Subgroups — C₂×#20257229 #27124208

Order 12032.

8082 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257229	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689821	C₂	1	4	yes	maximal, complemented
3	C₂×#15689821	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×#15689764	C₂	1	2	yes	maximal, complemented
8	C₂×#15689722	C₂	1	2	yes	maximal, complemented
9	C₂×#15689713	C₂	1	2	yes	maximal, complemented
10	C₂×#15689685	C₂	1	2	yes	maximal, complemented
11	C₂×#15689659	C₂	1	2	yes	maximal, complemented
12	C₂×#15689636	C₂	1	2	yes	maximal, complemented
13	C₂²×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15689596	C₂	1	2	yes	maximal, complemented
15	C₂²×C₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#10625354	C₂²	1	2	yes	complemented
18	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
20	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	—
21	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
22	#15689821	C₂²	1	64	yes	complemented
23	#15689821	C₂²	1	32	yes	complemented
24	#15689815	C₂²	1	32	yes	complemented
25	#15689800	C₂²	1	64	yes	complemented
26	#15689784	C₂²	1	32	yes	complemented
27	#15689764	C₂²	1	32	yes	complemented
28	#15689722	C₂²	1	32	yes	complemented
29	#15689713	C₂²	1	32	yes	complemented
30	#15689685	C₂²	1	32	yes	complemented
31	#15689659	C₂²	1	32	yes	complemented
32	C₂×#13094019	C₂²	1	4	yes	complemented
33	C₂×#13094019	C₂²	1	4	yes	complemented
34	C₂×#13094019	C₂²	1	4	yes	complemented
35	C₂×#13094015	C₂²	1	2	yes	complemented
36	C₂×#13094015	C₂²	1	4	yes	complemented
37	C₂×#13094013	C₂²	1	2	yes	complemented
38	C₂×#13094013	C₂²	1	4	yes	complemented
39	#15689636	C₂²	1	32	yes	complemented
40	C₂×#13094009	C₂²	1	4	yes	complemented
41	C₂×#13094009	C₂²	1	4	yes	complemented
42	C₂×#13094009	C₂²	1	4	yes	complemented
43	C₂×#13094008	C₂²	1	4	yes	—
44	C₂×#13094008	C₂²	1	4	yes	complemented
45	C₂×#13094000	C₂²	1	4	yes	complemented
46	C₂×#13094000	C₂²	1	2	yes	complemented
47	C₂×#13093999	C₂²	1	2	yes	complemented
48	C₂×#13093999	C₂²	1	4	yes	complemented
49	C₂×#13093998	C₂²	1	2	yes	—
50	C₂×#13093998	C₂²	1	2	yes	—
51	C₂×#13093998	C₂²	1	2	yes	complemented
52	C₂×#13093998	C₂²	1	4	yes	complemented
53	C₂×#13093998	C₂²	1	2	yes	complemented
54	C₂×#13093998	C₂²	1	4	yes	complemented
55	C₂×#13093998	C₂²	1	16	yes	complemented
56	C₂×#13093994	C₂²	1	4	yes	—
57	C₂×#13093994	C₂²	1	4	yes	complemented
58	#15689596	C₂²	1	32	yes	complemented
59	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
60	C₂×#13093986	C₂²	1	2	yes	complemented
61	C₂×#13093986	C₂²	1	4	yes	complemented
62	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
63	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
64	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
65	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
66	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
67	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
68	C₂×C₄×C₂²⋊D₄₇	C₂²	1	16	yes	complemented
69	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
70	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
71	C₂×#13093982	C₂²	1	4	yes	complemented
72	C₂×#13093982	C₂²	1	2	yes	complemented
73	C₂×#13093980	C₂²	1	4	yes	complemented
74	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₂²×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
76	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
77	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
78	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
79	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
80	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
81	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
82	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
83	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
84	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
85	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
86	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
87	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	16	yes	complemented
88	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
89	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
90	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
91	C₂⁴×D₄₇	C₂³	1	2	yes	—
92	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
93	C₂×#10625354	—	4	8	no	—
94	C₂×#10625354	C₂³	1	16	yes	complemented
95	C₂²×D₁₈₈	—	4	4	no	—
96	C₂²×D₁₈₈	C₂³	1	2	yes	—
97	C₂²×D₁₈₈	C₂³	1	4	yes	—
98	C₂²×D₁₈₈	C₂³	1	4	yes	—
99	C₂²×D₁₈₈	C₂³	1	2	yes	—
100	C₂²×D₁₈₈	C₂³	1	8	yes	complemented
101	C₂²×C₂²⋊D₄₇	—	2	8	no	—
102	C₂²×C₂²⋊D₄₇	—	2	16	no	—
103	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
104	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
106	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
108	C₂²×C₂²⋊D₄₇	C₂³	1	16	yes	—
109	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
110	C₂³×Dic₄₇	C₂³	1	2	yes	—
111	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
112	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₄×D₄₇	—	4	4	no	—
114	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
115	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
116	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
117	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
118	C₂²×C₄×D₄₇	C₂³	1	8	yes	complemented
119	#13094019	C₂³	1	32	yes	complemented
120	#13094019	C₂³	1	32	yes	complemented
121	#13094019	C₂³	1	32	yes	complemented
122	#13094015	C₂³	1	16	yes	complemented
123	#13094015	C₂³	1	32	yes	complemented
124	#13094013	C₂³	1	16	yes	complemented
125	#13094013	C₂³	1	32	yes	complemented
126	#13094009	C₂³	1	32	yes	complemented
127	#13094009	C₂³	1	32	yes	complemented
128	#13094009	C₂³	1	32	yes	complemented
129	#13094008	C₂³	1	32	yes	—
130	#13094008	C₂³	1	32	yes	complemented
131	#13094000	C₂³	1	32	yes	complemented
132	#13094000	C₂³	1	16	yes	complemented
133	#13093999	C₂³	1	16	yes	complemented
134	#13093999	C₂³	1	32	yes	complemented
135	#13093998	C₂³	1	16	yes	—
136	#13093998	C₂³	1	16	yes	—
137	#13093998	C₂³	1	16	yes	complemented
138	#13093998	C₂³	1	32	yes	complemented
139	#13093998	C₂³	1	16	yes	complemented
140	#13093998	C₂³	1	32	yes	complemented
141	#13093994	C₂³	1	32	yes	—
142	#13093994	C₂³	1	32	yes	complemented
143	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
144	#13093986	C₂³	1	16	yes	complemented
145	#13093986	C₂³	1	32	yes	complemented
146	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
147	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
148	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
149	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
150	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
151	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
152	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
153	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
154	#13093982	C₂³	1	32	yes	complemented
155	#13093982	C₂³	1	16	yes	complemented
156	#13093980	C₂³	1	32	yes	complemented
157	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
158	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
159	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
160	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
161	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	complemented
162	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
163	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
164	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
165	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
166	C₂×Dic₄₇⋊C₄	C₂³	1	8	yes	complemented
167	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
170	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
171	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
172	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
173	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
174	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
175	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
176	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
177	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
178	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
179	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
180	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	complemented
181	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	complemented
182	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	complemented
183	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
184	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
185	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
186	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
187	C₂×C₄×Dic₄₇	C₂³	1	8	yes	complemented
188	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₄₇	—	4	4	no	—
190	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
191	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
192	C₂²×Q₈×C₄₇	C₂³	1	8	yes	complemented
193	C₂³×C₄×C₄₇	—	4	4	no	—
194	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
198	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
199	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
203	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
204	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
205	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
206	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
207	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
209	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
210	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
211	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	complemented
212	C₂×C₄⋊C₄×C₄₇	C₂³	1	16	yes	complemented
213	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
214	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
216	C₂⁴×C₄₇	—	4	2	no	—
217	C₂⁴×C₄₇	—	4	2	no	—
218	C₂⁴×C₄₇	#41	1	8	yes	complemented
219	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
223	C₂³×D₄₇	—	2	4	no	—
224	C₂³×D₄₇	—	2	8	no	—
225	C₂³×D₄₇	—	4	2	no	—
226	C₂³×D₄₇	—	4	2	no	—
227	C₂³×D₄₇	—	4	4	no	—
228	C₂³×D₄₇	—	4	4	no	—
229	C₂³×D₄₇	C₂⁴	1	2	yes	—
230	C₂³×D₄₇	C₂⁴	1	4	yes	—
231	C₂³×D₄₇	C₂⁴	1	8	yes	—
232	C₂³×D₄₇	C₂⁴	1	4	yes	—
233	C₂×Q₈×C₄₇	—	2	8	no	—
234	C₂×Q₈×C₄₇	—	4	4	no	—
235	C₂×Q₈×C₄₇	—	4	16	no	—
236	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
237	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
238	C₂²×C₄×C₄₇	—	2	4	no	—
239	C₂²×C₄×C₄₇	—	2	4	no	—
240	C₂²×C₄×C₄₇	—	2	4	no	—
241	C₂²×C₄×C₄₇	—	4	16	no	—
242	C₂²×C₄×C₄₇	—	4	2	no	—
243	C₂²×C₄×C₄₇	—	4	2	no	—
244	C₂²×C₄×C₄₇	—	4	2	no	—
245	C₂²×C₄×C₄₇	—	4	4	no	—
246	C₂²×C₄×C₄₇	—	4	4	no	—
247	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
256	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
257	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
261	C₂×C₂²⋊D₄₇	—	2	8	no	—
262	C₂×C₂²⋊D₄₇	—	2	16	no	—
263	C₂×C₂²⋊D₄₇	—	2	8	no	—
264	C₂×C₂²⋊D₄₇	—	2	16	no	—
265	C₂×C₂²⋊D₄₇	—	2	32	no	—
266	C₂×C₂²⋊D₄₇	—	2	64	no	—
267	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
268	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
269	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
270	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
271	C₂²×Dic₄₇	—	2	8	no	—
272	C₂²×Dic₄₇	—	2	4	no	—
273	C₂²×Dic₄₇	—	4	2	no	—
274	C₂²×Dic₄₇	—	4	2	no	—
275	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
276	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
277	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
278	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
279	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
280	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
281	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
282	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
283	#10625354	—	4	32	no	—
284	C₂×D₁₈₈	—	2	8	no	—
285	C₂×D₁₈₈	—	4	16	no	—
286	C₂×D₁₈₈	—	4	4	no	—
287	C₂×D₁₈₈	—	4	8	no	—
288	C₂×D₁₈₈	—	4	8	no	—
289	C₂×D₁₈₈	C₂⁴	1	8	yes	—
290	C₂×D₁₈₈	C₂⁴	1	16	yes	—
291	C₂×D₁₈₈	C₂⁴	1	16	yes	—
292	C₂×D₁₈₈	C₂⁴	1	8	yes	—
293	C₂×C₄×D₄₇	—	2	8	no	—
294	C₂×C₄×D₄₇	—	4	16	no	—
295	C₂×C₄×D₄₇	—	4	4	no	—
296	C₂×C₄×D₄₇	—	4	8	no	—
297	C₂×C₄×D₄₇	—	4	8	no	—
298	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
299	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
300	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
301	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
302	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
305	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
306	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
307	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
308	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
309	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
310	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
311	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
312	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
313	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
314	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
315	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
316	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
317	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
318	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
319	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
320	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
321	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
322	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
323	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
324	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
325	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
326	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
327	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
328	C₄×Dic₄₇	C₂⁴	1	8	yes	—
329	C₄×Dic₄₇	C₂⁴	1	8	yes	—
330	C₄×Dic₄₇	C₂⁴	1	16	yes	—
331	C₄×Dic₄₇	C₂⁴	1	16	yes	—
332	C₂³×C₄₇	—	2	2	no	—
333	C₂³×C₄₇	—	2	2	no	—
334	C₂³×C₄₇	—	2	2	no	—
335	C₂³×C₄₇	—	2	2	no	—
336	C₂³×C₄₇	—	2	2	no	—
337	C₂³×C₄₇	—	2	2	no	—
338	C₂³×C₄₇	—	4	4	no	—
339	C₂³×C₄₇	—	4	16	no	—
340	C₂³×C₄₇	—	4	4	no	—
341	C₂³×C₄₇	C₂×#41	1	4	yes	—
342	C₂³×C₄₇	C₂×#41	1	4	yes	—
343	C₂³×C₄₇	C₂×#41	1	4	yes	—
344	C₂³×C₄₇	C₂×#41	1	16	yes	complemented
345	C₂³×C₄₇	C₂⁵	1	2	yes	—
346	C₂³×C₄₇	C₂⁵	1	2	yes	—
347	C₂³×C₄₇	C₂⁵	1	2	yes	—
348	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
349	C₂²×D₄₇	—	2	8	no	—
350	C₂²×D₄₇	—	2	4	no	—
351	C₂²×D₄₇	—	2	8	no	—
352	C₂²×D₄₇	—	2	4	no	—
353	C₂²×D₄₇	—	2	8	no	—
354	C₂²×D₄₇	—	2	8	no	—
355	C₂²×D₄₇	—	2	4	no	—
356	C₂²×D₄₇	—	2	16	no	—
357	C₂²×D₄₇	—	4	4	no	—
358	C₂²×D₄₇	—	4	4	no	—
359	C₂²×D₄₇	—	4	8	no	—
360	C₂²×D₄₇	—	4	8	no	—
361	C₂²×D₄₇	—	4	16	no	—
362	C₂²×D₄₇	—	8	16	no	—
363	C₂²×D₄₇	C₂⁵	1	4	yes	—
364	C₂²×D₄₇	C₂⁵	1	8	yes	—
365	Q₈×C₄₇	—	2	16	no	—
366	Q₈×C₄₇	—	4	8	no	—
367	C₂×C₄×C₄₇	—	2	2	no	—
368	C₂×C₄×C₄₇	—	2	8	no	—
369	C₂×C₄×C₄₇	—	2	2	no	—
370	C₂×C₄×C₄₇	—	2	2	no	—
371	C₂×C₄×C₄₇	—	2	8	no	—
372	C₂×C₄×C₄₇	—	2	8	no	—
373	C₂×C₄×C₄₇	—	2	8	no	—
374	C₂×C₄×C₄₇	—	2	8	no	—
375	C₂×C₄×C₄₇	—	4	4	no	—
376	C₂×C₄×C₄₇	—	4	4	no	—
377	C₂×C₄×C₄₇	—	4	4	no	—
378	C₂×C₄×C₄₇	—	4	8	no	—
379	C₂×C₄×C₄₇	—	4	8	no	—
380	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
381	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
382	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
383	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
384	C₂×C₄×C₄₇	C₂⁵	1	2	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	C₂²⋊D₄₇	—	2	16	no	—
390	C₂²⋊D₄₇	—	2	32	no	—
391	C₂×Dic₄₇	—	2	16	no	—
392	C₂×Dic₄₇	—	2	8	no	—
393	C₂×Dic₄₇	—	2	8	no	—
394	C₂×Dic₄₇	—	2	4	no	—
395	C₂×Dic₄₇	—	2	4	no	—
396	C₂×Dic₄₇	—	2	4	no	—
397	C₂×Dic₄₇	—	4	4	no	—
398	C₂×Dic₄₇	—	4	4	no	—
399	C₂×Dic₄₇	C₂⁵	1	4	yes	—
400	C₂×Dic₄₇	C₂⁵	1	4	yes	—
401	C₂×Dic₄₇	C₂⁵	1	4	yes	—
402	C₂×Dic₄₇	C₂⁵	1	8	yes	—
403	D₁₈₈	—	2	16	no	—
404	D₁₈₈	—	4	8	no	—
405	D₁₈₈	—	4	16	no	—
406	D₁₈₈	—	4	16	no	—
407	C₄×D₄₇	—	2	16	no	—
408	C₄×D₄₇	—	4	8	no	—
409	C₄×D₄₇	—	4	16	no	—
410	C₄×D₄₇	—	4	16	no	—
411	C₂×#3505	—	47	1	no	maximal, Sylow
412	C₂²×C₄₇	—	2	2	no	—
413	C₂²×C₄₇	—	2	2	no	—
414	C₂²×C₄₇	—	2	2	no	—
415	C₂²×C₄₇	—	2	2	no	—
416	C₂²×C₄₇	—	2	2	no	—
417	C₂²×C₄₇	—	2	2	no	—
418	C₂²×C₄₇	—	2	8	no	—
419	C₂²×C₄₇	—	2	8	no	—
420	C₂²×C₄₇	—	2	8	no	—
421	C₂²×C₄₇	—	4	16	no	—
422	C₂²×C₄₇	C₂²×#41	1	4	yes	—
423	C₂²×C₄₇	C₂²×#41	1	4	yes	—
424	C₂²×C₄₇	C₂²×#41	1	4	yes	—
425	C₂²×C₄₇	C₂²×#41	1	2	yes	—
426	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
427	C₂²×C₄₇	#585	1	2	yes	—
428	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
429	C₂×D₄₇	—	2	4	no	—
430	C₂×D₄₇	—	2	8	no	—
431	C₂×D₄₇	—	2	4	no	—
432	C₂×D₄₇	—	2	8	no	—
433	C₂×D₄₇	—	2	8	no	—
434	C₂×D₄₇	—	2	4	no	—
435	C₂×D₄₇	—	4	16	no	—
436	C₂×D₄₇	—	4	8	no	—
437	C₂×D₄₇	—	4	16	no	—
438	C₂×D₄₇	—	8	16	no	—
439	C₄×C₄₇	—	2	2	no	—
440	C₄×C₄₇	—	2	8	no	—
441	C₄×C₄₇	—	2	2	no	—
442	C₄×C₄₇	—	2	2	no	—
443	C₄×C₄₇	—	2	8	no	—
444	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
445	Dic₄₇	—	2	8	no	—
446	Dic₄₇	—	2	4	no	—
447	Dic₄₇	—	2	4	no	—
448	Dic₄₇	—	2	4	no	—
449	#3505	—	47	32	no	—
450	C₂×#553	—	47	2	no	—
451	C₂×#553	—	47	4	no	—
452	C₂×#552	—	47	2	no	—
453	C₂×#551	—	47	4	no	—
454	C₂×#548	—	47	2	no	—
455	C₂×#546	—	47	2	no	—
456	C₂×#539	—	47	2	no	—
457	C₂×#538	—	47	2	no	—
458	C₂×#534	—	47	2	no	—
459	C₂×#529	—	47	2	no	—
460	C₂×#525	—	47	2	no	—
461	C₂²×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
462	C₂²×#121	—	47	1	no	—
463	C₂×#518	—	47	2	no	—
464	C₂²×C₄×D₄	—	47	1	no	—
465	C₂×C₄₇	—	2	4	no	—
466	C₂×C₄₇	—	2	4	no	—
467	C₂×C₄₇	—	2	4	no	—
468	C₂×C₄₇	#3505	1	4	yes	complemented
469	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
470	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
472	D₄₇	—	4	4	no	—
473	D₄₇	—	4	8	no	—
474	C₂²×#41	—	47	2	no	—
475	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
476	C₂³×D₄	—	47	1	no	—
477	C₂³×D₄	—	47	2	no	—
478	C₂³×D₄	—	47	1	no	—
479	C₂⁴×C₄	—	47	1	no	—
480	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
481	#553	—	47	32	no	—
482	#553	—	47	64	no	—
483	#552	—	47	32	no	—
484	#551	—	47	64	no	—
485	#548	—	47	32	no	—
486	#546	—	47	32	no	—
487	#539	—	47	32	no	—
488	#538	—	47	32	no	—
489	#534	—	47	32	no	—
490	#529	—	47	32	no	—
491	C₂×#126	—	47	4	no	—
492	C₂×#126	—	47	4	no	—
493	C₂×#126	—	47	4	no	—
494	C₂×#125	—	47	2	no	—
495	C₂×#125	—	47	4	no	—
496	C₂×#124	—	47	2	no	—
497	C₂×#124	—	47	4	no	—
498	#525	—	47	32	no	—
499	C₂×#123	—	47	4	no	—
500	C₂×#123	—	47	4	no	—
501	C₂×#123	—	47	4	no	—
502	C₂×#123	—	47	4	no	—
503	C₂×#123	—	47	4	no	—
504	C₂×C₂²⋊Q₈	—	47	2	no	—
505	C₂×C₂²⋊Q₈	—	47	4	no	—
506	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
507	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
508	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
509	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
510	C₂×C₂²⋊Q₈	C₂×D₄₇	1	16	yes	complemented
511	C₂×#121	—	47	2	no	—
512	C₂×#121	—	47	2	no	—
513	C₂×#121	—	47	2	no	—
514	C₂×#121	—	47	2	no	—
515	C₂×#121	—	47	16	no	—
516	C₂×#121	—	47	4	no	—
517	C₂×#121	—	47	4	no	—
518	C₂×#121	—	47	2	no	—
519	C₂×#121	—	47	4	no	—
520	C₂×#120	—	47	4	no	—
521	C₂×#120	—	47	4	no	—
522	#518	—	47	32	no	—
523	C₂×C₄×Q₈	—	47	2	no	—
524	C₂×C₄×D₄	—	47	2	no	—
525	C₂×C₄×D₄	—	47	2	no	—
526	C₂×C₄×D₄	—	47	2	no	—
527	C₂×C₄×D₄	—	47	2	no	—
528	C₂×C₄×D₄	—	47	16	no	—
529	C₂×C₄×D₄	—	47	4	no	—
530	C₂×C₄×D₄	—	47	4	no	—
531	C₂×C₄×D₄	—	47	4	no	—
532	C₂×C₄×D₄	—	47	2	no	—
533	C₂×C₄×D₄	—	47	4	no	—
534	C₂×C₄×D₄	—	47	4	no	—
535	C₂×#117	—	47	2	no	—
536	C₂×#117	—	47	4	no	—
537	C₂×#117	—	47	4	no	—
538	C₂²×C₄⋊C₄	—	47	1	no	—
539	C₂²×C₄⋊C₄	—	47	1	no	—
540	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
541	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
542	C₂²×C₂²⋊C₄	—	47	1	no	—
543	C₂²×C₂²⋊C₄	—	47	1	no	—
544	C₂²×C₂²⋊C₄	—	47	2	no	—
545	C₂²×C₂²⋊C₄	—	47	4	no	—
546	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
547	C₂²×C₄²	—	47	1	no	—
548	C₄₇	C₂×#3505	1	1	yes	characteristic, complemented, Sylow
549	C₂⁵	—	47	2	no	—
550	C₂⁵	—	47	1	no	—
551	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
552	C₂×#41	—	47	16	no	—
553	C₂×#41	—	188	8	no	—
554	C₂²×Q₈	—	4	4	no	—
555	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
556	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
557	C₂²×Q₈	C₂²×D₄₇	1	8	yes	complemented
558	C₂²×D₄	—	47	2	no	—
559	C₂²×D₄	—	47	4	no	—
560	C₂²×D₄	—	47	2	no	—
561	C₂²×D₄	—	47	4	no	—
562	C₂²×D₄	—	47	8	no	—
563	C₂²×D₄	—	47	16	no	—
564	C₂²×D₄	—	47	2	no	—
565	C₂²×D₄	—	47	4	no	—
566	C₂²×D₄	—	47	4	no	—
567	C₂²×D₄	—	47	2	no	—
568	C₂²×D₄	—	47	8	no	—
569	C₂²×D₄	—	94	16	no	—
570	C₂²×D₄	—	94	8	no	—
571	C₂²×D₄	—	188	4	no	—
572	C₂³×C₄	—	4	4	no	—
573	C₂³×C₄	—	47	2	no	—
574	C₂³×C₄	—	47	1	no	—
575	C₂³×C₄	—	47	1	no	—
576	C₂³×C₄	—	47	1	no	—
577	C₂³×C₄	—	47	2	no	—
578	C₂³×C₄	—	47	4	no	—
579	C₂³×C₄	—	47	4	no	—
580	C₂³×C₄	—	47	2	no	—
581	C₂³×C₄	—	47	8	no	—
582	C₂³×C₄	—	188	4	no	—
583	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
584	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
585	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
586	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
587	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
588	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
589	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
590	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
591	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
592	#126	—	47	32	no	—
593	#126	—	47	32	no	—
594	#126	—	47	32	no	—
595	#125	—	47	16	no	—
596	#125	—	47	32	no	—
597	#124	—	47	16	no	—
598	#124	—	47	32	no	—
599	#123	—	47	32	no	—
600	#123	—	47	32	no	—
601	#123	—	47	32	no	—
602	#123	—	47	32	no	—
603	#123	—	47	32	no	—
604	C₂²⋊Q₈	—	47	16	no	—
605	C₂²⋊Q₈	—	47	32	no	—
606	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
607	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
608	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
609	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
610	#121	—	47	16	no	—
611	#121	—	47	16	no	—
612	#121	—	47	16	no	—
613	#121	—	47	16	no	—
614	#121	—	47	32	no	—
615	#121	—	47	32	no	—
616	#121	—	47	16	no	—
617	#121	—	47	32	no	—
618	#120	—	47	32	no	—
619	#120	—	47	32	no	—
620	C₄×Q₈	—	47	16	no	—
621	C₄×D₄	—	47	16	no	—
622	C₄×D₄	—	47	16	no	—
623	C₄×D₄	—	47	16	no	—
624	C₄×D₄	—	47	16	no	—
625	C₄×D₄	—	47	32	no	—
626	C₄×D₄	—	47	32	no	—
627	C₄×D₄	—	47	32	no	—
628	C₄×D₄	—	47	16	no	—
629	C₄×D₄	—	47	32	no	—
630	C₄×D₄	—	47	32	no	—
631	#117	—	47	16	no	—
632	#117	—	47	32	no	—
633	#117	—	47	32	no	—
634	C₂×C₄⋊C₄	—	47	2	no	—
635	C₂×C₄⋊C₄	—	47	2	no	—
636	C₂×C₄⋊C₄	—	47	2	no	—
637	C₂×C₄⋊C₄	—	47	8	no	—
638	C₂×C₄⋊C₄	—	47	2	no	—
639	C₂×C₄⋊C₄	—	47	8	no	—
640	C₂×C₄⋊C₄	—	47	4	no	—
641	C₂×C₄⋊C₄	—	47	4	no	—
642	C₂×C₄⋊C₄	—	47	4	no	—
643	C₂×C₄⋊C₄	—	47	4	no	—
644	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
645	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
646	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
647	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
648	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	complemented
649	C₂×C₄⋊C₄	C₂²×D₄₇	1	16	yes	complemented
650	C₂×C₂²⋊C₄	—	47	2	no	—
651	C₂×C₂²⋊C₄	—	47	2	no	—
652	C₂×C₂²⋊C₄	—	47	8	no	—
653	C₂×C₂²⋊C₄	—	47	4	no	—
654	C₂×C₂²⋊C₄	—	47	2	no	—
655	C₂×C₂²⋊C₄	—	47	4	no	—
656	C₂×C₂²⋊C₄	—	47	4	no	—
657	C₂×C₂²⋊C₄	—	47	2	no	—
658	C₂×C₂²⋊C₄	—	47	8	no	—
659	C₂×C₂²⋊C₄	—	47	4	no	—
660	C₂×C₂²⋊C₄	—	47	16	no	—
661	C₂×C₂²⋊C₄	—	47	4	no	—
662	C₂×C₂²⋊C₄	—	47	4	no	—
663	C₂×C₂²⋊C₄	—	47	4	no	—
664	C₂×C₂²⋊C₄	—	47	4	no	—
665	C₂×C₂²⋊C₄	—	47	32	no	—
666	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
667	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
668	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
669	C₂×C₄²	—	47	4	no	—
670	C₂×C₄²	—	47	4	no	—
671	C₂×C₄²	—	47	2	no	—
672	C₂×C₄²	—	47	2	no	—
673	C₂×C₄²	—	47	8	no	—
674	C₂⁴	—	4	2	no	—
675	C₂⁴	—	4	2	no	—
676	C₂⁴	—	47	2	no	—
677	C₂⁴	—	47	4	no	—
678	C₂⁴	—	47	8	no	—
679	C₂⁴	—	47	4	no	—
680	C₂⁴	—	94	8	no	—
681	C₂⁴	—	94	4	no	—
682	C₂⁴	—	188	4	no	—
683	C₂⁴	—	188	4	no	—
684	C₂⁴	—	188	2	no	—
685	C₂⁴	—	188	2	no	—
686	C₂⁴	#10625354	1	8	yes	complemented
687	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
688	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
689	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
690	C₂⁴	C₂³×D₄₇	1	4	yes	—
691	#41	—	188	32	no	—
692	C₂×Q₈	—	2	8	no	—
693	C₂×Q₈	—	4	4	no	—
694	C₂×Q₈	—	4	16	no	—
695	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
696	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
697	C₂×D₄	—	47	8	no	—
698	C₂×D₄	—	47	16	no	—
699	C₂×D₄	—	47	8	no	—
700	C₂×D₄	—	47	16	no	—
701	C₂×D₄	—	47	8	no	—
702	C₂×D₄	—	47	16	no	—
703	C₂×D₄	—	47	16	no	—
704	C₂×D₄	—	47	8	no	—
705	C₂×D₄	—	94	8	no	—
706	C₂×D₄	—	94	16	no	—
707	C₂×D₄	—	94	16	no	—
708	C₂×D₄	—	94	8	no	—
709	C₂×D₄	—	94	64	no	—
710	C₂×D₄	—	94	32	no	—
711	C₂×D₄	—	94	8	no	—
712	C₂×D₄	—	188	16	no	—
713	C₂×D₄	—	188	8	no	—
714	C₂×D₄	—	188	4	no	—
715	C₂×D₄	—	188	8	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	4	16	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	4	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	—	47	4	no	—
726	C₂²×C₄	—	47	8	no	—
727	C₂²×C₄	—	47	2	no	—
728	C₂²×C₄	—	47	4	no	—
729	C₂²×C₄	—	47	2	no	—
730	C₂²×C₄	—	47	2	no	—
731	C₂²×C₄	—	47	4	no	—
732	C₂²×C₄	—	47	4	no	—
733	C₂²×C₄	—	47	8	no	—
734	C₂²×C₄	—	47	16	no	—
735	C₂²×C₄	—	47	16	no	—
736	C₂²×C₄	—	47	8	no	—
737	C₂²×C₄	—	94	8	no	—
738	C₂²×C₄	—	94	4	no	—
739	C₂²×C₄	—	94	8	no	—
740	C₂²×C₄	—	188	16	no	—
741	C₂²×C₄	—	188	8	no	—
742	C₂²×C₄	—	188	4	no	—
743	C₂²×C₄	—	188	8	no	—
744	C₂²×C₄	—	188	2	no	—
745	C₂²×C₄	—	188	2	no	—
746	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
747	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
748	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
749	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
750	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
751	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
752	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
753	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
754	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
755	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
756	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
757	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
758	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
759	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
760	C₄⋊C₄	—	47	8	no	—
761	C₄⋊C₄	—	47	8	no	—
762	C₄⋊C₄	—	47	16	no	—
763	C₄⋊C₄	—	47	16	no	—
764	C₄⋊C₄	—	47	8	no	—
765	C₄⋊C₄	—	47	8	no	—
766	C₄⋊C₄	—	47	16	no	—
767	C₄⋊C₄	—	47	16	no	—
768	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
769	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
770	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
771	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
772	C₂²⋊C₄	—	47	8	no	—
773	C₂²⋊C₄	—	47	8	no	—
774	C₂²⋊C₄	—	47	16	no	—
775	C₂²⋊C₄	—	47	8	no	—
776	C₂²⋊C₄	—	47	16	no	—
777	C₂²⋊C₄	—	47	16	no	—
778	C₂²⋊C₄	—	47	8	no	—
779	C₂²⋊C₄	—	47	16	no	—
780	C₂²⋊C₄	—	47	16	no	—
781	C₂²⋊C₄	—	47	16	no	—
782	C₂²⋊C₄	—	47	16	no	—
783	C₂²⋊C₄	—	47	16	no	—
784	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
785	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
786	C₄²	—	47	8	no	—
787	C₄²	—	47	8	no	—
788	C₄²	—	47	16	no	—
789	C₄²	—	47	16	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	4	4	no	—
797	C₂³	—	4	16	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	47	4	no	—
800	C₂³	—	47	8	no	—
801	C₂³	—	94	16	no	—
802	C₂³	—	94	8	no	—
803	C₂³	—	94	8	no	—
804	C₂³	—	94	4	no	—
805	C₂³	—	94	4	no	—
806	C₂³	—	94	8	no	—
807	C₂³	—	94	8	no	—
808	C₂³	—	94	4	no	—
809	C₂³	—	376	16	no	—
810	C₂³	—	188	8	no	—
811	C₂³	—	188	8	no	—
812	C₂³	—	188	4	no	—
813	C₂³	—	188	4	no	—
814	C₂³	—	188	16	no	—
815	C₂³	C₂×#10625354	1	4	yes	—
816	C₂³	C₂×#10625354	1	4	yes	—
817	C₂³	C₂×#10625354	1	4	yes	—
818	C₂³	C₂×#10625354	1	16	yes	complemented
819	C₂³	C₂⁴×D₄₇	1	2	yes	—
820	C₂³	C₂⁴×D₄₇	1	2	yes	—
821	C₂³	C₂⁴×D₄₇	1	2	yes	—
822	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
823	Q₈	—	2	16	no	—
824	Q₈	—	4	8	no	—
825	D₄	—	94	16	no	—
826	D₄	—	94	32	no	—
827	D₄	—	94	32	no	—
828	D₄	—	94	16	no	—
829	D₄	—	94	16	no	—
830	D₄	—	188	16	no	—
831	D₄	—	188	8	no	—
832	D₄	—	188	16	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	8	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	8	no	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	—	4	8	no	—
846	C₂×C₄	—	47	4	no	—
847	C₂×C₄	—	47	4	no	—
848	C₂×C₄	—	47	8	no	—
849	C₂×C₄	—	47	4	no	—
850	C₂×C₄	—	94	16	no	—
851	C₂×C₄	—	94	8	no	—
852	C₂×C₄	—	94	8	no	—
853	C₂×C₄	—	94	4	no	—
854	C₂×C₄	—	94	4	no	—
855	C₂×C₄	—	94	4	no	—
856	C₂×C₄	—	94	16	no	—
857	C₂×C₄	—	188	16	no	—
858	C₂×C₄	—	188	8	no	—
859	C₂×C₄	—	188	16	no	—
860	C₂×C₄	—	188	4	no	—
861	C₂×C₄	—	188	4	no	—
862	C₂×C₄	#13094069	1	4	yes	—
863	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
864	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
865	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
866	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
867	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
868	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	8	no	—
876	C₂²	—	2	8	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	4	16	no	—
879	C₂²	—	94	8	no	—
880	C₂²	—	94	4	no	—
881	C₂²	—	94	4	no	—
882	C₂²	—	94	8	no	—
883	C₂²	—	94	8	no	—
884	C₂²	—	94	4	no	—
885	C₂²	—	376	16	no	—
886	C₂²	—	188	16	no	—
887	C₂²	—	188	16	no	—
888	C₂²	—	188	8	no	—
889	C₂²	C₂²×#10625354	1	4	yes	—
890	C₂²	C₂²×#10625354	1	4	yes	—
891	C₂²	C₂²×#10625354	1	4	yes	—
892	C₂²	C₂²×#10625354	1	2	yes	—
893	C₂²	C₂×#13094069	1	2	yes	—
894	C₂²	#15689959	1	2	yes	—
895	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	8	no	—
900	C₄	—	2	8	no	—
901	C₄	—	94	4	no	—
902	C₄	—	94	8	no	—
903	C₄	—	94	4	no	—
904	C₄	—	94	4	no	—
905	C₄	C₂×#13094069	1	4	yes	—
906	C₂	—	2	4	no	—
907	C₂	—	2	4	no	—
908	C₂	—	2	4	no	—
909	C₂	—	188	8	no	—
910	C₂	—	188	4	no	—
911	C₂	#20257229	1	4	yes	direct product factor
912	C₂	C₂³×#10625354	1	1	yes	characteristic
913	C₂	C₂²×#13094069	1	1	yes	characteristic
914	C₂	C₂×#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×C₂²⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	C₂×#3505
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #20257229	C₂	direct (N × H)
2. C₂×#15689821	C₂	semidirect
3. C₂×#15689821	C₂	semidirect
4. C₂×#15689815	C₂	semidirect
5. C₂×#15689800	C₂	semidirect
6. C₂×#15689784	C₂	semidirect
7. C₂×#15689764	C₂	semidirect
8. C₂×#15689722	C₂	semidirect
9. C₂×#15689713	C₂	semidirect
10. C₂×#15689685	C₂	semidirect
11. C₂×#15689659	C₂	semidirect
12. C₂×#15689636	C₂	semidirect
13. C₂²×#13093998	C₂	semidirect
14. C₂×#15689596	C₂	semidirect
15. C₂²×C₄×C₂²⋊D₄₇	C₂	semidirect
16. C₂²×C₂²⋊Q₈×C₄₇	C₂	semidirect
17. C₂²×#10625354	C₂²	semidirect
18. C₂³×D₁₈₈	C₂²	semidirect
21. C₂³×C₄×D₄₇	C₂²	semidirect
22. #15689821	C₂²	semidirect
23. #15689821	C₂²	semidirect
24. #15689815	C₂²	semidirect
25. #15689800	C₂²	semidirect
26. #15689784	C₂²	semidirect
27. #15689764	C₂²	semidirect
28. #15689722	C₂²	semidirect
29. #15689713	C₂²	semidirect
30. #15689685	C₂²	semidirect
31. #15689659	C₂²	semidirect
32. C₂×#13094019	C₂²	semidirect
33. C₂×#13094019	C₂²	semidirect
34. C₂×#13094019	C₂²	semidirect
35. C₂×#13094015	C₂²	semidirect
36. C₂×#13094015	C₂²	semidirect
37. C₂×#13094013	C₂²	semidirect
38. C₂×#13094013	C₂²	semidirect
39. #15689636	C₂²	semidirect
40. C₂×#13094009	C₂²	semidirect
41. C₂×#13094009	C₂²	semidirect
42. C₂×#13094009	C₂²	semidirect
44. C₂×#13094008	C₂²	semidirect
45. C₂×#13094000	C₂²	semidirect
46. C₂×#13094000	C₂²	semidirect
47. C₂×#13093999	C₂²	semidirect
48. C₂×#13093999	C₂²	semidirect
51. C₂×#13093998	C₂²	semidirect
52. C₂×#13093998	C₂²	semidirect
53. C₂×#13093998	C₂²	semidirect
54. C₂×#13093998	C₂²	semidirect
55. C₂×#13093998	C₂²	semidirect
57. C₂×#13093994	C₂²	semidirect
58. #15689596	C₂²	semidirect
59. C₂×Q₈×Dic₄₇	C₂²	semidirect
60. C₂×#13093986	C₂²	semidirect
61. C₂×#13093986	C₂²	semidirect
64. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
65. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
66. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
67. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
68. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
69. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
70. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
71. C₂×#13093982	C₂²	semidirect
72. C₂×#13093982	C₂²	semidirect
73. C₂×#13093980	C₂²	semidirect
74. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
75. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
77. C₂²×(C₂×D₄₇)⋊C₄	C₂²	semidirect
78. C₂²×(C₂×D₄₇)⋊C₄	C₂²	semidirect
79. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
80. C₂²×C₄×Dic₄₇	C₂²	semidirect
81. C₂³×Q₈×C₄₇	C₂²	semidirect
83. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
84. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
85. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
86. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
87. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
88. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
89. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
94. C₂×#10625354	C₂³	semidirect
100. C₂²×D₁₈₈	C₂³	semidirect
118. C₂²×C₄×D₄₇	C₂³	semidirect
119. #13094019	C₂³	semidirect
120. #13094019	C₂³	semidirect
121. #13094019	C₂³	semidirect
122. #13094015	C₂³	semidirect
123. #13094015	C₂³	semidirect
124. #13094013	C₂³	semidirect
125. #13094013	C₂³	semidirect
126. #13094009	C₂³	semidirect
127. #13094009	C₂³	semidirect
128. #13094009	C₂³	semidirect
130. #13094008	C₂³	semidirect
131. #13094000	C₂³	semidirect
132. #13094000	C₂³	semidirect
133. #13093999	C₂³	semidirect
134. #13093999	C₂³	semidirect
137. #13093998	C₂³	semidirect
138. #13093998	C₂³	semidirect
139. #13093998	C₂³	semidirect
140. #13093998	C₂³	semidirect
142. #13093994	C₂³	semidirect
143. Q₈×Dic₄₇	C₂³	semidirect
144. #13093986	C₂³	semidirect
145. #13093986	C₂³	semidirect
148. C₄×C₂²⋊D₄₇	C₂³	semidirect
149. C₄×C₂²⋊D₄₇	C₂³	semidirect
150. C₄×C₂²⋊D₄₇	C₂³	semidirect
151. C₄×C₂²⋊D₄₇	C₂³	semidirect
152. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
153. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
154. #13093982	C₂³	semidirect
155. #13093982	C₂³	semidirect
156. #13093980	C₂³	semidirect
161. C₂×C₄⋊Dic₄₇	C₂³	semidirect
166. C₂×Dic₄₇⋊C₄	C₂³	semidirect
180. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
181. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
182. C₂²⋊C₄×D₄₇	C₂³	semidirect
187. C₂×C₄×Dic₄₇	C₂³	semidirect
192. C₂²×Q₈×C₄₇	C₂³	semidirect
203. C₂²⋊Q₈×C₄₇	C₂³	semidirect
204. C₂²⋊Q₈×C₄₇	C₂³	semidirect
205. C₂²⋊Q₈×C₄₇	C₂³	semidirect
206. C₂²⋊Q₈×C₄₇	C₂³	semidirect
211. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
212. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
218. C₂⁴×C₄₇	#41	semidirect
344. C₂³×C₄₇	C₂×#41	semidirect
461. C₂²×C₂²⋊Q₈	D₄₇	semidirect
468. C₂×C₄₇	#3505	semidirect
475. C₂³×Q₈	C₂×D₄₇	semidirect
506. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
507. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
508. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
509. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
510. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
540. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
541. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
548. C₄₇	C₂×#3505	semidirect
557. C₂²×Q₈	C₂²×D₄₇	semidirect
606. C₂²⋊Q₈	C₂²×D₄₇	semidirect
607. C₂²⋊Q₈	C₂²×D₄₇	semidirect
608. C₂²⋊Q₈	C₂²×D₄₇	semidirect
609. C₂²⋊Q₈	C₂²×D₄₇	semidirect
648. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
649. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
686. C₂⁴	#10625354	semidirect
818. C₂³	C₂×#10625354	semidirect
911. C₂	#20257229	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257229	2
C₂×#15689821	2
C₂×#15689815	2
C₂×#15689800	2
C₂×#15689784	2
C₂×#15689764	2
C₂×#15689722	2
C₂×#15689713	2
C₂×#15689685	2
C₂×#15689659	2
C₂×#15689636	2
C₂²×#13093998	2
C₂×#15689596	2
C₂²×C₄×C₂²⋊D₄₇	2
C₂²×C₂²⋊Q₈×C₄₇	2
C₂×#3505	47

Subgroups — C2×#20257229 #27124208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257229 #27124208