Subgroups — C₂×#20257142 #27124709

Order 12032.

7206 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	#20257142	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689843	C₂	1	2	yes	maximal, complemented
3	C₂×#15689830	C₂	1	2	yes	maximal, complemented
4	C₂×#15689813	C₂	1	2	yes	maximal, complemented
5	C₂×#15689813	C₂	1	2	yes	maximal, complemented
6	C₂×#15689810	C₂	1	4	yes	maximal, complemented
7	C₂×#15689804	C₂	1	4	yes	maximal, complemented
8	C₂×#15689751	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689740	C₂	1	2	yes	maximal, complemented
10	C₂×#15689733	C₂	1	2	yes	maximal, complemented
11	C₂×#15689694	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15689675	C₂	1	2	yes	maximal, complemented
13	C₂×#15689654	C₂	1	2	yes	maximal, complemented
14	C₂²×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15689606	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15689600	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic
19	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic
20	#15689843	C₂²	1	32	yes	complemented
21	#15689830	C₂²	1	32	yes	complemented
22	#15689813	C₂²	1	32	yes	complemented
23	#15689813	C₂²	1	32	yes	complemented
24	#15689810	C₂²	1	64	yes	complemented
25	#15689804	C₂²	1	64	yes	complemented
26	#15689751	C₂²	1	16	yes	complemented
27	#15689740	C₂²	1	32	yes	complemented
28	#15689733	C₂²	1	32	yes	complemented
29	#15689694	C₂²	1	16	yes	complemented
30	#15689675	C₂²	1	32	yes	complemented
31	C₂×#13094024	C₂²	1	2	yes	complemented
32	C₂×#13094023	C₂²	1	2	yes	complemented
33	C₂×#13094022	C₂²	1	2	yes	complemented
34	#15689654	C₂²	1	32	yes	complemented
35	C₂×#13094017	C₂²	1	4	yes	—
36	C₂×#13094017	C₂²	1	4	yes	—
37	C₂×#13094017	C₂²	1	4	yes	complemented
38	C₂×#13094017	C₂²	1	4	yes	complemented
39	C₂×#13094016	C₂²	1	2	yes	complemented
40	C₂×#13094015	C₂²	1	2	yes	complemented
41	C₂×#13094015	C₂²	1	4	yes	complemented
42	C₂×#13094014	C₂²	1	4	yes	complemented
43	C₂×#13094014	C₂²	1	4	yes	complemented
44	C₂×#13094011	C₂²	1	4	yes	—
45	C₂×#13094011	C₂²	1	2	yes	complemented
46	C₂×#13094005	C₂²	1	4	yes	—
47	C₂×#13094005	C₂²	1	4	yes	—
48	C₂×#13094005	C₂²	1	4	yes	—
49	C₂×#13094003	C₂²	1	2	yes	—
50	C₂×#13094003	C₂²	1	2	yes	—
51	C₂×#13094003	C₂²	1	2	yes	—
52	C₂×#13094003	C₂²	1	2	yes	—
53	C₂×#13094003	C₂²	1	16	yes	complemented
54	C₂×#13094003	C₂²	1	2	yes	complemented
55	C₂×#13094003	C₂²	1	2	yes	complemented
56	C₂×#13094001	C₂²	1	4	yes	—
57	C₂×#13094001	C₂²	1	4	yes	—
58	C₂×#13094001	C₂²	1	4	yes	complemented
59	#15689606	C₂²	1	16	yes	complemented
60	#15689600	C₂²	1	16	yes	complemented
61	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
62	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
63	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
64	C₂×#13093989	C₂²	1	2	yes	complemented
65	C₂×#13093989	C₂²	1	2	yes	complemented
66	C₂×#13093989	C₂²	1	4	yes	complemented
67	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
68	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
69	C₂×D₄×Dic₄₇	C₂²	1	2	yes	complemented
70	C₂×#13093983	C₂²	1	1	yes	characteristic
71	C₂×#13093983	C₂²	1	1	yes	characteristic
72	C₂×#13093983	C₂²	1	2	yes	—
73	C₂×#13093983	C₂²	1	1	yes	characteristic
74	C₂×#13093983	C₂²	1	1	yes	characteristic
75	C₂×#13093983	C₂²	1	2	yes	—
76	C₂×#13093983	C₂²	1	16	yes	complemented
77	C₂×#13093983	C₂²	1	2	yes	complemented
78	C₂×#13093980	C₂²	1	4	yes	—
79	C₂×#13093980	C₂²	1	4	yes	—
80	C₂×#13093980	C₂²	1	4	yes	complemented
81	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
82	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
83	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
84	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
85	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
86	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
87	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
88	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
89	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
90	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
91	C₄₇×#525	C₂²	1	16	yes	—
92	C₂×#123×C₄₇	C₂²	1	2	yes	—
93	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
94	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
95	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
96	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
97	C₂×#120×C₄₇	C₂²	1	2	yes	—
98	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
99	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
100	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
101	C₂²×Dic₉₄	—	2	8	no	—
102	C₂²×Dic₉₄	C₂³	1	2	yes	—
103	C₂²×Dic₉₄	C₂³	1	2	yes	—
104	C₂²×Dic₉₄	C₂³	1	8	yes	—
105	C₂²×Dic₉₄	C₂³	1	4	yes	—
106	C₂³×Dic₄₇	C₂³	1	2	yes	—
107	C₂³×Dic₄₇	C₂³	1	2	yes	—
108	C₂³×Dic₄₇	C₂³	1	2	yes	—
109	C₂³×Dic₄₇	C₂³	1	2	yes	—
110	C₂³×Dic₄₇	C₂³	1	4	yes	—
111	#13094024	C₂³	1	16	yes	complemented
112	#13094023	C₂³	1	16	yes	complemented
113	#13094022	C₂³	1	16	yes	complemented
114	#13094017	C₂³	1	32	yes	—
115	#13094017	C₂³	1	32	yes	—
116	#13094017	C₂³	1	32	yes	complemented
117	#13094017	C₂³	1	32	yes	complemented
118	#13094016	C₂³	1	16	yes	complemented
119	#13094015	C₂³	1	16	yes	complemented
120	#13094015	C₂³	1	32	yes	complemented
121	#13094014	C₂³	1	32	yes	complemented
122	#13094014	C₂³	1	32	yes	complemented
123	#13094011	C₂³	1	32	yes	—
124	#13094011	C₂³	1	16	yes	complemented
125	#13094005	C₂³	1	32	yes	—
126	#13094005	C₂³	1	32	yes	—
127	#13094005	C₂³	1	32	yes	—
128	#13094003	C₂³	1	16	yes	—
129	#13094003	C₂³	1	16	yes	—
130	#13094003	C₂³	1	16	yes	—
131	#13094003	C₂³	1	16	yes	—
132	#13094003	C₂³	1	16	yes	complemented
133	#13094003	C₂³	1	16	yes	complemented
134	#13094001	C₂³	1	32	yes	—
135	#13094001	C₂³	1	32	yes	—
136	#13094001	C₂³	1	32	yes	complemented
137	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
138	C₄×Dic₉₄	C₂³	1	16	yes	complemented
139	C₄×Dic₉₄	C₂³	1	16	yes	complemented
140	#13093989	C₂³	1	16	yes	complemented
141	#13093989	C₂³	1	16	yes	complemented
142	#13093989	C₂³	1	32	yes	complemented
143	D₄×Dic₄₇	C₂³	1	32	yes	—
144	D₄×Dic₄₇	C₂³	1	32	yes	—
145	D₄×Dic₄₇	C₂³	1	16	yes	complemented
146	#13093983	C₂³	1	16	yes	—
147	#13093983	C₂³	1	8	yes	—
148	#13093983	C₂³	1	16	yes	—
149	#13093983	C₂³	1	8	yes	—
150	#13093983	C₂³	1	8	yes	—
151	#13093983	C₂³	1	8	yes	—
152	#13093983	C₂³	1	16	yes	complemented
153	#13093980	C₂³	1	32	yes	—
154	#13093980	C₂³	1	32	yes	—
155	#13093980	C₂³	1	32	yes	complemented
156	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
157	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
158	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
160	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
161	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
163	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
166	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
167	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
168	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
169	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
170	C₂×Dic₄₇⋊C₄	C₂³	1	16	yes	—
171	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
172	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
173	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
174	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
175	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
176	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
177	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
178	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
179	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
180	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
181	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
183	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊Dic₄₇	C₂³	1	4	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×C₄×Dic₄₇	C₂³	1	2	yes	—
191	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
192	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
193	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
194	C₂×C₄×Dic₄₇	C₂³	1	16	yes	—
195	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
196	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
197	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
198	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
199	C₂×#41×C₄₇	—	2	8	no	—
200	C₂×#41×C₄₇	C₂³	1	8	yes	—
201	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
202	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
203	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
204	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
206	C₂³×C₄×C₄₇	—	2	8	no	—
207	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
209	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
213	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
214	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
215	#123×C₄₇	C₂³	1	16	yes	—
216	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
217	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
218	#121×C₄₇	C₂³	1	8	yes	—
219	#121×C₄₇	C₂³	1	8	yes	—
220	#120×C₄₇	C₂³	1	16	yes	—
221	C₄×D₄×C₄₇	C₂³	1	16	yes	—
222	C₄×D₄×C₄₇	C₂³	1	16	yes	—
223	#117×C₄₇	C₂³	1	8	yes	—
224	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
227	C₂×C₄⋊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	2	yes	—
231	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
234	C₂⁴×C₄₇	—	2	4	no	—
235	C₂⁴×C₄₇	—	2	4	no	—
236	C₂⁴×C₄₇	—	4	2	no	—
237	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
239	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
240	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
242	#41×C₄₇	—	2	32	no	—
243	C₂×Q₈×C₄₇	—	2	4	no	—
244	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
245	C₂×D₄×C₄₇	—	2	8	no	—
246	C₂×D₄×C₄₇	—	2	8	no	—
247	C₂×D₄×C₄₇	—	2	4	no	—
248	C₂×D₄×C₄₇	—	4	4	no	—
249	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
250	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
251	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
252	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
253	C₂²×C₄×C₄₇	—	2	4	no	—
254	C₂²×C₄×C₄₇	—	2	4	no	—
255	C₂²×C₄×C₄₇	—	2	4	no	—
256	C₂²×C₄×C₄₇	—	2	4	no	—
257	C₂²×C₄×C₄₇	—	2	4	no	—
258	C₂²×C₄×C₄₇	—	2	32	no	—
259	C₂²×C₄×C₄₇	—	2	8	no	—
260	C₂²×C₄×C₄₇	#41	1	8	yes	—
261	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
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	1	yes	characteristic
273	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
275	C₂²×Dic₄₇	—	2	8	no	—
276	C₂²×Dic₄₇	—	2	8	no	—
277	C₂²×Dic₄₇	—	4	4	no	—
278	C₂²×Dic₄₇	—	4	4	no	—
279	C₂²×Dic₄₇	—	4	8	no	—
280	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
281	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
282	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
283	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
284	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
285	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
286	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
287	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
288	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
289	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
290	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
291	C₂×Dic₉₄	—	2	8	no	—
292	C₂×Dic₉₄	—	2	8	no	—
293	C₂×Dic₉₄	—	2	32	no	—
294	C₂×Dic₉₄	—	4	8	no	—
295	C₂×Dic₉₄	C₂⁴	1	8	yes	—
296	C₂×Dic₉₄	C₂⁴	1	8	yes	—
297	C₂×Dic₉₄	C₂⁴	1	16	yes	—
298	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
301	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
302	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
303	C₂²⋊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	C₄²×C₄₇	C₂⁴	1	8	yes	—
308	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
309	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
310	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
311	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
312	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
313	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
314	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
315	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
316	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
317	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
318	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
319	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
320	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
321	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
322	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
323	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
324	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
325	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
326	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
327	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
328	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
329	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
330	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
331	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
332	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
333	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
334	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
335	C₄×Dic₄₇	C₂⁴	1	8	yes	—
336	C₄×Dic₄₇	C₂⁴	1	8	yes	—
337	C₄×Dic₄₇	C₂⁴	1	8	yes	—
338	C₄×Dic₄₇	C₂⁴	1	8	yes	—
339	C₄×Dic₄₇	C₂⁴	1	16	yes	—
340	C₄×Dic₄₇	C₂⁴	1	16	yes	—
341	C₄×Dic₄₇	C₂⁴	1	16	yes	—
342	C₂³×C₄₇	—	2	2	no	—
343	C₂³×C₄₇	—	2	2	no	—
344	C₂³×C₄₇	—	2	2	no	—
345	C₂³×C₄₇	—	2	2	no	—
346	C₂³×C₄₇	—	2	8	no	—
347	C₂³×C₄₇	—	2	2	no	—
348	C₂³×C₄₇	—	2	4	no	—
349	C₂³×C₄₇	—	2	4	no	—
350	C₂³×C₄₇	—	2	8	no	—
351	C₂³×C₄₇	—	2	2	no	—
352	C₂³×C₄₇	—	2	4	no	—
353	C₂³×C₄₇	—	2	2	no	—
354	C₂³×C₄₇	—	4	4	no	—
355	C₂³×C₄₇	—	4	16	no	—
356	C₂³×C₄₇	C₂×#41	1	4	yes	—
357	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
358	C₂³×C₄₇	C₂⁵	1	2	yes	—
359	C₂³×C₄₇	C₂⁵	1	4	yes	—
360	C₂³×C₄₇	C₂⁵	1	2	yes	—
361	C₂³×C₄₇	C₂⁵	1	2	yes	—
362	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
363	Q₈×C₄₇	—	2	8	no	—
364	D₄×C₄₇	—	2	16	no	—
365	D₄×C₄₇	—	2	16	no	—
366	D₄×C₄₇	—	2	8	no	—
367	D₄×C₄₇	—	4	8	no	—
368	C₂×C₄×C₄₇	—	2	8	no	—
369	C₂×C₄×C₄₇	—	2	2	no	—
370	C₂×C₄×C₄₇	—	2	2	no	—
371	C₂×C₄×C₄₇	—	2	4	no	—
372	C₂×C₄×C₄₇	—	2	4	no	—
373	C₂×C₄×C₄₇	—	2	4	no	—
374	C₂×C₄×C₄₇	—	2	8	no	—
375	C₂×C₄×C₄₇	—	2	8	no	—
376	C₂×C₄×C₄₇	—	2	8	no	—
377	C₂×C₄×C₄₇	—	2	8	no	—
378	C₂×C₄×C₄₇	—	2	16	no	—
379	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
380	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
381	C₂×C₄×C₄₇	C₂×#41	1	16	yes	—
382	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
383	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
384	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
385	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
386	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
387	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
388	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
389	C₂×Dic₄₇	—	2	16	no	—
390	C₂×Dic₄₇	—	2	8	no	—
391	C₂×Dic₄₇	—	2	16	no	—
392	C₂×Dic₄₇	—	2	4	no	—
393	C₂×Dic₄₇	—	2	4	no	—
394	C₂×Dic₄₇	—	2	4	no	—
395	C₂×Dic₄₇	—	2	8	no	—
396	C₂×Dic₄₇	—	2	4	no	—
397	C₂×Dic₄₇	—	4	8	no	—
398	C₂×Dic₄₇	—	4	8	no	—
399	C₂×Dic₄₇	—	4	16	no	—
400	C₂×Dic₄₇	C₂⁵	1	4	yes	—
401	C₂×Dic₄₇	C₂⁵	1	4	yes	—
402	C₂×Dic₄₇	C₂⁵	1	4	yes	—
403	C₂×Dic₄₇	C₂⁵	1	8	yes	—
404	C₂×Dic₄₇	C₂⁵	1	4	yes	—
405	C₂×Dic₄₇	C₂⁵	1	8	yes	—
406	Dic₉₄	—	2	16	no	—
407	Dic₉₄	—	2	16	no	—
408	Dic₉₄	—	4	16	no	—
409	C₂×#3495	—	47	1	no	maximal, Sylow
410	C₂²×C₄₇	—	2	2	no	—
411	C₂²×C₄₇	—	2	2	no	—
412	C₂²×C₄₇	—	2	2	no	—
413	C₂²×C₄₇	—	2	2	no	—
414	C₂²×C₄₇	—	2	8	no	—
415	C₂²×C₄₇	—	2	8	no	—
416	C₂²×C₄₇	—	2	2	no	—
417	C₂²×C₄₇	—	2	4	no	—
418	C₂²×C₄₇	—	2	4	no	—
419	C₂²×C₄₇	—	2	2	no	—
420	C₂²×C₄₇	—	2	4	no	—
421	C₂²×C₄₇	—	2	2	no	—
422	C₂²×C₄₇	—	4	16	no	—
423	C₂²×C₄₇	—	4	8	no	—
424	C₂²×C₄₇	—	4	4	no	—
425	C₂²×C₄₇	C₂²×#41	1	4	yes	—
426	C₂²×C₄₇	C₂²×#41	1	2	yes	—
427	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
428	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
429	C₂²×C₄₇	#585	1	2	yes	—
430	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
431	C₄×C₄₇	—	2	2	no	—
432	C₄×C₄₇	—	2	2	no	—
433	C₄×C₄₇	—	2	4	no	—
434	C₄×C₄₇	—	2	4	no	—
435	C₄×C₄₇	—	2	4	no	—
436	C₄×C₄₇	C₂²×#41	1	4	yes	—
437	C₄×C₄₇	C₂²×#41	1	4	yes	—
438	Dic₄₇	—	2	8	no	—
439	Dic₄₇	—	2	4	no	—
440	Dic₄₇	—	2	4	no	—
441	Dic₄₇	—	2	4	no	—
442	Dic₄₇	—	2	8	no	—
443	Dic₄₇	—	2	4	no	—
444	#3495	—	47	32	no	—
445	C₂×#556	—	47	2	no	—
446	C₂×#554	—	47	2	no	—
447	C₂×#552	—	47	4	no	—
448	C₂×#552	—	47	2	no	—
449	C₂×#552	—	47	2	no	—
450	C₂×#551	—	47	4	no	—
451	C₂×#544	—	47	1	no	—
452	C₂×#542	—	47	2	no	—
453	C₂×#541	—	47	2	no	—
454	C₂×#536	—	47	1	no	—
455	C₂×#533	—	47	2	no	—
456	C₂×#529	—	47	2	no	—
457	C₂×#525	D₄₇	1	1	yes	characteristic
458	C₂²×C₂²⋊Q₈	—	47	1	no	—
459	C₂×#520	—	47	1	no	—
460	C₂×#519	—	47	1	no	—
461	C₂²×#117	—	47	1	no	—
462	C₂×C₄₇	—	2	4	no	—
463	C₂×C₄₇	—	2	4	no	—
464	C₂×C₄₇	—	4	4	no	—
465	C₂×C₄₇	—	4	2	no	—
466	C₂×C₄₇	#3495	1	4	yes	complemented
467	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
468	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
469	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
470	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
471	C₂³×Q₈	—	47	1	no	—
472	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
473	#556	—	47	32	no	—
474	#554	—	47	32	no	—
475	#552	—	47	64	no	—
476	#552	—	47	32	no	—
477	#552	—	47	32	no	—
478	#551	—	47	64	no	—
479	#544	—	47	16	no	—
480	#542	—	47	32	no	—
481	#541	—	47	32	no	—
482	#536	—	47	16	no	—
483	#533	—	47	32	no	—
484	C₂×C₄⋊Q₈	—	47	2	no	—
485	C₂×C₄⋊Q₈	—	47	2	no	—
486	C₂×C₄⋊Q₈	—	47	2	no	—
487	#529	—	47	32	no	—
488	C₂×#126	—	47	4	no	—
489	C₂×#126	—	47	4	no	—
490	C₂×#126	—	47	4	no	—
491	C₂×#126	—	47	4	no	—
492	C₂×#125	—	47	2	no	—
493	C₂×#125	—	47	4	no	—
494	C₂×#125	—	47	4	no	—
495	C₂×#125	—	47	4	no	—
496	C₂×#125	—	47	2	no	—
497	C₂×#124	—	47	2	no	—
498	C₂×#124	—	47	4	no	—
499	#525	C₂×D₄₇	1	16	yes	—
500	C₂×#123	—	47	4	no	—
501	C₂×#123	—	47	4	no	—
502	C₂×#123	—	47	4	no	—
503	C₂×#123	C₂×D₄₇	1	2	yes	—
504	C₂×C₂²⋊Q₈	—	47	2	no	—
505	C₂×C₂²⋊Q₈	—	47	2	no	—
506	C₂×C₂²⋊Q₈	—	47	2	no	—
507	C₂×C₂²⋊Q₈	—	47	2	no	—
508	C₂×C₂²⋊Q₈	—	47	16	no	—
509	C₂×C₂²⋊Q₈	—	47	2	no	—
510	C₂×C₂²⋊Q₈	—	47	2	no	—
511	C₂×C₂²⋊Q₈	—	47	4	no	—
512	C₂×C₂²⋊Q₈	—	47	4	no	—
513	C₂×C₂²⋊Q₈	—	47	4	no	—
514	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
515	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
516	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
517	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
518	C₂×#120	C₂×D₄₇	1	2	yes	—
519	#520	—	47	16	no	—
520	#519	—	47	16	no	—
521	C₂×C₄×Q₈	—	47	2	no	—
522	C₂×C₄×Q₈	—	47	2	no	—
523	C₂×C₄×Q₈	—	47	2	no	—
524	C₂×C₄×Q₈	—	47	4	no	—
525	C₂×C₄×Q₈	—	47	2	no	—
526	C₂×C₄×Q₈	—	47	2	no	—
527	C₂×C₄×D₄	—	47	2	no	—
528	C₂×C₄×D₄	—	47	4	no	—
529	C₂×C₄×D₄	—	47	4	no	—
530	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
531	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
532	C₂×#117	—	47	1	no	—
533	C₂×#117	—	47	1	no	—
534	C₂×#117	—	47	2	no	—
535	C₂×#117	—	47	1	no	—
536	C₂×#117	—	47	2	no	—
537	C₂×#117	—	47	1	no	—
538	C₂×#117	—	47	16	no	—
539	C₂×#117	—	47	2	no	—
540	C₂×#117	—	47	4	no	—
541	C₂×#117	—	47	4	no	—
542	C₂×#117	—	47	4	no	—
543	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
544	C₂²×C₄⋊C₄	—	47	1	no	—
545	C₂²×C₄⋊C₄	—	47	1	no	—
546	C₂²×C₄⋊C₄	—	47	1	no	—
547	C₂²×C₄⋊C₄	—	47	2	no	—
548	C₂²×C₄⋊C₄	—	47	2	no	—
549	C₂²×C₂²⋊C₄	—	47	2	no	—
550	C₂²×C₂²⋊C₄	—	47	2	no	—
551	C₂²×C₄²	—	47	2	no	—
552	C₄₇	C₂×#3495	1	1	yes	characteristic, complemented, Sylow
553	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
554	C₂×#41	—	2	8	no	—
555	C₂×#41	C₂²×D₄₇	1	8	yes	—
556	C₂²×Q₈	—	47	2	no	—
557	C₂²×Q₈	—	47	2	no	—
558	C₂²×Q₈	—	47	8	no	—
559	C₂²×Q₈	—	47	4	no	—
560	C₂²×Q₈	—	94	8	no	—
561	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
562	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
563	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
564	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
565	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
566	C₂³×C₄	—	2	8	no	—
567	C₂³×C₄	—	47	2	no	—
568	C₂³×C₄	—	47	2	no	—
569	C₂³×C₄	—	47	2	no	—
570	C₂³×C₄	—	47	2	no	—
571	C₂³×C₄	—	47	4	no	—
572	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
573	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
574	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
575	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
576	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
577	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
578	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
579	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
580	C₄⋊Q₈	—	47	16	no	—
581	C₄⋊Q₈	—	47	16	no	—
582	C₄⋊Q₈	—	47	16	no	—
583	#126	—	47	32	no	—
584	#126	—	47	32	no	—
585	#126	—	47	32	no	—
586	#126	—	47	32	no	—
587	#125	—	47	16	no	—
588	#125	—	47	32	no	—
589	#125	—	47	32	no	—
590	#125	—	47	32	no	—
591	#125	—	47	16	no	—
592	#124	—	47	16	no	—
593	#124	—	47	32	no	—
594	#123	—	47	32	no	—
595	#123	—	47	32	no	—
596	#123	—	47	32	no	—
597	#123	C₂²×D₄₇	1	16	yes	—
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	16	no	—
604	C₂²⋊Q₈	—	47	32	no	—
605	C₂²⋊Q₈	—	47	32	no	—
606	C₂²⋊Q₈	—	47	32	no	—
607	C₂²⋊Q₈	C₂²×D₄₇	1	8	yes	—
608	C₂²⋊Q₈	C₂²×D₄₇	1	8	yes	—
609	#121	C₂²×D₄₇	1	8	yes	—
610	#121	C₂²×D₄₇	1	8	yes	—
611	#120	C₂²×D₄₇	1	16	yes	—
612	C₄×Q₈	—	47	16	no	—
613	C₄×Q₈	—	47	16	no	—
614	C₄×Q₈	—	47	16	no	—
615	C₄×Q₈	—	47	32	no	—
616	C₄×Q₈	—	47	16	no	—
617	C₄×Q₈	—	47	16	no	—
618	C₄×D₄	—	47	16	no	—
619	C₄×D₄	—	47	32	no	—
620	C₄×D₄	—	47	32	no	—
621	C₄×D₄	C₂²×D₄₇	1	16	yes	—
622	C₄×D₄	C₂²×D₄₇	1	16	yes	—
623	#117	—	47	8	no	—
624	#117	—	47	8	no	—
625	#117	—	47	16	no	—
626	#117	—	47	8	no	—
627	#117	—	47	16	no	—
628	#117	—	47	8	no	—
629	#117	—	47	16	no	—
630	#117	—	47	32	no	—
631	#117	—	47	32	no	—
632	#117	—	47	32	no	—
633	#117	C₂²×D₄₇	1	8	yes	—
634	C₂×C₄⋊C₄	—	47	1	no	—
635	C₂×C₄⋊C₄	—	47	2	no	—
636	C₂×C₄⋊C₄	—	47	1	no	—
637	C₂×C₄⋊C₄	—	47	2	no	—
638	C₂×C₄⋊C₄	—	47	1	no	—
639	C₂×C₄⋊C₄	—	47	1	no	—
640	C₂×C₄⋊C₄	—	47	2	no	—
641	C₂×C₄⋊C₄	—	47	8	no	—
642	C₂×C₄⋊C₄	—	47	8	no	—
643	C₂×C₄⋊C₄	—	47	4	no	—
644	C₂×C₄⋊C₄	—	47	2	no	—
645	C₂×C₄⋊C₄	—	47	4	no	—
646	C₂×C₄⋊C₄	—	47	8	no	—
647	C₂×C₄⋊C₄	—	47	16	no	—
648	C₂×C₄⋊C₄	—	47	4	no	—
649	C₂×C₄⋊C₄	—	47	16	no	—
650	C₂×C₄⋊C₄	—	47	4	no	—
651	C₂×C₄⋊C₄	—	47	4	no	—
652	C₂×C₄⋊C₄	—	47	4	no	—
653	C₂×C₄⋊C₄	—	47	4	no	—
654	C₂×C₄⋊C₄	—	47	4	no	—
655	C₂×C₄⋊C₄	—	47	4	no	—
656	C₂×C₄⋊C₄	—	47	4	no	—
657	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
661	C₂×C₂²⋊C₄	—	47	2	no	—
662	C₂×C₂²⋊C₄	—	47	2	no	—
663	C₂×C₂²⋊C₄	—	47	2	no	—
664	C₂×C₂²⋊C₄	—	47	2	no	—
665	C₂×C₂²⋊C₄	—	47	16	no	—
666	C₂×C₂²⋊C₄	—	47	4	no	—
667	C₂×C₂²⋊C₄	—	47	4	no	—
668	C₂×C₂²⋊C₄	—	47	16	no	—
669	C₂×C₂²⋊C₄	—	47	4	no	—
670	C₂×C₂²⋊C₄	—	47	4	no	—
671	C₂×C₂²⋊C₄	—	47	4	no	—
672	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
677	C₂×C₄²	—	47	2	no	—
678	C₂×C₄²	—	47	2	no	—
679	C₂×C₄²	—	47	4	no	—
680	C₂×C₄²	—	47	4	no	—
681	C₂×C₄²	—	47	4	no	—
682	C₂×C₄²	—	47	2	no	—
683	C₂×C₄²	—	47	2	no	—
684	C₂×C₄²	—	47	16	no	—
685	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
686	C₂⁴	—	2	4	no	—
687	C₂⁴	—	2	4	no	—
688	C₂⁴	—	4	2	no	—
689	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
690	C₂⁴	C₂³×D₄₇	1	2	yes	—
691	C₂⁴	C₂³×D₄₇	1	4	yes	—
692	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
693	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
694	#41	—	2	32	no	—
695	C₂×Q₈	—	2	4	no	—
696	C₂×Q₈	—	47	8	no	—
697	C₂×Q₈	—	47	8	no	—
698	C₂×Q₈	—	47	16	no	—
699	C₂×Q₈	—	94	8	no	—
700	C₂×Q₈	—	94	8	no	—
701	C₂×Q₈	—	94	32	no	—
702	C₂×Q₈	—	188	8	no	—
703	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
704	C₂×D₄	—	2	8	no	—
705	C₂×D₄	—	2	8	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	C₂³×D₄₇	1	8	yes	—
709	C₂×D₄	C₂³×D₄₇	1	8	yes	—
710	C₂×D₄	C₂³×D₄₇	1	4	yes	—
711	C₂×D₄	C₂³×D₄₇	1	8	yes	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	32	no	—
718	C₂²×C₄	—	2	8	no	—
719	C₂²×C₄	—	47	8	no	—
720	C₂²×C₄	—	47	8	no	—
721	C₂²×C₄	—	47	2	no	—
722	C₂²×C₄	—	47	2	no	—
723	C₂²×C₄	—	47	2	no	—
724	C₂²×C₄	—	47	4	no	—
725	C₂²×C₄	—	47	2	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	—	94	8	no	—
731	C₂²×C₄	—	94	8	no	—
732	C₂²×C₄	—	188	8	no	—
733	C₂²×C₄	—	188	4	no	—
734	C₂²×C₄	—	188	4	no	—
735	C₂²×C₄	#10625352	1	8	yes	—
736	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
737	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
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	1	yes	characteristic
743	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
744	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
745	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
746	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
747	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
748	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
749	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
750	C₄⋊C₄	—	47	16	no	—
751	C₄⋊C₄	—	47	16	no	—
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	16	no	—
757	C₄⋊C₄	—	47	16	no	—
758	C₄⋊C₄	—	47	4	no	—
759	C₄⋊C₄	—	47	8	no	—
760	C₄⋊C₄	—	47	4	no	—
761	C₄⋊C₄	—	47	8	no	—
762	C₄⋊C₄	—	47	4	no	—
763	C₄⋊C₄	—	47	4	no	—
764	C₄⋊C₄	—	47	8	no	—
765	C₄⋊C₄	—	47	8	no	—
766	C₄⋊C₄	—	47	16	no	—
767	C₄⋊C₄	—	47	16	no	—
768	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
769	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
770	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
771	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
772	C₂²⋊C₄	—	47	8	no	—
773	C₂²⋊C₄	—	47	8	no	—
774	C₂²⋊C₄	—	47	8	no	—
775	C₂²⋊C₄	—	47	8	no	—
776	C₂²⋊C₄	—	47	16	no	—
777	C₂²⋊C₄	—	47	16	no	—
778	C₂²⋊C₄	—	47	16	no	—
779	C₂²⋊C₄	—	47	16	no	—
780	C₂²⋊C₄	—	47	16	no	—
781	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
782	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
783	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
784	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
785	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
786	C₄²	—	47	8	no	—
787	C₄²	—	47	8	no	—
788	C₄²	—	47	8	no	—
789	C₄²	—	47	8	no	—
790	C₄²	—	47	16	no	—
791	C₄²	—	47	16	no	—
792	C₄²	—	47	16	no	—
793	C₄²	C₂³×D₄₇	1	8	yes	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	8	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	8	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	4	16	no	—
808	C₂³	C₂×#10625352	1	4	yes	—
809	C₂³	#13094071	1	4	yes	—
810	C₂³	C₂⁴×D₄₇	1	2	yes	—
811	C₂³	C₂⁴×D₄₇	1	4	yes	—
812	C₂³	C₂⁴×D₄₇	1	2	yes	—
813	C₂³	C₂⁴×D₄₇	1	2	yes	—
814	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
815	Q₈	—	2	8	no	—
816	Q₈	—	94	16	no	—
817	Q₈	—	94	16	no	—
818	Q₈	—	188	16	no	—
819	D₄	—	2	16	no	—
820	D₄	—	2	16	no	—
821	D₄	—	2	8	no	—
822	D₄	—	4	8	no	—
823	C₂×C₄	—	2	8	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	8	no	—
830	C₂×C₄	—	2	8	no	—
831	C₂×C₄	—	2	8	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	16	no	—
834	C₂×C₄	—	47	4	no	—
835	C₂×C₄	—	47	4	no	—
836	C₂×C₄	—	47	4	no	—
837	C₂×C₄	—	47	8	no	—
838	C₂×C₄	—	47	4	no	—
839	C₂×C₄	—	47	8	no	—
840	C₂×C₄	—	94	16	no	—
841	C₂×C₄	—	94	8	no	—
842	C₂×C₄	—	94	16	no	—
843	C₂×C₄	—	94	4	no	—
844	C₂×C₄	—	94	4	no	—
845	C₂×C₄	—	94	4	no	—
846	C₂×C₄	—	94	8	no	—
847	C₂×C₄	—	94	4	no	—
848	C₂×C₄	—	188	16	no	—
849	C₂×C₄	—	188	8	no	—
850	C₂×C₄	—	188	8	no	—
851	C₂×C₄	C₂×#10625352	1	4	yes	—
852	C₂×C₄	C₂×#10625352	1	4	yes	—
853	C₂×C₄	C₂×#10625352	1	16	yes	—
854	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
855	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
856	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
857	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
858	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
859	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
860	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
861	C₂²	—	2	8	no	—
862	C₂²	—	2	8	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	4	16	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	8	no	—
876	C₂²	C₂²×#10625352	1	4	yes	—
877	C₂²	C₂²×#10625352	1	2	yes	—
878	C₂²	C₂×#13094071	1	4	yes	—
879	C₂²	C₂×#13094071	1	2	yes	—
880	C₂²	#15689959	1	2	yes	—
881	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	4	no	—
887	C₄	—	94	8	no	—
888	C₄	—	94	4	no	—
889	C₄	—	94	4	no	—
890	C₄	—	94	4	no	—
891	C₄	—	94	8	no	—
892	C₄	—	94	4	no	—
893	C₄	C₂²×#10625352	1	4	yes	—
894	C₄	C₂²×#10625352	1	4	yes	—
895	C₂	—	2	4	no	—
896	C₂	—	2	4	no	—
897	C₂	—	4	2	no	—
898	C₂	—	4	4	no	—
899	C₂	#20257142	1	4	yes	direct product factor
900	C₂	C₂³×#10625352	1	1	yes	characteristic
901	C₂	C₂²×#13094071	1	1	yes	characteristic
902	C₂	C₂×#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting, prime radical	C₂×C₄₇×#525	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#525	D₄₇
hypocenter	C₄₇	C₂×#3495
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. #20257142	C₂	direct (N × H)
2. C₂×#15689843	C₂	semidirect
3. C₂×#15689830	C₂	semidirect
4. C₂×#15689813	C₂	semidirect
5. C₂×#15689813	C₂	semidirect
6. C₂×#15689810	C₂	semidirect
7. C₂×#15689804	C₂	semidirect
8. C₂×#15689751	C₂	semidirect
9. C₂×#15689740	C₂	semidirect
10. C₂×#15689733	C₂	semidirect
11. C₂×#15689694	C₂	semidirect
12. C₂×#15689675	C₂	semidirect
13. C₂×#15689654	C₂	semidirect
14. C₂²×#13094003	C₂	semidirect
15. C₂×#15689606	C₂	semidirect
16. C₂×#15689600	C₂	semidirect
17. C₂²×#13093983	C₂	semidirect
20. #15689843	C₂²	semidirect
21. #15689830	C₂²	semidirect
22. #15689813	C₂²	semidirect
23. #15689813	C₂²	semidirect
24. #15689810	C₂²	semidirect
25. #15689804	C₂²	semidirect
26. #15689751	C₂²	semidirect
27. #15689740	C₂²	semidirect
28. #15689733	C₂²	semidirect
29. #15689694	C₂²	semidirect
30. #15689675	C₂²	semidirect
31. C₂×#13094024	C₂²	semidirect
32. C₂×#13094023	C₂²	semidirect
33. C₂×#13094022	C₂²	semidirect
34. #15689654	C₂²	semidirect
37. C₂×#13094017	C₂²	semidirect
38. C₂×#13094017	C₂²	semidirect
39. C₂×#13094016	C₂²	semidirect
40. C₂×#13094015	C₂²	semidirect
41. C₂×#13094015	C₂²	semidirect
42. C₂×#13094014	C₂²	semidirect
43. C₂×#13094014	C₂²	semidirect
45. C₂×#13094011	C₂²	semidirect
53. C₂×#13094003	C₂²	semidirect
54. C₂×#13094003	C₂²	semidirect
55. C₂×#13094003	C₂²	semidirect
58. C₂×#13094001	C₂²	semidirect
59. #15689606	C₂²	semidirect
60. #15689600	C₂²	semidirect
61. C₂×Q₈×Dic₄₇	C₂²	semidirect
62. C₂×C₄×Dic₉₄	C₂²	semidirect
63. C₂×C₄×Dic₉₄	C₂²	semidirect
64. C₂×#13093989	C₂²	semidirect
65. C₂×#13093989	C₂²	semidirect
66. C₂×#13093989	C₂²	semidirect
69. C₂×D₄×Dic₄₇	C₂²	semidirect
76. C₂×#13093983	C₂²	semidirect
77. C₂×#13093983	C₂²	semidirect
80. C₂×#13093980	C₂²	semidirect
84. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
111. #13094024	C₂³	semidirect
112. #13094023	C₂³	semidirect
113. #13094022	C₂³	semidirect
116. #13094017	C₂³	semidirect
117. #13094017	C₂³	semidirect
118. #13094016	C₂³	semidirect
119. #13094015	C₂³	semidirect
120. #13094015	C₂³	semidirect
121. #13094014	C₂³	semidirect
122. #13094014	C₂³	semidirect
124. #13094011	C₂³	semidirect
132. #13094003	C₂³	semidirect
133. #13094003	C₂³	semidirect
136. #13094001	C₂³	semidirect
137. Q₈×Dic₄₇	C₂³	semidirect
138. C₄×Dic₉₄	C₂³	semidirect
139. C₄×Dic₉₄	C₂³	semidirect
140. #13093989	C₂³	semidirect
141. #13093989	C₂³	semidirect
142. #13093989	C₂³	semidirect
145. D₄×Dic₄₇	C₂³	semidirect
152. #13093983	C₂³	semidirect
155. #13093980	C₂³	semidirect
169. C₂×C₄⋊Dic₄₇	C₂³	semidirect
466. C₂×C₄₇	#3495	semidirect
552. C₄₇	C₂×#3495	semidirect
899. C₂	#20257142	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257142	2
C₂×#15689843	2
C₂×#15689830	2
C₂×#15689813	2
C₂×#15689810	2
C₂×#15689804	2
C₂×#15689751	2
C₂×#15689740	2
C₂×#15689733	2
C₂×#15689694	2
C₂×#15689675	2
C₂×#15689654	2
C₂²×#13094003	2
C₂×#15689606	2
C₂×#15689600	2
C₂²×#13093983	2
C₂×C₄₇×#525	2
C₂×#3495	47

Subgroups — C2×#20257142 #27124709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257142 #27124709