Subgroups — C₂×#20257117 #27124615

Order 12032.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257117	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689837	C₂	1	2	yes	maximal, complemented
3	C₂×#15689825	C₂	1	2	yes	maximal, complemented
4	C₂×#15689820	C₂	1	2	yes	maximal, complemented
5	C₂×#15689799	C₂	1	4	yes	maximal, complemented
6	C₂×#15689773	C₂	1	2	yes	maximal, complemented
7	C₂×#15689767	C₂	1	4	yes	maximal, complemented
8	C₂×#15689754	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689740	C₂	1	2	yes	maximal, complemented
10	C₂×#15689726	C₂	1	2	yes	maximal, complemented
11	C₂×#15689690	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15689668	C₂	1	2	yes	maximal, complemented
13	C₂×#15689654	C₂	1	2	yes	maximal, complemented
14	C₂×#15689634	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15689604	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15689598	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#121×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10625350	C₂²	1	1	yes	characteristic
20	C₂²×#10625352	C₂²	1	4	yes	complemented
21	#15689837	C₂²	1	32	yes	complemented
22	#15689825	C₂²	1	32	yes	complemented
23	#15689820	C₂²	1	32	yes	complemented
24	#15689799	C₂²	1	64	yes	complemented
25	#15689773	C₂²	1	32	yes	complemented
26	#15689767	C₂²	1	64	yes	complemented
27	#15689754	C₂²	1	16	yes	complemented
28	#15689740	C₂²	1	32	yes	complemented
29	#15689726	C₂²	1	32	yes	complemented
30	#15689690	C₂²	1	16	yes	complemented
31	#15689668	C₂²	1	32	yes	complemented
32	C₂×#13094023	C₂²	1	2	yes	complemented
33	C₂×#13094023	C₂²	1	2	yes	complemented
34	C₂×#13094020	C₂²	1	2	yes	complemented
35	#15689654	C₂²	1	32	yes	complemented
36	C₂×#13094017	C₂²	1	4	yes	complemented
37	C₂×#13094017	C₂²	1	4	yes	complemented
38	C₂×#13094015	C₂²	1	2	yes	complemented
39	C₂×#13094015	C₂²	1	2	yes	complemented
40	C₂×#13094011	C₂²	1	4	yes	complemented
41	C₂×#13094011	C₂²	1	2	yes	complemented
42	C₂×#13094010	C₂²	1	4	yes	complemented
43	#15689634	C₂²	1	16	yes	complemented
44	C₂×#13094008	C₂²	1	4	yes	complemented
45	C₂×#13094007	C₂²	1	2	yes	—
46	C₂×#13094006	C₂²	1	4	yes	complemented
47	C₂×#13094005	C₂²	1	4	yes	complemented
48	C₂×#13094005	C₂²	1	4	yes	complemented
49	C₂×#13094003	C₂²	1	4	yes	—
50	C₂×#13094003	C₂²	1	1	yes	characteristic, complemented
51	C₂×#13094003	C₂²	1	1	yes	characteristic, complemented
52	C₂×#13094001	C₂²	1	4	yes	complemented
53	C₂×#13093998	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13093998	C₂²	1	1	yes	characteristic, complemented
55	C₂×#13093996	C₂²	1	4	yes	complemented
56	C₂×#13093996	C₂²	1	4	yes	complemented
57	C₂×#13093995	C₂²	1	4	yes	complemented
58	C₂×#13093995	C₂²	1	2	yes	complemented
59	C₂×#13093995	C₂²	1	2	yes	complemented
60	C₂×#13093993	C₂²	1	2	yes	—
61	C₂×#13093993	C₂²	1	4	yes	—
62	#15689604	C₂²	1	16	yes	complemented
63	#15689598	C₂²	1	16	yes	complemented
64	C₂×#13093989	C₂²	1	2	yes	complemented
65	C₂×D₄×Dic₄₇	C₂²	1	2	yes	complemented
66	C₂×D₄×Dic₄₇	C₂²	1	2	yes	complemented
67	C₂×D₄×Dic₄₇	C₂²	1	2	yes	complemented
68	C₂×D₄×Dic₄₇	C₂²	1	2	yes	complemented
69	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
70	C₂×#13093986	C₂²	1	2	yes	complemented
71	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
72	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
73	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
74	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
75	C₂×#13093983	C₂²	1	1	yes	characteristic
76	C₂×#13093983	C₂²	1	1	yes	characteristic
77	C₂×#13093983	C₂²	1	1	yes	characteristic
78	C₂×#13093983	C₂²	1	2	yes	—
79	C₂×#13093983	C₂²	1	1	yes	characteristic, complemented
80	C₂×#13093983	C₂²	1	1	yes	characteristic, complemented
81	C₂×#13093983	C₂²	1	2	yes	complemented
82	C₂×#13093983	C₂²	1	16	yes	complemented
83	C₂×#13093982	C₂²	1	2	yes	complemented
84	C₂×#13093980	C₂²	1	4	yes	complemented
85	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
86	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
88	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
89	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
90	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	complemented
91	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
92	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
93	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
94	C₂×#121×C₄₇	C₂²	1	2	yes	—
95	C₂×#121×C₄₇	C₂²	1	2	yes	—
96	C₂×#121×C₄₇	C₂²	1	2	yes	—
97	C₂×#121×C₄₇	C₂²	1	2	yes	—
98	C₂×#121×C₄₇	C₂²	1	16	yes	complemented
99	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
100	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
101	C₂×#10625350	—	2	8	no	—
102	C₂×#10625350	C₂³	1	8	yes	—
103	C₂×#10625352	—	4	16	no	—
104	C₂×#10625352	C₂³	1	32	yes	complemented
105	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
106	C₂²×Dic₉₄	C₂³	1	4	yes	—
107	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
108	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
109	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
110	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
112	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
113	C₂³×Dic₄₇	C₂³	1	2	yes	—
114	C₂³×Dic₄₇	C₂³	1	2	yes	—
115	C₂³×Dic₄₇	C₂³	1	4	yes	—
116	C₂³×Dic₄₇	C₂³	1	4	yes	—
117	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
118	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
119	#13094023	C₂³	1	16	yes	complemented
120	#13094023	C₂³	1	16	yes	complemented
121	#13094020	C₂³	1	16	yes	complemented
122	#13094017	C₂³	1	32	yes	complemented
123	#13094017	C₂³	1	32	yes	complemented
124	#13094015	C₂³	1	16	yes	complemented
125	#13094015	C₂³	1	16	yes	complemented
126	#13094011	C₂³	1	32	yes	complemented
127	#13094011	C₂³	1	16	yes	complemented
128	#13094010	C₂³	1	32	yes	complemented
129	#13094008	C₂³	1	32	yes	complemented
130	#13094007	C₂³	1	16	yes	—
131	#13094006	C₂³	1	32	yes	complemented
132	#13094005	C₂³	1	32	yes	complemented
133	#13094005	C₂³	1	32	yes	complemented
134	#13094003	C₂³	1	32	yes	—
135	#13094003	C₂³	1	8	yes	complemented
136	#13094003	C₂³	1	8	yes	complemented
137	#13094001	C₂³	1	32	yes	complemented
138	#13093998	C₂³	1	8	yes	complemented
139	#13093998	C₂³	1	8	yes	complemented
140	#13093996	C₂³	1	32	yes	complemented
141	#13093996	C₂³	1	32	yes	complemented
142	#13093995	C₂³	1	32	yes	complemented
143	#13093995	C₂³	1	16	yes	complemented
144	#13093995	C₂³	1	16	yes	complemented
145	#13093993	C₂³	1	16	yes	—
146	#13093993	C₂³	1	32	yes	—
147	#13093989	C₂³	1	16	yes	complemented
148	D₄×Dic₄₇	C₂³	1	16	yes	complemented
149	D₄×Dic₄₇	C₂³	1	32	yes	complemented
150	D₄×Dic₄₇	C₂³	1	16	yes	complemented
151	D₄×Dic₄₇	C₂³	1	16	yes	complemented
152	D₄×Dic₄₇	C₂³	1	16	yes	complemented
153	#13093986	C₂³	1	16	yes	complemented
154	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
155	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
156	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
157	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
158	#13093983	C₂³	1	8	yes	—
159	#13093983	C₂³	1	8	yes	—
160	#13093983	C₂³	1	16	yes	—
161	#13093983	C₂³	1	8	yes	—
162	#13093983	C₂³	1	16	yes	complemented
163	#13093983	C₂³	1	8	yes	complemented
164	#13093983	C₂³	1	8	yes	complemented
165	#13093982	C₂³	1	16	yes	complemented
166	#13093980	C₂³	1	32	yes	complemented
167	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
173	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
176	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	complemented
177	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	complemented
178	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
179	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
180	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
181	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
182	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
183	C₄⋊C₄×D₄₇	C₂³	1	16	yes	complemented
184	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
185	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	—
186	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
192	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
193	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
194	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
197	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
198	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
199	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
200	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
201	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
202	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
203	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
204	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
205	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
206	C₂×C₄×Dic₄₇	C₂³	1	16	yes	complemented
207	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
208	C₂⁵×C₄₇	C₂³	1	2	yes	—
209	C₂²×D₄×C₄₇	—	2	8	no	—
210	C₂²×D₄×C₄₇	—	4	8	no	—
211	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
212	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
213	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
214	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
215	C₂²×D₄×C₄₇	C₂³	1	16	yes	—
216	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
217	C₂³×C₄×C₄₇	—	2	8	no	—
218	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
219	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
220	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
221	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
222	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
223	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
224	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
225	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
226	#121×C₄₇	C₂³	1	16	yes	—
227	#121×C₄₇	C₂³	1	16	yes	—
228	#121×C₄₇	C₂³	1	16	yes	—
229	#121×C₄₇	C₂³	1	16	yes	—
230	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
231	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
234	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
235	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
236	C₂⁴×C₄₇	—	2	4	no	—
237	C₂⁴×C₄₇	—	2	4	no	—
238	C₂⁴×C₄₇	—	2	8	no	—
239	C₂⁴×C₄₇	—	4	2	no	—
240	C₂⁴×C₄₇	—	4	4	no	—
241	C₂⁴×C₄₇	—	4	4	no	—
242	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
243	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
245	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
248	C₂³×D₄₇	C₂⁴	1	2	yes	—
249	C₂×D₄×C₄₇	—	2	16	no	—
250	C₂×D₄×C₄₇	—	2	8	no	—
251	C₂×D₄×C₄₇	—	2	8	no	—
252	C₂×D₄×C₄₇	—	2	32	no	—
253	C₂×D₄×C₄₇	—	4	8	no	—
254	C₂×D₄×C₄₇	—	4	32	no	—
255	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
256	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
257	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
258	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
259	C₂²×C₄×C₄₇	—	2	4	no	—
260	C₂²×C₄×C₄₇	—	2	4	no	—
261	C₂²×C₄×C₄₇	—	2	4	no	—
262	C₂²×C₄×C₄₇	—	2	4	no	—
263	C₂²×C₄×C₄₇	—	2	4	no	—
264	C₂²×C₄×C₄₇	—	2	32	no	—
265	C₂²×C₄×C₄₇	—	4	4	no	—
266	C₂²×C₄×C₄₇	#41	1	8	yes	complemented
267	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
276	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
279	C₂×C₂²⋊D₄₇	—	2	8	no	—
280	C₂×C₂²⋊D₄₇	—	2	8	no	—
281	C₂×C₂²⋊D₄₇	—	4	4	no	—
282	C₂×C₂²⋊D₄₇	—	4	8	no	—
283	C₂×C₂²⋊D₄₇	—	4	8	no	—
284	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
285	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
286	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
287	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
288	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
289	C₂²×Dic₄₇	—	2	8	no	—
290	C₂²×Dic₄₇	—	4	8	no	—
291	C₂²×Dic₄₇	—	4	4	no	—
292	C₂²×Dic₄₇	—	4	8	no	—
293	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
294	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
295	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
296	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
297	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
298	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
299	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
300	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
301	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
302	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
303	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
304	#10625352	—	4	64	no	—
305	#10625350	—	2	32	no	—
306	C₂×D₁₈₈	—	2	4	no	—
307	C₂×D₁₈₈	C₂⁴	1	4	yes	—
308	C₂×C₄×D₄₇	—	2	8	no	—
309	C₂×C₄×D₄₇	—	4	8	no	—
310	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
311	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
312	C₂×Dic₉₄	—	2	4	no	—
313	C₂×Dic₉₄	—	4	8	no	—
314	C₂×Dic₉₄	C₂⁴	1	4	yes	—
315	C₂×Dic₉₄	C₂⁴	1	16	yes	—
316	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
318	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
319	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
320	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
321	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
322	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
323	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
324	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
325	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
326	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
327	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
328	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
329	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
330	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
331	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
332	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
333	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
334	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
335	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
336	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
337	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
338	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
339	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
340	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
341	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
342	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
343	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
344	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
345	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
346	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
347	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
348	C₄×Dic₄₇	C₂⁴	1	8	yes	—
349	C₄×Dic₄₇	C₂⁴	1	8	yes	—
350	C₄×Dic₄₇	C₂⁴	1	8	yes	—
351	C₄×Dic₄₇	C₂⁴	1	8	yes	—
352	C₄×Dic₄₇	C₂⁴	1	16	yes	—
353	C₄×Dic₄₇	C₂⁴	1	8	yes	—
354	C₂³×C₄₇	—	2	2	no	—
355	C₂³×C₄₇	—	2	2	no	—
356	C₂³×C₄₇	—	2	2	no	—
357	C₂³×C₄₇	—	2	2	no	—
358	C₂³×C₄₇	—	2	8	no	—
359	C₂³×C₄₇	—	2	2	no	—
360	C₂³×C₄₇	—	2	8	no	—
361	C₂³×C₄₇	—	2	8	no	—
362	C₂³×C₄₇	—	2	8	no	—
363	C₂³×C₄₇	—	2	2	no	—
364	C₂³×C₄₇	—	2	8	no	—
365	C₂³×C₄₇	—	2	2	no	—
366	C₂³×C₄₇	—	2	16	no	—
367	C₂³×C₄₇	—	4	4	no	—
368	C₂³×C₄₇	—	4	8	no	—
369	C₂³×C₄₇	—	4	8	no	—
370	C₂³×C₄₇	—	4	16	no	—
371	C₂³×C₄₇	—	8	16	no	—
372	C₂³×C₄₇	C₂×#41	1	4	yes	—
373	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
374	C₂³×C₄₇	C₂⁵	1	2	yes	—
375	C₂³×C₄₇	C₂⁵	1	8	yes	—
376	C₂³×C₄₇	C₂⁵	1	2	yes	—
377	C₂³×C₄₇	C₂⁵	1	2	yes	—
378	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
379	C₂²×D₄₇	—	2	4	no	—
380	C₂²×D₄₇	—	2	4	no	—
381	C₂²×D₄₇	—	2	4	no	—
382	C₂²×D₄₇	C₂⁵	1	4	yes	—
383	D₄×C₄₇	—	2	32	no	—
384	D₄×C₄₇	—	2	16	no	—
385	D₄×C₄₇	—	2	16	no	—
386	D₄×C₄₇	—	4	16	no	—
387	C₂×C₄×C₄₇	—	2	8	no	—
388	C₂×C₄×C₄₇	—	2	2	no	—
389	C₂×C₄×C₄₇	—	2	2	no	—
390	C₂×C₄×C₄₇	—	2	8	no	—
391	C₂×C₄×C₄₇	—	2	8	no	—
392	C₂×C₄×C₄₇	—	2	8	no	—
393	C₂×C₄×C₄₇	—	2	8	no	—
394	C₂×C₄×C₄₇	—	2	8	no	—
395	C₂×C₄×C₄₇	—	4	8	no	—
396	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
397	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
398	C₂×C₄×C₄₇	C₂×#41	1	16	yes	complemented
399	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
400	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
401	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
402	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
403	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
404	C₂²⋊D₄₇	—	2	16	no	—
405	C₂²⋊D₄₇	—	2	16	no	—
406	C₂²⋊D₄₇	—	4	16	no	—
407	C₂²⋊D₄₇	—	4	8	no	—
408	C₂²⋊D₄₇	—	4	16	no	—
409	C₂×Dic₄₇	—	2	4	no	—
410	C₂×Dic₄₇	—	2	4	no	—
411	C₂×Dic₄₇	—	2	4	no	—
412	C₂×Dic₄₇	—	2	4	no	—
413	C₂×Dic₄₇	—	2	16	no	—
414	C₂×Dic₄₇	—	2	4	no	—
415	C₂×Dic₄₇	—	2	4	no	—
416	C₂×Dic₄₇	—	2	4	no	—
417	C₂×Dic₄₇	—	4	16	no	—
418	C₂×Dic₄₇	—	4	16	no	—
419	C₂×Dic₄₇	—	4	8	no	—
420	C₂×Dic₄₇	C₂⁵	1	4	yes	—
421	C₂×Dic₄₇	C₂⁵	1	4	yes	—
422	C₂×Dic₄₇	C₂⁵	1	4	yes	—
423	C₂×Dic₄₇	C₂⁵	1	4	yes	—
424	C₂×Dic₄₇	C₂⁵	1	4	yes	—
425	C₂×Dic₄₇	C₂⁵	1	4	yes	—
426	C₂×Dic₄₇	C₂⁵	1	4	yes	—
427	D₁₈₈	—	2	8	no	—
428	C₄×D₄₇	—	2	16	no	—
429	C₄×D₄₇	—	4	16	no	—
430	Dic₉₄	—	2	8	no	—
431	Dic₉₄	—	4	16	no	—
432	C₂×#3494	—	47	1	no	maximal, Sylow
433	C₂²×C₄₇	—	2	2	no	—
434	C₂²×C₄₇	—	2	2	no	—
435	C₂²×C₄₇	—	2	2	no	—
436	C₂²×C₄₇	—	2	2	no	—
437	C₂²×C₄₇	—	2	8	no	—
438	C₂²×C₄₇	—	2	8	no	—
439	C₂²×C₄₇	—	2	2	no	—
440	C₂²×C₄₇	—	2	8	no	—
441	C₂²×C₄₇	—	2	8	no	—
442	C₂²×C₄₇	—	2	2	no	—
443	C₂²×C₄₇	—	2	8	no	—
444	C₂²×C₄₇	—	2	2	no	—
445	C₂²×C₄₇	—	4	16	no	—
446	C₂²×C₄₇	—	4	4	no	—
447	C₂²×C₄₇	—	4	16	no	—
448	C₂²×C₄₇	—	8	16	no	—
449	C₂²×C₄₇	C₂²×#41	1	4	yes	—
450	C₂²×C₄₇	C₂²×#41	1	2	yes	—
451	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
452	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
453	C₂²×C₄₇	#585	1	2	yes	—
454	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
455	C₂×D₄₇	—	2	4	no	—
456	C₂×D₄₇	—	2	4	no	—
457	C₂×D₄₇	—	2	4	no	—
458	C₂×D₄₇	—	4	8	no	—
459	C₄×C₄₇	—	2	2	no	—
460	C₄×C₄₇	—	2	2	no	—
461	C₄×C₄₇	—	2	8	no	—
462	C₄×C₄₇	C₂²×#41	1	4	yes	—
463	C₄×C₄₇	C₂²×#41	1	4	yes	—
464	Dic₄₇	—	2	4	no	—
465	Dic₄₇	—	2	4	no	—
466	Dic₄₇	—	2	4	no	—
467	Dic₄₇	—	2	4	no	—
468	Dic₄₇	—	2	4	no	—
469	Dic₄₇	—	2	4	no	—
470	Dic₄₇	—	2	4	no	—
471	#3494	—	47	32	no	—
472	C₂×#555	—	47	2	no	—
473	C₂×#553	—	47	2	no	—
474	C₂×#553	—	47	2	no	—
475	C₂×#551	—	47	4	no	—
476	C₂×#547	—	47	2	no	—
477	C₂×#546	—	47	4	no	—
478	C₂×#544	—	47	1	no	—
479	C₂×#542	—	47	2	no	—
480	C₂×#540	—	47	2	no	—
481	C₂×#535	—	47	1	no	—
482	C₂×#532	—	47	2	no	—
483	C₂×#529	—	47	2	no	—
484	C₂×#525	—	47	1	no	—
485	C₂²×#121	D₄₇	1	1	yes	characteristic, complemented
486	C₂×#520	—	47	1	no	—
487	C₂×#518	—	47	1	no	—
488	C₂²×#117	—	47	1	no	—
489	C₂×C₄₇	—	2	4	no	—
490	C₂×C₄₇	—	2	4	no	—
491	C₂×C₄₇	—	4	2	no	—
492	C₂×C₄₇	—	4	8	no	—
493	C₂×C₄₇	#3494	1	4	yes	complemented
494	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
495	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
496	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
497	D₄₇	—	4	4	no	—
498	C₂²×#41	—	47	4	no	—
499	C₂²×#41	—	47	1	no	—
500	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
501	C₂³×D₄	C₂×D₄₇	1	2	yes	—
502	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
503	#555	—	47	32	no	—
504	#553	—	47	32	no	—
505	#553	—	47	32	no	—
506	#551	—	47	64	no	—
507	#547	—	47	32	no	—
508	#546	—	47	64	no	—
509	#544	—	47	16	no	—
510	#542	—	47	32	no	—
511	#540	—	47	32	no	—
512	#535	—	47	16	no	—
513	#532	—	47	32	no	—
514	C₂×C₄⋊Q₈	—	47	2	no	—
515	C₂×C₄⋊Q₈	—	47	2	no	—
516	C₂×#127	—	47	2	no	—
517	#529	—	47	32	no	—
518	C₂×#126	—	47	4	no	—
519	C₂×#126	—	47	4	no	—
520	C₂×#125	—	47	2	no	—
521	C₂×#125	—	47	2	no	—
522	C₂×#124	—	47	2	no	—
523	C₂×#124	—	47	4	no	—
524	C₂×#124	—	47	4	no	—
525	#525	—	47	16	no	—
526	C₂×#123	—	47	4	no	—
527	C₂×#123	—	47	4	no	—
528	C₂×#123	—	47	2	no	—
529	C₂×#123	—	47	4	no	—
530	C₂×#123	—	47	4	no	—
531	C₂×C₂²⋊Q₈	—	47	1	no	—
532	C₂×C₂²⋊Q₈	—	47	1	no	—
533	C₂×C₂²⋊Q₈	—	47	4	no	—
534	C₂×C₂²⋊Q₈	—	47	4	no	—
535	C₂×#121	—	47	4	no	—
536	C₂×#121	—	47	2	no	—
537	C₂×#121	—	47	2	no	—
538	C₂×#121	—	47	4	no	—
539	C₂×#121	—	47	4	no	—
540	C₂×#121	—	47	1	no	—
541	C₂×#121	—	47	1	no	—
542	C₂×#121	C₂×D₄₇	1	2	yes	—
543	C₂×#121	C₂×D₄₇	1	2	yes	—
544	C₂×#121	C₂×D₄₇	1	2	yes	—
545	C₂×#121	C₂×D₄₇	1	2	yes	—
546	C₂×#121	C₂×D₄₇	1	16	yes	complemented
547	C₂×#120	—	47	2	no	—
548	C₂×#120	—	47	4	no	—
549	#520	—	47	16	no	—
550	#518	—	47	16	no	—
551	C₂×C₄×Q₈	—	47	2	no	—
552	C₂×C₄×D₄	—	47	2	no	—
553	C₂×C₄×D₄	—	47	2	no	—
554	C₂×C₄×D₄	—	47	2	no	—
555	C₂×C₄×D₄	—	47	2	no	—
556	C₂×C₄×D₄	—	47	4	no	—
557	C₂×C₄×D₄	—	47	4	no	—
558	C₂×C₄×D₄	—	47	2	no	—
559	C₂×C₄×D₄	—	47	2	no	—
560	C₂×C₄×D₄	—	47	2	no	—
561	C₂×C₄×D₄	—	47	4	no	—
562	C₂×#117	—	47	1	no	—
563	C₂×#117	—	47	1	no	—
564	C₂×#117	—	47	2	no	—
565	C₂×#117	—	47	2	no	—
566	C₂×#117	—	47	1	no	—
567	C₂×#117	—	47	1	no	—
568	C₂×#117	—	47	16	no	—
569	C₂×#117	—	47	1	no	—
570	C₂×#117	—	47	2	no	—
571	C₂×#117	—	47	4	no	—
572	C₂²×C₄⋊C₄	—	47	1	no	—
573	C₂²×C₄⋊C₄	—	47	1	no	—
574	C₂²×C₄⋊C₄	—	47	2	no	—
575	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
576	C₂²×C₂²⋊C₄	—	47	2	no	—
577	C₂²×C₂²⋊C₄	—	47	4	no	—
578	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
579	C₂²×C₄²	—	47	2	no	—
580	C₄₇	C₂×#3494	1	1	yes	characteristic, complemented, Sylow
581	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
582	C₂⁵	C₂²×D₄₇	1	2	yes	—
583	C₂×#41	—	47	32	no	—
584	C₂×#41	—	47	8	no	—
585	C₂×#41	—	94	8	no	—
586	C₂×#41	—	188	16	no	—
587	C₂²×Q₈	—	47	1	no	—
588	C₂²×Q₈	—	47	4	no	—
589	C₂²×D₄	—	2	8	no	—
590	C₂²×D₄	—	4	8	no	—
591	C₂²×D₄	—	47	2	no	—
592	C₂²×D₄	—	47	2	no	—
593	C₂²×D₄	—	47	2	no	—
594	C₂²×D₄	—	47	4	no	—
595	C₂²×D₄	—	47	4	no	—
596	C₂²×D₄	—	47	1	no	—
597	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
598	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
599	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
600	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
601	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
602	C₂²×D₄	C₂²×D₄₇	1	16	yes	—
603	C₂³×C₄	—	2	8	no	—
604	C₂³×C₄	—	47	2	no	—
605	C₂³×C₄	—	47	2	no	—
606	C₂³×C₄	—	47	4	no	—
607	C₂³×C₄	—	47	4	no	—
608	C₂³×C₄	—	47	2	no	—
609	C₂³×C₄	—	47	4	no	—
610	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
611	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
612	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
613	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
614	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
615	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
616	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
617	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
618	C₄⋊Q₈	—	47	16	no	—
619	C₄⋊Q₈	—	47	16	no	—
620	#127	—	47	16	no	—
621	#126	—	47	32	no	—
622	#126	—	47	32	no	—
623	#125	—	47	16	no	—
624	#125	—	47	16	no	—
625	#124	—	47	16	no	—
626	#124	—	47	32	no	—
627	#124	—	47	32	no	—
628	#123	—	47	32	no	—
629	#123	—	47	32	no	—
630	#123	—	47	16	no	—
631	#123	—	47	32	no	—
632	#123	—	47	32	no	—
633	C₂²⋊Q₈	—	47	8	no	—
634	C₂²⋊Q₈	—	47	8	no	—
635	C₂²⋊Q₈	—	47	32	no	—
636	C₂²⋊Q₈	—	47	32	no	—
637	#121	—	47	32	no	—
638	#121	—	47	16	no	—
639	#121	—	47	16	no	—
640	#121	—	47	32	no	—
641	#121	—	47	32	no	—
642	#121	—	47	8	no	—
643	#121	—	47	8	no	—
644	#121	C₂²×D₄₇	1	16	yes	—
645	#121	C₂²×D₄₇	1	16	yes	—
646	#121	C₂²×D₄₇	1	16	yes	—
647	#121	C₂²×D₄₇	1	16	yes	—
648	#120	—	47	16	no	—
649	#120	—	47	32	no	—
650	C₄×Q₈	—	47	16	no	—
651	C₄×D₄	—	47	16	no	—
652	C₄×D₄	—	47	16	no	—
653	C₄×D₄	—	47	16	no	—
654	C₄×D₄	—	47	16	no	—
655	C₄×D₄	—	47	32	no	—
656	C₄×D₄	—	47	32	no	—
657	C₄×D₄	—	47	16	no	—
658	C₄×D₄	—	47	16	no	—
659	C₄×D₄	—	47	16	no	—
660	C₄×D₄	—	47	32	no	—
661	#117	—	47	8	no	—
662	#117	—	47	8	no	—
663	#117	—	47	16	no	—
664	#117	—	47	16	no	—
665	#117	—	47	8	no	—
666	#117	—	47	8	no	—
667	#117	—	47	8	no	—
668	#117	—	47	16	no	—
669	#117	—	47	32	no	—
670	C₂×C₄⋊C₄	—	47	1	no	—
671	C₂×C₄⋊C₄	—	47	1	no	—
672	C₂×C₄⋊C₄	—	47	1	no	—
673	C₂×C₄⋊C₄	—	47	1	no	—
674	C₂×C₄⋊C₄	—	47	2	no	—
675	C₂×C₄⋊C₄	—	47	2	no	—
676	C₂×C₄⋊C₄	—	47	8	no	—
677	C₂×C₄⋊C₄	—	47	8	no	—
678	C₂×C₄⋊C₄	—	47	4	no	—
679	C₂×C₄⋊C₄	—	47	2	no	—
680	C₂×C₄⋊C₄	—	47	1	no	—
681	C₂×C₄⋊C₄	—	47	1	no	—
682	C₂×C₄⋊C₄	—	47	4	no	—
683	C₂×C₄⋊C₄	—	47	4	no	—
684	C₂×C₄⋊C₄	—	47	4	no	—
685	C₂×C₄⋊C₄	—	47	2	no	—
686	C₂×C₄⋊C₄	—	47	16	no	—
687	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
688	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
689	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
690	C₂×C₂²⋊C₄	—	47	2	no	—
691	C₂×C₂²⋊C₄	—	47	2	no	—
692	C₂×C₂²⋊C₄	—	47	2	no	—
693	C₂×C₂²⋊C₄	—	47	2	no	—
694	C₂×C₂²⋊C₄	—	47	2	no	—
695	C₂×C₂²⋊C₄	—	47	16	no	—
696	C₂×C₂²⋊C₄	—	47	4	no	—
697	C₂×C₂²⋊C₄	—	47	4	no	—
698	C₂×C₂²⋊C₄	—	47	32	no	—
699	C₂×C₂²⋊C₄	—	47	4	no	—
700	C₂×C₂²⋊C₄	—	47	2	no	—
701	C₂×C₂²⋊C₄	—	47	4	no	—
702	C₂×C₂²⋊C₄	—	47	2	no	—
703	C₂×C₂²⋊C₄	—	47	4	no	—
704	C₂×C₂²⋊C₄	—	47	2	no	—
705	C₂×C₂²⋊C₄	—	47	2	no	—
706	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
707	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
709	C₂×C₄²	—	47	2	no	—
710	C₂×C₄²	—	47	2	no	—
711	C₂×C₄²	—	47	4	no	—
712	C₂×C₄²	—	47	2	no	—
713	C₂×C₄²	—	47	2	no	—
714	C₂×C₄²	—	47	16	no	—
715	C₂×C₄²	—	47	2	no	—
716	C₂⁴	—	2	4	no	—
717	C₂⁴	—	2	4	no	—
718	C₂⁴	—	2	8	no	—
719	C₂⁴	—	4	2	no	—
720	C₂⁴	—	4	4	no	—
721	C₂⁴	—	4	4	no	—
722	C₂⁴	—	47	2	no	—
723	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
724	C₂⁴	C₂³×D₄₇	1	4	yes	—
725	C₂⁴	C₂³×D₄₇	1	4	yes	—
726	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
727	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
728	C₂⁴	C₂³×D₄₇	1	8	yes	—
729	#41	—	94	32	no	—
730	#41	—	188	64	no	—
731	C₂×Q₈	—	47	4	no	—
732	C₂×Q₈	—	47	16	no	—
733	C₂×Q₈	—	94	4	no	—
734	C₂×Q₈	—	188	8	no	—
735	C₂×D₄	—	2	16	no	—
736	C₂×D₄	—	2	8	no	—
737	C₂×D₄	—	2	8	no	—
738	C₂×D₄	—	2	32	no	—
739	C₂×D₄	—	4	8	no	—
740	C₂×D₄	—	4	32	no	—
741	C₂×D₄	—	47	8	no	—
742	C₂×D₄	—	47	8	no	—
743	C₂×D₄	—	47	8	no	—
744	C₂×D₄	—	47	16	no	—
745	C₂×D₄	—	47	16	no	—
746	C₂×D₄	—	47	4	no	—
747	C₂×D₄	—	94	8	no	—
748	C₂×D₄	—	94	8	no	—
749	C₂×D₄	—	94	4	no	—
750	C₂×D₄	—	188	4	no	—
751	C₂×D₄	—	188	8	no	—
752	C₂×D₄	—	188	8	no	—
753	C₂×D₄	C₂³×D₄₇	1	8	yes	—
754	C₂×D₄	C₂³×D₄₇	1	8	yes	—
755	C₂×D₄	C₂³×D₄₇	1	16	yes	—
756	C₂×D₄	C₂³×D₄₇	1	16	yes	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	32	no	—
763	C₂²×C₄	—	4	4	no	—
764	C₂²×C₄	—	47	8	no	—
765	C₂²×C₄	—	47	2	no	—
766	C₂²×C₄	—	47	2	no	—
767	C₂²×C₄	—	47	2	no	—
768	C₂²×C₄	—	47	2	no	—
769	C₂²×C₄	—	47	2	no	—
770	C₂²×C₄	—	47	2	no	—
771	C₂²×C₄	—	47	2	no	—
772	C₂²×C₄	—	47	8	no	—
773	C₂²×C₄	—	47	16	no	—
774	C₂²×C₄	—	47	16	no	—
775	C₂²×C₄	—	47	8	no	—
776	C₂²×C₄	—	47	16	no	—
777	C₂²×C₄	—	94	8	no	—
778	C₂²×C₄	—	94	8	no	—
779	C₂²×C₄	—	188	8	no	—
780	C₂²×C₄	—	188	8	no	—
781	C₂²×C₄	—	188	4	no	—
782	C₂²×C₄	—	188	8	no	—
783	C₂²×C₄	#10625352	1	8	yes	complemented
784	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
785	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
786	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
787	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
788	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
789	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
790	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
791	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
792	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
793	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
794	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
795	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
796	C₄⋊C₄	—	47	16	no	—
797	C₄⋊C₄	—	47	8	no	—
798	C₄⋊C₄	—	47	16	no	—
799	C₄⋊C₄	—	47	16	no	—
800	C₄⋊C₄	—	47	8	no	—
801	C₄⋊C₄	—	47	4	no	—
802	C₄⋊C₄	—	47	4	no	—
803	C₄⋊C₄	—	47	4	no	—
804	C₄⋊C₄	—	47	4	no	—
805	C₄⋊C₄	—	47	8	no	—
806	C₄⋊C₄	—	47	8	no	—
807	C₄⋊C₄	—	47	4	no	—
808	C₄⋊C₄	—	47	4	no	—
809	C₄⋊C₄	—	47	16	no	—
810	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
811	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
812	C₂²⋊C₄	—	47	8	no	—
813	C₂²⋊C₄	—	47	8	no	—
814	C₂²⋊C₄	—	47	8	no	—
815	C₂²⋊C₄	—	47	8	no	—
816	C₂²⋊C₄	—	47	8	no	—
817	C₂²⋊C₄	—	47	16	no	—
818	C₂²⋊C₄	—	47	16	no	—
819	C₂²⋊C₄	—	47	16	no	—
820	C₂²⋊C₄	—	47	8	no	—
821	C₂²⋊C₄	—	47	16	no	—
822	C₂²⋊C₄	—	47	8	no	—
823	C₂²⋊C₄	—	47	16	no	—
824	C₂²⋊C₄	—	47	8	no	—
825	C₂²⋊C₄	—	47	8	no	—
826	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
827	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
828	C₄²	—	47	8	no	—
829	C₄²	—	47	8	no	—
830	C₄²	—	47	8	no	—
831	C₄²	—	47	8	no	—
832	C₄²	—	47	16	no	—
833	C₄²	—	47	8	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	8	no	—
841	C₂³	—	2	8	no	—
842	C₂³	—	2	8	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	8	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	16	no	—
847	C₂³	—	4	4	no	—
848	C₂³	—	4	8	no	—
849	C₂³	—	4	8	no	—
850	C₂³	—	4	16	no	—
851	C₂³	—	8	16	no	—
852	C₂³	—	47	4	no	—
853	C₂³	—	94	4	no	—
854	C₂³	—	94	4	no	—
855	C₂³	—	94	4	no	—
856	C₂³	C₂×#10625352	1	4	yes	—
857	C₂³	#13094069	1	4	yes	—
858	C₂³	C₂⁴×D₄₇	1	2	yes	—
859	C₂³	C₂⁴×D₄₇	1	8	yes	—
860	C₂³	C₂⁴×D₄₇	1	2	yes	—
861	C₂³	C₂⁴×D₄₇	1	2	yes	—
862	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
863	Q₈	—	94	8	no	—
864	Q₈	—	188	16	no	—
865	D₄	—	2	32	no	—
866	D₄	—	2	16	no	—
867	D₄	—	2	16	no	—
868	D₄	—	4	16	no	—
869	D₄	—	94	16	no	—
870	D₄	—	94	16	no	—
871	D₄	—	94	8	no	—
872	D₄	—	188	8	no	—
873	D₄	—	188	16	no	—
874	D₄	—	188	16	no	—
875	C₂×C₄	—	2	8	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	8	no	—
879	C₂×C₄	—	2	8	no	—
880	C₂×C₄	—	2	8	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	4	8	no	—
884	C₂×C₄	—	47	4	no	—
885	C₂×C₄	—	47	4	no	—
886	C₂×C₄	—	47	4	no	—
887	C₂×C₄	—	47	4	no	—
888	C₂×C₄	—	47	4	no	—
889	C₂×C₄	—	47	4	no	—
890	C₂×C₄	—	47	4	no	—
891	C₂×C₄	—	94	4	no	—
892	C₂×C₄	—	94	4	no	—
893	C₂×C₄	—	94	4	no	—
894	C₂×C₄	—	94	16	no	—
895	C₂×C₄	—	94	4	no	—
896	C₂×C₄	—	94	4	no	—
897	C₂×C₄	—	94	4	no	—
898	C₂×C₄	—	94	4	no	—
899	C₂×C₄	—	94	16	no	—
900	C₂×C₄	—	188	16	no	—
901	C₂×C₄	—	188	16	no	—
902	C₂×C₄	—	188	8	no	—
903	C₂×C₄	—	188	16	no	—
904	C₂×C₄	C₂×#10625352	1	4	yes	—
905	C₂×C₄	C₂×#10625352	1	4	yes	—
906	C₂×C₄	C₂×#10625352	1	16	yes	complemented
907	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
908	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
909	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
910	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
911	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
912	C₂²	—	2	8	no	—
913	C₂²	—	2	8	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	8	no	—
920	C₂²	—	2	8	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	8	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	4	16	no	—
925	C₂²	—	4	4	no	—
926	C₂²	—	4	16	no	—
927	C₂²	—	8	16	no	—
928	C₂²	—	94	4	no	—
929	C₂²	—	94	4	no	—
930	C₂²	—	94	4	no	—
931	C₂²	—	188	8	no	—
932	C₂²	C₂²×#10625352	1	4	yes	—
933	C₂²	C₂²×#10625352	1	2	yes	—
934	C₂²	C₂×#13094069	1	4	yes	—
935	C₂²	C₂×#13094069	1	2	yes	—
936	C₂²	#15689959	1	2	yes	—
937	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	8	no	—
941	C₄	—	94	4	no	—
942	C₄	—	94	4	no	—
943	C₄	—	94	4	no	—
944	C₄	—	94	4	no	—
945	C₄	—	94	4	no	—
946	C₄	—	94	4	no	—
947	C₄	—	94	4	no	—
948	C₄	C₂²×#10625352	1	4	yes	—
949	C₄	C₂²×#10625352	1	4	yes	—
950	C₂	—	2	4	no	—
951	C₂	—	2	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	4	8	no	—
954	C₂	—	188	4	no	—
955	C₂	#20257117	1	4	yes	direct product factor
956	C₂	C₂³×#10625352	1	1	yes	characteristic
957	C₂	C₂²×#13094069	1	1	yes	characteristic
958	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×#121×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#121	D₄₇
hypocenter	C₄₇	C₂×#3494
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. #20257117	C₂	direct (N × H)
2. C₂×#15689837	C₂	semidirect
3. C₂×#15689825	C₂	semidirect
4. C₂×#15689820	C₂	semidirect
5. C₂×#15689799	C₂	semidirect
6. C₂×#15689773	C₂	semidirect
7. C₂×#15689767	C₂	semidirect
8. C₂×#15689754	C₂	semidirect
9. C₂×#15689740	C₂	semidirect
10. C₂×#15689726	C₂	semidirect
11. C₂×#15689690	C₂	semidirect
12. C₂×#15689668	C₂	semidirect
13. C₂×#15689654	C₂	semidirect
14. C₂×#15689634	C₂	semidirect
15. C₂×#15689604	C₂	semidirect
16. C₂×#15689598	C₂	semidirect
17. C₂²×#13093983	C₂	semidirect
18. C₂²×#121×C₄₇	C₂	semidirect
20. C₂²×#10625352	C₂²	semidirect
21. #15689837	C₂²	semidirect
22. #15689825	C₂²	semidirect
23. #15689820	C₂²	semidirect
24. #15689799	C₂²	semidirect
25. #15689773	C₂²	semidirect
26. #15689767	C₂²	semidirect
27. #15689754	C₂²	semidirect
28. #15689740	C₂²	semidirect
29. #15689726	C₂²	semidirect
30. #15689690	C₂²	semidirect
31. #15689668	C₂²	semidirect
32. C₂×#13094023	C₂²	semidirect
33. C₂×#13094023	C₂²	semidirect
34. C₂×#13094020	C₂²	semidirect
35. #15689654	C₂²	semidirect
36. C₂×#13094017	C₂²	semidirect
37. C₂×#13094017	C₂²	semidirect
38. C₂×#13094015	C₂²	semidirect
39. C₂×#13094015	C₂²	semidirect
40. C₂×#13094011	C₂²	semidirect
41. C₂×#13094011	C₂²	semidirect
42. C₂×#13094010	C₂²	semidirect
43. #15689634	C₂²	semidirect
44. C₂×#13094008	C₂²	semidirect
46. C₂×#13094006	C₂²	semidirect
47. C₂×#13094005	C₂²	semidirect
48. C₂×#13094005	C₂²	semidirect
50. C₂×#13094003	C₂²	semidirect
51. C₂×#13094003	C₂²	semidirect
52. C₂×#13094001	C₂²	semidirect
53. C₂×#13093998	C₂²	semidirect
54. C₂×#13093998	C₂²	semidirect
55. C₂×#13093996	C₂²	semidirect
56. C₂×#13093996	C₂²	semidirect
57. C₂×#13093995	C₂²	semidirect
58. C₂×#13093995	C₂²	semidirect
59. C₂×#13093995	C₂²	semidirect
62. #15689604	C₂²	semidirect
63. #15689598	C₂²	semidirect
64. C₂×#13093989	C₂²	semidirect
65. C₂×D₄×Dic₄₇	C₂²	semidirect
66. C₂×D₄×Dic₄₇	C₂²	semidirect
67. C₂×D₄×Dic₄₇	C₂²	semidirect
68. C₂×D₄×Dic₄₇	C₂²	semidirect
69. C₂×D₄×Dic₄₇	C₂²	semidirect
70. C₂×#13093986	C₂²	semidirect
72. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
73. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
74. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
79. C₂×#13093983	C₂²	semidirect
80. C₂×#13093983	C₂²	semidirect
81. C₂×#13093983	C₂²	semidirect
82. C₂×#13093983	C₂²	semidirect
83. C₂×#13093982	C₂²	semidirect
84. C₂×#13093980	C₂²	semidirect
85. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
86. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
87. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
90. C₂²×C₄×Dic₄₇	C₂²	semidirect
98. C₂×#121×C₄₇	C₂²	semidirect
104. C₂×#10625352	C₂³	semidirect
119. #13094023	C₂³	semidirect
120. #13094023	C₂³	semidirect
121. #13094020	C₂³	semidirect
122. #13094017	C₂³	semidirect
123. #13094017	C₂³	semidirect
124. #13094015	C₂³	semidirect
125. #13094015	C₂³	semidirect
126. #13094011	C₂³	semidirect
127. #13094011	C₂³	semidirect
128. #13094010	C₂³	semidirect
129. #13094008	C₂³	semidirect
131. #13094006	C₂³	semidirect
132. #13094005	C₂³	semidirect
133. #13094005	C₂³	semidirect
135. #13094003	C₂³	semidirect
136. #13094003	C₂³	semidirect
137. #13094001	C₂³	semidirect
138. #13093998	C₂³	semidirect
139. #13093998	C₂³	semidirect
140. #13093996	C₂³	semidirect
141. #13093996	C₂³	semidirect
142. #13093995	C₂³	semidirect
143. #13093995	C₂³	semidirect
144. #13093995	C₂³	semidirect
147. #13093989	C₂³	semidirect
148. D₄×Dic₄₇	C₂³	semidirect
149. D₄×Dic₄₇	C₂³	semidirect
150. D₄×Dic₄₇	C₂³	semidirect
151. D₄×Dic₄₇	C₂³	semidirect
152. D₄×Dic₄₇	C₂³	semidirect
153. #13093986	C₂³	semidirect
155. C₄×C₂²⋊D₄₇	C₂³	semidirect
156. C₄×C₂²⋊D₄₇	C₂³	semidirect
157. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
162. #13093983	C₂³	semidirect
163. #13093983	C₂³	semidirect
164. #13093983	C₂³	semidirect
165. #13093982	C₂³	semidirect
166. #13093980	C₂³	semidirect
176. C₂×C₄⋊Dic₄₇	C₂³	semidirect
177. C₂×C₄⋊Dic₄₇	C₂³	semidirect
183. C₄⋊C₄×D₄₇	C₂³	semidirect
206. C₂×C₄×Dic₄₇	C₂³	semidirect
266. C₂²×C₄×C₄₇	#41	semidirect
398. C₂×C₄×C₄₇	C₂×#41	semidirect
485. C₂²×#121	D₄₇	semidirect
493. C₂×C₄₇	#3494	semidirect
546. C₂×#121	C₂×D₄₇	semidirect
580. C₄₇	C₂×#3494	semidirect
783. C₂²×C₄	#10625352	semidirect
906. C₂×C₄	C₂×#10625352	semidirect
955. C₂	#20257117	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257117	2
C₂×#15689837	2
C₂×#15689825	2
C₂×#15689820	2
C₂×#15689799	2
C₂×#15689773	2
C₂×#15689767	2
C₂×#15689754	2
C₂×#15689740	2
C₂×#15689726	2
C₂×#15689690	2
C₂×#15689668	2
C₂×#15689654	2
C₂×#15689634	2
C₂×#15689604	2
C₂×#15689598	2
C₂²×#13093983	2
C₂²×#121×C₄₇	2
C₂×#3494	47

Subgroups — C2×#20257117 #27124615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257117 #27124615