Subgroups — C₄₇×#24041 #26063739

Order 12032.

1338 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#103×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2486	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2043	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2035	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1869	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1865	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1787	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	D₄×Q₈×C₄₇	—	2	4	no	—
16	D₄×Q₈×C₄₇	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
18	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#123×C₄₇	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₇	—	2	1	no	—
26	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#483	—	2	4	no	—
29	C₂×#106×C₄₇	C₂²	1	2	yes	—
30	C₂×#103×C₄₇	—	2	4	no	—
31	C₂×#103×C₄₇	C₂²	1	2	yes	—
32	C₂×#103×C₄₇	C₂²	1	2	yes	—
33	C₂×#103×C₄₇	C₂²	1	2	yes	—
34	C₂×#103×C₄₇	C₂²	1	2	yes	—
35	C₂×#103×C₄₇	C₂²	1	2	yes	—
36	C₂×#103×C₄₇	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#398	—	2	1	no	—
40	C₄₇×#397	—	2	1	no	—
41	C₄₇×#389	C₂²	1	2	yes	—
42	C₄₇×#381	—	2	1	no	—
43	C₄₇×#380	C₂²	1	2	yes	—
44	C₄₇×#380	C₂²	1	1	yes	characteristic
45	C₄₇×#340	C₂²	1	2	yes	—
46	C₄₇×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₇	—	2	2	no	—
48	C₂²×Q₈×C₄₇	—	2	2	no	—
49	C₂²×Q₈×C₄₇	—	2	1	no	—
50	C₂²×Q₈×C₄₇	—	2	1	no	—
51	C₂²×Q₈×C₄₇	—	2	2	no	—
52	C₂²×Q₈×C₄₇	—	2	4	no	—
53	C₂²×Q₈×C₄₇	—	2	4	no	—
54	C₂²×Q₈×C₄₇	—	4	2	no	—
55	C₂²×Q₈×C₄₇	—	4	2	no	—
56	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
57	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	—	2	1	no	—
62	C₂³×C₄×C₄₇	—	2	1	no	—
63	C₂³×C₄×C₄₇	—	2	1	no	—
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₇	—	2	2	no	—
67	C₂²×C₈×C₄₇	—	4	2	no	—
68	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
69	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₄₇	—	2	8	no	—
71	C₄⋊Q₈×C₄₇	—	2	2	no	—
72	C₄⋊Q₈×C₄₇	—	2	2	no	—
73	#123×C₄₇	—	4	4	no	—
74	C₂²⋊Q₈×C₄₇	—	2	8	no	—
75	C₂²⋊Q₈×C₄₇	—	2	8	no	—
76	C₂²⋊Q₈×C₄₇	—	2	2	no	—
77	C₂²⋊Q₈×C₄₇	—	2	2	no	—
78	C₂²⋊Q₈×C₄₇	—	2	2	no	—
79	C₂²⋊Q₈×C₄₇	D₄	1	4	yes	—
80	C₄×Q₈×C₄₇	—	2	2	no	—
81	C₄×Q₈×C₄₇	—	2	2	no	—
82	C₄×D₄×C₄₇	—	2	8	no	—
83	C₄×D₄×C₄₇	—	2	2	no	—
84	C₄×D₄×C₄₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
91	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
92	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	—	2	1	no	—
105	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
106	#106×C₄₇	—	2	4	no	—
107	#103×C₄₇	—	2	4	no	—
108	#103×C₄₇	—	2	4	no	—
109	#103×C₄₇	—	2	4	no	—
110	#103×C₄₇	—	2	4	no	—
111	#103×C₄₇	—	4	2	no	—
112	#103×C₄₇	—	4	2	no	—
113	C₂²⋊C₈×C₄₇	—	2	2	no	—
114	C₂²⋊C₈×C₄₇	—	4	2	no	—
115	#95×C₄₇	—	2	2	no	—
116	#95×C₄₇	—	2	1	no	—
117	#95×C₄₇	—	2	2	no	—
118	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₄₇	—	2	4	no	—
121	C₂×Q₈×C₄₇	—	2	4	no	—
122	C₂×Q₈×C₄₇	—	2	1	no	—
123	C₂×Q₈×C₄₇	—	2	1	no	—
124	C₂×Q₈×C₄₇	—	2	1	no	—
125	C₂×Q₈×C₄₇	—	2	2	no	—
126	C₂×Q₈×C₄₇	—	2	8	no	—
127	C₂×Q₈×C₄₇	—	2	2	no	—
128	C₂×Q₈×C₄₇	—	2	2	no	—
129	C₂×Q₈×C₄₇	—	2	2	no	—
130	C₂×Q₈×C₄₇	—	2	2	no	—
131	C₂×Q₈×C₄₇	—	4	4	no	—
132	C₂×Q₈×C₄₇	—	4	4	no	—
133	C₂×Q₈×C₄₇	—	4	4	no	—
134	C₂×Q₈×C₄₇	—	4	8	no	—
135	C₂×Q₈×C₄₇	—	4	8	no	—
136	C₂×Q₈×C₄₇	—	4	4	no	—
137	C₂×Q₈×C₄₇	—	4	4	no	—
138	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
140	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
141	C₂×Q₈×C₄₇	#41	1	4	yes	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	2	2	no	—
144	C₂×D₄×C₄₇	SD₁₆	1	4	yes	—
145	C₂²×C₄×C₄₇	—	2	1	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	4	no	—
149	C₂²×C₄×C₄₇	—	2	4	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	—	2	2	no	—
156	C₂²×C₄×C₄₇	—	2	2	no	—
157	C₂²×C₄×C₄₇	—	2	2	no	—
158	C₂²×C₄×C₄₇	—	2	2	no	—
159	C₂²×C₄×C₄₇	—	4	4	no	—
160	C₂²×C₄×C₄₇	—	4	4	no	—
161	C₂²×C₄×C₄₇	—	4	2	no	—
162	C₂²×C₄×C₄₇	—	4	2	no	—
163	C₂²×C₄×C₄₇	—	4	2	no	—
164	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₂×C₈×C₄₇	—	2	2	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	2	2	no	—
177	C₂×C₈×C₄₇	—	4	4	no	—
178	C₄⋊C₄×C₄₇	—	2	4	no	—
179	C₄⋊C₄×C₄₇	—	2	4	no	—
180	C₄⋊C₄×C₄₇	—	2	4	no	—
181	C₄⋊C₄×C₄₇	—	2	4	no	—
182	C₄⋊C₄×C₄₇	—	2	4	no	—
183	C₄⋊C₄×C₄₇	—	2	2	no	—
184	C₄⋊C₄×C₄₇	—	2	1	no	—
185	C₄⋊C₄×C₄₇	—	2	2	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₄⋊C₄×C₄₇	—	2	2	no	—
188	C₄⋊C₄×C₄₇	—	2	2	no	—
189	C₄⋊C₄×C₄₇	—	4	2	no	—
190	C₄⋊C₄×C₄₇	—	4	4	no	—
191	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
192	C₂²⋊C₄×C₄₇	—	2	4	no	—
193	C₂²⋊C₄×C₄₇	—	2	4	no	—
194	C₂²⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	2	2	no	—
196	C₂²⋊C₄×C₄₇	—	4	2	no	—
197	C₂²⋊C₄×C₄₇	—	4	4	no	—
198	C₄²×C₄₇	—	2	4	no	—
199	C₄²×C₄₇	—	2	1	no	—
200	C₄²×C₄₇	—	2	1	no	—
201	C₂³×C₄₇	—	2	2	no	—
202	C₂³×C₄₇	—	2	2	no	—
203	C₂³×C₄₇	—	2	1	no	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	1	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	#120	1	2	yes	—
208	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
209	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
210	C₂³×C₄₇	#137	1	2	yes	—
211	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₄₇	—	2	2	no	—
213	Q₈×C₄₇	—	2	4	no	—
214	Q₈×C₄₇	—	2	2	no	—
215	Q₈×C₄₇	—	2	2	no	—
216	Q₈×C₄₇	—	2	4	no	—
217	Q₈×C₄₇	—	4	8	no	—
218	Q₈×C₄₇	—	4	8	no	—
219	Q₈×C₄₇	—	4	1	no	—
220	Q₈×C₄₇	—	4	1	no	—
221	Q₈×C₄₇	—	4	2	no	—
222	Q₈×C₄₇	#123	1	4	yes	complemented
223	D₄×C₄₇	—	2	8	no	—
224	C₂×C₄×C₄₇	—	2	1	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	4	no	—
228	C₂×C₄×C₄₇	—	2	1	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	2	4	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	2	no	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	4	8	no	—
240	C₂×C₄×C₄₇	—	4	8	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	1	no	—
245	C₂×C₄×C₄₇	—	4	1	no	—
246	C₂×C₄×C₄₇	—	4	2	no	—
247	C₂×C₄×C₄₇	—	4	2	no	—
248	C₂×C₄×C₄₇	—	4	2	no	—
249	C₂×C₄×C₄₇	—	4	2	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	—	4	2	no	—
252	C₂×C₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	—	8	4	no	—
254	C₂×C₄×C₄₇	#120	1	2	yes	—
255	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
256	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
259	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
260	C₈×C₄₇	—	4	2	no	—
261	C₈×C₄₇	—	4	2	no	—
262	#24041	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂²×C₄₇	—	2	2	no	—
264	C₂²×C₄₇	—	2	2	no	—
265	C₂²×C₄₇	—	2	4	no	—
266	C₂²×C₄₇	—	2	4	no	—
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	2	4	no	—
269	C₂²×C₄₇	—	4	1	no	—
270	C₂²×C₄₇	—	4	1	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	#448	1	4	yes	—
273	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
274	C₂²×C₄₇	#546	1	2	yes	—
275	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
276	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
277	C₂²×C₄₇	#578	1	2	yes	—
278	C₄×C₄₇	—	2	2	no	—
279	C₄×C₄₇	—	2	4	no	—
280	C₄×C₄₇	—	2	2	no	—
281	C₄×C₄₇	—	4	1	no	—
282	C₄×C₄₇	—	4	2	no	—
283	C₄×C₄₇	—	4	2	no	—
284	C₄×C₄₇	—	4	1	no	—
285	C₄×C₄₇	—	4	2	no	—
286	C₄×C₄₇	—	8	2	no	—
287	C₄×C₄₇	—	8	2	no	—
288	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
289	C₄×C₄₇	#534	1	1	yes	characteristic
290	C₄×C₄₇	#546	1	2	yes	—
291	C₂×D₄×Q₈	C₂×C₄₇	1	1	yes	characteristic
292	C₂×#483	C₂×C₄₇	1	1	yes	characteristic, complemented
293	C₂²×#103	C₂×C₄₇	1	1	yes	characteristic, complemented
294	#2486	C₂×C₄₇	1	1	yes	characteristic
295	#2043	C₂×C₄₇	1	2	yes	complemented
296	#2035	C₂×C₄₇	1	2	yes	complemented
297	#1892	C₂×C₄₇	1	1	yes	characteristic, complemented
298	#1869	C₂×C₄₇	1	1	yes	characteristic
299	#1865	C₂×C₄₇	1	2	yes	complemented
300	#1787	C₂×C₄₇	1	2	yes	complemented
301	#1787	C₂×C₄₇	1	1	yes	characteristic, complemented
302	C₂×C₄₇	—	2	4	no	—
303	C₂×C₄₇	—	4	2	no	—
304	C₂×C₄₇	#2405	1	1	yes	characteristic
305	C₂×C₄₇	C₂×#448	1	1	yes	characteristic
306	C₂×C₄₇	#3011	1	1	yes	characteristic
307	C₂×C₄₇	#3298	1	2	yes	—
308	C₂×C₄₇	#3312	1	2	yes	—
309	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
310	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
311	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
312	D₄×Q₈	—	2	4	no	—
313	D₄×Q₈	—	2	4	no	—
314	C₂×C₄⋊Q₈	—	2	1	no	—
315	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
316	C₂×#123	—	2	1	no	—
317	C₂×C₂²⋊Q₈	—	2	1	no	—
318	C₂×C₂²⋊Q₈	—	2	1	no	—
319	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
320	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
321	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
322	C₂×C₄×D₄	—	2	1	no	—
323	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
325	#483	—	2	4	no	—
326	C₂×#106	C₂²×C₄₇	1	2	yes	—
327	C₂×#103	—	2	4	no	—
328	C₂×#103	C₂²×C₄₇	1	2	yes	—
329	C₂×#103	C₂²×C₄₇	1	2	yes	—
330	C₂×#103	C₂²×C₄₇	1	2	yes	—
331	C₂×#103	C₂²×C₄₇	1	2	yes	—
332	C₂×#103	C₂²×C₄₇	1	2	yes	—
333	C₂×#103	C₂²×C₄₇	1	2	yes	—
334	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
335	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
336	#398	—	2	1	no	—
337	#397	—	2	1	no	—
338	#389	C₂²×C₄₇	1	2	yes	—
339	#381	—	2	1	no	—
340	#380	C₂²×C₄₇	1	1	yes	characteristic
341	#380	C₂²×C₄₇	1	2	yes	—
342	#340	C₂²×C₄₇	1	2	yes	—
343	#336	C₂²×C₄₇	1	2	yes	—
344	C₄₇	#24041	1	1	yes	characteristic, direct product factor, Sylow
345	C₂²×Q₈	—	2	2	no	—
346	C₂²×Q₈	—	2	2	no	—
347	C₂²×Q₈	—	2	1	no	—
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×Q₈	—	2	2	no	—
350	C₂²×Q₈	—	2	4	no	—
351	C₂²×Q₈	—	2	4	no	—
352	C₂²×Q₈	—	4	2	no	—
353	C₂²×Q₈	—	4	2	no	—
354	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
355	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
356	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
357	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
358	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
359	C₂³×C₄	—	2	1	no	—
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
364	C₂²×C₈	—	2	2	no	—
365	C₂²×C₈	—	4	2	no	—
366	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
367	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
368	C₄⋊Q₈	—	2	8	no	—
369	C₄⋊Q₈	—	2	2	no	—
370	C₄⋊Q₈	—	2	2	no	—
371	#123	—	4	4	no	—
372	C₂²⋊Q₈	—	2	8	no	—
373	C₂²⋊Q₈	—	2	8	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	D₄×C₄₇	1	4	yes	—
378	C₄×Q₈	—	2	2	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×D₄	—	2	8	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	2	no	—
392	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
404	#106	—	2	4	no	—
405	#103	—	2	4	no	—
406	#103	—	2	4	no	—
407	#103	—	2	4	no	—
408	#103	—	2	4	no	—
409	#103	—	4	2	no	—
410	#103	—	4	2	no	—
411	C₂²⋊C₈	—	2	2	no	—
412	C₂²⋊C₈	—	4	2	no	—
413	#95	—	2	2	no	—
414	#95	—	2	1	no	—
415	#95	—	2	2	no	—
416	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
417	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	—	2	4	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	8	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	4	4	no	—
430	C₂×Q₈	—	4	4	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	—	4	8	no	—
433	C₂×Q₈	—	4	8	no	—
434	C₂×Q₈	—	4	4	no	—
435	C₂×Q₈	—	4	4	no	—
436	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
437	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
438	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
439	C₂×Q₈	#41×C₄₇	1	4	yes	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	SD₁₆×C₄₇	1	4	yes	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	4	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	4	no	—
489	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	4	no	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	2	no	—
505	C₂³	#120×C₄₇	1	2	yes	—
506	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
507	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
508	C₂³	#137×C₄₇	1	2	yes	—
509	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
510	Q₈	—	2	2	no	—
511	Q₈	—	2	4	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	2	4	no	—
515	Q₈	—	4	8	no	—
516	Q₈	—	4	8	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	2	no	—
520	Q₈	#123×C₄₇	1	4	yes	complemented
521	D₄	—	2	8	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	8	4	no	—
552	C₂×C₄	#120×C₄₇	1	2	yes	—
553	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
556	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
557	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
558	C₈	—	4	2	no	—
559	C₈	—	4	2	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	4	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	C₄₇×#448	1	4	yes	—
570	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
571	C₂²	C₄₇×#546	1	2	yes	—
572	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
573	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
574	C₂²	C₄₇×#578	1	2	yes	—
575	C₄	—	2	2	no	—
576	C₄	—	2	4	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	8	2	no	—
584	C₄	—	8	2	no	—
585	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
586	C₄	C₄₇×#534	1	1	yes	characteristic
587	C₄	C₄₇×#546	1	2	yes	—
588	C₂	—	2	4	no	—
589	C₂	—	4	2	no	—
590	C₂	C₄₇×#2405	1	1	yes	characteristic
591	C₂	C₂×C₄₇×#448	1	1	yes	characteristic
592	C₂	C₄₇×#3011	1	1	yes	characteristic
593	C₂	C₄₇×#3298	1	2	yes	—
594	C₂	C₄₇×#3312	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×D₄×C₄₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#483	C₂	semidirect
3. C₂²×#103×C₄₇	C₂	semidirect
5. C₄₇×#2043	C₂	semidirect
6. C₄₇×#2035	C₂	semidirect
7. C₄₇×#1892	C₂	semidirect
9. C₄₇×#1865	C₂	semidirect
10. C₄₇×#1787	C₂	semidirect
11. C₄₇×#1787	C₂	semidirect
222. Q₈×C₄₇	#123	semidirect
262. #24041	C₄₇	direct (N × H)
292. C₂×#483	C₂×C₄₇	semidirect
293. C₂²×#103	C₂×C₄₇	semidirect
295. #2043	C₂×C₄₇	semidirect
296. #2035	C₂×C₄₇	semidirect
297. #1892	C₂×C₄₇	semidirect
299. #1865	C₂×C₄₇	semidirect
300. #1787	C₂×C₄₇	semidirect
301. #1787	C₂×C₄₇	semidirect
344. C₄₇	#24041	direct (N × H)
520. Q₈	#123×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₄₇	2
C₂×C₄₇×#483	2
C₂²×#103×C₄₇	2
C₄₇×#2486	2
C₄₇×#2043	2
C₄₇×#2035	2
C₄₇×#1892	2
C₄₇×#1869	2
C₄₇×#1865	2
C₄₇×#1787	2
#24041	47

Subgroups — C47×#24041 #26063739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24041 #26063739