Subgroups — C₂×#20257184 #27124175

Order 12032.

7738 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257184	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689831	C₂	1	2	yes	maximal, complemented
3	C₂×#15689828	C₂	1	4	yes	maximal, complemented
4	C₂×#15689828	C₂	1	2	yes	maximal, complemented
5	C₂×#15689827	C₂	1	4	yes	maximal, complemented
6	C₂×Q₈×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
7	C₂×#15689786	C₂	1	2	yes	maximal, complemented
8	C₂×#15689752	C₂	1	2	yes	maximal, complemented
9	C₂×#15689749	C₂	1	2	yes	maximal, complemented
10	C₂×#15689748	C₂	1	2	yes	maximal, complemented
11	C₂×#15689675	C₂	1	2	yes	maximal, complemented
12	C₂²×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂²⋊Q₈×D₄₇	C₂	1	2	yes	maximal, complemented
14	C₂×#15689596	C₂	1	2	yes	maximal
15	C₂²×C₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×Q₈×D₄₇	C₂²	1	2	yes	complemented
19	C₂³×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
20	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
21	#15689831	C₂²	1	32	yes	complemented
22	#15689828	C₂²	1	64	yes	complemented
23	#15689828	C₂²	1	32	yes	complemented
24	#15689827	C₂²	1	64	yes	complemented
25	Q₈×C₂²⋊D₄₇	C₂²	1	32	yes	complemented
26	#15689786	C₂²	1	32	yes	complemented
27	#15689752	C₂²	1	32	yes	complemented
28	#15689749	C₂²	1	32	yes	complemented
29	#15689748	C₂²	1	32	yes	complemented
30	#15689675	C₂²	1	32	yes	complemented
31	C₂×#13094023	C₂²	1	4	yes	complemented
32	C₂×#13094023	C₂²	1	2	yes	complemented
33	C₂×#13094022	C₂²	1	4	yes	complemented
34	C₂×#13094022	C₂²	1	2	yes	complemented
35	C₂×#13094014	C₂²	1	4	yes	complemented
36	C₂×#13094014	C₂²	1	4	yes	complemented
37	C₂×#13094014	C₂²	1	4	yes	complemented
38	C₂×#13094004	C₂²	1	4	yes	complemented
39	C₂×#13094004	C₂²	1	2	yes	complemented
40	C₂×#13094003	C₂²	1	2	yes	—
41	C₂×#13094003	C₂²	1	2	yes	—
42	C₂×#13094003	C₂²	1	4	yes	complemented
43	C₂×#13094003	C₂²	1	4	yes	complemented
44	C₂×#13094003	C₂²	1	2	yes	complemented
45	C₂×#13094003	C₂²	1	2	yes	complemented
46	C₂×#13094003	C₂²	1	16	yes	complemented
47	C₂×#13094002	C₂²	1	4	yes	complemented
48	C₂×#13094002	C₂²	1	4	yes	complemented
49	C₂×#13094002	C₂²	1	4	yes	complemented
50	C₂×#13094001	C₂²	1	4	yes	—
51	C₂×#13094001	C₂²	1	4	yes	—
52	C₂×#13094001	C₂²	1	4	yes	complemented
53	C₂×#13094001	C₂²	1	4	yes	complemented
54	C₂×#13094000	C₂²	1	4	yes	complemented
55	C₂×#13094000	C₂²	1	2	yes	complemented
56	C₂²⋊Q₈×D₄₇	C₂²	1	32	yes	complemented
57	#15689596	C₂²	1	32	yes	—
58	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
59	C₂×#13093989	C₂²	1	2	yes	complemented
60	C₂×#13093989	C₂²	1	4	yes	complemented
61	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
62	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
63	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
64	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
65	C₂×C₄×C₂²⋊D₄₇	C₂²	1	16	yes	—
66	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
67	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
68	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
69	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
70	C₂×#13093980	C₂²	1	4	yes	—
71	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
72	C₂²×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
73	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
74	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	complemented
75	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
76	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
77	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
78	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
80	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
81	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
82	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
83	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
84	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
85	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
86	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
87	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	16	yes	complemented
88	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
89	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
90	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
91	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
92	C₂²×Dic₉₄	—	4	4	no	—
93	C₂²×Dic₉₄	C₂³	1	2	yes	—
94	C₂²×Dic₉₄	C₂³	1	4	yes	—
95	C₂²×Dic₉₄	C₂³	1	4	yes	—
96	C₂²×Dic₉₄	C₂³	1	2	yes	—
97	C₂²×Dic₉₄	C₂³	1	8	yes	complemented
98	C₂×Q₈×D₄₇	—	4	8	no	—
99	C₂×Q₈×D₄₇	C₂³	1	16	yes	complemented
100	C₂²×C₂²⋊D₄₇	Q₈	1	16	yes	complemented
101	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
102	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
103	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
104	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
105	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
106	C₂³×Dic₄₇	C₂³	1	2	yes	—
107	C₂³×Dic₄₇	C₂³	1	2	yes	—
108	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
109	C₂²×C₄×D₄₇	—	4	4	no	—
110	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
111	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
112	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
113	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
114	C₂²×C₄×D₄₇	C₂³	1	8	yes	—
115	#13094023	C₂³	1	32	yes	complemented
116	#13094023	C₂³	1	16	yes	complemented
117	#13094022	C₂³	1	32	yes	complemented
118	#13094022	C₂³	1	16	yes	complemented
119	#13094014	C₂³	1	32	yes	complemented
120	#13094014	C₂³	1	32	yes	complemented
121	#13094014	C₂³	1	32	yes	complemented
122	#13094004	C₂³	1	32	yes	complemented
123	#13094004	C₂³	1	16	yes	complemented
124	#13094003	C₂³	1	16	yes	—
125	#13094003	C₂³	1	16	yes	—
126	#13094003	C₂³	1	32	yes	complemented
127	#13094003	C₂³	1	32	yes	complemented
128	#13094003	C₂³	1	16	yes	complemented
129	#13094003	C₂³	1	16	yes	complemented
130	#13094002	C₂³	1	32	yes	complemented
131	#13094002	C₂³	1	32	yes	complemented
132	#13094002	C₂³	1	32	yes	complemented
133	#13094001	C₂³	1	32	yes	—
134	#13094001	C₂³	1	32	yes	—
135	#13094001	C₂³	1	32	yes	complemented
136	#13094001	C₂³	1	32	yes	complemented
137	#13094000	C₂³	1	32	yes	complemented
138	#13094000	C₂³	1	16	yes	complemented
139	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
140	#13093989	C₂³	1	16	yes	complemented
141	#13093989	C₂³	1	32	yes	complemented
142	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
143	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
144	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
145	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
146	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
147	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
148	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	—
149	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	—
150	#13093980	C₂³	1	32	yes	—
151	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
152	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
153	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
154	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
155	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	complemented
156	C₂×Dic₄₇⋊C₄	C₂³	1	8	yes	—
157	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
158	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
159	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
160	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
161	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
162	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
163	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
164	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
165	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
166	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
167	C₂×Dic₄₇⋊C₄	C₂³	1	16	yes	complemented
168	C₄⋊C₄×D₄₇	C₂³	1	32	yes	complemented
169	C₄⋊C₄×D₄₇	C₂³	1	16	yes	complemented
170	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
171	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
172	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
173	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
176	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
177	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
178	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
179	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
180	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
181	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	—
182	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
183	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
184	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
185	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
186	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
187	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₄₇	—	4	4	no	—
189	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
190	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
191	C₂²×Q₈×C₄₇	C₂³	1	8	yes	complemented
192	C₂³×C₄×C₄₇	—	4	4	no	—
193	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
197	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
198	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
202	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
203	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
204	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
205	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
206	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
210	C₂×C₄⋊C₄×C₄₇	C₂³	1	16	yes	complemented
211	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	complemented
212	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
213	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
214	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
215	C₂⁴×C₄₇	—	4	2	no	—
216	C₂⁴×C₄₇	—	4	2	no	—
217	C₂⁴×C₄₇	C₂×Q₈	1	8	yes	complemented
218	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
222	C₂³×D₄₇	—	4	2	no	—
223	C₂³×D₄₇	—	4	2	no	—
224	C₂³×D₄₇	C₂×Q₈	1	8	yes	complemented
225	C₂³×D₄₇	C₂⁴	1	2	yes	—
226	C₂³×D₄₇	C₂⁴	1	4	yes	—
227	C₂×Q₈×C₄₇	—	2	8	no	—
228	C₂×Q₈×C₄₇	—	4	4	no	—
229	C₂×Q₈×C₄₇	—	4	16	no	—
230	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
231	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
232	C₂²×C₄×C₄₇	—	2	4	no	—
233	C₂²×C₄×C₄₇	—	2	4	no	—
234	C₂²×C₄×C₄₇	—	2	4	no	—
235	C₂²×C₄×C₄₇	—	4	16	no	—
236	C₂²×C₄×C₄₇	—	4	2	no	—
237	C₂²×C₄×C₄₇	—	4	2	no	—
238	C₂²×C₄×C₄₇	—	4	2	no	—
239	C₂²×C₄×C₄₇	—	4	4	no	—
240	C₂²×C₄×C₄₇	—	4	4	no	—
241	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
250	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
251	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₂²⋊D₄₇	C₂×Q₈	1	16	yes	complemented
256	C₂×C₂²⋊D₄₇	C₂×Q₈	1	16	yes	complemented
257	C₂×C₂²⋊D₄₇	C₂×Q₈	1	64	yes	complemented
258	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
259	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
260	C₂²×Dic₄₇	—	4	2	no	—
261	C₂²×Dic₄₇	—	4	2	no	—
262	C₂²×Dic₄₇	—	4	4	no	—
263	C₂²×Dic₄₇	—	4	4	no	—
264	C₂²×Dic₄₇	C₂×Q₈	1	8	yes	complemented
265	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
266	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
267	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
268	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
269	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
270	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
271	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
272	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
273	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
274	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
275	Q₈×D₄₇	—	4	32	no	—
276	C₂×C₄×D₄₇	—	2	8	no	—
277	C₂×C₄×D₄₇	—	4	16	no	—
278	C₂×C₄×D₄₇	—	4	4	no	—
279	C₂×C₄×D₄₇	—	4	8	no	—
280	C₂×C₄×D₄₇	—	4	8	no	—
281	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
282	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
283	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
284	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
285	C₂×Dic₉₄	—	2	8	no	—
286	C₂×Dic₉₄	—	4	16	no	—
287	C₂×Dic₉₄	—	4	8	no	—
288	C₂×Dic₉₄	—	4	4	no	—
289	C₂×Dic₉₄	—	4	8	no	—
290	C₂×Dic₉₄	C₂⁴	1	8	yes	—
291	C₂×Dic₉₄	C₂⁴	1	16	yes	—
292	C₂×Dic₉₄	C₂⁴	1	16	yes	—
293	C₂×Dic₉₄	C₂⁴	1	8	yes	—
294	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
295	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
296	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
297	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
298	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
299	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
300	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
301	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
302	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
303	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
304	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
305	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
306	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
307	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
308	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
309	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
310	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
311	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
312	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
313	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
314	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
315	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
316	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
317	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
318	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
319	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
320	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
321	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
322	C₄×Dic₄₇	C₂⁴	1	8	yes	—
323	C₄×Dic₄₇	C₂⁴	1	8	yes	—
324	C₄×Dic₄₇	C₂⁴	1	16	yes	—
325	C₄×Dic₄₇	C₂⁴	1	16	yes	—
326	C₂³×C₄₇	—	2	2	no	—
327	C₂³×C₄₇	—	2	2	no	—
328	C₂³×C₄₇	—	2	2	no	—
329	C₂³×C₄₇	—	2	2	no	—
330	C₂³×C₄₇	—	2	2	no	—
331	C₂³×C₄₇	—	2	2	no	—
332	C₂³×C₄₇	—	4	4	no	—
333	C₂³×C₄₇	—	4	16	no	—
334	C₂³×C₄₇	—	4	4	no	—
335	C₂³×C₄₇	C₂²×Q₈	1	4	yes	—
336	C₂³×C₄₇	C₂²×Q₈	1	4	yes	—
337	C₂³×C₄₇	C₂²×Q₈	1	4	yes	—
338	C₂³×C₄₇	C₂²×Q₈	1	16	yes	complemented
339	C₂³×C₄₇	C₂⁵	1	2	yes	—
340	C₂³×C₄₇	C₂⁵	1	2	yes	—
341	C₂³×C₄₇	C₂⁵	1	2	yes	—
342	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
343	C₂²×D₄₇	—	2	4	no	—
344	C₂²×D₄₇	—	2	4	no	—
345	C₂²×D₄₇	—	4	4	no	—
346	C₂²×D₄₇	—	4	16	no	—
347	C₂²×D₄₇	—	4	4	no	—
348	C₂²×D₄₇	C₂²×Q₈	1	8	yes	—
349	C₂²×D₄₇	C₂²×Q₈	1	16	yes	complemented
350	C₂²×D₄₇	C₂⁵	1	4	yes	—
351	Q₈×C₄₇	—	2	16	no	—
352	Q₈×C₄₇	—	4	8	no	—
353	C₂×C₄×C₄₇	—	2	2	no	—
354	C₂×C₄×C₄₇	—	2	8	no	—
355	C₂×C₄×C₄₇	—	2	2	no	—
356	C₂×C₄×C₄₇	—	2	2	no	—
357	C₂×C₄×C₄₇	—	2	8	no	—
358	C₂×C₄×C₄₇	—	2	8	no	—
359	C₂×C₄×C₄₇	—	2	8	no	—
360	C₂×C₄×C₄₇	—	2	8	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	8	no	—
365	C₂×C₄×C₄₇	—	4	8	no	—
366	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
367	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
368	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
369	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
370	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
371	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
372	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
373	C₂²⋊D₄₇	C₂²×Q₈	1	32	yes	complemented
374	C₂²⋊D₄₇	C₂²×Q₈	1	32	yes	complemented
375	C₂×Dic₄₇	—	2	8	no	—
376	C₂×Dic₄₇	—	2	4	no	—
377	C₂×Dic₄₇	—	2	4	no	—
378	C₂×Dic₄₇	—	2	8	no	—
379	C₂×Dic₄₇	—	4	8	no	—
380	C₂×Dic₄₇	—	4	4	no	—
381	C₂×Dic₄₇	—	4	4	no	—
382	C₂×Dic₄₇	—	4	8	no	—
383	C₂×Dic₄₇	C₂²×Q₈	1	8	yes	—
384	C₂×Dic₄₇	C₂²×Q₈	1	16	yes	complemented
385	C₂×Dic₄₇	C₂⁵	1	4	yes	—
386	C₂×Dic₄₇	C₂⁵	1	8	yes	—
387	C₂×Dic₄₇	C₂⁵	1	8	yes	—
388	C₂×Dic₄₇	C₂⁵	1	4	yes	—
389	C₂×Dic₄₇	C₂⁵	1	4	yes	—
390	C₄×D₄₇	—	2	16	no	—
391	C₄×D₄₇	—	4	8	no	—
392	C₄×D₄₇	—	4	16	no	—
393	C₄×D₄₇	—	4	16	no	—
394	Dic₉₄	—	2	16	no	—
395	Dic₉₄	—	4	8	no	—
396	Dic₉₄	—	4	16	no	—
397	Dic₉₄	—	4	16	no	—
398	C₂×#3501	—	47	1	no	maximal, Sylow
399	C₂²×C₄₇	—	2	2	no	—
400	C₂²×C₄₇	—	2	2	no	—
401	C₂²×C₄₇	—	2	2	no	—
402	C₂²×C₄₇	—	2	2	no	—
403	C₂²×C₄₇	—	2	2	no	—
404	C₂²×C₄₇	—	2	2	no	—
405	C₂²×C₄₇	—	2	8	no	—
406	C₂²×C₄₇	—	2	8	no	—
407	C₂²×C₄₇	—	2	8	no	—
408	C₂²×C₄₇	—	4	16	no	—
409	C₂²×C₄₇	C₂³×Q₈	1	4	yes	—
410	C₂²×C₄₇	C₂³×Q₈	1	4	yes	—
411	C₂²×C₄₇	C₂³×Q₈	1	4	yes	—
412	C₂²×C₄₇	C₂³×Q₈	1	2	yes	—
413	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
414	C₂²×C₄₇	#585	1	2	yes	—
415	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
416	C₂×D₄₇	—	2	4	no	—
417	C₂×D₄₇	—	2	4	no	—
418	C₂×D₄₇	—	2	16	no	—
419	C₂×D₄₇	—	4	16	no	—
420	C₂×D₄₇	C₂³×Q₈	1	8	yes	—
421	C₄×C₄₇	—	2	2	no	—
422	C₄×C₄₇	—	2	8	no	—
423	C₄×C₄₇	—	2	2	no	—
424	C₄×C₄₇	—	2	2	no	—
425	C₄×C₄₇	—	2	8	no	—
426	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
427	Dic₄₇	—	2	8	no	—
428	Dic₄₇	—	2	4	no	—
429	Dic₄₇	—	2	4	no	—
430	Dic₄₇	—	2	8	no	—
431	Dic₄₇	C₂³×Q₈	1	8	yes	—
432	#3501	—	47	32	no	—
433	C₂×#554	—	47	4	no	—
434	C₂×#554	—	47	2	no	—
435	C₂×#554	—	47	2	no	—
436	C₂×#554	—	47	4	no	—
437	C₂×D₄×Q₈	—	47	2	no	—
438	C₂×D₄×Q₈	—	47	2	no	—
439	C₂×#544	—	47	2	no	—
440	C₂×#543	—	47	2	no	—
441	C₂×#543	—	47	2	no	—
442	C₂×#533	—	47	2	no	—
443	C₂²×C₂²⋊Q₈	—	47	1	no	—
444	C₂²×C₂²⋊Q₈	—	47	2	no	—
445	C₂²×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
446	C₂×#518	—	47	2	no	—
447	C₂²×C₄×D₄	—	47	1	no	—
448	C₂×C₄₇	—	2	4	no	—
449	C₂×C₄₇	—	2	4	no	—
450	C₂×C₄₇	—	2	4	no	—
451	C₂×C₄₇	#3501	1	4	yes	complemented
452	C₂×C₄₇	C₂⁴×Q₈	1	1	yes	characteristic
453	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
455	D₄₇	—	2	8	no	—
456	C₂³×Q₈	—	47	2	no	—
457	C₂³×Q₈	—	47	1	no	—
458	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
459	C₂³×D₄	—	47	1	no	—
460	C₂⁴×C₄	—	47	1	no	—
461	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
462	#554	—	47	64	no	—
463	#554	—	47	32	no	—
464	#554	—	47	32	no	—
465	#554	—	47	64	no	—
466	D₄×Q₈	—	47	32	no	—
467	D₄×Q₈	—	47	32	no	—
468	#544	—	47	32	no	—
469	#543	—	47	32	no	—
470	#543	—	47	32	no	—
471	#533	—	47	32	no	—
472	C₂×C₄⋊Q₈	—	47	2	no	—
473	C₂×C₄⋊Q₈	—	47	4	no	—
474	C₂×C₄⋊Q₈	—	47	2	no	—
475	C₂×C₄⋊Q₈	—	47	4	no	—
476	C₂×#125	—	47	4	no	—
477	C₂×#125	—	47	4	no	—
478	C₂×#125	—	47	4	no	—
479	C₂×C₂²⋊Q₈	—	47	2	no	—
480	C₂×C₂²⋊Q₈	—	47	4	no	—
481	C₂×C₂²⋊Q₈	—	47	2	no	—
482	C₂×C₂²⋊Q₈	—	47	2	no	—
483	C₂×C₂²⋊Q₈	—	47	2	no	—
484	C₂×C₂²⋊Q₈	—	47	2	no	—
485	C₂×C₂²⋊Q₈	—	47	16	no	—
486	C₂×C₂²⋊Q₈	—	47	4	no	—
487	C₂×C₂²⋊Q₈	—	47	4	no	—
488	C₂×C₂²⋊Q₈	—	47	32	no	—
489	C₂×C₂²⋊Q₈	—	47	2	no	—
490	C₂×C₂²⋊Q₈	—	47	4	no	—
491	C₂×C₂²⋊Q₈	—	47	4	no	—
492	C₂×C₂²⋊Q₈	—	47	4	no	—
493	C₂×C₂²⋊Q₈	—	47	4	no	—
494	C₂×C₂²⋊Q₈	—	47	4	no	—
495	C₂×C₂²⋊Q₈	—	47	4	no	—
496	C₂×C₂²⋊Q₈	—	47	4	no	—
497	C₂×C₂²⋊Q₈	—	47	4	no	—
498	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
499	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
500	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
501	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
502	C₂×C₂²⋊Q₈	C₂×D₄₇	1	16	yes	complemented
503	#518	—	47	32	no	—
504	C₂×C₄×Q₈	—	47	2	no	—
505	C₂×C₄×Q₈	—	47	2	no	—
506	C₂×C₄×Q₈	—	47	4	no	—
507	C₂×C₄×D₄	—	47	2	no	—
508	C₂×C₄×D₄	—	47	2	no	—
509	C₂×C₄×D₄	—	47	2	no	—
510	C₂×C₄×D₄	—	47	2	no	—
511	C₂×C₄×D₄	—	47	16	no	—
512	C₂×C₄×D₄	—	47	4	no	—
513	C₂×C₄×D₄	—	47	4	no	—
514	C₂×C₄×D₄	—	47	4	no	—
515	C₂×C₄×D₄	—	47	4	no	—
516	C₂×#117	—	47	4	no	—
517	C₂²×C₄⋊C₄	—	47	1	no	—
518	C₂²×C₄⋊C₄	—	47	2	no	—
519	C₂²×C₄⋊C₄	—	47	1	no	—
520	C₂²×C₄⋊C₄	—	47	4	no	—
521	C₂²×C₄⋊C₄	—	47	2	no	—
522	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
523	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
524	C₂²×C₂²⋊C₄	—	47	1	no	—
525	C₂²×C₂²⋊C₄	—	47	2	no	—
526	C₂²×C₂²⋊C₄	—	47	1	no	—
527	C₂²×C₂²⋊C₄	—	47	4	no	—
528	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
529	C₂²×C₄²	—	47	1	no	—
530	C₄₇	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
531	C₂⁵	—	47	1	no	—
532	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
533	C₂²×Q₈	—	4	4	no	—
534	C₂²×Q₈	—	47	16	no	—
535	C₂²×Q₈	—	47	2	no	—
536	C₂²×Q₈	—	47	4	no	—
537	C₂²×Q₈	—	47	2	no	—
538	C₂²×Q₈	—	47	4	no	—
539	C₂²×Q₈	—	47	8	no	—
540	C₂²×Q₈	—	188	4	no	—
541	C₂²×Q₈	—	188	8	no	—
542	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
543	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
544	C₂²×Q₈	C₂²×D₄₇	1	8	yes	complemented
545	C₂²×D₄	—	47	16	no	—
546	C₂²×D₄	—	47	2	no	—
547	C₂²×D₄	—	47	2	no	—
548	C₂²×D₄	—	47	8	no	—
549	C₂³×C₄	—	4	4	no	—
550	C₂³×C₄	—	47	1	no	—
551	C₂³×C₄	—	47	1	no	—
552	C₂³×C₄	—	47	2	no	—
553	C₂³×C₄	—	47	2	no	—
554	C₂³×C₄	—	47	1	no	—
555	C₂³×C₄	—	47	2	no	—
556	C₂³×C₄	—	47	4	no	—
557	C₂³×C₄	—	47	4	no	—
558	C₂³×C₄	—	47	2	no	—
559	C₂³×C₄	—	47	8	no	—
560	C₂³×C₄	—	188	4	no	—
561	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
562	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
563	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
564	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
565	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
566	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
567	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
568	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
569	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
570	C₄⋊Q₈	—	47	16	no	—
571	C₄⋊Q₈	—	47	32	no	—
572	C₄⋊Q₈	—	47	16	no	—
573	C₄⋊Q₈	—	47	32	no	—
574	#125	—	47	32	no	—
575	#125	—	47	32	no	—
576	#125	—	47	32	no	—
577	C₂²⋊Q₈	—	47	16	no	—
578	C₂²⋊Q₈	—	47	32	no	—
579	C₂²⋊Q₈	—	47	16	no	—
580	C₂²⋊Q₈	—	47	16	no	—
581	C₂²⋊Q₈	—	47	16	no	—
582	C₂²⋊Q₈	—	47	16	no	—
583	C₂²⋊Q₈	—	47	32	no	—
584	C₂²⋊Q₈	—	47	32	no	—
585	C₂²⋊Q₈	—	47	16	no	—
586	C₂²⋊Q₈	—	47	32	no	—
587	C₂²⋊Q₈	—	47	32	no	—
588	C₂²⋊Q₈	—	47	32	no	—
589	C₂²⋊Q₈	—	47	32	no	—
590	C₂²⋊Q₈	—	47	32	no	—
591	C₂²⋊Q₈	—	47	32	no	—
592	C₂²⋊Q₈	—	47	32	no	—
593	C₂²⋊Q₈	—	47	32	no	—
594	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	—
595	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	—
596	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
597	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
598	C₄×Q₈	—	47	16	no	—
599	C₄×Q₈	—	47	16	no	—
600	C₄×Q₈	—	47	32	no	—
601	C₄×D₄	—	47	16	no	—
602	C₄×D₄	—	47	16	no	—
603	C₄×D₄	—	47	16	no	—
604	C₄×D₄	—	47	16	no	—
605	C₄×D₄	—	47	32	no	—
606	C₄×D₄	—	47	32	no	—
607	C₄×D₄	—	47	32	no	—
608	C₄×D₄	—	47	32	no	—
609	#117	—	47	32	no	—
610	C₂×C₄⋊C₄	—	47	4	no	—
611	C₂×C₄⋊C₄	—	47	2	no	—
612	C₂×C₄⋊C₄	—	47	2	no	—
613	C₂×C₄⋊C₄	—	47	2	no	—
614	C₂×C₄⋊C₄	—	47	8	no	—
615	C₂×C₄⋊C₄	—	47	4	no	—
616	C₂×C₄⋊C₄	—	47	2	no	—
617	C₂×C₄⋊C₄	—	47	4	no	—
618	C₂×C₄⋊C₄	—	47	4	no	—
619	C₂×C₄⋊C₄	—	47	4	no	—
620	C₂×C₄⋊C₄	—	47	16	no	—
621	C₂×C₄⋊C₄	—	47	8	no	—
622	C₂×C₄⋊C₄	—	47	4	no	—
623	C₂×C₄⋊C₄	—	47	4	no	—
624	C₂×C₄⋊C₄	—	47	4	no	—
625	C₂×C₄⋊C₄	—	47	4	no	—
626	C₂×C₄⋊C₄	—	47	4	no	—
627	C₂×C₄⋊C₄	—	47	32	no	—
628	C₂×C₄⋊C₄	—	47	16	no	—
629	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
630	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
633	C₂×C₄⋊C₄	C₂²×D₄₇	1	16	yes	complemented
634	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	complemented
635	C₂×C₂²⋊C₄	—	47	4	no	—
636	C₂×C₂²⋊C₄	—	47	2	no	—
637	C₂×C₂²⋊C₄	—	47	2	no	—
638	C₂×C₂²⋊C₄	—	47	4	no	—
639	C₂×C₂²⋊C₄	—	47	8	no	—
640	C₂×C₂²⋊C₄	—	47	16	no	—
641	C₂×C₂²⋊C₄	—	47	2	no	—
642	C₂×C₂²⋊C₄	—	47	2	no	—
643	C₂×C₂²⋊C₄	—	47	4	no	—
644	C₂×C₂²⋊C₄	—	47	4	no	—
645	C₂×C₂²⋊C₄	—	47	8	no	—
646	C₂×C₂²⋊C₄	—	47	32	no	—
647	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
648	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
649	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
650	C₂×C₄²	—	47	4	no	—
651	C₂×C₄²	—	47	4	no	—
652	C₂×C₄²	—	47	2	no	—
653	C₂×C₄²	—	47	2	no	—
654	C₂×C₄²	—	47	8	no	—
655	C₂⁴	—	4	2	no	—
656	C₂⁴	—	4	2	no	—
657	C₂⁴	—	47	2	no	—
658	C₂⁴	—	47	8	no	—
659	C₂⁴	—	47	4	no	—
660	C₂⁴	—	188	2	no	—
661	C₂⁴	—	188	2	no	—
662	C₂⁴	Q₈×D₄₇	1	8	yes	complemented
663	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
664	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
665	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
666	C₂⁴	C₂³×D₄₇	1	4	yes	—
667	C₂×Q₈	—	2	8	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	—	4	16	no	—
670	C₂×Q₈	—	47	8	no	—
671	C₂×Q₈	—	47	16	no	—
672	C₂×Q₈	—	47	8	no	—
673	C₂×Q₈	—	47	16	no	—
674	C₂×Q₈	—	94	8	no	—
675	C₂×Q₈	—	188	8	no	—
676	C₂×Q₈	—	188	4	no	—
677	C₂×Q₈	—	188	8	no	—
678	C₂×Q₈	—	188	16	no	—
679	C₂×Q₈	—	188	32	no	—
680	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
681	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
682	C₂×D₄	—	47	16	no	—
683	C₂×D₄	—	47	16	no	—
684	C₂×D₄	—	47	64	no	—
685	C₂×D₄	—	47	8	no	—
686	C₂×D₄	—	47	8	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	4	16	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	4	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	—	47	8	no	—
697	C₂²×C₄	—	47	4	no	—
698	C₂²×C₄	—	47	2	no	—
699	C₂²×C₄	—	47	2	no	—
700	C₂²×C₄	—	47	4	no	—
701	C₂²×C₄	—	47	4	no	—
702	C₂²×C₄	—	47	2	no	—
703	C₂²×C₄	—	47	4	no	—
704	C₂²×C₄	—	47	8	no	—
705	C₂²×C₄	—	47	8	no	—
706	C₂²×C₄	—	47	4	no	—
707	C₂²×C₄	—	47	8	no	—
708	C₂²×C₄	—	47	16	no	—
709	C₂²×C₄	—	47	16	no	—
710	C₂²×C₄	—	47	8	no	—
711	C₂²×C₄	—	94	8	no	—
712	C₂²×C₄	—	188	16	no	—
713	C₂²×C₄	—	188	8	no	—
714	C₂²×C₄	—	188	4	no	—
715	C₂²×C₄	—	188	8	no	—
716	C₂²×C₄	—	188	4	no	—
717	C₂²×C₄	—	188	2	no	—
718	C₂²×C₄	—	188	2	no	—
719	C₂²×C₄	—	188	4	no	—
720	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
721	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
722	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
723	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
724	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
725	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
726	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
727	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
728	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
729	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
730	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
731	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
732	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
733	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
734	C₄⋊C₄	—	47	16	no	—
735	C₄⋊C₄	—	47	8	no	—
736	C₄⋊C₄	—	47	8	no	—
737	C₄⋊C₄	—	47	16	no	—
738	C₄⋊C₄	—	47	16	no	—
739	C₄⋊C₄	—	47	16	no	—
740	C₄⋊C₄	—	47	16	no	—
741	C₄⋊C₄	—	47	16	no	—
742	C₄⋊C₄	—	47	16	no	—
743	C₄⋊C₄	—	47	16	no	—
744	C₄⋊C₄	—	47	8	no	—
745	C₄⋊C₄	—	47	8	no	—
746	C₄⋊C₄	—	47	16	no	—
747	C₄⋊C₄	—	47	16	no	—
748	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
749	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
750	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
751	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
752	C₂²⋊C₄	—	47	16	no	—
753	C₂²⋊C₄	—	47	8	no	—
754	C₂²⋊C₄	—	47	8	no	—
755	C₂²⋊C₄	—	47	16	no	—
756	C₂²⋊C₄	—	47	8	no	—
757	C₂²⋊C₄	—	47	8	no	—
758	C₂²⋊C₄	—	47	16	no	—
759	C₂²⋊C₄	—	47	16	no	—
760	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
761	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
762	C₄²	—	47	8	no	—
763	C₄²	—	47	8	no	—
764	C₄²	—	47	16	no	—
765	C₄²	—	47	16	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	4	4	no	—
773	C₂³	—	4	16	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	47	8	no	—
776	C₂³	—	47	4	no	—
777	C₂³	—	47	16	no	—
778	C₂³	—	94	4	no	—
779	C₂³	—	94	4	no	—
780	C₂³	—	188	4	no	—
781	C₂³	—	188	4	no	—
782	C₂³	—	188	16	no	—
783	C₂³	C₂×Q₈×D₄₇	1	4	yes	—
784	C₂³	C₂×Q₈×D₄₇	1	4	yes	—
785	C₂³	C₂×Q₈×D₄₇	1	4	yes	—
786	C₂³	C₂×Q₈×D₄₇	1	16	yes	complemented
787	C₂³	C₂⁴×D₄₇	1	2	yes	—
788	C₂³	C₂⁴×D₄₇	1	2	yes	—
789	C₂³	C₂⁴×D₄₇	1	2	yes	—
790	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
791	Q₈	—	2	16	no	—
792	Q₈	—	4	8	no	—
793	Q₈	—	94	16	no	—
794	Q₈	—	188	16	no	—
795	Q₈	—	188	8	no	—
796	Q₈	—	188	16	no	—
797	D₄	—	47	32	no	—
798	D₄	—	47	32	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	2	8	no	—
804	C₂×C₄	—	2	8	no	—
805	C₂×C₄	—	2	8	no	—
806	C₂×C₄	—	2	8	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	47	8	no	—
813	C₂×C₄	—	47	16	no	—
814	C₂×C₄	—	47	4	no	—
815	C₂×C₄	—	47	4	no	—
816	C₂×C₄	—	47	8	no	—
817	C₂×C₄	—	47	8	no	—
818	C₂×C₄	—	47	4	no	—
819	C₂×C₄	—	94	4	no	—
820	C₂×C₄	—	94	8	no	—
821	C₂×C₄	—	94	8	no	—
822	C₂×C₄	—	94	4	no	—
823	C₂×C₄	—	94	16	no	—
824	C₂×C₄	—	188	16	no	—
825	C₂×C₄	—	188	8	no	—
826	C₂×C₄	—	188	16	no	—
827	C₂×C₄	—	188	8	no	—
828	C₂×C₄	—	188	4	no	—
829	C₂×C₄	—	188	4	no	—
830	C₂×C₄	—	188	8	no	—
831	C₂×C₄	#13094069	1	4	yes	—
832	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
833	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
834	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
835	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
836	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
837	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	8	no	—
845	C₂²	—	2	8	no	—
846	C₂²	—	2	8	no	—
847	C₂²	—	4	16	no	—
848	C₂²	—	47	8	no	—
849	C₂²	—	94	4	no	—
850	C₂²	—	94	4	no	—
851	C₂²	—	94	16	no	—
852	C₂²	—	188	16	no	—
853	C₂²	C₂²×Q₈×D₄₇	1	4	yes	—
854	C₂²	C₂²×Q₈×D₄₇	1	4	yes	—
855	C₂²	C₂²×Q₈×D₄₇	1	4	yes	—
856	C₂²	C₂²×Q₈×D₄₇	1	2	yes	—
857	C₂²	C₂×#13094069	1	2	yes	—
858	C₂²	#15689959	1	2	yes	—
859	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	8	no	—
864	C₄	—	2	8	no	—
865	C₄	—	47	8	no	—
866	C₄	—	94	4	no	—
867	C₄	—	94	8	no	—
868	C₄	—	94	8	no	—
869	C₄	—	94	4	no	—
870	C₄	C₂×#13094069	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	2	4	no	—
873	C₂	—	2	4	no	—
874	C₂	—	94	8	no	—
875	C₂	#20257184	1	4	yes	direct product factor
876	C₂	C₂³×Q₈×D₄₇	1	1	yes	characteristic
877	C₂	C₂²×#13094069	1	1	yes	characteristic
878	C₂	C₂×#15689959	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #20257184	C₂	direct (N × H)
2. C₂×#15689831	C₂	semidirect
3. C₂×#15689828	C₂	semidirect
4. C₂×#15689828	C₂	semidirect
5. C₂×#15689827	C₂	semidirect
6. C₂×Q₈×C₂²⋊D₄₇	C₂	semidirect
7. C₂×#15689786	C₂	semidirect
8. C₂×#15689752	C₂	semidirect
9. C₂×#15689749	C₂	semidirect
10. C₂×#15689748	C₂	semidirect
11. C₂×#15689675	C₂	semidirect
12. C₂²×#13094003	C₂	semidirect
13. C₂×C₂²⋊Q₈×D₄₇	C₂	semidirect
16. C₂²×C₂²⋊Q₈×C₄₇	C₂	semidirect
17. C₂³×Dic₉₄	C₂²	semidirect
18. C₂²×Q₈×D₄₇	C₂²	semidirect
21. #15689831	C₂²	semidirect
22. #15689828	C₂²	semidirect
23. #15689828	C₂²	semidirect
24. #15689827	C₂²	semidirect
25. Q₈×C₂²⋊D₄₇	C₂²	semidirect
26. #15689786	C₂²	semidirect
27. #15689752	C₂²	semidirect
28. #15689749	C₂²	semidirect
29. #15689748	C₂²	semidirect
30. #15689675	C₂²	semidirect
31. C₂×#13094023	C₂²	semidirect
32. C₂×#13094023	C₂²	semidirect
33. C₂×#13094022	C₂²	semidirect
34. C₂×#13094022	C₂²	semidirect
35. C₂×#13094014	C₂²	semidirect
36. C₂×#13094014	C₂²	semidirect
37. C₂×#13094014	C₂²	semidirect
38. C₂×#13094004	C₂²	semidirect
39. C₂×#13094004	C₂²	semidirect
42. C₂×#13094003	C₂²	semidirect
43. C₂×#13094003	C₂²	semidirect
44. C₂×#13094003	C₂²	semidirect
45. C₂×#13094003	C₂²	semidirect
46. C₂×#13094003	C₂²	semidirect
47. C₂×#13094002	C₂²	semidirect
48. C₂×#13094002	C₂²	semidirect
49. C₂×#13094002	C₂²	semidirect
52. C₂×#13094001	C₂²	semidirect
53. C₂×#13094001	C₂²	semidirect
54. C₂×#13094000	C₂²	semidirect
55. C₂×#13094000	C₂²	semidirect
56. C₂²⋊Q₈×D₄₇	C₂²	semidirect
58. C₂×Q₈×Dic₄₇	C₂²	semidirect
59. C₂×#13093989	C₂²	semidirect
60. C₂×#13093989	C₂²	semidirect
71. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
73. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
74. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
75. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
81. C₂³×Q₈×C₄₇	C₂²	semidirect
85. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
86. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
87. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
88. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
89. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
97. C₂²×Dic₉₄	C₂³	semidirect
99. C₂×Q₈×D₄₇	C₂³	semidirect
100. C₂²×C₂²⋊D₄₇	Q₈	semidirect
115. #13094023	C₂³	semidirect
116. #13094023	C₂³	semidirect
117. #13094022	C₂³	semidirect
118. #13094022	C₂³	semidirect
119. #13094014	C₂³	semidirect
120. #13094014	C₂³	semidirect
121. #13094014	C₂³	semidirect
122. #13094004	C₂³	semidirect
123. #13094004	C₂³	semidirect
126. #13094003	C₂³	semidirect
127. #13094003	C₂³	semidirect
128. #13094003	C₂³	semidirect
129. #13094003	C₂³	semidirect
130. #13094002	C₂³	semidirect
131. #13094002	C₂³	semidirect
132. #13094002	C₂³	semidirect
135. #13094001	C₂³	semidirect
136. #13094001	C₂³	semidirect
137. #13094000	C₂³	semidirect
138. #13094000	C₂³	semidirect
139. Q₈×Dic₄₇	C₂³	semidirect
140. #13093989	C₂³	semidirect
141. #13093989	C₂³	semidirect
155. C₂×C₄⋊Dic₄₇	C₂³	semidirect
167. C₂×Dic₄₇⋊C₄	C₂³	semidirect
168. C₄⋊C₄×D₄₇	C₂³	semidirect
169. C₄⋊C₄×D₄₇	C₂³	semidirect
191. C₂²×Q₈×C₄₇	C₂³	semidirect
204. C₂²⋊Q₈×C₄₇	C₂³	semidirect
205. C₂²⋊Q₈×C₄₇	C₂³	semidirect
210. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
211. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
217. C₂⁴×C₄₇	C₂×Q₈	semidirect
224. C₂³×D₄₇	C₂×Q₈	semidirect
255. C₂×C₂²⋊D₄₇	C₂×Q₈	semidirect
256. C₂×C₂²⋊D₄₇	C₂×Q₈	semidirect
257. C₂×C₂²⋊D₄₇	C₂×Q₈	semidirect
264. C₂²×Dic₄₇	C₂×Q₈	semidirect
338. C₂³×C₄₇	C₂²×Q₈	semidirect
349. C₂²×D₄₇	C₂²×Q₈	semidirect
373. C₂²⋊D₄₇	C₂²×Q₈	semidirect
374. C₂²⋊D₄₇	C₂²×Q₈	semidirect
384. C₂×Dic₄₇	C₂²×Q₈	semidirect
445. C₂²×C₂²⋊Q₈	D₄₇	semidirect
451. C₂×C₄₇	#3501	semidirect
458. C₂³×Q₈	C₂×D₄₇	semidirect
500. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
501. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
502. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
522. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
523. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
530. C₄₇	C₂×#3501	semidirect
544. C₂²×Q₈	C₂²×D₄₇	semidirect
596. C₂²⋊Q₈	C₂²×D₄₇	semidirect
597. C₂²⋊Q₈	C₂²×D₄₇	semidirect
633. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
634. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
662. C₂⁴	Q₈×D₄₇	semidirect
786. C₂³	C₂×Q₈×D₄₇	semidirect
875. C₂	#20257184	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257184	2
C₂×#15689831	2
C₂×#15689828	2
C₂×#15689827	2
C₂×Q₈×C₂²⋊D₄₇	2
C₂×#15689786	2
C₂×#15689752	2
C₂×#15689749	2
C₂×#15689748	2
C₂×#15689675	2
C₂²×#13094003	2
C₂×C₂²⋊Q₈×D₄₇	2
C₂×#15689596	2
C₂²×C₄×C₂²⋊D₄₇	2
C₂²×C₂²⋊Q₈×C₄₇	2
C₂×#3501	47

Subgroups — C2×#20257184 #27124175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257184 #27124175