Subgroups — #27081208

Order 12032.

2130 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252464	C₂	1	2	yes	maximal, complemented
2	#20252455	C₂	1	2	yes	maximal, complemented
3	#20252450	C₂	1	4	yes	maximal, complemented
4	#20252436	C₂	1	4	yes	maximal, complemented
5	#20252429	C₂	1	2	yes	maximal, complemented
6	#20252423	C₂	1	2	yes	maximal, complemented
7	#20252132	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
9	#20252115	C₂	1	2	yes	maximal, complemented
10	#20252100	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252092	C₂	1	2	yes	maximal, complemented
12	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
13	#20252054	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252032	C₂	1	1	yes	maximal, characteristic, complemented
15	#20251837	C₂	1	2	yes	maximal, complemented
16	#20251833	C₂	1	2	yes	maximal, complemented
17	D₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
18	C₂×#13094031	C₂²	1	2	yes	complemented
19	C₂×#13094031	C₂²	1	2	yes	complemented
20	C₂²×#10625329	C₂²	1	2	yes	complemented
21	C₂²×#10625329	C₂²	1	2	yes	complemented
22	#15689201	C₂²	1	1	yes	characteristic
23	#15689201	C₂²	1	2	yes	—
24	#15689201	C₂²	1	1	yes	characteristic
25	#15689201	C₂²	1	4	yes	complemented
26	#15689201	C₂²	1	4	yes	complemented
27	#15689201	C₂²	1	2	yes	complemented
28	#15689201	C₂²	1	2	yes	complemented
29	#15689201	C₂²	1	2	yes	complemented
30	#15689201	C₂²	1	2	yes	complemented
31	#15689201	C₂²	1	2	yes	complemented
32	#15689201	C₂²	1	4	yes	complemented
33	#15689201	C₂²	1	1	yes	characteristic, complemented
34	#15689201	C₂²	1	1	yes	characteristic, complemented
35	#15689195	C₂²	1	4	yes	complemented
36	#15689195	C₂²	1	4	yes	complemented
37	#15689195	C₂²	1	4	yes	complemented
38	#15689195	C₂²	1	4	yes	complemented
39	#15689195	C₂²	1	4	yes	complemented
40	#15689195	C₂²	1	4	yes	complemented
41	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
42	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
43	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
44	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
45	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
46	#15689184	C₂²	1	2	yes	complemented
47	#15689184	C₂²	1	4	yes	complemented
48	#15689184	C₂²	1	2	yes	complemented
49	#15689180	C₂²	1	2	yes	complemented
50	#15689176	C₂²	1	2	yes	complemented
51	#15689176	C₂²	1	2	yes	complemented
52	#15689176	C₂²	1	2	yes	complemented
53	#15689150	C₂²	1	1	yes	characteristic, complemented
54	#15689150	C₂²	1	1	yes	characteristic, complemented
55	#15689147	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
57	#15689090	C₂²	1	1	yes	characteristic
58	#15689090	C₂²	1	1	yes	characteristic
59	#15689090	C₂²	1	2	yes	—
60	#15689090	C₂²	1	4	yes	complemented
61	#15689090	C₂²	1	4	yes	complemented
62	#15689090	C₂²	1	4	yes	complemented
63	#15689090	C₂²	1	4	yes	complemented
64	#15689090	C₂²	1	2	yes	complemented
65	#15689090	C₂²	1	2	yes	complemented
66	#15689087	C₂²	1	4	yes	complemented
67	#15689087	C₂²	1	4	yes	complemented
68	#15689087	C₂²	1	4	yes	complemented
69	#15689087	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
72	#15689079	C₂²	1	2	yes	complemented
73	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
75	C₂²×#41×C₄₇	C₂²	1	2	yes	—
76	C₄₇×#550	C₄	1	1	yes	characteristic
77	D₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
78	C₄₇×#548	C₄	1	2	yes	—
79	C₄₇×#547	C₄	1	2	yes	—
80	C₄₇×#547	C₄	1	1	yes	characteristic
81	C₄₇×#546	C₄	1	4	yes	—
82	C₄₇×#546	C₄	1	2	yes	—
83	D₄²×C₄₇	C₄	1	1	yes	characteristic
84	D₄²×C₄₇	C₄	1	2	yes	—
85	C₄₇×#532	C₂²	1	2	yes	—
86	C₄₇×#532	C₂²	1	1	yes	characteristic
87	C₄₇×#525	C₂²	1	4	yes	—
88	C₄₇×#525	C₂²	1	2	yes	—
89	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
91	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
92	#13094031	—	4	4	no	—
93	#13094031	—	4	4	no	—
94	C₂×#10625329	—	4	4	no	—
95	C₂×#10625329	—	4	4	no	—
96	C₂×#10625329	C₂³	1	1	yes	characteristic
97	C₂×#10625329	C₂³	1	1	yes	characteristic
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	2	yes	—
102	C₂×#10625329	C₂³	1	4	yes	—
103	C₂×#10625329	C₂³	1	4	yes	—
104	C₂×#10625329	C₂³	1	2	yes	—
105	C₂×#10625329	C₂³	1	2	yes	—
106	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
109	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
110	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
111	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
112	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
113	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
114	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
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	2	yes	—
120	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
121	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
122	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
123	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
124	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
125	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
126	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
127	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
128	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
129	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
130	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
131	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
132	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
133	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
134	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
135	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
136	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
137	#13093935	C₂³	1	2	yes	—
138	#13093935	C₂³	1	4	yes	—
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	1	yes	characteristic
143	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
144	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
145	C₂×#41×C₄₇	—	4	4	no	—
146	C₂×#41×C₄₇	—	4	4	no	—
147	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
148	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
149	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
150	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
151	C₂×#41×C₄₇	C₂³	1	2	yes	—
152	C₂×#41×C₄₇	C₂³	1	4	yes	—
153	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
154	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
155	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
156	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
157	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
158	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
159	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
160	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
161	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
162	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
163	#127×C₄₇	C₂×C₄	1	2	yes	—
164	#124×C₄₇	C₂×C₄	1	2	yes	—
165	#124×C₄₇	C₂×C₄	1	4	yes	—
166	#123×C₄₇	C₂×C₄	1	4	yes	—
167	#123×C₄₇	C₂×C₄	1	4	yes	—
168	#123×C₄₇	C₂×C₄	1	4	yes	—
169	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
170	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
171	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
172	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
173	#121×C₄₇	C₂×C₄	1	2	yes	—
174	#121×C₄₇	C₂×C₄	1	4	yes	—
175	#121×C₄₇	C₂×C₄	1	2	yes	—
176	#121×C₄₇	C₂×C₄	1	4	yes	—
177	#121×C₄₇	C₂×C₄	1	2	yes	—
178	#121×C₄₇	C₂×C₄	1	2	yes	—
179	#121×C₄₇	C₂×C₄	1	2	yes	—
180	#121×C₄₇	C₂×C₄	1	2	yes	—
181	#121×C₄₇	C₂×C₄	1	4	yes	—
182	#120×C₄₇	C₂×C₄	1	4	yes	—
183	#120×C₄₇	C₂×C₄	1	4	yes	—
184	#120×C₄₇	C₂×C₄	1	4	yes	—
185	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
186	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
192	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
193	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
194	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
195	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
196	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
197	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
198	C₄×D₄×C₄₇	C₂³	1	4	yes	—
199	C₄×D₄×C₄₇	C₂³	1	2	yes	—
200	C₄×D₄×C₄₇	C₂³	1	2	yes	—
201	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
202	C₄×D₄×C₄₇	C₂³	1	2	yes	—
203	C₄×D₄×C₄₇	C₂³	1	4	yes	—
204	#117×C₄₇	C₂³	1	1	yes	characteristic
205	#117×C₄₇	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
208	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
209	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
210	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
212	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
213	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
214	#41×C₄₇	—	2	2	no	—
215	#41×C₄₇	—	2	2	no	—
216	#41×C₄₇	—	2	4	no	—
217	#41×C₄₇	—	2	4	no	—
218	#41×C₄₇	—	4	4	no	—
219	#41×C₄₇	—	4	4	no	—
220	#41×C₄₇	—	4	8	no	—
221	#41×C₄₇	—	4	4	no	—
222	#41×C₄₇	—	4	4	no	—
223	C₂×Q₈×C₄₇	—	4	4	no	—
224	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
225	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
226	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₄₇	—	4	2	no	—
228	C₂×D₄×C₄₇	—	4	4	no	—
229	C₂×D₄×C₄₇	—	4	4	no	—
230	C₂×D₄×C₄₇	—	4	8	no	—
231	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
232	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
233	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
234	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
235	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
236	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
237	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
238	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
239	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
240	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
241	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
242	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
243	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
244	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
245	C₂²×C₄×C₄₇	—	2	4	no	—
246	C₂²×C₄×C₄₇	—	2	4	no	—
247	C₂²×C₄×C₄₇	—	4	4	no	—
248	C₂²×C₄×C₄₇	—	4	4	no	—
249	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
250	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
251	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
252	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
253	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
254	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
255	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
256	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
257	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
258	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
259	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
265	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
266	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
267	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
268	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
269	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
270	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
271	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
272	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
273	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
274	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
275	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
276	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
277	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
278	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
279	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
280	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
281	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
282	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
283	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
284	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
285	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
286	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
287	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
288	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
289	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
290	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
291	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
292	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
293	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
294	C₄²×C₄₇	C₂⁴	1	2	yes	—
295	#10625329	—	2	2	no	—
296	#10625329	—	2	4	no	—
297	#10625329	—	2	2	no	—
298	#10625329	—	4	2	no	—
299	#10625329	—	4	2	no	—
300	#10625329	—	4	2	no	—
301	#10625329	—	4	2	no	—
302	#10625329	—	4	4	no	—
303	#10625329	—	4	4	no	—
304	#10625329	—	4	4	no	—
305	C₂×C₄₇⋊C₈	—	2	2	no	—
306	C₂×C₄₇⋊C₈	—	2	4	no	—
307	C₂×C₄₇⋊C₈	—	2	2	no	—
308	C₂×C₄₇⋊C₈	—	4	4	no	—
309	C₂×C₄₇⋊C₈	—	4	4	no	—
310	C₂×C₄₇⋊C₈	—	4	4	no	—
311	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
312	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
313	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
314	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
315	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
316	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
317	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
318	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
319	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
320	C₂³×C₄₇	—	2	4	no	—
321	C₂³×C₄₇	—	4	4	no	—
322	C₂³×C₄₇	—	4	2	no	—
323	C₂³×C₄₇	—	4	4	no	—
324	C₂³×C₄₇	—	4	2	no	—
325	C₂³×C₄₇	—	4	4	no	—
326	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
327	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
328	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
329	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
330	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
331	Q₈×C₄₇	—	2	2	no	—
332	Q₈×C₄₇	—	2	4	no	—
333	Q₈×C₄₇	—	4	4	no	—
334	D₄×C₄₇	—	2	4	no	—
335	D₄×C₄₇	—	2	8	no	—
336	D₄×C₄₇	—	2	2	no	—
337	D₄×C₄₇	—	2	4	no	—
338	D₄×C₄₇	—	2	2	no	—
339	D₄×C₄₇	—	2	2	no	—
340	D₄×C₄₇	—	2	4	no	—
341	D₄×C₄₇	—	4	2	no	—
342	D₄×C₄₇	—	4	4	no	—
343	D₄×C₄₇	—	4	4	no	—
344	D₄×C₄₇	—	4	4	no	—
345	D₄×C₄₇	—	4	4	no	—
346	D₄×C₄₇	—	4	2	no	—
347	D₄×C₄₇	—	4	4	no	—
348	C₂×C₄×C₄₇	—	2	4	no	—
349	C₂×C₄×C₄₇	—	2	4	no	—
350	C₂×C₄×C₄₇	—	2	4	no	—
351	C₂×C₄×C₄₇	—	2	2	no	—
352	C₂×C₄×C₄₇	—	2	4	no	—
353	C₂×C₄×C₄₇	—	2	2	no	—
354	C₂×C₄×C₄₇	—	2	4	no	—
355	C₂×C₄×C₄₇	—	2	4	no	—
356	C₂×C₄×C₄₇	—	2	2	no	—
357	C₂×C₄×C₄₇	—	2	2	no	—
358	C₂×C₄×C₄₇	—	2	2	no	—
359	C₂×C₄×C₄₇	—	2	2	no	—
360	C₂×C₄×C₄₇	—	2	2	no	—
361	C₂×C₄×C₄₇	—	4	4	no	—
362	C₂×C₄×C₄₇	—	4	4	no	—
363	C₂×C₄×C₄₇	—	4	4	no	—
364	C₂×C₄×C₄₇	—	4	1	no	—
365	C₂×C₄×C₄₇	—	4	2	no	—
366	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
367	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
368	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
369	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
370	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
371	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
372	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
373	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
374	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
375	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
376	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
377	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
378	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
380	C₄₇⋊C₈	—	2	1	no	—
381	C₄₇⋊C₈	—	2	2	no	—
382	C₄₇⋊C₈	—	2	1	no	—
383	C₄₇⋊C₈	—	2	1	no	—
384	C₄₇⋊C₈	—	2	2	no	—
385	C₄₇⋊C₈	—	2	1	no	—
386	C₄₇⋊C₈	—	2	2	no	—
387	C₄₇⋊C₈	—	2	4	no	—
388	C₄₇⋊C₈	—	2	2	no	—
389	#60241	—	47	1	no	maximal, Sylow
390	C₂²×C₄₇	—	2	1	no	—
391	C₂²×C₄₇	—	2	1	no	—
392	C₂²×C₄₇	—	2	2	no	—
393	C₂²×C₄₇	—	2	2	no	—
394	C₂²×C₄₇	—	2	2	no	—
395	C₂²×C₄₇	—	2	4	no	—
396	C₂²×C₄₇	—	2	2	no	—
397	C₂²×C₄₇	—	2	2	no	—
398	C₂²×C₄₇	—	2	2	no	—
399	C₂²×C₄₇	—	2	4	no	—
400	C₂²×C₄₇	—	2	2	no	—
401	C₂²×C₄₇	—	2	2	no	—
402	C₂²×C₄₇	—	2	4	no	—
403	C₂²×C₄₇	—	2	2	no	—
404	C₂²×C₄₇	—	8	4	no	—
405	C₂²×C₄₇	—	8	8	no	—
406	C₂²×C₄₇	#518	1	2	yes	—
407	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
408	C₄×C₄₇	—	2	2	no	—
409	C₄×C₄₇	—	2	2	no	—
410	C₄×C₄₇	—	2	2	no	—
411	C₄×C₄₇	—	2	4	no	—
412	C₄×C₄₇	—	2	1	no	—
413	C₄×C₄₇	—	2	2	no	—
414	C₄×C₄₇	—	2	1	no	—
415	C₄×C₄₇	—	2	1	no	—
416	C₄×C₄₇	—	2	2	no	—
417	C₄×C₄₇	#518	1	2	yes	—
418	C₄×C₄₇	#568	1	2	yes	—
419	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	D₄×#41	D₄₇	1	1	yes	characteristic
422	#2981	—	47	2	no	—
423	#2979	—	47	2	no	—
424	#2978	—	47	4	no	—
425	#2976	—	47	4	no	—
426	#2975	—	47	2	no	—
427	#2974	—	47	2	no	—
428	#2935	—	47	1	no	—
429	D₄×M₁₆	—	47	1	no	—
430	#2933	—	47	2	no	—
431	#2931	—	47	1	no	—
432	#2930	—	47	2	no	—
433	C₂×#436	—	47	1	no	—
434	#2925	—	47	1	no	—
435	#2922	—	47	1	no	—
436	#2880	—	47	2	no	—
437	#2879	—	47	2	no	—
438	C₂×C₄₇	—	2	2	no	—
439	C₂×C₄₇	—	4	2	no	—
440	C₂×C₄₇	—	4	4	no	—
441	C₂×C₄₇	—	4	2	no	—
442	C₂×C₄₇	—	4	2	no	—
443	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
444	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
445	C₂×C₄₇	#3573	1	1	yes	characteristic
446	C₂²×#41	C₂×D₄₇	1	2	yes	—
447	C₂×#131	—	47	2	no	—
448	C₂×#131	—	47	2	no	—
449	C₂²×M₁₆	—	47	2	no	—
450	C₂²×M₁₆	—	47	2	no	—
451	#550	Dic₄₇	1	1	yes	characteristic
452	D₄×Q₈	Dic₄₇	1	1	yes	characteristic
453	#548	Dic₄₇	1	2	yes	—
454	#547	Dic₄₇	1	2	yes	—
455	#547	Dic₄₇	1	1	yes	characteristic
456	#546	Dic₄₇	1	4	yes	—
457	#546	Dic₄₇	1	2	yes	—
458	D₄²	Dic₄₇	1	1	yes	characteristic
459	D₄²	Dic₄₇	1	2	yes	—
460	#532	C₂×D₄₇	1	1	yes	characteristic
461	#532	C₂×D₄₇	1	2	yes	—
462	#525	C₂×D₄₇	1	2	yes	—
463	#525	C₂×D₄₇	1	4	yes	—
464	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
467	#436	—	47	1	no	—
468	#436	—	47	1	no	—
469	#436	—	47	2	no	—
470	#436	—	47	2	no	—
471	#436	—	47	1	no	—
472	#436	—	47	1	no	—
473	#436	—	47	4	no	—
474	#436	—	47	4	no	—
475	#436	—	47	2	no	—
476	#436	—	47	2	no	—
477	#436	—	47	4	no	—
478	#436	—	47	2	no	—
479	#436	—	47	2	no	—
480	#435	—	47	4	no	—
481	#435	—	47	4	no	—
482	#435	—	47	4	no	—
483	#435	—	47	4	no	—
484	#435	—	47	4	no	—
485	#435	—	47	4	no	—
486	C₈×D₄	—	47	2	no	—
487	C₈×D₄	—	47	2	no	—
488	C₈×D₄	—	47	4	no	—
489	C₈×D₄	—	47	2	no	—
490	C₈×D₄	—	47	2	no	—
491	#433	—	47	2	no	—
492	#433	—	47	2	no	—
493	#433	—	47	4	no	—
494	#432	—	47	2	no	—
495	#431	—	47	2	no	—
496	#431	—	47	2	no	—
497	#431	—	47	2	no	—
498	#424	—	47	1	no	—
499	#424	—	47	1	no	—
500	#423	—	47	1	no	—
501	C₂×C₄⋊C₈	—	47	1	no	—
502	#408	—	47	1	no	—
503	#408	—	47	2	no	—
504	#408	—	47	2	no	—
505	#408	—	47	2	no	—
506	#408	—	47	4	no	—
507	#408	—	47	4	no	—
508	#408	—	47	1	no	—
509	#408	—	47	4	no	—
510	#408	—	47	4	no	—
511	#407	—	47	4	no	—
512	#407	—	47	4	no	—
513	#407	—	47	2	no	—
514	#407	—	47	4	no	—
515	C₂×C₂²⋊C₈	—	47	2	no	—
516	C₂×C₂²⋊C₈	—	47	4	no	—
517	#405	—	47	2	no	—
518	C₄×M₁₆	—	47	1	no	—
519	C₂×C₄×C₈	—	47	1	no	—
520	C₄₇	#60241	1	1	yes	characteristic, complemented, Sylow
521	C₂×#41	—	4	4	no	—
522	C₂×#41	—	4	4	no	—
523	C₂×#41	C₂×Dic₄₇	1	4	yes	—
524	C₂×#41	C₂×Dic₄₇	1	2	yes	—
525	C₂×#41	C₂×Dic₄₇	1	2	yes	—
526	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
527	C₂×#41	C₂²×D₄₇	1	2	yes	—
528	C₂×#41	C₂²×D₄₇	1	4	yes	—
529	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
530	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
531	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
532	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
533	C₂²×D₄	C₂×Dic₄₇	1	4	yes	—
534	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
535	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
536	#131	—	188	4	no	—
537	#131	—	188	4	no	—
538	C₂×M₁₆	—	47	1	no	—
539	C₂×M₁₆	—	47	2	no	—
540	C₂×M₁₆	—	47	1	no	—
541	C₂×M₁₆	—	47	2	no	—
542	C₂×M₁₆	—	47	4	no	—
543	C₂×M₁₆	—	47	2	no	—
544	C₂×M₁₆	—	47	2	no	—
545	C₂×M₁₆	—	47	2	no	—
546	C₂×M₁₆	—	47	4	no	—
547	C₂×M₁₆	—	47	4	no	—
548	C₂×M₁₆	—	188	4	no	—
549	C₂×M₁₆	—	188	4	no	—
550	C₂²×C₈	—	47	1	no	—
551	C₂²×C₈	—	47	2	no	—
552	C₂²×C₈	—	47	1	no	—
553	C₂²×C₈	—	47	4	no	—
554	C₂²×C₈	—	47	4	no	—
555	C₂²×C₈	—	47	4	no	—
556	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
557	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
558	#127	C₂×Dic₄₇	1	1	yes	characteristic
559	#127	C₂×Dic₄₇	1	2	yes	—
560	#124	C₂×Dic₄₇	1	2	yes	—
561	#124	C₂×Dic₄₇	1	4	yes	—
562	#123	C₂×Dic₄₇	1	4	yes	—
563	#123	C₂×Dic₄₇	1	4	yes	—
564	#123	C₂×Dic₄₇	1	4	yes	—
565	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
566	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
567	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
568	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
569	#121	C₂×Dic₄₇	1	2	yes	—
570	#121	C₂×Dic₄₇	1	4	yes	—
571	#121	C₂×Dic₄₇	1	2	yes	—
572	#121	C₂×Dic₄₇	1	4	yes	—
573	#121	C₂×Dic₄₇	1	2	yes	—
574	#121	C₂×Dic₄₇	1	2	yes	—
575	#121	C₂×Dic₄₇	1	2	yes	—
576	#121	C₂×Dic₄₇	1	2	yes	—
577	#121	C₂×Dic₄₇	1	4	yes	—
578	#120	C₂×Dic₄₇	1	4	yes	—
579	#120	C₂×Dic₄₇	1	4	yes	—
580	#120	C₂×Dic₄₇	1	4	yes	—
581	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
582	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
583	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
584	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
585	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
586	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
587	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
588	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
589	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
590	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
591	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
592	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
593	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
594	C₄×D₄	C₂²×D₄₇	1	2	yes	—
595	C₄×D₄	C₂²×D₄₇	1	4	yes	—
596	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
597	C₄×D₄	C₂²×D₄₇	1	2	yes	—
598	C₄×D₄	C₂²×D₄₇	1	4	yes	—
599	C₄×D₄	C₂²×D₄₇	1	2	yes	—
600	#117	C₂²×D₄₇	1	1	yes	characteristic
601	#117	C₂²×D₄₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
606	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
607	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
608	C₄⋊C₈	—	47	1	no	—
609	C₄⋊C₈	—	47	1	no	—
610	C₄⋊C₈	—	47	2	no	—
611	C₄⋊C₈	—	47	2	no	—
612	C₄⋊C₈	—	47	2	no	—
613	C₄⋊C₈	—	47	2	no	—
614	C₄⋊C₈	—	47	2	no	—
615	C₄⋊C₈	—	47	2	no	—
616	C₄⋊C₈	—	47	2	no	—
617	C₂²⋊C₈	—	47	2	no	—
618	C₂²⋊C₈	—	47	2	no	—
619	C₂²⋊C₈	—	47	4	no	—
620	C₂²⋊C₈	—	47	2	no	—
621	C₂²⋊C₈	—	47	4	no	—
622	C₂²⋊C₈	—	47	2	no	—
623	C₂²⋊C₈	—	47	2	no	—
624	C₂²⋊C₈	—	47	2	no	—
625	C₂²⋊C₈	—	47	2	no	—
626	C₂²⋊C₈	—	47	4	no	—
627	C₂²⋊C₈	—	47	2	no	—
628	C₂²⋊C₈	—	47	4	no	—
629	C₂²⋊C₈	—	47	4	no	—
630	C₂²⋊C₈	—	47	4	no	—
631	C₂²⋊C₈	—	47	4	no	—
632	C₂²⋊C₈	—	47	4	no	—
633	#97	—	47	2	no	—
634	#97	—	47	4	no	—
635	C₄×C₈	—	47	1	no	—
636	C₄×C₈	—	47	1	no	—
637	C₄×C₈	—	47	1	no	—
638	C₄×C₈	—	47	1	no	—
639	C₄×C₈	—	47	2	no	—
640	C₄×C₈	—	47	4	no	—
641	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
642	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	2	2	no	—
646	#41	—	2	2	no	—
647	#41	—	4	4	no	—
648	#41	—	4	4	no	—
649	#41	—	4	8	no	—
650	#41	—	4	4	no	—
651	#41	—	4	4	no	—
652	C₂×Q₈	—	4	4	no	—
653	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
654	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
655	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	4	4	no	—
659	C₂×D₄	—	4	8	no	—
660	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
661	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
662	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
663	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
664	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
665	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
666	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
667	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
668	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
669	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
670	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
671	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
672	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
673	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	4	4	no	—
677	C₂²×C₄	—	4	4	no	—
678	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
679	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
680	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
681	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
682	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
683	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
684	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
685	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
686	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
687	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
688	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
689	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
690	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
691	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
692	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
693	M₁₆	—	94	2	no	—
694	M₁₆	—	94	4	no	—
695	M₁₆	—	94	2	no	—
696	M₁₆	—	188	2	no	—
697	M₁₆	—	188	2	no	—
698	M₁₆	—	188	2	no	—
699	M₁₆	—	188	2	no	—
700	M₁₆	—	188	4	no	—
701	M₁₆	—	188	4	no	—
702	M₁₆	—	188	4	no	—
703	C₂×C₈	—	47	1	no	—
704	C₂×C₈	—	47	1	no	—
705	C₂×C₈	—	47	1	no	—
706	C₂×C₈	—	47	1	no	—
707	C₂×C₈	—	47	2	no	—
708	C₂×C₈	—	47	2	no	—
709	C₂×C₈	—	47	2	no	—
710	C₂×C₈	—	47	4	no	—
711	C₂×C₈	—	47	2	no	—
712	C₂×C₈	—	94	2	no	—
713	C₂×C₈	—	94	4	no	—
714	C₂×C₈	—	94	2	no	—
715	C₂×C₈	—	188	4	no	—
716	C₂×C₈	—	188	4	no	—
717	C₂×C₈	—	188	4	no	—
718	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
720	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
721	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
722	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
723	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
724	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
725	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
728	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
729	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
730	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
731	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
732	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
733	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
734	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
735	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
736	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
737	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
738	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
739	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
740	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
741	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
742	C₄²	C₂²×Dic₄₇	1	2	yes	—
743	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
744	C₄²	C₂²×Dic₄₇	1	2	yes	—
745	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
746	C₄²	C₂³×D₄₇	1	1	yes	characteristic
747	C₄²	C₂³×D₄₇	1	1	yes	characteristic
748	C₄²	C₂³×D₄₇	1	2	yes	—
749	C₂³	—	2	4	no	—
750	C₂³	—	4	4	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	4	no	—
753	C₂³	—	4	2	no	—
754	C₂³	—	4	4	no	—
755	C₂³	C₂³×Dic₄₇	1	2	yes	—
756	C₂³	C₂³×Dic₄₇	1	2	yes	—
757	C₂³	C₂³×Dic₄₇	1	4	yes	—
758	C₂³	C₂³×Dic₄₇	1	2	yes	—
759	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
760	Q₈	—	2	2	no	—
761	Q₈	—	2	4	no	—
762	Q₈	—	4	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	8	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	4	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	4	no	—
770	D₄	—	4	2	no	—
771	D₄	—	4	4	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	4	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
796	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
797	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
798	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
799	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
800	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
801	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
802	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
803	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
804	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
805	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
806	C₂×C₄	#13094069	1	2	yes	—
807	C₂×C₄	#13094069	1	2	yes	—
808	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
809	C₈	—	94	1	no	—
810	C₈	—	94	2	no	—
811	C₈	—	94	1	no	—
812	C₈	—	94	1	no	—
813	C₈	—	94	2	no	—
814	C₈	—	94	1	no	—
815	C₈	—	94	2	no	—
816	C₈	—	94	4	no	—
817	C₈	—	94	2	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	8	4	no	—
833	C₂²	—	8	8	no	—
834	C₂²	#15689598	1	2	yes	—
835	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
836	C₄	—	2	1	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	4	no	—
845	C₄	#15689598	1	2	yes	—
846	C₄	#15689890	1	2	yes	—
847	C₄	C₂×#13094069	1	1	yes	characteristic
848	C₄	C₂×#13094069	1	1	yes	characteristic
849	C₂	—	2	2	no	—
850	C₂	—	4	2	no	—
851	C₂	—	4	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	4	no	—
854	C₂	C₂×#15689598	1	1	yes	characteristic
855	C₂	C₂×#15689890	1	1	yes	characteristic
856	C₂	#20258100	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	D₄×#41×C₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	D₄×#41	D₄₇
hypocenter	C₄₇	#60241
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ D₄×#41

Complements

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

N	H ≅ G/N	type
1. #20252464	C₂	semidirect
2. #20252455	C₂	semidirect
3. #20252450	C₂	semidirect
4. #20252436	C₂	semidirect
5. #20252429	C₂	semidirect
6. #20252423	C₂	semidirect
7. #20252132	C₂	semidirect
8. D₄×#10625329	C₂	semidirect
9. #20252115	C₂	semidirect
10. #20252100	C₂	semidirect
11. #20252092	C₂	semidirect
12. C₂×#15689201	C₂	semidirect
13. #20252054	C₂	semidirect
14. #20252032	C₂	semidirect
15. #20251837	C₂	semidirect
16. #20251833	C₂	semidirect
18. C₂×#13094031	C₂²	semidirect
19. C₂×#13094031	C₂²	semidirect
20. C₂²×#10625329	C₂²	semidirect
21. C₂²×#10625329	C₂²	semidirect
25. #15689201	C₂²	semidirect
26. #15689201	C₂²	semidirect
27. #15689201	C₂²	semidirect
28. #15689201	C₂²	semidirect
29. #15689201	C₂²	semidirect
30. #15689201	C₂²	semidirect
31. #15689201	C₂²	semidirect
32. #15689201	C₂²	semidirect
33. #15689201	C₂²	semidirect
34. #15689201	C₂²	semidirect
35. #15689195	C₂²	semidirect
36. #15689195	C₂²	semidirect
37. #15689195	C₂²	semidirect
38. #15689195	C₂²	semidirect
39. #15689195	C₂²	semidirect
40. #15689195	C₂²	semidirect
41. D₄×C₄₇⋊C₈	C₂²	semidirect
42. D₄×C₄₇⋊C₈	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. #15689176	C₂²	semidirect
51. #15689176	C₂²	semidirect
52. #15689176	C₂²	semidirect
53. #15689150	C₂²	semidirect
54. #15689150	C₂²	semidirect
55. #15689147	C₂²	semidirect
56. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
60. #15689090	C₂²	semidirect
61. #15689090	C₂²	semidirect
62. #15689090	C₂²	semidirect
63. #15689090	C₂²	semidirect
64. #15689090	C₂²	semidirect
65. #15689090	C₂²	semidirect
66. #15689087	C₂²	semidirect
67. #15689087	C₂²	semidirect
68. #15689087	C₂²	semidirect
69. #15689087	C₂²	semidirect
70. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
71. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
72. #15689079	C₂²	semidirect
73. C₄×#10625329	C₂²	semidirect
74. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
520. C₄₇	#60241	semidirect

Maximal subgroups

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

subgroup	index
#20252464	2
#20252455	2
#20252450	2
#20252436	2
#20252429	2
#20252423	2
#20252132	2
D₄×#10625329	2
#20252115	2
#20252100	2
#20252092	2
C₂×#15689201	2
#20252054	2
#20252032	2
#20251837	2
#20251833	2
D₄×#41×C₄₇	2
#60241	47