Subgroups — C₂×C₄₇×#3297 #26100813

Order 12032.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3297	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₇×#416	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#102×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
24	C₄₇×#553	—	2	4	no	—
25	C₄₇×#553	C₂²	1	8	yes	complemented
26	C₄₇×#546	—	2	4	no	—
27	C₄₇×#546	C₂²	1	8	yes	complemented
28	C₂×#126×C₄₇	—	2	1	no	—
29	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#123×C₄₇	—	2	1	no	—
32	C₂×#123×C₄₇	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#121×C₄₇	—	2	1	no	—
35	C₂×#121×C₄₇	—	2	1	no	—
36	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#120×C₄₇	—	2	1	no	—
40	C₂×C₄×D₄×C₄₇	—	2	1	no	—
41	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
47	C₄₇×#488	C₂²	1	8	yes	complemented
48	C₄₇×#484	C₂²	1	8	yes	complemented
49	C₄₇×#482	C₂²	1	8	yes	complemented
50	C₄₇×#478	C₂²	1	8	yes	complemented
51	C₄₇×#466	C₂²	1	8	yes	complemented
52	C₄₇×#465	C₂²	1	8	yes	complemented
53	C₄₇×#463	C₂²	1	8	yes	complemented
54	C₄₇×#449	C₂²	1	8	yes	complemented
55	C₄₇×#447	C₂²	1	8	yes	complemented
56	C₄×D₈×C₄₇	C₂²	1	8	yes	complemented
57	C₈×D₄×C₄₇	C₂²	1	8	yes	complemented
58	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
62	C₄₇×#416	C₂²	1	8	yes	complemented
63	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic, complemented
65	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic, complemented
66	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
67	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
68	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
69	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
70	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
71	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
72	C₂×#102×C₄₇	C₂²	1	8	yes	complemented
73	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₄₇	—	2	1	no	—
78	C₂×#41×C₄₇	—	2	2	no	—
79	C₂×#41×C₄₇	—	2	4	no	—
80	C₂×#41×C₄₇	—	4	2	no	—
81	C₂×#41×C₄₇	C₂³	1	4	yes	—
82	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₄₇	—	2	4	no	—
84	C₂²×D₄×C₄₇	—	2	1	no	—
85	C₂²×D₄×C₄₇	—	2	1	no	—
86	C₂²×D₄×C₄₇	—	2	1	no	—
87	C₂²×D₄×C₄₇	—	2	1	no	—
88	C₂²×D₄×C₄₇	—	2	1	no	—
89	C₂²×D₄×C₄₇	—	2	2	no	—
90	C₂²×D₄×C₄₇	—	4	2	no	—
91	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
95	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₄₇	—	2	1	no	—
97	C₂³×C₄×C₄₇	—	2	1	no	—
98	C₂³×C₄×C₄₇	—	2	1	no	—
99	C₂³×C₄×C₄₇	—	2	1	no	—
100	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×SD₁₆×C₄₇	—	4	2	no	—
103	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	complemented
104	C₂×D₈×C₄₇	—	2	4	no	—
105	C₂×D₈×C₄₇	—	4	2	no	—
106	C₂×D₈×C₄₇	C₂³	1	4	yes	—
107	C₂×D₈×C₄₇	C₂³	1	4	yes	—
108	C₂²×C₈×C₄₇	—	4	2	no	—
109	C₂²×C₈×C₄₇	—	4	2	no	—
110	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
115	C₂²×C₈×C₄₇	C₂³	1	4	yes	complemented
116	#126×C₄₇	—	2	8	no	—
117	#125×C₄₇	—	2	2	no	—
118	#125×C₄₇	C₂³	1	4	yes	complemented
119	#124×C₄₇	—	2	2	no	—
120	#124×C₄₇	C₂³	1	4	yes	—
121	#123×C₄₇	—	2	8	no	—
122	#123×C₄₇	—	2	8	no	—
123	C₂²⋊Q₈×C₄₇	—	2	2	no	—
124	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
125	#121×C₄₇	—	2	8	no	—
126	#121×C₄₇	—	2	2	no	—
127	#121×C₄₇	—	2	2	no	—
128	#121×C₄₇	—	2	2	no	—
129	#121×C₄₇	—	2	8	no	—
130	#121×C₄₇	C₂³	1	4	yes	—
131	#121×C₄₇	C₂³	1	4	yes	—
132	#121×C₄₇	C₂³	1	4	yes	complemented
133	#120×C₄₇	—	2	8	no	—
134	C₄×D₄×C₄₇	—	2	8	no	—
135	C₄×D₄×C₄₇	—	2	2	no	—
136	C₄×D₄×C₄₇	—	2	2	no	—
137	C₄×D₄×C₄₇	D₄	1	4	yes	—
138	C₄×D₄×C₄₇	C₂³	1	4	yes	—
139	C₄×D₄×C₄₇	C₂³	1	4	yes	—
140	C₄×D₄×C₄₇	C₂³	1	4	yes	complemented
141	#117×C₄₇	—	2	2	no	—
142	#117×C₄₇	C₂³	1	4	yes	complemented
143	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
144	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
146	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
147	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
148	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
164	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₄₇	—	2	1	no	—
167	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
168	#107×C₄₇	C₂³	1	4	yes	complemented
169	#107×C₄₇	C₂³	1	4	yes	complemented
170	#106×C₄₇	C₂³	1	4	yes	complemented
171	C₄⋊C₈×C₄₇	C₂³	1	4	yes	complemented
172	#103×C₄₇	C₂³	1	4	yes	complemented
173	#103×C₄₇	C₂³	1	4	yes	complemented
174	#103×C₄₇	C₂³	1	4	yes	complemented
175	#102×C₄₇	C₂³	1	4	yes	—
176	#102×C₄₇	C₂³	1	4	yes	—
177	#102×C₄₇	C₂³	1	4	yes	—
178	#102×C₄₇	C₂³	1	4	yes	—
179	#102×C₄₇	C₂³	1	4	yes	—
180	#102×C₄₇	C₂³	1	4	yes	—
181	#102×C₄₇	C₂³	1	4	yes	complemented
182	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
183	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	complemented
184	C₄×C₈×C₄₇	C₂³	1	4	yes	complemented
185	C₂⁴×C₄₇	—	2	1	no	—
186	C₂⁴×C₄₇	—	2	1	no	—
187	C₂⁴×C₄₇	—	2	1	no	—
188	C₂⁴×C₄₇	—	2	4	no	—
189	C₂⁴×C₄₇	—	4	4	no	—
190	C₂⁴×C₄₇	—	4	4	no	—
191	C₂⁴×C₄₇	—	8	2	no	—
192	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
194	#41×C₄₇	—	2	8	no	—
195	#41×C₄₇	—	4	4	no	—
196	#41×C₄₇	—	4	8	no	—
197	C₂×Q₈×C₄₇	—	2	1	no	—
198	C₂×Q₈×C₄₇	—	2	2	no	—
199	C₂×Q₈×C₄₇	—	2	2	no	—
200	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
201	C₂×D₄×C₄₇	—	2	4	no	—
202	C₂×D₄×C₄₇	—	2	8	no	—
203	C₂×D₄×C₄₇	—	2	4	no	—
204	C₂×D₄×C₄₇	—	2	4	no	—
205	C₂×D₄×C₄₇	—	2	4	no	—
206	C₂×D₄×C₄₇	—	2	4	no	—
207	C₂×D₄×C₄₇	—	2	1	no	—
208	C₂×D₄×C₄₇	—	2	1	no	—
209	C₂×D₄×C₄₇	—	2	4	no	—
210	C₂×D₄×C₄₇	—	2	1	no	—
211	C₂×D₄×C₄₇	—	2	2	no	—
212	C₂×D₄×C₄₇	—	2	2	no	—
213	C₂×D₄×C₄₇	—	2	2	no	—
214	C₂×D₄×C₄₇	—	2	2	no	—
215	C₂×D₄×C₄₇	—	2	2	no	—
216	C₂×D₄×C₄₇	—	4	4	no	—
217	C₂×D₄×C₄₇	—	4	8	no	—
218	C₂×D₄×C₄₇	—	4	4	no	—
219	C₂×D₄×C₄₇	—	4	4	no	—
220	C₂×D₄×C₄₇	—	4	4	no	—
221	C₂×D₄×C₄₇	—	8	2	no	—
222	C₂×D₄×C₄₇	—	8	2	no	—
223	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
224	C₂×D₄×C₄₇	#41	1	4	yes	—
225	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
226	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
227	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₄₇	—	2	2	no	—
229	C₂²×C₄×C₄₇	—	2	2	no	—
230	C₂²×C₄×C₄₇	—	2	2	no	—
231	C₂²×C₄×C₄₇	—	2	2	no	—
232	C₂²×C₄×C₄₇	—	2	1	no	—
233	C₂²×C₄×C₄₇	—	2	1	no	—
234	C₂²×C₄×C₄₇	—	2	1	no	—
235	C₂²×C₄×C₄₇	—	2	1	no	—
236	C₂²×C₄×C₄₇	—	2	1	no	—
237	C₂²×C₄×C₄₇	—	2	4	no	—
238	C₂²×C₄×C₄₇	—	2	4	no	—
239	C₂²×C₄×C₄₇	—	2	4	no	—
240	C₂²×C₄×C₄₇	—	2	4	no	—
241	C₂²×C₄×C₄₇	—	4	4	no	—
242	C₂²×C₄×C₄₇	—	8	2	no	—
243	C₂²×C₄×C₄₇	—	8	2	no	—
244	C₂²×C₄×C₄₇	—	8	2	no	—
245	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₄₇	—	4	4	no	—
255	D₈×C₄₇	—	2	8	no	—
256	D₈×C₄₇	—	4	4	no	—
257	C₂×C₈×C₄₇	—	2	2	no	—
258	C₂×C₈×C₄₇	—	2	2	no	—
259	C₂×C₈×C₄₇	—	2	2	no	—
260	C₂×C₈×C₄₇	—	2	2	no	—
261	C₂×C₈×C₄₇	—	4	4	no	—
262	C₂×C₈×C₄₇	—	4	4	no	—
263	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
265	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
266	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₄₇	—	2	1	no	—
268	C₄⋊C₄×C₄₇	—	2	1	no	—
269	C₄⋊C₄×C₄₇	—	2	4	no	—
270	C₄⋊C₄×C₄₇	—	2	4	no	—
271	C₄⋊C₄×C₄₇	—	2	4	no	—
272	C₄⋊C₄×C₄₇	—	2	4	no	—
273	C₄⋊C₄×C₄₇	—	2	1	no	—
274	C₄⋊C₄×C₄₇	—	2	1	no	—
275	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
280	C₂²⋊C₄×C₄₇	—	2	4	no	—
281	C₂²⋊C₄×C₄₇	—	2	4	no	—
282	C₂²⋊C₄×C₄₇	—	2	4	no	—
283	C₂²⋊C₄×C₄₇	—	2	4	no	—
284	C₂²⋊C₄×C₄₇	—	2	4	no	—
285	C₂²⋊C₄×C₄₇	—	2	4	no	—
286	C₂²⋊C₄×C₄₇	—	2	4	no	—
287	C₂²⋊C₄×C₄₇	—	2	4	no	—
288	C₂²⋊C₄×C₄₇	—	2	4	no	—
289	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
291	C₄²×C₄₇	—	2	4	no	—
292	C₄²×C₄₇	C₂×D₄	1	2	yes	—
293	C₄²×C₄₇	C₂⁴	1	2	yes	—
294	C₂³×C₄₇	—	2	2	no	—
295	C₂³×C₄₇	—	2	2	no	—
296	C₂³×C₄₇	—	2	2	no	—
297	C₂³×C₄₇	—	2	4	no	—
298	C₂³×C₄₇	—	2	2	no	—
299	C₂³×C₄₇	—	2	2	no	—
300	C₂³×C₄₇	—	2	2	no	—
301	C₂³×C₄₇	—	2	2	no	—
302	C₂³×C₄₇	—	2	2	no	—
303	C₂³×C₄₇	—	4	8	no	—
304	C₂³×C₄₇	—	4	2	no	—
305	C₂³×C₄₇	—	4	2	no	—
306	C₂³×C₄₇	—	4	2	no	—
307	C₂³×C₄₇	—	4	2	no	—
308	C₂³×C₄₇	—	4	2	no	—
309	C₂³×C₄₇	—	4	8	no	—
310	C₂³×C₄₇	—	4	2	no	—
311	C₂³×C₄₇	—	4	2	no	—
312	C₂³×C₄₇	—	4	2	no	—
313	C₂³×C₄₇	—	8	4	no	—
314	C₂³×C₄₇	—	8	16	no	—
315	C₂³×C₄₇	#135	1	4	yes	—
316	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
317	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
318	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₄₇	—	2	2	no	—
320	Q₈×C₄₇	—	2	2	no	—
321	Q₈×C₄₇	—	4	2	no	—
322	D₄×C₄₇	—	2	8	no	—
323	D₄×C₄₇	—	2	4	no	—
324	D₄×C₄₇	—	2	2	no	—
325	D₄×C₄₇	—	2	2	no	—
326	D₄×C₄₇	—	2	2	no	—
327	D₄×C₄₇	—	2	2	no	—
328	D₄×C₄₇	—	2	2	no	—
329	D₄×C₄₇	—	4	8	no	—
330	D₄×C₄₇	—	4	8	no	—
331	D₄×C₄₇	—	4	8	no	—
332	D₄×C₄₇	—	4	2	no	—
333	D₄×C₄₇	—	4	2	no	—
334	D₄×C₄₇	—	8	4	no	—
335	D₄×C₄₇	—	8	4	no	—
336	D₄×C₄₇	C₂×#41	1	4	yes	—
337	C₂×C₄×C₄₇	—	2	2	no	—
338	C₂×C₄×C₄₇	—	2	2	no	—
339	C₂×C₄×C₄₇	—	2	2	no	—
340	C₂×C₄×C₄₇	—	2	2	no	—
341	C₂×C₄×C₄₇	—	2	4	no	—
342	C₂×C₄×C₄₇	—	2	4	no	—
343	C₂×C₄×C₄₇	—	2	2	no	—
344	C₂×C₄×C₄₇	—	2	2	no	—
345	C₂×C₄×C₄₇	—	2	2	no	—
346	C₂×C₄×C₄₇	—	2	2	no	—
347	C₂×C₄×C₄₇	—	2	2	no	—
348	C₂×C₄×C₄₇	—	2	2	no	—
349	C₂×C₄×C₄₇	—	2	2	no	—
350	C₂×C₄×C₄₇	—	2	2	no	—
351	C₂×C₄×C₄₇	—	2	2	no	—
352	C₂×C₄×C₄₇	—	4	8	no	—
353	C₂×C₄×C₄₇	—	4	2	no	—
354	C₂×C₄×C₄₇	—	4	2	no	—
355	C₂×C₄×C₄₇	—	4	2	no	—
356	C₂×C₄×C₄₇	—	4	2	no	—
357	C₂×C₄×C₄₇	—	4	2	no	—
358	C₂×C₄×C₄₇	—	8	4	no	—
359	C₂×C₄×C₄₇	—	8	4	no	—
360	C₂×C₄×C₄₇	—	8	4	no	—
361	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
367	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
368	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
369	C₈×C₄₇	—	2	2	no	—
370	C₈×C₄₇	—	2	2	no	—
371	C₈×C₄₇	—	2	2	no	—
372	C₈×C₄₇	—	2	2	no	—
373	C₂×#3297	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
374	C₂²×C₄₇	—	2	2	no	—
375	C₂²×C₄₇	—	2	8	no	—
376	C₂²×C₄₇	—	2	2	no	—
377	C₂²×C₄₇	—	2	2	no	—
378	C₂²×C₄₇	—	2	4	no	—
379	C₂²×C₄₇	—	2	2	no	—
380	C₂²×C₄₇	—	2	2	no	—
381	C₂²×C₄₇	—	4	4	no	—
382	C₂²×C₄₇	—	4	8	no	—
383	C₂²×C₄₇	—	4	2	no	—
384	C₂²×C₄₇	—	4	2	no	—
385	C₂²×C₄₇	—	4	2	no	—
386	C₂²×C₄₇	—	4	2	no	—
387	C₂²×C₄₇	—	4	2	no	—
388	C₂²×C₄₇	—	4	2	no	—
389	C₂²×C₄₇	—	4	2	no	—
390	C₂²×C₄₇	—	4	2	no	—
391	C₂²×C₄₇	—	8	16	no	—
392	C₂²×C₄₇	—	8	4	no	—
393	C₂²×C₄₇	—	8	4	no	—
394	C₂²×C₄₇	#546	1	2	yes	—
395	C₂²×C₄₇	C₂×#135	1	4	yes	—
396	C₂²×C₄₇	C₂×#135	1	2	yes	—
397	C₂²×C₄₇	#576	1	2	yes	—
398	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
399	C₄×C₄₇	—	2	2	no	—
400	C₄×C₄₇	—	2	2	no	—
401	C₄×C₄₇	—	2	2	no	—
402	C₄×C₄₇	—	2	2	no	—
403	C₄×C₄₇	—	4	2	no	—
404	C₄×C₄₇	—	4	2	no	—
405	C₄×C₄₇	—	4	2	no	—
406	C₄×C₄₇	—	4	2	no	—
407	C₄×C₄₇	—	4	2	no	—
408	C₄×C₄₇	#546	1	2	yes	—
409	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
410	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂×#553	C₂×C₄₇	1	1	yes	characteristic, complemented
412	C₂×#546	C₂×C₄₇	1	1	yes	characteristic, complemented
413	#3297	C₂×C₄₇	1	16	yes	direct product factor
414	C₂×#488	C₂×C₄₇	1	1	yes	characteristic, complemented
415	C₂×#484	C₂×C₄₇	1	1	yes	characteristic, complemented
416	C₂×#482	C₂×C₄₇	1	1	yes	characteristic, complemented
417	C₂×#478	C₂×C₄₇	1	1	yes	characteristic, complemented
418	C₂×#466	C₂×C₄₇	1	1	yes	characteristic, complemented
419	C₂×#465	C₂×C₄₇	1	1	yes	characteristic, complemented
420	C₂×#463	C₂×C₄₇	1	1	yes	characteristic, complemented
421	C₂×#449	C₂×C₄₇	1	1	yes	characteristic, complemented
422	C₂×#447	C₂×C₄₇	1	1	yes	characteristic, complemented
423	C₂×C₄×D₈	C₂×C₄₇	1	1	yes	characteristic, complemented
424	C₂×C₈×D₄	C₂×C₄₇	1	1	yes	characteristic, complemented
425	C₂×#416	C₂×C₄₇	1	1	yes	characteristic, complemented
426	C₂²×#102	C₂×C₄₇	1	1	yes	characteristic, complemented
427	C₂×C₄₇	—	2	4	no	—
428	C₂×C₄₇	—	4	2	no	—
429	C₂×C₄₇	—	4	4	no	—
430	C₂×C₄₇	—	8	2	no	—
431	C₂×C₄₇	—	8	2	no	—
432	C₂×C₄₇	#3297	1	4	yes	direct product factor
433	C₂×C₄₇	C₂×#546	1	1	yes	characteristic
434	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
435	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
436	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
437	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
438	C₂²×SD₁₆	C₂²×C₄₇	1	1	yes	characteristic, complemented
439	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
440	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
441	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
442	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
443	#553	—	2	4	no	—
444	#553	C₂²×C₄₇	1	8	yes	complemented
445	#546	—	2	4	no	—
446	#546	C₂²×C₄₇	1	8	yes	complemented
447	C₂×#126	—	2	1	no	—
448	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic, complemented
449	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
450	C₂×#123	—	2	1	no	—
451	C₂×#123	—	2	1	no	—
452	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
453	C₂×#121	—	2	1	no	—
454	C₂×#121	—	2	1	no	—
455	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
456	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
457	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic, complemented
458	C₂×#120	—	2	1	no	—
459	C₂×C₄×D₄	—	2	1	no	—
460	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
463	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic, complemented
464	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
465	C₂²×C₂²⋊C₄	—	2	1	no	—
466	#488	C₂²×C₄₇	1	8	yes	complemented
467	#484	C₂²×C₄₇	1	8	yes	complemented
468	#482	C₂²×C₄₇	1	8	yes	complemented
469	#478	C₂²×C₄₇	1	8	yes	complemented
470	#466	C₂²×C₄₇	1	8	yes	complemented
471	#465	C₂²×C₄₇	1	8	yes	complemented
472	#463	C₂²×C₄₇	1	8	yes	complemented
473	#449	C₂²×C₄₇	1	8	yes	complemented
474	#447	C₂²×C₄₇	1	8	yes	complemented
475	C₄×D₈	C₂²×C₄₇	1	8	yes	complemented
476	C₈×D₄	C₂²×C₄₇	1	8	yes	complemented
477	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic, complemented
478	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic, complemented
479	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic, complemented
480	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
481	#416	C₂²×C₄₇	1	8	yes	complemented
482	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic, complemented
483	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic, complemented
484	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic, complemented
485	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
486	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
487	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
488	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
489	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
490	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
491	C₂×#102	C₂²×C₄₇	1	8	yes	complemented
492	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic, complemented
493	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
494	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
495	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
496	C₄₇	C₂×#3297	1	1	yes	characteristic, direct product factor, Sylow
497	C₂⁵	—	2	1	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	4	no	—
500	C₂×#41	—	4	2	no	—
501	C₂×#41	C₂³×C₄₇	1	4	yes	—
502	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
503	C₂²×D₄	—	2	4	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	—	4	2	no	—
511	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
515	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
522	C₂×SD₁₆	—	4	2	no	—
523	C₂×SD₁₆	C₂³×C₄₇	1	4	yes	complemented
524	C₂×D₈	—	2	4	no	—
525	C₂×D₈	—	4	2	no	—
526	C₂×D₈	C₂³×C₄₇	1	4	yes	—
527	C₂×D₈	C₂³×C₄₇	1	4	yes	—
528	C₂²×C₈	—	4	2	no	—
529	C₂²×C₈	—	4	2	no	—
530	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
535	C₂²×C₈	C₂³×C₄₇	1	4	yes	complemented
536	#126	—	2	8	no	—
537	#125	—	2	2	no	—
538	#125	C₂³×C₄₇	1	4	yes	complemented
539	#124	—	2	2	no	—
540	#124	C₂³×C₄₇	1	4	yes	—
541	#123	—	2	8	no	—
542	#123	—	2	8	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
545	#121	—	2	8	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	8	no	—
550	#121	C₂³×C₄₇	1	4	yes	—
551	#121	C₂³×C₄₇	1	4	yes	—
552	#121	C₂³×C₄₇	1	4	yes	complemented
553	#120	—	2	8	no	—
554	C₄×D₄	—	2	8	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	D₄×C₄₇	1	4	yes	—
558	C₄×D₄	C₂³×C₄₇	1	4	yes	—
559	C₄×D₄	C₂³×C₄₇	1	4	yes	—
560	C₄×D₄	C₂³×C₄₇	1	4	yes	complemented
561	#117	—	2	2	no	—
562	#117	C₂³×C₄₇	1	4	yes	complemented
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	2	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	8	no	—
584	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
586	C₂×C₄²	—	2	1	no	—
587	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
588	#107	C₂³×C₄₇	1	4	yes	complemented
589	#107	C₂³×C₄₇	1	4	yes	complemented
590	#106	C₂³×C₄₇	1	4	yes	complemented
591	C₄⋊C₈	C₂³×C₄₇	1	4	yes	complemented
592	#103	C₂³×C₄₇	1	4	yes	complemented
593	#103	C₂³×C₄₇	1	4	yes	complemented
594	#103	C₂³×C₄₇	1	4	yes	complemented
595	#102	C₂³×C₄₇	1	4	yes	—
596	#102	C₂³×C₄₇	1	4	yes	—
597	#102	C₂³×C₄₇	1	4	yes	—
598	#102	C₂³×C₄₇	1	4	yes	—
599	#102	C₂³×C₄₇	1	4	yes	—
600	#102	C₂³×C₄₇	1	4	yes	—
601	#102	C₂³×C₄₇	1	4	yes	complemented
602	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
603	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	complemented
604	C₄×C₈	C₂³×C₄₇	1	4	yes	complemented
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	1	no	—
607	C₂⁴	—	2	1	no	—
608	C₂⁴	—	2	4	no	—
609	C₂⁴	—	4	4	no	—
610	C₂⁴	—	4	4	no	—
611	C₂⁴	—	8	2	no	—
612	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
613	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
614	#41	—	2	8	no	—
615	#41	—	4	4	no	—
616	#41	—	4	8	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	8	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	4	no	—
640	C₂×D₄	—	4	4	no	—
641	C₂×D₄	—	8	2	no	—
642	C₂×D₄	—	8	2	no	—
643	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
644	C₂×D₄	#41×C₄₇	1	4	yes	—
645	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
646	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
647	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	4	4	no	—
662	C₂²×C₄	—	8	2	no	—
663	C₂²×C₄	—	8	2	no	—
664	C₂²×C₄	—	8	2	no	—
665	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
674	SD₁₆	—	4	4	no	—
675	D₈	—	2	8	no	—
676	D₈	—	4	4	no	—
677	C₂×C₈	—	2	2	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	2	2	no	—
681	C₂×C₈	—	4	4	no	—
682	C₂×C₈	—	4	4	no	—
683	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
684	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
685	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
686	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
696	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₄₇	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
710	C₂²⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
711	C₄²	—	2	4	no	—
712	C₄²	C₂×D₄×C₄₇	1	2	yes	—
713	C₄²	C₂⁴×C₄₇	1	2	yes	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	8	no	—
724	C₂³	—	4	2	no	—
725	C₂³	—	4	2	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	8	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	8	4	no	—
734	C₂³	—	8	16	no	—
735	C₂³	#135×C₄₇	1	4	yes	—
736	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
737	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
738	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	4	2	no	—
742	D₄	—	2	8	no	—
743	D₄	—	2	4	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	2	2	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	2	no	—
754	D₄	—	8	4	no	—
755	D₄	—	8	4	no	—
756	D₄	C₂×#41×C₄₇	1	4	yes	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	8	4	no	—
779	C₂×C₄	—	8	4	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
783	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
786	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
787	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
788	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
789	C₈	—	2	2	no	—
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₂²	—	2	8	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	8	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	8	16	no	—
811	C₂²	—	8	4	no	—
812	C₂²	—	8	4	no	—
813	C₂²	C₄₇×#546	1	2	yes	—
814	C₂²	C₂×#135×C₄₇	1	4	yes	—
815	C₂²	C₂×#135×C₄₇	1	2	yes	—
816	C₂²	C₄₇×#576	1	2	yes	—
817	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	C₄₇×#546	1	2	yes	—
828	C₄	C₂²×#41×C₄₇	1	1	yes	characteristic
829	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
830	C₂	—	2	4	no	—
831	C₂	—	4	2	no	—
832	C₂	—	4	4	no	—
833	C₂	—	8	2	no	—
834	C₂	—	8	2	no	—
835	C₂	C₄₇×#3297	1	4	yes	direct product factor
836	C₂	C₂×C₄₇×#546	1	1	yes	characteristic
837	C₂	C₂²×#135×C₄₇	1	1	yes	characteristic
838	C₂	C₂×C₄₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#553	C₂	semidirect
2. C₂×C₄₇×#546	C₂	semidirect
3. C₄₇×#3297	C₂	direct (N × H)
4. C₂×C₄₇×#488	C₂	semidirect
5. C₂×C₄₇×#484	C₂	semidirect
6. C₂×C₄₇×#482	C₂	semidirect
7. C₂×C₄₇×#478	C₂	semidirect
8. C₂×C₄₇×#466	C₂	semidirect
9. C₂×C₄₇×#465	C₂	semidirect
10. C₂×C₄₇×#463	C₂	semidirect
11. C₂×C₄₇×#449	C₂	semidirect
12. C₂×C₄₇×#447	C₂	semidirect
13. C₂×C₄×D₈×C₄₇	C₂	semidirect
14. C₂×C₈×D₄×C₄₇	C₂	semidirect
15. C₂×C₄₇×#416	C₂	semidirect
16. C₂²×#102×C₄₇	C₂	semidirect
19. C₂²×SD₁₆×C₄₇	C₂²	semidirect
23. C₂³×C₈×C₄₇	C₂²	semidirect
25. C₄₇×#553	C₂²	semidirect
27. C₄₇×#546	C₂²	semidirect
29. C₂×#125×C₄₇	C₂²	semidirect
38. C₂×#121×C₄₇	C₂²	semidirect
43. C₂×C₄×D₄×C₄₇	C₂²	semidirect
44. C₂×#117×C₄₇	C₂²	semidirect
47. C₄₇×#488	C₂²	semidirect
48. C₄₇×#484	C₂²	semidirect
49. C₄₇×#482	C₂²	semidirect
50. C₄₇×#478	C₂²	semidirect
51. C₄₇×#466	C₂²	semidirect
52. C₄₇×#465	C₂²	semidirect
53. C₄₇×#463	C₂²	semidirect
54. C₄₇×#449	C₂²	semidirect
55. C₄₇×#447	C₂²	semidirect
56. C₄×D₈×C₄₇	C₂²	semidirect
57. C₈×D₄×C₄₇	C₂²	semidirect
58. C₂×#107×C₄₇	C₂²	semidirect
59. C₂×#107×C₄₇	C₂²	semidirect
60. C₂×#106×C₄₇	C₂²	semidirect
61. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
62. C₄₇×#416	C₂²	semidirect
63. C₂×#103×C₄₇	C₂²	semidirect
64. C₂×#103×C₄₇	C₂²	semidirect
65. C₂×#103×C₄₇	C₂²	semidirect
72. C₂×#102×C₄₇	C₂²	semidirect
73. C₂×#102×C₄₇	C₂²	semidirect
75. C₂×C₂²⋊C₈×C₄₇	C₂²	semidirect
76. C₂×C₄×C₈×C₄₇	C₂²	semidirect
103. C₂×SD₁₆×C₄₇	C₂³	semidirect
115. C₂²×C₈×C₄₇	C₂³	semidirect
118. #125×C₄₇	C₂³	semidirect
132. #121×C₄₇	C₂³	semidirect
140. C₄×D₄×C₄₇	C₂³	semidirect
142. #117×C₄₇	C₂³	semidirect
168. #107×C₄₇	C₂³	semidirect
169. #107×C₄₇	C₂³	semidirect
170. #106×C₄₇	C₂³	semidirect
171. C₄⋊C₈×C₄₇	C₂³	semidirect
172. #103×C₄₇	C₂³	semidirect
173. #103×C₄₇	C₂³	semidirect
174. #103×C₄₇	C₂³	semidirect
181. #102×C₄₇	C₂³	semidirect
183. C₂²⋊C₈×C₄₇	C₂³	semidirect
184. C₄×C₈×C₄₇	C₂³	semidirect
373. C₂×#3297	C₄₇	direct (N × H)
411. C₂×#553	C₂×C₄₇	semidirect
412. C₂×#546	C₂×C₄₇	semidirect
413. #3297	C₂×C₄₇	direct (N × H)
414. C₂×#488	C₂×C₄₇	semidirect
415. C₂×#484	C₂×C₄₇	semidirect
416. C₂×#482	C₂×C₄₇	semidirect
417. C₂×#478	C₂×C₄₇	semidirect
418. C₂×#466	C₂×C₄₇	semidirect
419. C₂×#465	C₂×C₄₇	semidirect
420. C₂×#463	C₂×C₄₇	semidirect
421. C₂×#449	C₂×C₄₇	semidirect
422. C₂×#447	C₂×C₄₇	semidirect
423. C₂×C₄×D₈	C₂×C₄₇	semidirect
424. C₂×C₈×D₄	C₂×C₄₇	semidirect
425. C₂×#416	C₂×C₄₇	semidirect
426. C₂²×#102	C₂×C₄₇	semidirect
432. C₂×C₄₇	#3297	direct (N × H)
438. C₂²×SD₁₆	C₂²×C₄₇	semidirect
442. C₂³×C₈	C₂²×C₄₇	semidirect
444. #553	C₂²×C₄₇	semidirect
446. #546	C₂²×C₄₇	semidirect
448. C₂×#125	C₂²×C₄₇	semidirect
457. C₂×#121	C₂²×C₄₇	semidirect
462. C₂×C₄×D₄	C₂²×C₄₇	semidirect
463. C₂×#117	C₂²×C₄₇	semidirect
466. #488	C₂²×C₄₇	semidirect
467. #484	C₂²×C₄₇	semidirect
468. #482	C₂²×C₄₇	semidirect
469. #478	C₂²×C₄₇	semidirect
470. #466	C₂²×C₄₇	semidirect
471. #465	C₂²×C₄₇	semidirect
472. #463	C₂²×C₄₇	semidirect
473. #449	C₂²×C₄₇	semidirect
474. #447	C₂²×C₄₇	semidirect
475. C₄×D₈	C₂²×C₄₇	semidirect
476. C₈×D₄	C₂²×C₄₇	semidirect
477. C₂×#107	C₂²×C₄₇	semidirect
478. C₂×#107	C₂²×C₄₇	semidirect
479. C₂×#106	C₂²×C₄₇	semidirect
480. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
481. #416	C₂²×C₄₇	semidirect
482. C₂×#103	C₂²×C₄₇	semidirect
483. C₂×#103	C₂²×C₄₇	semidirect
484. C₂×#103	C₂²×C₄₇	semidirect
491. C₂×#102	C₂²×C₄₇	semidirect
492. C₂×#102	C₂²×C₄₇	semidirect
494. C₂×C₂²⋊C₈	C₂²×C₄₇	semidirect
495. C₂×C₄×C₈	C₂²×C₄₇	semidirect
496. C₄₇	C₂×#3297	direct (N × H)
523. C₂×SD₁₆	C₂³×C₄₇	semidirect
535. C₂²×C₈	C₂³×C₄₇	semidirect
538. #125	C₂³×C₄₇	semidirect
552. #121	C₂³×C₄₇	semidirect
560. C₄×D₄	C₂³×C₄₇	semidirect
562. #117	C₂³×C₄₇	semidirect
588. #107	C₂³×C₄₇	semidirect
589. #107	C₂³×C₄₇	semidirect
590. #106	C₂³×C₄₇	semidirect
591. C₄⋊C₈	C₂³×C₄₇	semidirect
592. #103	C₂³×C₄₇	semidirect
593. #103	C₂³×C₄₇	semidirect
594. #103	C₂³×C₄₇	semidirect
601. #102	C₂³×C₄₇	semidirect
603. C₂²⋊C₈	C₂³×C₄₇	semidirect
604. C₄×C₈	C₂³×C₄₇	semidirect
835. C₂	C₄₇×#3297	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#553	2
C₂×C₄₇×#546	2
C₄₇×#3297	2
C₂×C₄₇×#488	2
C₂×C₄₇×#484	2
C₂×C₄₇×#482	2
C₂×C₄₇×#478	2
C₂×C₄₇×#466	2
C₂×C₄₇×#465	2
C₂×C₄₇×#463	2
C₂×C₄₇×#449	2
C₂×C₄₇×#447	2
C₂×C₄×D₈×C₄₇	2
C₂×C₈×D₄×C₄₇	2
C₂×C₄₇×#416	2
C₂²×#102×C₄₇	2
C₂×#3297	47

Subgroups — C2×C47×#3297 #26100813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#3297 #26100813