Subgroups — C₂×#20256804 #27123076

Order 12032.

7994 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256804	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689751	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689745	C₂	1	2	yes	maximal, complemented
4	C₂×#15689744	C₂	1	2	yes	maximal, complemented
5	C₂×#15689728	C₂	1	2	yes	maximal, complemented
6	C₂×#15689724	C₂	1	2	yes	maximal, complemented
7	C₂×#15689706	C₂	1	4	yes	maximal, complemented
8	C₂×#15689701	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689692	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15689687	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15689673	C₂	1	2	yes	maximal, complemented
12	C₂×#15689670	C₂	1	2	yes	maximal, complemented
13	C₂×#15689660	C₂	1	2	yes	maximal, complemented
14	C₂×#15689657	C₂	1	2	yes	maximal, complemented
15	C₂×#15689632	C₂	1	4	yes	maximal, complemented
16	C₂×C₄×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10625350	C₂²	1	1	yes	characteristic
20	C₂²×#10625350	C₂²	1	4	yes	complemented
21	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
23	#15689751	C₂²	1	16	yes	complemented
24	#15689745	C₂²	1	32	yes	complemented
25	#15689744	C₂²	1	32	yes	complemented
26	#15689728	C₂²	1	32	yes	complemented
27	#15689724	C₂²	1	32	yes	complemented
28	#15689706	C₂²	1	64	yes	complemented
29	#15689701	C₂²	1	16	yes	complemented
30	#15689692	C₂²	1	16	yes	complemented
31	#15689687	C₂²	1	16	yes	complemented
32	#15689673	C₂²	1	32	yes	complemented
33	#15689670	C₂²	1	32	yes	complemented
34	C₂×#13094024	C₂²	1	2	yes	complemented
35	C₂×#13094023	C₂²	1	2	yes	complemented
36	C₂×#13094021	C₂²	1	2	yes	—
37	C₂×#13094020	C₂²	1	2	yes	—
38	#15689660	C₂²	1	32	yes	complemented
39	#15689657	C₂²	1	32	yes	complemented
40	C₂×#13094019	C₂²	1	4	yes	complemented
41	C₂×#13094018	C₂²	1	4	yes	complemented
42	C₂×#13094016	C₂²	1	2	yes	complemented
43	C₂×#13094015	C₂²	1	2	yes	complemented
44	C₂×#13094013	C₂²	1	2	yes	—
45	C₂×#13094012	C₂²	1	2	yes	—
46	C₂×#13094012	C₂²	1	4	yes	complemented
47	C₂×#13094010	C₂²	1	4	yes	complemented
48	#15689632	C₂²	1	64	yes	complemented
49	C₂×#13094009	C₂²	1	4	yes	complemented
50	C₂×#13094009	C₂²	1	4	yes	complemented
51	C₂×#13094007	C₂²	1	4	yes	complemented
52	C₂×#13094006	C₂²	1	4	yes	complemented
53	C₂×#13094003	C₂²	1	2	yes	complemented
54	C₂×#13094002	C₂²	1	4	yes	complemented
55	C₂×#13094001	C₂²	1	4	yes	—
56	C₂×#13094000	C₂²	1	2	yes	complemented
57	C₂×#13093999	C₂²	1	2	yes	—
58	C₂×#13093999	C₂²	1	2	yes	—
59	C₂×#13093998	C₂²	1	2	yes	—
60	C₂×#13093998	C₂²	1	2	yes	—
61	C₂×#13093998	C₂²	1	2	yes	complemented
62	C₂×#13093998	C₂²	1	4	yes	complemented
63	C₂×#13093997	C₂²	1	4	yes	complemented
64	C₂×#13093997	C₂²	1	4	yes	complemented
65	C₂×#13093996	C₂²	1	4	yes	—
66	C₂×#13093995	C₂²	1	2	yes	complemented
67	C₂×#13093994	C₂²	1	4	yes	—
68	C₂×#13093992	C₂²	1	4	yes	—
69	C₄×#10625350	C₂²	1	16	yes	complemented
70	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
73	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
74	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
75	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
76	C₂×C₄×D₁₈₈	C₂²	1	16	yes	complemented
77	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄×D₁₈₈	C₂²	1	4	yes	complemented
80	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
81	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
82	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
83	C₂×#13093983	C₂²	1	1	yes	characteristic
84	C₂×#13093981	C₂²	1	2	yes	complemented
85	C₂×#13093981	C₂²	1	4	yes	complemented
86	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
87	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
88	C₂×C₄²×D₄₇	C₂²	1	2	yes	complemented
89	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
90	C₄×#41×C₄₇	C₂²	1	16	yes	complemented
91	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
94	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
95	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
97	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
98	C₂×#117×C₄₇	C₂²	1	2	yes	complemented
99	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
100	C₂²×C₄²×C₄₇	C₂²	1	2	yes	complemented
101	C₂⁴×D₄₇	C₂³	1	2	yes	—
102	C₂×#10625350	—	2	8	no	—
103	C₂×#10625350	—	4	16	no	—
104	C₂×#10625350	C₂³	1	8	yes	—
105	C₂×#10625350	C₂³	1	32	yes	complemented
106	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
107	C₂²×Dic₉₄	C₂³	1	4	yes	—
108	C₂²×D₁₈₈	—	2	8	no	—
109	C₂²×D₁₈₈	C₂³	1	2	yes	—
110	C₂²×D₁₈₈	C₂³	1	2	yes	—
111	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
112	C₂²×D₁₈₈	C₂³	1	8	yes	—
113	C₂²×D₁₈₈	C₂³	1	4	yes	—
114	C₂²×D₁₈₈	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
116	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
117	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
118	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
119	C₂³×Dic₄₇	C₂³	1	2	yes	—
120	C₂²×C₄×D₄₇	—	4	8	no	—
121	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
122	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
123	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
124	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
125	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
126	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
127	#13094024	C₂³	1	16	yes	complemented
128	#13094023	C₂³	1	16	yes	complemented
129	#13094021	C₂³	1	16	yes	—
130	#13094020	C₂³	1	16	yes	—
131	#13094019	C₂³	1	32	yes	complemented
132	#13094018	C₂³	1	32	yes	complemented
133	#13094016	C₂³	1	16	yes	complemented
134	#13094015	C₂³	1	16	yes	complemented
135	#13094013	C₂³	1	16	yes	—
136	#13094012	C₂³	1	16	yes	—
137	#13094012	C₂³	1	32	yes	complemented
138	#13094010	C₂³	1	32	yes	complemented
139	#13094009	C₂³	1	32	yes	complemented
140	#13094009	C₂³	1	32	yes	complemented
141	#13094007	C₂³	1	32	yes	complemented
142	#13094006	C₂³	1	32	yes	complemented
143	#13094003	C₂³	1	16	yes	complemented
144	#13094002	C₂³	1	32	yes	complemented
145	#13094001	C₂³	1	32	yes	—
146	#13094000	C₂³	1	16	yes	complemented
147	#13093999	C₂³	1	16	yes	—
148	#13093999	C₂³	1	16	yes	—
149	#13093998	C₂³	1	16	yes	—
150	#13093998	C₂³	1	16	yes	—
151	#13093998	C₂³	1	16	yes	complemented
152	#13093998	C₂³	1	32	yes	complemented
153	#13093997	C₂³	1	32	yes	complemented
154	#13093997	C₂³	1	32	yes	complemented
155	#13093996	C₂³	1	32	yes	—
156	#13093995	C₂³	1	16	yes	complemented
157	#13093994	C₂³	1	32	yes	—
158	#13093992	C₂³	1	32	yes	—
159	C₄×Dic₉₄	C₂³	1	8	yes	complemented
160	C₄×Dic₉₄	C₂³	1	8	yes	complemented
161	C₄×D₁₈₈	C₂³	1	16	yes	—
162	C₄×D₁₈₈	C₂³	1	16	yes	—
163	C₄×D₁₈₈	C₂³	1	16	yes	—
164	C₄×D₁₈₈	C₂³	1	16	yes	—
165	C₄×D₁₈₈	C₂³	1	8	yes	complemented
166	C₄×D₁₈₈	C₂³	1	8	yes	complemented
167	C₄×D₁₈₈	C₂³	1	32	yes	complemented
168	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
169	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
170	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
171	#13093983	C₂³	1	8	yes	—
172	#13093981	C₂³	1	16	yes	complemented
173	#13093981	C₂³	1	32	yes	complemented
174	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
175	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
176	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
177	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
180	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
181	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
182	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
183	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
184	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
185	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
187	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
188	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
189	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
190	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
191	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
192	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
193	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
194	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
195	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
196	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
197	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
198	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
199	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
200	C₄²×D₄₇	C₂³	1	16	yes	complemented
201	C₂×#41×C₄₇	—	2	8	no	—
202	C₂×#41×C₄₇	C₂³	1	8	yes	—
203	C₂²×Q₈×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	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
208	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
209	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
211	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
213	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
214	C₄×D₄×C₄₇	C₂³	1	16	yes	—
215	C₄×D₄×C₄₇	C₂³	1	16	yes	—
216	C₄×D₄×C₄₇	C₂³	1	8	yes	complemented
217	C₄×D₄×C₄₇	C₂³	1	8	yes	complemented
218	#117×C₄₇	C₂³	1	8	yes	—
219	#117×C₄₇	C₂³	1	16	yes	complemented
220	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
227	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
232	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
235	C₂×C₄²×C₄₇	C₂³	1	16	yes	complemented
236	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
237	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂³×D₄₇	—	2	8	no	—
239	C₂³×D₄₇	—	4	4	no	—
240	C₂³×D₄₇	—	4	4	no	—
241	C₂³×D₄₇	C₂⁴	1	4	yes	—
242	C₂³×D₄₇	C₂⁴	1	2	yes	—
243	C₂³×D₄₇	C₂⁴	1	8	yes	—
244	#41×C₄₇	—	2	32	no	—
245	C₂×Q₈×C₄₇	—	2	4	no	—
246	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
247	C₂×D₄×C₄₇	—	2	8	no	—
248	C₂×D₄×C₄₇	—	2	4	no	—
249	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
250	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₄₇	—	2	8	no	—
252	C₂²×C₄×C₄₇	—	2	4	no	—
253	C₂²×C₄×C₄₇	—	2	8	no	—
254	C₂²×C₄×C₄₇	—	4	2	no	—
255	C₂²×C₄×C₄₇	—	4	4	no	—
256	C₂²×C₄×C₄₇	#41	1	8	yes	complemented
257	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
266	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
268	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₂²⋊D₄₇	—	2	8	no	—
273	C₂×C₂²⋊D₄₇	—	4	8	no	—
274	C₂×C₂²⋊D₄₇	—	4	8	no	—
275	C₂×C₂²⋊D₄₇	—	4	8	no	—
276	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
277	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
278	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
279	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
280	C₂²×Dic₄₇	—	4	4	no	—
281	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
282	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
283	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
284	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
285	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
286	#10625350	—	2	32	no	—
287	#10625350	—	4	64	no	—
288	C₂×D₁₈₈	—	2	8	no	—
289	C₂×D₁₈₈	—	2	8	no	—
290	C₂×D₁₈₈	—	2	4	no	—
291	C₂×D₁₈₈	—	2	32	no	—
292	C₂×D₁₈₈	—	4	8	no	—
293	C₂×D₁₈₈	—	4	8	no	—
294	C₂×D₁₈₈	C₂⁴	1	8	yes	—
295	C₂×D₁₈₈	C₂⁴	1	8	yes	—
296	C₂×D₁₈₈	C₂⁴	1	4	yes	—
297	C₂×D₁₈₈	C₂⁴	1	16	yes	—
298	C₂×D₁₈₈	C₂⁴	1	16	yes	—
299	C₂×C₄×D₄₇	—	2	8	no	—
300	C₂×C₄×D₄₇	—	2	16	no	—
301	C₂×C₄×D₄₇	—	2	8	no	—
302	C₂×C₄×D₄₇	—	4	32	no	—
303	C₂×C₄×D₄₇	—	4	8	no	—
304	C₂×C₄×D₄₇	—	4	4	no	—
305	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
306	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
307	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
308	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
309	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
310	C₂×Dic₉₄	—	2	4	no	—
311	C₂×Dic₉₄	—	4	8	no	—
312	C₂×Dic₉₄	C₂⁴	1	4	yes	—
313	C₂×Dic₉₄	C₂⁴	1	16	yes	—
314	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
315	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
316	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
318	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
319	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
321	C₄²×C₄₇	C₂⁴	1	4	yes	—
322	C₄²×C₄₇	C₂⁴	1	4	yes	—
323	C₄²×C₄₇	C₂⁴	1	4	yes	—
324	C₄²×C₄₇	C₂⁴	1	4	yes	—
325	C₄²×C₄₇	C₂⁴	1	8	yes	—
326	C₄²×C₄₇	C₂⁴	1	8	yes	—
327	C₄²×C₄₇	C₂⁴	1	8	yes	—
328	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
329	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
330	(C₂×D₄₇)⋊C₄	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	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
335	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
336	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
337	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
338	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
339	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
340	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
341	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
342	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
343	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
344	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
345	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
346	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
347	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
348	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
349	C₄×Dic₄₇	C₂⁴	1	8	yes	—
350	C₄×Dic₄₇	C₂⁴	1	8	yes	—
351	C₄×Dic₄₇	C₂⁴	1	8	yes	—
352	C₂³×C₄₇	—	2	2	no	—
353	C₂³×C₄₇	—	2	2	no	—
354	C₂³×C₄₇	—	2	4	no	—
355	C₂³×C₄₇	—	2	4	no	—
356	C₂³×C₄₇	—	2	4	no	—
357	C₂³×C₄₇	C₂×#41	1	4	yes	—
358	C₂³×C₄₇	C₂⁵	1	4	yes	—
359	C₂³×C₄₇	C₂⁵	1	2	yes	—
360	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
361	C₂²×D₄₇	—	2	4	no	—
362	C₂²×D₄₇	—	2	16	no	—
363	C₂²×D₄₇	—	2	8	no	—
364	C₂²×D₄₇	—	2	8	no	—
365	C₂²×D₄₇	—	2	4	no	—
366	C₂²×D₄₇	—	2	4	no	—
367	C₂²×D₄₇	—	2	8	no	—
368	C₂²×D₄₇	—	4	8	no	—
369	C₂²×D₄₇	—	4	8	no	—
370	C₂²×D₄₇	—	4	32	no	—
371	C₂²×D₄₇	C₂⁵	1	8	yes	—
372	C₂²×D₄₇	C₂⁵	1	4	yes	—
373	Q₈×C₄₇	—	2	8	no	—
374	D₄×C₄₇	—	2	16	no	—
375	D₄×C₄₇	—	2	8	no	—
376	C₂×C₄×C₄₇	—	2	4	no	—
377	C₂×C₄×C₄₇	—	2	4	no	—
378	C₂×C₄×C₄₇	—	2	2	no	—
379	C₂×C₄×C₄₇	—	2	2	no	—
380	C₂×C₄×C₄₇	—	2	4	no	—
381	C₂×C₄×C₄₇	—	2	2	no	—
382	C₂×C₄×C₄₇	—	2	16	no	—
383	C₂×C₄×C₄₇	—	2	8	no	—
384	C₂×C₄×C₄₇	—	2	16	no	—
385	C₂×C₄×C₄₇	—	4	4	no	—
386	C₂×C₄×C₄₇	—	4	8	no	—
387	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
388	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
389	C₂×C₄×C₄₇	C₂×#41	1	16	yes	complemented
390	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
391	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
392	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
393	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
394	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
395	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
396	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
397	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
398	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
399	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
400	C₂²⋊D₄₇	—	2	16	no	—
401	C₂²⋊D₄₇	—	4	16	no	—
402	C₂²⋊D₄₇	—	4	16	no	—
403	C₂²⋊D₄₇	—	4	16	no	—
404	C₂×Dic₄₇	—	2	4	no	—
405	C₂×Dic₄₇	—	2	4	no	—
406	C₂×Dic₄₇	—	2	8	no	—
407	C₂×Dic₄₇	—	2	4	no	—
408	C₂×Dic₄₇	—	4	8	no	—
409	C₂×Dic₄₇	C₂⁵	1	4	yes	—
410	C₂×Dic₄₇	C₂⁵	1	4	yes	—
411	C₂×Dic₄₇	C₂⁵	1	4	yes	—
412	C₂×Dic₄₇	C₂⁵	1	8	yes	—
413	D₁₈₈	—	2	16	no	—
414	D₁₈₈	—	2	16	no	—
415	D₁₈₈	—	2	8	no	—
416	D₁₈₈	—	4	16	no	—
417	D₁₈₈	—	4	16	no	—
418	C₄×D₄₇	—	2	16	no	—
419	C₄×D₄₇	—	2	32	no	—
420	C₄×D₄₇	—	2	16	no	—
421	C₄×D₄₇	—	4	16	no	—
422	C₄×D₄₇	—	4	8	no	—
423	Dic₉₄	—	2	8	no	—
424	Dic₉₄	—	4	16	no	—
425	C₂×#3460	—	47	1	no	maximal, Sylow
426	C₂²×C₄₇	—	2	2	no	—
427	C₂²×C₄₇	—	2	2	no	—
428	C₂²×C₄₇	—	2	8	no	—
429	C₂²×C₄₇	—	2	4	no	—
430	C₂²×C₄₇	—	2	4	no	—
431	C₂²×C₄₇	—	2	4	no	—
432	C₂²×C₄₇	—	4	8	no	—
433	C₂²×C₄₇	C₂²×#41	1	4	yes	—
434	C₂²×C₄₇	C₂²×#41	1	2	yes	—
435	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
436	C₂²×C₄₇	#585	1	2	yes	—
437	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
438	C₂×D₄₇	—	2	4	no	—
439	C₂×D₄₇	—	2	8	no	—
440	C₂×D₄₇	—	2	8	no	—
441	C₂×D₄₇	—	2	4	no	—
442	C₂×D₄₇	—	2	4	no	—
443	C₂×D₄₇	—	2	8	no	—
444	C₂×D₄₇	—	4	32	no	—
445	C₂×D₄₇	—	4	8	no	—
446	C₂×D₄₇	—	4	16	no	—
447	C₄×C₄₇	—	2	4	no	—
448	C₄×C₄₇	—	2	4	no	—
449	C₄×C₄₇	—	2	2	no	—
450	C₄×C₄₇	—	2	2	no	—
451	C₄×C₄₇	—	2	4	no	—
452	C₄×C₄₇	—	2	2	no	—
453	C₄×C₄₇	C₂²×#41	1	4	yes	—
454	C₄×C₄₇	C₂²×#41	1	4	yes	—
455	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
456	Dic₄₇	—	2	4	no	—
457	Dic₄₇	—	2	4	no	—
458	Dic₄₇	—	2	8	no	—
459	Dic₄₇	—	2	4	no	—
460	#3460	—	47	32	no	—
461	C₂×#544	—	47	1	no	—
462	C₂×#542	—	47	2	no	—
463	C₂×#542	—	47	2	no	—
464	C₂×#540	—	47	2	no	—
465	C₂×#540	—	47	2	no	—
466	C₂×#538	—	47	4	no	—
467	C₂×#537	—	47	1	no	—
468	C₂×#535	—	47	1	no	—
469	C₂×#535	—	47	1	no	—
470	C₂×#532	—	47	2	no	—
471	C₂×#532	—	47	2	no	—
472	C₂×#529	—	47	2	no	—
473	C₂×#529	—	47	2	no	—
474	C₂×#525	—	47	4	no	—
475	C₂×C₄×#41	—	47	1	no	—
476	C₂×C₄×#41	D₄₇	1	1	yes	characteristic, complemented
477	C₂²×C₄×D₄	—	47	1	no	—
478	C₂×C₄₇	—	2	4	no	—
479	C₂×C₄₇	—	4	4	no	—
480	C₂×C₄₇	#3460	1	4	yes	complemented
481	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
482	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
484	D₄₇	—	4	4	no	—
485	D₄₇	—	4	8	no	—
486	C₂²×#41	—	47	1	no	—
487	C₂²×#41	—	47	4	no	—
488	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
489	C₂³×D₄	—	47	1	no	—
490	C₂⁴×C₄	—	47	2	no	—
491	#544	—	47	16	no	—
492	#542	—	47	32	no	—
493	#542	—	47	32	no	—
494	#540	—	47	32	no	—
495	#540	—	47	32	no	—
496	#538	—	47	64	no	—
497	#537	—	47	16	no	—
498	#535	—	47	16	no	—
499	#535	—	47	16	no	—
500	#532	—	47	32	no	—
501	#532	—	47	32	no	—
502	C₂×C₄⋊Q₈	—	47	2	no	—
503	C₂×C₄⋊Q₈	—	47	2	no	—
504	C₂×#127	—	47	2	no	—
505	C₂×#127	—	47	2	no	—
506	#529	—	47	32	no	—
507	#529	—	47	32	no	—
508	C₂×#126	—	47	4	no	—
509	C₂×#126	—	47	4	no	—
510	C₂×#125	—	47	2	no	—
511	C₂×#125	—	47	2	no	—
512	C₂×#124	—	47	2	no	—
513	C₂×#124	—	47	4	no	—
514	C₂×#124	—	47	2	no	—
515	C₂×#124	—	47	4	no	—
516	#525	—	47	64	no	—
517	C₂×#123	—	47	4	no	—
518	C₂×#123	—	47	4	no	—
519	C₂×#123	—	47	4	no	—
520	C₂×#123	—	47	4	no	—
521	C₂×C₂²⋊Q₈	—	47	2	no	—
522	C₂×C₂²⋊Q₈	—	47	2	no	—
523	C₂×C₂²⋊Q₈	—	47	4	no	—
524	C₂×C₂²⋊Q₈	—	47	4	no	—
525	C₂×#121	—	47	4	no	—
526	C₂×#121	—	47	2	no	—
527	C₂×#121	—	47	2	no	—
528	C₂×#121	—	47	2	no	—
529	C₂×#121	—	47	2	no	—
530	C₂×#121	—	47	4	no	—
531	C₂×#121	—	47	2	no	—
532	C₂×#121	—	47	2	no	—
533	C₂×#121	—	47	4	no	—
534	C₂×#121	—	47	4	no	—
535	C₂×#120	—	47	4	no	—
536	C₂×#120	—	47	4	no	—
537	C₄×#41	—	47	16	no	—
538	C₄×#41	C₂×D₄₇	1	16	yes	complemented
539	C₂×C₄×Q₈	—	47	1	no	—
540	C₂×C₄×Q₈	—	47	1	no	—
541	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
542	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
543	C₂×C₄×D₄	—	47	2	no	—
544	C₂×C₄×D₄	—	47	2	no	—
545	C₂×C₄×D₄	—	47	4	no	—
546	C₂×C₄×D₄	—	47	2	no	—
547	C₂×C₄×D₄	—	47	2	no	—
548	C₂×C₄×D₄	—	47	2	no	—
549	C₂×C₄×D₄	—	47	2	no	—
550	C₂×C₄×D₄	—	47	16	no	—
551	C₂×C₄×D₄	—	47	1	no	—
552	C₂×C₄×D₄	—	47	1	no	—
553	C₂×C₄×D₄	—	47	4	no	—
554	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
555	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
556	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
557	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
558	C₂×#117	—	47	1	no	—
559	C₂×#117	—	47	2	no	—
560	C₂×#117	—	47	4	no	—
561	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
562	C₂×#117	C₂×D₄₇	1	2	yes	complemented
563	C₂²×C₄⋊C₄	—	47	1	no	—
564	C₂²×C₂²⋊C₄	—	47	2	no	—
565	C₂²×C₄²	—	47	2	no	—
566	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
567	C₂²×C₄²	C₂×D₄₇	1	2	yes	complemented
568	C₄₇	C₂×#3460	1	1	yes	characteristic, complemented, Sylow
569	C₂⁵	—	47	2	no	—
570	C₂×#41	—	2	8	no	—
571	C₂×#41	—	47	8	no	—
572	C₂×#41	—	47	32	no	—
573	C₂×#41	—	94	8	no	—
574	C₂×#41	—	188	16	no	—
575	C₂×#41	C₂²×D₄₇	1	8	yes	—
576	C₂²×Q₈	—	47	1	no	—
577	C₂²×Q₈	—	47	4	no	—
578	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
579	C₂²×D₄	—	47	2	no	—
580	C₂²×D₄	—	47	4	no	—
581	C₂²×D₄	—	47	4	no	—
582	C₂²×D₄	—	47	4	no	—
583	C₂²×D₄	—	47	2	no	—
584	C₂²×D₄	—	47	2	no	—
585	C₂²×D₄	—	47	1	no	—
586	C₂²×D₄	—	47	8	no	—
587	C₂²×D₄	—	47	4	no	—
588	C₂²×D₄	—	47	4	no	—
589	C₂²×D₄	—	94	8	no	—
590	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
591	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
592	C₂³×C₄	—	47	2	no	—
593	C₂³×C₄	—	47	2	no	—
594	C₂³×C₄	—	47	4	no	—
595	C₂³×C₄	—	47	2	no	—
596	C₂³×C₄	—	47	2	no	—
597	C₂³×C₄	—	47	4	no	—
598	C₂³×C₄	—	47	16	no	—
599	C₂³×C₄	—	188	8	no	—
600	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
601	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
602	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
603	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
604	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
605	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
606	C₄⋊Q₈	—	47	16	no	—
607	C₄⋊Q₈	—	47	16	no	—
608	#127	—	47	16	no	—
609	#127	—	47	16	no	—
610	#126	—	47	32	no	—
611	#126	—	47	32	no	—
612	#125	—	47	16	no	—
613	#125	—	47	16	no	—
614	#124	—	47	16	no	—
615	#124	—	47	32	no	—
616	#124	—	47	16	no	—
617	#124	—	47	32	no	—
618	#123	—	47	32	no	—
619	#123	—	47	32	no	—
620	#123	—	47	32	no	—
621	#123	—	47	32	no	—
622	C₂²⋊Q₈	—	47	16	no	—
623	C₂²⋊Q₈	—	47	16	no	—
624	C₂²⋊Q₈	—	47	32	no	—
625	C₂²⋊Q₈	—	47	32	no	—
626	#121	—	47	32	no	—
627	#121	—	47	16	no	—
628	#121	—	47	16	no	—
629	#121	—	47	16	no	—
630	#121	—	47	16	no	—
631	#121	—	47	32	no	—
632	#121	—	47	16	no	—
633	#121	—	47	16	no	—
634	#121	—	47	32	no	—
635	#121	—	47	32	no	—
636	#120	—	47	32	no	—
637	#120	—	47	32	no	—
638	C₄×Q₈	—	47	8	no	—
639	C₄×Q₈	—	47	8	no	—
640	C₄×Q₈	C₂²×D₄₇	1	8	yes	complemented
641	C₄×Q₈	C₂²×D₄₇	1	8	yes	complemented
642	C₄×D₄	—	47	16	no	—
643	C₄×D₄	—	47	16	no	—
644	C₄×D₄	—	47	32	no	—
645	C₄×D₄	—	47	16	no	—
646	C₄×D₄	—	47	16	no	—
647	C₄×D₄	—	47	16	no	—
648	C₄×D₄	—	47	16	no	—
649	C₄×D₄	—	47	8	no	—
650	C₄×D₄	—	47	8	no	—
651	C₄×D₄	—	47	32	no	—
652	C₄×D₄	C₂²×D₄₇	1	16	yes	—
653	C₄×D₄	C₂²×D₄₇	1	16	yes	—
654	C₄×D₄	C₂²×D₄₇	1	8	yes	complemented
655	C₄×D₄	C₂²×D₄₇	1	8	yes	complemented
656	#117	—	47	8	no	—
657	#117	—	47	16	no	—
658	#117	—	47	32	no	—
659	#117	C₂²×D₄₇	1	8	yes	—
660	#117	C₂²×D₄₇	1	16	yes	complemented
661	C₂×C₄⋊C₄	—	47	2	no	—
662	C₂×C₄⋊C₄	—	47	2	no	—
663	C₂×C₄⋊C₄	—	47	8	no	—
664	C₂×C₄⋊C₄	—	47	1	no	—
665	C₂×C₄⋊C₄	—	47	1	no	—
666	C₂×C₄⋊C₄	—	47	2	no	—
667	C₂×C₄⋊C₄	—	47	2	no	—
668	C₂×C₄⋊C₄	—	47	4	no	—
669	C₂×C₄⋊C₄	—	47	4	no	—
670	C₂×C₄⋊C₄	—	47	4	no	—
671	C₂×C₄⋊C₄	—	47	4	no	—
672	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
675	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
676	C₂×C₂²⋊C₄	—	47	2	no	—
677	C₂×C₂²⋊C₄	—	47	4	no	—
678	C₂×C₂²⋊C₄	—	47	4	no	—
679	C₂×C₂²⋊C₄	—	47	4	no	—
680	C₂×C₂²⋊C₄	—	47	16	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	4	no	—
685	C₂×C₂²⋊C₄	—	47	4	no	—
686	C₂×C₂²⋊C₄	—	47	4	no	—
687	C₂×C₂²⋊C₄	—	47	4	no	—
688	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
691	C₂×C₄²	—	47	2	no	—
692	C₂×C₄²	—	47	2	no	—
693	C₂×C₄²	—	47	2	no	—
694	C₂×C₄²	—	47	16	no	—
695	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
696	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
697	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
698	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
699	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
700	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
701	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
702	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
703	C₂×C₄²	C₂²×D₄₇	1	16	yes	complemented
704	C₂⁴	—	47	4	no	—
705	C₂⁴	—	47	2	no	—
706	C₂⁴	—	47	8	no	—
707	C₂⁴	—	94	8	no	—
708	C₂⁴	—	188	4	no	—
709	C₂⁴	—	188	4	no	—
710	C₂⁴	C₂³×D₄₇	1	2	yes	—
711	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
712	#41	—	2	32	no	—
713	#41	—	94	32	no	—
714	#41	—	188	64	no	—
715	C₂×Q₈	—	2	4	no	—
716	C₂×Q₈	—	47	4	no	—
717	C₂×Q₈	—	47	16	no	—
718	C₂×Q₈	—	94	4	no	—
719	C₂×Q₈	—	188	8	no	—
720	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
721	C₂×D₄	—	2	8	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	47	8	no	—
724	C₂×D₄	—	47	16	no	—
725	C₂×D₄	—	47	16	no	—
726	C₂×D₄	—	47	16	no	—
727	C₂×D₄	—	47	8	no	—
728	C₂×D₄	—	47	8	no	—
729	C₂×D₄	—	47	4	no	—
730	C₂×D₄	—	47	16	no	—
731	C₂×D₄	—	47	16	no	—
732	C₂×D₄	—	94	8	no	—
733	C₂×D₄	—	94	8	no	—
734	C₂×D₄	—	94	8	no	—
735	C₂×D₄	—	94	4	no	—
736	C₂×D₄	—	94	32	no	—
737	C₂×D₄	—	188	8	no	—
738	C₂×D₄	—	188	8	no	—
739	C₂×D₄	—	188	8	no	—
740	C₂×D₄	—	188	8	no	—
741	C₂×D₄	—	188	8	no	—
742	C₂×D₄	C₂³×D₄₇	1	8	yes	—
743	C₂×D₄	C₂³×D₄₇	1	4	yes	—
744	C₂²×C₄	—	2	8	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	8	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	4	no	—
749	C₂²×C₄	—	47	2	no	—
750	C₂²×C₄	—	47	2	no	—
751	C₂²×C₄	—	47	2	no	—
752	C₂²×C₄	—	47	4	no	—
753	C₂²×C₄	—	47	8	no	—
754	C₂²×C₄	—	47	8	no	—
755	C₂²×C₄	—	47	8	no	—
756	C₂²×C₄	—	47	16	no	—
757	C₂²×C₄	—	47	8	no	—
758	C₂²×C₄	—	47	16	no	—
759	C₂²×C₄	—	94	8	no	—
760	C₂²×C₄	—	94	16	no	—
761	C₂²×C₄	—	94	8	no	—
762	C₂²×C₄	—	188	32	no	—
763	C₂²×C₄	—	188	4	no	—
764	C₂²×C₄	—	188	8	no	—
765	C₂²×C₄	—	188	4	no	—
766	C₂²×C₄	#10625350	1	8	yes	complemented
767	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
768	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
770	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
771	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
772	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
773	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
774	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
775	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
776	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
777	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
778	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
779	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
780	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
781	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
782	C₄⋊C₄	—	47	8	no	—
783	C₄⋊C₄	—	47	8	no	—
784	C₄⋊C₄	—	47	16	no	—
785	C₄⋊C₄	—	47	16	no	—
786	C₄⋊C₄	—	47	16	no	—
787	C₄⋊C₄	—	47	8	no	—
788	C₄⋊C₄	—	47	8	no	—
789	C₄⋊C₄	—	47	4	no	—
790	C₄⋊C₄	—	47	4	no	—
791	C₄⋊C₄	—	47	16	no	—
792	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
793	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
794	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
795	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
796	C₂²⋊C₄	—	47	8	no	—
797	C₂²⋊C₄	—	47	16	no	—
798	C₂²⋊C₄	—	47	16	no	—
799	C₂²⋊C₄	—	47	16	no	—
800	C₂²⋊C₄	—	47	8	no	—
801	C₂²⋊C₄	—	47	8	no	—
802	C₂²⋊C₄	—	47	16	no	—
803	C₂²⋊C₄	—	47	16	no	—
804	C₂²⋊C₄	—	47	16	no	—
805	C₂²⋊C₄	—	47	16	no	—
806	C₂²⋊C₄	—	47	16	no	—
807	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
808	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
809	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
810	C₄²	—	47	8	no	—
811	C₄²	—	47	8	no	—
812	C₄²	—	47	8	no	—
813	C₄²	C₂³×D₄₇	1	4	yes	—
814	C₄²	C₂³×D₄₇	1	4	yes	—
815	C₄²	C₂³×D₄₇	1	4	yes	—
816	C₄²	C₂³×D₄₇	1	4	yes	—
817	C₄²	C₂³×D₄₇	1	8	yes	—
818	C₄²	C₂³×D₄₇	1	8	yes	—
819	C₄²	C₂³×D₄₇	1	8	yes	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	2	4	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	47	8	no	—
826	C₂³	—	47	4	no	—
827	C₂³	—	94	4	no	—
828	C₂³	—	94	16	no	—
829	C₂³	—	94	8	no	—
830	C₂³	—	94	8	no	—
831	C₂³	—	94	4	no	—
832	C₂³	—	94	4	no	—
833	C₂³	—	94	8	no	—
834	C₂³	—	188	8	no	—
835	C₂³	—	188	8	no	—
836	C₂³	—	188	32	no	—
837	C₂³	C₂×#10625350	1	4	yes	—
838	C₂³	C₂⁴×D₄₇	1	4	yes	—
839	C₂³	C₂⁴×D₄₇	1	2	yes	—
840	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
841	Q₈	—	2	8	no	—
842	Q₈	—	94	8	no	—
843	Q₈	—	188	16	no	—
844	D₄	—	2	16	no	—
845	D₄	—	2	8	no	—
846	D₄	—	94	16	no	—
847	D₄	—	94	16	no	—
848	D₄	—	94	16	no	—
849	D₄	—	94	8	no	—
850	D₄	—	188	16	no	—
851	D₄	—	188	16	no	—
852	D₄	—	188	16	no	—
853	D₄	—	188	16	no	—
854	D₄	—	188	16	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	16	no	—
862	C₂×C₄	—	2	8	no	—
863	C₂×C₄	—	2	16	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	47	4	no	—
867	C₂×C₄	—	47	4	no	—
868	C₂×C₄	—	47	4	no	—
869	C₂×C₄	—	47	8	no	—
870	C₂×C₄	—	94	4	no	—
871	C₂×C₄	—	94	8	no	—
872	C₂×C₄	—	94	4	no	—
873	C₂×C₄	—	94	4	no	—
874	C₂×C₄	—	94	16	no	—
875	C₂×C₄	—	94	32	no	—
876	C₂×C₄	—	94	16	no	—
877	C₂×C₄	—	188	8	no	—
878	C₂×C₄	—	188	16	no	—
879	C₂×C₄	—	188	8	no	—
880	C₂×C₄	C₂×#10625350	1	4	yes	—
881	C₂×C₄	C₂×#10625350	1	4	yes	—
882	C₂×C₄	C₂×#10625350	1	16	yes	complemented
883	C₂×C₄	#13094070	1	4	yes	—
884	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
885	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
886	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
887	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
888	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
889	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
890	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
891	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
892	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
893	C₂²	—	2	8	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	4	8	no	—
900	C₂²	—	94	4	no	—
901	C₂²	—	94	8	no	—
902	C₂²	—	94	8	no	—
903	C₂²	—	94	4	no	—
904	C₂²	—	94	4	no	—
905	C₂²	—	94	8	no	—
906	C₂²	—	188	32	no	—
907	C₂²	—	188	16	no	—
908	C₂²	—	188	8	no	—
909	C₂²	C₂²×#10625350	1	4	yes	—
910	C₂²	C₂²×#10625350	1	2	yes	—
911	C₂²	C₂×#13094070	1	2	yes	—
912	C₂²	#15689959	1	2	yes	—
913	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
914	C₄	—	2	4	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	4	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	4	no	—
920	C₄	—	94	4	no	—
921	C₄	—	94	8	no	—
922	C₄	—	94	4	no	—
923	C₄	—	94	4	no	—
924	C₄	C₂²×#10625350	1	4	yes	—
925	C₄	C₂²×#10625350	1	4	yes	—
926	C₄	C₂×#13094070	1	4	yes	—
927	C₂	—	2	4	no	—
928	C₂	—	4	4	no	—
929	C₂	—	188	8	no	—
930	C₂	—	188	4	no	—
931	C₂	#20256804	1	4	yes	direct product factor
932	C₂	C₂³×#10625350	1	1	yes	characteristic
933	C₂	C₂²×#13094070	1	1	yes	characteristic
934	C₂	C₂×#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄×#41×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×C₄×#41	D₄₇
hypocenter	C₄₇	C₂×#3460
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20256804	C₂	direct (N × H)
2. C₂×#15689751	C₂	semidirect
3. C₂×#15689745	C₂	semidirect
4. C₂×#15689744	C₂	semidirect
5. C₂×#15689728	C₂	semidirect
6. C₂×#15689724	C₂	semidirect
7. C₂×#15689706	C₂	semidirect
8. C₂×#15689701	C₂	semidirect
9. C₂×#15689692	C₂	semidirect
10. C₂×#15689687	C₂	semidirect
11. C₂×#15689673	C₂	semidirect
12. C₂×#15689670	C₂	semidirect
13. C₂×#15689660	C₂	semidirect
14. C₂×#15689657	C₂	semidirect
15. C₂×#15689632	C₂	semidirect
16. C₂×C₄×#10625350	C₂	semidirect
17. C₂²×C₄×D₁₈₈	C₂	semidirect
18. C₂×C₄×#41×C₄₇	C₂	semidirect
20. C₂²×#10625350	C₂²	semidirect
23. #15689751	C₂²	semidirect
24. #15689745	C₂²	semidirect
25. #15689744	C₂²	semidirect
26. #15689728	C₂²	semidirect
27. #15689724	C₂²	semidirect
28. #15689706	C₂²	semidirect
29. #15689701	C₂²	semidirect
30. #15689692	C₂²	semidirect
31. #15689687	C₂²	semidirect
32. #15689673	C₂²	semidirect
33. #15689670	C₂²	semidirect
34. C₂×#13094024	C₂²	semidirect
35. C₂×#13094023	C₂²	semidirect
38. #15689660	C₂²	semidirect
39. #15689657	C₂²	semidirect
40. C₂×#13094019	C₂²	semidirect
41. C₂×#13094018	C₂²	semidirect
42. C₂×#13094016	C₂²	semidirect
43. C₂×#13094015	C₂²	semidirect
46. C₂×#13094012	C₂²	semidirect
47. C₂×#13094010	C₂²	semidirect
48. #15689632	C₂²	semidirect
49. C₂×#13094009	C₂²	semidirect
50. C₂×#13094009	C₂²	semidirect
51. C₂×#13094007	C₂²	semidirect
52. C₂×#13094006	C₂²	semidirect
53. C₂×#13094003	C₂²	semidirect
54. C₂×#13094002	C₂²	semidirect
56. C₂×#13094000	C₂²	semidirect
61. C₂×#13093998	C₂²	semidirect
62. C₂×#13093998	C₂²	semidirect
63. C₂×#13093997	C₂²	semidirect
64. C₂×#13093997	C₂²	semidirect
66. C₂×#13093995	C₂²	semidirect
69. C₄×#10625350	C₂²	semidirect
70. C₂×C₄×Dic₉₄	C₂²	semidirect
71. C₂×C₄×Dic₉₄	C₂²	semidirect
76. C₂×C₄×D₁₈₈	C₂²	semidirect
77. C₂×C₄×D₁₈₈	C₂²	semidirect
78. C₂×C₄×D₁₈₈	C₂²	semidirect
79. C₂×C₄×D₁₈₈	C₂²	semidirect
82. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
84. C₂×#13093981	C₂²	semidirect
85. C₂×#13093981	C₂²	semidirect
88. C₂×C₄²×D₄₇	C₂²	semidirect
90. C₄×#41×C₄₇	C₂²	semidirect
91. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
92. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
95. C₂×C₄×D₄×C₄₇	C₂²	semidirect
96. C₂×C₄×D₄×C₄₇	C₂²	semidirect
98. C₂×#117×C₄₇	C₂²	semidirect
100. C₂²×C₄²×C₄₇	C₂²	semidirect
105. C₂×#10625350	C₂³	semidirect
127. #13094024	C₂³	semidirect
128. #13094023	C₂³	semidirect
131. #13094019	C₂³	semidirect
132. #13094018	C₂³	semidirect
133. #13094016	C₂³	semidirect
134. #13094015	C₂³	semidirect
137. #13094012	C₂³	semidirect
138. #13094010	C₂³	semidirect
139. #13094009	C₂³	semidirect
140. #13094009	C₂³	semidirect
141. #13094007	C₂³	semidirect
142. #13094006	C₂³	semidirect
143. #13094003	C₂³	semidirect
144. #13094002	C₂³	semidirect
146. #13094000	C₂³	semidirect
151. #13093998	C₂³	semidirect
152. #13093998	C₂³	semidirect
153. #13093997	C₂³	semidirect
154. #13093997	C₂³	semidirect
156. #13093995	C₂³	semidirect
159. C₄×Dic₉₄	C₂³	semidirect
160. C₄×Dic₉₄	C₂³	semidirect
165. C₄×D₁₈₈	C₂³	semidirect
166. C₄×D₁₈₈	C₂³	semidirect
167. C₄×D₁₈₈	C₂³	semidirect
170. C₄×C₂²⋊D₄₇	C₂³	semidirect
172. #13093981	C₂³	semidirect
173. #13093981	C₂³	semidirect
200. C₄²×D₄₇	C₂³	semidirect
212. C₄×Q₈×C₄₇	C₂³	semidirect
213. C₄×Q₈×C₄₇	C₂³	semidirect
216. C₄×D₄×C₄₇	C₂³	semidirect
217. C₄×D₄×C₄₇	C₂³	semidirect
219. #117×C₄₇	C₂³	semidirect
235. C₂×C₄²×C₄₇	C₂³	semidirect
256. C₂²×C₄×C₄₇	#41	semidirect
389. C₂×C₄×C₄₇	C₂×#41	semidirect
476. C₂×C₄×#41	D₄₇	semidirect
480. C₂×C₄₇	#3460	semidirect
538. C₄×#41	C₂×D₄₇	semidirect
541. C₂×C₄×Q₈	C₂×D₄₇	semidirect
542. C₂×C₄×Q₈	C₂×D₄₇	semidirect
556. C₂×C₄×D₄	C₂×D₄₇	semidirect
557. C₂×C₄×D₄	C₂×D₄₇	semidirect
562. C₂×#117	C₂×D₄₇	semidirect
567. C₂²×C₄²	C₂×D₄₇	semidirect
568. C₄₇	C₂×#3460	semidirect
640. C₄×Q₈	C₂²×D₄₇	semidirect
641. C₄×Q₈	C₂²×D₄₇	semidirect
654. C₄×D₄	C₂²×D₄₇	semidirect
655. C₄×D₄	C₂²×D₄₇	semidirect
660. #117	C₂²×D₄₇	semidirect
703. C₂×C₄²	C₂²×D₄₇	semidirect
766. C₂²×C₄	#10625350	semidirect
882. C₂×C₄	C₂×#10625350	semidirect
931. C₂	#20256804	direct (N × H)

Maximal subgroups

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

subgroup	index
#20256804	2
C₂×#15689751	2
C₂×#15689745	2
C₂×#15689744	2
C₂×#15689728	2
C₂×#15689724	2
C₂×#15689706	2
C₂×#15689701	2
C₂×#15689692	2
C₂×#15689687	2
C₂×#15689673	2
C₂×#15689670	2
C₂×#15689660	2
C₂×#15689657	2
C₂×#15689632	2
C₂×C₄×#10625350	2
C₂²×C₄×D₁₈₈	2
C₂×C₄×#41×C₄₇	2
C₂×#3460	47

Subgroups — C2×#20256804 #27123076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20256804 #27123076