Subgroups — C₂×#20257960 #27123629

Order 12032.

7258 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257960	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689873	C₂	1	2	yes	maximal, complemented
3	C₂×#15689867	C₂	1	2	yes	maximal, complemented
4	C₂×#15689842	C₂	1	2	yes	maximal, complemented
5	C₂×#15689799	C₂	1	4	yes	maximal, complemented
6	C₂×Q₈×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
7	C₂×#15689781	C₂	1	2	yes	maximal, complemented
8	C₂×#15689767	C₂	1	2	yes	maximal, complemented
9	C₂×#15689749	C₂	1	2	yes	maximal, complemented
10	C₂×#15689742	C₂	1	2	yes	maximal, complemented
11	C₂×#15689737	C₂	1	4	yes	maximal, complemented
12	C₂×#15689711	C₂	1	2	yes	maximal, complemented
13	C₂×#15689693	C₂	1	2	yes	maximal, complemented
14	C₂×#15689680	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15689657	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#124×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#10625352	C₂²	1	2	yes	—
18	C₂²×Q₈×D₄₇	C₂²	1	2	yes	complemented
19	#15689873	C₂²	1	32	yes	complemented
20	#15689867	C₂²	1	32	yes	complemented
21	#15689842	C₂²	1	32	yes	complemented
22	#15689799	C₂²	1	64	yes	complemented
23	Q₈×C₂²⋊D₄₇	C₂²	1	32	yes	complemented
24	#15689781	C₂²	1	32	yes	complemented
25	#15689767	C₂²	1	32	yes	complemented
26	#15689749	C₂²	1	32	yes	complemented
27	#15689742	C₂²	1	32	yes	complemented
28	#15689737	C₂²	1	64	yes	complemented
29	#15689711	C₂²	1	32	yes	complemented
30	#15689693	C₂²	1	32	yes	complemented
31	#15689680	C₂²	1	16	yes	complemented
32	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13094022	C₂²	1	2	yes	complemented
35	C₂×#13094022	C₂²	1	4	yes	complemented
36	#15689657	C₂²	1	16	yes	complemented
37	C₂×#13094018	C₂²	1	2	yes	complemented
38	C₂×#13094017	C₂²	1	4	yes	complemented
39	C₂×#13094017	C₂²	1	4	yes	complemented
40	C₂×#13094017	C₂²	1	4	yes	complemented
41	C₂×#13094016	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13094016	C₂²	1	2	yes	complemented
43	C₂×#13094012	C₂²	1	1	yes	characteristic, complemented
44	C₂×#13094011	C₂²	1	2	yes	—
45	C₂×#13094010	C₂²	1	4	yes	complemented
46	C₂×#13094010	C₂²	1	4	yes	complemented
47	C₂×#13094008	C₂²	1	4	yes	complemented
48	C₂×#13094007	C₂²	1	2	yes	—
49	C₂×#13094006	C₂²	1	4	yes	complemented
50	C₂×#13094006	C₂²	1	4	yes	complemented
51	C₂×#13094005	C₂²	1	4	yes	—
52	C₂×#13094003	C₂²	1	1	yes	characteristic
53	C₂×#13094003	C₂²	1	4	yes	—
54	C₂×#13094003	C₂²	1	2	yes	—
55	C₂×#13094003	C₂²	1	2	yes	—
56	C₂×#13094001	C₂²	1	4	yes	complemented
57	C₂×#13094001	C₂²	1	4	yes	complemented
58	C₂×#13094001	C₂²	1	4	yes	complemented
59	C₂×#13094001	C₂²	1	4	yes	complemented
60	C₂×#13094001	C₂²	1	4	yes	complemented
61	C₂×#13094000	C₂²	1	2	yes	complemented
62	C₂×#13094000	C₂²	1	4	yes	complemented
63	C₂×#13093998	C₂²	1	1	yes	characteristic
64	C₂×#13093997	C₂²	1	4	yes	complemented
65	C₂×#13093996	C₂²	1	4	yes	—
66	C₂×#13093995	C₂²	1	2	yes	—
67	C₂×#13093993	C₂²	1	4	yes	—
68	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
69	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
70	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
72	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
73	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
74	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
75	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
76	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
77	C₂×#13093983	C₂²	1	2	yes	—
78	C₂×#13093981	C₂²	1	2	yes	complemented
79	C₂×#13093980	C₂²	1	4	yes	complemented
80	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
81	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
82	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
83	C₂×#124×C₄₇	C₂²	1	2	yes	—
84	C₂×#124×C₄₇	C₂²	1	2	yes	—
85	C₂×#124×C₄₇	C₂²	1	2	yes	—
86	C₂×#124×C₄₇	C₂²	1	2	yes	—
87	C₂×#124×C₄₇	C₂²	1	16	yes	complemented
88	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
89	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
90	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
91	C₂×#10625352	—	4	8	no	—
92	C₂×#10625352	C₂³	1	16	yes	—
93	C₂²×Dic₉₄	C₂³	1	2	yes	—
94	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
95	C₂²×Dic₉₄	C₂³	1	2	yes	—
96	C₂²×Dic₉₄	C₂³	1	4	yes	—
97	C₂×Q₈×D₄₇	—	4	8	no	—
98	C₂×Q₈×D₄₇	C₂³	1	16	yes	complemented
99	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
100	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
101	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
102	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
103	C₂³×Dic₄₇	C₂³	1	4	yes	—
104	C₂³×Dic₄₇	C₂³	1	4	yes	—
105	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
106	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
107	#13094024	C₂³	1	8	yes	complemented
108	#13094024	C₂³	1	8	yes	complemented
109	#13094022	C₂³	1	32	yes	complemented
110	#13094022	C₂³	1	16	yes	complemented
111	#13094018	C₂³	1	16	yes	complemented
112	#13094017	C₂³	1	32	yes	complemented
113	#13094017	C₂³	1	32	yes	complemented
114	#13094017	C₂³	1	32	yes	complemented
115	#13094016	C₂³	1	16	yes	complemented
116	#13094016	C₂³	1	8	yes	complemented
117	#13094012	C₂³	1	8	yes	complemented
118	#13094011	C₂³	1	16	yes	—
119	#13094010	C₂³	1	32	yes	complemented
120	#13094010	C₂³	1	32	yes	complemented
121	#13094008	C₂³	1	32	yes	complemented
122	#13094007	C₂³	1	16	yes	—
123	#13094006	C₂³	1	32	yes	complemented
124	#13094006	C₂³	1	32	yes	complemented
125	#13094005	C₂³	1	32	yes	—
126	#13094003	C₂³	1	8	yes	—
127	#13094003	C₂³	1	32	yes	—
128	#13094003	C₂³	1	16	yes	—
129	#13094003	C₂³	1	16	yes	—
130	#13094001	C₂³	1	32	yes	complemented
131	#13094001	C₂³	1	32	yes	complemented
132	#13094001	C₂³	1	32	yes	complemented
133	#13094001	C₂³	1	32	yes	complemented
134	#13094001	C₂³	1	32	yes	complemented
135	#13094000	C₂³	1	32	yes	complemented
136	#13094000	C₂³	1	16	yes	complemented
137	#13093998	C₂³	1	8	yes	—
138	#13093997	C₂³	1	32	yes	complemented
139	#13093996	C₂³	1	32	yes	—
140	#13093995	C₂³	1	16	yes	—
141	#13093993	C₂³	1	32	yes	—
142	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
143	C₄×Dic₉₄	C₂³	1	16	yes	complemented
144	C₄×Dic₉₄	C₂³	1	16	yes	complemented
145	C₄×Dic₉₄	C₂³	1	8	yes	complemented
146	C₄×D₁₈₈	C₂³	1	8	yes	complemented
147	D₄×Dic₄₇	C₂³	1	16	yes	—
148	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
149	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
150	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
151	#13093983	C₂³	1	16	yes	—
152	#13093981	C₂³	1	16	yes	complemented
153	#13093980	C₂³	1	32	yes	complemented
154	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
155	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
156	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
157	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
160	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
161	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
162	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
163	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
164	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
165	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
166	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
167	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
168	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
169	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
170	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	—
171	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
173	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
174	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
175	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
176	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
177	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
178	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
179	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
180	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
181	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
182	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
183	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
184	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
185	C₂⁵×C₄₇	C₂³	1	2	yes	—
186	C₂²×Q₈×C₄₇	—	4	4	no	—
187	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
188	C₂²×Q₈×C₄₇	C₂³	1	8	yes	—
189	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
190	C₂²×D₄×C₄₇	—	4	4	no	—
191	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
192	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
193	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
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	#124×C₄₇	C₂³	1	16	yes	—
199	#124×C₄₇	C₂³	1	16	yes	—
200	#124×C₄₇	C₂³	1	16	yes	—
201	#124×C₄₇	C₂³	1	16	yes	—
202	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
203	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
204	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
206	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
207	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
208	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
213	C₂⁴×C₄₇	—	2	8	no	—
214	C₂⁴×C₄₇	—	4	4	no	—
215	C₂⁴×C₄₇	—	4	4	no	—
216	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
217	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
219	C₂³×D₄₇	C₂⁴	1	2	yes	—
220	C₂×Q₈×C₄₇	—	2	8	no	—
221	C₂×Q₈×C₄₇	—	4	4	no	—
222	C₂×Q₈×C₄₇	—	4	16	no	—
223	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
224	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
225	C₂×D₄×C₄₇	—	2	8	no	—
226	C₂×D₄×C₄₇	—	4	16	no	—
227	C₂×D₄×C₄₇	—	4	4	no	—
228	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
229	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
230	C₂²×C₄×C₄₇	—	2	4	no	—
231	C₂²×C₄×C₄₇	—	2	4	no	—
232	C₂²×C₄×C₄₇	—	4	2	no	—
233	C₂²×C₄×C₄₇	—	4	4	no	—
234	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
244	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₂²⋊D₄₇	—	2	8	no	—
246	C₂×C₂²⋊D₄₇	—	4	8	no	—
247	C₂×C₂²⋊D₄₇	—	4	8	no	—
248	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
249	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
250	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
251	C₂²×Dic₄₇	—	4	8	no	—
252	C₂²×Dic₄₇	—	4	8	no	—
253	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
254	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
255	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
256	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
257	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
258	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
259	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
260	Q₈×D₄₇	—	4	32	no	—
261	#10625352	—	4	32	no	—
262	C₂×D₁₈₈	—	4	2	no	—
263	C₂×D₁₈₈	C₂⁴	1	4	yes	—
264	C₂×C₄×D₄₇	—	2	8	no	—
265	C₂×C₄×D₄₇	—	4	8	no	—
266	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
267	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
268	C₂×Dic₉₄	—	2	8	no	—
269	C₂×Dic₉₄	—	4	8	no	—
270	C₂×Dic₉₄	—	4	2	no	—
271	C₂×Dic₉₄	—	4	4	no	—
272	C₂×Dic₉₄	C₂⁴	1	8	yes	—
273	C₂×Dic₉₄	C₂⁴	1	4	yes	—
274	C₂×Dic₉₄	C₂⁴	1	8	yes	—
275	C₂×Dic₉₄	C₂⁴	1	16	yes	—
276	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
277	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
278	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
279	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
280	C₄²×C₄₇	C₂⁴	1	4	yes	—
281	C₄²×C₄₇	C₂⁴	1	4	yes	—
282	C₄²×C₄₇	C₂⁴	1	4	yes	—
283	C₄²×C₄₇	C₂⁴	1	4	yes	—
284	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
285	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
286	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
287	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
288	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
289	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
290	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
291	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
292	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
293	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
294	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
295	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
296	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
297	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
298	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
299	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
300	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
301	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
302	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
303	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
304	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
305	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
306	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
307	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
308	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
309	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
310	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
311	C₄×Dic₄₇	C₂⁴	1	16	yes	—
312	C₄×Dic₄₇	C₂⁴	1	16	yes	—
313	C₄×Dic₄₇	C₂⁴	1	8	yes	—
314	C₂³×C₄₇	—	2	2	no	—
315	C₂³×C₄₇	—	2	2	no	—
316	C₂³×C₄₇	—	2	8	no	—
317	C₂³×C₄₇	—	2	8	no	—
318	C₂³×C₄₇	—	2	8	no	—
319	C₂³×C₄₇	—	2	16	no	—
320	C₂³×C₄₇	—	4	8	no	—
321	C₂³×C₄₇	—	4	8	no	—
322	C₂³×C₄₇	—	8	16	no	—
323	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
324	C₂³×C₄₇	C₂⁵	1	8	yes	—
325	C₂³×C₄₇	C₂⁵	1	2	yes	—
326	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
327	C₂²×D₄₇	—	2	4	no	—
328	C₂²×D₄₇	—	2	4	no	—
329	C₂²×D₄₇	—	2	4	no	—
330	C₂²×D₄₇	C₂⁵	1	4	yes	—
331	Q₈×C₄₇	—	2	16	no	—
332	Q₈×C₄₇	—	4	8	no	—
333	D₄×C₄₇	—	2	16	no	—
334	D₄×C₄₇	—	4	8	no	—
335	C₂×C₄×C₄₇	—	2	8	no	—
336	C₂×C₄×C₄₇	—	2	2	no	—
337	C₂×C₄×C₄₇	—	2	8	no	—
338	C₂×C₄×C₄₇	—	2	2	no	—
339	C₂×C₄×C₄₇	—	2	2	no	—
340	C₂×C₄×C₄₇	—	2	2	no	—
341	C₂×C₄×C₄₇	—	2	2	no	—
342	C₂×C₄×C₄₇	—	2	8	no	—
343	C₂×C₄×C₄₇	—	4	4	no	—
344	C₂×C₄×C₄₇	—	4	8	no	—
345	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
346	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
347	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
348	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
349	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
350	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
351	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
352	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
353	C₂²⋊D₄₇	—	2	16	no	—
354	C₂²⋊D₄₇	—	4	16	no	—
355	C₂²⋊D₄₇	—	4	16	no	—
356	C₂×Dic₄₇	—	2	8	no	—
357	C₂×Dic₄₇	—	2	4	no	—
358	C₂×Dic₄₇	—	2	4	no	—
359	C₂×Dic₄₇	—	2	4	no	—
360	C₂×Dic₄₇	—	2	8	no	—
361	C₂×Dic₄₇	—	4	16	no	—
362	C₂×Dic₄₇	—	4	16	no	—
363	C₂×Dic₄₇	C₂⁵	1	4	yes	—
364	C₂×Dic₄₇	C₂⁵	1	8	yes	—
365	C₂×Dic₄₇	C₂⁵	1	4	yes	—
366	C₂×Dic₄₇	C₂⁵	1	8	yes	—
367	C₂×Dic₄₇	C₂⁵	1	4	yes	—
368	D₁₈₈	—	4	4	no	—
369	C₄×D₄₇	—	2	16	no	—
370	C₄×D₄₇	—	4	16	no	—
371	Dic₉₄	—	2	16	no	—
372	Dic₉₄	—	4	4	no	—
373	Dic₉₄	—	4	8	no	—
374	Dic₉₄	—	4	16	no	—
375	C₂×#3561	—	47	1	no	maximal, Sylow
376	C₂²×C₄₇	—	2	2	no	—
377	C₂²×C₄₇	—	2	2	no	—
378	C₂²×C₄₇	—	2	8	no	—
379	C₂²×C₄₇	—	2	8	no	—
380	C₂²×C₄₇	—	2	8	no	—
381	C₂²×C₄₇	—	2	8	no	—
382	C₂²×C₄₇	—	4	16	no	—
383	C₂²×C₄₇	—	8	16	no	—
384	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
385	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
386	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
387	C₂²×C₄₇	#585	1	2	yes	—
388	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
389	C₂×D₄₇	—	2	4	no	—
390	C₂×D₄₇	—	2	4	no	—
391	C₂×D₄₇	—	2	4	no	—
392	C₂×D₄₇	—	4	8	no	—
393	C₄×C₄₇	—	2	8	no	—
394	C₄×C₄₇	—	2	2	no	—
395	C₄×C₄₇	—	2	2	no	—
396	C₄×C₄₇	—	2	2	no	—
397	C₄×C₄₇	—	2	2	no	—
398	C₄×C₄₇	—	2	2	no	—
399	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
400	Dic₄₇	—	2	8	no	—
401	Dic₄₇	—	2	4	no	—
402	Dic₄₇	—	2	4	no	—
403	Dic₄₇	—	2	4	no	—
404	Dic₄₇	—	2	8	no	—
405	#3561	—	47	32	no	—
406	C₂×#563	—	47	2	no	—
407	C₂×#562	—	47	2	no	—
408	C₂×#556	—	47	2	no	—
409	C₂×#551	—	47	4	no	—
410	C₂×D₄×Q₈	—	47	2	no	—
411	C₂×#548	—	47	2	no	—
412	C₂×#546	—	47	2	no	—
413	C₂×#543	—	47	2	no	—
414	C₂×#542	—	47	4	no	—
415	C₂×#542	—	47	2	no	—
416	C₂×#538	—	47	2	no	—
417	C₂×#536	—	47	2	no	—
418	C₂×#533	—	47	1	no	—
419	C₂×#529	—	47	1	no	—
420	C₂²×#124	D₄₇	1	1	yes	characteristic, complemented
421	C₂×C₄₇	—	2	4	no	—
422	C₂×C₄₇	—	4	8	no	—
423	C₂×C₄₇	#3561	1	4	yes	complemented
424	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
427	D₄₇	—	4	4	no	—
428	C₂²×#41	—	47	2	no	—
429	C₂³×Q₈	—	47	2	no	—
430	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
431	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
432	#563	—	47	32	no	—
433	#562	—	47	32	no	—
434	#556	—	47	32	no	—
435	#551	—	47	64	no	—
436	D₄×Q₈	—	47	32	no	—
437	#548	—	47	32	no	—
438	#546	—	47	32	no	—
439	#543	—	47	32	no	—
440	#542	—	47	64	no	—
441	#542	—	47	32	no	—
442	#538	—	47	32	no	—
443	#536	—	47	32	no	—
444	#533	—	47	16	no	—
445	C₂×C₄⋊Q₈	—	47	2	no	—
446	C₂×C₄⋊Q₈	—	47	4	no	—
447	C₂×C₄⋊Q₈	—	47	1	no	—
448	C₂×C₄⋊Q₈	—	47	1	no	—
449	#529	—	47	16	no	—
450	C₂×#126	—	47	4	no	—
451	C₂×#126	—	47	4	no	—
452	C₂×#126	—	47	4	no	—
453	C₂×#126	—	47	2	no	—
454	C₂×#125	—	47	1	no	—
455	C₂×#125	—	47	2	no	—
456	C₂×#124	—	47	2	no	—
457	C₂×#124	—	47	4	no	—
458	C₂×#124	—	47	4	no	—
459	C₂×#124	—	47	1	no	—
460	C₂×#124	C₂×D₄₇	1	2	yes	—
461	C₂×#124	C₂×D₄₇	1	2	yes	—
462	C₂×#124	C₂×D₄₇	1	2	yes	—
463	C₂×#124	C₂×D₄₇	1	2	yes	—
464	C₂×#124	C₂×D₄₇	1	16	yes	complemented
465	C₂×#123	—	47	4	no	—
466	C₂×#123	—	47	2	no	—
467	C₂×#123	—	47	4	no	—
468	C₂×#123	—	47	4	no	—
469	C₂×#123	—	47	4	no	—
470	C₂×C₂²⋊Q₈	—	47	2	no	—
471	C₂×C₂²⋊Q₈	—	47	4	no	—
472	C₂×C₂²⋊Q₈	—	47	1	no	—
473	C₂×C₂²⋊Q₈	—	47	2	no	—
474	C₂×C₂²⋊Q₈	—	47	2	no	—
475	C₂×C₂²⋊Q₈	—	47	4	no	—
476	C₂×C₂²⋊Q₈	—	47	4	no	—
477	C₂×C₂²⋊Q₈	—	47	4	no	—
478	C₂×C₂²⋊Q₈	—	47	4	no	—
479	C₂×C₂²⋊Q₈	—	47	4	no	—
480	C₂×C₂²⋊Q₈	—	47	4	no	—
481	C₂×#121	—	47	2	no	—
482	C₂×#121	—	47	4	no	—
483	C₂×#121	—	47	1	no	—
484	C₂×#121	—	47	4	no	—
485	C₂×#120	—	47	4	no	—
486	C₂×C₄×Q₈	—	47	2	no	—
487	C₂×C₄×Q₈	—	47	1	no	—
488	C₂×C₄×Q₈	—	47	2	no	—
489	C₂×C₄×Q₈	—	47	2	no	—
490	C₂×C₄×D₄	—	47	2	no	—
491	C₂×C₄×D₄	—	47	2	no	—
492	C₂×C₄×D₄	—	47	4	no	—
493	C₂×C₄×D₄	—	47	4	no	—
494	C₂×C₄×D₄	—	47	1	no	—
495	C₂×#117	—	47	2	no	—
496	C₂×#117	—	47	4	no	—
497	C₂×#117	—	47	2	no	—
498	C₂²×C₂²⋊C₄	—	47	4	no	—
499	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
500	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
501	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
502	C₄₇	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
503	C₂⁵	C₂²×D₄₇	1	2	yes	—
504	C₂×#41	—	47	16	no	—
505	C₂×#41	—	188	8	no	—
506	C₂²×Q₈	—	4	4	no	—
507	C₂²×Q₈	—	47	16	no	—
508	C₂²×Q₈	—	47	2	no	—
509	C₂²×Q₈	—	47	1	no	—
510	C₂²×Q₈	—	47	2	no	—
511	C₂²×Q₈	—	47	4	no	—
512	C₂²×Q₈	—	188	8	no	—
513	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
514	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
515	C₂²×Q₈	C₂²×D₄₇	1	8	yes	—
516	C₂²×D₄	—	4	4	no	—
517	C₂²×D₄	—	47	2	no	—
518	C₂²×D₄	—	47	4	no	—
519	C₂²×D₄	—	47	4	no	—
520	C₂²×D₄	—	47	1	no	—
521	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
522	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
523	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
524	C₂³×C₄	—	47	4	no	—
525	C₂³×C₄	—	47	4	no	—
526	C₂³×C₄	—	47	2	no	—
527	C₂³×C₄	—	47	4	no	—
528	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
529	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
530	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
531	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
532	C₄⋊Q₈	—	47	16	no	—
533	C₄⋊Q₈	—	47	32	no	—
534	C₄⋊Q₈	—	47	8	no	—
535	C₄⋊Q₈	—	47	8	no	—
536	#126	—	47	32	no	—
537	#126	—	47	32	no	—
538	#126	—	47	32	no	—
539	#126	—	47	16	no	—
540	#125	—	47	8	no	—
541	#125	—	47	16	no	—
542	#124	—	47	16	no	—
543	#124	—	47	32	no	—
544	#124	—	47	32	no	—
545	#124	—	47	8	no	—
546	#124	C₂²×D₄₇	1	16	yes	—
547	#124	C₂²×D₄₇	1	16	yes	—
548	#124	C₂²×D₄₇	1	16	yes	—
549	#124	C₂²×D₄₇	1	16	yes	—
550	#123	—	47	32	no	—
551	#123	—	47	16	no	—
552	#123	—	47	32	no	—
553	#123	—	47	32	no	—
554	#123	—	47	32	no	—
555	C₂²⋊Q₈	—	47	16	no	—
556	C₂²⋊Q₈	—	47	32	no	—
557	C₂²⋊Q₈	—	47	8	no	—
558	C₂²⋊Q₈	—	47	16	no	—
559	C₂²⋊Q₈	—	47	16	no	—
560	C₂²⋊Q₈	—	47	32	no	—
561	C₂²⋊Q₈	—	47	32	no	—
562	C₂²⋊Q₈	—	47	32	no	—
563	C₂²⋊Q₈	—	47	32	no	—
564	C₂²⋊Q₈	—	47	32	no	—
565	C₂²⋊Q₈	—	47	32	no	—
566	#121	—	47	16	no	—
567	#121	—	47	32	no	—
568	#121	—	47	8	no	—
569	#121	—	47	32	no	—
570	#120	—	47	32	no	—
571	C₄×Q₈	—	47	16	no	—
572	C₄×Q₈	—	47	8	no	—
573	C₄×Q₈	—	47	16	no	—
574	C₄×Q₈	—	47	16	no	—
575	C₄×D₄	—	47	16	no	—
576	C₄×D₄	—	47	16	no	—
577	C₄×D₄	—	47	32	no	—
578	C₄×D₄	—	47	32	no	—
579	C₄×D₄	—	47	8	no	—
580	#117	—	47	16	no	—
581	#117	—	47	32	no	—
582	#117	—	47	16	no	—
583	C₂×C₄⋊C₄	—	47	2	no	—
584	C₂×C₄⋊C₄	—	47	2	no	—
585	C₂×C₄⋊C₄	—	47	4	no	—
586	C₂×C₄⋊C₄	—	47	2	no	—
587	C₂×C₄⋊C₄	—	47	2	no	—
588	C₂×C₄⋊C₄	—	47	2	no	—
589	C₂×C₄⋊C₄	—	47	2	no	—
590	C₂×C₄⋊C₄	—	47	1	no	—
591	C₂×C₄⋊C₄	—	47	4	no	—
592	C₂×C₄⋊C₄	—	47	4	no	—
593	C₂×C₄⋊C₄	—	47	2	no	—
594	C₂×C₄⋊C₄	—	47	4	no	—
595	C₂×C₄⋊C₄	—	47	4	no	—
596	C₂×C₄⋊C₄	—	47	1	no	—
597	C₂×C₄⋊C₄	—	47	4	no	—
598	C₂×C₄⋊C₄	—	47	2	no	—
599	C₂×C₂²⋊C₄	—	47	2	no	—
600	C₂×C₂²⋊C₄	—	47	4	no	—
601	C₂×C₂²⋊C₄	—	47	4	no	—
602	C₂×C₂²⋊C₄	—	47	4	no	—
603	C₂×C₂²⋊C₄	—	47	32	no	—
604	C₂×C₂²⋊C₄	—	47	4	no	—
605	C₂×C₂²⋊C₄	—	47	4	no	—
606	C₂×C₂²⋊C₄	—	47	2	no	—
607	C₂×C₂²⋊C₄	—	47	2	no	—
608	C₂×C₂²⋊C₄	—	47	2	no	—
609	C₂×C₂²⋊C₄	—	47	2	no	—
610	C₂×C₂²⋊C₄	—	47	4	no	—
611	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
612	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
613	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
614	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
615	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
616	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
617	C₂×C₄²	—	47	4	no	—
618	C₂×C₄²	—	47	2	no	—
619	C₂×C₄²	—	47	4	no	—
620	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
621	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
622	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
623	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
624	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
625	C₂⁴	—	2	8	no	—
626	C₂⁴	—	4	4	no	—
627	C₂⁴	—	4	4	no	—
628	C₂⁴	—	47	2	no	—
629	C₂⁴	C₂³×D₄₇	1	4	yes	—
630	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
631	C₂⁴	C₂³×D₄₇	1	8	yes	—
632	#41	—	188	32	no	—
633	C₂×Q₈	—	2	8	no	—
634	C₂×Q₈	—	4	4	no	—
635	C₂×Q₈	—	4	16	no	—
636	C₂×Q₈	—	47	8	no	—
637	C₂×Q₈	—	47	4	no	—
638	C₂×Q₈	—	47	8	no	—
639	C₂×Q₈	—	47	16	no	—
640	C₂×Q₈	—	94	8	no	—
641	C₂×Q₈	—	188	2	no	—
642	C₂×Q₈	—	188	4	no	—
643	C₂×Q₈	—	188	8	no	—
644	C₂×Q₈	—	188	32	no	—
645	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
646	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	4	16	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	47	8	no	—
651	C₂×D₄	—	47	16	no	—
652	C₂×D₄	—	47	16	no	—
653	C₂×D₄	—	47	4	no	—
654	C₂×D₄	—	94	8	no	—
655	C₂×D₄	—	188	2	no	—
656	C₂×D₄	—	188	8	no	—
657	C₂×D₄	—	188	8	no	—
658	C₂×D₄	C₂³×D₄₇	1	8	yes	—
659	C₂×D₄	C₂³×D₄₇	1	8	yes	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	4	no	—
664	C₂²×C₄	—	47	2	no	—
665	C₂²×C₄	—	47	4	no	—
666	C₂²×C₄	—	47	2	no	—
667	C₂²×C₄	—	47	4	no	—
668	C₂²×C₄	—	47	2	no	—
669	C₂²×C₄	—	47	16	no	—
670	C₂²×C₄	—	47	16	no	—
671	C₂²×C₄	—	47	8	no	—
672	C₂²×C₄	—	47	16	no	—
673	C₂²×C₄	—	94	8	no	—
674	C₂²×C₄	—	188	8	no	—
675	C₂²×C₄	—	188	8	no	—
676	C₂²×C₄	—	188	8	no	—
677	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
678	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
679	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
680	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
681	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
682	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
683	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
684	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
685	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
686	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
687	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
688	C₄⋊C₄	—	47	8	no	—
689	C₄⋊C₄	—	47	8	no	—
690	C₄⋊C₄	—	47	16	no	—
691	C₄⋊C₄	—	47	8	no	—
692	C₄⋊C₄	—	47	16	no	—
693	C₄⋊C₄	—	47	16	no	—
694	C₄⋊C₄	—	47	8	no	—
695	C₄⋊C₄	—	47	16	no	—
696	C₄⋊C₄	—	47	16	no	—
697	C₄⋊C₄	—	47	8	no	—
698	C₄⋊C₄	—	47	8	no	—
699	C₄⋊C₄	—	47	8	no	—
700	C₄⋊C₄	—	47	4	no	—
701	C₄⋊C₄	—	47	4	no	—
702	C₄⋊C₄	—	47	16	no	—
703	C₄⋊C₄	—	47	8	no	—
704	C₂²⋊C₄	—	47	8	no	—
705	C₂²⋊C₄	—	47	16	no	—
706	C₂²⋊C₄	—	47	16	no	—
707	C₂²⋊C₄	—	47	16	no	—
708	C₂²⋊C₄	—	47	16	no	—
709	C₂²⋊C₄	—	47	16	no	—
710	C₂²⋊C₄	—	47	8	no	—
711	C₂²⋊C₄	—	47	8	no	—
712	C₂²⋊C₄	—	47	8	no	—
713	C₂²⋊C₄	—	47	8	no	—
714	C₂²⋊C₄	—	47	16	no	—
715	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
716	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
717	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
718	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
719	C₄²	—	47	16	no	—
720	C₄²	—	47	8	no	—
721	C₄²	—	47	16	no	—
722	C₄²	C₂³×D₄₇	1	4	yes	—
723	C₄²	C₂³×D₄₇	1	4	yes	—
724	C₄²	C₂³×D₄₇	1	4	yes	—
725	C₄²	C₂³×D₄₇	1	4	yes	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	8	no	—
729	C₂³	—	2	8	no	—
730	C₂³	—	2	8	no	—
731	C₂³	—	2	16	no	—
732	C₂³	—	4	8	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	8	16	no	—
735	C₂³	—	47	4	no	—
736	C₂³	—	94	4	no	—
737	C₂³	—	94	4	no	—
738	C₂³	—	94	4	no	—
739	C₂³	#13094071	1	4	yes	—
740	C₂³	C₂⁴×D₄₇	1	8	yes	—
741	C₂³	C₂⁴×D₄₇	1	2	yes	—
742	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
743	Q₈	—	2	16	no	—
744	Q₈	—	4	8	no	—
745	Q₈	—	94	16	no	—
746	Q₈	—	188	4	no	—
747	Q₈	—	188	8	no	—
748	Q₈	—	188	16	no	—
749	D₄	—	2	16	no	—
750	D₄	—	4	8	no	—
751	D₄	—	94	16	no	—
752	D₄	—	188	4	no	—
753	D₄	—	188	16	no	—
754	D₄	—	188	16	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	8	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	8	no	—
765	C₂×C₄	—	47	4	no	—
766	C₂×C₄	—	47	8	no	—
767	C₂×C₄	—	47	4	no	—
768	C₂×C₄	—	47	8	no	—
769	C₂×C₄	—	47	4	no	—
770	C₂×C₄	—	94	4	no	—
771	C₂×C₄	—	94	8	no	—
772	C₂×C₄	—	94	4	no	—
773	C₂×C₄	—	94	4	no	—
774	C₂×C₄	—	94	8	no	—
775	C₂×C₄	—	94	16	no	—
776	C₂×C₄	—	188	16	no	—
777	C₂×C₄	—	188	16	no	—
778	C₂×C₄	—	188	16	no	—
779	C₂×C₄	#13094069	1	4	yes	—
780	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
781	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
782	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
783	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
784	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
785	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
786	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	8	no	—
790	C₂²	—	2	8	no	—
791	C₂²	—	2	8	no	—
792	C₂²	—	2	8	no	—
793	C₂²	—	4	16	no	—
794	C₂²	—	8	16	no	—
795	C₂²	—	94	4	no	—
796	C₂²	—	94	4	no	—
797	C₂²	—	94	4	no	—
798	C₂²	—	188	8	no	—
799	C₂²	C₂×#13094069	1	2	yes	—
800	C₂²	C₂×#13094071	1	4	yes	—
801	C₂²	C₂×#13094071	1	2	yes	—
802	C₂²	#15689959	1	2	yes	—
803	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	8	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	94	4	no	—
811	C₄	—	94	8	no	—
812	C₄	—	94	4	no	—
813	C₄	—	94	4	no	—
814	C₄	—	94	8	no	—
815	C₄	C₂×#13094069	1	4	yes	—
816	C₂	—	2	4	no	—
817	C₂	—	4	8	no	—
818	C₂	—	188	4	no	—
819	C₂	#20257960	1	4	yes	direct product factor
820	C₂	C₂²×#13094069	1	1	yes	characteristic
821	C₂	C₂²×#13094071	1	1	yes	characteristic
822	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×#124×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#124	D₄₇
hypocenter	C₄₇	C₂×#3561
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. #20257960	C₂	direct (N × H)
2. C₂×#15689873	C₂	semidirect
3. C₂×#15689867	C₂	semidirect
4. C₂×#15689842	C₂	semidirect
5. C₂×#15689799	C₂	semidirect
6. C₂×Q₈×C₂²⋊D₄₇	C₂	semidirect
7. C₂×#15689781	C₂	semidirect
8. C₂×#15689767	C₂	semidirect
9. C₂×#15689749	C₂	semidirect
10. C₂×#15689742	C₂	semidirect
11. C₂×#15689737	C₂	semidirect
12. C₂×#15689711	C₂	semidirect
13. C₂×#15689693	C₂	semidirect
14. C₂×#15689680	C₂	semidirect
15. C₂×#15689657	C₂	semidirect
16. C₂²×#124×C₄₇	C₂	semidirect
18. C₂²×Q₈×D₄₇	C₂²	semidirect
19. #15689873	C₂²	semidirect
20. #15689867	C₂²	semidirect
21. #15689842	C₂²	semidirect
22. #15689799	C₂²	semidirect
23. Q₈×C₂²⋊D₄₇	C₂²	semidirect
24. #15689781	C₂²	semidirect
25. #15689767	C₂²	semidirect
26. #15689749	C₂²	semidirect
27. #15689742	C₂²	semidirect
28. #15689737	C₂²	semidirect
29. #15689711	C₂²	semidirect
30. #15689693	C₂²	semidirect
31. #15689680	C₂²	semidirect
32. C₂×#13094024	C₂²	semidirect
33. C₂×#13094024	C₂²	semidirect
34. C₂×#13094022	C₂²	semidirect
35. C₂×#13094022	C₂²	semidirect
36. #15689657	C₂²	semidirect
37. C₂×#13094018	C₂²	semidirect
38. C₂×#13094017	C₂²	semidirect
39. C₂×#13094017	C₂²	semidirect
40. C₂×#13094017	C₂²	semidirect
41. C₂×#13094016	C₂²	semidirect
42. C₂×#13094016	C₂²	semidirect
43. C₂×#13094012	C₂²	semidirect
45. C₂×#13094010	C₂²	semidirect
46. C₂×#13094010	C₂²	semidirect
47. C₂×#13094008	C₂²	semidirect
49. C₂×#13094006	C₂²	semidirect
50. C₂×#13094006	C₂²	semidirect
56. C₂×#13094001	C₂²	semidirect
57. C₂×#13094001	C₂²	semidirect
58. C₂×#13094001	C₂²	semidirect
59. C₂×#13094001	C₂²	semidirect
60. C₂×#13094001	C₂²	semidirect
61. C₂×#13094000	C₂²	semidirect
62. C₂×#13094000	C₂²	semidirect
64. C₂×#13093997	C₂²	semidirect
68. C₂×Q₈×Dic₄₇	C₂²	semidirect
69. C₂×C₄×Dic₉₄	C₂²	semidirect
70. C₂×C₄×Dic₉₄	C₂²	semidirect
71. C₂×C₄×Dic₉₄	C₂²	semidirect
72. C₂×C₄×D₁₈₈	C₂²	semidirect
76. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
78. C₂×#13093981	C₂²	semidirect
79. C₂×#13093980	C₂²	semidirect
87. C₂×#124×C₄₇	C₂²	semidirect
98. C₂×Q₈×D₄₇	C₂³	semidirect
107. #13094024	C₂³	semidirect
108. #13094024	C₂³	semidirect
109. #13094022	C₂³	semidirect
110. #13094022	C₂³	semidirect
111. #13094018	C₂³	semidirect
112. #13094017	C₂³	semidirect
113. #13094017	C₂³	semidirect
114. #13094017	C₂³	semidirect
115. #13094016	C₂³	semidirect
116. #13094016	C₂³	semidirect
117. #13094012	C₂³	semidirect
119. #13094010	C₂³	semidirect
120. #13094010	C₂³	semidirect
121. #13094008	C₂³	semidirect
123. #13094006	C₂³	semidirect
124. #13094006	C₂³	semidirect
130. #13094001	C₂³	semidirect
131. #13094001	C₂³	semidirect
132. #13094001	C₂³	semidirect
133. #13094001	C₂³	semidirect
134. #13094001	C₂³	semidirect
135. #13094000	C₂³	semidirect
136. #13094000	C₂³	semidirect
138. #13093997	C₂³	semidirect
142. Q₈×Dic₄₇	C₂³	semidirect
143. C₄×Dic₉₄	C₂³	semidirect
144. C₄×Dic₉₄	C₂³	semidirect
145. C₄×Dic₉₄	C₂³	semidirect
146. C₄×D₁₈₈	C₂³	semidirect
150. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
152. #13093981	C₂³	semidirect
153. #13093980	C₂³	semidirect
420. C₂²×#124	D₄₇	semidirect
423. C₂×C₄₇	#3561	semidirect
464. C₂×#124	C₂×D₄₇	semidirect
502. C₄₇	C₂×#3561	semidirect
819. C₂	#20257960	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257960	2
C₂×#15689873	2
C₂×#15689867	2
C₂×#15689842	2
C₂×#15689799	2
C₂×Q₈×C₂²⋊D₄₇	2
C₂×#15689781	2
C₂×#15689767	2
C₂×#15689749	2
C₂×#15689742	2
C₂×#15689737	2
C₂×#15689711	2
C₂×#15689693	2
C₂×#15689680	2
C₂×#15689657	2
C₂²×#124×C₄₇	2
C₂×#3561	47

Subgroups — C2×#20257960 #27123629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257960 #27123629