Subgroups — C₂×#20257437 #27124291

Order 12032.

7910 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257437	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689843	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689828	C₂	1	2	yes	maximal, complemented
4	C₂×#15689813	C₂	1	2	yes	maximal, complemented
5	C₂×#15689799	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689782	C₂	1	2	yes	maximal, complemented
8	C₂×#15689778	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689777	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15689767	C₂	1	2	yes	maximal, complemented
11	C₂×#15689738	C₂	1	2	yes	maximal, complemented
12	C₂×#15689715	C₂	1	4	yes	maximal, complemented
13	C₂×#15689680	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15689657	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15689634	C₂	1	2	yes	maximal, complemented
16	C₂²×#13094003	C₂	1	2	yes	maximal, complemented
17	C₂×#15689602	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10625350	C₂²	1	2	yes	complemented
20	C₂²×#10625352	C₂²	1	2	yes	—
21	C₂³×Dic₉₄	C₂²	1	2	yes	complemented
22	#15689843	C₂²	1	16	yes	complemented
23	#15689828	C₂²	1	32	yes	complemented
24	#15689813	C₂²	1	32	yes	complemented
25	#15689799	C₂²	1	64	yes	complemented
26	D₄×Dic₉₄	C₂²	1	16	yes	complemented
27	#15689782	C₂²	1	32	yes	complemented
28	#15689778	C₂²	1	16	yes	complemented
29	#15689777	C₂²	1	16	yes	complemented
30	#15689767	C₂²	1	32	yes	complemented
31	#15689738	C₂²	1	32	yes	complemented
32	#15689715	C₂²	1	64	yes	complemented
33	#15689680	C₂²	1	16	yes	complemented
34	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13094023	C₂²	1	2	yes	complemented
37	#15689657	C₂²	1	16	yes	complemented
38	C₂×#13094018	C₂²	1	2	yes	complemented
39	C₂×#13094017	C₂²	1	4	yes	complemented
40	C₂×#13094017	C₂²	1	4	yes	complemented
41	C₂×#13094016	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13094016	C₂²	1	2	yes	complemented
43	C₂×#13094014	C₂²	1	4	yes	complemented
44	C₂×#13094012	C₂²	1	1	yes	characteristic, complemented
45	C₂×#13094011	C₂²	1	2	yes	—
46	C₂×#13094010	C₂²	1	4	yes	complemented
47	#15689634	C₂²	1	32	yes	complemented
48	C₂×#13094008	C₂²	1	4	yes	complemented
49	C₂×#13094007	C₂²	1	2	yes	—
50	C₂×#13094007	C₂²	1	4	yes	complemented
51	C₂×#13094006	C₂²	1	4	yes	complemented
52	C₂×#13094005	C₂²	1	4	yes	—
53	C₂×#13094004	C₂²	1	2	yes	complemented
54	C₂×#13094003	C₂²	1	2	yes	—
55	C₂×#13094003	C₂²	1	1	yes	characteristic
56	C₂×#13094003	C₂²	1	4	yes	—
57	C₂×#13094003	C₂²	1	2	yes	—
58	C₂×#13094003	C₂²	1	2	yes	complemented
59	C₂×#13094003	C₂²	1	2	yes	complemented
60	C₂×#13094003	C₂²	1	2	yes	complemented
61	C₂×#13094003	C₂²	1	4	yes	complemented
62	C₂×#13094003	C₂²	1	32	yes	complemented
63	C₂×#13094002	C₂²	1	4	yes	complemented
64	C₂×#13094001	C₂²	1	4	yes	complemented
65	C₂×#13093998	C₂²	1	1	yes	characteristic
66	C₂×#13093998	C₂²	1	2	yes	complemented
67	C₂×#13093996	C₂²	1	4	yes	—
68	C₂×#13093995	C₂²	1	2	yes	—
69	C₂×#13093993	C₂²	1	4	yes	—
70	#15689602	C₂²	1	32	yes	complemented
71	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
72	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
73	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
74	C₂×#13093989	C₂²	1	2	yes	complemented
75	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
77	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
78	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
79	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
80	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
81	C₂×#13093983	C₂²	1	2	yes	—
82	C₂×#13093983	C₂²	1	2	yes	complemented
83	C₂×#13093981	C₂²	1	2	yes	complemented
84	C₂×#13093980	C₂²	1	4	yes	complemented
85	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
86	C₂²×Dic₄₇⋊C₄	C₂²	1	4	yes	complemented
87	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
88	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
89	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
90	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
91	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
92	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
93	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
94	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
95	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
96	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
97	C₂×C₄×D₄×C₄₇	C₂²	1	16	yes	complemented
98	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
99	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
100	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
101	C₂×#10625350	—	4	8	no	—
102	C₂×#10625350	C₂³	1	16	yes	complemented
103	C₂×#10625352	—	2	16	no	—
104	C₂×#10625352	C₂³	1	16	yes	—
105	C₂²×Dic₉₄	—	4	8	no	—
106	C₂²×Dic₉₄	C₂³	1	2	yes	—
107	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
108	C₂²×Dic₉₄	C₂³	1	2	yes	—
109	C₂²×Dic₉₄	C₂³	1	4	yes	—
110	C₂²×Dic₉₄	C₂³	1	16	yes	complemented
111	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
112	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
113	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
114	C₂²×C₂²⋊D₄₇	C₂³	1	4	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	#13094024	C₂³	1	8	yes	complemented
120	#13094024	C₂³	1	8	yes	complemented
121	#13094023	C₂³	1	16	yes	complemented
122	#13094018	C₂³	1	16	yes	complemented
123	#13094017	C₂³	1	32	yes	complemented
124	#13094017	C₂³	1	32	yes	complemented
125	#13094016	C₂³	1	8	yes	complemented
126	#13094016	C₂³	1	16	yes	complemented
127	#13094014	C₂³	1	32	yes	complemented
128	#13094012	C₂³	1	8	yes	complemented
129	#13094011	C₂³	1	16	yes	—
130	#13094010	C₂³	1	32	yes	complemented
131	#13094008	C₂³	1	32	yes	complemented
132	#13094007	C₂³	1	16	yes	—
133	#13094007	C₂³	1	32	yes	complemented
134	#13094006	C₂³	1	32	yes	complemented
135	#13094005	C₂³	1	32	yes	—
136	#13094004	C₂³	1	16	yes	complemented
137	#13094003	C₂³	1	16	yes	—
138	#13094003	C₂³	1	32	yes	—
139	#13094003	C₂³	1	8	yes	—
140	#13094003	C₂³	1	16	yes	—
141	#13094003	C₂³	1	32	yes	complemented
142	#13094003	C₂³	1	16	yes	complemented
143	#13094003	C₂³	1	16	yes	complemented
144	#13094003	C₂³	1	16	yes	complemented
145	#13094002	C₂³	1	32	yes	complemented
146	#13094001	C₂³	1	32	yes	complemented
147	#13093998	C₂³	1	8	yes	—
148	#13093998	C₂³	1	16	yes	complemented
149	#13093996	C₂³	1	32	yes	—
150	#13093995	C₂³	1	16	yes	—
151	#13093993	C₂³	1	32	yes	—
152	C₄×Dic₉₄	C₂³	1	16	yes	complemented
153	C₄×Dic₉₄	C₂³	1	16	yes	complemented
154	C₄×Dic₉₄	C₂³	1	8	yes	complemented
155	#13093989	C₂³	1	16	yes	complemented
156	C₄×D₁₈₈	C₂³	1	8	yes	complemented
157	D₄×Dic₄₇	C₂³	1	16	yes	—
158	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
159	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
160	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
161	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
162	#13093983	C₂³	1	16	yes	—
163	#13093983	C₂³	1	16	yes	complemented
164	#13093981	C₂³	1	16	yes	complemented
165	#13093980	C₂³	1	32	yes	complemented
166	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
167	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
169	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
170	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
171	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
174	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
175	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
176	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
177	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
178	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
179	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
180	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
181	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
182	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
183	C₂×Dic₄₇⋊C₄	C₂³	1	32	yes	complemented
184	C₄⋊C₄×D₄₇	C₂³	1	16	yes	complemented
185	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	—
186	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
188	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
189	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
190	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
191	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
192	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
193	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
194	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
195	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
196	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
197	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
198	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
199	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
200	C₂⁵×C₄₇	C₂³	1	2	yes	—
201	C₂²×D₄×C₄₇	—	2	8	no	—
202	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
203	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
204	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
205	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₄₇	—	4	8	no	—
207	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
211	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
212	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
213	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
214	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
215	C₂³×C₄×C₄₇	C₂³	1	16	yes	—
216	C₄×D₄×C₄₇	C₂³	1	8	yes	—
217	C₄×D₄×C₄₇	C₂³	1	8	yes	—
218	C₄×D₄×C₄₇	C₂³	1	8	yes	—
219	C₄×D₄×C₄₇	C₂³	1	16	yes	—
220	C₄×D₄×C₄₇	C₂³	1	8	yes	—
221	C₄×D₄×C₄₇	C₂³	1	16	yes	—
222	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
226	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
231	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
236	C₂⁴×C₄₇	—	2	8	no	—
237	C₂⁴×C₄₇	—	2	8	no	—
238	C₂⁴×C₄₇	—	4	4	no	—
239	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
240	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
241	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
242	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂³×D₄₇	C₂⁴	1	2	yes	—
244	C₂×D₄×C₄₇	—	2	8	no	—
245	C₂×D₄×C₄₇	—	2	32	no	—
246	C₂×D₄×C₄₇	—	2	4	no	—
247	C₂×D₄×C₄₇	#41	1	8	yes	complemented
248	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
249	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
250	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₄₇	—	2	4	no	—
252	C₂²×C₄×C₄₇	—	2	4	no	—
253	C₂²×C₄×C₄₇	—	2	4	no	—
254	C₂²×C₄×C₄₇	—	2	8	no	—
255	C₂²×C₄×C₄₇	—	2	8	no	—
256	C₂²×C₄×C₄₇	—	4	32	no	—
257	C₂²×C₄×C₄₇	—	4	4	no	—
258	C₂²×C₄×C₄₇	—	4	4	no	—
259	C₂²×C₄×C₄₇	—	4	4	no	—
260	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
270	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
272	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
273	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
274	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₂²⋊D₄₇	—	2	16	no	—
277	C₂×C₂²⋊D₄₇	—	2	8	no	—
278	C₂×C₂²⋊D₄₇	—	4	8	no	—
279	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
280	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
281	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
282	C₂²×Dic₄₇	—	2	16	no	—
283	C₂²×Dic₄₇	—	4	8	no	—
284	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
285	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
286	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
287	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
288	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
289	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
290	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
291	#10625352	—	2	64	no	—
292	#10625350	—	4	32	no	—
293	C₂×D₁₈₈	—	2	4	no	—
294	C₂×D₁₈₈	C₂⁴	1	4	yes	—
295	C₂×C₄×D₄₇	—	2	8	no	—
296	C₂×C₄×D₄₇	—	4	8	no	—
297	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
298	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
299	C₂×Dic₉₄	—	2	8	no	—
300	C₂×Dic₉₄	—	2	4	no	—
301	C₂×Dic₉₄	—	2	8	no	—
302	C₂×Dic₉₄	—	4	32	no	—
303	C₂×Dic₉₄	—	4	8	no	—
304	C₂×Dic₉₄	C₂⁴	1	8	yes	—
305	C₂×Dic₉₄	C₂⁴	1	4	yes	—
306	C₂×Dic₉₄	C₂⁴	1	8	yes	—
307	C₂×Dic₉₄	C₂⁴	1	16	yes	—
308	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
311	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
312	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
313	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
314	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
315	C₄²×C₄₇	C₂⁴	1	4	yes	—
316	C₄²×C₄₇	C₂⁴	1	4	yes	—
317	C₄²×C₄₇	C₂⁴	1	4	yes	—
318	C₄²×C₄₇	C₂⁴	1	4	yes	—
319	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
320	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
321	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
322	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
323	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
324	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
325	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
326	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
327	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
328	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
329	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
330	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
331	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
332	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
333	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
334	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
335	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
336	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
337	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
338	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
339	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
340	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
341	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
342	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
343	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
344	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
345	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
346	C₄×Dic₄₇	C₂⁴	1	16	yes	—
347	C₄×Dic₄₇	C₂⁴	1	16	yes	—
348	C₄×Dic₄₇	C₂⁴	1	8	yes	—
349	C₂³×C₄₇	—	2	2	no	—
350	C₂³×C₄₇	—	2	4	no	—
351	C₂³×C₄₇	—	2	2	no	—
352	C₂³×C₄₇	—	2	4	no	—
353	C₂³×C₄₇	—	2	16	no	—
354	C₂³×C₄₇	—	2	4	no	—
355	C₂³×C₄₇	—	2	4	no	—
356	C₂³×C₄₇	—	2	16	no	—
357	C₂³×C₄₇	—	2	4	no	—
358	C₂³×C₄₇	—	4	8	no	—
359	C₂³×C₄₇	—	4	32	no	—
360	C₂³×C₄₇	C₂×#41	1	8	yes	—
361	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
362	C₂³×C₄₇	C₂⁵	1	4	yes	—
363	C₂³×C₄₇	C₂⁵	1	4	yes	—
364	C₂³×C₄₇	C₂⁵	1	2	yes	—
365	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
366	C₂²×D₄₇	—	2	4	no	—
367	C₂²×D₄₇	—	2	4	no	—
368	C₂²×D₄₇	—	2	4	no	—
369	C₂²×D₄₇	C₂⁵	1	4	yes	—
370	D₄×C₄₇	—	2	16	no	—
371	D₄×C₄₇	—	2	8	no	—
372	D₄×C₄₇	C₂×#41	1	16	yes	complemented
373	C₂×C₄×C₄₇	—	2	2	no	—
374	C₂×C₄×C₄₇	—	2	4	no	—
375	C₂×C₄×C₄₇	—	2	4	no	—
376	C₂×C₄×C₄₇	—	2	2	no	—
377	C₂×C₄×C₄₇	—	2	8	no	—
378	C₂×C₄×C₄₇	—	2	2	no	—
379	C₂×C₄×C₄₇	—	2	2	no	—
380	C₂×C₄×C₄₇	—	2	8	no	—
381	C₂×C₄×C₄₇	—	2	16	no	—
382	C₂×C₄×C₄₇	—	2	16	no	—
383	C₂×C₄×C₄₇	—	2	8	no	—
384	C₂×C₄×C₄₇	—	4	8	no	—
385	C₂×C₄×C₄₇	—	4	8	no	—
386	C₂×C₄×C₄₇	—	4	8	no	—
387	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
388	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
389	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
390	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
391	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
392	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
393	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
394	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
395	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
396	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
397	C₂²⋊D₄₇	—	2	32	no	—
398	C₂²⋊D₄₇	—	2	16	no	—
399	C₂²⋊D₄₇	—	4	16	no	—
400	C₂×Dic₄₇	—	2	8	no	—
401	C₂×Dic₄₇	—	2	4	no	—
402	C₂×Dic₄₇	—	2	32	no	—
403	C₂×Dic₄₇	—	2	4	no	—
404	C₂×Dic₄₇	—	2	8	no	—
405	C₂×Dic₄₇	—	2	4	no	—
406	C₂×Dic₄₇	—	4	16	no	—
407	C₂×Dic₄₇	C₂⁵	1	4	yes	—
408	C₂×Dic₄₇	C₂⁵	1	8	yes	—
409	C₂×Dic₄₇	C₂⁵	1	8	yes	—
410	C₂×Dic₄₇	C₂⁵	1	4	yes	—
411	C₂×Dic₄₇	C₂⁵	1	4	yes	—
412	D₁₈₈	—	2	8	no	—
413	C₄×D₄₇	—	2	16	no	—
414	C₄×D₄₇	—	4	16	no	—
415	Dic₉₄	—	2	16	no	—
416	Dic₉₄	—	2	8	no	—
417	Dic₉₄	—	2	16	no	—
418	Dic₉₄	—	4	16	no	—
419	C₂×#3520	—	47	1	no	maximal, Sylow
420	C₂²×C₄₇	—	2	2	no	—
421	C₂²×C₄₇	—	2	4	no	—
422	C₂²×C₄₇	—	2	2	no	—
423	C₂²×C₄₇	—	2	4	no	—
424	C₂²×C₄₇	—	2	8	no	—
425	C₂²×C₄₇	—	2	16	no	—
426	C₂²×C₄₇	—	2	4	no	—
427	C₂²×C₄₇	—	2	4	no	—
428	C₂²×C₄₇	—	2	4	no	—
429	C₂²×C₄₇	—	4	32	no	—
430	C₂²×C₄₇	—	4	8	no	—
431	C₂²×C₄₇	C₂²×#41	1	8	yes	—
432	C₂²×C₄₇	C₂²×#41	1	2	yes	—
433	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
434	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
435	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
436	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
437	C₂×D₄₇	—	2	4	no	—
438	C₂×D₄₇	—	2	4	no	—
439	C₂×D₄₇	—	2	4	no	—
440	C₂×D₄₇	—	4	8	no	—
441	C₄×C₄₇	—	2	2	no	—
442	C₄×C₄₇	—	2	4	no	—
443	C₄×C₄₇	—	2	4	no	—
444	C₄×C₄₇	—	2	2	no	—
445	C₄×C₄₇	—	2	2	no	—
446	C₄×C₄₇	—	2	2	no	—
447	C₄×C₄₇	C₂²×#41	1	4	yes	—
448	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
449	Dic₄₇	—	2	8	no	—
450	Dic₄₇	—	2	4	no	—
451	Dic₄₇	—	2	4	no	—
452	Dic₄₇	—	2	8	no	—
453	Dic₄₇	—	2	4	no	—
454	#3520	—	47	32	no	—
455	C₂×#556	—	47	1	no	—
456	C₂×#554	—	47	2	no	—
457	C₂×#552	—	47	2	no	—
458	C₂×#551	—	47	4	no	—
459	C₂×D₄×Q₈	—	47	1	no	—
460	C₂×#548	—	47	2	no	—
461	C₂×#547	—	47	1	no	—
462	C₂×#547	—	47	1	no	—
463	C₂×#546	—	47	2	no	—
464	C₂×#542	—	47	2	no	—
465	C₂×#539	—	47	4	no	—
466	C₂×#533	—	47	1	no	—
467	C₂×#529	—	47	1	no	—
468	C₂×#525	—	47	2	no	—
469	C₂²×C₂²⋊Q₈	—	47	2	no	—
470	C₂×#520	—	47	2	no	—
471	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic, complemented
472	C₂×C₄₇	—	2	4	no	—
473	C₂×C₄₇	—	2	8	no	—
474	C₂×C₄₇	—	4	4	no	—
475	C₂×C₄₇	#3520	1	4	yes	complemented
476	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
477	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
479	D₄₇	—	4	4	no	—
480	C₂²×#41	—	47	2	no	—
481	C₂²×#41	—	47	2	no	—
482	C₂³×Q₈	—	47	2	no	—
483	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
484	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
485	#556	—	47	16	no	—
486	#554	—	47	32	no	—
487	#552	—	47	32	no	—
488	#551	—	47	64	no	—
489	D₄×Q₈	—	47	16	no	—
490	#548	—	47	32	no	—
491	#547	—	47	16	no	—
492	#547	—	47	16	no	—
493	#546	—	47	32	no	—
494	#542	—	47	32	no	—
495	#539	—	47	64	no	—
496	#533	—	47	16	no	—
497	C₂×C₄⋊Q₈	—	47	2	no	—
498	C₂×C₄⋊Q₈	—	47	1	no	—
499	C₂×C₄⋊Q₈	—	47	1	no	—
500	#529	—	47	16	no	—
501	C₂×#126	—	47	4	no	—
502	C₂×#126	—	47	4	no	—
503	C₂×#126	—	47	2	no	—
504	C₂×#125	—	47	4	no	—
505	C₂×#125	—	47	1	no	—
506	C₂×#125	—	47	2	no	—
507	C₂×#124	—	47	2	no	—
508	C₂×#124	—	47	4	no	—
509	C₂×#124	—	47	1	no	—
510	#525	—	47	32	no	—
511	C₂×#123	—	47	4	no	—
512	C₂×#123	—	47	4	no	—
513	C₂×#123	—	47	2	no	—
514	C₂×#123	—	47	4	no	—
515	C₂×#123	—	47	4	no	—
516	C₂×C₂²⋊Q₈	—	47	1	no	—
517	C₂×C₂²⋊Q₈	—	47	2	no	—
518	C₂×C₂²⋊Q₈	—	47	4	no	—
519	C₂×C₂²⋊Q₈	—	47	2	no	—
520	C₂×C₂²⋊Q₈	—	47	2	no	—
521	C₂×C₂²⋊Q₈	—	47	4	no	—
522	C₂×C₂²⋊Q₈	—	47	32	no	—
523	C₂×C₂²⋊Q₈	—	47	2	no	—
524	C₂×C₂²⋊Q₈	—	47	2	no	—
525	C₂×C₂²⋊Q₈	—	47	4	no	—
526	C₂×C₂²⋊Q₈	—	47	2	no	—
527	C₂×C₂²⋊Q₈	—	47	4	no	—
528	C₂×#121	—	47	4	no	—
529	C₂×#121	—	47	2	no	—
530	C₂×#121	—	47	1	no	—
531	C₂×#121	—	47	2	no	—
532	C₂×#120	—	47	4	no	—
533	#520	—	47	32	no	—
534	C₂×C₄×Q₈	—	47	2	no	—
535	C₂×C₄×Q₈	—	47	2	no	—
536	C₂×C₄×Q₈	—	47	1	no	—
537	C₂×C₄×Q₈	—	47	2	no	—
538	C₂×C₄×D₄	—	47	2	no	—
539	C₂×C₄×D₄	—	47	4	no	—
540	C₂×C₄×D₄	—	47	4	no	—
541	C₂×C₄×D₄	—	47	2	no	—
542	C₂×C₄×D₄	—	47	4	no	—
543	C₂×C₄×D₄	—	47	1	no	—
544	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
545	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
546	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
547	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
548	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
549	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
550	C₂×C₄×D₄	C₂×D₄₇	1	16	yes	complemented
551	C₂×#117	—	47	2	no	—
552	C₂×#117	—	47	2	no	—
553	C₂×#117	—	47	4	no	—
554	C₂×#117	—	47	2	no	—
555	C₂²×C₄⋊C₄	—	47	4	no	—
556	C₂²×C₄⋊C₄	—	47	2	no	—
557	C₂²×C₄⋊C₄	—	47	2	no	—
558	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
559	C₂²×C₂²⋊C₄	—	47	4	no	—
560	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
561	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
562	C₄₇	C₂×#3520	1	1	yes	characteristic, complemented, Sylow
563	C₂⁵	C₂²×D₄₇	1	2	yes	—
564	C₂×#41	—	47	16	no	—
565	C₂×#41	—	47	16	no	—
566	C₂×#41	—	94	16	no	—
567	C₂×#41	—	188	8	no	—
568	C₂²×Q₈	—	47	2	no	—
569	C₂²×Q₈	—	47	1	no	—
570	C₂²×Q₈	—	47	2	no	—
571	C₂²×Q₈	—	47	4	no	—
572	C₂²×Q₈	—	47	16	no	—
573	C₂²×Q₈	—	188	8	no	—
574	C₂²×D₄	—	2	8	no	—
575	C₂²×D₄	—	47	2	no	—
576	C₂²×D₄	—	47	4	no	—
577	C₂²×D₄	—	47	4	no	—
578	C₂²×D₄	—	47	1	no	—
579	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
580	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
581	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
582	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
583	C₂³×C₄	—	4	8	no	—
584	C₂³×C₄	—	47	4	no	—
585	C₂³×C₄	—	47	4	no	—
586	C₂³×C₄	—	47	2	no	—
587	C₂³×C₄	—	47	4	no	—
588	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
589	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
590	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
591	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
592	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
593	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
594	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
595	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
596	C₂³×C₄	C₂²×D₄₇	1	16	yes	—
597	C₄⋊Q₈	—	47	16	no	—
598	C₄⋊Q₈	—	47	8	no	—
599	C₄⋊Q₈	—	47	8	no	—
600	#126	—	47	32	no	—
601	#126	—	47	32	no	—
602	#126	—	47	16	no	—
603	#125	—	47	32	no	—
604	#125	—	47	8	no	—
605	#125	—	47	16	no	—
606	#124	—	47	16	no	—
607	#124	—	47	32	no	—
608	#124	—	47	8	no	—
609	#123	—	47	32	no	—
610	#123	—	47	32	no	—
611	#123	—	47	16	no	—
612	#123	—	47	32	no	—
613	#123	—	47	32	no	—
614	C₂²⋊Q₈	—	47	8	no	—
615	C₂²⋊Q₈	—	47	16	no	—
616	C₂²⋊Q₈	—	47	32	no	—
617	C₂²⋊Q₈	—	47	16	no	—
618	C₂²⋊Q₈	—	47	16	no	—
619	C₂²⋊Q₈	—	47	32	no	—
620	C₂²⋊Q₈	—	47	16	no	—
621	C₂²⋊Q₈	—	47	16	no	—
622	C₂²⋊Q₈	—	47	32	no	—
623	C₂²⋊Q₈	—	47	16	no	—
624	C₂²⋊Q₈	—	47	32	no	—
625	#121	—	47	32	no	—
626	#121	—	47	16	no	—
627	#121	—	47	8	no	—
628	#121	—	47	16	no	—
629	#120	—	47	32	no	—
630	C₄×Q₈	—	47	16	no	—
631	C₄×Q₈	—	47	16	no	—
632	C₄×Q₈	—	47	8	no	—
633	C₄×Q₈	—	47	16	no	—
634	C₄×D₄	—	47	16	no	—
635	C₄×D₄	—	47	32	no	—
636	C₄×D₄	—	47	32	no	—
637	C₄×D₄	—	47	16	no	—
638	C₄×D₄	—	47	32	no	—
639	C₄×D₄	—	47	8	no	—
640	C₄×D₄	C₂²×D₄₇	1	8	yes	—
641	C₄×D₄	C₂²×D₄₇	1	16	yes	—
642	C₄×D₄	C₂²×D₄₇	1	8	yes	—
643	C₄×D₄	C₂²×D₄₇	1	8	yes	—
644	C₄×D₄	C₂²×D₄₇	1	8	yes	—
645	C₄×D₄	C₂²×D₄₇	1	16	yes	—
646	#117	—	47	16	no	—
647	#117	—	47	16	no	—
648	#117	—	47	32	no	—
649	#117	—	47	16	no	—
650	C₂×C₄⋊C₄	—	47	2	no	—
651	C₂×C₄⋊C₄	—	47	4	no	—
652	C₂×C₄⋊C₄	—	47	1	no	—
653	C₂×C₄⋊C₄	—	47	2	no	—
654	C₂×C₄⋊C₄	—	47	2	no	—
655	C₂×C₄⋊C₄	—	47	4	no	—
656	C₂×C₄⋊C₄	—	47	4	no	—
657	C₂×C₄⋊C₄	—	47	32	no	—
658	C₂×C₄⋊C₄	—	47	4	no	—
659	C₂×C₄⋊C₄	—	47	16	no	—
660	C₂×C₄⋊C₄	—	47	2	no	—
661	C₂×C₄⋊C₄	—	47	1	no	—
662	C₂×C₄⋊C₄	—	47	2	no	—
663	C₂×C₄⋊C₄	—	47	2	no	—
664	C₂×C₄⋊C₄	—	47	4	no	—
665	C₂×C₄⋊C₄	—	47	2	no	—
666	C₂×C₄⋊C₄	—	47	4	no	—
667	C₂×C₄⋊C₄	—	47	2	no	—
668	C₂×C₄⋊C₄	—	47	16	no	—
669	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
671	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
673	C₂×C₂²⋊C₄	—	47	2	no	—
674	C₂×C₂²⋊C₄	—	47	4	no	—
675	C₂×C₂²⋊C₄	—	47	4	no	—
676	C₂×C₂²⋊C₄	—	47	4	no	—
677	C₂×C₂²⋊C₄	—	47	32	no	—
678	C₂×C₂²⋊C₄	—	47	4	no	—
679	C₂×C₂²⋊C₄	—	47	4	no	—
680	C₂×C₂²⋊C₄	—	47	2	no	—
681	C₂×C₂²⋊C₄	—	47	2	no	—
682	C₂×C₂²⋊C₄	—	47	2	no	—
683	C₂×C₂²⋊C₄	—	47	4	no	—
684	C₂×C₂²⋊C₄	—	47	2	no	—
685	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
690	C₂×C₄²	—	47	4	no	—
691	C₂×C₄²	—	47	4	no	—
692	C₂×C₄²	—	47	2	no	—
693	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
694	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
695	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
696	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
697	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
698	C₂⁴	—	2	8	no	—
699	C₂⁴	—	2	8	no	—
700	C₂⁴	—	4	4	no	—
701	C₂⁴	—	47	2	no	—
702	C₂⁴	C₂³×D₄₇	1	2	yes	—
703	C₂⁴	C₂³×D₄₇	1	8	yes	—
704	C₂⁴	C₂³×D₄₇	1	2	yes	—
705	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
706	#41	—	94	64	no	—
707	#41	—	188	32	no	—
708	C₂×Q₈	—	47	8	no	—
709	C₂×Q₈	—	47	4	no	—
710	C₂×Q₈	—	47	8	no	—
711	C₂×Q₈	—	47	16	no	—
712	C₂×Q₈	—	94	8	no	—
713	C₂×Q₈	—	94	4	no	—
714	C₂×Q₈	—	94	8	no	—
715	C₂×Q₈	—	188	8	no	—
716	C₂×Q₈	—	188	32	no	—
717	C₂×D₄	—	2	8	no	—
718	C₂×D₄	—	2	32	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	47	8	no	—
721	C₂×D₄	—	47	16	no	—
722	C₂×D₄	—	47	16	no	—
723	C₂×D₄	—	47	4	no	—
724	C₂×D₄	—	94	16	no	—
725	C₂×D₄	—	94	8	no	—
726	C₂×D₄	—	94	4	no	—
727	C₂×D₄	—	188	8	no	—
728	C₂×D₄	#10625350	1	8	yes	complemented
729	C₂×D₄	C₂³×D₄₇	1	8	yes	—
730	C₂×D₄	C₂³×D₄₇	1	4	yes	—
731	C₂×D₄	C₂³×D₄₇	1	4	yes	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	8	no	—
736	C₂²×C₄	—	2	8	no	—
737	C₂²×C₄	—	4	32	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	—	4	4	no	—
740	C₂²×C₄	—	4	4	no	—
741	C₂²×C₄	—	47	16	no	—
742	C₂²×C₄	—	47	2	no	—
743	C₂²×C₄	—	47	4	no	—
744	C₂²×C₄	—	47	2	no	—
745	C₂²×C₄	—	47	4	no	—
746	C₂²×C₄	—	47	2	no	—
747	C₂²×C₄	—	47	16	no	—
748	C₂²×C₄	—	47	8	no	—
749	C₂²×C₄	—	47	16	no	—
750	C₂²×C₄	—	94	16	no	—
751	C₂²×C₄	—	94	8	no	—
752	C₂²×C₄	—	188	8	no	—
753	C₂²×C₄	—	188	8	no	—
754	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
755	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
756	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
757	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
758	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
759	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
760	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
761	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
762	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
763	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
765	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
766	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
767	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
768	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
770	C₄⋊C₄	—	47	8	no	—
771	C₄⋊C₄	—	47	16	no	—
772	C₄⋊C₄	—	47	16	no	—
773	C₄⋊C₄	—	47	16	no	—
774	C₄⋊C₄	—	47	8	no	—
775	C₄⋊C₄	—	47	16	no	—
776	C₄⋊C₄	—	47	8	no	—
777	C₄⋊C₄	—	47	16	no	—
778	C₄⋊C₄	—	47	8	no	—
779	C₄⋊C₄	—	47	4	no	—
780	C₄⋊C₄	—	47	8	no	—
781	C₄⋊C₄	—	47	8	no	—
782	C₄⋊C₄	—	47	16	no	—
783	C₄⋊C₄	—	47	4	no	—
784	C₄⋊C₄	—	47	8	no	—
785	C₄⋊C₄	—	47	8	no	—
786	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
787	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
788	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
789	C₂²⋊C₄	—	47	8	no	—
790	C₂²⋊C₄	—	47	16	no	—
791	C₂²⋊C₄	—	47	16	no	—
792	C₂²⋊C₄	—	47	16	no	—
793	C₂²⋊C₄	—	47	16	no	—
794	C₂²⋊C₄	—	47	16	no	—
795	C₂²⋊C₄	—	47	8	no	—
796	C₂²⋊C₄	—	47	8	no	—
797	C₂²⋊C₄	—	47	8	no	—
798	C₂²⋊C₄	—	47	16	no	—
799	C₂²⋊C₄	—	47	8	no	—
800	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
801	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
802	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
803	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
804	C₄²	—	47	16	no	—
805	C₄²	—	47	16	no	—
806	C₄²	—	47	8	no	—
807	C₄²	C₂³×D₄₇	1	4	yes	—
808	C₄²	C₂³×D₄₇	1	4	yes	—
809	C₄²	C₂³×D₄₇	1	4	yes	—
810	C₄²	C₂³×D₄₇	1	4	yes	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	16	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	16	no	—
819	C₂³	—	2	4	no	—
820	C₂³	—	4	8	no	—
821	C₂³	—	4	32	no	—
822	C₂³	—	47	4	no	—
823	C₂³	—	94	4	no	—
824	C₂³	—	94	4	no	—
825	C₂³	—	94	4	no	—
826	C₂³	C₂×#10625350	1	8	yes	—
827	C₂³	#13094071	1	4	yes	—
828	C₂³	C₂⁴×D₄₇	1	4	yes	—
829	C₂³	C₂⁴×D₄₇	1	4	yes	—
830	C₂³	C₂⁴×D₄₇	1	2	yes	—
831	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
832	Q₈	—	94	16	no	—
833	Q₈	—	94	8	no	—
834	Q₈	—	94	16	no	—
835	Q₈	—	188	16	no	—
836	D₄	—	2	16	no	—
837	D₄	—	2	8	no	—
838	D₄	—	94	32	no	—
839	D₄	—	94	16	no	—
840	D₄	—	94	8	no	—
841	D₄	—	188	16	no	—
842	D₄	C₂×#10625350	1	16	yes	complemented
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	2	4	no	—
847	C₂×C₄	—	2	8	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	8	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	2	16	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	8	no	—
857	C₂×C₄	—	47	4	no	—
858	C₂×C₄	—	47	8	no	—
859	C₂×C₄	—	47	4	no	—
860	C₂×C₄	—	47	8	no	—
861	C₂×C₄	—	47	4	no	—
862	C₂×C₄	—	94	4	no	—
863	C₂×C₄	—	94	8	no	—
864	C₂×C₄	—	94	32	no	—
865	C₂×C₄	—	94	8	no	—
866	C₂×C₄	—	94	4	no	—
867	C₂×C₄	—	94	4	no	—
868	C₂×C₄	—	94	16	no	—
869	C₂×C₄	—	188	16	no	—
870	C₂×C₄	—	188	16	no	—
871	C₂×C₄	C₂×#10625350	1	4	yes	—
872	C₂×C₄	#13094069	1	4	yes	—
873	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
874	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
875	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
876	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
877	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
878	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
879	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
880	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	8	no	—
886	C₂²	—	2	16	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	4	32	no	—
891	C₂²	—	4	8	no	—
892	C₂²	—	94	4	no	—
893	C₂²	—	94	4	no	—
894	C₂²	—	94	4	no	—
895	C₂²	—	188	8	no	—
896	C₂²	C₂²×#10625350	1	8	yes	—
897	C₂²	C₂²×#10625350	1	2	yes	—
898	C₂²	C₂×#13094069	1	2	yes	—
899	C₂²	C₂×#13094071	1	4	yes	—
900	C₂²	C₂×#13094071	1	2	yes	—
901	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	4	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	94	4	no	—
909	C₄	—	94	8	no	—
910	C₄	—	94	8	no	—
911	C₄	—	94	4	no	—
912	C₄	—	94	4	no	—
913	C₄	C₂²×#10625350	1	4	yes	—
914	C₄	C₂×#13094069	1	4	yes	—
915	C₂	—	2	4	no	—
916	C₂	—	2	8	no	—
917	C₂	—	4	4	no	—
918	C₂	—	188	4	no	—
919	C₂	#20257437	1	4	yes	direct product factor
920	C₂	C₂³×#10625350	1	1	yes	characteristic
921	C₂	C₂²×#13094069	1	1	yes	characteristic
922	C₂	C₂²×#13094071	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂×#3520
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20257437	C₂	direct (N × H)
2. C₂×#15689843	C₂	semidirect
3. C₂×#15689828	C₂	semidirect
4. C₂×#15689813	C₂	semidirect
5. C₂×#15689799	C₂	semidirect
6. C₂×D₄×Dic₉₄	C₂	semidirect
7. C₂×#15689782	C₂	semidirect
8. C₂×#15689778	C₂	semidirect
9. C₂×#15689777	C₂	semidirect
10. C₂×#15689767	C₂	semidirect
11. C₂×#15689738	C₂	semidirect
12. C₂×#15689715	C₂	semidirect
13. C₂×#15689680	C₂	semidirect
14. C₂×#15689657	C₂	semidirect
15. C₂×#15689634	C₂	semidirect
16. C₂²×#13094003	C₂	semidirect
17. C₂×#15689602	C₂	semidirect
18. C₂²×C₄×D₄×C₄₇	C₂	semidirect
19. C₂²×#10625350	C₂²	semidirect
21. C₂³×Dic₉₄	C₂²	semidirect
22. #15689843	C₂²	semidirect
23. #15689828	C₂²	semidirect
24. #15689813	C₂²	semidirect
25. #15689799	C₂²	semidirect
26. D₄×Dic₉₄	C₂²	semidirect
27. #15689782	C₂²	semidirect
28. #15689778	C₂²	semidirect
29. #15689777	C₂²	semidirect
30. #15689767	C₂²	semidirect
31. #15689738	C₂²	semidirect
32. #15689715	C₂²	semidirect
33. #15689680	C₂²	semidirect
34. C₂×#13094024	C₂²	semidirect
35. C₂×#13094024	C₂²	semidirect
36. C₂×#13094023	C₂²	semidirect
37. #15689657	C₂²	semidirect
38. C₂×#13094018	C₂²	semidirect
39. C₂×#13094017	C₂²	semidirect
40. C₂×#13094017	C₂²	semidirect
41. C₂×#13094016	C₂²	semidirect
42. C₂×#13094016	C₂²	semidirect
43. C₂×#13094014	C₂²	semidirect
44. C₂×#13094012	C₂²	semidirect
46. C₂×#13094010	C₂²	semidirect
47. #15689634	C₂²	semidirect
48. C₂×#13094008	C₂²	semidirect
50. C₂×#13094007	C₂²	semidirect
51. C₂×#13094006	C₂²	semidirect
53. C₂×#13094004	C₂²	semidirect
58. C₂×#13094003	C₂²	semidirect
59. C₂×#13094003	C₂²	semidirect
60. C₂×#13094003	C₂²	semidirect
61. C₂×#13094003	C₂²	semidirect
62. C₂×#13094003	C₂²	semidirect
63. C₂×#13094002	C₂²	semidirect
64. C₂×#13094001	C₂²	semidirect
66. C₂×#13093998	C₂²	semidirect
70. #15689602	C₂²	semidirect
71. C₂×C₄×Dic₉₄	C₂²	semidirect
72. C₂×C₄×Dic₉₄	C₂²	semidirect
73. C₂×C₄×Dic₉₄	C₂²	semidirect
74. C₂×#13093989	C₂²	semidirect
75. C₂×C₄×D₁₈₈	C₂²	semidirect
79. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
80. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
82. C₂×#13093983	C₂²	semidirect
83. C₂×#13093981	C₂²	semidirect
84. C₂×#13093980	C₂²	semidirect
85. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
86. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
87. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
97. C₂×C₄×D₄×C₄₇	C₂²	semidirect
102. C₂×#10625350	C₂³	semidirect
110. C₂²×Dic₉₄	C₂³	semidirect
119. #13094024	C₂³	semidirect
120. #13094024	C₂³	semidirect
121. #13094023	C₂³	semidirect
122. #13094018	C₂³	semidirect
123. #13094017	C₂³	semidirect
124. #13094017	C₂³	semidirect
125. #13094016	C₂³	semidirect
126. #13094016	C₂³	semidirect
127. #13094014	C₂³	semidirect
128. #13094012	C₂³	semidirect
130. #13094010	C₂³	semidirect
131. #13094008	C₂³	semidirect
133. #13094007	C₂³	semidirect
134. #13094006	C₂³	semidirect
136. #13094004	C₂³	semidirect
141. #13094003	C₂³	semidirect
142. #13094003	C₂³	semidirect
143. #13094003	C₂³	semidirect
144. #13094003	C₂³	semidirect
145. #13094002	C₂³	semidirect
146. #13094001	C₂³	semidirect
148. #13093998	C₂³	semidirect
152. C₄×Dic₉₄	C₂³	semidirect
153. C₄×Dic₉₄	C₂³	semidirect
154. C₄×Dic₉₄	C₂³	semidirect
155. #13093989	C₂³	semidirect
156. C₄×D₁₈₈	C₂³	semidirect
160. C₄×C₂²⋊D₄₇	C₂³	semidirect
161. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
163. #13093983	C₂³	semidirect
164. #13093981	C₂³	semidirect
165. #13093980	C₂³	semidirect
173. C₂×C₄⋊Dic₄₇	C₂³	semidirect
183. C₂×Dic₄₇⋊C₄	C₂³	semidirect
184. C₄⋊C₄×D₄₇	C₂³	semidirect
247. C₂×D₄×C₄₇	#41	semidirect
372. D₄×C₄₇	C₂×#41	semidirect
471. C₂²×C₄×D₄	D₄₇	semidirect
475. C₂×C₄₇	#3520	semidirect
550. C₂×C₄×D₄	C₂×D₄₇	semidirect
562. C₄₇	C₂×#3520	semidirect
728. C₂×D₄	#10625350	semidirect
842. D₄	C₂×#10625350	semidirect
919. C₂	#20257437	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257437	2
C₂×#15689843	2
C₂×#15689828	2
C₂×#15689813	2
C₂×#15689799	2
C₂×D₄×Dic₉₄	2
C₂×#15689782	2
C₂×#15689778	2
C₂×#15689777	2
C₂×#15689767	2
C₂×#15689738	2
C₂×#15689715	2
C₂×#15689680	2
C₂×#15689657	2
C₂×#15689634	2
C₂²×#13094003	2
C₂×#15689602	2
C₂²×C₄×D₄×C₄₇	2
C₂×#3520	47

Subgroups — C2×#20257437 #27124291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257437 #27124291