Subgroups — C₂×#20257438 #27124278

Order 12032.

7910 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257438	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689846	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689834	C₂	1	2	yes	maximal, complemented
4	C₂×#15689815	C₂	1	2	yes	maximal, complemented
5	C₂×#15689800	C₂	1	4	yes	maximal, complemented
6	C₂×#15689784	C₂	1	2	yes	maximal, complemented
7	C₂×#15689777	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689776	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689768	C₂	1	2	yes	maximal, complemented
10	C₂×#15689747	C₂	1	2	yes	maximal, complemented
11	C₂×#15689722	C₂	1	4	yes	maximal, complemented
12	C₂×#15689678	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15689660	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15689636	C₂	1	2	yes	maximal, complemented
15	C₂²×#13094000	C₂	1	2	yes	maximal, complemented
16	C₂×#15689602	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10625354	C₂²	1	2	yes	complemented
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	#15689834	C₂²	1	32	yes	complemented
25	#15689815	C₂²	1	32	yes	complemented
26	#15689800	C₂²	1	64	yes	complemented
27	#15689784	C₂²	1	32	yes	complemented
28	#15689777	C₂²	1	16	yes	complemented
29	#15689776	C₂²	1	16	yes	complemented
30	#15689768	C₂²	1	32	yes	complemented
31	#15689747	C₂²	1	32	yes	complemented
32	#15689722	C₂²	1	64	yes	complemented
33	#15689678	C₂²	1	16	yes	complemented
34	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
35	#15689660	C₂²	1	16	yes	complemented
36	C₂×#13094019	C₂²	1	4	yes	complemented
37	C₂×#13094019	C₂²	1	4	yes	complemented
38	C₂×#13094019	C₂²	1	2	yes	complemented
39	C₂×#13094015	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13094015	C₂²	1	4	yes	complemented
41	C₂×#13094015	C₂²	1	2	yes	complemented
42	C₂×#13094013	C₂²	1	4	yes	complemented
43	C₂×#13094013	C₂²	1	1	yes	characteristic, complemented
44	C₂×#13094012	C₂²	1	2	yes	—
45	#15689636	C₂²	1	32	yes	complemented
46	C₂×#13094009	C₂²	1	2	yes	—
47	C₂×#13094009	C₂²	1	4	yes	complemented
48	C₂×#13094009	C₂²	1	4	yes	complemented
49	C₂×#13094008	C₂²	1	4	yes	—
50	C₂×#13094008	C₂²	1	4	yes	complemented
51	C₂×#13094004	C₂²	1	2	yes	—
52	C₂×#13094004	C₂²	1	2	yes	complemented
53	C₂×#13094000	C₂²	1	1	yes	characteristic
54	C₂×#13094000	C₂²	1	4	yes	—
55	C₂×#13094000	C₂²	1	2	yes	—
56	C₂×#13094000	C₂²	1	4	yes	complemented
57	C₂×#13094000	C₂²	1	2	yes	complemented
58	C₂×#13094000	C₂²	1	2	yes	complemented
59	C₂×#13094000	C₂²	1	4	yes	complemented
60	C₂×#13094000	C₂²	1	32	yes	complemented
61	C₂×#13093999	C₂²	1	2	yes	—
62	C₂×#13093999	C₂²	1	1	yes	characteristic
63	C₂×#13093998	C₂²	1	4	yes	—
64	C₂×#13093998	C₂²	1	2	yes	complemented
65	C₂×#13093994	C₂²	1	4	yes	—
66	#15689602	C₂²	1	32	yes	complemented
67	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
68	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
69	C₂×#13093989	C₂²	1	2	yes	complemented
70	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
71	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
72	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
73	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
74	C₂×#13093986	C₂²	1	1	yes	characteristic
75	C₂×#13093986	C₂²	1	4	yes	—
76	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
77	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
78	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
79	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
80	C₄×D₄×D₄₇	C₂²	1	16	yes	complemented
81	C₂×#13093982	C₂²	1	2	yes	—
82	C₂×#13093982	C₂²	1	2	yes	complemented
83	C₂×#13093981	C₂²	1	2	yes	complemented
84	C₂×#13093980	C₂²	1	4	yes	complemented
85	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
86	C₂²×Dic₄₇⋊C₄	C₂²	1	4	yes	complemented
87	C₂×C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
88	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
89	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
90	C₂×C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
91	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
92	C₂³×Q₈×C₄₇	C₂²	1	2	yes	complemented
93	D₄×Q₈×C₄₇	C₂²	1	16	yes	complemented
94	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
95	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
97	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
98	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
100	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
101	C₂⁴×D₄₇	C₂³	1	2	yes	—
102	C₂×#10625354	—	4	8	no	—
103	C₂×#10625354	C₂³	1	16	yes	complemented
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	4	yes	—
116	C₂³×Dic₄₇	C₂³	1	2	yes	—
117	C₂²×C₄×D₄₇	—	4	8	no	—
118	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
122	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
123	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
124	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
125	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
126	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
127	#13094024	C₂³	1	8	yes	complemented
128	#13094019	C₂³	1	32	yes	complemented
129	#13094019	C₂³	1	32	yes	complemented
130	#13094019	C₂³	1	16	yes	complemented
131	#13094015	C₂³	1	8	yes	complemented
132	#13094015	C₂³	1	32	yes	complemented
133	#13094015	C₂³	1	16	yes	complemented
134	#13094013	C₂³	1	32	yes	complemented
135	#13094013	C₂³	1	8	yes	complemented
136	#13094012	C₂³	1	16	yes	—
137	#13094009	C₂³	1	16	yes	—
138	#13094009	C₂³	1	32	yes	complemented
139	#13094009	C₂³	1	32	yes	complemented
140	#13094008	C₂³	1	32	yes	—
141	#13094008	C₂³	1	32	yes	complemented
142	#13094004	C₂³	1	16	yes	—
143	#13094004	C₂³	1	16	yes	complemented
144	#13094000	C₂³	1	32	yes	—
145	#13094000	C₂³	1	8	yes	—
146	#13094000	C₂³	1	16	yes	—
147	#13094000	C₂³	1	32	yes	complemented
148	#13094000	C₂³	1	16	yes	complemented
149	#13094000	C₂³	1	32	yes	complemented
150	#13094000	C₂³	1	16	yes	complemented
151	#13093999	C₂³	1	16	yes	—
152	#13093999	C₂³	1	8	yes	—
153	#13093998	C₂³	1	32	yes	—
154	#13093998	C₂³	1	16	yes	complemented
155	#13093994	C₂³	1	32	yes	—
156	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
157	C₄×Dic₉₄	C₂³	1	16	yes	complemented
158	#13093989	C₂³	1	16	yes	complemented
159	C₄×D₁₈₈	C₂³	1	16	yes	—
160	C₄×D₁₈₈	C₂³	1	8	yes	—
161	C₄×D₁₈₈	C₂³	1	8	yes	complemented
162	D₄×Dic₄₇	C₂³	1	8	yes	—
163	#13093986	C₂³	1	8	yes	—
164	#13093986	C₂³	1	32	yes	—
165	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
166	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
167	(C₂²⋊D₄₇)⋊C₄	C₂³	1	16	yes	—
168	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
169	#13093982	C₂³	1	16	yes	—
170	#13093982	C₂³	1	16	yes	complemented
171	#13093981	C₂³	1	16	yes	complemented
172	#13093980	C₂³	1	32	yes	complemented
173	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
176	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
177	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
178	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
179	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
180	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
181	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
182	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
183	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
184	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
185	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
186	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
187	C₂×Dic₄₇⋊C₄	C₂³	1	32	yes	complemented
188	C₄⋊C₄×D₄₇	C₂³	1	8	yes	—
189	C₄⋊C₄×D₄₇	C₂³	1	16	yes	complemented
190	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
191	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	32	yes	—
192	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
193	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
194	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
195	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
196	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
197	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
198	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
199	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
200	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
201	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
202	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
203	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
204	C₂²⋊C₄×D₄₇	C₂³	1	16	yes	—
205	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
206	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
207	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
208	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
209	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
210	C₄²×D₄₇	C₂³	1	8	yes	—
211	C₂²×Q₈×C₄₇	—	4	8	no	—
212	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
213	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
214	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
215	C₂²×Q₈×C₄₇	C₂³	1	16	yes	complemented
216	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
217	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
218	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
219	C₄⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
220	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
221	C₂²⋊Q₈×C₄₇	C₂³	1	32	yes	complemented
222	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
223	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
224	C₄×D₄×C₄₇	C₂³	1	16	yes	—
225	C₄×D₄×C₄₇	C₂³	1	8	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	1	yes	characteristic
229	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
232	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
234	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
236	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
237	C₂³×D₄₇	—	2	8	no	—
238	C₂³×D₄₇	—	2	8	no	—
239	C₂³×D₄₇	—	4	4	no	—
240	C₂³×D₄₇	C₂⁴	1	2	yes	—
241	C₂³×D₄₇	C₂⁴	1	2	yes	—
242	C₂³×D₄₇	C₂⁴	1	8	yes	—
243	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
244	C₂×Q₈×C₄₇	—	2	4	no	—
245	C₂×Q₈×C₄₇	—	2	8	no	—
246	C₂×Q₈×C₄₇	—	4	8	no	—
247	C₂×Q₈×C₄₇	—	4	32	no	—
248	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
249	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
250	C₂×Q₈×C₄₇	C₂⁴	1	16	yes	—
251	C₂×D₄×C₄₇	#41	1	8	yes	complemented
252	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₄₇	—	2	8	no	—
254	C₂²×C₄×C₄₇	—	4	8	no	—
255	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
261	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
262	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₂²⋊D₄₇	—	2	8	no	—
265	C₂×C₂²⋊D₄₇	—	2	16	no	—
266	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
267	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
268	C₂²×Dic₄₇	—	2	16	no	—
269	C₂²×Dic₄₇	—	4	4	no	—
270	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
271	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
272	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
273	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
274	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
275	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
276	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
277	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
278	#10625354	—	4	32	no	—
279	#10625352	—	2	64	no	—
280	D₄×D₄₇	—	2	32	no	—
281	C₂×D₁₈₈	—	2	8	no	—
282	C₂×D₁₈₈	—	2	4	no	—
283	C₂×D₁₈₈	—	2	4	no	—
284	C₂×D₁₈₈	—	4	8	no	—
285	C₂×D₁₈₈	C₂⁴	1	8	yes	—
286	C₂×D₁₈₈	C₂⁴	1	4	yes	—
287	C₂×D₁₈₈	C₂⁴	1	4	yes	—
288	C₂×D₁₈₈	C₂⁴	1	16	yes	—
289	C₂×C₄×D₄₇	—	2	4	no	—
290	C₂×C₄×D₄₇	—	2	4	no	—
291	C₂×C₄×D₄₇	—	2	8	no	—
292	C₂×C₄×D₄₇	—	2	4	no	—
293	C₂×C₄×D₄₇	—	2	8	no	—
294	C₂×C₄×D₄₇	—	4	32	no	—
295	C₂×C₄×D₄₇	—	4	4	no	—
296	C₂×C₄×D₄₇	—	4	4	no	—
297	C₂×C₄×D₄₇	—	4	8	no	—
298	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
299	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
300	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
301	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
302	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
303	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
304	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
305	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
306	C₂×Dic₉₄	—	2	8	no	—
307	C₂×Dic₉₄	C₂⁴	1	8	yes	—
308	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
315	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
316	C₄²×C₄₇	C₂⁴	1	4	yes	—
317	C₄²×C₄₇	C₂⁴	1	8	yes	—
318	C₂²⋊Dic₄₇	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	8	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	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
330	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
331	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
332	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
333	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
334	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
335	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
336	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
337	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
338	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
339	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
340	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
341	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
342	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
343	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
344	C₄×Dic₄₇	C₂⁴	1	4	yes	—
345	C₄×Dic₄₇	C₂⁴	1	4	yes	—
346	C₄×Dic₄₇	C₂⁴	1	4	yes	—
347	C₄×Dic₄₇	C₂⁴	1	16	yes	—
348	C₄×Dic₄₇	C₂⁴	1	16	yes	—
349	C₂³×C₄₇	—	2	4	no	—
350	C₂³×C₄₇	—	2	4	no	—
351	C₂³×C₄₇	C₂×#41	1	8	yes	—
352	C₂³×C₄₇	C₂⁵	1	4	yes	—
353	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
354	C₂²×D₄₇	—	2	2	no	—
355	C₂²×D₄₇	—	2	2	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	4	no	—
362	C₂²×D₄₇	—	2	4	no	—
363	C₂²×D₄₇	—	2	16	no	—
364	C₂²×D₄₇	—	4	8	no	—
365	C₂²×D₄₇	—	4	32	no	—
366	C₂²×D₄₇	2₋¹⁺⁴	1	4	yes	—
367	C₂²×D₄₇	C₂⁵	1	4	yes	—
368	C₂²×D₄₇	C₂⁵	1	4	yes	—
369	C₂²×D₄₇	C₂⁵	1	2	yes	—
370	Q₈×C₄₇	—	2	16	no	—
371	Q₈×C₄₇	—	2	8	no	—
372	Q₈×C₄₇	—	4	16	no	—
373	D₄×C₄₇	C₂×#41	1	16	yes	complemented
374	C₂×C₄×C₄₇	—	2	4	no	—
375	C₂×C₄×C₄₇	—	2	8	no	—
376	C₂×C₄×C₄₇	—	2	4	no	—
377	C₂×C₄×C₄₇	—	2	2	no	—
378	C₂×C₄×C₄₇	—	2	4	no	—
379	C₂×C₄×C₄₇	—	2	16	no	—
380	C₂×C₄×C₄₇	—	4	16	no	—
381	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
382	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
383	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
384	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
385	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
386	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
387	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
388	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
389	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
390	C₂²⋊D₄₇	—	2	16	no	—
391	C₂²⋊D₄₇	—	2	32	no	—
392	C₂×Dic₄₇	—	2	8	no	—
393	C₂×Dic₄₇	—	2	4	no	—
394	C₂×Dic₄₇	—	2	2	no	—
395	C₂×Dic₄₇	—	2	32	no	—
396	C₂×Dic₄₇	—	2	4	no	—
397	C₂×Dic₄₇	—	2	2	no	—
398	C₂×Dic₄₇	—	2	2	no	—
399	C₂×Dic₄₇	—	4	8	no	—
400	C₂×Dic₄₇	C₂⁵	1	2	yes	—
401	C₂×Dic₄₇	C₂⁵	1	2	yes	—
402	C₂×Dic₄₇	C₂⁵	1	4	yes	—
403	C₂×Dic₄₇	C₂⁵	1	2	yes	—
404	C₂×Dic₄₇	C₂⁵	1	8	yes	—
405	C₂×Dic₄₇	C₂⁵	1	4	yes	—
406	D₁₈₈	—	2	16	no	—
407	D₁₈₈	—	2	8	no	—
408	D₁₈₈	—	2	8	no	—
409	D₁₈₈	—	4	16	no	—
410	C₄×D₄₇	—	2	8	no	—
411	C₄×D₄₇	—	2	8	no	—
412	C₄×D₄₇	—	2	16	no	—
413	C₄×D₄₇	—	2	8	no	—
414	C₄×D₄₇	—	2	16	no	—
415	C₄×D₄₇	—	4	8	no	—
416	C₄×D₄₇	—	4	8	no	—
417	C₄×D₄₇	—	4	16	no	—
418	Dic₉₄	—	2	16	no	—
419	C₂×#3520	—	47	1	no	maximal, Sylow
420	C₂²×C₄₇	—	2	4	no	—
421	C₂²×C₄₇	—	2	4	no	—
422	C₂²×C₄₇	—	2	16	no	—
423	C₂²×C₄₇	C₂²×#41	1	8	yes	—
424	C₂²×C₄₇	C₂²×#41	1	2	yes	—
425	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
426	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
427	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
428	C₂×D₄₇	—	2	2	no	—
429	C₂×D₄₇	—	2	2	no	—
430	C₂×D₄₇	—	2	8	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	—	2	4	no	—
436	C₂×D₄₇	—	2	4	no	—
437	C₂×D₄₇	—	4	32	no	—
438	C₂×D₄₇	—	4	8	no	—
439	C₂×D₄₇	—	4	8	no	—
440	C₂×D₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
441	C₄×C₄₇	—	2	4	no	—
442	C₄×C₄₇	—	2	8	no	—
443	C₄×C₄₇	—	2	4	no	—
444	C₄×C₄₇	—	2	2	no	—
445	C₄×C₄₇	—	2	4	no	—
446	C₄×C₄₇	C₂²×#41	1	4	yes	—
447	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
448	Dic₄₇	—	2	8	no	—
449	Dic₄₇	—	2	4	no	—
450	Dic₄₇	—	2	2	no	—
451	Dic₄₇	—	2	4	no	—
452	Dic₄₇	—	2	2	no	—
453	Dic₄₇	—	2	2	no	—
454	#3520	—	47	32	no	—
455	C₂×#556	—	47	1	no	—
456	C₂×#554	—	47	2	no	—
457	C₂×#552	—	47	2	no	—
458	C₂×#551	—	47	4	no	—
459	C₂×D₄×Q₈	D₄₇	1	1	yes	characteristic, complemented
460	C₂×#548	—	47	2	no	—
461	C₂×#547	—	47	1	no	—
462	C₂×#547	—	47	1	no	—
463	C₂×#546	—	47	2	no	—
464	C₂×#542	—	47	2	no	—
465	C₂×#539	—	47	4	no	—
466	C₂×#533	—	47	1	no	—
467	C₂×#529	—	47	1	no	—
468	C₂×#525	—	47	2	no	—
469	C₂²×C₂²⋊Q₈	—	47	2	no	—
470	C₂×#520	—	47	2	no	—
471	C₂²×C₄×D₄	—	47	1	no	—
472	C₂×C₄₇	—	2	8	no	—
473	C₂×C₄₇	#3520	1	4	yes	complemented
474	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
475	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
477	D₄₇	—	2	4	no	—
478	D₄₇	—	4	4	no	—
479	D₄₇	—	4	4	no	—
480	C₂²×#41	—	47	2	no	—
481	C₂²×#41	—	47	2	no	—
482	C₂³×Q₈	C₂×D₄₇	1	2	yes	complemented
483	C₂³×D₄	—	47	1	no	—
484	C₂⁴×C₄	—	47	2	no	—
485	#556	—	47	16	no	—
486	#554	—	47	32	no	—
487	#552	—	47	32	no	—
488	#551	—	47	64	no	—
489	D₄×Q₈	C₂×D₄₇	1	16	yes	complemented
490	#548	—	47	32	no	—
491	#547	—	47	16	no	—
492	#547	—	47	16	no	—
493	#546	—	47	32	no	—
494	#542	—	47	32	no	—
495	#539	—	47	64	no	—
496	#533	—	47	16	no	—
497	C₂×C₄⋊Q₈	—	47	1	no	—
498	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
499	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	complemented
500	#529	—	47	16	no	—
501	C₂×#126	—	47	2	no	—
502	C₂×#126	—	47	4	no	—
503	C₂×#126	—	47	4	no	—
504	C₂×#125	—	47	1	no	—
505	C₂×#125	—	47	2	no	—
506	C₂×#125	—	47	4	no	—
507	C₂×#124	—	47	1	no	—
508	C₂×#124	—	47	4	no	—
509	C₂×#124	—	47	2	no	—
510	#525	—	47	32	no	—
511	C₂×#123	—	47	4	no	—
512	C₂×#123	—	47	2	no	—
513	C₂×#123	—	47	4	no	—
514	C₂×#123	—	47	4	no	—
515	C₂×#123	—	47	4	no	—
516	C₂×C₂²⋊Q₈	—	47	1	no	—
517	C₂×C₂²⋊Q₈	—	47	2	no	—
518	C₂×C₂²⋊Q₈	—	47	4	no	—
519	C₂×C₂²⋊Q₈	—	47	2	no	—
520	C₂×C₂²⋊Q₈	—	47	2	no	—
521	C₂×C₂²⋊Q₈	—	47	4	no	—
522	C₂×C₂²⋊Q₈	—	47	4	no	—
523	C₂×C₂²⋊Q₈	—	47	32	no	—
524	C₂×C₂²⋊Q₈	—	47	2	no	—
525	C₂×C₂²⋊Q₈	—	47	2	no	—
526	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
527	C₂×C₂²⋊Q₈	C₂×D₄₇	1	4	yes	complemented
528	C₂×#121	—	47	2	no	—
529	C₂×#121	—	47	4	no	—
530	C₂×#121	—	47	1	no	—
531	C₂×#121	—	47	2	no	—
532	C₂×#120	—	47	4	no	—
533	#520	—	47	32	no	—
534	C₂×C₄×Q₈	—	47	2	no	—
535	C₂×C₄×Q₈	—	47	2	no	—
536	C₂×C₄×Q₈	—	47	2	no	—
537	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
538	C₂×C₄×D₄	—	47	1	no	—
539	C₂×C₄×D₄	—	47	2	no	—
540	C₂×C₄×D₄	—	47	4	no	—
541	C₂×C₄×D₄	—	47	16	no	—
542	C₂×C₄×D₄	—	47	1	no	—
543	C₂×C₄×D₄	—	47	4	no	—
544	C₂×C₄×D₄	—	47	2	no	—
545	C₂×C₄×D₄	—	47	4	no	—
546	C₂×C₄×D₄	—	47	1	no	—
547	C₂×C₄×D₄	—	47	2	no	—
548	C₂×C₄×D₄	—	47	1	no	—
549	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
550	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
551	C₂×#117	—	47	2	no	—
552	C₂×#117	—	47	2	no	—
553	C₂×#117	—	47	4	no	—
554	C₂×#117	—	47	2	no	—
555	C₂²×C₄⋊C₄	—	47	4	no	—
556	C₂²×C₄⋊C₄	—	47	2	no	—
557	C₂²×C₄⋊C₄	—	47	1	no	—
558	C₂²×C₄⋊C₄	—	47	2	no	—
559	C₂²×C₂²⋊C₄	—	47	4	no	—
560	C₂²×C₂²⋊C₄	—	47	2	no	—
561	C₂²×C₄²	—	47	1	no	—
562	C₄₇	C₂×#3520	1	1	yes	characteristic, complemented, Sylow
563	C₂⁵	—	47	2	no	—
564	C₂×#41	—	47	16	no	—
565	C₂×#41	—	47	16	no	—
566	C₂×#41	—	94	16	no	—
567	C₂×#41	—	188	8	no	—
568	C₂²×Q₈	—	4	8	no	—
569	C₂²×Q₈	—	47	2	no	—
570	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
571	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
572	C₂²×Q₈	C₂²×D₄₇	1	4	yes	—
573	C₂²×Q₈	C₂²×D₄₇	1	16	yes	complemented
574	C₂²×D₄	—	47	4	no	—
575	C₂²×D₄	—	47	2	no	—
576	C₂²×D₄	—	47	8	no	—
577	C₂²×D₄	—	47	2	no	—
578	C₂²×D₄	—	47	1	no	—
579	C₂²×D₄	—	47	1	no	—
580	C₂²×D₄	—	47	4	no	—
581	C₂²×D₄	—	94	8	no	—
582	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
583	C₂³×C₄	—	47	4	no	—
584	C₂³×C₄	—	47	2	no	—
585	C₂³×C₄	—	47	1	no	—
586	C₂³×C₄	—	47	2	no	—
587	C₂³×C₄	—	47	1	no	—
588	C₂³×C₄	—	47	2	no	—
589	C₂³×C₄	—	47	1	no	—
590	C₂³×C₄	—	47	2	no	—
591	C₂³×C₄	—	47	4	no	—
592	C₂³×C₄	—	47	2	no	—
593	C₂³×C₄	—	47	16	no	—
594	C₂³×C₄	—	188	8	no	—
595	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
596	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
597	C₄⋊Q₈	—	47	8	no	—
598	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
599	C₄⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
600	#126	—	47	16	no	—
601	#126	—	47	32	no	—
602	#126	—	47	32	no	—
603	#125	—	47	8	no	—
604	#125	—	47	16	no	—
605	#125	—	47	32	no	—
606	#124	—	47	8	no	—
607	#124	—	47	32	no	—
608	#124	—	47	16	no	—
609	#123	—	47	32	no	—
610	#123	—	47	16	no	—
611	#123	—	47	32	no	—
612	#123	—	47	32	no	—
613	#123	—	47	32	no	—
614	C₂²⋊Q₈	—	47	8	no	—
615	C₂²⋊Q₈	—	47	16	no	—
616	C₂²⋊Q₈	—	47	32	no	—
617	C₂²⋊Q₈	—	47	16	no	—
618	C₂²⋊Q₈	—	47	16	no	—
619	C₂²⋊Q₈	—	47	32	no	—
620	C₂²⋊Q₈	—	47	32	no	—
621	C₂²⋊Q₈	—	47	16	no	—
622	C₂²⋊Q₈	—	47	16	no	—
623	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
624	C₂²⋊Q₈	C₂²×D₄₇	1	32	yes	complemented
625	#121	—	47	16	no	—
626	#121	—	47	32	no	—
627	#121	—	47	8	no	—
628	#121	—	47	16	no	—
629	#120	—	47	32	no	—
630	C₄×Q₈	—	47	16	no	—
631	C₄×Q₈	—	47	16	no	—
632	C₄×Q₈	—	47	16	no	—
633	C₄×Q₈	C₂²×D₄₇	1	8	yes	complemented
634	C₄×D₄	—	47	8	no	—
635	C₄×D₄	—	47	16	no	—
636	C₄×D₄	—	47	32	no	—
637	C₄×D₄	—	47	8	no	—
638	C₄×D₄	—	47	32	no	—
639	C₄×D₄	—	47	16	no	—
640	C₄×D₄	—	47	32	no	—
641	C₄×D₄	—	47	8	no	—
642	C₄×D₄	—	47	16	no	—
643	C₄×D₄	—	47	8	no	—
644	C₄×D₄	C₂²×D₄₇	1	8	yes	—
645	C₄×D₄	C₂²×D₄₇	1	16	yes	—
646	#117	—	47	16	no	—
647	#117	—	47	16	no	—
648	#117	—	47	32	no	—
649	#117	—	47	16	no	—
650	C₂×C₄⋊C₄	—	47	1	no	—
651	C₂×C₄⋊C₄	—	47	2	no	—
652	C₂×C₄⋊C₄	—	47	4	no	—
653	C₂×C₄⋊C₄	—	47	1	no	—
654	C₂×C₄⋊C₄	—	47	2	no	—
655	C₂×C₄⋊C₄	—	47	2	no	—
656	C₂×C₄⋊C₄	—	47	4	no	—
657	C₂×C₄⋊C₄	—	47	4	no	—
658	C₂×C₄⋊C₄	—	47	32	no	—
659	C₂×C₄⋊C₄	—	47	4	no	—
660	C₂×C₄⋊C₄	—	47	16	no	—
661	C₂×C₄⋊C₄	—	47	2	no	—
662	C₂×C₄⋊C₄	—	47	2	no	—
663	C₂×C₄⋊C₄	—	47	2	no	—
664	C₂×C₄⋊C₄	—	47	4	no	—
665	C₂×C₄⋊C₄	—	47	8	no	—
666	C₂×C₄⋊C₄	—	47	16	no	—
667	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
669	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
671	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
672	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
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	2	no	—
678	C₂×C₂²⋊C₄	—	47	4	no	—
679	C₂×C₂²⋊C₄	—	47	4	no	—
680	C₂×C₂²⋊C₄	—	47	32	no	—
681	C₂×C₂²⋊C₄	—	47	2	no	—
682	C₂×C₂²⋊C₄	—	47	2	no	—
683	C₂×C₂²⋊C₄	—	47	4	no	—
684	C₂×C₂²⋊C₄	—	47	2	no	—
685	C₂×C₂²⋊C₄	—	47	4	no	—
686	C₂×C₂²⋊C₄	—	47	2	no	—
687	C₂×C₂²⋊C₄	—	47	16	no	—
688	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
690	C₂×C₄²	—	47	1	no	—
691	C₂×C₄²	—	47	4	no	—
692	C₂×C₄²	—	47	4	no	—
693	C₂×C₄²	—	47	1	no	—
694	C₂×C₄²	—	47	1	no	—
695	C₂×C₄²	—	47	8	no	—
696	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
697	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
698	C₂⁴	—	47	1	no	—
699	C₂⁴	—	47	2	no	—
700	C₂⁴	—	47	2	no	—
701	C₂⁴	—	47	8	no	—
702	C₂⁴	—	94	8	no	—
703	C₂⁴	—	94	8	no	—
704	C₂⁴	—	188	4	no	—
705	C₂⁴	C₂³×D₄₇	1	2	yes	—
706	#41	—	94	64	no	—
707	#41	—	188	32	no	—
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	2	8	no	—
710	C₂×Q₈	—	4	8	no	—
711	C₂×Q₈	—	4	32	no	—
712	C₂×Q₈	—	47	8	no	—
713	C₂×Q₈	—	94	8	no	—
714	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
715	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
716	C₂×Q₈	C₂³×D₄₇	1	16	yes	—
717	C₂×D₄	—	47	16	no	—
718	C₂×D₄	—	47	8	no	—
719	C₂×D₄	—	47	8	no	—
720	C₂×D₄	—	47	4	no	—
721	C₂×D₄	—	47	4	no	—
722	C₂×D₄	—	47	16	no	—
723	C₂×D₄	—	94	8	no	—
724	C₂×D₄	—	94	8	no	—
725	C₂×D₄	—	94	16	no	—
726	C₂×D₄	—	94	32	no	—
727	C₂×D₄	—	94	4	no	—
728	C₂×D₄	—	94	4	no	—
729	C₂×D₄	—	188	8	no	—
730	C₂×D₄	#10625354	1	8	yes	complemented
731	C₂×D₄	C₂³×D₄₇	1	4	yes	—
732	C₂²×C₄	—	2	8	no	—
733	C₂²×C₄	—	4	8	no	—
734	C₂²×C₄	—	47	16	no	—
735	C₂²×C₄	—	47	1	no	—
736	C₂²×C₄	—	47	4	no	—
737	C₂²×C₄	—	47	1	no	—
738	C₂²×C₄	—	47	1	no	—
739	C₂²×C₄	—	47	2	no	—
740	C₂²×C₄	—	47	2	no	—
741	C₂²×C₄	—	47	8	no	—
742	C₂²×C₄	—	47	4	no	—
743	C₂²×C₄	—	47	4	no	—
744	C₂²×C₄	—	47	4	no	—
745	C₂²×C₄	—	47	8	no	—
746	C₂²×C₄	—	47	8	no	—
747	C₂²×C₄	—	47	8	no	—
748	C₂²×C₄	—	47	16	no	—
749	C₂²×C₄	—	47	8	no	—
750	C₂²×C₄	—	94	4	no	—
751	C₂²×C₄	—	94	16	no	—
752	C₂²×C₄	—	94	4	no	—
753	C₂²×C₄	—	94	8	no	—
754	C₂²×C₄	—	94	4	no	—
755	C₂²×C₄	—	94	8	no	—
756	C₂²×C₄	—	188	32	no	—
757	C₂²×C₄	—	188	4	no	—
758	C₂²×C₄	—	188	4	no	—
759	C₂²×C₄	—	188	8	no	—
760	C₂²×C₄	—	188	4	no	—
761	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
762	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
763	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
765	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
766	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
767	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
768	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
770	C₄⋊C₄	—	47	8	no	—
771	C₄⋊C₄	—	47	16	no	—
772	C₄⋊C₄	—	47	8	no	—
773	C₄⋊C₄	—	47	16	no	—
774	C₄⋊C₄	—	47	16	no	—
775	C₄⋊C₄	—	47	8	no	—
776	C₄⋊C₄	—	47	4	no	—
777	C₄⋊C₄	—	47	4	no	—
778	C₄⋊C₄	—	47	8	no	—
779	C₄⋊C₄	—	47	16	no	—
780	C₄⋊C₄	—	47	8	no	—
781	C₄⋊C₄	—	47	8	no	—
782	C₄⋊C₄	—	47	16	no	—
783	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
784	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
785	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
786	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
787	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
788	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
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	8	no	—
794	C₂²⋊C₄	—	47	16	no	—
795	C₂²⋊C₄	—	47	16	no	—
796	C₂²⋊C₄	—	47	8	no	—
797	C₂²⋊C₄	—	47	8	no	—
798	C₂²⋊C₄	—	47	16	no	—
799	C₂²⋊C₄	—	47	8	no	—
800	C₂²⋊C₄	—	47	16	no	—
801	C₂²⋊C₄	—	47	8	no	—
802	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
803	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
804	C₄²	—	47	4	no	—
805	C₄²	—	47	4	no	—
806	C₄²	—	47	4	no	—
807	C₄²	—	47	16	no	—
808	C₄²	—	47	16	no	—
809	C₄²	C₂³×D₄₇	1	4	yes	—
810	C₄²	C₂³×D₄₇	1	8	yes	—
811	C₂³	—	2	4	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	47	4	no	—
814	C₂³	—	47	2	no	—
815	C₂³	—	47	4	no	—
816	C₂³	—	47	4	no	—
817	C₂³	—	94	16	no	—
818	C₂³	—	94	2	no	—
819	C₂³	—	94	2	no	—
820	C₂³	—	94	4	no	—
821	C₂³	—	94	16	no	—
822	C₂³	—	94	4	no	—
823	C₂³	—	94	4	no	—
824	C₂³	—	94	4	no	—
825	C₂³	—	94	4	no	—
826	C₂³	—	94	4	no	—
827	C₂³	—	188	8	no	—
828	C₂³	—	188	32	no	—
829	C₂³	C₂×#10625354	1	8	yes	—
830	C₂³	C₂⁴×D₄₇	1	4	yes	—
831	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
832	Q₈	—	2	8	no	—
833	Q₈	—	2	16	no	—
834	Q₈	—	4	16	no	—
835	Q₈	—	94	16	no	—
836	D₄	—	94	16	no	—
837	D₄	—	94	16	no	—
838	D₄	—	94	32	no	—
839	D₄	—	94	8	no	—
840	D₄	—	94	8	no	—
841	D₄	—	188	16	no	—
842	D₄	C₂×#10625354	1	16	yes	complemented
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	16	no	—
849	C₂×C₄	—	4	16	no	—
850	C₂×C₄	—	47	2	no	—
851	C₂×C₄	—	47	8	no	—
852	C₂×C₄	—	47	2	no	—
853	C₂×C₄	—	47	2	no	—
854	C₂×C₄	—	47	4	no	—
855	C₂×C₄	—	47	4	no	—
856	C₂×C₄	—	94	8	no	—
857	C₂×C₄	—	94	4	no	—
858	C₂×C₄	—	94	2	no	—
859	C₂×C₄	—	94	8	no	—
860	C₂×C₄	—	94	32	no	—
861	C₂×C₄	—	94	4	no	—
862	C₂×C₄	—	94	2	no	—
863	C₂×C₄	—	94	2	no	—
864	C₂×C₄	—	94	8	no	—
865	C₂×C₄	—	94	16	no	—
866	C₂×C₄	—	94	8	no	—
867	C₂×C₄	—	94	16	no	—
868	C₂×C₄	—	188	8	no	—
869	C₂×C₄	—	188	8	no	—
870	C₂×C₄	—	188	16	no	—
871	C₂×C₄	—	188	8	no	—
872	C₂×C₄	C₂×#10625354	1	4	yes	—
873	C₂×C₄	#13094069	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	8	yes	—
877	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
878	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
879	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
880	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	16	no	—
884	C₂²	—	47	4	no	—
885	C₂²	—	94	2	no	—
886	C₂²	—	94	2	no	—
887	C₂²	—	94	8	no	—
888	C₂²	—	94	4	no	—
889	C₂²	—	94	4	no	—
890	C₂²	—	94	4	no	—
891	C₂²	—	94	4	no	—
892	C₂²	—	94	4	no	—
893	C₂²	—	94	4	no	—
894	C₂²	—	188	32	no	—
895	C₂²	—	188	8	no	—
896	C₂²	—	188	8	no	—
897	C₂²	C₂²×#10625354	1	8	yes	—
898	C₂²	C₂²×#10625354	1	2	yes	—
899	C₂²	C₂×#13094069	1	2	yes	—
900	C₂²	2₋¹⁺⁴×D₄₇	1	2	yes	—
901	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
902	C₄	—	2	4	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	8	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	4	no	—
907	C₄	—	94	4	no	—
908	C₄	—	94	2	no	—
909	C₄	—	94	8	no	—
910	C₄	—	94	2	no	—
911	C₄	—	94	4	no	—
912	C₄	—	94	2	no	—
913	C₄	C₂²×#10625354	1	4	yes	—
914	C₄	C₂×#13094069	1	4	yes	—
915	C₂	—	2	8	no	—
916	C₂	—	94	4	no	—
917	C₂	—	188	4	no	—
918	C₂	—	188	4	no	—
919	C₂	#20257438	1	4	yes	direct product factor
920	C₂	C₂³×#10625354	1	1	yes	characteristic
921	C₂	C₂²×#13094069	1	1	yes	characteristic
922	C₂	C₂×2₋¹⁺⁴×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×D₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×D₄×Q₈	D₄₇
hypocenter	C₄₇	C₂×#3520
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #20257438	C₂	direct (N × H)
2. C₂×#15689846	C₂	semidirect
3. C₂×#15689834	C₂	semidirect
4. C₂×#15689815	C₂	semidirect
5. C₂×#15689800	C₂	semidirect
6. C₂×#15689784	C₂	semidirect
7. C₂×#15689777	C₂	semidirect
8. C₂×#15689776	C₂	semidirect
9. C₂×#15689768	C₂	semidirect
10. C₂×#15689747	C₂	semidirect
11. C₂×#15689722	C₂	semidirect
12. C₂×#15689678	C₂	semidirect
13. C₂×#15689660	C₂	semidirect
14. C₂×#15689636	C₂	semidirect
15. C₂²×#13094000	C₂	semidirect
16. C₂×#15689602	C₂	semidirect
17. C₂×C₄×D₄×D₄₇	C₂	semidirect
18. C₂×D₄×Q₈×C₄₇	C₂	semidirect
19. C₂²×#10625354	C₂²	semidirect
23. #15689846	C₂²	semidirect
24. #15689834	C₂²	semidirect
25. #15689815	C₂²	semidirect
26. #15689800	C₂²	semidirect
27. #15689784	C₂²	semidirect
28. #15689777	C₂²	semidirect
29. #15689776	C₂²	semidirect
30. #15689768	C₂²	semidirect
31. #15689747	C₂²	semidirect
32. #15689722	C₂²	semidirect
33. #15689678	C₂²	semidirect
34. C₂×#13094024	C₂²	semidirect
35. #15689660	C₂²	semidirect
36. C₂×#13094019	C₂²	semidirect
37. C₂×#13094019	C₂²	semidirect
38. C₂×#13094019	C₂²	semidirect
39. C₂×#13094015	C₂²	semidirect
40. C₂×#13094015	C₂²	semidirect
41. C₂×#13094015	C₂²	semidirect
42. C₂×#13094013	C₂²	semidirect
43. C₂×#13094013	C₂²	semidirect
45. #15689636	C₂²	semidirect
47. C₂×#13094009	C₂²	semidirect
48. C₂×#13094009	C₂²	semidirect
50. C₂×#13094008	C₂²	semidirect
52. C₂×#13094004	C₂²	semidirect
56. C₂×#13094000	C₂²	semidirect
57. C₂×#13094000	C₂²	semidirect
58. C₂×#13094000	C₂²	semidirect
59. C₂×#13094000	C₂²	semidirect
60. C₂×#13094000	C₂²	semidirect
64. C₂×#13093998	C₂²	semidirect
66. #15689602	C₂²	semidirect
67. C₂×Q₈×Dic₄₇	C₂²	semidirect
68. C₂×C₄×Dic₉₄	C₂²	semidirect
69. C₂×#13093989	C₂²	semidirect
72. C₂×C₄×D₁₈₈	C₂²	semidirect
77. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
79. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
80. C₄×D₄×D₄₇	C₂²	semidirect
82. C₂×#13093982	C₂²	semidirect
83. C₂×#13093981	C₂²	semidirect
84. C₂×#13093980	C₂²	semidirect
85. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
86. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
88. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
92. C₂³×Q₈×C₄₇	C₂²	semidirect
93. D₄×Q₈×C₄₇	C₂²	semidirect
94. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
95. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
97. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
98. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
103. C₂×#10625354	C₂³	semidirect
127. #13094024	C₂³	semidirect
128. #13094019	C₂³	semidirect
129. #13094019	C₂³	semidirect
130. #13094019	C₂³	semidirect
131. #13094015	C₂³	semidirect
132. #13094015	C₂³	semidirect
133. #13094015	C₂³	semidirect
134. #13094013	C₂³	semidirect
135. #13094013	C₂³	semidirect
138. #13094009	C₂³	semidirect
139. #13094009	C₂³	semidirect
141. #13094008	C₂³	semidirect
143. #13094004	C₂³	semidirect
147. #13094000	C₂³	semidirect
148. #13094000	C₂³	semidirect
149. #13094000	C₂³	semidirect
150. #13094000	C₂³	semidirect
154. #13093998	C₂³	semidirect
156. Q₈×Dic₄₇	C₂³	semidirect
157. C₄×Dic₉₄	C₂³	semidirect
158. #13093989	C₂³	semidirect
161. C₄×D₁₈₈	C₂³	semidirect
166. C₄×C₂²⋊D₄₇	C₂³	semidirect
168. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
170. #13093982	C₂³	semidirect
171. #13093981	C₂³	semidirect
172. #13093980	C₂³	semidirect
180. C₂×C₄⋊Dic₄₇	C₂³	semidirect
187. C₂×Dic₄₇⋊C₄	C₂³	semidirect
189. C₄⋊C₄×D₄₇	C₂³	semidirect
215. C₂²×Q₈×C₄₇	C₂³	semidirect
219. C₄⋊Q₈×C₄₇	C₂³	semidirect
220. C₄⋊Q₈×C₄₇	C₂³	semidirect
221. C₂²⋊Q₈×C₄₇	C₂³	semidirect
222. C₂²⋊Q₈×C₄₇	C₂³	semidirect
223. C₄×Q₈×C₄₇	C₂³	semidirect
251. C₂×D₄×C₄₇	#41	semidirect
373. D₄×C₄₇	C₂×#41	semidirect
459. C₂×D₄×Q₈	D₄₇	semidirect
473. C₂×C₄₇	#3520	semidirect
482. C₂³×Q₈	C₂×D₄₇	semidirect
489. D₄×Q₈	C₂×D₄₇	semidirect
498. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
499. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
526. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
527. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
537. C₂×C₄×Q₈	C₂×D₄₇	semidirect
562. C₄₇	C₂×#3520	semidirect
573. C₂²×Q₈	C₂²×D₄₇	semidirect
598. C₄⋊Q₈	C₂²×D₄₇	semidirect
599. C₄⋊Q₈	C₂²×D₄₇	semidirect
623. C₂²⋊Q₈	C₂²×D₄₇	semidirect
624. C₂²⋊Q₈	C₂²×D₄₇	semidirect
633. C₄×Q₈	C₂²×D₄₇	semidirect
730. C₂×D₄	#10625354	semidirect
842. D₄	C₂×#10625354	semidirect
919. C₂	#20257438	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257438	2
C₂×#15689846	2
C₂×#15689834	2
C₂×#15689815	2
C₂×#15689800	2
C₂×#15689784	2
C₂×#15689777	2
C₂×#15689776	2
C₂×#15689768	2
C₂×#15689747	2
C₂×#15689722	2
C₂×#15689678	2
C₂×#15689660	2
C₂×#15689636	2
C₂²×#13094000	2
C₂×#15689602	2
C₂×C₄×D₄×D₄₇	2
C₂×D₄×Q₈×C₄₇	2
C₂×#3520	47

Subgroups — C2×#20257438 #27124278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257438 #27124278