626	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
627	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
628	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
629	M₁₆	—	47	4	no	—
630	M₁₆	—	94	4	no	—
631	M₁₆	—	94	8	no	—
632	M₁₆	—	94	4	no	—
633	M₁₆	—	94	8	no	—
634	M₁₆	—	94	2	no	—
635	M₁₆	—	94	4	no	—
636	C₂×C₈	—	47	4	no	—
637	C₂×C₈	—	47	1	no	—
638	C₂×C₈	—	47	2	no	—
639	C₂×C₈	—	47	1	no	—
640	C₂×C₈	—	47	1	no	—
641	C₂×C₈	—	47	1	no	—
642	C₂×C₈	—	47	2	no	—
643	C₂×C₈	—	47	2	no	—
644	C₂×C₈	—	47	4	no	—
645	C₂×C₈	—	47	2	no	—
646	C₂×C₈	—	94	8	no	—
647	C₂×C₈	—	94	4	no	—
648	C₂×C₈	—	94	4	no	—
649	C₂×C₈	—	94	8	no	—
650	C₂×C₈	—	94	2	no	—
651	C₂×C₈	—	94	4	no	—
652	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
653	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
654	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
655	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
656	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
657	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
658	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
659	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
660	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
661	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
662	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
663	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
664	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
665	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
666	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
667	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
668	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
669	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
670	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
671	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
672	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
673	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
674	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
675	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
676	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
677	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
678	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
679	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
680	C₄²	C₂²×Dic₄₇	1	2	yes	—
681	C₄²	C₂²×Dic₄₇	1	4	yes	—
682	C₄²	C₂²×Dic₄₇	1	4	yes	—
683	C₄²	C₂²×Dic₄₇	1	2	yes	—
684	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
685	C₄²	C₂²×Dic₄₇	1	2	yes	—
686	C₄²	C₂²×Dic₄₇	1	2	yes	—
687	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
688	C₄²	C₂³×D₄₇	1	2	yes	—
689	C₄²	C₂³×D₄₇	1	1	yes	characteristic
690	C₄²	C₂³×D₄₇	1	1	yes	characteristic
691	C₄²	C₂³×D₄₇	1	2	yes	—
692	C₄²	C₂³×D₄₇	1	2	yes	—
693	C₂³	C₂³×Dic₄₇	1	2	yes	—
694	C₂³	C₂³×Dic₄₇	1	4	yes	—
695	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
696	Q₈	—	2	2	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	2	no	—
701	D₄	—	2	4	no	—
702	D₄	—	2	8	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	4	no	—
705	D₄	—	2	4	no	—
706	D₄	—	4	4	no	—
707	D₄	—	4	2	no	—
708	D₄	—	4	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
722	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
723	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
724	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
725	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
726	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
727	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
728	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
729	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
730	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
731	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
732	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
733	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
734	C₂×C₄	#41×D₄₇	1	2	yes	—
735	C₂×C₄	#41×D₄₇	1	2	yes	—
736	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
737	C₈	—	47	2	no	—
738	C₈	—	47	2	no	—
739	C₈	—	47	4	no	—
740	C₈	—	94	1	no	—
741	C₈	—	94	2	no	—
742	C₈	—	94	2	no	—
743	C₈	—	94	4	no	—
744	C₈	—	94	1	no	—
745	C₈	—	94	2	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	#41×Dic₄₇	1	2	yes	—
755	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
756	C₄	—	2	2	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	4	no	—
766	C₄	—	2	2	no	—
767	C₄	#41×Dic₄₇	1	2	yes	—
768	C₄	#15689890	1	2	yes	—
769	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
770	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
771	C₂	—	2	2	no	—
772	C₂	—	4	2	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
775	C₂	C₂×#15689890	1	1	yes	characteristic
776	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×#3480	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#3480	D₄₇
hypocenter	C₄₇	#60219
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #3480

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. #20252375	C₂	semidirect
5. #20252364	C₂	semidirect
6. #20252355	C₂	semidirect
7. Q₈×#10625329	C₂	semidirect
8. C₂×#15689254	C₂	semidirect
9. #20252132	C₂	semidirect
10. #20252132	C₂	semidirect
11. #20252106	C₂	semidirect
12. #20252100	C₂	semidirect
13. #20252054	C₂	semidirect
14. #20252054	C₂	semidirect
15. #20251816	C₂	semidirect
16. C₄×#13094031	C₂	semidirect
287. #10625329	#41	semidirect
294. C₂×C₄₇⋊C₈	#41	semidirect
480. C₄₇	#60219	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
#20252375	2
#20252364	2
#20252355	2
Q₈×#10625329	2
C₂×#15689254	2
#20252132	2
#20252106	2
#20252100	2
#20252054	2
#20251816	2
C₄×#13094031	2
C₄₇×#3480	2
#60219	47