Subgroups — C₂×#20257615 #27123499

Order 12032.

7962 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	#20257615	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689870	C₂	1	4	yes	maximal, complemented
3	C₂×#15689830	C₂	1	2	yes	maximal, complemented
4	C₂×#15689782	C₂	1	2	yes	maximal, complemented
5	C₂×#15689777	C₂	1	2	yes	maximal, complemented
6	C₂×#15689769	C₂	1	2	yes	maximal, complemented
7	C₂×#15689760	C₂	1	4	yes	maximal, complemented
8	C₂×#15689748	C₂	1	2	yes	maximal, complemented
9	C₂×#15689744	C₂	1	2	yes	maximal, complemented
10	C₂×#15689722	C₂	1	2	yes	maximal, complemented
11	C₂×#15689710	C₂	1	2	yes	maximal, complemented
12	C₂×#15689701	C₂	1	2	yes	maximal, complemented
13	C₂×#15689700	C₂	1	2	yes	maximal, complemented
14	C₂²×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#10625350	C₂²	1	2	yes	complemented
18	C₂²×#10625352	C₂²	1	4	yes	complemented
19	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
21	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	—
22	#15689870	C₂²	1	64	yes	complemented
23	#15689830	C₂²	1	32	yes	complemented
24	#15689782	C₂²	1	32	yes	complemented
25	#15689777	C₂²	1	32	yes	complemented
26	#15689769	C₂²	1	32	yes	complemented
27	#15689760	C₂²	1	64	yes	complemented
28	#15689748	C₂²	1	32	yes	complemented
29	#15689744	C₂²	1	32	yes	complemented
30	#15689722	C₂²	1	32	yes	complemented
31	#15689710	C₂²	1	32	yes	complemented
32	#15689701	C₂²	1	32	yes	complemented
33	#15689700	C₂²	1	32	yes	complemented
34	C₂×#13094024	C₂²	1	2	yes	complemented
35	C₂×#13094019	C₂²	1	4	yes	complemented
36	C₂×#13094015	C₂²	1	4	yes	complemented
37	C₂×#13094012	C₂²	1	2	yes	complemented
38	C₂×#13094010	C₂²	1	4	yes	complemented
39	C₂×#13094010	C₂²	1	4	yes	complemented
40	C₂×#13094009	C₂²	1	4	yes	complemented
41	C₂×#13094008	C₂²	1	4	yes	complemented
42	C₂×#13094008	C₂²	1	4	yes	complemented
43	C₂×#13094006	C₂²	1	4	yes	complemented
44	C₂×#13094004	C₂²	1	4	yes	complemented
45	C₂×#13094003	C₂²	1	2	yes	—
46	C₂×#13094003	C₂²	1	2	yes	—
47	C₂×#13094003	C₂²	1	2	yes	complemented
48	C₂×#13094003	C₂²	1	2	yes	complemented
49	C₂×#13094003	C₂²	1	2	yes	complemented
50	C₂×#13094003	C₂²	1	16	yes	complemented
51	C₂×#13094002	C₂²	1	4	yes	complemented
52	C₂×#13094002	C₂²	1	4	yes	complemented
53	C₂×#13094001	C₂²	1	4	yes	—
54	C₂×#13094001	C₂²	1	4	yes	complemented
55	C₂×#13094000	C₂²	1	4	yes	complemented
56	C₂×#13093998	C₂²	1	2	yes	—
57	C₂×#13093998	C₂²	1	2	yes	—
58	C₂×#13093998	C₂²	1	2	yes	—
59	C₂×#13093998	C₂²	1	2	yes	—
60	C₂×#13093998	C₂²	1	16	yes	complemented
61	C₂×#13093998	C₂²	1	2	yes	complemented
62	C₂×#13093997	C₂²	1	4	yes	complemented
63	C₂×#13093996	C₂²	1	4	yes	complemented
64	C₂×#13093996	C₂²	1	4	yes	complemented
65	C₂×#13093996	C₂²	1	4	yes	complemented
66	C₂×#13093995	C₂²	1	4	yes	complemented
67	C₂×#13093992	C₂²	1	4	yes	—
68	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
69	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
70	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
71	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
72	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
73	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
74	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
75	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
76	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
77	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
78	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
79	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
80	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
81	C₄₇×#525	C₂²	1	16	yes	complemented
82	C₂×#123×C₄₇	C₂²	1	2	yes	complemented
83	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
84	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
85	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
86	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×#120×C₄₇	C₂²	1	2	yes	—
88	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
89	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
90	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₄₇	C₂³	1	2	yes	—
92	C₂×#10625350	—	4	8	no	—
93	C₂×#10625350	C₂³	1	16	yes	complemented
94	C₂×#10625352	—	4	16	no	—
95	C₂×#10625352	C₂³	1	32	yes	complemented
96	C₂²×Dic₉₄	—	4	4	no	—
97	C₂²×Dic₉₄	C₂³	1	2	yes	—
98	C₂²×Dic₉₄	C₂³	1	4	yes	—
99	C₂²×Dic₉₄	C₂³	1	2	yes	—
100	C₂²×Dic₉₄	C₂³	1	8	yes	complemented
101	C₂²×D₁₈₈	—	4	4	no	—
102	C₂²×D₁₈₈	C₂³	1	2	yes	—
103	C₂²×D₁₈₈	C₂³	1	8	yes	—
104	C₂²×D₁₈₈	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₄₇	—	4	8	no	—
106	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₄₇	C₂³	1	16	yes	—
108	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
109	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
111	C₂³×Dic₄₇	C₂³	1	2	yes	—
112	C₂³×Dic₄₇	C₂³	1	2	yes	—
113	C₂³×Dic₄₇	C₂³	1	2	yes	—
114	C₂³×Dic₄₇	C₂³	1	4	yes	—
115	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
116	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
117	#13094024	C₂³	1	16	yes	complemented
118	#13094019	C₂³	1	32	yes	complemented
119	#13094015	C₂³	1	32	yes	complemented
120	#13094012	C₂³	1	16	yes	complemented
121	#13094010	C₂³	1	32	yes	complemented
122	#13094010	C₂³	1	32	yes	complemented
123	#13094009	C₂³	1	32	yes	complemented
124	#13094008	C₂³	1	32	yes	complemented
125	#13094008	C₂³	1	32	yes	complemented
126	#13094006	C₂³	1	32	yes	complemented
127	#13094004	C₂³	1	32	yes	complemented
128	#13094003	C₂³	1	16	yes	—
129	#13094003	C₂³	1	16	yes	—
130	#13094003	C₂³	1	16	yes	complemented
131	#13094003	C₂³	1	16	yes	complemented
132	#13094003	C₂³	1	16	yes	complemented
133	#13094002	C₂³	1	32	yes	complemented
134	#13094002	C₂³	1	32	yes	complemented
135	#13094001	C₂³	1	32	yes	—
136	#13094001	C₂³	1	32	yes	complemented
137	#13094000	C₂³	1	32	yes	complemented
138	#13093998	C₂³	1	16	yes	—
139	#13093998	C₂³	1	16	yes	—
140	#13093998	C₂³	1	16	yes	—
141	#13093998	C₂³	1	16	yes	—
142	#13093998	C₂³	1	16	yes	complemented
143	#13093997	C₂³	1	32	yes	complemented
144	#13093996	C₂³	1	32	yes	complemented
145	#13093996	C₂³	1	32	yes	complemented
146	#13093996	C₂³	1	32	yes	complemented
147	#13093995	C₂³	1	32	yes	complemented
148	#13093992	C₂³	1	32	yes	—
149	C₄×Dic₉₄	C₂³	1	16	yes	complemented
150	C₄×D₁₈₈	C₂³	1	16	yes	complemented
151	D₄×Dic₄₇	C₂³	1	32	yes	—
152	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
153	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
154	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
155	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
156	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
157	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
158	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
159	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
160	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	complemented
161	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
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	16	yes	complemented
167	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
168	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
169	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
170	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
171	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
172	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
173	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
174	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
175	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
176	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
177	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
178	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	—
179	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
180	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
181	C₂×#41×C₄₇	—	4	4	no	—
182	C₂×#41×C₄₇	C₂³	1	8	yes	complemented
183	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
184	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
185	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
186	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
187	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
188	C₂³×C₄×C₄₇	—	4	4	no	—
189	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
192	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	8	yes	—
197	#123×C₄₇	C₂³	1	16	yes	complemented
198	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
199	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
200	#121×C₄₇	C₂³	1	8	yes	—
201	#121×C₄₇	C₂³	1	8	yes	complemented
202	#120×C₄₇	C₂³	1	16	yes	—
203	C₄×D₄×C₄₇	C₂³	1	16	yes	—
204	C₄×D₄×C₄₇	C₂³	1	16	yes	complemented
205	#117×C₄₇	C₂³	1	8	yes	complemented
206	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
216	C₂⁴×C₄₇	—	2	4	no	—
217	C₂⁴×C₄₇	—	2	4	no	—
218	C₂⁴×C₄₇	—	4	2	no	—
219	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
221	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
222	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
224	C₂³×D₄₇	—	2	8	no	—
225	C₂³×D₄₇	—	4	4	no	—
226	C₂³×D₄₇	—	4	4	no	—
227	C₂³×D₄₇	C₂⁴	1	4	yes	—
228	C₂³×D₄₇	C₂⁴	1	8	yes	—
229	#41×C₄₇	—	4	16	no	—
230	C₂×Q₈×C₄₇	—	4	2	no	—
231	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
232	C₂×D₄×C₄₇	—	2	8	no	—
233	C₂×D₄×C₄₇	—	2	8	no	—
234	C₂×D₄×C₄₇	—	4	4	no	—
235	C₂×D₄×C₄₇	—	4	2	no	—
236	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
237	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
238	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
239	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₄₇	—	2	4	no	—
241	C₂²×C₄×C₄₇	—	2	4	no	—
242	C₂²×C₄×C₄₇	—	2	4	no	—
243	C₂²×C₄×C₄₇	—	2	8	no	—
244	C₂²×C₄×C₄₇	—	4	16	no	—
245	C₂²×C₄×C₄₇	—	4	2	no	—
246	C₂²×C₄×C₄₇	—	4	2	no	—
247	C₂²×C₄×C₄₇	—	4	2	no	—
248	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
257	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₂²⋊D₄₇	—	2	16	no	—
263	C₂×C₂²⋊D₄₇	—	4	8	no	—
264	C₂×C₂²⋊D₄₇	—	4	8	no	—
265	C₂×C₂²⋊D₄₇	—	4	8	no	—
266	C₂×C₂²⋊D₄₇	—	4	32	no	—
267	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
268	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
269	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
270	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
271	C₂²×Dic₄₇	—	2	8	no	—
272	C₂²×Dic₄₇	—	4	4	no	—
273	C₂²×Dic₄₇	—	4	4	no	—
274	C₂²×Dic₄₇	—	4	8	no	—
275	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
276	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
277	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
278	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
279	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
280	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
281	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
282	#10625352	—	4	64	no	—
283	#10625350	—	4	32	no	—
284	C₂×D₁₈₈	—	2	8	no	—
285	C₂×D₁₈₈	—	4	16	no	—
286	C₂×D₁₈₈	—	4	4	no	—
287	C₂×D₁₈₈	C₂⁴	1	8	yes	—
288	C₂×D₁₈₈	C₂⁴	1	8	yes	—
289	C₂×C₄×D₄₇	—	4	8	no	—
290	C₂×C₄×D₄₇	—	4	8	no	—
291	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
292	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
293	C₂×Dic₉₄	—	2	8	no	—
294	C₂×Dic₉₄	—	4	16	no	—
295	C₂×Dic₉₄	—	4	4	no	—
296	C₂×Dic₉₄	—	4	8	no	—
297	C₂×Dic₉₄	C₂⁴	1	8	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	4	yes	—
302	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
304	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
305	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
306	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
307	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
308	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
309	C₄²×C₄₇	C₂⁴	1	8	yes	—
310	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
311	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
312	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
313	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
314	(C₂×D₄₇)⋊C₄	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	16	yes	—
318	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
319	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
320	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
321	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
322	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
323	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
324	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
325	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
326	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
327	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
328	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
329	C₄×Dic₄₇	C₂⁴	1	16	yes	—
330	C₂³×C₄₇	—	2	2	no	—
331	C₂³×C₄₇	—	2	2	no	—
332	C₂³×C₄₇	—	2	2	no	—
333	C₂³×C₄₇	—	2	2	no	—
334	C₂³×C₄₇	—	2	4	no	—
335	C₂³×C₄₇	—	2	8	no	—
336	C₂³×C₄₇	—	2	2	no	—
337	C₂³×C₄₇	—	2	4	no	—
338	C₂³×C₄₇	—	2	2	no	—
339	C₂³×C₄₇	—	2	4	no	—
340	C₂³×C₄₇	—	2	8	no	—
341	C₂³×C₄₇	—	2	2	no	—
342	C₂³×C₄₇	—	4	4	no	—
343	C₂³×C₄₇	—	4	16	no	—
344	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
345	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
346	C₂³×C₄₇	C₂⁵	1	2	yes	—
347	C₂³×C₄₇	C₂⁵	1	4	yes	—
348	C₂³×C₄₇	C₂⁵	1	2	yes	—
349	C₂³×C₄₇	C₂⁵	1	2	yes	—
350	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
351	C₂²×D₄₇	—	2	8	no	—
352	C₂²×D₄₇	—	2	8	no	—
353	C₂²×D₄₇	—	2	8	no	—
354	C₂²×D₄₇	—	2	16	no	—
355	C₂²×D₄₇	—	4	8	no	—
356	C₂²×D₄₇	—	4	8	no	—
357	C₂²×D₄₇	—	8	16	no	—
358	C₂²×D₄₇	C₂⁵	1	8	yes	—
359	Q₈×C₄₇	—	4	4	no	—
360	D₄×C₄₇	—	2	16	no	—
361	D₄×C₄₇	—	2	16	no	—
362	D₄×C₄₇	—	4	8	no	—
363	D₄×C₄₇	—	4	4	no	—
364	C₂×C₄×C₄₇	—	2	4	no	—
365	C₂×C₄×C₄₇	—	2	2	no	—
366	C₂×C₄×C₄₇	—	2	4	no	—
367	C₂×C₄×C₄₇	—	2	2	no	—
368	C₂×C₄×C₄₇	—	2	2	no	—
369	C₂×C₄×C₄₇	—	2	4	no	—
370	C₂×C₄×C₄₇	—	2	8	no	—
371	C₂×C₄×C₄₇	—	2	8	no	—
372	C₂×C₄×C₄₇	—	2	16	no	—
373	C₂×C₄×C₄₇	—	2	8	no	—
374	C₂×C₄×C₄₇	—	4	4	no	—
375	C₂×C₄×C₄₇	—	4	4	no	—
376	C₂×C₄×C₄₇	—	4	4	no	—
377	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
378	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
379	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
380	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
381	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
382	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
383	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
384	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
385	C₂²⋊D₄₇	—	2	32	no	—
386	C₂²⋊D₄₇	—	4	16	no	—
387	C₂²⋊D₄₇	—	4	16	no	—
388	C₂²⋊D₄₇	—	4	16	no	—
389	C₂×Dic₄₇	—	2	8	no	—
390	C₂×Dic₄₇	—	2	8	no	—
391	C₂×Dic₄₇	—	2	8	no	—
392	C₂×Dic₄₇	—	2	16	no	—
393	C₂×Dic₄₇	—	4	8	no	—
394	C₂×Dic₄₇	—	4	16	no	—
395	C₂×Dic₄₇	—	4	8	no	—
396	C₂×Dic₄₇	C₂⁵	1	8	yes	—
397	C₂×Dic₄₇	C₂⁵	1	8	yes	—
398	C₂×Dic₄₇	C₂⁵	1	8	yes	—
399	D₁₈₈	—	2	16	no	—
400	D₁₈₈	—	4	8	no	—
401	C₄×D₄₇	—	4	16	no	—
402	C₄×D₄₇	—	4	16	no	—
403	Dic₉₄	—	2	16	no	—
404	Dic₉₄	—	4	8	no	—
405	Dic₉₄	—	4	16	no	—
406	C₂×#3536	—	47	1	no	maximal, Sylow
407	C₂²×C₄₇	—	2	2	no	—
408	C₂²×C₄₇	—	2	2	no	—
409	C₂²×C₄₇	—	2	2	no	—
410	C₂²×C₄₇	—	2	2	no	—
411	C₂²×C₄₇	—	2	8	no	—
412	C₂²×C₄₇	—	2	8	no	—
413	C₂²×C₄₇	—	2	4	no	—
414	C₂²×C₄₇	—	2	2	no	—
415	C₂²×C₄₇	—	2	4	no	—
416	C₂²×C₄₇	—	2	2	no	—
417	C₂²×C₄₇	—	2	4	no	—
418	C₂²×C₄₇	—	2	2	no	—
419	C₂²×C₄₇	—	4	16	no	—
420	C₂²×C₄₇	—	4	8	no	—
421	C₂²×C₄₇	—	4	4	no	—
422	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
423	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
424	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
425	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
426	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
427	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
428	C₂×D₄₇	—	2	8	no	—
429	C₂×D₄₇	—	2	8	no	—
430	C₂×D₄₇	—	2	8	no	—
431	C₂×D₄₇	—	4	16	no	—
432	C₂×D₄₇	—	8	16	no	—
433	C₄×C₄₇	—	2	4	no	—
434	C₄×C₄₇	—	2	2	no	—
435	C₄×C₄₇	—	2	4	no	—
436	C₄×C₄₇	—	2	2	no	—
437	C₄×C₄₇	—	2	2	no	—
438	C₄×C₄₇	—	2	4	no	—
439	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
440	Dic₄₇	—	2	8	no	—
441	Dic₄₇	—	2	8	no	—
442	Dic₄₇	—	2	8	no	—
443	#3536	—	47	32	no	—
444	C₂×#562	—	47	4	no	—
445	C₂×#554	—	47	2	no	—
446	C₂×#548	—	47	2	no	—
447	C₂×#547	—	47	2	no	—
448	C₂×#546	—	47	4	no	—
449	C₂×#546	—	47	2	no	—
450	C₂×#543	—	47	2	no	—
451	C₂×#542	—	47	2	no	—
452	C₂×#539	—	47	2	no	—
453	C₂×#538	—	47	2	no	—
454	C₂×#537	—	47	2	no	—
455	C₂×#537	—	47	2	no	—
456	C₂×#525	D₄₇	1	1	yes	characteristic, complemented
457	C₂²×C₂²⋊Q₈	—	47	1	no	—
458	C₂²×#121	—	47	1	no	—
459	C₂×C₄₇	—	2	4	no	—
460	C₂×C₄₇	—	2	4	no	—
461	C₂×C₄₇	—	4	4	no	—
462	C₂×C₄₇	—	4	2	no	—
463	C₂×C₄₇	#3536	1	4	yes	complemented
464	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
465	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
467	D₄₇	—	4	8	no	—
468	C₂²×#41	—	47	4	no	—
469	C₂²×#41	—	47	2	no	—
470	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
471	C₂³×Q₈	—	47	1	no	—
472	C₂³×D₄	—	47	2	no	—
473	C₂³×D₄	—	47	1	no	—
474	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
475	#562	—	47	64	no	—
476	#554	—	47	32	no	—
477	#548	—	47	32	no	—
478	#547	—	47	32	no	—
479	#546	—	47	64	no	—
480	#546	—	47	32	no	—
481	#543	—	47	32	no	—
482	#542	—	47	32	no	—
483	#539	—	47	32	no	—
484	#538	—	47	32	no	—
485	#537	—	47	32	no	—
486	#537	—	47	32	no	—
487	C₂×C₄⋊Q₈	—	47	2	no	—
488	C₂×#126	—	47	4	no	—
489	C₂×#125	—	47	4	no	—
490	C₂×#124	—	47	4	no	—
491	C₂×#124	—	47	4	no	—
492	C₂×#124	—	47	2	no	—
493	#525	C₂×D₄₇	1	16	yes	complemented
494	C₂×#123	—	47	4	no	—
495	C₂×#123	—	47	4	no	—
496	C₂×#123	—	47	4	no	—
497	C₂×#123	—	47	4	no	—
498	C₂×#123	C₂×D₄₇	1	2	yes	complemented
499	C₂×C₂²⋊Q₈	—	47	4	no	—
500	C₂×C₂²⋊Q₈	—	47	2	no	—
501	C₂×C₂²⋊Q₈	—	47	2	no	—
502	C₂×C₂²⋊Q₈	—	47	2	no	—
503	C₂×C₂²⋊Q₈	—	47	2	no	—
504	C₂×C₂²⋊Q₈	—	47	16	no	—
505	C₂×C₂²⋊Q₈	—	47	2	no	—
506	C₂×C₂²⋊Q₈	—	47	4	no	—
507	C₂×C₂²⋊Q₈	—	47	4	no	—
508	C₂×C₂²⋊Q₈	—	47	4	no	—
509	C₂×C₂²⋊Q₈	—	47	4	no	—
510	C₂×C₂²⋊Q₈	—	47	4	no	—
511	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
512	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
513	C₂×#121	—	47	4	no	—
514	C₂×#121	—	47	4	no	—
515	C₂×#121	—	47	4	no	—
516	C₂×#121	—	47	4	no	—
517	C₂×#121	—	47	2	no	—
518	C₂×#121	—	47	2	no	—
519	C₂×#121	—	47	2	no	—
520	C₂×#121	—	47	2	no	—
521	C₂×#121	—	47	16	no	—
522	C₂×#121	—	47	2	no	—
523	C₂×#121	—	47	4	no	—
524	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
525	C₂×#121	C₂×D₄₇	1	1	yes	characteristic, complemented
526	C₂×#120	—	47	4	no	—
527	C₂×#120	C₂×D₄₇	1	2	yes	—
528	C₂×C₄×Q₈	—	47	2	no	—
529	C₂×C₄×D₄	—	47	4	no	—
530	C₂×C₄×D₄	—	47	4	no	—
531	C₂×C₄×D₄	—	47	2	no	—
532	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
533	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	complemented
534	C₂×#117	C₂×D₄₇	1	1	yes	characteristic, complemented
535	C₂²×C₄⋊C₄	—	47	2	no	—
536	C₂²×C₄⋊C₄	—	47	1	no	—
537	C₂²×C₄⋊C₄	—	47	1	no	—
538	C₂²×C₄⋊C₄	—	47	2	no	—
539	C₂²×C₂²⋊C₄	—	47	2	no	—
540	C₂²×C₂²⋊C₄	—	47	2	no	—
541	C₂²×C₂²⋊C₄	—	47	4	no	—
542	C₄₇	C₂×#3536	1	1	yes	characteristic, complemented, Sylow
543	C₂⁵	—	47	2	no	—
544	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
545	C₂×#41	—	4	4	no	—
546	C₂×#41	—	47	32	no	—
547	C₂×#41	—	47	16	no	—
548	C₂×#41	—	188	8	no	—
549	C₂×#41	—	188	16	no	—
550	C₂×#41	C₂²×D₄₇	1	8	yes	complemented
551	C₂²×Q₈	—	47	2	no	—
552	C₂²×Q₈	—	47	2	no	—
553	C₂²×Q₈	—	47	4	no	—
554	C₂²×Q₈	—	47	8	no	—
555	C₂²×Q₈	—	188	4	no	—
556	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
557	C₂²×D₄	—	47	4	no	—
558	C₂²×D₄	—	47	4	no	—
559	C₂²×D₄	—	47	4	no	—
560	C₂²×D₄	—	47	4	no	—
561	C₂²×D₄	—	47	16	no	—
562	C₂²×D₄	—	47	2	no	—
563	C₂²×D₄	—	47	2	no	—
564	C₂²×D₄	—	47	8	no	—
565	C₂²×D₄	—	188	4	no	—
566	C₂²×D₄	—	188	8	no	—
567	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
568	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
569	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
570	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
571	C₂³×C₄	—	4	4	no	—
572	C₂³×C₄	—	47	2	no	—
573	C₂³×C₄	—	47	2	no	—
574	C₂³×C₄	—	47	2	no	—
575	C₂³×C₄	—	47	4	no	—
576	C₂³×C₄	—	47	4	no	—
577	C₂³×C₄	—	47	4	no	—
578	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
579	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
580	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
581	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
582	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
583	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
584	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
585	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
586	C₄⋊Q₈	—	47	16	no	—
587	#126	—	47	32	no	—
588	#125	—	47	32	no	—
589	#124	—	47	32	no	—
590	#124	—	47	32	no	—
591	#124	—	47	16	no	—
592	#123	—	47	32	no	—
593	#123	—	47	32	no	—
594	#123	—	47	32	no	—
595	#123	—	47	32	no	—
596	#123	C₂²×D₄₇	1	16	yes	complemented
597	C₂²⋊Q₈	—	47	32	no	—
598	C₂²⋊Q₈	—	47	16	no	—
599	C₂²⋊Q₈	—	47	16	no	—
600	C₂²⋊Q₈	—	47	16	no	—
601	C₂²⋊Q₈	—	47	16	no	—
602	C₂²⋊Q₈	—	47	16	no	—
603	C₂²⋊Q₈	—	47	32	no	—
604	C₂²⋊Q₈	—	47	32	no	—
605	C₂²⋊Q₈	—	47	32	no	—
606	C₂²⋊Q₈	—	47	32	no	—
607	C₂²⋊Q₈	—	47	32	no	—
608	C₂²⋊Q₈	C₂²×D₄₇	1	8	yes	—
609	C₂²⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
610	#121	—	47	32	no	—
611	#121	—	47	32	no	—
612	#121	—	47	32	no	—
613	#121	—	47	32	no	—
614	#121	—	47	16	no	—
615	#121	—	47	16	no	—
616	#121	—	47	16	no	—
617	#121	—	47	16	no	—
618	#121	—	47	16	no	—
619	#121	—	47	32	no	—
620	#121	C₂²×D₄₇	1	8	yes	—
621	#121	C₂²×D₄₇	1	8	yes	complemented
622	#120	—	47	32	no	—
623	#120	C₂²×D₄₇	1	16	yes	—
624	C₄×Q₈	—	47	16	no	—
625	C₄×D₄	—	47	32	no	—
626	C₄×D₄	—	47	32	no	—
627	C₄×D₄	—	47	16	no	—
628	C₄×D₄	C₂²×D₄₇	1	16	yes	—
629	C₄×D₄	C₂²×D₄₇	1	16	yes	complemented
630	#117	C₂²×D₄₇	1	8	yes	complemented
631	C₂×C₄⋊C₄	—	47	2	no	—
632	C₂×C₄⋊C₄	—	47	2	no	—
633	C₂×C₄⋊C₄	—	47	2	no	—
634	C₂×C₄⋊C₄	—	47	8	no	—
635	C₂×C₄⋊C₄	—	47	4	no	—
636	C₂×C₄⋊C₄	—	47	4	no	—
637	C₂×C₄⋊C₄	—	47	4	no	—
638	C₂×C₄⋊C₄	—	47	2	no	—
639	C₂×C₄⋊C₄	—	47	16	no	—
640	C₂×C₄⋊C₄	—	47	8	no	—
641	C₂×C₄⋊C₄	—	47	16	no	—
642	C₂×C₄⋊C₄	—	47	4	no	—
643	C₂×C₄⋊C₄	—	47	4	no	—
644	C₂×C₄⋊C₄	—	47	4	no	—
645	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
648	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
649	C₂×C₂²⋊C₄	—	47	4	no	—
650	C₂×C₂²⋊C₄	—	47	4	no	—
651	C₂×C₂²⋊C₄	—	47	16	no	—
652	C₂×C₂²⋊C₄	—	47	4	no	—
653	C₂×C₂²⋊C₄	—	47	4	no	—
654	C₂×C₂²⋊C₄	—	47	4	no	—
655	C₂×C₂²⋊C₄	—	47	4	no	—
656	C₂×C₂²⋊C₄	—	47	4	no	—
657	C₂×C₂²⋊C₄	—	47	16	no	—
658	C₂×C₂²⋊C₄	—	47	4	no	—
659	C₂×C₂²⋊C₄	—	47	4	no	—
660	C₂×C₂²⋊C₄	—	47	32	no	—
661	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
666	C₂×C₄²	—	47	4	no	—
667	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
668	C₂⁴	—	2	4	no	—
669	C₂⁴	—	2	4	no	—
670	C₂⁴	—	4	2	no	—
671	C₂⁴	—	47	4	no	—
672	C₂⁴	—	47	8	no	—
673	C₂⁴	—	94	8	no	—
674	C₂⁴	—	188	4	no	—
675	C₂⁴	—	188	4	no	—
676	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
677	C₂⁴	C₂³×D₄₇	1	2	yes	—
678	C₂⁴	C₂³×D₄₇	1	4	yes	—
679	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
680	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
681	#41	—	4	16	no	—
682	#41	—	188	32	no	—
683	#41	—	188	64	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	—	47	8	no	—
686	C₂×Q₈	—	47	8	no	—
687	C₂×Q₈	—	47	16	no	—
688	C₂×Q₈	—	94	8	no	—
689	C₂×Q₈	—	188	4	no	—
690	C₂×Q₈	—	188	8	no	—
691	C₂×Q₈	—	188	16	no	—
692	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	2	8	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	47	16	no	—
698	C₂×D₄	—	47	16	no	—
699	C₂×D₄	—	47	16	no	—
700	C₂×D₄	—	47	16	no	—
701	C₂×D₄	—	47	8	no	—
702	C₂×D₄	—	47	8	no	—
703	C₂×D₄	—	94	16	no	—
704	C₂×D₄	—	94	8	no	—
705	C₂×D₄	—	188	16	no	—
706	C₂×D₄	—	188	4	no	—
707	C₂×D₄	—	188	8	no	—
708	C₂×D₄	—	188	8	no	—
709	C₂×D₄	—	188	8	no	—
710	C₂×D₄	—	188	32	no	—
711	C₂×D₄	C₂³×D₄₇	1	8	yes	—
712	C₂×D₄	C₂³×D₄₇	1	8	yes	—
713	C₂×D₄	C₂³×D₄₇	1	8	yes	—
714	C₂×D₄	C₂³×D₄₇	1	4	yes	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	8	no	—
719	C₂²×C₄	—	4	16	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	47	8	no	—
724	C₂²×C₄	—	47	4	no	—
725	C₂²×C₄	—	47	4	no	—
726	C₂²×C₄	—	47	4	no	—
727	C₂²×C₄	—	47	8	no	—
728	C₂²×C₄	—	47	8	no	—
729	C₂²×C₄	—	47	16	no	—
730	C₂²×C₄	—	47	16	no	—
731	C₂²×C₄	—	47	16	no	—
732	C₂²×C₄	—	94	8	no	—
733	C₂²×C₄	—	188	8	no	—
734	C₂²×C₄	—	188	8	no	—
735	C₂²×C₄	—	188	4	no	—
736	C₂²×C₄	—	188	4	no	—
737	C₂²×C₄	—	188	8	no	—
738	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
739	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
740	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
741	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
742	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
743	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
744	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
745	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
746	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
747	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
748	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
749	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
750	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
751	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
752	C₄⋊C₄	—	47	16	no	—
753	C₄⋊C₄	—	47	16	no	—
754	C₄⋊C₄	—	47	16	no	—
755	C₄⋊C₄	—	47	16	no	—
756	C₄⋊C₄	—	47	8	no	—
757	C₄⋊C₄	—	47	8	no	—
758	C₄⋊C₄	—	47	8	no	—
759	C₄⋊C₄	—	47	16	no	—
760	C₄⋊C₄	—	47	8	no	—
761	C₄⋊C₄	—	47	16	no	—
762	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
763	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
764	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
765	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
766	C₂²⋊C₄	—	47	16	no	—
767	C₂²⋊C₄	—	47	16	no	—
768	C₂²⋊C₄	—	47	16	no	—
769	C₂²⋊C₄	—	47	16	no	—
770	C₂²⋊C₄	—	47	16	no	—
771	C₂²⋊C₄	—	47	16	no	—
772	C₂²⋊C₄	—	47	16	no	—
773	C₂²⋊C₄	—	47	16	no	—
774	C₂²⋊C₄	—	47	16	no	—
775	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
776	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
777	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
778	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
779	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
780	C₄²	—	47	16	no	—
781	C₄²	C₂³×D₄₇	1	8	yes	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	8	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	4	no	—
792	C₂³	—	2	8	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	16	no	—
796	C₂³	—	47	8	no	—
797	C₂³	—	94	16	no	—
798	C₂³	—	94	8	no	—
799	C₂³	—	94	8	no	—
800	C₂³	—	94	8	no	—
801	C₂³	—	376	16	no	—
802	C₂³	—	188	8	no	—
803	C₂³	—	188	8	no	—
804	C₂³	#13094070	1	4	yes	—
805	C₂³	#13094071	1	4	yes	—
806	C₂³	C₂⁴×D₄₇	1	2	yes	—
807	C₂³	C₂⁴×D₄₇	1	4	yes	—
808	C₂³	C₂⁴×D₄₇	1	2	yes	—
809	C₂³	C₂⁴×D₄₇	1	2	yes	—
810	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
811	Q₈	—	4	4	no	—
812	Q₈	—	94	16	no	—
813	Q₈	—	188	8	no	—
814	Q₈	—	188	16	no	—
815	D₄	—	2	16	no	—
816	D₄	—	2	16	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	8	no	—
819	D₄	—	94	32	no	—
820	D₄	—	94	16	no	—
821	D₄	—	188	8	no	—
822	D₄	—	188	16	no	—
823	D₄	—	188	16	no	—
824	D₄	—	188	16	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	8	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	16	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	47	8	no	—
839	C₂×C₄	—	47	8	no	—
840	C₂×C₄	—	47	8	no	—
841	C₂×C₄	—	94	8	no	—
842	C₂×C₄	—	94	8	no	—
843	C₂×C₄	—	94	16	no	—
844	C₂×C₄	—	94	8	no	—
845	C₂×C₄	—	188	16	no	—
846	C₂×C₄	—	188	16	no	—
847	C₂×C₄	—	188	8	no	—
848	C₂×C₄	—	188	8	no	—
849	C₂×C₄	—	188	16	no	—
850	C₂×C₄	#13094069	1	4	yes	—
851	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
852	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
853	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
854	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
855	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
856	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
857	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
858	C₂²	—	2	8	no	—
859	C₂²	—	2	8	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	16	no	—
871	C₂²	—	4	4	no	—
872	C₂²	—	4	8	no	—
873	C₂²	—	94	8	no	—
874	C₂²	—	94	8	no	—
875	C₂²	—	94	8	no	—
876	C₂²	—	376	16	no	—
877	C₂²	—	188	16	no	—
878	C₂²	C₂×#13094069	1	2	yes	—
879	C₂²	C₂×#13094070	1	4	yes	—
880	C₂²	C₂×#13094070	1	2	yes	—
881	C₂²	C₂×#13094071	1	4	yes	—
882	C₂²	C₂×#13094071	1	2	yes	—
883	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	94	8	no	—
891	C₄	—	94	8	no	—
892	C₄	—	94	8	no	—
893	C₄	C₂×#13094069	1	4	yes	—
894	C₂	—	2	4	no	—
895	C₂	—	2	4	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	4	no	—
898	C₂	—	188	8	no	—
899	C₂	#20257615	1	4	yes	direct product factor
900	C₂	C₂²×#13094069	1	1	yes	characteristic
901	C₂	C₂²×#13094070	1	1	yes	characteristic
902	C₂	C₂²×#13094071	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#525	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#525	D₄₇
hypocenter	C₄₇	C₂×#3536
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. #20257615	C₂	direct (N × H)
2. C₂×#15689870	C₂	semidirect
3. C₂×#15689830	C₂	semidirect
4. C₂×#15689782	C₂	semidirect
5. C₂×#15689777	C₂	semidirect
6. C₂×#15689769	C₂	semidirect
7. C₂×#15689760	C₂	semidirect
8. C₂×#15689748	C₂	semidirect
9. C₂×#15689744	C₂	semidirect
10. C₂×#15689722	C₂	semidirect
11. C₂×#15689710	C₂	semidirect
12. C₂×#15689701	C₂	semidirect
13. C₂×#15689700	C₂	semidirect
14. C₂²×#13094003	C₂	semidirect
15. C₂²×#13093998	C₂	semidirect
16. C₂×C₄₇×#525	C₂	semidirect
17. C₂²×#10625350	C₂²	semidirect
18. C₂²×#10625352	C₂²	semidirect
19. C₂³×Dic₉₄	C₂²	semidirect
22. #15689870	C₂²	semidirect
23. #15689830	C₂²	semidirect
24. #15689782	C₂²	semidirect
25. #15689777	C₂²	semidirect
26. #15689769	C₂²	semidirect
27. #15689760	C₂²	semidirect
28. #15689748	C₂²	semidirect
29. #15689744	C₂²	semidirect
30. #15689722	C₂²	semidirect
31. #15689710	C₂²	semidirect
32. #15689701	C₂²	semidirect
33. #15689700	C₂²	semidirect
34. C₂×#13094024	C₂²	semidirect
35. C₂×#13094019	C₂²	semidirect
36. C₂×#13094015	C₂²	semidirect
37. C₂×#13094012	C₂²	semidirect
38. C₂×#13094010	C₂²	semidirect
39. C₂×#13094010	C₂²	semidirect
40. C₂×#13094009	C₂²	semidirect
41. C₂×#13094008	C₂²	semidirect
42. C₂×#13094008	C₂²	semidirect
43. C₂×#13094006	C₂²	semidirect
44. C₂×#13094004	C₂²	semidirect
47. C₂×#13094003	C₂²	semidirect
48. C₂×#13094003	C₂²	semidirect
49. C₂×#13094003	C₂²	semidirect
50. C₂×#13094003	C₂²	semidirect
51. C₂×#13094002	C₂²	semidirect
52. C₂×#13094002	C₂²	semidirect
54. C₂×#13094001	C₂²	semidirect
55. C₂×#13094000	C₂²	semidirect
60. C₂×#13093998	C₂²	semidirect
61. C₂×#13093998	C₂²	semidirect
62. C₂×#13093997	C₂²	semidirect
63. C₂×#13093996	C₂²	semidirect
64. C₂×#13093996	C₂²	semidirect
65. C₂×#13093996	C₂²	semidirect
66. C₂×#13093995	C₂²	semidirect
68. C₂×C₄×Dic₉₄	C₂²	semidirect
69. C₂×C₄×D₁₈₈	C₂²	semidirect
71. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
73. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
74. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
75. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
79. C₂²×#41×C₄₇	C₂²	semidirect
81. C₄₇×#525	C₂²	semidirect
82. C₂×#123×C₄₇	C₂²	semidirect
84. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
86. C₂×#121×C₄₇	C₂²	semidirect
89. C₂×C₄×D₄×C₄₇	C₂²	semidirect
90. C₂×#117×C₄₇	C₂²	semidirect
93. C₂×#10625350	C₂³	semidirect
95. C₂×#10625352	C₂³	semidirect
100. C₂²×Dic₉₄	C₂³	semidirect
117. #13094024	C₂³	semidirect
118. #13094019	C₂³	semidirect
119. #13094015	C₂³	semidirect
120. #13094012	C₂³	semidirect
121. #13094010	C₂³	semidirect
122. #13094010	C₂³	semidirect
123. #13094009	C₂³	semidirect
124. #13094008	C₂³	semidirect
125. #13094008	C₂³	semidirect
126. #13094006	C₂³	semidirect
127. #13094004	C₂³	semidirect
130. #13094003	C₂³	semidirect
131. #13094003	C₂³	semidirect
132. #13094003	C₂³	semidirect
133. #13094002	C₂³	semidirect
134. #13094002	C₂³	semidirect
136. #13094001	C₂³	semidirect
137. #13094000	C₂³	semidirect
142. #13093998	C₂³	semidirect
143. #13093997	C₂³	semidirect
144. #13093996	C₂³	semidirect
145. #13093996	C₂³	semidirect
146. #13093996	C₂³	semidirect
147. #13093995	C₂³	semidirect
149. C₄×Dic₉₄	C₂³	semidirect
150. C₄×D₁₈₈	C₂³	semidirect
152. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
160. C₂×C₄⋊Dic₄₇	C₂³	semidirect
161. C₂×C₄⋊Dic₄₇	C₂³	semidirect
166. C₂×Dic₄₇⋊C₄	C₂³	semidirect
182. C₂×#41×C₄₇	C₂³	semidirect
197. #123×C₄₇	C₂³	semidirect
199. C₂²⋊Q₈×C₄₇	C₂³	semidirect
201. #121×C₄₇	C₂³	semidirect
204. C₄×D₄×C₄₇	C₂³	semidirect
205. #117×C₄₇	C₂³	semidirect
456. C₂×#525	D₄₇	semidirect
463. C₂×C₄₇	#3536	semidirect
470. C₂²×#41	C₂×D₄₇	semidirect
493. #525	C₂×D₄₇	semidirect
498. C₂×#123	C₂×D₄₇	semidirect
512. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
525. C₂×#121	C₂×D₄₇	semidirect
533. C₂×C₄×D₄	C₂×D₄₇	semidirect
534. C₂×#117	C₂×D₄₇	semidirect
542. C₄₇	C₂×#3536	semidirect
550. C₂×#41	C₂²×D₄₇	semidirect
596. #123	C₂²×D₄₇	semidirect
609. C₂²⋊Q₈	C₂²×D₄₇	semidirect
621. #121	C₂²×D₄₇	semidirect
629. C₄×D₄	C₂²×D₄₇	semidirect
630. #117	C₂²×D₄₇	semidirect
899. C₂	#20257615	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257615	2
C₂×#15689870	2
C₂×#15689830	2
C₂×#15689782	2
C₂×#15689777	2
C₂×#15689769	2
C₂×#15689760	2
C₂×#15689748	2
C₂×#15689744	2
C₂×#15689722	2
C₂×#15689710	2
C₂×#15689701	2
C₂×#15689700	2
C₂²×#13094003	2
C₂²×#13093998	2
C₂×C₄₇×#525	2
C₂×#3536	47

Subgroups — C2×#20257615 #27123499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257615 #27123499