Subgroups — C₂×C₄₇×#1964 #26060909

Order 12032.

2218 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#99×C₄₇	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1964	C₂	1	8	yes	maximal, direct product factor
6	C₂³×D₄×C₄₇	C₄	1	1	yes	characteristic, complemented
7	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×#121×C₄₇	—	2	1	no	—
10	C₂×#121×C₄₇	—	2	1	no	—
11	C₂×#121×C₄₇	—	2	1	no	—
12	C₂×#121×C₄₇	—	2	1	no	—
13	C₂×#121×C₄₇	—	2	2	no	—
14	C₂×#121×C₄₇	—	2	2	no	—
15	C₂×#121×C₄₇	C₄	1	4	yes	complemented
16	C₂×#121×C₄₇	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic, complemented
19	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	complemented
20	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₇	—	2	1	no	—
23	C₂×#99×C₄₇	—	2	16	no	—
24	C₂×#99×C₄₇	C₂²	1	16	yes	complemented
25	C₄₇×#380	—	2	2	no	—
26	C₄₇×#380	C₂²	1	4	yes	complemented
27	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
28	C₄×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	complemented
29	C₂×#95×C₄₇	—	2	1	no	—
30	C₂×#95×C₄₇	—	2	1	no	—
31	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
32	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₄₇	—	2	2	no	—
34	C₂²×D₄×C₄₇	—	2	2	no	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	—	2	2	no	—
37	C₂²×D₄×C₄₇	—	2	8	no	—
38	C₂²×D₄×C₄₇	—	2	8	no	—
39	C₂²×D₄×C₄₇	—	2	2	no	—
40	C₂²×D₄×C₄₇	—	2	1	no	—
41	C₂²×D₄×C₄₇	—	2	1	no	—
42	C₂²×D₄×C₄₇	—	4	4	no	—
43	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
44	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
45	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
46	C₂³×C₄×C₄₇	—	2	2	no	—
47	C₂³×C₄×C₄₇	—	2	2	no	—
48	C₂³×C₄×C₄₇	—	4	4	no	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	D₄	1	2	yes	—
58	C₂³×C₄×C₄₇	D₄	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
60	#121×C₄₇	—	2	4	no	—
61	#121×C₄₇	—	2	4	no	—
62	#121×C₄₇	—	2	4	no	—
63	#121×C₄₇	—	2	4	no	—
64	#121×C₄₇	—	2	4	no	—
65	#121×C₄₇	—	2	4	no	—
66	#121×C₄₇	—	2	4	no	—
67	#121×C₄₇	—	2	4	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
72	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
82	C₂×C₂²⋊C₄×C₄₇	D₄	1	8	yes	complemented
83	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
85	C₂×C₄²×C₄₇	—	2	4	no	—
86	C₂×C₄²×C₄₇	—	4	4	no	—
87	#99×C₄₇	—	2	32	no	—
88	#95×C₄₇	—	2	4	no	—
89	#95×C₄₇	—	2	4	no	—
90	C₂⁴×C₄₇	—	2	2	no	—
91	C₂⁴×C₄₇	—	2	2	no	—
92	C₂⁴×C₄₇	—	2	8	no	—
93	C₂⁴×C₄₇	—	4	2	no	—
94	C₂⁴×C₄₇	—	4	2	no	—
95	C₂⁴×C₄₇	—	4	4	no	—
96	C₂⁴×C₄₇	—	4	4	no	—
97	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
99	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
105	C₂⁴×C₄₇	#41	1	4	yes	—
106	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂×D₄×C₄₇	—	2	4	no	—
108	C₂×D₄×C₄₇	—	2	4	no	—
109	C₂×D₄×C₄₇	—	2	16	no	—
110	C₂×D₄×C₄₇	—	2	4	no	—
111	C₂×D₄×C₄₇	—	2	4	no	—
112	C₂×D₄×C₄₇	—	2	8	no	—
113	C₂×D₄×C₄₇	—	2	8	no	—
114	C₂×D₄×C₄₇	—	2	4	no	—
115	C₂×D₄×C₄₇	—	2	4	no	—
116	C₂×D₄×C₄₇	—	4	4	no	—
117	C₂×D₄×C₄₇	—	4	8	no	—
118	C₂×D₄×C₄₇	—	4	8	no	—
119	C₂×D₄×C₄₇	—	4	8	no	—
120	C₂×D₄×C₄₇	—	4	8	no	—
121	C₂×D₄×C₄₇	—	4	4	no	—
122	C₂×D₄×C₄₇	—	4	4	no	—
123	C₂×D₄×C₄₇	—	4	4	no	—
124	C₂×D₄×C₄₇	—	4	4	no	—
125	C₂×D₄×C₄₇	—	4	4	no	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	2	4	no	—
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	8	no	—
132	C₂²×C₄×C₄₇	—	2	8	no	—
133	C₂²×C₄×C₄₇	—	2	4	no	—
134	C₂²×C₄×C₄₇	—	2	4	no	—
135	C₂²×C₄×C₄₇	—	4	4	no	—
136	C₂²×C₄×C₄₇	—	4	4	no	—
137	C₂²×C₄×C₄₇	—	4	4	no	—
138	C₂²×C₄×C₄₇	—	4	4	no	—
139	C₂²×C₄×C₄₇	—	4	2	no	—
140	C₂²×C₄×C₄₇	—	4	2	no	—
141	C₂²×C₄×C₄₇	—	4	2	no	—
142	C₂²×C₄×C₄₇	—	4	4	no	—
143	C₂²×C₄×C₄₇	—	4	4	no	—
144	C₂²×C₄×C₄₇	—	4	4	no	—
145	C₂²×C₄×C₄₇	—	4	4	no	—
146	C₂²×C₄×C₄₇	—	4	4	no	—
147	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
154	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
155	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
156	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
158	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₄₇	—	2	4	no	—
165	C₄⋊C₄×C₄₇	—	2	4	no	—
166	C₄⋊C₄×C₄₇	—	4	8	no	—
167	C₂²⋊C₄×C₄₇	—	2	8	no	—
168	C₂²⋊C₄×C₄₇	—	2	4	no	—
169	C₂²⋊C₄×C₄₇	—	2	8	no	—
170	C₂²⋊C₄×C₄₇	—	2	8	no	—
171	C₂²⋊C₄×C₄₇	—	2	8	no	—
172	C₂²⋊C₄×C₄₇	—	4	4	no	—
173	C₂²⋊C₄×C₄₇	C₂×D₄	1	8	yes	complemented
174	C₄²×C₄₇	—	4	8	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	—	2	2	no	—
179	C₂³×C₄₇	—	2	2	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	2	4	no	—
182	C₂³×C₄₇	—	2	8	no	—
183	C₂³×C₄₇	—	4	1	no	—
184	C₂³×C₄₇	—	4	1	no	—
185	C₂³×C₄₇	—	4	1	no	—
186	C₂³×C₄₇	—	4	1	no	—
187	C₂³×C₄₇	—	4	1	no	—
188	C₂³×C₄₇	—	4	1	no	—
189	C₂³×C₄₇	—	4	1	no	—
190	C₂³×C₄₇	—	4	8	no	—
191	C₂³×C₄₇	—	4	8	no	—
192	C₂³×C₄₇	—	4	1	no	—
193	C₂³×C₄₇	—	4	4	no	—
194	C₂³×C₄₇	—	4	4	no	—
195	C₂³×C₄₇	—	4	4	no	—
196	C₂³×C₄₇	—	4	4	no	—
197	C₂³×C₄₇	—	4	4	no	—
198	C₂³×C₄₇	—	4	4	no	—
199	C₂³×C₄₇	—	4	4	no	—
200	C₂³×C₄₇	—	4	4	no	—
201	C₂³×C₄₇	—	8	16	no	—
202	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₄₇	C₄×D₄	1	4	yes	—
207	C₂³×C₄₇	C₄×D₄	1	4	yes	—
208	C₂³×C₄₇	#121	1	4	yes	—
209	C₂³×C₄₇	#121	1	4	yes	—
210	C₂³×C₄₇	#124	1	2	yes	—
211	C₂³×C₄₇	#124	1	2	yes	—
212	C₂³×C₄₇	#127	1	2	yes	—
213	C₂³×C₄₇	#127	1	2	yes	—
214	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
215	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
216	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
218	C₂³×C₄₇	C₂×#41	1	2	yes	—
219	D₄×C₄₇	—	4	8	no	—
220	D₄×C₄₇	—	4	8	no	—
221	D₄×C₄₇	—	4	4	no	—
222	D₄×C₄₇	—	4	4	no	—
223	D₄×C₄₇	—	4	8	no	—
224	D₄×C₄₇	—	4	8	no	—
225	D₄×C₄₇	—	4	8	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	4	no	—
230	C₂×C₄×C₄₇	—	2	4	no	—
231	C₂×C₄×C₄₇	—	2	4	no	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	4	no	—
235	C₂×C₄×C₄₇	—	2	4	no	—
236	C₂×C₄×C₄₇	—	2	8	no	—
237	C₂×C₄×C₄₇	—	2	8	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	—	4	2	no	—
240	C₂×C₄×C₄₇	—	4	2	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	2	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	4	no	—
245	C₂×C₄×C₄₇	—	4	4	no	—
246	C₂×C₄×C₄₇	—	4	16	no	—
247	C₂×C₄×C₄₇	—	4	4	no	—
248	C₂×C₄×C₄₇	—	4	4	no	—
249	C₂×C₄×C₄₇	—	4	4	no	—
250	C₂×C₄×C₄₇	—	4	4	no	—
251	C₂×C₄×C₄₇	—	4	4	no	—
252	C₂×C₄×C₄₇	—	8	8	no	—
253	C₂×C₄×C₄₇	#99	1	4	yes	complemented
254	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂×#1964	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂²×C₄₇	—	2	1	no	—
260	C₂²×C₄₇	—	2	1	no	—
261	C₂²×C₄₇	—	2	1	no	—
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	1	no	—
264	C₂²×C₄₇	—	2	1	no	—
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	2	1	no	—
267	C₂²×C₄₇	—	2	1	no	—
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	1	no	—
270	C₂²×C₄₇	—	2	1	no	—
271	C₂²×C₄₇	—	2	8	no	—
272	C₂²×C₄₇	—	2	4	no	—
273	C₂²×C₄₇	—	2	8	no	—
274	C₂²×C₄₇	—	2	4	no	—
275	C₂²×C₄₇	—	4	4	no	—
276	C₂²×C₄₇	—	4	4	no	—
277	C₂²×C₄₇	—	4	2	no	—
278	C₂²×C₄₇	—	4	2	no	—
279	C₂²×C₄₇	—	4	2	no	—
280	C₂²×C₄₇	—	4	2	no	—
281	C₂²×C₄₇	—	4	4	no	—
282	C₂²×C₄₇	—	4	4	no	—
283	C₂²×C₄₇	—	4	4	no	—
284	C₂²×C₄₇	—	8	8	no	—
285	C₂²×C₄₇	—	8	8	no	—
286	C₂²×C₄₇	—	8	8	no	—
287	C₂²×C₄₇	#390	1	2	yes	—
288	C₂²×C₄₇	#390	1	2	yes	—
289	C₂²×C₄₇	#390	1	2	yes	—
290	C₂²×C₄₇	#390	1	2	yes	—
291	C₂²×C₄₇	C₂×#99	1	2	yes	—
292	C₂²×C₄₇	#410	1	2	yes	—
293	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
295	C₂²×C₄₇	C₂×#121	1	2	yes	—
296	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
297	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
298	C₄×C₄₇	—	2	2	no	—
299	C₄×C₄₇	—	2	2	no	—
300	C₄×C₄₇	—	2	2	no	—
301	C₄×C₄₇	—	4	8	no	—
302	C₄×C₄₇	—	4	4	no	—
303	C₄×C₄₇	—	8	4	no	—
304	C₄×C₄₇	C₂×#99	1	4	yes	complemented
305	C₂²×#121	C₂×C₄₇	1	1	yes	characteristic
306	C₂²×#99	C₂×C₄₇	1	4	yes	complemented
307	C₂×#380	C₂×C₄₇	1	1	yes	characteristic, complemented
308	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
309	#1964	C₂×C₄₇	1	8	yes	direct product factor
310	C₂×C₄₇	—	2	2	no	—
311	C₂×C₄₇	—	2	1	no	—
312	C₂×C₄₇	—	2	2	no	—
313	C₂×C₄₇	—	2	2	no	—
314	C₂×C₄₇	—	2	1	no	—
315	C₂×C₄₇	—	2	2	no	—
316	C₂×C₄₇	—	2	2	no	—
317	C₂×C₄₇	—	8	4	no	—
318	C₂×C₄₇	#1964	1	4	yes	direct product factor
319	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
320	C₂×C₄₇	C₂²×#99	1	1	yes	characteristic
321	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
322	C₂³×D₄	C₄×C₄₇	1	1	yes	characteristic, complemented
323	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
324	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
325	C₂×#121	—	2	1	no	—
326	C₂×#121	—	2	1	no	—
327	C₂×#121	—	2	1	no	—
328	C₂×#121	—	2	1	no	—
329	C₂×#121	—	2	2	no	—
330	C₂×#121	—	2	2	no	—
331	C₂×#121	C₄×C₄₇	1	4	yes	complemented
332	C₂×#121	C₂²×C₄₇	1	4	yes	—
333	C₂²×C₄⋊C₄	—	2	1	no	—
334	C₂²×C₄⋊C₄	C₄×C₄₇	1	1	yes	characteristic, complemented
335	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	complemented
336	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
337	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
338	C₂²×C₄²	—	2	1	no	—
339	C₂×#99	—	2	16	no	—
340	C₂×#99	C₂²×C₄₇	1	16	yes	complemented
341	#380	—	2	2	no	—
342	#380	C₂²×C₄₇	1	4	yes	complemented
343	C₄×C₂²⋊C₄	—	2	2	no	—
344	C₄×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	complemented
345	C₂×#95	—	2	1	no	—
346	C₂×#95	—	2	1	no	—
347	C₄₇	C₂×#1964	1	1	yes	characteristic, direct product factor, Sylow
348	C₂⁵	C₂×C₄×C₄₇	1	2	yes	—
349	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	8	no	—
355	C₂²×D₄	—	2	8	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	—	4	4	no	—
360	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
361	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	complemented
362	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
363	C₂³×C₄	—	2	2	no	—
364	C₂³×C₄	—	2	2	no	—
365	C₂³×C₄	—	4	4	no	—
366	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
367	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
368	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
369	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
370	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
371	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
372	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
373	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
374	C₂³×C₄	D₄×C₄₇	1	2	yes	—
375	C₂³×C₄	D₄×C₄₇	1	2	yes	—
376	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
377	#121	—	2	4	no	—
378	#121	—	2	4	no	—
379	#121	—	2	4	no	—
380	#121	—	2	4	no	—
381	#121	—	2	4	no	—
382	#121	—	2	4	no	—
383	#121	—	2	4	no	—
384	#121	—	2	4	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	—	4	4	no	—
390	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	complemented
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	4	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	—	2	4	no	—
396	C₂×C₂²⋊C₄	—	2	8	no	—
397	C₂×C₂²⋊C₄	—	2	2	no	—
398	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	complemented
399	C₂×C₂²⋊C₄	D₄×C₄₇	1	8	yes	complemented
400	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
402	C₂×C₄²	—	2	4	no	—
403	C₂×C₄²	—	4	4	no	—
404	#99	—	2	32	no	—
405	#95	—	2	4	no	—
406	#95	—	2	4	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	8	no	—
410	C₂⁴	—	4	2	no	—
411	C₂⁴	—	4	2	no	—
412	C₂⁴	—	4	4	no	—
413	C₂⁴	—	4	4	no	—
414	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
415	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
416	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
417	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
418	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
419	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
420	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
421	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
422	C₂⁴	#41×C₄₇	1	4	yes	—
423	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	16	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	8	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	—	4	8	no	—
437	C₂×D₄	—	4	8	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	—	4	4	no	—
461	C₂²×C₄	—	4	4	no	—
462	C₂²×C₄	—	4	4	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
468	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
469	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
470	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
471	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
472	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
473	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
474	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
475	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
476	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
479	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
480	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	4	8	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	C₂×D₄×C₄₇	1	8	yes	complemented
491	C₄²	—	4	8	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	8	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	8	no	—
508	C₂³	—	4	8	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	4	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	4	4	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	4	no	—
517	C₂³	—	4	4	no	—
518	C₂³	—	8	16	no	—
519	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
520	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
521	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
522	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
523	C₂³	C₄×D₄×C₄₇	1	4	yes	—
524	C₂³	C₄×D₄×C₄₇	1	4	yes	—
525	C₂³	#121×C₄₇	1	4	yes	—
526	C₂³	#121×C₄₇	1	4	yes	—
527	C₂³	#124×C₄₇	1	2	yes	—
528	C₂³	#124×C₄₇	1	2	yes	—
529	C₂³	#127×C₄₇	1	2	yes	—
530	C₂³	#127×C₄₇	1	2	yes	—
531	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
532	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
533	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
534	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
535	C₂³	C₂×#41×C₄₇	1	2	yes	—
536	D₄	—	4	8	no	—
537	D₄	—	4	8	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	8	no	—
541	D₄	—	4	8	no	—
542	D₄	—	4	8	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	16	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	8	8	no	—
570	C₂×C₄	#99×C₄₇	1	4	yes	complemented
571	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
572	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
573	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
574	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	8	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	2	8	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	8	8	no	—
601	C₂²	—	8	8	no	—
602	C₂²	—	8	8	no	—
603	C₂²	C₄₇×#390	1	2	yes	—
604	C₂²	C₄₇×#390	1	2	yes	—
605	C₂²	C₄₇×#390	1	2	yes	—
606	C₂²	C₄₇×#390	1	2	yes	—
607	C₂²	C₂×#99×C₄₇	1	2	yes	—
608	C₂²	C₄₇×#410	1	2	yes	—
609	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
610	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
611	C₂²	C₂×#121×C₄₇	1	2	yes	—
612	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
613	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
614	C₄	—	2	2	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	2	no	—
617	C₄	—	4	8	no	—
618	C₄	—	4	4	no	—
619	C₄	—	8	4	no	—
620	C₄	C₂×#99×C₄₇	1	4	yes	complemented
621	C₂	—	2	2	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	2	no	—
624	C₂	—	2	2	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	2	no	—
627	C₂	—	2	2	no	—
628	C₂	—	8	4	no	—
629	C₂	C₄₇×#1964	1	4	yes	direct product factor
630	C₂	C₂×C₄₇×#390	1	1	yes	characteristic
631	C₂	C₂²×#99×C₄₇	1	1	yes	characteristic
632	C₂	C₂×C₄₇×#410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂²×#121×C₄₇	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#99×C₄₇	C₂	semidirect
3. C₂×C₄₇×#380	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
5. C₄₇×#1964	C₂	direct (N × H)
6. C₂³×D₄×C₄₇	C₄	semidirect
15. C₂×#121×C₄₇	C₄	semidirect
18. C₂²×C₄⋊C₄×C₄₇	C₄	semidirect
19. C₂²×C₂²⋊C₄×C₄₇	C₄	semidirect
24. C₂×#99×C₄₇	C₂²	semidirect
26. C₄₇×#380	C₂²	semidirect
28. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
44. C₂²×D₄×C₄₇	C₂×C₄	semidirect
73. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
81. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
82. C₂×C₂²⋊C₄×C₄₇	D₄	semidirect
173. C₂²⋊C₄×C₄₇	C₂×D₄	semidirect
253. C₂×C₄×C₄₇	#99	semidirect
258. C₂×#1964	C₄₇	direct (N × H)
304. C₄×C₄₇	C₂×#99	semidirect
306. C₂²×#99	C₂×C₄₇	semidirect
307. C₂×#380	C₂×C₄₇	semidirect
308. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
309. #1964	C₂×C₄₇	direct (N × H)
318. C₂×C₄₇	#1964	direct (N × H)
322. C₂³×D₄	C₄×C₄₇	semidirect
331. C₂×#121	C₄×C₄₇	semidirect
334. C₂²×C₄⋊C₄	C₄×C₄₇	semidirect
335. C₂²×C₂²⋊C₄	C₄×C₄₇	semidirect
340. C₂×#99	C₂²×C₄₇	semidirect
342. #380	C₂²×C₄₇	semidirect
344. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
347. C₄₇	C₂×#1964	direct (N × H)
361. C₂²×D₄	C₂×C₄×C₄₇	semidirect
390. C₂×C₄⋊C₄	C₂×C₄×C₄₇	semidirect
398. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
399. C₂×C₂²⋊C₄	D₄×C₄₇	semidirect
490. C₂²⋊C₄	C₂×D₄×C₄₇	semidirect
570. C₂×C₄	#99×C₄₇	semidirect
620. C₄	C₂×#99×C₄₇	semidirect
629. C₂	C₄₇×#1964	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#121×C₄₇	2
C₂²×#99×C₄₇	2
C₂×C₄₇×#380	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₄₇×#1964	2
C₂×#1964	47

Subgroups — C2×C47×#1964 #26060909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1964 #26060909