Subgroups — C₂×#20257183 #27124174

Order 12032.

7738 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257183	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689834	C₂	1	2	yes	maximal, complemented
3	C₂×#15689833	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689832	C₂	1	2	yes	maximal, complemented
5	C₂×#15689831	C₂	1	2	yes	maximal, complemented
6	C₂×#15689830	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689827	C₂	1	4	yes	maximal, complemented
8	C₂×#15689788	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×Q₈×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
10	C₂×#15689750	C₂	1	2	yes	maximal, complemented
11	C₂×#15689748	C₂	1	4	yes	maximal, complemented
12	C₂×#15689678	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15689677	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#13094000	C₂	1	2	yes	maximal, complemented
15	C₂×C₂²⋊Q₈×D₄₇	C₂	1	2	yes	maximal, complemented
16	C₂×#15689595	C₂	1	2	yes	maximal
17	C₂×C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic
18	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×Q₈×D₄₇	C₂²	1	2	yes	complemented
20	C₂²×D₄×D₄₇	C₂²	1	1	yes	characteristic
21	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
22	#15689834	C₂²	1	32	yes	complemented
23	#15689833	C₂²	1	16	yes	complemented
24	#15689832	C₂²	1	32	yes	complemented
25	#15689831	C₂²	1	32	yes	complemented
26	#15689830	C₂²	1	16	yes	complemented
27	#15689827	C₂²	1	64	yes	complemented
28	#15689788	C₂²	1	16	yes	complemented
29	Q₈×C₂²⋊D₄₇	C₂²	1	32	yes	complemented
30	#15689750	C₂²	1	32	yes	complemented
31	#15689748	C₂²	1	64	yes	complemented
32	#15689678	C₂²	1	16	yes	complemented
33	#15689677	C₂²	1	16	yes	complemented
34	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13094023	C₂²	1	2	yes	complemented
36	C₂×#13094023	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13094022	C₂²	1	4	yes	complemented
38	C₂×#13094022	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13094016	C₂²	1	2	yes	complemented
40	C₂×#13094015	C₂²	1	2	yes	complemented
41	C₂×#13094015	C₂²	1	2	yes	complemented
42	C₂×#13094014	C₂²	1	4	yes	complemented
43	C₂×#13094014	C₂²	1	2	yes	complemented
44	C₂×#13094004	C₂²	1	2	yes	—
45	C₂×#13094004	C₂²	1	1	yes	characteristic
46	C₂×#13094004	C₂²	1	4	yes	complemented
47	C₂×#13094003	C₂²	1	4	yes	complemented
48	C₂×#13094003	C₂²	1	2	yes	complemented
49	C₂×#13094002	C₂²	1	2	yes	—
50	C₂×#13094002	C₂²	1	4	yes	—
51	C₂×#13094002	C₂²	1	4	yes	complemented
52	C₂×#13094002	C₂²	1	4	yes	complemented
53	C₂×#13094001	C₂²	1	4	yes	complemented
54	C₂×#13094001	C₂²	1	4	yes	complemented
55	C₂×#13094001	C₂²	1	4	yes	complemented
56	C₂×#13094000	C₂²	1	4	yes	—
57	C₂×#13094000	C₂²	1	2	yes	—
58	C₂×#13094000	C₂²	1	1	yes	characteristic
59	C₂×#13094000	C₂²	1	4	yes	complemented
60	C₂×#13094000	C₂²	1	2	yes	complemented
61	C₂×#13094000	C₂²	1	2	yes	complemented
62	C₂×#13094000	C₂²	1	4	yes	complemented
63	C₂×#13094000	C₂²	1	32	yes	complemented
64	C₂²⋊Q₈×D₄₇	C₂²	1	32	yes	complemented
65	#15689595	C₂²	1	32	yes	—
66	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
67	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
69	C₂×#13093989	C₂²	1	2	yes	complemented
70	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
71	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
72	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
73	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
74	C₂×#13093986	C₂²	1	1	yes	characteristic
75	C₂×#13093986	C₂²	1	2	yes	—
76	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
77	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
78	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
79	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
80	C₄×D₄×D₄₇	C₂²	1	16	yes	—
81	C₂×#13093982	C₂²	1	2	yes	—
82	C₂×#13093981	C₂²	1	2	yes	—
83	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
84	C₂²×Dic₄₇⋊C₄	C₂²	1	4	yes	complemented
85	C₂×C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
86	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	complemented
87	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
88	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
89	C₂×C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
90	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
91	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
92	C₂³×Q₈×C₄₇	C₂²	1	2	yes	complemented
93	D₄×Q₈×C₄₇	C₂²	1	16	yes	complemented
94	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
95	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
97	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
98	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
100	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
101	C₂⁴×D₄₇	C₂³	1	2	yes	—
102	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
103	C₂²×Dic₉₄	C₂³	1	2	yes	—
104	C₂²×Dic₉₄	C₂³	1	2	yes	—
105	C₂²×Dic₉₄	C₂³	1	4	yes	—
106	C₂×Q₈×D₄₇	—	4	8	no	—
107	C₂×Q₈×D₄₇	C₂³	1	16	yes	complemented
108	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
109	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
110	C₂×D₄×D₄₇	Q₈	1	16	yes	complemented
111	C₂×D₄×D₄₇	C₂³	1	8	yes	—
112	C₂³×Dic₄₇	C₂³	1	4	yes	—
113	C₂³×Dic₄₇	C₂³	1	2	yes	—
114	C₂²×C₄×D₄₇	—	4	8	no	—
115	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
116	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
117	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
118	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
119	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
120	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
121	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
122	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
123	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
124	#13094024	C₂³	1	8	yes	complemented
125	#13094023	C₂³	1	16	yes	complemented
126	#13094023	C₂³	1	8	yes	complemented
127	#13094022	C₂³	1	32	yes	complemented
128	#13094022	C₂³	1	8	yes	complemented
129	#13094016	C₂³	1	16	yes	complemented
130	#13094015	C₂³	1	16	yes	complemented
131	#13094015	C₂³	1	16	yes	complemented
132	#13094014	C₂³	1	32	yes	complemented
133	#13094014	C₂³	1	16	yes	complemented
134	#13094004	C₂³	1	16	yes	—
135	#13094004	C₂³	1	8	yes	—
136	#13094004	C₂³	1	32	yes	complemented
137	#13094003	C₂³	1	32	yes	complemented
138	#13094003	C₂³	1	16	yes	complemented
139	#13094002	C₂³	1	16	yes	—
140	#13094002	C₂³	1	32	yes	—
141	#13094002	C₂³	1	32	yes	complemented
142	#13094002	C₂³	1	32	yes	complemented
143	#13094001	C₂³	1	32	yes	complemented
144	#13094001	C₂³	1	32	yes	complemented
145	#13094001	C₂³	1	32	yes	complemented
146	#13094000	C₂³	1	32	yes	—
147	#13094000	C₂³	1	16	yes	—
148	#13094000	C₂³	1	8	yes	—
149	#13094000	C₂³	1	32	yes	complemented
150	#13094000	C₂³	1	16	yes	complemented
151	#13094000	C₂³	1	16	yes	complemented
152	#13094000	C₂³	1	32	yes	complemented
153	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
154	C₄×Dic₉₄	C₂³	1	8	yes	complemented
155	C₄×Dic₉₄	C₂³	1	16	yes	complemented
156	#13093989	C₂³	1	16	yes	complemented
157	C₄×D₁₈₈	C₂³	1	8	yes	—
158	C₄×D₁₈₈	C₂³	1	16	yes	—
159	D₄×Dic₄₇	C₂³	1	16	yes	—
160	D₄×Dic₄₇	C₂³	1	8	yes	—
161	#13093986	C₂³	1	16	yes	—
162	#13093986	C₂³	1	8	yes	—
163	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
164	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
165	(C₂²⋊D₄₇)⋊C₄	C₂³	1	16	yes	—
166	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	—
167	#13093982	C₂³	1	16	yes	—
168	#13093981	C₂³	1	16	yes	—
169	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
171	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
174	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
175	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
176	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
177	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
178	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
179	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
180	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
181	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
182	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
183	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
184	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
185	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
186	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
187	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
188	C₂×Dic₄₇⋊C₄	C₂³	1	32	yes	complemented
189	C₄⋊C₄×D₄₇	C₂³	1	8	yes	—
190	C₄⋊C₄×D₄₇	C₂³	1	32	yes	complemented
191	C₄⋊C₄×D₄₇	C₂³	1	16	yes	complemented
192	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
194	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	32	yes	—
195	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
196	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
197	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
198	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
199	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
200	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
201	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
202	C₂²⋊C₄×D₄₇	C₂³	1	16	yes	—
203	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	—
204	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
205	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
206	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
207	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
208	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
209	C₄²×D₄₇	C₂³	1	8	yes	—
210	C₂²×Q₈×C₄₇	—	4	8	no	—
211	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
212	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
213	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
214	C₂²×Q₈×C₄₇	C₂³	1	16	yes	complemented
215	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
216	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
217	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
218	C₄⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
219	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
220	C₂²⋊Q₈×C₄₇	C₂³	1	32	yes	complemented
221	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
222	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
223	C₄×D₄×C₄₇	C₂³	1	8	yes	—
224	C₄×D₄×C₄₇	C₂³	1	16	yes	—
225	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
230	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
233	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
235	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
236	C₂³×D₄₇	—	4	4	no	—
237	C₂³×D₄₇	—	4	4	no	—
238	C₂³×D₄₇	C₂×Q₈	1	16	yes	complemented
239	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
240	C₂³×D₄₇	C₂⁴	1	2	yes	—
241	C₂³×D₄₇	C₂⁴	1	8	yes	—
242	C₂×Q₈×C₄₇	—	2	4	no	—
243	C₂×Q₈×C₄₇	—	2	8	no	—
244	C₂×Q₈×C₄₇	—	4	8	no	—
245	C₂×Q₈×C₄₇	—	4	32	no	—
246	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
248	C₂×Q₈×C₄₇	C₂⁴	1	16	yes	—
249	C₂×D₄×C₄₇	C₂×Q₈	1	8	yes	complemented
250	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₄₇	—	2	8	no	—
252	C₂²×C₄×C₄₇	—	4	8	no	—
253	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
259	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
260	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₂²⋊D₄₇	C₂×Q₈	1	16	yes	complemented
263	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
264	C₂²×Dic₄₇	—	4	4	no	—
265	C₂²×Dic₄₇	—	4	8	no	—
266	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
267	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
268	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
269	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
270	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
271	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
272	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
273	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
274	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
275	Q₈×D₄₇	—	4	32	no	—
276	D₄×D₄₇	C₂×Q₈	1	64	yes	complemented
277	C₂×D₁₈₈	C₂×Q₈	1	8	yes	complemented
278	C₂×D₁₈₈	C₂⁴	1	4	yes	—
279	C₂×C₄×D₄₇	—	2	4	no	—
280	C₂×C₄×D₄₇	—	2	8	no	—
281	C₂×C₄×D₄₇	—	4	32	no	—
282	C₂×C₄×D₄₇	—	4	4	no	—
283	C₂×C₄×D₄₇	—	4	4	no	—
284	C₂×C₄×D₄₇	—	4	2	no	—
285	C₂×C₄×D₄₇	—	4	8	no	—
286	C₂×C₄×D₄₇	—	4	8	no	—
287	C₂×C₄×D₄₇	C₂×Q₈	1	8	yes	complemented
288	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
289	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
290	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
291	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
292	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
293	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
294	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
295	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
296	C₂×Dic₉₄	—	2	4	no	—
297	C₂×Dic₉₄	—	4	8	no	—
298	C₂×Dic₉₄	—	4	4	no	—
299	C₂×Dic₉₄	—	4	4	no	—
300	C₂×Dic₉₄	C₂⁴	1	4	yes	—
301	C₂×Dic₉₄	C₂⁴	1	8	yes	—
302	C₂×Dic₉₄	C₂⁴	1	8	yes	—
303	C₂×Dic₉₄	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
306	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
308	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
309	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
310	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
311	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
312	C₄²×C₄₇	C₂⁴	1	4	yes	—
313	C₄²×C₄₇	C₂⁴	1	8	yes	—
314	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
315	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
316	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
317	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
318	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
319	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
320	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
321	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
322	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
323	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
324	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
325	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
326	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
327	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
328	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
329	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
330	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
331	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
332	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
333	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
334	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
335	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
336	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
337	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
338	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
339	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
340	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
341	C₄×Dic₄₇	C₂⁴	1	4	yes	—
342	C₄×Dic₄₇	C₂⁴	1	4	yes	—
343	C₄×Dic₄₇	C₂⁴	1	4	yes	—
344	C₄×Dic₄₇	C₂⁴	1	8	yes	—
345	C₄×Dic₄₇	C₂⁴	1	16	yes	—
346	C₂³×C₄₇	—	2	4	no	—
347	C₂³×C₄₇	—	2	4	no	—
348	C₂³×C₄₇	C₂²×Q₈	1	8	yes	—
349	C₂³×C₄₇	C₂⁵	1	4	yes	—
350	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
351	C₂²×D₄₇	—	2	4	no	—
352	C₂²×D₄₇	—	2	2	no	—
353	C₂²×D₄₇	—	2	4	no	—
354	C₂²×D₄₇	—	2	2	no	—
355	C₂²×D₄₇	—	4	8	no	—
356	C₂²×D₄₇	—	4	32	no	—
357	C₂²×D₄₇	—	4	8	no	—
358	C₂²×D₄₇	C₂²×Q₈	1	4	yes	—
359	C₂²×D₄₇	C₂²×Q₈	1	8	yes	—
360	C₂²×D₄₇	C₂²×Q₈	1	32	yes	complemented
361	C₂²×D₄₇	C₂⁵	1	2	yes	—
362	C₂²×D₄₇	C₂⁵	1	4	yes	—
363	Q₈×C₄₇	—	2	16	no	—
364	Q₈×C₄₇	—	2	8	no	—
365	Q₈×C₄₇	—	4	16	no	—
366	D₄×C₄₇	C₂²×Q₈	1	16	yes	complemented
367	C₂×C₄×C₄₇	—	2	8	no	—
368	C₂×C₄×C₄₇	—	2	4	no	—
369	C₂×C₄×C₄₇	—	2	4	no	—
370	C₂×C₄×C₄₇	—	2	2	no	—
371	C₂×C₄×C₄₇	—	2	4	no	—
372	C₂×C₄×C₄₇	—	2	16	no	—
373	C₂×C₄×C₄₇	—	4	16	no	—
374	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
375	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
376	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
377	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
378	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
379	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
380	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
381	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
382	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
383	C₂²⋊D₄₇	C₂²×Q₈	1	32	yes	complemented
384	C₂×Dic₄₇	—	2	4	no	—
385	C₂×Dic₄₇	—	2	4	no	—
386	C₂×Dic₄₇	—	2	2	no	—
387	C₂×Dic₄₇	—	2	2	no	—
388	C₂×Dic₄₇	—	2	8	no	—
389	C₂×Dic₄₇	—	2	4	no	—
390	C₂×Dic₄₇	—	4	8	no	—
391	C₂×Dic₄₇	—	4	16	no	—
392	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
393	C₂×Dic₄₇	C₂⁵	1	2	yes	—
394	C₂×Dic₄₇	C₂⁵	1	2	yes	—
395	C₂×Dic₄₇	C₂⁵	1	4	yes	—
396	C₂×Dic₄₇	C₂⁵	1	4	yes	—
397	C₂×Dic₄₇	C₂⁵	1	8	yes	—
398	C₂×Dic₄₇	C₂⁵	1	4	yes	—
399	C₂×Dic₄₇	C₂⁵	1	2	yes	—
400	D₁₈₈	C₂²×Q₈	1	16	yes	complemented
401	C₄×D₄₇	—	2	8	no	—
402	C₄×D₄₇	—	2	16	no	—
403	C₄×D₄₇	—	4	8	no	—
404	C₄×D₄₇	—	4	8	no	—
405	C₄×D₄₇	—	4	4	no	—
406	C₄×D₄₇	—	4	16	no	—
407	C₄×D₄₇	—	4	16	no	—
408	C₄×D₄₇	C₂²×Q₈	1	16	yes	complemented
409	Dic₉₄	—	2	8	no	—
410	Dic₉₄	—	4	8	no	—
411	Dic₉₄	—	4	8	no	—
412	Dic₉₄	—	4	16	no	—
413	C₂×#3501	—	47	1	no	maximal, Sylow
414	C₂²×C₄₇	—	2	4	no	—
415	C₂²×C₄₇	—	2	4	no	—
416	C₂²×C₄₇	—	2	16	no	—
417	C₂²×C₄₇	C₂³×Q₈	1	8	yes	—
418	C₂²×C₄₇	C₂³×Q₈	1	2	yes	—
419	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
420	C₂²×C₄₇	#585	1	2	yes	—
421	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
422	C₂×D₄₇	—	2	4	no	—
423	C₂×D₄₇	—	2	2	no	—
424	C₂×D₄₇	—	2	4	no	—
425	C₂×D₄₇	—	2	2	no	—
426	C₂×D₄₇	—	2	8	no	—
427	C₂×D₄₇	—	2	16	no	—
428	C₂×D₄₇	—	4	32	no	—
429	C₂×D₄₇	C₂³×Q₈	1	4	yes	—
430	C₂×D₄₇	C₂³×Q₈	1	8	yes	—
431	C₄×C₄₇	—	2	8	no	—
432	C₄×C₄₇	—	2	4	no	—
433	C₄×C₄₇	—	2	4	no	—
434	C₄×C₄₇	—	2	2	no	—
435	C₄×C₄₇	—	2	4	no	—
436	C₄×C₄₇	C₂³×Q₈	1	4	yes	—
437	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
438	Dic₄₇	—	2	4	no	—
439	Dic₄₇	—	2	4	no	—
440	Dic₄₇	—	2	2	no	—
441	Dic₄₇	—	2	2	no	—
442	Dic₄₇	—	2	8	no	—
443	Dic₄₇	—	2	4	no	—
444	Dic₄₇	C₂³×Q₈	1	4	yes	—
445	#3501	—	47	32	no	—
446	C₂×#554	—	47	2	no	—
447	C₂×#554	—	47	4	no	—
448	C₂×#554	—	47	2	no	—
449	C₂×#554	—	47	1	no	—
450	C₂×#554	—	47	1	no	—
451	C₂×#554	—	47	2	no	—
452	C₂×D₄×Q₈	—	47	2	no	—
453	C₂×D₄×Q₈	—	47	1	no	—
454	C₂×D₄×Q₈	D₄₇	1	1	yes	characteristic, complemented
455	C₂×#544	—	47	2	no	—
456	C₂×#543	—	47	4	no	—
457	C₂×#533	—	47	1	no	—
458	C₂×#533	—	47	1	no	—
459	C₂²×C₂²⋊Q₈	—	47	2	no	—
460	C₂²×C₂²⋊Q₈	—	47	2	no	—
461	C₂×#518	—	47	2	no	—
462	C₂²×C₄×D₄	—	47	1	no	—
463	C₂×C₄₇	—	2	8	no	—
464	C₂×C₄₇	#3501	1	4	yes	complemented
465	C₂×C₄₇	C₂⁴×Q₈	1	1	yes	characteristic
466	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
468	D₄₇	—	2	4	no	—
469	D₄₇	—	2	8	no	—
470	C₂³×Q₈	—	47	2	no	—
471	C₂³×Q₈	C₂×D₄₇	1	2	yes	complemented
472	C₂³×D₄	—	47	1	no	—
473	C₂⁴×C₄	—	47	2	no	—
474	#554	—	47	32	no	—
475	#554	—	47	64	no	—
476	#554	—	47	32	no	—
477	#554	—	47	16	no	—
478	#554	—	47	16	no	—
479	#554	—	47	32	no	—
480	D₄×Q₈	—	47	32	no	—
481	D₄×Q₈	—	47	16	no	—
482	D₄×Q₈	C₂×D₄₇	1	16	yes	complemented
483	#544	—	47	32	no	—
484	#543	—	47	64	no	—
485	#533	—	47	16	no	—
486	#533	—	47	16	no	—
487	C₂×C₄⋊Q₈	—	47	1	no	—
488	C₂×C₄⋊Q₈	—	47	4	no	—
489	C₂×C₄⋊Q₈	—	47	1	no	—
490	C₂×C₄⋊Q₈	—	47	2	no	—
491	C₂×C₄⋊Q₈	—	47	1	no	—
492	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
493	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	complemented
494	C₂×#125	—	47	2	no	—
495	C₂×#125	—	47	2	no	—
496	C₂×#125	—	47	4	no	—
497	C₂×#125	—	47	2	no	—
498	C₂×#125	—	47	2	no	—
499	C₂×C₂²⋊Q₈	—	47	2	no	—
500	C₂×C₂²⋊Q₈	—	47	1	no	—
501	C₂×C₂²⋊Q₈	—	47	4	no	—
502	C₂×C₂²⋊Q₈	—	47	2	no	—
503	C₂×C₂²⋊Q₈	—	47	2	no	—
504	C₂×C₂²⋊Q₈	—	47	4	no	—
505	C₂×C₂²⋊Q₈	—	47	4	no	—
506	C₂×C₂²⋊Q₈	—	47	32	no	—
507	C₂×C₂²⋊Q₈	—	47	2	no	—
508	C₂×C₂²⋊Q₈	—	47	4	no	—
509	C₂×C₂²⋊Q₈	—	47	32	no	—
510	C₂×C₂²⋊Q₈	—	47	1	no	—
511	C₂×C₂²⋊Q₈	—	47	4	no	—
512	C₂×C₂²⋊Q₈	—	47	2	no	—
513	C₂×C₂²⋊Q₈	—	47	2	no	—
514	C₂×C₂²⋊Q₈	—	47	4	no	—
515	C₂×C₂²⋊Q₈	—	47	4	no	—
516	C₂×C₂²⋊Q₈	—	47	4	no	—
517	C₂×C₂²⋊Q₈	—	47	4	no	—
518	C₂×C₂²⋊Q₈	—	47	4	no	—
519	C₂×C₂²⋊Q₈	—	47	4	no	—
520	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
521	C₂×C₂²⋊Q₈	C₂×D₄₇	1	4	yes	complemented
522	#518	—	47	32	no	—
523	C₂×C₄×Q₈	—	47	2	no	—
524	C₂×C₄×Q₈	—	47	2	no	—
525	C₂×C₄×Q₈	—	47	1	no	—
526	C₂×C₄×Q₈	—	47	2	no	—
527	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
528	C₂×C₄×D₄	—	47	1	no	—
529	C₂×C₄×D₄	—	47	2	no	—
530	C₂×C₄×D₄	—	47	2	no	—
531	C₂×C₄×D₄	—	47	4	no	—
532	C₂×C₄×D₄	—	47	16	no	—
533	C₂×C₄×D₄	—	47	1	no	—
534	C₂×C₄×D₄	—	47	2	no	—
535	C₂×C₄×D₄	—	47	2	no	—
536	C₂×C₄×D₄	—	47	4	no	—
537	C₂×C₄×D₄	—	47	1	no	—
538	C₂×C₄×D₄	—	47	2	no	—
539	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
540	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
541	C₂×#117	—	47	2	no	—
542	C₂×#117	—	47	2	no	—
543	C₂²×C₄⋊C₄	—	47	4	no	—
544	C₂²×C₄⋊C₄	—	47	2	no	—
545	C₂²×C₄⋊C₄	—	47	1	no	—
546	C₂²×C₄⋊C₄	—	47	4	no	—
547	C₂²×C₄⋊C₄	—	47	2	no	—
548	C₂²×C₂²⋊C₄	—	47	4	no	—
549	C₂²×C₂²⋊C₄	—	47	2	no	—
550	C₂²×C₂²⋊C₄	—	47	4	no	—
551	C₂²×C₄²	—	47	1	no	—
552	C₄₇	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
553	C₂⁵	—	47	2	no	—
554	C₂²×Q₈	—	4	8	no	—
555	C₂²×Q₈	—	47	16	no	—
556	C₂²×Q₈	—	47	1	no	—
557	C₂²×Q₈	—	47	2	no	—
558	C₂²×Q₈	—	47	2	no	—
559	C₂²×Q₈	—	47	4	no	—
560	C₂²×Q₈	—	188	8	no	—
561	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
562	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
563	C₂²×Q₈	C₂²×D₄₇	1	4	yes	—
564	C₂²×Q₈	C₂²×D₄₇	1	16	yes	complemented
565	C₂²×D₄	—	47	2	no	—
566	C₂²×D₄	—	47	16	no	—
567	C₂²×D₄	—	47	8	no	—
568	C₂²×D₄	—	47	1	no	—
569	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
570	C₂³×C₄	—	47	1	no	—
571	C₂³×C₄	—	47	4	no	—
572	C₂³×C₄	—	47	2	no	—
573	C₂³×C₄	—	47	2	no	—
574	C₂³×C₄	—	47	1	no	—
575	C₂³×C₄	—	47	1	no	—
576	C₂³×C₄	—	47	4	no	—
577	C₂³×C₄	—	47	4	no	—
578	C₂³×C₄	—	47	2	no	—
579	C₂³×C₄	—	47	2	no	—
580	C₂³×C₄	—	47	16	no	—
581	C₂³×C₄	—	188	8	no	—
582	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
583	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
584	C₄⋊Q₈	—	47	8	no	—
585	C₄⋊Q₈	—	47	32	no	—
586	C₄⋊Q₈	—	47	8	no	—
587	C₄⋊Q₈	—	47	16	no	—
588	C₄⋊Q₈	—	47	8	no	—
589	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
590	C₄⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
591	#125	—	47	16	no	—
592	#125	—	47	16	no	—
593	#125	—	47	32	no	—
594	#125	—	47	16	no	—
595	#125	—	47	16	no	—
596	C₂²⋊Q₈	—	47	16	no	—
597	C₂²⋊Q₈	—	47	8	no	—
598	C₂²⋊Q₈	—	47	32	no	—
599	C₂²⋊Q₈	—	47	16	no	—
600	C₂²⋊Q₈	—	47	16	no	—
601	C₂²⋊Q₈	—	47	32	no	—
602	C₂²⋊Q₈	—	47	32	no	—
603	C₂²⋊Q₈	—	47	16	no	—
604	C₂²⋊Q₈	—	47	32	no	—
605	C₂²⋊Q₈	—	47	8	no	—
606	C₂²⋊Q₈	—	47	32	no	—
607	C₂²⋊Q₈	—	47	16	no	—
608	C₂²⋊Q₈	—	47	16	no	—
609	C₂²⋊Q₈	—	47	32	no	—
610	C₂²⋊Q₈	—	47	32	no	—
611	C₂²⋊Q₈	—	47	32	no	—
612	C₂²⋊Q₈	—	47	32	no	—
613	C₂²⋊Q₈	—	47	32	no	—
614	C₂²⋊Q₈	—	47	32	no	—
615	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
616	C₂²⋊Q₈	C₂²×D₄₇	1	32	yes	complemented
617	C₄×Q₈	—	47	16	no	—
618	C₄×Q₈	—	47	16	no	—
619	C₄×Q₈	—	47	8	no	—
620	C₄×Q₈	—	47	16	no	—
621	C₄×Q₈	C₂²×D₄₇	1	8	yes	complemented
622	C₄×D₄	—	47	8	no	—
623	C₄×D₄	—	47	16	no	—
624	C₄×D₄	—	47	16	no	—
625	C₄×D₄	—	47	32	no	—
626	C₄×D₄	—	47	8	no	—
627	C₄×D₄	—	47	16	no	—
628	C₄×D₄	—	47	16	no	—
629	C₄×D₄	—	47	32	no	—
630	C₄×D₄	—	47	8	no	—
631	C₄×D₄	—	47	16	no	—
632	C₄×D₄	C₂²×D₄₇	1	8	yes	—
633	C₄×D₄	C₂²×D₄₇	1	16	yes	—
634	#117	—	47	16	no	—
635	#117	—	47	16	no	—
636	C₂×C₄⋊C₄	—	47	4	no	—
637	C₂×C₄⋊C₄	—	47	2	no	—
638	C₂×C₄⋊C₄	—	47	2	no	—
639	C₂×C₄⋊C₄	—	47	1	no	—
640	C₂×C₄⋊C₄	—	47	2	no	—
641	C₂×C₄⋊C₄	—	47	2	no	—
642	C₂×C₄⋊C₄	—	47	1	no	—
643	C₂×C₄⋊C₄	—	47	4	no	—
644	C₂×C₄⋊C₄	—	47	4	no	—
645	C₂×C₄⋊C₄	—	47	4	no	—
646	C₂×C₄⋊C₄	—	47	4	no	—
647	C₂×C₄⋊C₄	—	47	4	no	—
648	C₂×C₄⋊C₄	—	47	32	no	—
649	C₂×C₄⋊C₄	—	47	16	no	—
650	C₂×C₄⋊C₄	—	47	2	no	—
651	C₂×C₄⋊C₄	—	47	2	no	—
652	C₂×C₄⋊C₄	—	47	2	no	—
653	C₂×C₄⋊C₄	—	47	2	no	—
654	C₂×C₄⋊C₄	—	47	4	no	—
655	C₂×C₄⋊C₄	—	47	2	no	—
656	C₂×C₄⋊C₄	—	47	8	no	—
657	C₂×C₄⋊C₄	—	47	32	no	—
658	C₂×C₄⋊C₄	—	47	16	no	—
659	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
662	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
664	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
665	C₂×C₂²⋊C₄	—	47	2	no	—
666	C₂×C₂²⋊C₄	—	47	4	no	—
667	C₂×C₂²⋊C₄	—	47	4	no	—
668	C₂×C₂²⋊C₄	—	47	2	no	—
669	C₂×C₂²⋊C₄	—	47	2	no	—
670	C₂×C₂²⋊C₄	—	47	2	no	—
671	C₂×C₂²⋊C₄	—	47	4	no	—
672	C₂×C₂²⋊C₄	—	47	4	no	—
673	C₂×C₂²⋊C₄	—	47	2	no	—
674	C₂×C₂²⋊C₄	—	47	32	no	—
675	C₂×C₂²⋊C₄	—	47	16	no	—
676	C₂×C₂²⋊C₄	—	47	32	no	—
677	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
679	C₂×C₄²	—	47	4	no	—
680	C₂×C₄²	—	47	2	no	—
681	C₂×C₄²	—	47	1	no	—
682	C₂×C₄²	—	47	1	no	—
683	C₂×C₄²	—	47	1	no	—
684	C₂×C₄²	—	47	8	no	—
685	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
686	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
687	C₂⁴	—	47	1	no	—
688	C₂⁴	—	47	2	no	—
689	C₂⁴	—	47	16	no	—
690	C₂⁴	—	47	8	no	—
691	C₂⁴	—	188	4	no	—
692	C₂⁴	—	188	4	no	—
693	C₂⁴	C₂³×D₄₇	1	2	yes	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	2	8	no	—
696	C₂×Q₈	—	4	8	no	—
697	C₂×Q₈	—	4	32	no	—
698	C₂×Q₈	—	47	4	no	—
699	C₂×Q₈	—	47	8	no	—
700	C₂×Q₈	—	47	8	no	—
701	C₂×Q₈	—	47	16	no	—
702	C₂×Q₈	—	94	4	no	—
703	C₂×Q₈	—	188	4	no	—
704	C₂×Q₈	—	188	4	no	—
705	C₂×Q₈	—	188	8	no	—
706	C₂×Q₈	—	188	32	no	—
707	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
708	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
709	C₂×Q₈	C₂³×D₄₇	1	16	yes	—
710	C₂×D₄	—	47	16	no	—
711	C₂×D₄	—	47	8	no	—
712	C₂×D₄	—	47	64	no	—
713	C₂×D₄	—	47	8	no	—
714	C₂×D₄	—	47	4	no	—
715	C₂×D₄	Q₈×D₄₇	1	8	yes	complemented
716	C₂×D₄	C₂³×D₄₇	1	4	yes	—
717	C₂²×C₄	—	2	8	no	—
718	C₂²×C₄	—	4	8	no	—
719	C₂²×C₄	—	47	1	no	—
720	C₂²×C₄	—	47	8	no	—
721	C₂²×C₄	—	47	4	no	—
722	C₂²×C₄	—	47	1	no	—
723	C₂²×C₄	—	47	1	no	—
724	C₂²×C₄	—	47	2	no	—
725	C₂²×C₄	—	47	4	no	—
726	C₂²×C₄	—	47	2	no	—
727	C₂²×C₄	—	47	2	no	—
728	C₂²×C₄	—	47	16	no	—
729	C₂²×C₄	—	47	8	no	—
730	C₂²×C₄	—	47	4	no	—
731	C₂²×C₄	—	47	8	no	—
732	C₂²×C₄	—	47	4	no	—
733	C₂²×C₄	—	47	16	no	—
734	C₂²×C₄	—	47	16	no	—
735	C₂²×C₄	—	47	8	no	—
736	C₂²×C₄	—	47	8	no	—
737	C₂²×C₄	—	94	4	no	—
738	C₂²×C₄	—	94	8	no	—
739	C₂²×C₄	—	188	32	no	—
740	C₂²×C₄	—	188	8	no	—
741	C₂²×C₄	—	188	2	no	—
742	C₂²×C₄	—	188	4	no	—
743	C₂²×C₄	—	188	4	no	—
744	C₂²×C₄	—	188	8	no	—
745	C₂²×C₄	—	188	8	no	—
746	C₂²×C₄	—	188	4	no	—
747	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
748	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
749	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
750	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
751	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
752	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
753	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
754	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
755	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
756	C₄⋊C₄	—	47	16	no	—
757	C₄⋊C₄	—	47	8	no	—
758	C₄⋊C₄	—	47	8	no	—
759	C₄⋊C₄	—	47	16	no	—
760	C₄⋊C₄	—	47	16	no	—
761	C₄⋊C₄	—	47	16	no	—
762	C₄⋊C₄	—	47	16	no	—
763	C₄⋊C₄	—	47	8	no	—
764	C₄⋊C₄	—	47	8	no	—
765	C₄⋊C₄	—	47	8	no	—
766	C₄⋊C₄	—	47	8	no	—
767	C₄⋊C₄	—	47	8	no	—
768	C₄⋊C₄	—	47	8	no	—
769	C₄⋊C₄	—	47	4	no	—
770	C₄⋊C₄	—	47	4	no	—
771	C₄⋊C₄	—	47	16	no	—
772	C₄⋊C₄	—	47	8	no	—
773	C₄⋊C₄	—	47	16	no	—
774	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
775	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
776	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
777	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
778	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
779	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
780	C₂²⋊C₄	—	47	8	no	—
781	C₂²⋊C₄	—	47	16	no	—
782	C₂²⋊C₄	—	47	16	no	—
783	C₂²⋊C₄	—	47	8	no	—
784	C₂²⋊C₄	—	47	8	no	—
785	C₂²⋊C₄	—	47	8	no	—
786	C₂²⋊C₄	—	47	16	no	—
787	C₂²⋊C₄	—	47	16	no	—
788	C₂²⋊C₄	—	47	8	no	—
789	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
790	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
791	C₄²	—	47	4	no	—
792	C₄²	—	47	4	no	—
793	C₄²	—	47	4	no	—
794	C₄²	—	47	16	no	—
795	C₄²	—	47	8	no	—
796	C₄²	C₂³×D₄₇	1	4	yes	—
797	C₄²	C₂³×D₄₇	1	8	yes	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	47	4	no	—
801	C₂³	—	47	8	no	—
802	C₂³	—	47	2	no	—
803	C₂³	—	47	4	no	—
804	C₂³	—	47	32	no	—
805	C₂³	—	94	4	no	—
806	C₂³	—	94	2	no	—
807	C₂³	—	94	4	no	—
808	C₂³	—	94	2	no	—
809	C₂³	—	188	8	no	—
810	C₂³	—	188	8	no	—
811	C₂³	—	188	32	no	—
812	C₂³	C₂×Q₈×D₄₇	1	8	yes	—
813	C₂³	C₂⁴×D₄₇	1	4	yes	—
814	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
815	Q₈	—	2	8	no	—
816	Q₈	—	2	16	no	—
817	Q₈	—	4	16	no	—
818	Q₈	—	94	8	no	—
819	Q₈	—	188	8	no	—
820	Q₈	—	188	8	no	—
821	Q₈	—	188	16	no	—
822	D₄	—	47	32	no	—
823	D₄	—	47	16	no	—
824	D₄	C₂×Q₈×D₄₇	1	16	yes	complemented
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	16	no	—
831	C₂×C₄	—	4	16	no	—
832	C₂×C₄	—	47	4	no	—
833	C₂×C₄	—	47	2	no	—
834	C₂×C₄	—	47	16	no	—
835	C₂×C₄	—	47	2	no	—
836	C₂×C₄	—	47	2	no	—
837	C₂×C₄	—	47	4	no	—
838	C₂×C₄	—	47	8	no	—
839	C₂×C₄	—	47	4	no	—
840	C₂×C₄	—	47	4	no	—
841	C₂×C₄	—	94	2	no	—
842	C₂×C₄	—	94	4	no	—
843	C₂×C₄	—	94	4	no	—
844	C₂×C₄	—	94	8	no	—
845	C₂×C₄	—	94	4	no	—
846	C₂×C₄	—	94	2	no	—
847	C₂×C₄	—	94	8	no	—
848	C₂×C₄	—	94	16	no	—
849	C₂×C₄	—	188	16	no	—
850	C₂×C₄	—	188	4	no	—
851	C₂×C₄	—	188	8	no	—
852	C₂×C₄	—	188	8	no	—
853	C₂×C₄	—	188	16	no	—
854	C₂×C₄	—	188	16	no	—
855	C₂×C₄	—	188	8	no	—
856	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
857	C₂×C₄	#13094069	1	4	yes	—
858	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
859	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
860	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
861	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
862	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
863	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
864	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	16	no	—
868	C₂²	—	47	4	no	—
869	C₂²	—	47	8	no	—
870	C₂²	—	94	4	no	—
871	C₂²	—	94	2	no	—
872	C₂²	—	94	4	no	—
873	C₂²	—	94	2	no	—
874	C₂²	—	94	8	no	—
875	C₂²	—	94	16	no	—
876	C₂²	—	188	32	no	—
877	C₂²	C₂²×Q₈×D₄₇	1	8	yes	—
878	C₂²	C₂²×Q₈×D₄₇	1	2	yes	—
879	C₂²	C₂×#13094069	1	2	yes	—
880	C₂²	#15689960	1	2	yes	—
881	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
882	C₄	—	2	4	no	—
883	C₄	—	2	4	no	—
884	C₄	—	2	8	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	2	no	—
887	C₄	—	47	4	no	—
888	C₄	—	94	2	no	—
889	C₄	—	94	4	no	—
890	C₄	—	94	4	no	—
891	C₄	—	94	8	no	—
892	C₄	—	94	4	no	—
893	C₄	—	94	2	no	—
894	C₄	C₂²×Q₈×D₄₇	1	4	yes	—
895	C₄	C₂×#13094069	1	4	yes	—
896	C₂	—	2	8	no	—
897	C₂	—	94	4	no	—
898	C₂	—	94	8	no	—
899	C₂	#20257183	1	4	yes	direct product factor
900	C₂	C₂³×Q₈×D₄₇	1	1	yes	characteristic
901	C₂	C₂²×#13094069	1	1	yes	characteristic
902	C₂	C₂×#15689960	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×D₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
prime radical	C₂²×D₄×D₄₇	C₂²
hypercenter	C₂×D₄×Q₈	D₄₇
hypocenter	C₄₇	C₂×#3501
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #20257183	C₂	direct (N × H)
2. C₂×#15689834	C₂	semidirect
3. C₂×#15689833	C₂	semidirect
4. C₂×#15689832	C₂	semidirect
5. C₂×#15689831	C₂	semidirect
6. C₂×#15689830	C₂	semidirect
7. C₂×#15689827	C₂	semidirect
8. C₂×#15689788	C₂	semidirect
9. C₂×Q₈×C₂²⋊D₄₇	C₂	semidirect
10. C₂×#15689750	C₂	semidirect
11. C₂×#15689748	C₂	semidirect
12. C₂×#15689678	C₂	semidirect
13. C₂×#15689677	C₂	semidirect
14. C₂²×#13094000	C₂	semidirect
15. C₂×C₂²⋊Q₈×D₄₇	C₂	semidirect
18. C₂×D₄×Q₈×C₄₇	C₂	semidirect
19. C₂²×Q₈×D₄₇	C₂²	semidirect
22. #15689834	C₂²	semidirect
23. #15689833	C₂²	semidirect
24. #15689832	C₂²	semidirect
25. #15689831	C₂²	semidirect
26. #15689830	C₂²	semidirect
27. #15689827	C₂²	semidirect
28. #15689788	C₂²	semidirect
29. Q₈×C₂²⋊D₄₇	C₂²	semidirect
30. #15689750	C₂²	semidirect
31. #15689748	C₂²	semidirect
32. #15689678	C₂²	semidirect
33. #15689677	C₂²	semidirect
34. C₂×#13094024	C₂²	semidirect
35. C₂×#13094023	C₂²	semidirect
36. C₂×#13094023	C₂²	semidirect
37. C₂×#13094022	C₂²	semidirect
38. C₂×#13094022	C₂²	semidirect
39. C₂×#13094016	C₂²	semidirect
40. C₂×#13094015	C₂²	semidirect
41. C₂×#13094015	C₂²	semidirect
42. C₂×#13094014	C₂²	semidirect
43. C₂×#13094014	C₂²	semidirect
46. C₂×#13094004	C₂²	semidirect
47. C₂×#13094003	C₂²	semidirect
48. C₂×#13094003	C₂²	semidirect
51. C₂×#13094002	C₂²	semidirect
52. C₂×#13094002	C₂²	semidirect
53. C₂×#13094001	C₂²	semidirect
54. C₂×#13094001	C₂²	semidirect
55. C₂×#13094001	C₂²	semidirect
59. C₂×#13094000	C₂²	semidirect
60. C₂×#13094000	C₂²	semidirect
61. C₂×#13094000	C₂²	semidirect
62. C₂×#13094000	C₂²	semidirect
63. C₂×#13094000	C₂²	semidirect
64. C₂²⋊Q₈×D₄₇	C₂²	semidirect
66. C₂×Q₈×Dic₄₇	C₂²	semidirect
67. C₂×C₄×Dic₉₄	C₂²	semidirect
68. C₂×C₄×Dic₉₄	C₂²	semidirect
69. C₂×#13093989	C₂²	semidirect
83. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
84. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
86. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
87. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
92. C₂³×Q₈×C₄₇	C₂²	semidirect
93. D₄×Q₈×C₄₇	C₂²	semidirect
94. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
95. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
97. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
98. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
107. C₂×Q₈×D₄₇	C₂³	semidirect
110. C₂×D₄×D₄₇	Q₈	semidirect
124. #13094024	C₂³	semidirect
125. #13094023	C₂³	semidirect
126. #13094023	C₂³	semidirect
127. #13094022	C₂³	semidirect
128. #13094022	C₂³	semidirect
129. #13094016	C₂³	semidirect
130. #13094015	C₂³	semidirect
131. #13094015	C₂³	semidirect
132. #13094014	C₂³	semidirect
133. #13094014	C₂³	semidirect
136. #13094004	C₂³	semidirect
137. #13094003	C₂³	semidirect
138. #13094003	C₂³	semidirect
141. #13094002	C₂³	semidirect
142. #13094002	C₂³	semidirect
143. #13094001	C₂³	semidirect
144. #13094001	C₂³	semidirect
145. #13094001	C₂³	semidirect
149. #13094000	C₂³	semidirect
150. #13094000	C₂³	semidirect
151. #13094000	C₂³	semidirect
152. #13094000	C₂³	semidirect
153. Q₈×Dic₄₇	C₂³	semidirect
154. C₄×Dic₉₄	C₂³	semidirect
155. C₄×Dic₉₄	C₂³	semidirect
156. #13093989	C₂³	semidirect
176. C₂×C₄⋊Dic₄₇	C₂³	semidirect
188. C₂×Dic₄₇⋊C₄	C₂³	semidirect
190. C₄⋊C₄×D₄₇	C₂³	semidirect
191. C₄⋊C₄×D₄₇	C₂³	semidirect
214. C₂²×Q₈×C₄₇	C₂³	semidirect
218. C₄⋊Q₈×C₄₇	C₂³	semidirect
219. C₄⋊Q₈×C₄₇	C₂³	semidirect
220. C₂²⋊Q₈×C₄₇	C₂³	semidirect
221. C₂²⋊Q₈×C₄₇	C₂³	semidirect
222. C₄×Q₈×C₄₇	C₂³	semidirect
238. C₂³×D₄₇	C₂×Q₈	semidirect
249. C₂×D₄×C₄₇	C₂×Q₈	semidirect
262. C₂×C₂²⋊D₄₇	C₂×Q₈	semidirect
276. D₄×D₄₇	C₂×Q₈	semidirect
277. C₂×D₁₈₈	C₂×Q₈	semidirect
287. C₂×C₄×D₄₇	C₂×Q₈	semidirect
360. C₂²×D₄₇	C₂²×Q₈	semidirect
366. D₄×C₄₇	C₂²×Q₈	semidirect
383. C₂²⋊D₄₇	C₂²×Q₈	semidirect
400. D₁₈₈	C₂²×Q₈	semidirect
408. C₄×D₄₇	C₂²×Q₈	semidirect
454. C₂×D₄×Q₈	D₄₇	semidirect
464. C₂×C₄₇	#3501	semidirect
471. C₂³×Q₈	C₂×D₄₇	semidirect
482. D₄×Q₈	C₂×D₄₇	semidirect
492. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
493. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
520. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
521. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
527. C₂×C₄×Q₈	C₂×D₄₇	semidirect
552. C₄₇	C₂×#3501	semidirect
564. C₂²×Q₈	C₂²×D₄₇	semidirect
589. C₄⋊Q₈	C₂²×D₄₇	semidirect
590. C₄⋊Q₈	C₂²×D₄₇	semidirect
615. C₂²⋊Q₈	C₂²×D₄₇	semidirect
616. C₂²⋊Q₈	C₂²×D₄₇	semidirect
621. C₄×Q₈	C₂²×D₄₇	semidirect
715. C₂×D₄	Q₈×D₄₇	semidirect
824. D₄	C₂×Q₈×D₄₇	semidirect
899. C₂	#20257183	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257183	2
C₂×#15689834	2
C₂×#15689833	2
C₂×#15689832	2
C₂×#15689831	2
C₂×#15689830	2
C₂×#15689827	2
C₂×#15689788	2
C₂×Q₈×C₂²⋊D₄₇	2
C₂×#15689750	2
C₂×#15689748	2
C₂×#15689678	2
C₂×#15689677	2
C₂²×#13094000	2
C₂×C₂²⋊Q₈×D₄₇	2
C₂×#15689595	2
C₂×C₄×D₄×D₄₇	2
C₂×D₄×Q₈×C₄₇	2
C₂×#3501	47

Subgroups — C2×#20257183 #27124174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257183 #27124174