Subgroups — C₂×#20256954 #27123317

Order 12032.

7954 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256954	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689846	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689839	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689821	C₂	1	2	yes	maximal, complemented
5	C₂×#15689815	C₂	1	2	yes	maximal, complemented
6	C₂×#15689811	C₂	1	2	yes	maximal, complemented
7	C₂×#15689800	C₂	1	4	yes	maximal, complemented
8	C₂×#15689777	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689768	C₂	1	2	yes	maximal, complemented
10	C₂×#15689678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15689659	C₂	1	4	yes	maximal, complemented
12	C₂×#15689658	C₂	1	2	yes	maximal, complemented
13	C₂×#15689636	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×#10625354	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×#10625352	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#13093982	C₂	1	2	yes	maximal, complemented
18	C₂×C₄₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10625354	C₂²	1	1	yes	characteristic
20	C₂²×#10625352	C₂²	1	2	yes	—
21	C₂²×D₄×D₄₇	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
23	#15689846	C₂²	1	16	yes	complemented
24	#15689839	C₂²	1	16	yes	complemented
25	#15689821	C₂²	1	32	yes	complemented
26	#15689815	C₂²	1	32	yes	complemented
27	#15689811	C₂²	1	32	yes	complemented
28	#15689800	C₂²	1	64	yes	complemented
29	#15689777	C₂²	1	16	yes	complemented
30	#15689768	C₂²	1	32	yes	complemented
31	#15689678	C₂²	1	16	yes	complemented
32	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
33	#15689659	C₂²	1	64	yes	complemented
34	#15689658	C₂²	1	32	yes	complemented
35	C₂×#13094019	C₂²	1	4	yes	complemented
36	C₂×#13094019	C₂²	1	4	yes	complemented
37	C₂×#13094019	C₂²	1	4	yes	complemented
38	C₂×#13094015	C₂²	1	4	yes	complemented
39	C₂×#13094015	C₂²	1	2	yes	complemented
40	C₂×#13094013	C₂²	1	4	yes	complemented
41	C₂×#13094012	C₂²	1	2	yes	—
42	#15689636	C₂²	1	32	yes	complemented
43	C₂×#13094009	C₂²	1	4	yes	—
44	C₂×#13094009	C₂²	1	4	yes	complemented
45	C₂×#13094008	C₂²	1	4	yes	—
46	C₂×#13094008	C₂²	1	4	yes	complemented
47	C₂×#13094004	C₂²	1	2	yes	—
48	C₂×#13094004	C₂²	1	2	yes	complemented
49	C₂×#13094000	C₂²	1	2	yes	—
50	C₂×#13094000	C₂²	1	2	yes	complemented
51	C₂×#13093999	C₂²	1	2	yes	—
52	C₂×#13093999	C₂²	1	2	yes	complemented
53	C₂×#13093998	C₂²	1	4	yes	—
54	C₂×#13093998	C₂²	1	2	yes	complemented
55	C₂×#13093994	C₂²	1	4	yes	—
56	C₄×#10625354	C₂²	1	16	yes	complemented
57	C₄×#10625352	C₂²	1	32	yes	complemented
58	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
60	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
61	C₂×#13093989	C₂²	1	2	yes	complemented
62	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
64	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
66	C₂×#13093986	C₂²	1	1	yes	characteristic
67	C₂×#13093986	C₂²	1	2	yes	—
68	C₂×#13093986	C₂²	1	1	yes	characteristic, complemented
69	C₂×#13093986	C₂²	1	4	yes	complemented
70	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
71	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
72	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
73	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
74	C₄×D₄×D₄₇	C₂²	1	16	yes	complemented
75	C₂×#13093982	C₂²	1	1	yes	characteristic
76	C₂×#13093982	C₂²	1	4	yes	—
77	C₂×#13093982	C₂²	1	2	yes	—
78	C₂×#13093982	C₂²	1	2	yes	complemented
79	C₂×#13093982	C₂²	1	2	yes	complemented
80	C₂×#13093982	C₂²	1	4	yes	complemented
81	C₂×#13093982	C₂²	1	2	yes	complemented
82	C₂×#13093982	C₂²	1	2	yes	complemented
83	C₂×#13093982	C₂²	1	32	yes	complemented
84	C₂×#13093980	C₂²	1	4	yes	complemented
85	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
86	C₂×C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
87	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
88	C₂×C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
89	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	complemented
90	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
91	C₂×C₄²×D₄₇	C₂²	1	2	yes	complemented
92	C₄₇×#554	C₂²	1	16	yes	complemented
93	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
94	C₂×#125×C₄₇	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
96	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
97	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
99	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
100	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
101	C₂⁴×D₄₇	C₂³	1	2	yes	—
102	C₂×#10625354	—	2	8	no	—
103	C₂×#10625354	C₂³	1	8	yes	—
104	C₂×#10625352	—	2	16	no	—
105	C₂×#10625352	C₂³	1	16	yes	—
106	C₂²×Dic₉₄	C₂³	1	2	yes	—
107	C₂²×D₁₈₈	C₂³	1	2	yes	—
108	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
109	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
110	C₂²×D₁₈₈	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
112	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
113	C₂×D₄×D₄₇	—	2	8	no	—
114	C₂×D₄×D₄₇	C₂³	1	8	yes	—
115	C₂³×Dic₄₇	C₂³	1	2	yes	—
116	C₂³×Dic₄₇	C₂³	1	4	yes	—
117	C₂²×C₄×D₄₇	—	2	16	no	—
118	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
120	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
121	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
122	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
123	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
124	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
125	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
126	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
127	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
128	#13094024	C₂³	1	8	yes	complemented
129	#13094019	C₂³	1	32	yes	complemented
130	#13094019	C₂³	1	32	yes	complemented
131	#13094019	C₂³	1	32	yes	complemented
132	#13094015	C₂³	1	32	yes	complemented
133	#13094015	C₂³	1	16	yes	complemented
134	#13094013	C₂³	1	32	yes	complemented
135	#13094012	C₂³	1	16	yes	—
136	#13094009	C₂³	1	32	yes	—
137	#13094009	C₂³	1	32	yes	complemented
138	#13094008	C₂³	1	32	yes	—
139	#13094008	C₂³	1	32	yes	complemented
140	#13094004	C₂³	1	16	yes	—
141	#13094004	C₂³	1	16	yes	complemented
142	#13094000	C₂³	1	16	yes	—
143	#13094000	C₂³	1	16	yes	complemented
144	#13093999	C₂³	1	16	yes	—
145	#13093999	C₂³	1	16	yes	complemented
146	#13093998	C₂³	1	32	yes	—
147	#13093998	C₂³	1	16	yes	complemented
148	#13093994	C₂³	1	32	yes	—
149	Q₈×Dic₄₇	C₂³	1	8	yes	complemented
150	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
151	C₄×Dic₉₄	C₂³	1	16	yes	complemented
152	#13093989	C₂³	1	16	yes	complemented
153	C₄×D₁₈₈	C₂³	1	16	yes	—
154	C₄×D₁₈₈	C₂³	1	8	yes	—
155	C₄×D₁₈₈	C₂³	1	8	yes	complemented
156	D₄×Dic₄₇	C₂³	1	8	yes	—
157	#13093986	C₂³	1	16	yes	—
158	#13093986	C₂³	1	8	yes	—
159	#13093986	C₂³	1	8	yes	complemented
160	#13093986	C₂³	1	32	yes	complemented
161	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
162	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
163	(C₂²⋊D₄₇)⋊C₄	C₂³	1	16	yes	—
164	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
165	#13093982	C₂³	1	32	yes	—
166	#13093982	C₂³	1	8	yes	—
167	#13093982	C₂³	1	16	yes	—
168	#13093982	C₂³	1	16	yes	complemented
169	#13093982	C₂³	1	16	yes	complemented
170	#13093982	C₂³	1	16	yes	complemented
171	#13093982	C₂³	1	32	yes	complemented
172	#13093982	C₂³	1	16	yes	complemented
173	#13093980	C₂³	1	32	yes	complemented
174	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
177	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
178	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
179	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
180	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
181	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
182	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
183	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
184	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
185	C₄⋊C₄×D₄₇	C₂³	1	8	yes	—
186	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
187	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	32	yes	—
188	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
189	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
190	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
191	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	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	2	yes	—
196	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
197	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
198	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
199	C₂²⋊C₄×D₄₇	C₂³	1	16	yes	—
200	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
201	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
202	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
203	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
204	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
205	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
206	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
207	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
208	C₂×C₄×Dic₄₇	C₂³	1	32	yes	complemented
209	C₄²×D₄₇	C₂³	1	8	yes	—
210	C₄²×D₄₇	C₂³	1	16	yes	complemented
211	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
212	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
213	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
215	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
216	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
217	#125×C₄₇	C₂³	1	16	yes	complemented
218	C₂²⋊Q₈×C₄₇	C₂³	1	32	yes	complemented
219	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
220	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
221	C₄×D₄×C₄₇	C₂³	1	16	yes	—
222	C₄×D₄×C₄₇	C₂³	1	8	yes	—
223	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
225	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
230	C₂×C₄⋊C₄×C₄₇	C₂³	1	16	yes	complemented
231	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
233	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
235	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
236	C₂³×D₄₇	—	2	8	no	—
237	C₂³×D₄₇	—	2	8	no	—
238	C₂³×D₄₇	—	4	4	no	—
239	C₂³×D₄₇	C₂⁴	1	2	yes	—
240	C₂³×D₄₇	C₂⁴	1	2	yes	—
241	C₂³×D₄₇	C₂⁴	1	8	yes	—
242	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₄₇	—	2	4	no	—
244	C₂×Q₈×C₄₇	—	4	4	no	—
245	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
246	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
247	C₂×D₄×C₄₇	#41	1	8	yes	complemented
248	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₄₇	—	2	8	no	—
250	C₂²×C₄×C₄₇	—	4	8	no	—
251	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
257	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
258	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
260	C₂×C₂²⋊D₄₇	—	2	8	no	—
261	C₂×C₂²⋊D₄₇	—	2	16	no	—
262	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
263	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
264	C₂²×Dic₄₇	—	2	16	no	—
265	C₂²×Dic₄₇	—	2	8	no	—
266	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
267	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
268	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
269	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
270	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
271	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
272	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
273	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
274	#10625354	—	2	32	no	—
275	#10625352	—	2	64	no	—
276	D₄×D₄₇	—	2	32	no	—
277	C₂×D₁₈₈	—	2	8	no	—
278	C₂×D₁₈₈	—	2	4	no	—
279	C₂×D₁₈₈	—	2	4	no	—
280	C₂×D₁₈₈	—	4	8	no	—
281	C₂×D₁₈₈	C₂⁴	1	8	yes	—
282	C₂×D₁₈₈	C₂⁴	1	4	yes	—
283	C₂×D₁₈₈	C₂⁴	1	4	yes	—
284	C₂×D₁₈₈	C₂⁴	1	16	yes	—
285	C₂×C₄×D₄₇	—	2	8	no	—
286	C₂×C₄×D₄₇	—	2	8	no	—
287	C₂×C₄×D₄₇	—	2	4	no	—
288	C₂×C₄×D₄₇	—	2	8	no	—
289	C₂×C₄×D₄₇	—	2	8	no	—
290	C₂×C₄×D₄₇	—	2	8	no	—
291	C₂×C₄×D₄₇	—	2	64	no	—
292	C₂×C₄×D₄₇	—	4	4	no	—
293	C₂×C₄×D₄₇	—	4	2	no	—
294	C₂×C₄×D₄₇	#41	1	8	yes	complemented
295	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
296	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
297	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
298	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
299	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
300	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
301	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
302	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
303	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
304	C₂×Dic₉₄	—	2	8	no	—
305	C₂×Dic₉₄	C₂⁴	1	8	yes	—
306	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
308	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
309	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
311	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
313	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
314	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
315	C₄²×C₄₇	C₂⁴	1	8	yes	—
316	C₄²×C₄₇	C₂⁴	1	4	yes	—
317	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
318	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
319	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
320	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
321	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
322	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
323	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
324	(C₂×D₄₇)⋊C₄	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	16	yes	—
328	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
329	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
330	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
331	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
332	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
333	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
334	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
335	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
336	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
337	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
338	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
339	C₄×Dic₄₇	C₂⁴	1	4	yes	—
340	C₄×Dic₄₇	C₂⁴	1	4	yes	—
341	C₄×Dic₄₇	C₂⁴	1	4	yes	—
342	C₄×Dic₄₇	C₂⁴	1	8	yes	—
343	C₄×Dic₄₇	C₂⁴	1	8	yes	—
344	C₄×Dic₄₇	C₂⁴	1	16	yes	—
345	C₄×Dic₄₇	C₂⁴	1	16	yes	—
346	C₄×Dic₄₇	C₂⁴	1	16	yes	—
347	C₂³×C₄₇	—	2	4	no	—
348	C₂³×C₄₇	—	2	4	no	—
349	C₂³×C₄₇	C₂×#41	1	8	yes	—
350	C₂³×C₄₇	C₂⁵	1	4	yes	—
351	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
352	C₂²×D₄₇	—	2	2	no	—
353	C₂²×D₄₇	—	2	2	no	—
354	C₂²×D₄₇	—	2	4	no	—
355	C₂²×D₄₇	—	2	4	no	—
356	C₂²×D₄₇	—	2	4	no	—
357	C₂²×D₄₇	—	2	4	no	—
358	C₂²×D₄₇	—	2	16	no	—
359	C₂²×D₄₇	—	2	4	no	—
360	C₂²×D₄₇	—	2	4	no	—
361	C₂²×D₄₇	—	2	16	no	—
362	C₂²×D₄₇	—	4	8	no	—
363	C₂²×D₄₇	—	4	32	no	—
364	C₂²×D₄₇	C₂×#41	1	4	yes	—
365	C₂²×D₄₇	C₂⁵	1	4	yes	—
366	C₂²×D₄₇	C₂⁵	1	4	yes	—
367	C₂²×D₄₇	C₂⁵	1	2	yes	—
368	Q₈×C₄₇	—	2	8	no	—
369	Q₈×C₄₇	—	4	8	no	—
370	D₄×C₄₇	C₂×#41	1	16	yes	complemented
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	2	no	—
375	C₂×C₄×C₄₇	—	2	8	no	—
376	C₂×C₄×C₄₇	—	2	16	no	—
377	C₂×C₄×C₄₇	—	4	16	no	—
378	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
379	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
380	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
381	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
382	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
383	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
384	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
385	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
386	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
387	C₂²⋊D₄₇	—	2	16	no	—
388	C₂²⋊D₄₇	—	2	32	no	—
389	C₂×Dic₄₇	—	2	8	no	—
390	C₂×Dic₄₇	—	2	4	no	—
391	C₂×Dic₄₇	—	2	4	no	—
392	C₂×Dic₄₇	—	2	2	no	—
393	C₂×Dic₄₇	—	2	32	no	—
394	C₂×Dic₄₇	—	2	2	no	—
395	C₂×Dic₄₇	—	2	16	no	—
396	C₂×Dic₄₇	C₂×#41	1	4	yes	—
397	C₂×Dic₄₇	C₂⁵	1	2	yes	—
398	C₂×Dic₄₇	C₂⁵	1	4	yes	—
399	C₂×Dic₄₇	C₂⁵	1	4	yes	—
400	C₂×Dic₄₇	C₂⁵	1	2	yes	—
401	C₂×Dic₄₇	C₂⁵	1	8	yes	—
402	C₂×Dic₄₇	C₂⁵	1	2	yes	—
403	D₁₈₈	—	2	16	no	—
404	D₁₈₈	—	2	8	no	—
405	D₁₈₈	—	2	8	no	—
406	D₁₈₈	—	4	16	no	—
407	C₄×D₄₇	—	2	16	no	—
408	C₄×D₄₇	—	2	16	no	—
409	C₄×D₄₇	—	2	8	no	—
410	C₄×D₄₇	—	2	16	no	—
411	C₄×D₄₇	—	2	16	no	—
412	C₄×D₄₇	—	2	16	no	—
413	C₄×D₄₇	—	4	8	no	—
414	C₄×D₄₇	—	4	4	no	—
415	C₄×D₄₇	C₂×#41	1	16	yes	complemented
416	Dic₉₄	—	2	16	no	—
417	C₂×#3475	—	47	1	no	maximal, Sylow
418	C₂²×C₄₇	—	2	4	no	—
419	C₂²×C₄₇	—	2	4	no	—
420	C₂²×C₄₇	—	2	16	no	—
421	C₂²×C₄₇	C₂²×#41	1	2	yes	—
422	C₂²×C₄₇	C₂²×#41	1	8	yes	—
423	C₂²×C₄₇	C₂²×#41	1	2	yes	—
424	C₂²×C₄₇	#585	1	2	yes	—
425	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
426	C₂×D₄₇	—	2	2	no	—
427	C₂×D₄₇	—	2	2	no	—
428	C₂×D₄₇	—	2	8	no	—
429	C₂×D₄₇	—	2	4	no	—
430	C₂×D₄₇	—	2	4	no	—
431	C₂×D₄₇	—	2	4	no	—
432	C₂×D₄₇	—	2	4	no	—
433	C₂×D₄₇	—	2	4	no	—
434	C₂×D₄₇	—	2	4	no	—
435	C₂×D₄₇	—	4	32	no	—
436	C₂×D₄₇	—	4	8	no	—
437	C₂×D₄₇	—	4	8	no	—
438	C₂×D₄₇	C₂²×#41	1	4	yes	—
439	C₄×C₄₇	—	2	4	no	—
440	C₄×C₄₇	—	2	4	no	—
441	C₄×C₄₇	—	2	4	no	—
442	C₄×C₄₇	—	2	2	no	—
443	C₄×C₄₇	—	2	8	no	—
444	C₄×C₄₇	C₂²×#41	1	4	yes	—
445	C₄×C₄₇	C₂²×#41	1	4	yes	—
446	Dic₄₇	—	2	8	no	—
447	Dic₄₇	—	2	4	no	—
448	Dic₄₇	—	2	4	no	—
449	Dic₄₇	—	2	2	no	—
450	Dic₄₇	—	2	2	no	—
451	Dic₄₇	C₂²×#41	1	4	yes	—
452	#3475	—	47	32	no	—
453	C₂×#556	—	47	1	no	—
454	C₂×#555	—	47	1	no	—
455	C₂×#554	D₄₇	1	1	yes	characteristic, complemented
456	C₂×#553	—	47	2	no	—
457	C₂×#552	—	47	2	no	—
458	C₂×#552	—	47	2	no	—
459	C₂×#551	—	47	4	no	—
460	C₂×#547	—	47	1	no	—
461	C₂×#546	—	47	2	no	—
462	C₂×#533	—	47	1	no	—
463	C₂×#529	—	47	2	no	—
464	C₂×#529	—	47	4	no	—
465	C₂×#525	—	47	2	no	—
466	C₂×C₄×#41	—	47	1	no	—
467	C₂×C₄×#41	—	47	2	no	—
468	C₂²×C₄×D₄	—	47	1	no	—
469	C₂²×#117	—	47	2	no	—
470	C₂×C₄₇	—	2	8	no	—
471	C₂×C₄₇	#3475	1	4	yes	complemented
472	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
473	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
474	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
475	D₄₇	—	2	4	no	—
476	D₄₇	—	4	4	no	—
477	D₄₇	—	4	4	no	—
478	C₂²×#41	—	47	1	no	—
479	C₂²×#41	—	47	2	no	—
480	C₂³×D₄	—	47	1	no	—
481	C₂⁴×C₄	—	47	2	no	—
482	#556	—	47	16	no	—
483	#555	—	47	16	no	—
484	#554	C₂×D₄₇	1	16	yes	complemented
485	#553	—	47	32	no	—
486	#552	—	47	32	no	—
487	#552	—	47	32	no	—
488	#551	—	47	64	no	—
489	#547	—	47	16	no	—
490	#546	—	47	32	no	—
491	#533	—	47	16	no	—
492	C₂×C₄⋊Q₈	—	47	1	no	—
493	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
494	#529	—	47	32	no	—
495	#529	—	47	64	no	—
496	C₂×#126	—	47	4	no	—
497	C₂×#126	—	47	4	no	—
498	C₂×#126	—	47	4	no	—
499	C₂×#125	—	47	4	no	—
500	C₂×#125	—	47	2	no	—
501	C₂×#125	C₂×D₄₇	1	2	yes	complemented
502	C₂×#124	—	47	4	no	—
503	C₂×#124	—	47	2	no	—
504	#525	—	47	32	no	—
505	C₂×#123	—	47	4	no	—
506	C₂×#123	—	47	4	no	—
507	C₂×#123	—	47	4	no	—
508	C₂×#123	—	47	4	no	—
509	C₂×C₂²⋊Q₈	—	47	2	no	—
510	C₂×C₂²⋊Q₈	—	47	2	no	—
511	C₂×C₂²⋊Q₈	—	47	2	no	—
512	C₂×C₂²⋊Q₈	—	47	2	no	—
513	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
514	C₂×C₂²⋊Q₈	C₂×D₄₇	1	4	yes	complemented
515	C₂×#121	—	47	2	no	—
516	C₂×#121	—	47	4	no	—
517	C₂×#121	—	47	2	no	—
518	C₂×#121	—	47	2	no	—
519	C₂×#120	—	47	4	no	—
520	C₄×#41	—	47	16	no	—
521	C₄×#41	—	47	32	no	—
522	C₂×C₄×Q₈	—	47	1	no	—
523	C₂×C₄×Q₈	—	47	2	no	—
524	C₂×C₄×Q₈	—	47	2	no	—
525	C₂×C₄×Q₈	—	47	2	no	—
526	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
527	C₂×C₄×D₄	—	47	1	no	—
528	C₂×C₄×D₄	—	47	2	no	—
529	C₂×C₄×D₄	—	47	4	no	—
530	C₂×C₄×D₄	—	47	16	no	—
531	C₂×C₄×D₄	—	47	1	no	—
532	C₂×C₄×D₄	—	47	2	no	—
533	C₂×C₄×D₄	—	47	1	no	—
534	C₂×C₄×D₄	—	47	4	no	—
535	C₂×C₄×D₄	—	47	2	no	—
536	C₂×C₄×D₄	—	47	4	no	—
537	C₂×C₄×D₄	—	47	1	no	—
538	C₂×C₄×D₄	—	47	2	no	—
539	C₂×C₄×D₄	—	47	1	no	—
540	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
542	C₂×#117	—	47	1	no	—
543	C₂×#117	—	47	2	no	—
544	C₂×#117	—	47	4	no	—
545	C₂×#117	—	47	4	no	—
546	C₂×#117	—	47	2	no	—
547	C₂×#117	—	47	2	no	—
548	C₂×#117	—	47	2	no	—
549	C₂×#117	—	47	2	no	—
550	C₂×#117	—	47	32	no	—
551	C₂×#117	—	47	4	no	—
552	C₂²×C₄⋊C₄	—	47	2	no	—
553	C₂²×C₄⋊C₄	—	47	1	no	—
554	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
555	C₂²×C₂²⋊C₄	—	47	4	no	—
556	C₂²×C₂²⋊C₄	—	47	2	no	—
557	C₂²×C₄²	—	47	4	no	—
558	C₂²×C₄²	—	47	1	no	—
559	C₂²×C₄²	—	47	2	no	—
560	C₄₇	C₂×#3475	1	1	yes	characteristic, complemented, Sylow
561	C₂⁵	—	47	2	no	—
562	C₂×#41	—	47	8	no	—
563	C₂×#41	—	47	16	no	—
564	C₂×#41	—	94	8	no	—
565	C₂×#41	—	94	16	no	—
566	C₂²×Q₈	—	47	2	no	—
567	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
568	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
569	C₂²×D₄	—	47	4	no	—
570	C₂²×D₄	—	47	2	no	—
571	C₂²×D₄	—	47	8	no	—
572	C₂²×D₄	—	47	2	no	—
573	C₂²×D₄	—	47	1	no	—
574	C₂²×D₄	—	47	1	no	—
575	C₂²×D₄	—	47	4	no	—
576	C₂²×D₄	—	94	8	no	—
577	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
578	C₂³×C₄	—	47	1	no	—
579	C₂³×C₄	—	47	4	no	—
580	C₂³×C₄	—	47	2	no	—
581	C₂³×C₄	—	47	2	no	—
582	C₂³×C₄	—	47	1	no	—
583	C₂³×C₄	—	47	2	no	—
584	C₂³×C₄	—	47	2	no	—
585	C₂³×C₄	—	47	16	no	—
586	C₂³×C₄	—	47	2	no	—
587	C₂³×C₄	—	47	2	no	—
588	C₂³×C₄	—	47	1	no	—
589	C₂³×C₄	—	47	2	no	—
590	C₂³×C₄	—	94	16	no	—
591	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
592	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
593	C₄⋊Q₈	—	47	8	no	—
594	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
595	#126	—	47	32	no	—
596	#126	—	47	32	no	—
597	#126	—	47	32	no	—
598	#125	—	47	32	no	—
599	#125	—	47	16	no	—
600	#125	C₂²×D₄₇	1	16	yes	complemented
601	#124	—	47	32	no	—
602	#124	—	47	16	no	—
603	#123	—	47	32	no	—
604	#123	—	47	32	no	—
605	#123	—	47	32	no	—
606	#123	—	47	32	no	—
607	C₂²⋊Q₈	—	47	16	no	—
608	C₂²⋊Q₈	—	47	16	no	—
609	C₂²⋊Q₈	—	47	16	no	—
610	C₂²⋊Q₈	—	47	16	no	—
611	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
612	C₂²⋊Q₈	C₂²×D₄₇	1	32	yes	complemented
613	#121	—	47	16	no	—
614	#121	—	47	32	no	—
615	#121	—	47	16	no	—
616	#121	—	47	16	no	—
617	#120	—	47	32	no	—
618	C₄×Q₈	—	47	8	no	—
619	C₄×Q₈	—	47	16	no	—
620	C₄×Q₈	—	47	16	no	—
621	C₄×Q₈	—	47	16	no	—
622	C₄×Q₈	C₂²×D₄₇	1	8	yes	complemented
623	C₄×D₄	—	47	8	no	—
624	C₄×D₄	—	47	16	no	—
625	C₄×D₄	—	47	32	no	—
626	C₄×D₄	—	47	8	no	—
627	C₄×D₄	—	47	16	no	—
628	C₄×D₄	—	47	8	no	—
629	C₄×D₄	—	47	32	no	—
630	C₄×D₄	—	47	16	no	—
631	C₄×D₄	—	47	32	no	—
632	C₄×D₄	—	47	8	no	—
633	C₄×D₄	—	47	16	no	—
634	C₄×D₄	—	47	8	no	—
635	C₄×D₄	C₂²×D₄₇	1	8	yes	—
636	C₄×D₄	C₂²×D₄₇	1	16	yes	—
637	#117	—	47	8	no	—
638	#117	—	47	16	no	—
639	#117	—	47	32	no	—
640	#117	—	47	32	no	—
641	#117	—	47	16	no	—
642	#117	—	47	16	no	—
643	#117	—	47	16	no	—
644	#117	—	47	16	no	—
645	#117	—	47	32	no	—
646	C₂×C₄⋊C₄	—	47	1	no	—
647	C₂×C₄⋊C₄	—	47	1	no	—
648	C₂×C₄⋊C₄	—	47	2	no	—
649	C₂×C₄⋊C₄	—	47	4	no	—
650	C₂×C₄⋊C₄	—	47	16	no	—
651	C₂×C₄⋊C₄	—	47	2	no	—
652	C₂×C₄⋊C₄	—	47	4	no	—
653	C₂×C₄⋊C₄	—	47	4	no	—
654	C₂×C₄⋊C₄	—	47	2	no	—
655	C₂×C₄⋊C₄	—	47	4	no	—
656	C₂×C₄⋊C₄	—	47	2	no	—
657	C₂×C₄⋊C₄	—	47	8	no	—
658	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
662	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
664	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
665	C₂×C₄⋊C₄	C₂²×D₄₇	1	16	yes	complemented
666	C₂×C₂²⋊C₄	—	47	2	no	—
667	C₂×C₂²⋊C₄	—	47	2	no	—
668	C₂×C₂²⋊C₄	—	47	4	no	—
669	C₂×C₂²⋊C₄	—	47	4	no	—
670	C₂×C₂²⋊C₄	—	47	4	no	—
671	C₂×C₂²⋊C₄	—	47	32	no	—
672	C₂×C₂²⋊C₄	—	47	2	no	—
673	C₂×C₂²⋊C₄	—	47	2	no	—
674	C₂×C₂²⋊C₄	—	47	2	no	—
675	C₂×C₂²⋊C₄	—	47	4	no	—
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	16	no	—
680	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
682	C₂×C₄²	—	47	4	no	—
683	C₂×C₄²	—	47	2	no	—
684	C₂×C₄²	—	47	4	no	—
685	C₂×C₄²	—	47	1	no	—
686	C₂×C₄²	—	47	2	no	—
687	C₂×C₄²	—	47	4	no	—
688	C₂×C₄²	—	47	32	no	—
689	C₂×C₄²	—	47	1	no	—
690	C₂×C₄²	—	47	1	no	—
691	C₂×C₄²	—	47	8	no	—
692	C₂×C₄²	—	47	16	no	—
693	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
694	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
695	C₂⁴	—	47	1	no	—
696	C₂⁴	—	47	2	no	—
697	C₂⁴	—	47	2	no	—
698	C₂⁴	—	47	8	no	—
699	C₂⁴	—	94	8	no	—
700	C₂⁴	—	94	8	no	—
701	C₂⁴	—	188	4	no	—
702	C₂⁴	C₂³×D₄₇	1	2	yes	—
703	#41	—	94	32	no	—
704	#41	—	94	64	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	4	4	no	—
707	C₂×Q₈	—	47	8	no	—
708	C₂×Q₈	—	94	8	no	—
709	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
710	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
711	C₂×D₄	—	47	16	no	—
712	C₂×D₄	—	47	8	no	—
713	C₂×D₄	—	47	8	no	—
714	C₂×D₄	—	47	4	no	—
715	C₂×D₄	—	47	4	no	—
716	C₂×D₄	—	47	16	no	—
717	C₂×D₄	—	94	8	no	—
718	C₂×D₄	—	94	8	no	—
719	C₂×D₄	—	94	16	no	—
720	C₂×D₄	—	94	32	no	—
721	C₂×D₄	—	94	4	no	—
722	C₂×D₄	—	94	4	no	—
723	C₂×D₄	—	188	8	no	—
724	C₂×D₄	#10625354	1	8	yes	complemented
725	C₂×D₄	C₂³×D₄₇	1	4	yes	—
726	C₂²×C₄	—	2	8	no	—
727	C₂²×C₄	—	4	8	no	—
728	C₂²×C₄	—	47	1	no	—
729	C₂²×C₄	—	47	8	no	—
730	C₂²×C₄	—	47	4	no	—
731	C₂²×C₄	—	47	8	no	—
732	C₂²×C₄	—	47	16	no	—
733	C₂²×C₄	—	47	2	no	—
734	C₂²×C₄	—	47	2	no	—
735	C₂²×C₄	—	47	1	no	—
736	C₂²×C₄	—	47	4	no	—
737	C₂²×C₄	—	47	1	no	—
738	C₂²×C₄	—	47	4	no	—
739	C₂²×C₄	—	47	8	no	—
740	C₂²×C₄	—	47	8	no	—
741	C₂²×C₄	—	47	8	no	—
742	C₂²×C₄	—	47	8	no	—
743	C₂²×C₄	—	47	8	no	—
744	C₂²×C₄	—	47	4	no	—
745	C₂²×C₄	—	47	8	no	—
746	C₂²×C₄	—	94	8	no	—
747	C₂²×C₄	—	94	64	no	—
748	C₂²×C₄	—	94	8	no	—
749	C₂²×C₄	—	94	8	no	—
750	C₂²×C₄	—	94	8	no	—
751	C₂²×C₄	—	94	16	no	—
752	C₂²×C₄	—	94	8	no	—
753	C₂²×C₄	—	94	4	no	—
754	C₂²×C₄	—	94	8	no	—
755	C₂²×C₄	—	188	4	no	—
756	C₂²×C₄	—	188	2	no	—
757	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
758	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
759	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
760	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
761	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
762	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
763	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
764	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
765	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
766	C₄⋊C₄	—	47	8	no	—
767	C₄⋊C₄	—	47	16	no	—
768	C₄⋊C₄	—	47	16	no	—
769	C₄⋊C₄	—	47	4	no	—
770	C₄⋊C₄	—	47	4	no	—
771	C₄⋊C₄	—	47	8	no	—
772	C₄⋊C₄	—	47	16	no	—
773	C₄⋊C₄	—	47	8	no	—
774	C₄⋊C₄	—	47	16	no	—
775	C₄⋊C₄	—	47	8	no	—
776	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
777	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
778	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
779	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
780	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
781	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
782	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
783	C₂²⋊C₄	—	47	8	no	—
784	C₂²⋊C₄	—	47	8	no	—
785	C₂²⋊C₄	—	47	16	no	—
786	C₂²⋊C₄	—	47	16	no	—
787	C₂²⋊C₄	—	47	16	no	—
788	C₂²⋊C₄	—	47	8	no	—
789	C₂²⋊C₄	—	47	8	no	—
790	C₂²⋊C₄	—	47	8	no	—
791	C₂²⋊C₄	—	47	16	no	—
792	C₂²⋊C₄	—	47	8	no	—
793	C₂²⋊C₄	—	47	16	no	—
794	C₂²⋊C₄	—	47	16	no	—
795	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
796	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
797	C₄²	—	47	8	no	—
798	C₄²	—	47	4	no	—
799	C₄²	—	47	16	no	—
800	C₄²	—	47	16	no	—
801	C₄²	—	47	4	no	—
802	C₄²	—	47	8	no	—
803	C₄²	—	47	16	no	—
804	C₄²	—	47	4	no	—
805	C₄²	C₂³×D₄₇	1	4	yes	—
806	C₄²	C₂³×D₄₇	1	8	yes	—
807	C₂³	—	2	4	no	—
808	C₂³	—	2	4	no	—
809	C₂³	—	47	4	no	—
810	C₂³	—	47	2	no	—
811	C₂³	—	47	4	no	—
812	C₂³	—	47	4	no	—
813	C₂³	—	94	16	no	—
814	C₂³	—	94	2	no	—
815	C₂³	—	94	2	no	—
816	C₂³	—	94	4	no	—
817	C₂³	—	94	4	no	—
818	C₂³	—	94	4	no	—
819	C₂³	—	94	16	no	—
820	C₂³	—	94	4	no	—
821	C₂³	—	94	4	no	—
822	C₂³	—	94	4	no	—
823	C₂³	—	188	8	no	—
824	C₂³	—	188	32	no	—
825	C₂³	C₂×#10625354	1	8	yes	—
826	C₂³	C₂⁴×D₄₇	1	4	yes	—
827	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
828	Q₈	—	2	8	no	—
829	Q₈	—	4	8	no	—
830	Q₈	—	94	16	no	—
831	D₄	—	94	16	no	—
832	D₄	—	94	16	no	—
833	D₄	—	94	32	no	—
834	D₄	—	94	8	no	—
835	D₄	—	94	8	no	—
836	D₄	—	188	16	no	—
837	D₄	C₂×#10625354	1	16	yes	complemented
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	8	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	16	no	—
844	C₂×C₄	—	4	16	no	—
845	C₂×C₄	—	47	4	no	—
846	C₂×C₄	—	47	2	no	—
847	C₂×C₄	—	47	16	no	—
848	C₂×C₄	—	47	4	no	—
849	C₂×C₄	—	47	4	no	—
850	C₂×C₄	—	47	2	no	—
851	C₂×C₄	—	47	8	no	—
852	C₂×C₄	—	47	2	no	—
853	C₂×C₄	—	94	16	no	—
854	C₂×C₄	—	94	16	no	—
855	C₂×C₄	—	94	16	no	—
856	C₂×C₄	—	94	16	no	—
857	C₂×C₄	—	94	4	no	—
858	C₂×C₄	—	94	4	no	—
859	C₂×C₄	—	94	2	no	—
860	C₂×C₄	—	94	8	no	—
861	C₂×C₄	—	94	32	no	—
862	C₂×C₄	—	94	2	no	—
863	C₂×C₄	—	94	16	no	—
864	C₂×C₄	—	94	8	no	—
865	C₂×C₄	—	94	16	no	—
866	C₂×C₄	—	188	8	no	—
867	C₂×C₄	—	188	4	no	—
868	C₂×C₄	#41×D₄₇	1	4	yes	—
869	C₂×C₄	C₂×#10625354	1	4	yes	—
870	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
871	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
872	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
873	C₂×C₄	C₂⁴×D₄₇	1	4	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	C₂²	—	2	4	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	16	no	—
880	C₂²	—	47	4	no	—
881	C₂²	—	94	2	no	—
882	C₂²	—	94	2	no	—
883	C₂²	—	94	8	no	—
884	C₂²	—	94	4	no	—
885	C₂²	—	94	4	no	—
886	C₂²	—	94	4	no	—
887	C₂²	—	94	4	no	—
888	C₂²	—	94	4	no	—
889	C₂²	—	94	4	no	—
890	C₂²	—	188	32	no	—
891	C₂²	—	188	8	no	—
892	C₂²	—	188	8	no	—
893	C₂²	C₂×#41×D₄₇	1	2	yes	—
894	C₂²	C₂²×#10625354	1	8	yes	—
895	C₂²	C₂²×#10625354	1	2	yes	—
896	C₂²	#15689958	1	2	yes	—
897	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
898	C₄	—	2	4	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	8	no	—
902	C₄	—	2	2	no	—
903	C₄	—	47	4	no	—
904	C₄	—	94	4	no	—
905	C₄	—	94	4	no	—
906	C₄	—	94	2	no	—
907	C₄	—	94	8	no	—
908	C₄	—	94	2	no	—
909	C₄	C₂×#41×D₄₇	1	4	yes	—
910	C₄	C₂²×#10625354	1	4	yes	—
911	C₂	—	2	8	no	—
912	C₂	—	94	4	no	—
913	C₂	—	188	4	no	—
914	C₂	—	188	4	no	—
915	C₂	#20256954	1	4	yes	direct product factor
916	C₂	C₂²×#41×D₄₇	1	1	yes	characteristic
917	C₂	C₂³×#10625354	1	1	yes	characteristic
918	C₂	C₂×#15689958	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#554	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#554	D₄₇
hypocenter	C₄₇	C₂×#3475
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#554

Complements

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

N	H ≅ G/N	type
1. #20256954	C₂	direct (N × H)
2. C₂×#15689846	C₂	semidirect
3. C₂×#15689839	C₂	semidirect
4. C₂×#15689821	C₂	semidirect
5. C₂×#15689815	C₂	semidirect
6. C₂×#15689811	C₂	semidirect
7. C₂×#15689800	C₂	semidirect
8. C₂×#15689777	C₂	semidirect
9. C₂×#15689768	C₂	semidirect
10. C₂×#15689678	C₂	semidirect
11. C₂×#15689659	C₂	semidirect
12. C₂×#15689658	C₂	semidirect
13. C₂×#15689636	C₂	semidirect
14. C₂×C₄×#10625354	C₂	semidirect
15. C₂×C₄×#10625352	C₂	semidirect
16. C₂×C₄×D₄×D₄₇	C₂	semidirect
17. C₂²×#13093982	C₂	semidirect
18. C₂×C₄₇×#554	C₂	semidirect
23. #15689846	C₂²	semidirect
24. #15689839	C₂²	semidirect
25. #15689821	C₂²	semidirect
26. #15689815	C₂²	semidirect
27. #15689811	C₂²	semidirect
28. #15689800	C₂²	semidirect
29. #15689777	C₂²	semidirect
30. #15689768	C₂²	semidirect
31. #15689678	C₂²	semidirect
32. C₂×#13094024	C₂²	semidirect
33. #15689659	C₂²	semidirect
34. #15689658	C₂²	semidirect
35. C₂×#13094019	C₂²	semidirect
36. C₂×#13094019	C₂²	semidirect
37. C₂×#13094019	C₂²	semidirect
38. C₂×#13094015	C₂²	semidirect
39. C₂×#13094015	C₂²	semidirect
40. C₂×#13094013	C₂²	semidirect
42. #15689636	C₂²	semidirect
44. C₂×#13094009	C₂²	semidirect
46. C₂×#13094008	C₂²	semidirect
48. C₂×#13094004	C₂²	semidirect
50. C₂×#13094000	C₂²	semidirect
52. C₂×#13093999	C₂²	semidirect
54. C₂×#13093998	C₂²	semidirect
56. C₄×#10625354	C₂²	semidirect
57. C₄×#10625352	C₂²	semidirect
58. C₂×Q₈×Dic₄₇	C₂²	semidirect
59. C₂×Q₈×Dic₄₇	C₂²	semidirect
60. C₂×C₄×Dic₉₄	C₂²	semidirect
61. C₂×#13093989	C₂²	semidirect
64. C₂×C₄×D₁₈₈	C₂²	semidirect
68. C₂×#13093986	C₂²	semidirect
69. C₂×#13093986	C₂²	semidirect
71. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
73. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
74. C₄×D₄×D₄₇	C₂²	semidirect
78. C₂×#13093982	C₂²	semidirect
79. C₂×#13093982	C₂²	semidirect
80. C₂×#13093982	C₂²	semidirect
81. C₂×#13093982	C₂²	semidirect
82. C₂×#13093982	C₂²	semidirect
83. C₂×#13093982	C₂²	semidirect
84. C₂×#13093980	C₂²	semidirect
85. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
89. C₂²×C₄×Dic₄₇	C₂²	semidirect
91. C₂×C₄²×D₄₇	C₂²	semidirect
92. C₄₇×#554	C₂²	semidirect
93. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
94. C₂×#125×C₄₇	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
97. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
100. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
128. #13094024	C₂³	semidirect
129. #13094019	C₂³	semidirect
130. #13094019	C₂³	semidirect
131. #13094019	C₂³	semidirect
132. #13094015	C₂³	semidirect
133. #13094015	C₂³	semidirect
134. #13094013	C₂³	semidirect
137. #13094009	C₂³	semidirect
139. #13094008	C₂³	semidirect
141. #13094004	C₂³	semidirect
143. #13094000	C₂³	semidirect
145. #13093999	C₂³	semidirect
147. #13093998	C₂³	semidirect
149. Q₈×Dic₄₇	C₂³	semidirect
150. Q₈×Dic₄₇	C₂³	semidirect
151. C₄×Dic₉₄	C₂³	semidirect
152. #13093989	C₂³	semidirect
155. C₄×D₁₈₈	C₂³	semidirect
159. #13093986	C₂³	semidirect
160. #13093986	C₂³	semidirect
162. C₄×C₂²⋊D₄₇	C₂³	semidirect
164. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
168. #13093982	C₂³	semidirect
169. #13093982	C₂³	semidirect
170. #13093982	C₂³	semidirect
171. #13093982	C₂³	semidirect
172. #13093982	C₂³	semidirect
173. #13093980	C₂³	semidirect
181. C₂×C₄⋊Dic₄₇	C₂³	semidirect
208. C₂×C₄×Dic₄₇	C₂³	semidirect
210. C₄²×D₄₇	C₂³	semidirect
216. C₄⋊Q₈×C₄₇	C₂³	semidirect
217. #125×C₄₇	C₂³	semidirect
218. C₂²⋊Q₈×C₄₇	C₂³	semidirect
219. C₂²⋊Q₈×C₄₇	C₂³	semidirect
220. C₄×Q₈×C₄₇	C₂³	semidirect
230. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
247. C₂×D₄×C₄₇	#41	semidirect
294. C₂×C₄×D₄₇	#41	semidirect
370. D₄×C₄₇	C₂×#41	semidirect
415. C₄×D₄₇	C₂×#41	semidirect
455. C₂×#554	D₄₇	semidirect
471. C₂×C₄₇	#3475	semidirect
484. #554	C₂×D₄₇	semidirect
493. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
501. C₂×#125	C₂×D₄₇	semidirect
513. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
514. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
526. C₂×C₄×Q₈	C₂×D₄₇	semidirect
554. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
560. C₄₇	C₂×#3475	semidirect
594. C₄⋊Q₈	C₂²×D₄₇	semidirect
600. #125	C₂²×D₄₇	semidirect
611. C₂²⋊Q₈	C₂²×D₄₇	semidirect
612. C₂²⋊Q₈	C₂²×D₄₇	semidirect
622. C₄×Q₈	C₂²×D₄₇	semidirect
665. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
724. C₂×D₄	#10625354	semidirect
837. D₄	C₂×#10625354	semidirect
915. C₂	#20256954	direct (N × H)

Maximal subgroups

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

subgroup	index
#20256954	2
C₂×#15689846	2
C₂×#15689839	2
C₂×#15689821	2
C₂×#15689815	2
C₂×#15689811	2
C₂×#15689800	2
C₂×#15689777	2
C₂×#15689768	2
C₂×#15689678	2
C₂×#15689659	2
C₂×#15689658	2
C₂×#15689636	2
C₂×C₄×#10625354	2
C₂×C₄×#10625352	2
C₂×C₄×D₄×D₄₇	2
C₂²×#13093982	2
C₂×C₄₇×#554	2
C₂×#3475	47

Subgroups — C2×#20256954 #27123317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20256954 #27123317