Subgroups — C₂×C₄₇×#3043 #26100116

Order 12032.

2858 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#535	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#3043	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₇×#464	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#460	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₇×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#137×C₄₇	—	2	8	no	—
15	C₂×#137×C₄₇	C₂²	1	8	yes	complemented
16	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	complemented
17	C₂²×SD₁₆×C₄₇	—	2	8	no	—
18	C₂²×SD₁₆×C₄₇	C₂²	1	4	yes	—
19	C₂²×SD₁₆×C₄₇	C₂²	1	8	yes	complemented
20	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
21	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#535	—	2	4	no	—
24	C₄₇×#535	C₂²	1	8	yes	—
25	C₂×#127×C₄₇	C₂²	1	2	yes	—
26	C₂×#124×C₄₇	C₂²	1	2	yes	—
27	C₂×#121×C₄₇	—	2	2	no	—
28	C₂×#120×C₄₇	—	2	2	no	—
29	C₄₇×#519	—	2	4	no	—
30	C₄₇×#519	C₂²	1	8	yes	complemented
31	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
32	C₂×C₄×Q₈×C₄₇	C₂²	1	4	yes	complemented
33	C₂×#117×C₄₇	—	2	2	no	—
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#464	C₂²	1	32	yes	complemented
37	C₄₇×#460	C₂²	1	32	yes	complemented
38	C₄₇×#424	C₂²	1	8	yes	complemented
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	complemented
40	C₄₇×#418	C₂²	1	8	yes	complemented
41	C₄₇×#416	C₂²	1	8	yes	complemented
42	C₂×#103×C₄₇	C₂²	1	2	yes	complemented
43	C₂×#102×C₄₇	C₂²	1	4	yes	—
44	C₂×#102×C₄₇	C₂²	1	2	yes	complemented
45	C₂⁵×C₄₇	—	2	1	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	4	no	—
48	C₂×#41×C₄₇	—	2	4	no	—
49	C₂×#41×C₄₇	C₂³	1	4	yes	—
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	D₄	1	8	yes	complemented
54	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
57	C₂²×D₄×C₄₇	—	2	1	no	—
58	C₂²×D₄×C₄₇	—	2	4	no	—
59	C₂²×D₄×C₄₇	—	2	1	no	—
60	C₂²×D₄×C₄₇	—	2	2	no	—
61	C₂²×D₄×C₄₇	—	2	4	no	—
62	C₂²×D₄×C₄₇	—	2	4	no	—
63	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
64	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
66	C₂³×C₄×C₄₇	—	2	1	no	—
67	C₂³×C₄×C₄₇	—	2	1	no	—
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	#137×C₄₇	—	2	32	no	—
70	C₂×Q₁₆×C₄₇	—	2	8	no	—
71	C₂×Q₁₆×C₄₇	C₂³	1	8	yes	complemented
72	C₂×SD₁₆×C₄₇	—	2	16	no	—
73	C₂×SD₁₆×C₄₇	—	2	8	no	—
74	C₂×SD₁₆×C₄₇	—	2	32	no	—
75	C₂×SD₁₆×C₄₇	C₂³	1	16	yes	—
76	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	complemented
77	C₂×M₁₆×C₄₇	—	2	4	no	—
78	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
79	C₂²×C₈×C₄₇	—	2	4	no	—
80	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
81	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
83	#127×C₄₇	—	2	4	no	—
84	#127×C₄₇	C₂³	1	8	yes	—
85	#124×C₄₇	—	2	4	no	—
86	#124×C₄₇	C₂³	1	8	yes	—
87	#121×C₄₇	—	2	16	no	—
88	#120×C₄₇	—	2	16	no	—
89	C₄×Q₈×C₄₇	—	2	16	no	—
90	C₄×Q₈×C₄₇	—	2	8	no	—
91	C₄×Q₈×C₄₇	C₂³	1	16	yes	complemented
92	#117×C₄₇	—	2	2	no	—
93	#117×C₄₇	—	2	16	no	—
94	#117×C₄₇	D₄	1	4	yes	—
95	#117×C₄₇	C₂³	1	4	yes	—
96	#117×C₄₇	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
103	C₂×C₄²×C₄₇	—	2	4	no	—
104	C₂×C₄²×C₄₇	—	2	1	no	—
105	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
106	C₄⋊C₈×C₄₇	C₂³	1	16	yes	complemented
107	#103×C₄₇	C₂³	1	8	yes	complemented
108	#102×C₄₇	C₂³	1	16	yes	—
109	#102×C₄₇	C₂³	1	8	yes	complemented
110	C₂⁴×C₄₇	—	2	2	no	—
111	C₂⁴×C₄₇	—	2	1	no	—
112	C₂⁴×C₄₇	—	2	4	no	—
113	C₂⁴×C₄₇	—	4	4	no	—
114	C₂⁴×C₄₇	—	8	4	no	—
115	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
116	#41×C₄₇	—	2	8	no	—
117	#41×C₄₇	—	2	8	no	—
118	#41×C₄₇	—	4	8	no	—
119	C₂×Q₈×C₄₇	—	2	8	no	—
120	C₂×Q₈×C₄₇	—	2	16	no	—
121	C₂×Q₈×C₄₇	—	2	4	no	—
122	C₂×Q₈×C₄₇	—	2	2	no	—
123	C₂×Q₈×C₄₇	—	2	1	no	—
124	C₂×Q₈×C₄₇	—	2	4	no	—
125	C₂×Q₈×C₄₇	—	2	8	no	—
126	C₂×Q₈×C₄₇	—	2	2	no	—
127	C₂×Q₈×C₄₇	—	2	2	no	—
128	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	—
129	C₂×Q₈×C₄₇	C₂×D₄	1	16	yes	complemented
130	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
131	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
132	C₂×D₄×C₄₇	—	2	4	no	—
133	C₂×D₄×C₄₇	—	2	4	no	—
134	C₂×D₄×C₄₇	—	2	8	no	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	2	4	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	1	no	—
139	C₂×D₄×C₄₇	—	2	16	no	—
140	C₂×D₄×C₄₇	—	2	4	no	—
141	C₂×D₄×C₄₇	—	2	8	no	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	4	4	no	—
144	C₂×D₄×C₄₇	—	4	4	no	—
145	C₂×D₄×C₄₇	—	4	8	no	—
146	C₂×D₄×C₄₇	—	8	8	no	—
147	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
148	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₄₇	—	2	8	no	—
150	C₂²×C₄×C₄₇	—	2	4	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	4	no	—
155	C₂²×C₄×C₄₇	—	4	4	no	—
156	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₄₇	#41	1	4	yes	—
161	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
163	Q₁₆×C₄₇	—	2	16	no	—
164	SD₁₆×C₄₇	—	2	32	no	—
165	SD₁₆×C₄₇	—	2	16	no	—
166	M₁₆×C₄₇	—	2	8	no	—
167	C₂×C₈×C₄₇	—	2	4	no	—
168	C₂×C₈×C₄₇	—	2	8	no	—
169	C₂×C₈×C₄₇	—	2	4	no	—
170	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
171	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
172	C₄⋊C₄×C₄₇	—	2	16	no	—
173	C₄⋊C₄×C₄₇	—	2	2	no	—
174	C₄⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
175	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
176	C₂²⋊C₄×C₄₇	—	2	4	no	—
177	C₂²⋊C₄×C₄₇	—	2	16	no	—
178	C₂²⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
179	C₄²×C₄₇	—	2	16	no	—
180	C₄²×C₄₇	—	2	4	no	—
181	C₄²×C₄₇	C₂×D₄	1	4	yes	—
182	C₄²×C₄₇	C₂⁴	1	4	yes	—
183	C₂³×C₄₇	—	2	4	no	—
184	C₂³×C₄₇	—	2	4	no	—
185	C₂³×C₄₇	—	2	2	no	—
186	C₂³×C₄₇	—	4	2	no	—
187	C₂³×C₄₇	—	4	8	no	—
188	C₂³×C₄₇	—	4	4	no	—
189	C₂³×C₄₇	—	4	4	no	—
190	C₂³×C₄₇	—	4	8	no	—
191	C₂³×C₄₇	—	8	8	no	—
192	C₂³×C₄₇	—	8	16	no	—
193	C₂³×C₄₇	#121	1	4	yes	—
194	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
195	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₄₇	—	2	8	no	—
197	Q₈×C₄₇	—	2	16	no	—
198	Q₈×C₄₇	—	2	4	no	—
199	Q₈×C₄₇	—	2	2	no	—
200	Q₈×C₄₇	—	2	2	no	—
201	Q₈×C₄₇	—	4	2	no	—
202	Q₈×C₄₇	C₂²×D₄	1	8	yes	—
203	D₄×C₄₇	—	2	4	no	—
204	D₄×C₄₇	—	2	2	no	—
205	D₄×C₄₇	—	2	4	no	—
206	D₄×C₄₇	—	2	2	no	—
207	D₄×C₄₇	—	4	8	no	—
208	D₄×C₄₇	—	4	8	no	—
209	D₄×C₄₇	—	4	4	no	—
210	D₄×C₄₇	—	4	2	no	—
211	D₄×C₄₇	—	8	16	no	—
212	C₂×C₄×C₄₇	—	2	8	no	—
213	C₂×C₄×C₄₇	—	2	16	no	—
214	C₂×C₄×C₄₇	—	2	8	no	—
215	C₂×C₄×C₄₇	—	2	4	no	—
216	C₂×C₄×C₄₇	—	2	4	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	4	4	no	—
220	C₂×C₄×C₄₇	—	4	8	no	—
221	C₂×C₄×C₄₇	#121	1	4	yes	—
222	C₂×C₄×C₄₇	#121	1	8	yes	—
223	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
224	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
229	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
230	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
231	C₈×C₄₇	—	2	4	no	—
232	C₈×C₄₇	—	2	4	no	—
233	C₂×#3043	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂²×C₄₇	—	2	8	no	—
235	C₂²×C₄₇	—	2	4	no	—
236	C₂²×C₄₇	—	4	2	no	—
237	C₂²×C₄₇	—	4	4	no	—
238	C₂²×C₄₇	—	4	4	no	—
239	C₂²×C₄₇	—	4	8	no	—
240	C₂²×C₄₇	—	8	16	no	—
241	C₂²×C₄₇	—	8	4	no	—
242	C₂²×C₄₇	—	8	8	no	—
243	C₂²×C₄₇	C₂×#121	1	4	yes	—
244	C₂²×C₄₇	C₂×#121	1	2	yes	—
245	C₂²×C₄₇	#577	1	4	yes	—
246	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
247	C₄×C₄₇	—	2	8	no	—
248	C₄×C₄₇	—	2	8	no	—
249	C₄×C₄₇	—	4	2	no	—
250	C₄×C₄₇	—	4	4	no	—
251	C₄×C₄₇	C₂×#121	1	4	yes	—
252	C₄×C₄₇	C₂×#121	1	2	yes	—
253	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
254	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
255	C₂²×#137	C₂×C₄₇	1	1	yes	characteristic, complemented
256	C₂³×SD₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
257	C₂×#535	C₂×C₄₇	1	1	yes	characteristic
258	C₂×#519	C₂×C₄₇	1	1	yes	characteristic, complemented
259	#3043	C₂×C₄₇	1	16	yes	direct product factor
260	C₂×#464	C₂×C₄₇	1	4	yes	complemented
261	C₂×#460	C₂×C₄₇	1	4	yes	complemented
262	C₂×#424	C₂×C₄₇	1	1	yes	characteristic, complemented
263	C₂×#418	C₂×C₄₇	1	1	yes	characteristic, complemented
264	C₂×#416	C₂×C₄₇	1	1	yes	characteristic, complemented
265	C₂×C₄₇	—	2	4	no	—
266	C₂×C₄₇	—	8	2	no	—
267	C₂×C₄₇	—	8	4	no	—
268	C₂×C₄₇	#3043	1	4	yes	direct product factor
269	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
270	C₂×C₄₇	C₂×#577	1	2	yes	—
271	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
272	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
273	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
274	C₂×#137	—	2	8	no	—
275	C₂×#137	C₂²×C₄₇	1	8	yes	complemented
276	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	complemented
277	C₂²×SD₁₆	—	2	8	no	—
278	C₂²×SD₁₆	C₂²×C₄₇	1	4	yes	—
279	C₂²×SD₁₆	C₂²×C₄₇	1	8	yes	complemented
280	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	complemented
281	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
282	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
283	#535	—	2	4	no	—
284	#535	C₂²×C₄₇	1	8	yes	—
285	C₂×#127	C₂²×C₄₇	1	2	yes	—
286	C₂×#124	C₂²×C₄₇	1	2	yes	—
287	C₂×#121	—	2	2	no	—
288	C₂×#120	—	2	2	no	—
289	#519	—	2	4	no	—
290	#519	C₂²×C₄₇	1	8	yes	complemented
291	C₂×C₄×Q₈	—	2	2	no	—
292	C₂×C₄×Q₈	C₂²×C₄₇	1	4	yes	complemented
293	C₂×#117	—	2	2	no	—
294	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
295	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
296	#464	C₂²×C₄₇	1	32	yes	complemented
297	#460	C₂²×C₄₇	1	32	yes	complemented
298	#424	C₂²×C₄₇	1	8	yes	complemented
299	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
300	#418	C₂²×C₄₇	1	8	yes	complemented
301	#416	C₂²×C₄₇	1	8	yes	complemented
302	C₂×#103	C₂²×C₄₇	1	2	yes	complemented
303	C₂×#102	C₂²×C₄₇	1	4	yes	—
304	C₂×#102	C₂²×C₄₇	1	2	yes	complemented
305	C₄₇	C₂×#3043	1	1	yes	characteristic, direct product factor, Sylow
306	C₂⁵	—	2	1	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	4	no	—
309	C₂×#41	—	2	4	no	—
310	C₂×#41	C₂³×C₄₇	1	4	yes	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	2	no	—
313	C₂²×Q₈	—	2	4	no	—
314	C₂²×Q₈	D₄×C₄₇	1	8	yes	complemented
315	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
316	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
317	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	—	2	4	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	4	no	—
323	C₂²×D₄	—	2	4	no	—
324	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
325	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
326	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
330	#137	—	2	32	no	—
331	C₂×Q₁₆	—	2	8	no	—
332	C₂×Q₁₆	C₂³×C₄₇	1	8	yes	complemented
333	C₂×SD₁₆	—	2	16	no	—
334	C₂×SD₁₆	—	2	8	no	—
335	C₂×SD₁₆	—	2	32	no	—
336	C₂×SD₁₆	C₂³×C₄₇	1	16	yes	—
337	C₂×SD₁₆	C₂³×C₄₇	1	8	yes	complemented
338	C₂×M₁₆	—	2	4	no	—
339	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
340	C₂²×C₈	—	2	4	no	—
341	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
342	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
343	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
344	#127	—	2	4	no	—
345	#127	C₂³×C₄₇	1	8	yes	—
346	#124	—	2	4	no	—
347	#124	C₂³×C₄₇	1	8	yes	—
348	#121	—	2	16	no	—
349	#120	—	2	16	no	—
350	C₄×Q₈	—	2	16	no	—
351	C₄×Q₈	—	2	8	no	—
352	C₄×Q₈	C₂³×C₄₇	1	16	yes	complemented
353	#117	—	2	2	no	—
354	#117	—	2	16	no	—
355	#117	D₄×C₄₇	1	4	yes	—
356	#117	C₂³×C₄₇	1	4	yes	—
357	#117	C₂³×C₄₇	1	4	yes	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
367	C₄⋊C₈	C₂³×C₄₇	1	16	yes	complemented
368	#103	C₂³×C₄₇	1	8	yes	complemented
369	#102	C₂³×C₄₇	1	16	yes	—
370	#102	C₂³×C₄₇	1	8	yes	complemented
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	2	1	no	—
373	C₂⁴	—	2	4	no	—
374	C₂⁴	—	4	4	no	—
375	C₂⁴	—	8	4	no	—
376	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
377	#41	—	2	8	no	—
378	#41	—	2	8	no	—
379	#41	—	4	8	no	—
380	C₂×Q₈	—	2	8	no	—
381	C₂×Q₈	—	2	16	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	8	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	C₂×D₄×C₄₇	1	8	yes	—
390	C₂×Q₈	C₂×D₄×C₄₇	1	16	yes	complemented
391	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
392	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	16	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	—	8	8	no	—
408	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
409	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
418	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
421	C₂²×C₄	#41×C₄₇	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
424	Q₁₆	—	2	16	no	—
425	SD₁₆	—	2	32	no	—
426	SD₁₆	—	2	16	no	—
427	M₁₆	—	2	8	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	8	no	—
430	C₂×C₈	—	2	4	no	—
431	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
432	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
433	C₄⋊C₄	—	2	16	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
436	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	16	no	—
439	C₂²⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
440	C₄²	—	2	16	no	—
441	C₄²	—	2	4	no	—
442	C₄²	C₂×D₄×C₄₇	1	4	yes	—
443	C₄²	C₂⁴×C₄₇	1	4	yes	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	8	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	8	no	—
452	C₂³	—	8	8	no	—
453	C₂³	—	8	16	no	—
454	C₂³	#121×C₄₇	1	4	yes	—
455	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
456	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
457	Q₈	—	2	8	no	—
458	Q₈	—	2	16	no	—
459	Q₈	—	2	4	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	C₂²×D₄×C₄₇	1	8	yes	—
464	D₄	—	2	4	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	8	no	—
470	D₄	—	4	4	no	—
471	D₄	—	4	2	no	—
472	D₄	—	8	16	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	16	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	#121×C₄₇	1	4	yes	—
483	C₂×C₄	#121×C₄₇	1	8	yes	—
484	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
485	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
488	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
489	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
490	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
491	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
492	C₈	—	2	4	no	—
493	C₈	—	2	4	no	—
494	C₂²	—	2	8	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	8	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	8	16	no	—
501	C₂²	—	8	8	no	—
502	C₂²	—	8	4	no	—
503	C₂²	C₂×#121×C₄₇	1	4	yes	—
504	C₂²	C₂×#121×C₄₇	1	2	yes	—
505	C₂²	C₄₇×#577	1	4	yes	—
506	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
507	C₄	—	2	8	no	—
508	C₄	—	2	8	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	2	no	—
511	C₄	C₂×#121×C₄₇	1	4	yes	—
512	C₄	C₂×#121×C₄₇	1	2	yes	—
513	C₄	C₂³×D₄×C₄₇	1	1	yes	characteristic
514	C₄	C₂²×#41×C₄₇	1	1	yes	characteristic
515	C₂	—	2	4	no	—
516	C₂	—	8	4	no	—
517	C₂	—	8	2	no	—
518	C₂	C₄₇×#3043	1	4	yes	direct product factor
519	C₂	C₂²×#121×C₄₇	1	1	yes	characteristic
520	C₂	C₂×C₄₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
prime radical	C₂×C₄₇×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#137×C₄₇	C₂	semidirect
2. C₂³×SD₁₆×C₄₇	C₂	semidirect
4. C₂×C₄₇×#519	C₂	semidirect
5. C₄₇×#3043	C₂	direct (N × H)
6. C₂×C₄₇×#464	C₂	semidirect
7. C₂×C₄₇×#460	C₂	semidirect
8. C₂×C₄₇×#424	C₂	semidirect
9. C₂×C₄₇×#418	C₂	semidirect
10. C₂×C₄₇×#416	C₂	semidirect
15. C₂×#137×C₄₇	C₂²	semidirect
16. C₂²×Q₁₆×C₄₇	C₂²	semidirect
19. C₂²×SD₁₆×C₄₇	C₂²	semidirect
20. C₂²×SD₁₆×C₄₇	C₂²	semidirect
30. C₄₇×#519	C₂²	semidirect
32. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
36. C₄₇×#464	C₂²	semidirect
37. C₄₇×#460	C₂²	semidirect
38. C₄₇×#424	C₂²	semidirect
39. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
40. C₄₇×#418	C₂²	semidirect
41. C₄₇×#416	C₂²	semidirect
42. C₂×#103×C₄₇	C₂²	semidirect
44. C₂×#102×C₄₇	C₂²	semidirect
53. C₂²×Q₈×C₄₇	D₄	semidirect
71. C₂×Q₁₆×C₄₇	C₂³	semidirect
76. C₂×SD₁₆×C₄₇	C₂³	semidirect
91. C₄×Q₈×C₄₇	C₂³	semidirect
106. C₄⋊C₈×C₄₇	C₂³	semidirect
107. #103×C₄₇	C₂³	semidirect
109. #102×C₄₇	C₂³	semidirect
129. C₂×Q₈×C₄₇	C₂×D₄	semidirect
233. C₂×#3043	C₄₇	direct (N × H)
255. C₂²×#137	C₂×C₄₇	semidirect
256. C₂³×SD₁₆	C₂×C₄₇	semidirect
258. C₂×#519	C₂×C₄₇	semidirect
259. #3043	C₂×C₄₇	direct (N × H)
260. C₂×#464	C₂×C₄₇	semidirect
261. C₂×#460	C₂×C₄₇	semidirect
262. C₂×#424	C₂×C₄₇	semidirect
263. C₂×#418	C₂×C₄₇	semidirect
264. C₂×#416	C₂×C₄₇	semidirect
268. C₂×C₄₇	#3043	direct (N × H)
275. C₂×#137	C₂²×C₄₇	semidirect
276. C₂²×Q₁₆	C₂²×C₄₇	semidirect
279. C₂²×SD₁₆	C₂²×C₄₇	semidirect
280. C₂²×SD₁₆	C₂²×C₄₇	semidirect
290. #519	C₂²×C₄₇	semidirect
292. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
296. #464	C₂²×C₄₇	semidirect
297. #460	C₂²×C₄₇	semidirect
298. #424	C₂²×C₄₇	semidirect
299. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
300. #418	C₂²×C₄₇	semidirect
301. #416	C₂²×C₄₇	semidirect
302. C₂×#103	C₂²×C₄₇	semidirect
304. C₂×#102	C₂²×C₄₇	semidirect
305. C₄₇	C₂×#3043	direct (N × H)
314. C₂²×Q₈	D₄×C₄₇	semidirect
332. C₂×Q₁₆	C₂³×C₄₇	semidirect
337. C₂×SD₁₆	C₂³×C₄₇	semidirect
352. C₄×Q₈	C₂³×C₄₇	semidirect
367. C₄⋊C₈	C₂³×C₄₇	semidirect
368. #103	C₂³×C₄₇	semidirect
370. #102	C₂³×C₄₇	semidirect
390. C₂×Q₈	C₂×D₄×C₄₇	semidirect
518. C₂	C₄₇×#3043	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×#137×C₄₇	2
C₂³×SD₁₆×C₄₇	2
C₂×C₄₇×#535	2
C₂×C₄₇×#519	2
C₄₇×#3043	2
C₂×C₄₇×#464	2
C₂×C₄₇×#460	2
C₂×C₄₇×#424	2
C₂×C₄₇×#418	2
C₂×C₄₇×#416	2
C₂×#3043	47

Subgroups — C2×C47×#3043 #26100116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#3043 #26100116