Subgroups — C₂×#20257665 #27123571

Order 12032.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257665	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689865	C₂	1	2	yes	maximal, complemented
3	C₂×#15689863	C₂	1	2	yes	maximal, complemented
4	C₂×#15689857	C₂	1	2	yes	maximal, complemented
5	C₂×#15689844	C₂	1	2	yes	maximal, complemented
6	C₂×#15689836	C₂	1	2	yes	maximal, complemented
7	C₂×#15689803	C₂	1	2	yes	maximal, complemented
8	C₂×#15689784	C₂	1	2	yes	maximal, complemented
9	C₂×#15689764	C₂	1	2	yes	maximal, complemented
10	C₂×#15689747	C₂	1	4	yes	maximal, complemented
11	C₂×#15689746	C₂	1	2	yes	maximal, complemented
12	C₂×#15689709	C₂	1	4	yes	maximal, complemented
13	C₂×#15689687	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15689636	C₂	1	2	yes	maximal, complemented
15	C₂×#15689630	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#10625354	C₂²	1	2	yes	—
18	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
20	#15689865	C₂²	1	32	yes	complemented
21	#15689863	C₂²	1	32	yes	complemented
22	#15689857	C₂²	1	32	yes	complemented
23	#15689844	C₂²	1	32	yes	complemented
24	#15689836	C₂²	1	32	yes	complemented
25	#15689803	C₂²	1	32	yes	complemented
26	#15689784	C₂²	1	32	yes	complemented
27	#15689764	C₂²	1	32	yes	complemented
28	#15689747	C₂²	1	64	yes	complemented
29	#15689746	C₂²	1	32	yes	complemented
30	#15689709	C₂²	1	64	yes	complemented
31	#15689687	C₂²	1	16	yes	complemented
32	C₂×#13094023	C₂²	1	2	yes	complemented
33	C₂×#13094020	C₂²	1	2	yes	—
34	C₂×#13094019	C₂²	1	4	yes	complemented
35	C₂×#13094019	C₂²	1	4	yes	complemented
36	C₂×#13094017	C₂²	1	4	yes	complemented
37	C₂×#13094013	C₂²	1	2	yes	complemented
38	C₂×#13094013	C₂²	1	2	yes	complemented
39	C₂×#13094013	C₂²	1	4	yes	complemented
40	C₂×#13094012	C₂²	1	4	yes	complemented
41	C₂×#13094010	C₂²	1	4	yes	—
42	C₂×#13094010	C₂²	1	4	yes	complemented
43	C₂×#13094010	C₂²	1	4	yes	complemented
44	#15689636	C₂²	1	32	yes	complemented
45	#15689630	C₂²	1	16	yes	complemented
46	C₂×#13094009	C₂²	1	4	yes	complemented
47	C₂×#13094009	C₂²	1	4	yes	complemented
48	C₂×#13094006	C₂²	1	4	yes	complemented
49	C₂×#13094005	C₂²	1	1	yes	characteristic
50	C₂×#13094005	C₂²	1	1	yes	characteristic, complemented
51	C₂×#13094004	C₂²	1	4	yes	complemented
52	C₂×#13094000	C₂²	1	2	yes	complemented
53	C₂×#13094000	C₂²	1	4	yes	complemented
54	C₂×#13094000	C₂²	1	2	yes	complemented
55	C₂×#13093999	C₂²	1	4	yes	—
56	C₂×#13093999	C₂²	1	2	yes	—
57	C₂×#13093998	C₂²	1	2	yes	—
58	C₂×#13093998	C₂²	1	2	yes	complemented
59	C₂×#13093998	C₂²	1	4	yes	complemented
60	C₂×#13093997	C₂²	1	4	yes	complemented
61	C₂×#13093995	C₂²	1	2	yes	—
62	C₂×#13093994	C₂²	1	4	yes	—
63	C₂×#13093994	C₂²	1	4	yes	complemented
64	C₂×#13093992	C₂²	1	1	yes	characteristic
65	C₂×#13093992	C₂²	1	2	yes	—
66	C₂×#13093992	C₂²	1	1	yes	characteristic, complemented
67	C₂×#13093992	C₂²	1	2	yes	complemented
68	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
69	C₂×#13093989	C₂²	1	4	yes	complemented
70	C₂×#13093986	C₂²	1	2	yes	complemented
71	C₂×#13093986	C₂²	1	4	yes	complemented
72	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
73	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
74	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
75	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
76	C₂×#13093983	C₂²	1	1	yes	characteristic, complemented
77	C₂×#13093983	C₂²	1	1	yes	characteristic, complemented
78	C₂×#13093982	C₂²	1	2	yes	complemented
79	C₂×#13093981	C₂²	1	4	yes	complemented
80	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
81	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
82	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
83	C₄₇×#536	C₂²	1	16	yes	complemented
84	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
85	C₂×#124×C₄₇	C₂²	1	2	yes	—
86	C₂×#123×C₄₇	C₂²	1	2	yes	complemented
87	C₂×#123×C₄₇	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
90	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
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	—
95	C₂²×Dic₉₄	C₂³	1	4	yes	—
96	C₂²×D₁₈₈	—	4	4	no	—
97	C₂²×D₁₈₈	C₂³	1	2	yes	—
98	C₂²×D₁₈₈	C₂³	1	4	yes	—
99	C₂²×D₁₈₈	C₂³	1	4	yes	—
100	C₂²×D₁₈₈	C₂³	1	2	yes	—
101	C₂²×D₁₈₈	C₂³	1	8	yes	complemented
102	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
103	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
104	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
106	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
107	C₂²×C₄×D₄₇	—	4	4	no	—
108	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
109	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
110	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
111	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
112	C₂²×C₄×D₄₇	C₂³	1	8	yes	complemented
113	#13094023	C₂³	1	16	yes	complemented
114	#13094020	C₂³	1	16	yes	—
115	#13094019	C₂³	1	32	yes	complemented
116	#13094019	C₂³	1	32	yes	complemented
117	#13094017	C₂³	1	32	yes	complemented
118	#13094013	C₂³	1	16	yes	complemented
119	#13094013	C₂³	1	16	yes	complemented
120	#13094013	C₂³	1	32	yes	complemented
121	#13094012	C₂³	1	32	yes	complemented
122	#13094010	C₂³	1	32	yes	—
123	#13094010	C₂³	1	32	yes	complemented
124	#13094010	C₂³	1	32	yes	complemented
125	#13094009	C₂³	1	32	yes	complemented
126	#13094009	C₂³	1	32	yes	complemented
127	#13094006	C₂³	1	32	yes	complemented
128	#13094005	C₂³	1	8	yes	—
129	#13094005	C₂³	1	8	yes	complemented
130	#13094004	C₂³	1	32	yes	complemented
131	#13094000	C₂³	1	16	yes	complemented
132	#13094000	C₂³	1	32	yes	complemented
133	#13094000	C₂³	1	16	yes	complemented
134	#13093999	C₂³	1	32	yes	—
135	#13093999	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	#13093997	C₂³	1	32	yes	complemented
140	#13093995	C₂³	1	16	yes	—
141	#13093994	C₂³	1	32	yes	—
142	#13093994	C₂³	1	32	yes	complemented
143	#13093992	C₂³	1	16	yes	—
144	#13093992	C₂³	1	8	yes	—
145	#13093992	C₂³	1	8	yes	complemented
146	#13093992	C₂³	1	16	yes	complemented
147	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
148	#13093989	C₂³	1	32	yes	complemented
149	#13093986	C₂³	1	16	yes	complemented
150	#13093986	C₂³	1	32	yes	complemented
151	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
152	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
153	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
154	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
155	#13093983	C₂³	1	8	yes	complemented
156	#13093983	C₂³	1	8	yes	complemented
157	#13093982	C₂³	1	16	yes	complemented
158	#13093981	C₂³	1	32	yes	complemented
159	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
160	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
161	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
162	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
163	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
164	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
165	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
166	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊Dic₄₇	C₂³	1	2	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	4	yes	—
174	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
175	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
176	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	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	4	yes	—
181	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	complemented
182	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
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×#41×C₄₇	—	4	4	no	—
187	C₂×#41×C₄₇	C₂³	1	8	yes	—
188	C₂²×Q₈×C₄₇	—	4	4	no	—
189	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
190	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
191	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
192	C₂²×Q₈×C₄₇	C₂³	1	8	yes	complemented
193	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
195	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
200	C₄⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
201	#124×C₄₇	C₂³	1	16	yes	—
202	#123×C₄₇	C₂³	1	16	yes	complemented
203	#123×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	#117×C₄₇	C₂³	1	8	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×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
212	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
213	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
214	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
217	C₂³×D₄₇	—	4	2	no	—
218	C₂³×D₄₇	—	4	4	no	—
219	C₂³×D₄₇	—	4	4	no	—
220	C₂³×D₄₇	—	4	8	no	—
221	C₂³×D₄₇	C₂⁴	1	2	yes	—
222	C₂³×D₄₇	C₂⁴	1	4	yes	—
223	C₂³×D₄₇	C₂⁴	1	8	yes	—
224	C₂³×D₄₇	C₂⁴	1	4	yes	—
225	#41×C₄₇	—	4	16	no	—
226	C₂×Q₈×C₄₇	—	2	8	no	—
227	C₂×Q₈×C₄₇	—	4	4	no	—
228	C₂×Q₈×C₄₇	—	4	2	no	—
229	C₂×Q₈×C₄₇	—	4	16	no	—
230	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
231	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
232	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
233	C₂×D₄×C₄₇	—	4	2	no	—
234	C₂×D₄×C₄₇	—	4	2	no	—
235	C₂×D₄×C₄₇	—	4	2	no	—
236	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
237	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
238	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₄₇	—	2	4	no	—
240	C₂²×C₄×C₄₇	—	2	4	no	—
241	C₂²×C₄×C₄₇	—	2	4	no	—
242	C₂²×C₄×C₄₇	—	4	4	no	—
243	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
252	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₂²⋊D₄₇	—	4	4	no	—
254	C₂×C₂²⋊D₄₇	—	4	8	no	—
255	C₂×C₂²⋊D₄₇	—	4	8	no	—
256	C₂×C₂²⋊D₄₇	—	4	4	no	—
257	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
258	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
259	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
260	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
261	C₂²×Dic₄₇	—	4	2	no	—
262	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
263	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
264	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
265	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
266	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
267	#10625354	—	4	32	no	—
268	C₂×D₁₈₈	—	2	8	no	—
269	C₂×D₁₈₈	—	4	16	no	—
270	C₂×D₁₈₈	—	4	4	no	—
271	C₂×D₁₈₈	—	4	8	no	—
272	C₂×D₁₈₈	—	4	8	no	—
273	C₂×D₁₈₈	C₂⁴	1	8	yes	—
274	C₂×D₁₈₈	C₂⁴	1	16	yes	—
275	C₂×D₁₈₈	C₂⁴	1	16	yes	—
276	C₂×D₁₈₈	C₂⁴	1	8	yes	—
277	C₂×C₄×D₄₇	—	2	8	no	—
278	C₂×C₄×D₄₇	—	4	16	no	—
279	C₂×C₄×D₄₇	—	4	4	no	—
280	C₂×C₄×D₄₇	—	4	8	no	—
281	C₂×C₄×D₄₇	—	4	8	no	—
282	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
283	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
284	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
285	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
286	C₂×Dic₉₄	—	4	8	no	—
287	C₂×Dic₉₄	C₂⁴	1	16	yes	—
288	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
289	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
290	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
291	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
292	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
293	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
294	C₄²×C₄₇	C₂⁴	1	8	yes	—
295	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
296	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
297	C₂²⋊Dic₄₇	C₂⁴	1	4	yes	—
298	C₂²⋊Dic₄₇	C₂⁴	1	4	yes	—
299	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
300	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
301	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
302	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
303	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
304	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
305	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
306	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
307	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
308	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
309	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
310	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
311	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
312	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
313	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
314	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
315	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
316	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
317	C₄×Dic₄₇	C₂⁴	1	16	yes	—
318	C₄×Dic₄₇	C₂⁴	1	8	yes	—
319	C₄×Dic₄₇	C₂⁴	1	8	yes	—
320	C₄×Dic₄₇	C₂⁴	1	16	yes	—
321	C₂³×C₄₇	—	2	2	no	—
322	C₂³×C₄₇	—	2	2	no	—
323	C₂³×C₄₇	—	2	2	no	—
324	C₂³×C₄₇	—	2	4	no	—
325	C₂³×C₄₇	—	2	4	no	—
326	C₂³×C₄₇	—	2	4	no	—
327	C₂³×C₄₇	C₂⁵	1	2	yes	—
328	C₂³×C₄₇	C₂⁵	1	2	yes	—
329	C₂³×C₄₇	C₂⁵	1	2	yes	—
330	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
331	C₂²×D₄₇	—	2	4	no	—
332	C₂²×D₄₇	—	2	8	no	—
333	C₂²×D₄₇	—	2	8	no	—
334	C₂²×D₄₇	—	2	4	no	—
335	C₂²×D₄₇	—	2	8	no	—
336	C₂²×D₄₇	—	2	4	no	—
337	C₂²×D₄₇	—	4	4	no	—
338	C₂²×D₄₇	—	4	8	no	—
339	C₂²×D₄₇	—	4	8	no	—
340	C₂²×D₄₇	—	4	16	no	—
341	C₂²×D₄₇	—	4	16	no	—
342	C₂²×D₄₇	—	8	16	no	—
343	C₂²×D₄₇	C₂⁵	1	4	yes	—
344	C₂²×D₄₇	C₂⁵	1	8	yes	—
345	Q₈×C₄₇	—	2	16	no	—
346	Q₈×C₄₇	—	4	8	no	—
347	Q₈×C₄₇	—	4	4	no	—
348	D₄×C₄₇	—	4	4	no	—
349	D₄×C₄₇	—	4	4	no	—
350	D₄×C₄₇	—	4	4	no	—
351	C₂×C₄×C₄₇	—	2	2	no	—
352	C₂×C₄×C₄₇	—	2	8	no	—
353	C₂×C₄×C₄₇	—	2	2	no	—
354	C₂×C₄×C₄₇	—	2	2	no	—
355	C₂×C₄×C₄₇	—	2	8	no	—
356	C₂×C₄×C₄₇	—	2	8	no	—
357	C₂×C₄×C₄₇	—	2	8	no	—
358	C₂×C₄×C₄₇	—	2	8	no	—
359	C₂×C₄×C₄₇	—	4	8	no	—
360	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
361	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
362	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
363	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
364	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
365	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
366	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
367	C₂²⋊D₄₇	—	4	8	no	—
368	C₂²⋊D₄₇	—	4	16	no	—
369	C₂²⋊D₄₇	—	4	16	no	—
370	C₂²⋊D₄₇	—	4	8	no	—
371	C₂×Dic₄₇	—	2	4	no	—
372	C₂×Dic₄₇	—	2	4	no	—
373	C₂×Dic₄₇	—	2	8	no	—
374	C₂×Dic₄₇	—	2	4	no	—
375	C₂×Dic₄₇	—	4	4	no	—
376	C₂×Dic₄₇	C₂⁵	1	8	yes	—
377	C₂×Dic₄₇	C₂⁵	1	4	yes	—
378	C₂×Dic₄₇	C₂⁵	1	4	yes	—
379	C₂×Dic₄₇	C₂⁵	1	4	yes	—
380	D₁₈₈	—	2	16	no	—
381	D₁₈₈	—	4	8	no	—
382	D₁₈₈	—	4	16	no	—
383	D₁₈₈	—	4	16	no	—
384	C₄×D₄₇	—	2	16	no	—
385	C₄×D₄₇	—	4	8	no	—
386	C₄×D₄₇	—	4	16	no	—
387	C₄×D₄₇	—	4	16	no	—
388	Dic₉₄	—	4	16	no	—
389	C₂×#3540	—	47	1	no	maximal, Sylow
390	C₂²×C₄₇	—	2	2	no	—
391	C₂²×C₄₇	—	2	2	no	—
392	C₂²×C₄₇	—	2	2	no	—
393	C₂²×C₄₇	—	2	4	no	—
394	C₂²×C₄₇	—	2	4	no	—
395	C₂²×C₄₇	—	2	4	no	—
396	C₂²×C₄₇	—	4	4	no	—
397	C₂²×C₄₇	—	4	4	no	—
398	C₂²×C₄₇	—	4	4	no	—
399	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
400	C₂²×C₄₇	#585	1	4	yes	—
401	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
402	C₂×D₄₇	—	2	4	no	—
403	C₂×D₄₇	—	2	8	no	—
404	C₂×D₄₇	—	2	8	no	—
405	C₂×D₄₇	—	2	4	no	—
406	C₂×D₄₇	—	2	8	no	—
407	C₂×D₄₇	—	2	4	no	—
408	C₂×D₄₇	—	4	16	no	—
409	C₂×D₄₇	—	4	8	no	—
410	C₂×D₄₇	—	4	16	no	—
411	C₂×D₄₇	—	8	16	no	—
412	C₄×C₄₇	—	2	2	no	—
413	C₄×C₄₇	—	2	8	no	—
414	C₄×C₄₇	—	2	2	no	—
415	C₄×C₄₇	—	2	2	no	—
416	C₄×C₄₇	—	2	8	no	—
417	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
418	Dic₄₇	—	2	4	no	—
419	Dic₄₇	—	2	4	no	—
420	Dic₄₇	—	2	8	no	—
421	Dic₄₇	—	2	4	no	—
422	#3540	—	47	32	no	—
423	C₂×H(3,𝔽₄)	—	47	2	no	—
424	C₂×#560	—	47	2	no	—
425	C₂×#559	—	47	2	no	—
426	C₂×#556	—	47	2	no	—
427	C₂×#555	—	47	2	no	—
428	C₂×#551	—	47	2	no	—
429	C₂×#548	—	47	2	no	—
430	C₂×#546	—	47	2	no	—
431	C₂×#542	—	47	4	no	—
432	C₂×#542	—	47	2	no	—
433	C₂×#538	—	47	4	no	—
434	C₂×#536	D₄₇	1	1	yes	characteristic, complemented
435	C₂×#535	—	47	1	no	—
436	C₂×#525	—	47	1	no	—
437	C₂×#525	—	47	2	no	—
438	C₂×C₄₇	—	4	2	no	—
439	C₂×C₄₇	—	4	2	no	—
440	C₂×C₄₇	—	4	2	no	—
441	C₂×C₄₇	#3540	1	4	yes	complemented
442	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂×C₄₇	C₂×#585	1	2	yes	—
444	D₄₇	—	4	4	no	—
445	D₄₇	—	4	8	no	—
446	C₂²×#41	—	47	2	no	—
447	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
448	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
449	C₂³×D₄	—	47	1	no	—
450	C₂⁴×C₄	—	47	1	no	—
451	H(3,𝔽₄)	—	47	32	no	—
452	#560	—	47	32	no	—
453	#559	—	47	32	no	—
454	#556	—	47	32	no	—
455	#555	—	47	32	no	—
456	#551	—	47	32	no	—
457	#548	—	47	32	no	—
458	#546	—	47	32	no	—
459	#542	—	47	64	no	—
460	#542	—	47	32	no	—
461	#538	—	47	64	no	—
462	#536	C₂×D₄₇	1	16	yes	complemented
463	#535	—	47	16	no	—
464	C₂×C₄⋊Q₈	—	47	2	no	—
465	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	complemented
466	C₂×#127	—	47	2	no	—
467	C₂×#126	—	47	4	no	—
468	C₂×#126	—	47	4	no	—
469	C₂×#126	—	47	4	no	—
470	C₂×#124	—	47	2	no	—
471	C₂×#124	—	47	2	no	—
472	C₂×#124	—	47	4	no	—
473	C₂×#124	—	47	4	no	—
474	C₂×#124	—	47	4	no	—
475	C₂×#124	—	47	4	no	—
476	C₂×#124	—	47	4	no	—
477	C₂×#124	C₂×D₄₇	1	2	yes	—
478	#525	—	47	16	no	—
479	#525	—	47	32	no	—
480	C₂×#123	—	47	1	no	—
481	C₂×#123	—	47	1	no	—
482	C₂×#123	—	47	4	no	—
483	C₂×#123	—	47	4	no	—
484	C₂×#123	—	47	4	no	—
485	C₂×#123	C₂×D₄₇	1	2	yes	complemented
486	C₂×#123	C₂×D₄₇	1	2	yes	complemented
487	C₂×C₂²⋊Q₈	—	47	2	no	—
488	C₂×C₂²⋊Q₈	—	47	2	no	—
489	C₂×C₂²⋊Q₈	—	47	4	no	—
490	C₂×C₂²⋊Q₈	—	47	4	no	—
491	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
492	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
493	C₂×#121	—	47	2	no	—
494	C₂×#121	—	47	2	no	—
495	C₂×#121	—	47	2	no	—
496	C₂×#121	—	47	4	no	—
497	C₂×#121	—	47	2	no	—
498	C₂×#121	—	47	4	no	—
499	C₂×#121	—	47	4	no	—
500	C₂×#120	—	47	1	no	—
501	C₂×#120	—	47	1	no	—
502	C₂×#120	—	47	2	no	—
503	C₂×#120	—	47	2	no	—
504	C₂×#120	—	47	4	no	—
505	C₂×#120	—	47	4	no	—
506	C₂×C₄×Q₈	—	47	2	no	—
507	C₂×C₄×Q₈	—	47	4	no	—
508	C₂×C₄×D₄	—	47	2	no	—
509	C₂×C₄×D₄	—	47	2	no	—
510	C₂×C₄×D₄	—	47	4	no	—
511	C₂×C₄×D₄	—	47	4	no	—
512	C₂×C₄×D₄	—	47	2	no	—
513	C₂×C₄×D₄	—	47	4	no	—
514	C₂×#117	—	47	1	no	—
515	C₂×#117	—	47	1	no	—
516	C₂×#117	—	47	2	no	—
517	C₂×#117	—	47	4	no	—
518	C₂×#117	C₂×D₄₇	1	1	yes	characteristic, complemented
519	C₂²×C₂²⋊C₄	—	47	4	no	—
520	C₄₇	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
521	C₂⁵	—	47	2	no	—
522	C₂⁵	—	47	1	no	—
523	C₂×#41	—	4	4	no	—
524	C₂×#41	—	47	16	no	—
525	C₂×#41	—	188	8	no	—
526	C₂×#41	C₂²×D₄₇	1	8	yes	—
527	C₂²×Q₈	—	4	4	no	—
528	C₂²×Q₈	—	47	4	no	—
529	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
530	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
531	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
532	C₂²×Q₈	C₂²×D₄₇	1	8	yes	complemented
533	C₂²×D₄	—	47	2	no	—
534	C₂²×D₄	—	47	4	no	—
535	C₂²×D₄	—	47	2	no	—
536	C₂²×D₄	—	47	4	no	—
537	C₂²×D₄	—	47	2	no	—
538	C₂²×D₄	—	47	4	no	—
539	C₂²×D₄	—	47	4	no	—
540	C₂²×D₄	—	47	2	no	—
541	C₂²×D₄	—	47	8	no	—
542	C₂²×D₄	—	188	4	no	—
543	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
544	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
545	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
546	C₂³×C₄	—	47	1	no	—
547	C₂³×C₄	—	47	2	no	—
548	C₂³×C₄	—	47	4	no	—
549	C₂³×C₄	—	47	4	no	—
550	C₂³×C₄	—	47	2	no	—
551	C₂³×C₄	—	47	8	no	—
552	C₂³×C₄	—	188	4	no	—
553	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
554	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
555	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
556	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
557	C₄⋊Q₈	—	47	16	no	—
558	C₄⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
559	#127	—	47	16	no	—
560	#126	—	47	32	no	—
561	#126	—	47	32	no	—
562	#126	—	47	32	no	—
563	#124	—	47	16	no	—
564	#124	—	47	16	no	—
565	#124	—	47	32	no	—
566	#124	—	47	32	no	—
567	#124	—	47	32	no	—
568	#124	—	47	32	no	—
569	#124	—	47	32	no	—
570	#124	C₂²×D₄₇	1	16	yes	—
571	#123	—	47	8	no	—
572	#123	—	47	8	no	—
573	#123	—	47	32	no	—
574	#123	—	47	32	no	—
575	#123	—	47	32	no	—
576	#123	C₂²×D₄₇	1	16	yes	complemented
577	#123	C₂²×D₄₇	1	16	yes	complemented
578	C₂²⋊Q₈	—	47	16	no	—
579	C₂²⋊Q₈	—	47	16	no	—
580	C₂²⋊Q₈	—	47	32	no	—
581	C₂²⋊Q₈	—	47	32	no	—
582	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
583	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
584	#121	—	47	16	no	—
585	#121	—	47	16	no	—
586	#121	—	47	16	no	—
587	#121	—	47	32	no	—
588	#121	—	47	16	no	—
589	#121	—	47	32	no	—
590	#121	—	47	32	no	—
591	#120	—	47	8	no	—
592	#120	—	47	8	no	—
593	#120	—	47	16	no	—
594	#120	—	47	16	no	—
595	#120	—	47	32	no	—
596	#120	—	47	32	no	—
597	C₄×Q₈	—	47	16	no	—
598	C₄×Q₈	—	47	32	no	—
599	C₄×D₄	—	47	16	no	—
600	C₄×D₄	—	47	16	no	—
601	C₄×D₄	—	47	32	no	—
602	C₄×D₄	—	47	32	no	—
603	C₄×D₄	—	47	16	no	—
604	C₄×D₄	—	47	32	no	—
605	#117	—	47	8	no	—
606	#117	—	47	8	no	—
607	#117	—	47	16	no	—
608	#117	—	47	32	no	—
609	#117	C₂²×D₄₇	1	8	yes	complemented
610	C₂×C₄⋊C₄	—	47	2	no	—
611	C₂×C₄⋊C₄	—	47	2	no	—
612	C₂×C₄⋊C₄	—	47	2	no	—
613	C₂×C₄⋊C₄	—	47	4	no	—
614	C₂×C₄⋊C₄	—	47	4	no	—
615	C₂×C₄⋊C₄	—	47	2	no	—
616	C₂×C₄⋊C₄	—	47	4	no	—
617	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
619	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
620	C₂×C₂²⋊C₄	—	47	2	no	—
621	C₂×C₂²⋊C₄	—	47	2	no	—
622	C₂×C₂²⋊C₄	—	47	1	no	—
623	C₂×C₂²⋊C₄	—	47	1	no	—
624	C₂×C₂²⋊C₄	—	47	2	no	—
625	C₂×C₂²⋊C₄	—	47	4	no	—
626	C₂×C₂²⋊C₄	—	47	4	no	—
627	C₂×C₂²⋊C₄	—	47	4	no	—
628	C₂×C₂²⋊C₄	—	47	4	no	—
629	C₂×C₂²⋊C₄	—	47	2	no	—
630	C₂×C₂²⋊C₄	—	47	4	no	—
631	C₂×C₂²⋊C₄	—	47	4	no	—
632	C₂×C₂²⋊C₄	—	47	4	no	—
633	C₂×C₂²⋊C₄	—	47	2	no	—
634	C₂×C₂²⋊C₄	—	47	4	no	—
635	C₂×C₂²⋊C₄	—	47	32	no	—
636	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
639	C₂×C₄²	—	47	4	no	—
640	C₂×C₄²	—	47	2	no	—
641	C₂×C₄²	—	47	2	no	—
642	C₂×C₄²	—	47	4	no	—
643	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
644	C₂⁴	—	47	2	no	—
645	C₂⁴	—	47	4	no	—
646	C₂⁴	—	47	8	no	—
647	C₂⁴	—	47	4	no	—
648	C₂⁴	—	188	4	no	—
649	C₂⁴	—	188	8	no	—
650	C₂⁴	—	188	2	no	—
651	C₂⁴	—	188	4	no	—
652	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
653	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
654	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
655	#41	—	4	16	no	—
656	#41	—	188	32	no	—
657	C₂×Q₈	—	2	8	no	—
658	C₂×Q₈	—	4	4	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	16	no	—
661	C₂×Q₈	—	47	16	no	—
662	C₂×Q₈	—	188	8	no	—
663	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
664	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
665	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	47	8	no	—
670	C₂×D₄	—	47	16	no	—
671	C₂×D₄	—	47	8	no	—
672	C₂×D₄	—	47	16	no	—
673	C₂×D₄	—	47	8	no	—
674	C₂×D₄	—	47	16	no	—
675	C₂×D₄	—	47	16	no	—
676	C₂×D₄	—	47	8	no	—
677	C₂×D₄	—	94	8	no	—
678	C₂×D₄	—	188	16	no	—
679	C₂×D₄	—	188	8	no	—
680	C₂×D₄	—	188	4	no	—
681	C₂×D₄	—	188	8	no	—
682	C₂×D₄	—	188	4	no	—
683	C₂×D₄	—	188	8	no	—
684	C₂×D₄	—	188	8	no	—
685	C₂×D₄	—	188	4	no	—
686	C₂×D₄	C₂³×D₄₇	1	4	yes	—
687	C₂×D₄	C₂³×D₄₇	1	4	yes	—
688	C₂×D₄	C₂³×D₄₇	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	4	4	no	—
693	C₂²×C₄	—	47	2	no	—
694	C₂²×C₄	—	47	4	no	—
695	C₂²×C₄	—	47	2	no	—
696	C₂²×C₄	—	47	2	no	—
697	C₂²×C₄	—	47	4	no	—
698	C₂²×C₄	—	47	8	no	—
699	C₂²×C₄	—	47	16	no	—
700	C₂²×C₄	—	47	16	no	—
701	C₂²×C₄	—	47	8	no	—
702	C₂²×C₄	—	94	8	no	—
703	C₂²×C₄	—	188	16	no	—
704	C₂²×C₄	—	188	8	no	—
705	C₂²×C₄	—	188	4	no	—
706	C₂²×C₄	—	188	8	no	—
707	C₂²×C₄	—	188	2	no	—
708	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
709	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
710	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
711	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
712	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
713	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
714	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
715	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
716	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
717	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
718	C₄⋊C₄	—	47	8	no	—
719	C₄⋊C₄	—	47	16	no	—
720	C₄⋊C₄	—	47	16	no	—
721	C₄⋊C₄	—	47	8	no	—
722	C₄⋊C₄	—	47	8	no	—
723	C₄⋊C₄	—	47	8	no	—
724	C₄⋊C₄	—	47	16	no	—
725	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
726	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
727	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
728	C₂²⋊C₄	—	47	8	no	—
729	C₂²⋊C₄	—	47	8	no	—
730	C₂²⋊C₄	—	47	4	no	—
731	C₂²⋊C₄	—	47	4	no	—
732	C₂²⋊C₄	—	47	8	no	—
733	C₂²⋊C₄	—	47	16	no	—
734	C₂²⋊C₄	—	47	16	no	—
735	C₂²⋊C₄	—	47	16	no	—
736	C₂²⋊C₄	—	47	16	no	—
737	C₂²⋊C₄	—	47	8	no	—
738	C₂²⋊C₄	—	47	16	no	—
739	C₂²⋊C₄	—	47	16	no	—
740	C₂²⋊C₄	—	47	16	no	—
741	C₂²⋊C₄	—	47	8	no	—
742	C₂²⋊C₄	—	47	16	no	—
743	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
744	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
745	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
746	C₄²	—	47	16	no	—
747	C₄²	—	47	8	no	—
748	C₄²	—	47	8	no	—
749	C₄²	—	47	16	no	—
750	C₄²	C₂³×D₄₇	1	8	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	47	4	no	—
758	C₂³	—	47	8	no	—
759	C₂³	—	94	4	no	—
760	C₂³	—	94	8	no	—
761	C₂³	—	94	8	no	—
762	C₂³	—	94	8	no	—
763	C₂³	—	94	4	no	—
764	C₂³	—	94	4	no	—
765	C₂³	—	376	16	no	—
766	C₂³	—	188	8	no	—
767	C₂³	—	188	16	no	—
768	C₂³	—	188	4	no	—
769	C₂³	—	188	8	no	—
770	C₂³	—	188	16	no	—
771	C₂³	C₂⁴×D₄₇	1	2	yes	—
772	C₂³	C₂⁴×D₄₇	1	2	yes	—
773	C₂³	C₂⁴×D₄₇	1	2	yes	—
774	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
775	Q₈	—	2	16	no	—
776	Q₈	—	4	8	no	—
777	Q₈	—	4	4	no	—
778	Q₈	—	188	16	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	94	16	no	—
783	D₄	—	188	16	no	—
784	D₄	—	188	8	no	—
785	D₄	—	188	16	no	—
786	D₄	—	188	8	no	—
787	D₄	—	188	16	no	—
788	D₄	—	188	16	no	—
789	D₄	—	188	8	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	47	4	no	—
800	C₂×C₄	—	47	8	no	—
801	C₂×C₄	—	47	4	no	—
802	C₂×C₄	—	47	4	no	—
803	C₂×C₄	—	94	4	no	—
804	C₂×C₄	—	94	4	no	—
805	C₂×C₄	—	94	8	no	—
806	C₂×C₄	—	94	4	no	—
807	C₂×C₄	—	94	16	no	—
808	C₂×C₄	—	188	16	no	—
809	C₂×C₄	—	188	8	no	—
810	C₂×C₄	—	188	16	no	—
811	C₂×C₄	—	188	4	no	—
812	C₂×C₄	#13094069	1	4	yes	—
813	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
814	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
815	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
816	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
817	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
818	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	4	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	94	4	no	—
829	C₂²	—	94	8	no	—
830	C₂²	—	94	8	no	—
831	C₂²	—	94	8	no	—
832	C₂²	—	94	4	no	—
833	C₂²	—	94	4	no	—
834	C₂²	—	376	16	no	—
835	C₂²	—	188	16	no	—
836	C₂²	—	188	16	no	—
837	C₂²	—	188	8	no	—
838	C₂²	C₂×#13094069	1	2	yes	—
839	C₂²	#15689960	1	4	yes	—
840	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	8	no	—
845	C₄	—	2	8	no	—
846	C₄	—	94	4	no	—
847	C₄	—	94	4	no	—
848	C₄	—	94	8	no	—
849	C₄	—	94	4	no	—
850	C₄	C₂×#13094069	1	4	yes	—
851	C₂	—	4	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	2	no	—
854	C₂	—	188	8	no	—
855	C₂	—	188	4	no	—
856	C₂	#20257665	1	4	yes	direct product factor
857	C₂	C₂²×#13094069	1	1	yes	characteristic
858	C₂	C₂×#15689960	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#536	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#536	D₄₇
hypocenter	C₄₇	C₂×#3540
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#536

Complements

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

N	H ≅ G/N	type
1. #20257665	C₂	direct (N × H)
2. C₂×#15689865	C₂	semidirect
3. C₂×#15689863	C₂	semidirect
4. C₂×#15689857	C₂	semidirect
5. C₂×#15689844	C₂	semidirect
6. C₂×#15689836	C₂	semidirect
7. C₂×#15689803	C₂	semidirect
8. C₂×#15689784	C₂	semidirect
9. C₂×#15689764	C₂	semidirect
10. C₂×#15689747	C₂	semidirect
11. C₂×#15689746	C₂	semidirect
12. C₂×#15689709	C₂	semidirect
13. C₂×#15689687	C₂	semidirect
14. C₂×#15689636	C₂	semidirect
15. C₂×#15689630	C₂	semidirect
16. C₂×C₄₇×#536	C₂	semidirect
18. C₂³×D₁₈₈	C₂²	semidirect
19. C₂³×C₄×D₄₇	C₂²	semidirect
20. #15689865	C₂²	semidirect
21. #15689863	C₂²	semidirect
22. #15689857	C₂²	semidirect
23. #15689844	C₂²	semidirect
24. #15689836	C₂²	semidirect
25. #15689803	C₂²	semidirect
26. #15689784	C₂²	semidirect
27. #15689764	C₂²	semidirect
28. #15689747	C₂²	semidirect
29. #15689746	C₂²	semidirect
30. #15689709	C₂²	semidirect
31. #15689687	C₂²	semidirect
32. C₂×#13094023	C₂²	semidirect
34. C₂×#13094019	C₂²	semidirect
35. C₂×#13094019	C₂²	semidirect
36. C₂×#13094017	C₂²	semidirect
37. C₂×#13094013	C₂²	semidirect
38. C₂×#13094013	C₂²	semidirect
39. C₂×#13094013	C₂²	semidirect
40. C₂×#13094012	C₂²	semidirect
42. C₂×#13094010	C₂²	semidirect
43. C₂×#13094010	C₂²	semidirect
44. #15689636	C₂²	semidirect
45. #15689630	C₂²	semidirect
46. C₂×#13094009	C₂²	semidirect
47. C₂×#13094009	C₂²	semidirect
48. C₂×#13094006	C₂²	semidirect
50. C₂×#13094005	C₂²	semidirect
51. C₂×#13094004	C₂²	semidirect
52. C₂×#13094000	C₂²	semidirect
53. C₂×#13094000	C₂²	semidirect
54. C₂×#13094000	C₂²	semidirect
58. C₂×#13093998	C₂²	semidirect
59. C₂×#13093998	C₂²	semidirect
60. C₂×#13093997	C₂²	semidirect
63. C₂×#13093994	C₂²	semidirect
66. C₂×#13093992	C₂²	semidirect
67. C₂×#13093992	C₂²	semidirect
68. C₂×Q₈×Dic₄₇	C₂²	semidirect
69. C₂×#13093989	C₂²	semidirect
70. C₂×#13093986	C₂²	semidirect
71. C₂×#13093986	C₂²	semidirect
73. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
75. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
76. C₂×#13093983	C₂²	semidirect
77. C₂×#13093983	C₂²	semidirect
78. C₂×#13093982	C₂²	semidirect
79. C₂×#13093981	C₂²	semidirect
80. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
82. C₂³×Q₈×C₄₇	C₂²	semidirect
83. C₄₇×#536	C₂²	semidirect
84. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
86. C₂×#123×C₄₇	C₂²	semidirect
87. C₂×#123×C₄₇	C₂²	semidirect
88. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
89. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
90. C₂×#117×C₄₇	C₂²	semidirect
101. C₂²×D₁₈₈	C₂³	semidirect
112. C₂²×C₄×D₄₇	C₂³	semidirect
113. #13094023	C₂³	semidirect
115. #13094019	C₂³	semidirect
116. #13094019	C₂³	semidirect
117. #13094017	C₂³	semidirect
118. #13094013	C₂³	semidirect
119. #13094013	C₂³	semidirect
120. #13094013	C₂³	semidirect
121. #13094012	C₂³	semidirect
123. #13094010	C₂³	semidirect
124. #13094010	C₂³	semidirect
125. #13094009	C₂³	semidirect
126. #13094009	C₂³	semidirect
127. #13094006	C₂³	semidirect
129. #13094005	C₂³	semidirect
130. #13094004	C₂³	semidirect
131. #13094000	C₂³	semidirect
132. #13094000	C₂³	semidirect
133. #13094000	C₂³	semidirect
137. #13093998	C₂³	semidirect
138. #13093998	C₂³	semidirect
139. #13093997	C₂³	semidirect
142. #13093994	C₂³	semidirect
145. #13093992	C₂³	semidirect
146. #13093992	C₂³	semidirect
147. Q₈×Dic₄₇	C₂³	semidirect
148. #13093989	C₂³	semidirect
149. #13093986	C₂³	semidirect
150. #13093986	C₂³	semidirect
152. C₄×C₂²⋊D₄₇	C₂³	semidirect
153. C₄×C₂²⋊D₄₇	C₂³	semidirect
154. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
155. #13093983	C₂³	semidirect
156. #13093983	C₂³	semidirect
157. #13093982	C₂³	semidirect
158. #13093981	C₂³	semidirect
181. C₂²⋊C₄×D₄₇	C₂³	semidirect
192. C₂²×Q₈×C₄₇	C₂³	semidirect
200. C₄⋊Q₈×C₄₇	C₂³	semidirect
202. #123×C₄₇	C₂³	semidirect
203. #123×C₄₇	C₂³	semidirect
204. C₂²⋊Q₈×C₄₇	C₂³	semidirect
205. C₂²⋊Q₈×C₄₇	C₂³	semidirect
206. #117×C₄₇	C₂³	semidirect
434. C₂×#536	D₄₇	semidirect
441. C₂×C₄₇	#3540	semidirect
448. C₂³×Q₈	C₂×D₄₇	semidirect
462. #536	C₂×D₄₇	semidirect
465. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
485. C₂×#123	C₂×D₄₇	semidirect
486. C₂×#123	C₂×D₄₇	semidirect
491. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
492. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
518. C₂×#117	C₂×D₄₇	semidirect
520. C₄₇	C₂×#3540	semidirect
532. C₂²×Q₈	C₂²×D₄₇	semidirect
558. C₄⋊Q₈	C₂²×D₄₇	semidirect
576. #123	C₂²×D₄₇	semidirect
577. #123	C₂²×D₄₇	semidirect
582. C₂²⋊Q₈	C₂²×D₄₇	semidirect
583. C₂²⋊Q₈	C₂²×D₄₇	semidirect
609. #117	C₂²×D₄₇	semidirect
856. C₂	#20257665	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257665	2
C₂×#15689865	2
C₂×#15689863	2
C₂×#15689857	2
C₂×#15689844	2
C₂×#15689836	2
C₂×#15689803	2
C₂×#15689784	2
C₂×#15689764	2
C₂×#15689747	2
C₂×#15689746	2
C₂×#15689709	2
C₂×#15689687	2
C₂×#15689636	2
C₂×#15689630	2
C₂×C₄₇×#536	2
C₂×#3540	47

Subgroups — C2×#20257665 #27123571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257665 #27123571