Subgroups — C₂×#556×D₄₇ #27123286

Order 12032.

7846 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689847	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689846	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689845	C₂	1	2	yes	maximal, complemented
4	C₂×#15689844	C₂	1	2	yes	maximal, complemented
5	C₂×#15689843	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15689842	C₂	1	2	yes	maximal, complemented
7	C₂×#15689841	C₂	1	2	yes	maximal, complemented
8	C₂×#15689840	C₂	1	4	yes	maximal, complemented
9	#556×D₄₇	C₂	1	32	yes	maximal, direct product factor
10	C₂×C₄⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#126×D₄₇	C₂	1	4	yes	maximal, complemented
12	C₂×#124×D₄₇	C₂	1	2	yes	maximal
13	C₂×C₂²⋊Q₈×D₄₇	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×Q₈×D₄₇	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic
17	C₂×#117×D₄₇	C₂	1	2	yes	maximal, complemented
18	C₂×C₄₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×Q₈×D₄₇	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×D₄₇	C₂²	1	2	yes	—
21	C₂²×D₄×D₄₇	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
23	#15689847	C₂²	1	16	yes	complemented
24	#15689846	C₂²	1	16	yes	complemented
25	#15689845	C₂²	1	32	yes	complemented
26	#15689844	C₂²	1	32	yes	complemented
27	#15689843	C₂²	1	16	yes	complemented
28	#15689842	C₂²	1	32	yes	complemented
29	#15689841	C₂²	1	32	yes	complemented
30	#15689840	C₂²	1	64	yes	complemented
31	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
32	C₂×#13094023	C₂²	1	2	yes	complemented
33	C₂×#13094023	C₂²	1	2	yes	complemented
34	C₂×#13094022	C₂²	1	2	yes	complemented
35	C₄⋊Q₈×D₄₇	C₂²	1	16	yes	complemented
36	C₂×#13094019	C₂²	1	4	yes	complemented
37	C₂×#13094019	C₂²	1	4	yes	complemented
38	C₂×#13094019	C₂²	1	4	yes	complemented
39	C₂×#13094018	C₂²	1	4	yes	complemented
40	C₂×#13094017	C₂²	1	4	yes	complemented
41	C₂×#13094017	C₂²	1	4	yes	complemented
42	C₂×#13094017	C₂²	1	4	yes	complemented
43	#126×D₄₇	C₂²	1	64	yes	complemented
44	C₂×#13094013	C₂²	1	2	yes	—
45	C₂×#13094012	C₂²	1	2	yes	—
46	C₂×#13094011	C₂²	1	2	yes	—
47	C₂×#13094010	C₂²	1	4	yes	—
48	C₂×#13094010	C₂²	1	4	yes	—
49	#124×D₄₇	C₂²	1	32	yes	—
50	C₂×#13094004	C₂²	1	2	yes	complemented
51	C₂×#13094003	C₂²	1	2	yes	complemented
52	C₂×#13094002	C₂²	1	4	yes	complemented
53	C₂×#13094001	C₂²	1	4	yes	complemented
54	C₂×#13094000	C₂²	1	2	yes	complemented
55	C₂²⋊Q₈×D₄₇	C₂²	1	32	yes	complemented
56	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
57	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₉₄	C₂²	1	4	yes	complemented
59	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
60	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
61	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
62	C₂×#13093989	C₂²	1	2	yes	complemented
63	C₂×#13093989	C₂²	1	4	yes	complemented
64	C₂×#13093989	C₂²	1	1	yes	characteristic, complemented
65	C₂×#13093989	C₂²	1	2	yes	complemented
66	C₄×Q₈×D₄₇	C₂²	1	32	yes	complemented
67	C₄×Q₈×D₄₇	C₂²	1	16	yes	complemented
68	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
69	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
70	C₂×#13093986	C₂²	1	1	yes	characteristic
71	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
72	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
73	C₄×D₄×D₄₇	C₂²	1	16	yes	—
74	C₂×#13093983	C₂²	1	2	yes	complemented
75	C₂×#13093982	C₂²	1	2	yes	complemented
76	C₂×#13093982	C₂²	1	2	yes	complemented
77	C₂×#13093981	C₂²	1	4	yes	complemented
78	C₂×#13093980	C₂²	1	4	yes	complemented
79	#117×D₄₇	C₂²	1	32	yes	complemented
80	C₂×C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
81	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
83	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
84	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
85	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
86	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
87	C₂×C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
88	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
89	C₂×C₄²×D₄₇	C₂²	1	4	yes	—
90	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
91	C₂×C₄²×D₄₇	C₂²	1	2	yes	—
92	C₄₇×#556	C₂²	1	16	yes	complemented
93	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
94	C₂×#126×C₄₇	C₂²	1	4	yes	complemented
95	C₂×#124×C₄₇	C₂²	1	2	yes	—
96	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
97	C₂×C₄×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×#117×C₄₇	C₂²	1	2	yes	complemented
101	C₂⁴×D₄₇	C₂³	1	2	yes	—
102	C₂²×Dic₉₄	C₂³	1	2	yes	—
103	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
104	C₂²×Dic₉₄	C₂³	1	4	yes	—
105	C₂²×Dic₉₄	C₂³	1	2	yes	—
106	C₂×Q₈×D₄₇	—	2	8	no	—
107	C₂×Q₈×D₄₇	—	2	16	no	—
108	C₂×Q₈×D₄₇	C₂³	1	8	yes	—
109	C₂×Q₈×D₄₇	C₂³	1	16	yes	—
110	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
111	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
112	C₂×D₄×D₄₇	—	2	8	no	—
113	C₂×D₄×D₄₇	C₂³	1	8	yes	—
114	C₂³×Dic₄₇	C₂³	1	2	yes	—
115	C₂²×C₄×D₄₇	—	2	16	no	—
116	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
117	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
118	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
120	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
121	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
122	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
123	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
124	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
125	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
126	#13094024	C₂³	1	8	yes	complemented
127	#13094023	C₂³	1	16	yes	complemented
128	#13094023	C₂³	1	16	yes	complemented
129	#13094022	C₂³	1	16	yes	complemented
130	#13094019	C₂³	1	32	yes	complemented
131	#13094019	C₂³	1	32	yes	complemented
132	#13094019	C₂³	1	32	yes	complemented
133	#13094018	C₂³	1	32	yes	complemented
134	#13094017	C₂³	1	32	yes	complemented
135	#13094017	C₂³	1	32	yes	complemented
136	#13094017	C₂³	1	32	yes	complemented
137	#13094013	C₂³	1	16	yes	—
138	#13094012	C₂³	1	16	yes	—
139	#13094011	C₂³	1	16	yes	—
140	#13094010	C₂³	1	32	yes	—
141	#13094010	C₂³	1	32	yes	—
142	#13094004	C₂³	1	16	yes	complemented
143	#13094003	C₂³	1	16	yes	complemented
144	#13094002	C₂³	1	32	yes	complemented
145	#13094001	C₂³	1	32	yes	complemented
146	#13094000	C₂³	1	16	yes	complemented
147	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
148	Q₈×Dic₄₇	C₂³	1	8	yes	complemented
149	C₄×Dic₉₄	C₂³	1	32	yes	complemented
150	C₄×Dic₉₄	C₂³	1	16	yes	complemented
151	C₄×Dic₉₄	C₂³	1	16	yes	complemented
152	C₄×Dic₉₄	C₂³	1	8	yes	complemented
153	#13093989	C₂³	1	16	yes	complemented
154	#13093989	C₂³	1	32	yes	complemented
155	#13093989	C₂³	1	8	yes	complemented
156	#13093989	C₂³	1	16	yes	complemented
157	C₄×D₁₈₈	C₂³	1	8	yes	—
158	D₄×Dic₄₇	C₂³	1	8	yes	—
159	#13093986	C₂³	1	8	yes	—
160	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
161	(C₂²⋊D₄₇)⋊C₄	C₂³	1	16	yes	—
162	#13093983	C₂³	1	16	yes	complemented
163	#13093982	C₂³	1	16	yes	complemented
164	#13093982	C₂³	1	16	yes	complemented
165	#13093981	C₂³	1	32	yes	complemented
166	#13093980	C₂³	1	32	yes	complemented
167	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
169	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
171	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
173	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
174	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
175	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
176	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
177	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
178	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
179	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
180	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
181	C₄⋊C₄×D₄₇	C₂³	1	8	yes	—
182	C₄⋊C₄×D₄₇	C₂³	1	16	yes	—
183	C₄⋊C₄×D₄₇	C₂³	1	8	yes	—
184	C₄⋊C₄×D₄₇	C₂³	1	32	yes	—
185	C₄⋊C₄×D₄₇	C₂³	1	16	yes	—
186	C₄⋊C₄×D₄₇	C₂³	1	16	yes	—
187	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
188	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
190	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
191	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
192	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
193	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
194	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
195	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
196	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	—
197	C₂²⋊C₄×D₄₇	C₂³	1	16	yes	—
198	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	—
199	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
200	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
201	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
202	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
203	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
204	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
205	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
206	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
207	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
208	C₄²×D₄₇	C₂³	1	32	yes	—
209	C₄²×D₄₇	C₂³	1	8	yes	—
210	C₄²×D₄₇	C₂³	1	16	yes	—
211	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
212	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
213	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
215	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
216	#126×C₄₇	C₂³	1	32	yes	complemented
217	#124×C₄₇	C₂³	1	16	yes	—
218	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
219	C₄×Q₈×C₄₇	C₂³	1	16	yes	complemented
220	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
221	C₄×D₄×C₄₇	C₂³	1	8	yes	—
222	#117×C₄₇	C₂³	1	16	yes	complemented
223	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
225	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
227	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
230	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
232	C₂×C₄²×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	—	2	8	no	—
237	C₂³×D₄₇	—	2	8	no	—
238	C₂³×D₄₇	—	2	8	no	—
239	C₂³×D₄₇	C₂⁴	1	8	yes	—
240	C₂³×D₄₇	C₂⁴	1	2	yes	—
241	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₄₇	—	2	8	no	—
243	C₂×Q₈×C₄₇	—	2	4	no	—
244	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
245	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
246	C₂×D₄×C₄₇	—	2	4	no	—
247	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₄₇	—	2	8	no	—
249	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
255	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₂²⋊D₄₇	—	2	8	no	—
258	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
259	C₂²×Dic₄₇	—	2	8	no	—
260	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
261	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
262	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
263	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
264	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
265	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
266	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
267	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
268	Q₈×D₄₇	—	2	32	no	—
269	Q₈×D₄₇	—	2	64	no	—
270	D₄×D₄₇	—	2	32	no	—
271	C₂×D₁₈₈	—	2	4	no	—
272	C₂×D₁₈₈	C₂⁴	1	4	yes	—
273	C₂×C₄×D₄₇	—	2	8	no	—
274	C₂×C₄×D₄₇	—	2	8	no	—
275	C₂×C₄×D₄₇	—	2	16	no	—
276	C₂×C₄×D₄₇	—	2	8	no	—
277	C₂×C₄×D₄₇	—	2	4	no	—
278	C₂×C₄×D₄₇	—	2	8	no	—
279	C₂×C₄×D₄₇	—	2	8	no	—
280	C₂×C₄×D₄₇	—	2	64	no	—
281	C₂×C₄×D₄₇	#41	1	8	yes	—
282	C₂×C₄×D₄₇	#41	1	8	yes	—
283	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
284	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
285	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
286	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
287	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
288	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
289	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
290	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
291	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
292	C₂×Dic₉₄	—	2	8	no	—
293	C₂×Dic₉₄	—	2	4	no	—
294	C₂×Dic₉₄	—	2	16	no	—
295	C₂×Dic₉₄	—	2	8	no	—
296	C₂×Dic₉₄	C₂⁴	1	8	yes	—
297	C₂×Dic₉₄	C₂⁴	1	4	yes	—
298	C₂×Dic₉₄	C₂⁴	1	16	yes	—
299	C₂×Dic₉₄	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
302	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
306	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
307	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
308	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
309	C₄²×C₄₇	C₂⁴	1	16	yes	—
310	C₄²×C₄₇	C₂⁴	1	4	yes	—
311	C₄²×C₄₇	C₂⁴	1	8	yes	—
312	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
313	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
314	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
315	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
316	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
317	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
318	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
319	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
320	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
321	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
322	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
323	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
324	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
325	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
326	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
327	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
328	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
329	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
330	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
331	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
332	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
333	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
334	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
335	C₄×Dic₄₇	C₂⁴	1	16	yes	—
336	C₄×Dic₄₇	C₂⁴	1	16	yes	—
337	C₄×Dic₄₇	C₂⁴	1	16	yes	—
338	C₄×Dic₄₇	C₂⁴	1	4	yes	—
339	C₄×Dic₄₇	C₂⁴	1	4	yes	—
340	C₄×Dic₄₇	C₂⁴	1	4	yes	—
341	C₄×Dic₄₇	C₂⁴	1	8	yes	—
342	C₄×Dic₄₇	C₂⁴	1	8	yes	—
343	C₄×Dic₄₇	C₂⁴	1	8	yes	—
344	C₂³×C₄₇	—	2	4	no	—
345	C₂³×C₄₇	—	2	4	no	—
346	C₂³×C₄₇	—	2	4	no	—
347	C₂³×C₄₇	C₂⁵	1	4	yes	—
348	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
349	C₂²×D₄₇	—	2	4	no	—
350	C₂²×D₄₇	—	2	4	no	—
351	C₂²×D₄₇	—	2	4	no	—
352	C₂²×D₄₇	—	2	16	no	—
353	C₂²×D₄₇	—	2	16	no	—
354	C₂²×D₄₇	—	2	16	no	—
355	C₂²×D₄₇	—	4	32	no	—
356	C₂²×D₄₇	C₂×#41	1	4	yes	—
357	C₂²×D₄₇	C₂×#41	1	4	yes	—
358	C₂²×D₄₇	2₋¹⁺⁴	1	4	yes	—
359	C₂²×D₄₇	C₂⁵	1	4	yes	—
360	C₂²×D₄₇	C₂⁵	1	2	yes	—
361	Q₈×C₄₇	—	2	16	no	—
362	Q₈×C₄₇	—	2	8	no	—
363	D₄×C₄₇	—	2	8	no	—
364	C₂×C₄×C₄₇	—	2	8	no	—
365	C₂×C₄×C₄₇	—	2	4	no	—
366	C₂×C₄×C₄₇	—	2	4	no	—
367	C₂×C₄×C₄₇	—	2	4	no	—
368	C₂×C₄×C₄₇	—	2	2	no	—
369	C₂×C₄×C₄₇	—	2	16	no	—
370	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
371	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
372	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
373	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
374	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
375	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
376	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
377	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
378	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
379	C₂²⋊D₄₇	—	2	16	no	—
380	C₂×Dic₄₇	—	2	8	no	—
381	C₂×Dic₄₇	—	2	4	no	—
382	C₂×Dic₄₇	—	2	4	no	—
383	C₂×Dic₄₇	—	2	4	no	—
384	C₂×Dic₄₇	—	2	2	no	—
385	C₂×Dic₄₇	—	2	16	no	—
386	C₂×Dic₄₇	C₂×#41	1	4	yes	—
387	C₂×Dic₄₇	C₂×#41	1	4	yes	—
388	C₂×Dic₄₇	C₂⁵	1	4	yes	—
389	C₂×Dic₄₇	C₂⁵	1	4	yes	—
390	C₂×Dic₄₇	C₂⁵	1	2	yes	—
391	C₂×Dic₄₇	C₂⁵	1	8	yes	—
392	C₂×Dic₄₇	C₂⁵	1	4	yes	—
393	C₂×Dic₄₇	C₂⁵	1	2	yes	—
394	C₂×Dic₄₇	C₂⁵	1	2	yes	—
395	D₁₈₈	—	2	8	no	—
396	C₄×D₄₇	—	2	16	no	—
397	C₄×D₄₇	—	2	16	no	—
398	C₄×D₄₇	—	2	32	no	—
399	C₄×D₄₇	—	2	16	no	—
400	C₄×D₄₇	—	2	8	no	—
401	C₄×D₄₇	—	2	16	no	—
402	C₄×D₄₇	—	2	16	no	—
403	C₄×D₄₇	C₂×#41	1	16	yes	—
404	C₄×D₄₇	C₂×#41	1	16	yes	—
405	Dic₉₄	—	2	16	no	—
406	Dic₉₄	—	2	8	no	—
407	Dic₉₄	—	2	32	no	—
408	Dic₉₄	—	2	16	no	—
409	C₂²×#556	—	47	1	no	maximal, Sylow
410	C₂²×C₄₇	—	2	4	no	—
411	C₂²×C₄₇	—	2	4	no	—
412	C₂²×C₄₇	—	2	4	no	—
413	C₂²×C₄₇	—	4	8	no	—
414	C₂²×C₄₇	C₂²×#41	1	2	yes	—
415	C₂²×C₄₇	C₂²×#41	1	2	yes	—
416	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
417	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
418	C₂×D₄₇	—	2	4	no	—
419	C₂×D₄₇	—	2	4	no	—
420	C₂×D₄₇	—	2	4	no	—
421	C₂×D₄₇	—	4	8	no	—
422	C₂×D₄₇	—	4	32	no	—
423	C₂×D₄₇	#556	1	16	yes	direct product factor
424	C₂×D₄₇	C₂²×#41	1	4	yes	—
425	C₂×D₄₇	C₂²×#41	1	4	yes	—
426	C₂×D₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
427	C₄×C₄₇	—	2	8	no	—
428	C₄×C₄₇	—	2	4	no	—
429	C₄×C₄₇	—	2	4	no	—
430	C₄×C₄₇	—	2	4	no	—
431	C₄×C₄₇	—	2	2	no	—
432	C₄×C₄₇	C₂²×#41	1	4	yes	—
433	C₄×C₄₇	C₂²×#41	1	4	yes	—
434	Dic₄₇	—	2	8	no	—
435	Dic₄₇	—	2	4	no	—
436	Dic₄₇	—	2	4	no	—
437	Dic₄₇	—	2	4	no	—
438	Dic₄₇	—	2	2	no	—
439	Dic₄₇	C₂²×#41	1	4	yes	—
440	Dic₄₇	C₂²×#41	1	4	yes	—
441	C₂×#556	—	47	32	no	—
442	C₂×#556	—	47	1	no	—
443	C₂×#556	—	47	4	no	—
444	C₂×#556	—	47	2	no	—
445	C₂×#556	—	47	2	no	—
446	C₂×#556	—	47	2	no	—
447	C₂×#556	—	47	1	no	—
448	C₂×#556	—	47	1	no	—
449	C₂×#556	—	47	2	no	—
450	C₂×#556	D₄₇	1	1	yes	characteristic, direct product factor
451	C₂²×C₄⋊Q₈	—	47	1	no	—
452	C₂²×#126	—	47	4	no	—
453	C₂²×#124	—	47	2	no	—
454	C₂²×C₂²⋊Q₈	—	47	2	no	—
455	C₂²×C₄×Q₈	—	47	1	no	—
456	C₂²×C₄×Q₈	—	47	2	no	—
457	C₂²×C₄×D₄	—	47	1	no	—
458	C₂²×#117	—	47	2	no	—
459	C₂×C₄₇	—	4	4	no	—
460	C₂×C₄₇	C₂×#556	1	4	yes	complemented
461	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
462	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
463	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
464	D₄₇	—	4	4	no	—
465	D₄₇	C₂×#556	1	8	yes	direct product factor
466	C₂³×Q₈	—	47	1	no	—
467	C₂³×Q₈	—	47	2	no	—
468	C₂³×D₄	—	47	1	no	—
469	C₂⁴×C₄	—	47	2	no	—
470	#556	—	47	16	no	—
471	#556	—	47	64	no	—
472	#556	—	47	32	no	—
473	#556	—	47	32	no	—
474	#556	—	47	32	no	—
475	#556	—	47	16	no	—
476	#556	—	47	16	no	—
477	#556	—	47	32	no	—
478	#556	C₂×D₄₇	1	16	yes	direct product factor
479	C₂×C₄⋊Q₈	—	47	2	no	—
480	C₂×C₄⋊Q₈	—	47	16	no	—
481	C₂×C₄⋊Q₈	—	47	2	no	—
482	C₂×C₄⋊Q₈	—	47	2	no	—
483	C₂×C₄⋊Q₈	—	47	1	no	—
484	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
485	C₂×#126	—	47	64	no	—
486	C₂×#126	—	47	4	no	—
487	C₂×#126	—	47	4	no	—
488	C₂×#126	—	47	4	no	—
489	C₂×#126	—	47	4	no	—
490	C₂×#126	—	47	4	no	—
491	C₂×#126	—	47	4	no	—
492	C₂×#126	—	47	4	no	—
493	C₂×#126	C₂×D₄₇	1	4	yes	complemented
494	C₂×#124	—	47	2	no	—
495	C₂×#124	—	47	2	no	—
496	C₂×#124	—	47	32	no	—
497	C₂×#124	—	47	4	no	—
498	C₂×#124	—	47	4	no	—
499	C₂×#124	—	47	2	no	—
500	C₂×#124	C₂×D₄₇	1	2	yes	—
501	C₂×C₂²⋊Q₈	—	47	2	no	—
502	C₂×C₂²⋊Q₈	—	47	2	no	—
503	C₂×C₂²⋊Q₈	—	47	32	no	—
504	C₂×C₂²⋊Q₈	—	47	4	no	—
505	C₂×C₂²⋊Q₈	—	47	2	no	—
506	C₂×C₂²⋊Q₈	—	47	4	no	—
507	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
508	C₂×C₄×Q₈	—	47	2	no	—
509	C₂×C₄×Q₈	—	47	1	no	—
510	C₂×C₄×Q₈	—	47	32	no	—
511	C₂×C₄×Q₈	—	47	16	no	—
512	C₂×C₄×Q₈	—	47	4	no	—
513	C₂×C₄×Q₈	—	47	2	no	—
514	C₂×C₄×Q₈	—	47	2	no	—
515	C₂×C₄×Q₈	—	47	1	no	—
516	C₂×C₄×Q₈	—	47	2	no	—
517	C₂×C₄×Q₈	—	47	4	no	—
518	C₂×C₄×Q₈	—	47	2	no	—
519	C₂×C₄×Q₈	—	47	1	no	—
520	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	complemented
521	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
522	C₂×C₄×D₄	—	47	1	no	—
523	C₂×C₄×D₄	—	47	2	no	—
524	C₂×C₄×D₄	—	47	16	no	—
525	C₂×C₄×D₄	—	47	1	no	—
526	C₂×C₄×D₄	—	47	2	no	—
527	C₂×C₄×D₄	—	47	1	no	—
528	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
529	C₂×#117	—	47	2	no	—
530	C₂×#117	—	47	32	no	—
531	C₂×#117	—	47	2	no	—
532	C₂×#117	—	47	2	no	—
533	C₂×#117	—	47	4	no	—
534	C₂×#117	—	47	4	no	—
535	C₂×#117	C₂×D₄₇	1	2	yes	complemented
536	C₂²×C₄⋊C₄	—	47	1	no	—
537	C₂²×C₄⋊C₄	—	47	2	no	—
538	C₂²×C₄⋊C₄	—	47	1	no	—
539	C₂²×C₄⋊C₄	—	47	4	no	—
540	C₂²×C₄⋊C₄	—	47	2	no	—
541	C₂²×C₄⋊C₄	—	47	2	no	—
542	C₂²×C₂²⋊C₄	—	47	4	no	—
543	C₂²×C₂²⋊C₄	—	47	2	no	—
544	C₂²×C₂²⋊C₄	—	47	4	no	—
545	C₂²×C₄²	—	47	4	no	—
546	C₂²×C₄²	—	47	1	no	—
547	C₂²×C₄²	—	47	2	no	—
548	C₄₇	C₂²×#556	1	1	yes	characteristic, complemented, Sylow
549	C₂⁵	—	47	2	no	—
550	C₂²×Q₈	—	47	8	no	—
551	C₂²×Q₈	—	47	16	no	—
552	C₂²×Q₈	—	47	2	no	—
553	C₂²×Q₈	—	47	1	no	—
554	C₂²×Q₈	—	47	4	no	—
555	C₂²×Q₈	—	47	2	no	—
556	C₂²×Q₈	—	94	8	no	—
557	C₂²×Q₈	—	94	16	no	—
558	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
559	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
560	C₂²×D₄	—	47	2	no	—
561	C₂²×D₄	—	47	8	no	—
562	C₂²×D₄	—	47	1	no	—
563	C₂²×D₄	—	94	8	no	—
564	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
565	C₂³×C₄	—	47	1	no	—
566	C₂³×C₄	—	47	1	no	—
567	C₂³×C₄	—	47	2	no	—
568	C₂³×C₄	—	47	1	no	—
569	C₂³×C₄	—	47	4	no	—
570	C₂³×C₄	—	47	2	no	—
571	C₂³×C₄	—	47	2	no	—
572	C₂³×C₄	—	47	2	no	—
573	C₂³×C₄	—	47	2	no	—
574	C₂³×C₄	—	47	16	no	—
575	C₂³×C₄	—	47	2	no	—
576	C₂³×C₄	—	94	16	no	—
577	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
578	C₄⋊Q₈	—	47	16	no	—
579	C₄⋊Q₈	—	47	16	no	—
580	C₄⋊Q₈	—	47	16	no	—
581	C₄⋊Q₈	—	47	8	no	—
582	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
583	#126	—	47	32	no	—
584	#126	—	47	32	no	—
585	#126	—	47	32	no	—
586	#126	—	47	32	no	—
587	#126	—	47	32	no	—
588	#126	—	47	32	no	—
589	#126	—	47	32	no	—
590	#126	C₂²×D₄₇	1	32	yes	complemented
591	#124	—	47	16	no	—
592	#124	—	47	16	no	—
593	#124	—	47	32	no	—
594	#124	—	47	32	no	—
595	#124	—	47	16	no	—
596	#124	C₂²×D₄₇	1	16	yes	—
597	C₂²⋊Q₈	—	47	16	no	—
598	C₂²⋊Q₈	—	47	16	no	—
599	C₂²⋊Q₈	—	47	32	no	—
600	C₂²⋊Q₈	—	47	16	no	—
601	C₂²⋊Q₈	—	47	32	no	—
602	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
603	C₄×Q₈	—	47	16	no	—
604	C₄×Q₈	—	47	8	no	—
605	C₄×Q₈	—	47	32	no	—
606	C₄×Q₈	—	47	16	no	—
607	C₄×Q₈	—	47	16	no	—
608	C₄×Q₈	—	47	8	no	—
609	C₄×Q₈	—	47	16	no	—
610	C₄×Q₈	—	47	32	no	—
611	C₄×Q₈	—	47	16	no	—
612	C₄×Q₈	—	47	8	no	—
613	C₄×Q₈	C₂²×D₄₇	1	16	yes	complemented
614	C₄×Q₈	C₂²×D₄₇	1	8	yes	complemented
615	C₄×D₄	—	47	8	no	—
616	C₄×D₄	—	47	16	no	—
617	C₄×D₄	—	47	8	no	—
618	C₄×D₄	—	47	16	no	—
619	C₄×D₄	—	47	8	no	—
620	C₄×D₄	C₂²×D₄₇	1	8	yes	—
621	#117	—	47	16	no	—
622	#117	—	47	16	no	—
623	#117	—	47	16	no	—
624	#117	—	47	32	no	—
625	#117	—	47	32	no	—
626	#117	C₂²×D₄₇	1	16	yes	complemented
627	C₂×C₄⋊C₄	—	47	2	no	—
628	C₂×C₄⋊C₄	—	47	1	no	—
629	C₂×C₄⋊C₄	—	47	4	no	—
630	C₂×C₄⋊C₄	—	47	2	no	—
631	C₂×C₄⋊C₄	—	47	2	no	—
632	C₂×C₄⋊C₄	—	47	1	no	—
633	C₂×C₄⋊C₄	—	47	4	no	—
634	C₂×C₄⋊C₄	—	47	4	no	—
635	C₂×C₄⋊C₄	—	47	4	no	—
636	C₂×C₄⋊C₄	—	47	2	no	—
637	C₂×C₄⋊C₄	—	47	2	no	—
638	C₂×C₄⋊C₄	—	47	2	no	—
639	C₂×C₄⋊C₄	—	47	4	no	—
640	C₂×C₄⋊C₄	—	47	2	no	—
641	C₂×C₄⋊C₄	—	47	8	no	—
642	C₂×C₄⋊C₄	—	47	16	no	—
643	C₂×C₄⋊C₄	—	47	8	no	—
644	C₂×C₄⋊C₄	—	47	32	no	—
645	C₂×C₄⋊C₄	—	47	16	no	—
646	C₂×C₄⋊C₄	—	47	16	no	—
647	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
649	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
651	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
652	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
653	C₂×C₂²⋊C₄	—	47	4	no	—
654	C₂×C₂²⋊C₄	—	47	2	no	—
655	C₂×C₂²⋊C₄	—	47	4	no	—
656	C₂×C₂²⋊C₄	—	47	4	no	—
657	C₂×C₂²⋊C₄	—	47	4	no	—
658	C₂×C₂²⋊C₄	—	47	2	no	—
659	C₂×C₂²⋊C₄	—	47	2	no	—
660	C₂×C₂²⋊C₄	—	47	4	no	—
661	C₂×C₂²⋊C₄	—	47	4	no	—
662	C₂×C₂²⋊C₄	—	47	32	no	—
663	C₂×C₂²⋊C₄	—	47	16	no	—
664	C₂×C₂²⋊C₄	—	47	32	no	—
665	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
666	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
668	C₂×C₄²	—	47	4	no	—
669	C₂×C₄²	—	47	4	no	—
670	C₂×C₄²	—	47	4	no	—
671	C₂×C₄²	—	47	1	no	—
672	C₂×C₄²	—	47	1	no	—
673	C₂×C₄²	—	47	1	no	—
674	C₂×C₄²	—	47	2	no	—
675	C₂×C₄²	—	47	2	no	—
676	C₂×C₄²	—	47	2	no	—
677	C₂×C₄²	—	47	32	no	—
678	C₂×C₄²	—	47	8	no	—
679	C₂×C₄²	—	47	16	no	—
680	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
681	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
682	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
683	C₂⁴	—	47	1	no	—
684	C₂⁴	—	47	8	no	—
685	C₂⁴	—	47	2	no	—
686	C₂⁴	—	94	8	no	—
687	C₂⁴	—	94	8	no	—
688	C₂⁴	—	94	8	no	—
689	C₂⁴	C₂³×D₄₇	1	2	yes	—
690	C₂×Q₈	—	2	4	no	—
691	C₂×Q₈	—	2	8	no	—
692	C₂×Q₈	—	47	8	no	—
693	C₂×Q₈	—	47	4	no	—
694	C₂×Q₈	—	47	16	no	—
695	C₂×Q₈	—	47	8	no	—
696	C₂×Q₈	—	94	8	no	—
697	C₂×Q₈	—	94	16	no	—
698	C₂×Q₈	—	94	32	no	—
699	C₂×Q₈	—	94	64	no	—
700	C₂×Q₈	—	94	4	no	—
701	C₂×Q₈	—	94	8	no	—
702	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
703	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	47	8	no	—
706	C₂×D₄	—	47	4	no	—
707	C₂×D₄	—	94	32	no	—
708	C₂×D₄	—	94	8	no	—
709	C₂×D₄	—	94	4	no	—
710	C₂×D₄	C₂³×D₄₇	1	4	yes	—
711	C₂²×C₄	—	2	8	no	—
712	C₂²×C₄	—	47	1	no	—
713	C₂²×C₄	—	47	1	no	—
714	C₂²×C₄	—	47	8	no	—
715	C₂²×C₄	—	47	8	no	—
716	C₂²×C₄	—	47	4	no	—
717	C₂²×C₄	—	47	4	no	—
718	C₂²×C₄	—	47	8	no	—
719	C₂²×C₄	—	47	2	no	—
720	C₂²×C₄	—	47	2	no	—
721	C₂²×C₄	—	47	1	no	—
722	C₂²×C₄	—	47	4	no	—
723	C₂²×C₄	—	47	2	no	—
724	C₂²×C₄	—	47	8	no	—
725	C₂²×C₄	—	47	8	no	—
726	C₂²×C₄	—	47	4	no	—
727	C₂²×C₄	—	47	16	no	—
728	C₂²×C₄	—	47	8	no	—
729	C₂²×C₄	—	47	8	no	—
730	C₂²×C₄	—	47	8	no	—
731	C₂²×C₄	—	94	8	no	—
732	C₂²×C₄	—	94	64	no	—
733	C₂²×C₄	—	94	4	no	—
734	C₂²×C₄	—	94	8	no	—
735	C₂²×C₄	—	94	8	no	—
736	C₂²×C₄	—	94	8	no	—
737	C₂²×C₄	—	94	16	no	—
738	C₂²×C₄	—	94	8	no	—
739	C₂²×C₄	—	94	8	no	—
740	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
741	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
742	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
743	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
744	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
745	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
746	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
747	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
748	C₄⋊C₄	—	47	8	no	—
749	C₄⋊C₄	—	47	16	no	—
750	C₄⋊C₄	—	47	8	no	—
751	C₄⋊C₄	—	47	16	no	—
752	C₄⋊C₄	—	47	16	no	—
753	C₄⋊C₄	—	47	8	no	—
754	C₄⋊C₄	—	47	8	no	—
755	C₄⋊C₄	—	47	16	no	—
756	C₄⋊C₄	—	47	4	no	—
757	C₄⋊C₄	—	47	8	no	—
758	C₄⋊C₄	—	47	4	no	—
759	C₄⋊C₄	—	47	16	no	—
760	C₄⋊C₄	—	47	8	no	—
761	C₄⋊C₄	—	47	8	no	—
762	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
763	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
764	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
765	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
766	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
767	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
768	C₂²⋊C₄	—	47	16	no	—
769	C₂²⋊C₄	—	47	8	no	—
770	C₂²⋊C₄	—	47	16	no	—
771	C₂²⋊C₄	—	47	16	no	—
772	C₂²⋊C₄	—	47	16	no	—
773	C₂²⋊C₄	—	47	8	no	—
774	C₂²⋊C₄	—	47	8	no	—
775	C₂²⋊C₄	—	47	16	no	—
776	C₂²⋊C₄	—	47	16	no	—
777	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
778	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
779	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
780	C₄²	—	47	16	no	—
781	C₄²	—	47	16	no	—
782	C₄²	—	47	16	no	—
783	C₄²	—	47	4	no	—
784	C₄²	—	47	4	no	—
785	C₄²	—	47	4	no	—
786	C₄²	—	47	8	no	—
787	C₄²	—	47	8	no	—
788	C₄²	—	47	8	no	—
789	C₄²	C₂³×D₄₇	1	16	yes	—
790	C₄²	C₂³×D₄₇	1	4	yes	—
791	C₄²	C₂³×D₄₇	1	8	yes	—
792	C₂³	—	2	4	no	—
793	C₂³	—	2	4	no	—
794	C₂³	—	2	4	no	—
795	C₂³	—	47	4	no	—
796	C₂³	—	47	4	no	—
797	C₂³	—	47	4	no	—
798	C₂³	—	47	2	no	—
799	C₂³	—	47	4	no	—
800	C₂³	—	94	16	no	—
801	C₂³	—	94	16	no	—
802	C₂³	—	94	16	no	—
803	C₂³	—	94	4	no	—
804	C₂³	—	94	4	no	—
805	C₂³	—	94	4	no	—
806	C₂³	—	188	32	no	—
807	C₂³	C₂⁴×D₄₇	1	4	yes	—
808	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
809	Q₈	—	2	8	no	—
810	Q₈	—	2	16	no	—
811	Q₈	—	94	16	no	—
812	Q₈	—	94	32	no	—
813	Q₈	—	94	8	no	—
814	Q₈	—	94	16	no	—
815	D₄	—	2	8	no	—
816	D₄	—	94	16	no	—
817	D₄	—	94	8	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	8	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	16	no	—
824	C₂×C₄	—	47	4	no	—
825	C₂×C₄	—	47	4	no	—
826	C₂×C₄	—	47	2	no	—
827	C₂×C₄	—	47	2	no	—
828	C₂×C₄	—	47	16	no	—
829	C₂×C₄	—	47	16	no	—
830	C₂×C₄	—	47	4	no	—
831	C₂×C₄	—	47	4	no	—
832	C₂×C₄	—	47	2	no	—
833	C₂×C₄	—	47	8	no	—
834	C₂×C₄	—	47	4	no	—
835	C₂×C₄	—	94	16	no	—
836	C₂×C₄	—	94	16	no	—
837	C₂×C₄	—	94	8	no	—
838	C₂×C₄	—	94	16	no	—
839	C₂×C₄	—	94	16	no	—
840	C₂×C₄	—	94	32	no	—
841	C₂×C₄	—	94	16	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	16	no	—
848	C₂×C₄	#41×D₄₇	1	4	yes	—
849	C₂×C₄	#41×D₄₇	1	4	yes	—
850	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
851	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
852	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
853	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
854	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
855	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
856	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
857	C₂²	—	2	4	no	—
858	C₂²	—	2	4	no	—
859	C₂²	—	2	4	no	—
860	C₂²	—	4	8	no	—
861	C₂²	—	47	4	no	—
862	C₂²	—	47	4	no	—
863	C₂²	—	47	4	no	—
864	C₂²	—	47	16	no	—
865	C₂²	—	94	4	no	—
866	C₂²	—	94	4	no	—
867	C₂²	—	94	4	no	—
868	C₂²	—	188	32	no	—
869	C₂²	—	188	8	no	—
870	C₂²	C₂×#41×D₄₇	1	2	yes	—
871	C₂²	C₂×#41×D₄₇	1	2	yes	—
872	C₂²	2₋¹⁺⁴×D₄₇	1	2	yes	—
873	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
874	C₄	—	2	4	no	—
875	C₄	—	2	4	no	—
876	C₄	—	2	8	no	—
877	C₄	—	2	4	no	—
878	C₄	—	2	2	no	—
879	C₄	—	47	4	no	—
880	C₄	—	47	4	no	—
881	C₄	—	94	4	no	—
882	C₄	—	94	4	no	—
883	C₄	—	94	8	no	—
884	C₄	—	94	4	no	—
885	C₄	—	94	2	no	—
886	C₄	C₂×#41×D₄₇	1	4	yes	—
887	C₄	C₂×#41×D₄₇	1	4	yes	—
888	C₂	—	4	4	no	—
889	C₂	—	47	8	no	—
890	C₂	—	188	4	no	—
891	C₂	#556×D₄₇	1	4	yes	direct product factor
892	C₂	C₂²×#41×D₄₇	1	1	yes	characteristic
893	C₂	C₂²×#41×D₄₇	1	1	yes	characteristic
894	C₂	C₂×2₋¹⁺⁴×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#556	C₂
socle	C₂³×C₄₇	C₂⁵
prime radical	C₂²×D₄×D₄₇	C₂²
hypercenter	C₂×#556	D₄₇
hypocenter	C₄₇	C₂²×#556
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#556

Complements

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

N	H ≅ G/N	type
1. C₂×#15689847	C₂	semidirect
2. C₂×#15689846	C₂	semidirect
3. C₂×#15689845	C₂	semidirect
4. C₂×#15689844	C₂	semidirect
5. C₂×#15689843	C₂	semidirect
6. C₂×#15689842	C₂	semidirect
7. C₂×#15689841	C₂	semidirect
8. C₂×#15689840	C₂	semidirect
9. #556×D₄₇	C₂	direct (N × H)
10. C₂×C₄⋊Q₈×D₄₇	C₂	semidirect
11. C₂×#126×D₄₇	C₂	semidirect
13. C₂×C₂²⋊Q₈×D₄₇	C₂	semidirect
14. C₂×C₄×Q₈×D₄₇	C₂	semidirect
15. C₂×C₄×Q₈×D₄₇	C₂	semidirect
17. C₂×#117×D₄₇	C₂	semidirect
18. C₂×C₄₇×#556	C₂	semidirect
23. #15689847	C₂²	semidirect
24. #15689846	C₂²	semidirect
25. #15689845	C₂²	semidirect
26. #15689844	C₂²	semidirect
27. #15689843	C₂²	semidirect
28. #15689842	C₂²	semidirect
29. #15689841	C₂²	semidirect
30. #15689840	C₂²	semidirect
31. C₂×#13094024	C₂²	semidirect
32. C₂×#13094023	C₂²	semidirect
33. C₂×#13094023	C₂²	semidirect
34. C₂×#13094022	C₂²	semidirect
35. C₄⋊Q₈×D₄₇	C₂²	semidirect
36. C₂×#13094019	C₂²	semidirect
37. C₂×#13094019	C₂²	semidirect
38. C₂×#13094019	C₂²	semidirect
39. C₂×#13094018	C₂²	semidirect
40. C₂×#13094017	C₂²	semidirect
41. C₂×#13094017	C₂²	semidirect
42. C₂×#13094017	C₂²	semidirect
43. #126×D₄₇	C₂²	semidirect
50. C₂×#13094004	C₂²	semidirect
51. C₂×#13094003	C₂²	semidirect
52. C₂×#13094002	C₂²	semidirect
53. C₂×#13094001	C₂²	semidirect
54. C₂×#13094000	C₂²	semidirect
55. C₂²⋊Q₈×D₄₇	C₂²	semidirect
56. C₂×Q₈×Dic₄₇	C₂²	semidirect
57. C₂×Q₈×Dic₄₇	C₂²	semidirect
58. C₂×C₄×Dic₉₄	C₂²	semidirect
59. C₂×C₄×Dic₉₄	C₂²	semidirect
60. C₂×C₄×Dic₉₄	C₂²	semidirect
61. C₂×C₄×Dic₉₄	C₂²	semidirect
62. C₂×#13093989	C₂²	semidirect
63. C₂×#13093989	C₂²	semidirect
64. C₂×#13093989	C₂²	semidirect
65. C₂×#13093989	C₂²	semidirect
66. C₄×Q₈×D₄₇	C₂²	semidirect
67. C₄×Q₈×D₄₇	C₂²	semidirect
74. C₂×#13093983	C₂²	semidirect
75. C₂×#13093982	C₂²	semidirect
76. C₂×#13093982	C₂²	semidirect
77. C₂×#13093981	C₂²	semidirect
78. C₂×#13093980	C₂²	semidirect
79. #117×D₄₇	C₂²	semidirect
92. C₄₇×#556	C₂²	semidirect
93. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
94. C₂×#126×C₄₇	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
97. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
98. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
100. C₂×#117×C₄₇	C₂²	semidirect
126. #13094024	C₂³	semidirect
127. #13094023	C₂³	semidirect
128. #13094023	C₂³	semidirect
129. #13094022	C₂³	semidirect
130. #13094019	C₂³	semidirect
131. #13094019	C₂³	semidirect
132. #13094019	C₂³	semidirect
133. #13094018	C₂³	semidirect
134. #13094017	C₂³	semidirect
135. #13094017	C₂³	semidirect
136. #13094017	C₂³	semidirect
142. #13094004	C₂³	semidirect
143. #13094003	C₂³	semidirect
144. #13094002	C₂³	semidirect
145. #13094001	C₂³	semidirect
146. #13094000	C₂³	semidirect
147. Q₈×Dic₄₇	C₂³	semidirect
148. Q₈×Dic₄₇	C₂³	semidirect
149. C₄×Dic₉₄	C₂³	semidirect
150. C₄×Dic₉₄	C₂³	semidirect
151. C₄×Dic₉₄	C₂³	semidirect
152. C₄×Dic₉₄	C₂³	semidirect
153. #13093989	C₂³	semidirect
154. #13093989	C₂³	semidirect
155. #13093989	C₂³	semidirect
156. #13093989	C₂³	semidirect
162. #13093983	C₂³	semidirect
163. #13093982	C₂³	semidirect
164. #13093982	C₂³	semidirect
165. #13093981	C₂³	semidirect
166. #13093980	C₂³	semidirect
215. C₄⋊Q₈×C₄₇	C₂³	semidirect
216. #126×C₄₇	C₂³	semidirect
218. C₂²⋊Q₈×C₄₇	C₂³	semidirect
219. C₄×Q₈×C₄₇	C₂³	semidirect
220. C₄×Q₈×C₄₇	C₂³	semidirect
222. #117×C₄₇	C₂³	semidirect
423. C₂×D₄₇	#556	direct (N × H)
450. C₂×#556	D₄₇	direct (N × H)
460. C₂×C₄₇	C₂×#556	semidirect
465. D₄₇	C₂×#556	direct (N × H)
478. #556	C₂×D₄₇	direct (N × H)
484. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
493. C₂×#126	C₂×D₄₇	semidirect
507. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
520. C₂×C₄×Q₈	C₂×D₄₇	semidirect
521. C₂×C₄×Q₈	C₂×D₄₇	semidirect
535. C₂×#117	C₂×D₄₇	semidirect
548. C₄₇	C₂²×#556	semidirect
582. C₄⋊Q₈	C₂²×D₄₇	semidirect
590. #126	C₂²×D₄₇	semidirect
602. C₂²⋊Q₈	C₂²×D₄₇	semidirect
613. C₄×Q₈	C₂²×D₄₇	semidirect
614. C₄×Q₈	C₂²×D₄₇	semidirect
626. #117	C₂²×D₄₇	semidirect
891. C₂	#556×D₄₇	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×#15689847	2
C₂×#15689846	2
C₂×#15689845	2
C₂×#15689844	2
C₂×#15689843	2
C₂×#15689842	2
C₂×#15689841	2
C₂×#15689840	2
#556×D₄₇	2
C₂×C₄⋊Q₈×D₄₇	2
C₂×#126×D₄₇	2
C₂×#124×D₄₇	2
C₂×C₂²⋊Q₈×D₄₇	2
C₂×C₄×Q₈×D₄₇	2
C₂×C₄×D₄×D₄₇	2
C₂×#117×D₄₇	2
C₂×C₄₇×#556	2
C₂²×#556	47

Subgroups — C2×#556×D47 #27123286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#556×D₄₇ #27123286