Subgroups — C₄₇×#23493 #26063191

Order 12032.

1586 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#535	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#100×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2309	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2037	C₂	1	8	yes	maximal, complemented
8	C₄₇×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₄₇×#535	—	2	2	no	—
14	C₄₇×#535	—	2	2	no	—
15	C₄₇×#535	—	2	2	no	—
16	C₄₇×#535	C₂²	1	4	yes	—
17	C₂×#127×C₄₇	—	2	1	no	—
18	C₂×#124×C₄₇	—	2	1	no	—
19	C₂×#121×C₄₇	—	2	2	no	—
20	C₂×#120×C₄₇	—	2	2	no	—
21	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#428	—	2	2	no	—
25	C₄₇×#428	C₂²	1	4	yes	complemented
26	C₄₇×#427	—	2	2	no	—
27	C₄₇×#421	—	2	4	no	—
28	C₂×#104×C₄₇	C₂²	1	4	yes	complemented
29	C₄₇×#419	—	2	1	no	—
30	C₄₇×#418	—	2	1	no	—
31	C₄₇×#417	C₂²	1	4	yes	complemented
32	C₄₇×#416	—	2	2	no	—
33	C₂×#100×C₄₇	—	2	4	no	—
34	C₂×#100×C₄₇	C₂²	1	4	yes	complemented
35	C₄₇×#390	—	2	2	no	—
36	C₄₇×#390	C₂²	1	4	yes	complemented
37	C₄₇×#379	—	2	2	no	—
38	C₄₇×#339	C₂²	1	4	yes	complemented
39	C₂⁵×C₄₇	D₄	1	2	yes	—
40	C₂×#41×C₄₇	—	2	1	no	—
41	C₂×#41×C₄₇	—	2	1	no	—
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	D₄	1	2	yes	—
47	C₂×#41×C₄₇	C₂³	1	2	yes	—
48	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₄₇	—	2	1	no	—
50	C₂²×D₄×C₄₇	—	2	4	no	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	—	2	1	no	—
54	C₂²×D₄×C₄₇	—	2	1	no	—
55	C₂²×D₄×C₄₇	—	2	2	no	—
56	C₂²×D₄×C₄₇	—	2	2	no	—
57	C₂²×D₄×C₄₇	—	2	2	no	—
58	C₂²×D₄×C₄₇	—	2	2	no	—
59	C₂²×D₄×C₄₇	D₄	1	2	yes	—
60	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₇	—	2	1	no	—
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₄₇	—	2	1	no	—
65	C₂×M₁₆×C₄₇	—	2	2	no	—
66	C₂×M₁₆×C₄₇	—	2	1	no	—
67	C₂×M₁₆×C₄₇	—	2	2	no	—
68	C₂×M₁₆×C₄₇	—	2	2	no	—
69	C₂×M₁₆×C₄₇	D₄	1	4	yes	complemented
70	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
71	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₇	—	2	1	no	—
73	C₂²×C₈×C₄₇	—	2	1	no	—
74	#127×C₄₇	—	2	4	no	—
75	#127×C₄₇	—	2	4	no	—
76	#124×C₄₇	—	2	4	no	—
77	#124×C₄₇	—	2	4	no	—
78	#121×C₄₇	—	2	8	no	—
79	#121×C₄₇	—	2	8	no	—
80	#120×C₄₇	—	2	8	no	—
81	#120×C₄₇	—	2	8	no	—
82	#117×C₄₇	—	2	1	no	—
83	#117×C₄₇	—	2	1	no	—
84	#117×C₄₇	—	2	2	no	—
85	#117×C₄₇	—	2	2	no	—
86	#117×C₄₇	—	2	1	no	—
87	#117×C₄₇	—	2	1	no	—
88	#117×C₄₇	—	2	1	no	—
89	#117×C₄₇	—	2	1	no	—
90	#117×C₄₇	D₄	1	2	yes	—
91	#117×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
95	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂×C₄²×C₄₇	—	2	1	no	—
102	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
103	#107×C₄₇	—	2	4	no	—
104	#106×C₄₇	—	2	4	no	—
105	#104×C₄₇	—	2	8	no	—
106	#103×C₄₇	—	2	4	no	—
107	#102×C₄₇	—	2	4	no	—
108	#100×C₄₇	—	2	8	no	—
109	C₂⁴×C₄₇	—	2	2	no	—
110	C₂⁴×C₄₇	—	2	1	no	—
111	C₂⁴×C₄₇	—	2	2	no	—
112	C₂⁴×C₄₇	—	2	4	no	—
113	C₂⁴×C₄₇	—	2	4	no	—
114	C₂⁴×C₄₇	—	8	4	no	—
115	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
116	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
117	#41×C₄₇	—	2	4	no	—
118	#41×C₄₇	—	2	4	no	—
119	#41×C₄₇	—	2	2	no	—
120	#41×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	2	no	—
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	4	2	no	—
124	#41×C₄₇	—	4	2	no	—
125	#41×C₄₇	—	4	2	no	—
126	#41×C₄₇	—	4	2	no	—
127	C₂×Q₈×C₄₇	—	2	1	no	—
128	C₂×Q₈×C₄₇	—	2	2	no	—
129	C₂×Q₈×C₄₇	—	2	2	no	—
130	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₄₇	—	2	2	no	—
132	C₂×D₄×C₄₇	—	2	2	no	—
133	C₂×D₄×C₄₇	—	2	16	no	—
134	C₂×D₄×C₄₇	—	2	2	no	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	2	1	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	4	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	4	no	—
141	C₂×D₄×C₄₇	—	2	2	no	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	2	2	no	—
144	C₂×D₄×C₄₇	—	2	2	no	—
145	C₂×D₄×C₄₇	—	2	2	no	—
146	C₂×D₄×C₄₇	—	2	2	no	—
147	C₂×D₄×C₄₇	—	4	2	no	—
148	C₂×D₄×C₄₇	—	4	2	no	—
149	C₂×D₄×C₄₇	—	4	2	no	—
150	C₂×D₄×C₄₇	—	4	2	no	—
151	C₂×D₄×C₄₇	—	4	2	no	—
152	C₂×D₄×C₄₇	—	4	2	no	—
153	C₂×D₄×C₄₇	—	4	2	no	—
154	C₂×D₄×C₄₇	—	4	2	no	—
155	C₂×D₄×C₄₇	—	4	2	no	—
156	C₂×D₄×C₄₇	—	4	2	no	—
157	C₂×D₄×C₄₇	—	8	8	no	—
158	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₇	—	2	2	no	—
160	C₂²×C₄×C₄₇	—	2	1	no	—
161	C₂²×C₄×C₄₇	—	2	2	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	—	4	2	no	—
166	C₂²×C₄×C₄₇	—	4	2	no	—
167	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₄₇	#41	1	2	yes	—
174	C₂²×C₄×C₄₇	#41	1	2	yes	—
175	C₂²×C₄×C₄₇	#41	1	2	yes	—
176	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
177	M₁₆×C₄₇	—	2	4	no	—
178	M₁₆×C₄₇	—	2	2	no	—
179	M₁₆×C₄₇	—	2	2	no	—
180	M₁₆×C₄₇	—	2	2	no	—
181	M₁₆×C₄₇	—	4	2	no	—
182	M₁₆×C₄₇	C₂×D₄	1	4	yes	complemented
183	C₂×C₈×C₄₇	—	2	4	no	—
184	C₂×C₈×C₄₇	—	2	2	no	—
185	C₂×C₈×C₄₇	—	2	2	no	—
186	C₂×C₈×C₄₇	—	4	2	no	—
187	C₄⋊C₄×C₄₇	—	2	2	no	—
188	C₄⋊C₄×C₄₇	—	2	2	no	—
189	C₄⋊C₄×C₄₇	—	2	2	no	—
190	C₄⋊C₄×C₄₇	—	4	2	no	—
191	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
192	C₂²⋊C₄×C₄₇	—	2	16	no	—
193	C₂²⋊C₄×C₄₇	—	2	2	no	—
194	C₂²⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	4	1	no	—
196	C₂²⋊C₄×C₄₇	—	4	1	no	—
197	C₂²⋊C₄×C₄₇	—	4	2	no	—
198	C₂²⋊C₄×C₄₇	—	8	8	no	—
199	C₄²×C₄₇	—	2	2	no	—
200	C₄²×C₄₇	—	2	2	no	—
201	C₄²×C₄₇	—	2	2	no	—
202	C₄²×C₄₇	—	2	2	no	—
203	C₄²×C₄₇	—	4	1	no	—
204	C₄²×C₄₇	—	4	1	no	—
205	C₂³×C₄₇	—	2	4	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	2	4	no	—
208	C₂³×C₄₇	—	2	4	no	—
209	C₂³×C₄₇	—	4	2	no	—
210	C₂³×C₄₇	—	4	8	no	—
211	C₂³×C₄₇	—	4	4	no	—
212	C₂³×C₄₇	—	4	8	no	—
213	C₂³×C₄₇	—	4	2	no	—
214	C₂³×C₄₇	—	4	4	no	—
215	C₂³×C₄₇	—	4	4	no	—
216	C₂³×C₄₇	—	8	4	no	—
217	C₂³×C₄₇	—	8	8	no	—
218	C₂³×C₄₇	—	8	8	no	—
219	C₂³×C₄₇	#120	1	1	yes	characteristic
220	C₂³×C₄₇	#120	1	1	yes	characteristic
221	C₂³×C₄₇	#121	1	2	yes	—
222	C₂³×C₄₇	#123	1	2	yes	—
223	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₄₇	—	2	2	no	—
225	Q₈×C₄₇	—	2	2	no	—
226	Q₈×C₄₇	—	4	2	no	—
227	D₄×C₄₇	—	2	2	no	—
228	D₄×C₄₇	—	2	2	no	—
229	D₄×C₄₇	—	4	2	no	—
230	D₄×C₄₇	—	4	2	no	—
231	D₄×C₄₇	—	4	4	no	—
232	D₄×C₄₇	—	4	2	no	—
233	D₄×C₄₇	—	4	2	no	—
234	D₄×C₄₇	—	4	2	no	—
235	D₄×C₄₇	—	4	2	no	—
236	D₄×C₄₇	—	4	4	no	—
237	D₄×C₄₇	—	4	4	no	—
238	D₄×C₄₇	—	4	2	no	—
239	D₄×C₄₇	—	8	16	no	—
240	C₂×C₄×C₄₇	—	2	4	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	4	4	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	4	2	no	—
246	C₂×C₄×C₄₇	—	4	4	no	—
247	C₂×C₄×C₄₇	—	4	4	no	—
248	C₂×C₄×C₄₇	—	4	4	no	—
249	C₂×C₄×C₄₇	—	4	2	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
252	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
253	C₂×C₄×C₄₇	#121	1	2	yes	—
254	C₂×C₄×C₄₇	#121	1	2	yes	—
255	C₂×C₄×C₄₇	#121	1	2	yes	—
256	C₂×C₄×C₄₇	#121	1	2	yes	—
257	C₂×C₄×C₄₇	#121	1	2	yes	—
258	C₂×C₄×C₄₇	#123	1	2	yes	—
259	C₂×C₄×C₄₇	#123	1	2	yes	—
260	C₂×C₄×C₄₇	#123	1	2	yes	—
261	C₂×C₄×C₄₇	#124	1	2	yes	—
262	C₂×C₄×C₄₇	#124	1	2	yes	—
263	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
269	C₈×C₄₇	—	2	4	no	—
270	C₈×C₄₇	—	4	2	no	—
271	#23493	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂²×C₄₇	—	2	2	no	—
273	C₂²×C₄₇	—	2	2	no	—
274	C₂²×C₄₇	—	2	2	no	—
275	C₂²×C₄₇	—	4	2	no	—
276	C₂²×C₄₇	—	4	2	no	—
277	C₂²×C₄₇	—	4	8	no	—
278	C₂²×C₄₇	—	4	2	no	—
279	C₂²×C₄₇	—	4	4	no	—
280	C₂²×C₄₇	—	4	4	no	—
281	C₂²×C₄₇	—	4	8	no	—
282	C₂²×C₄₇	—	8	4	no	—
283	C₂²×C₄₇	—	8	4	no	—
284	C₂²×C₄₇	—	8	8	no	—
285	C₂²×C₄₇	—	8	8	no	—
286	C₂²×C₄₇	#394	1	2	yes	—
287	C₂²×C₄₇	#394	1	2	yes	—
288	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
289	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
290	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
291	C₄×C₄₇	—	4	2	no	—
292	C₄×C₄₇	—	4	4	no	—
293	C₄×C₄₇	—	8	2	no	—
294	C₄×C₄₇	—	8	2	no	—
295	C₄×C₄₇	#394	1	2	yes	—
296	C₄×C₄₇	#394	1	2	yes	—
297	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
298	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
299	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
300	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
301	C₂×#535	C₂×C₄₇	1	1	yes	characteristic
302	#2911	C₂×C₄₇	1	1	yes	characteristic, complemented
303	C₂×#421	C₂×C₄₇	1	1	yes	characteristic, complemented
304	#2896	C₂×C₄₇	1	1	yes	characteristic, complemented
305	C₂²×#100	C₂×C₄₇	1	1	yes	characteristic, complemented
306	#2309	C₂×C₄₇	1	1	yes	characteristic, complemented
307	#2037	C₂×C₄₇	1	8	yes	complemented
308	#1733	C₂×C₄₇	1	1	yes	characteristic, complemented
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	—	2	2	no	—
312	C₂×C₄₇	—	2	2	no	—
313	C₂×C₄₇	—	8	4	no	—
314	C₂×C₄₇	—	8	2	no	—
315	C₂×C₄₇	C₂×#394	1	1	yes	characteristic
316	C₂×C₄₇	#3019	1	2	yes	—
317	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
318	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
319	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
320	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
321	#535	—	2	2	no	—
322	#535	—	2	2	no	—
323	#535	—	2	2	no	—
324	#535	C₂²×C₄₇	1	4	yes	—
325	C₂×#127	—	2	1	no	—
326	C₂×#124	—	2	1	no	—
327	C₂×#121	—	2	2	no	—
328	C₂×#120	—	2	2	no	—
329	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
330	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
331	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
332	#428	—	2	2	no	—
333	#428	C₂²×C₄₇	1	4	yes	complemented
334	#427	—	2	2	no	—
335	#421	—	2	4	no	—
336	C₂×#104	C₂²×C₄₇	1	4	yes	complemented
337	#419	—	2	1	no	—
338	#418	—	2	1	no	—
339	#417	C₂²×C₄₇	1	4	yes	complemented
340	#416	—	2	2	no	—
341	C₂×#100	—	2	4	no	—
342	C₂×#100	C₂²×C₄₇	1	4	yes	complemented
343	#390	—	2	2	no	—
344	#390	C₂²×C₄₇	1	4	yes	complemented
345	#379	—	2	2	no	—
346	#339	C₂²×C₄₇	1	4	yes	complemented
347	C₄₇	#23493	1	1	yes	characteristic, direct product factor, Sylow
348	C₂⁵	D₄×C₄₇	1	2	yes	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	2	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	2	no	—
355	C₂×#41	D₄×C₄₇	1	2	yes	—
356	C₂×#41	C₂³×C₄₇	1	2	yes	—
357	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	—	2	4	no	—
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	—	2	1	no	—
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	—	2	2	no	—
368	C₂²×D₄	D₄×C₄₇	1	2	yes	—
369	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	2	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	D₄×C₄₇	1	4	yes	complemented
379	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
380	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	#127	—	2	4	no	—
384	#127	—	2	4	no	—
385	#124	—	2	4	no	—
386	#124	—	2	4	no	—
387	#121	—	2	8	no	—
388	#121	—	2	8	no	—
389	#120	—	2	8	no	—
390	#120	—	2	8	no	—
391	#117	—	2	1	no	—
392	#117	—	2	1	no	—
393	#117	—	2	2	no	—
394	#117	—	2	2	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	D₄×C₄₇	1	2	yes	—
400	#117	C₂³×C₄₇	1	2	yes	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
404	C₂×C₂²⋊C₄	—	2	4	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	8	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
412	#107	—	2	4	no	—
413	#106	—	2	4	no	—
414	#104	—	2	8	no	—
415	#103	—	2	4	no	—
416	#102	—	2	4	no	—
417	#100	—	2	8	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	—	2	1	no	—
420	C₂⁴	—	2	2	no	—
421	C₂⁴	—	2	4	no	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	8	4	no	—
424	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
425	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
426	#41	—	2	4	no	—
427	#41	—	2	4	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	#41	—	4	2	no	—
435	#41	—	4	2	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	16	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	—	4	2	no	—
466	C₂×D₄	—	8	8	no	—
467	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
482	C₂²×C₄	#41×C₄₇	1	2	yes	—
483	C₂²×C₄	#41×C₄₇	1	2	yes	—
484	C₂²×C₄	#41×C₄₇	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
486	M₁₆	—	2	4	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	4	2	no	—
491	M₁₆	C₂×D₄×C₄₇	1	4	yes	complemented
492	C₂×C₈	—	2	4	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	4	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
501	C₂²⋊C₄	—	2	16	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	2	no	—
507	C₂²⋊C₄	—	8	8	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	4	1	no	—
513	C₄²	—	4	1	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	8	no	—
520	C₂³	—	4	4	no	—
521	C₂³	—	4	8	no	—
522	C₂³	—	4	2	no	—
523	C₂³	—	4	4	no	—
524	C₂³	—	4	4	no	—
525	C₂³	—	8	4	no	—
526	C₂³	—	8	8	no	—
527	C₂³	—	8	8	no	—
528	C₂³	#120×C₄₇	1	1	yes	characteristic
529	C₂³	#120×C₄₇	1	1	yes	characteristic
530	C₂³	#121×C₄₇	1	2	yes	—
531	C₂³	#123×C₄₇	1	2	yes	—
532	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	4	2	no	—
536	D₄	—	2	2	no	—
537	D₄	—	2	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	4	no	—
547	D₄	—	4	2	no	—
548	D₄	—	8	16	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
561	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
562	C₂×C₄	#121×C₄₇	1	2	yes	—
563	C₂×C₄	#121×C₄₇	1	2	yes	—
564	C₂×C₄	#121×C₄₇	1	2	yes	—
565	C₂×C₄	#121×C₄₇	1	2	yes	—
566	C₂×C₄	#121×C₄₇	1	2	yes	—
567	C₂×C₄	#123×C₄₇	1	2	yes	—
568	C₂×C₄	#123×C₄₇	1	2	yes	—
569	C₂×C₄	#123×C₄₇	1	2	yes	—
570	C₂×C₄	#124×C₄₇	1	2	yes	—
571	C₂×C₄	#124×C₄₇	1	2	yes	—
572	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
575	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
576	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
577	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
578	C₈	—	2	4	no	—
579	C₈	—	4	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	8	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	8	no	—
590	C₂²	—	8	4	no	—
591	C₂²	—	8	8	no	—
592	C₂²	—	8	4	no	—
593	C₂²	—	8	8	no	—
594	C₂²	C₄₇×#394	1	2	yes	—
595	C₂²	C₄₇×#394	1	2	yes	—
596	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
597	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
598	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
599	C₄	—	4	2	no	—
600	C₄	—	4	4	no	—
601	C₄	—	8	2	no	—
602	C₄	—	8	2	no	—
603	C₄	C₄₇×#394	1	2	yes	—
604	C₄	C₄₇×#394	1	2	yes	—
605	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
606	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
607	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
608	C₄	C₂×#124×C₄₇	1	1	yes	characteristic
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	2	no	—
612	C₂	—	2	2	no	—
613	C₂	—	8	4	no	—
614	C₂	—	8	2	no	—
615	C₂	C₂×C₄₇×#394	1	1	yes	characteristic
616	C₂	C₄₇×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2911	C₂	semidirect
3. C₂×C₄₇×#421	C₂	semidirect
4. C₄₇×#2896	C₂	semidirect
5. C₂²×#100×C₄₇	C₂	semidirect
6. C₄₇×#2309	C₂	semidirect
7. C₄₇×#2037	C₂	semidirect
8. C₄₇×#1733	C₂	semidirect
25. C₄₇×#428	C₂²	semidirect
28. C₂×#104×C₄₇	C₂²	semidirect
31. C₄₇×#417	C₂²	semidirect
34. C₂×#100×C₄₇	C₂²	semidirect
36. C₄₇×#390	C₂²	semidirect
38. C₄₇×#339	C₂²	semidirect
69. C₂×M₁₆×C₄₇	D₄	semidirect
182. M₁₆×C₄₇	C₂×D₄	semidirect
271. #23493	C₄₇	direct (N × H)
302. #2911	C₂×C₄₇	semidirect
303. C₂×#421	C₂×C₄₇	semidirect
304. #2896	C₂×C₄₇	semidirect
305. C₂²×#100	C₂×C₄₇	semidirect
306. #2309	C₂×C₄₇	semidirect
307. #2037	C₂×C₄₇	semidirect
308. #1733	C₂×C₄₇	semidirect
333. #428	C₂²×C₄₇	semidirect
336. C₂×#104	C₂²×C₄₇	semidirect
339. #417	C₂²×C₄₇	semidirect
342. C₂×#100	C₂²×C₄₇	semidirect
344. #390	C₂²×C₄₇	semidirect
346. #339	C₂²×C₄₇	semidirect
347. C₄₇	#23493	direct (N × H)
378. C₂×M₁₆	D₄×C₄₇	semidirect
491. M₁₆	C₂×D₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#535	2
C₄₇×#2911	2
C₂×C₄₇×#421	2
C₄₇×#2896	2
C₂²×#100×C₄₇	2
C₄₇×#2309	2
C₄₇×#2037	2
C₄₇×#1733	2
#23493	47

Subgroups — C47×#23493 #26063191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#23493 #26063191