Subgroups — C₄₇×#18826 #26058524

Order 12032.

1114 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1654	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1651	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1627	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1625	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1556	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₄₇	—	2	1	no	—
13	D₄×Q₈×C₄₇	—	2	1	no	—
14	D₄×Q₈×C₄₇	C₂²	1	2	yes	—
15	C₄₇×#547	—	2	2	no	—
16	C₄₇×#547	—	2	1	no	—
17	C₄₇×#547	—	2	2	no	—
18	C₄₇×#547	C₂²	1	2	yes	—
19	C₄₇×#536	—	2	2	no	—
20	C₄₇×#536	—	2	1	no	—
21	C₄₇×#532	—	2	1	no	—
22	C₄₇×#532	C₂²	1	1	yes	characteristic
23	C₄₇×#532	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#498	C₂²	1	2	yes	—
28	C₄₇×#496	—	2	1	no	—
29	C₄₇×#489	—	2	1	no	—
30	C₄₇×#486	C₂²	1	2	yes	—
31	C₄₇×#482	—	2	1	no	—
32	C₄₇×#481	—	2	2	no	—
33	C₄₇×#476	—	2	2	no	—
34	C₄₇×#475	C₂²	1	1	yes	characteristic
35	C₄₇×#474	C₂²	1	1	yes	characteristic
36	C₄₇×#461	C₂²	1	2	yes	—
37	C₄₇×#460	C₂²	1	1	yes	characteristic
38	C₄₇×#459	C₂²	1	1	yes	characteristic
39	C₄₇×#459	C₂²	1	2	yes	—
40	C₄₇×#449	—	2	1	no	—
41	C₄₇×#449	—	2	2	no	—
42	C₄₇×#442	—	2	1	no	—
43	C₄₇×#440	—	2	1	no	—
44	C₄₇×#432	C₂²	1	1	yes	characteristic
45	C₄₇×#432	C₂²	1	1	yes	characteristic
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₄₇×#332	C₂²	1	2	yes	—
48	C₄₇×#332	C₂²	1	2	yes	—
49	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
52	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
53	2₋¹⁺⁴×C₄₇	—	4	4	no	—
54	2₋¹⁺⁴×C₄₇	—	4	4	no	—
55	C₂×#41×C₄₇	—	2	2	no	—
56	C₂×#41×C₄₇	—	2	4	no	—
57	C₂×#41×C₄₇	—	2	2	no	—
58	C₂×#41×C₄₇	—	2	1	no	—
59	C₂×#41×C₄₇	—	2	1	no	—
60	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
61	C₂²×Q₈×C₄₇	—	2	2	no	—
62	C₂²×Q₈×C₄₇	—	2	2	no	—
63	C₂²×Q₈×C₄₇	—	2	1	no	—
64	C₂×SD₁₆×C₄₇	—	2	1	no	—
65	C₂×SD₁₆×C₄₇	—	2	2	no	—
66	C₂×D₈×C₄₇	—	2	1	no	—
67	C₂×D₈×C₄₇	—	2	2	no	—
68	C₄⋊Q₈×C₄₇	—	2	2	no	—
69	C₄⋊Q₈×C₄₇	—	2	2	no	—
70	C₄⋊Q₈×C₄₇	—	2	2	no	—
71	C₄⋊Q₈×C₄₇	—	2	1	no	—
72	C₄⋊Q₈×C₄₇	—	2	1	no	—
73	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
74	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
77	#127×C₄₇	D₄	1	1	yes	characteristic
78	#127×C₄₇	C₂³	1	1	yes	characteristic
79	#124×C₄₇	—	2	2	no	—
80	#124×C₄₇	—	2	1	no	—
81	#124×C₄₇	—	2	1	no	—
82	#123×C₄₇	—	2	4	no	—
83	#123×C₄₇	—	2	4	no	—
84	#123×C₄₇	—	2	4	no	—
85	C₂²⋊Q₈×C₄₇	—	2	4	no	—
86	C₂²⋊Q₈×C₄₇	—	2	2	no	—
87	C₂²⋊Q₈×C₄₇	—	2	4	no	—
88	C₂²⋊Q₈×C₄₇	—	2	2	no	—
89	#121×C₄₇	—	2	2	no	—
90	#121×C₄₇	—	2	2	no	—
91	#121×C₄₇	—	2	1	no	—
92	#121×C₄₇	—	2	1	no	—
93	#121×C₄₇	—	2	1	no	—
94	#121×C₄₇	D₄	1	2	yes	—
95	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₄₇	—	2	2	no	—
98	C₄×D₄×C₄₇	—	2	2	no	—
99	C₄×D₄×C₄₇	—	2	1	no	—
100	C₄×D₄×C₄₇	—	2	1	no	—
101	C₄×D₄×C₄₇	—	2	1	no	—
102	C₄×D₄×C₄₇	—	2	1	no	—
103	C₄×D₄×C₄₇	—	2	1	no	—
104	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
105	C₄×D₄×C₄₇	C₂³	1	2	yes	—
106	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
107	#117×C₄₇	—	2	1	no	—
108	#117×C₄₇	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
113	C₂×C₄²×C₄₇	—	2	1	no	—
114	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
115	#107×C₄₇	—	2	1	no	—
116	#106×C₄₇	—	2	1	no	—
117	#106×C₄₇	—	2	4	no	—
118	C₄⋊C₈×C₄₇	—	2	1	no	—
119	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
120	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
121	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
122	#103×C₄₇	—	2	1	no	—
123	#103×C₄₇	—	2	2	no	—
124	#102×C₄₇	—	2	1	no	—
125	#102×C₄₇	—	2	2	no	—
126	#102×C₄₇	—	2	1	no	—
127	#102×C₄₇	—	2	1	no	—
128	#102×C₄₇	—	2	4	no	—
129	C₂²⋊C₈×C₄₇	—	2	1	no	—
130	C₂²⋊C₈×C₄₇	—	2	1	no	—
131	C₂²⋊C₈×C₄₇	—	2	1	no	—
132	#97×C₄₇	—	2	1	no	—
133	#97×C₄₇	—	2	1	no	—
134	C₄×C₈×C₄₇	C₂³	1	2	yes	—
135	#41×C₄₇	—	2	2	no	—
136	#41×C₄₇	—	2	2	no	—
137	#41×C₄₇	—	4	8	no	—
138	#41×C₄₇	—	4	2	no	—
139	#41×C₄₇	—	4	2	no	—
140	#41×C₄₇	—	4	16	no	—
141	#41×C₄₇	—	4	4	no	—
142	#41×C₄₇	—	4	4	no	—
143	#41×C₄₇	—	8	2	no	—
144	C₂×Q₈×C₄₇	—	2	4	no	—
145	C₂×Q₈×C₄₇	—	2	2	no	—
146	C₂×Q₈×C₄₇	—	2	1	no	—
147	C₂×Q₈×C₄₇	—	2	2	no	—
148	C₂×Q₈×C₄₇	—	2	1	no	—
149	C₂×Q₈×C₄₇	—	4	8	no	—
150	C₂×Q₈×C₄₇	—	4	2	no	—
151	C₂×Q₈×C₄₇	—	4	2	no	—
152	C₂×Q₈×C₄₇	—	4	4	no	—
153	C₂×Q₈×C₄₇	—	4	4	no	—
154	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₄₇	—	2	1	no	—
156	C₂×D₄×C₄₇	—	2	4	no	—
157	C₂×D₄×C₄₇	—	2	2	no	—
158	C₂×D₄×C₄₇	—	2	1	no	—
159	C₂×D₄×C₄₇	—	2	1	no	—
160	C₂×D₄×C₄₇	—	2	1	no	—
161	C₂×D₄×C₄₇	—	2	1	no	—
162	C₂×D₄×C₄₇	—	2	1	no	—
163	C₂×D₄×C₄₇	—	4	1	no	—
164	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	2	4	no	—
168	C₂²×C₄×C₄₇	—	2	4	no	—
169	C₂²×C₄×C₄₇	—	2	2	no	—
170	C₂²×C₄×C₄₇	—	2	1	no	—
171	C₂²×C₄×C₄₇	—	2	1	no	—
172	C₂²×C₄×C₄₇	—	2	2	no	—
173	C₂²×C₄×C₄₇	—	4	1	no	—
174	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
177	SD₁₆×C₄₇	—	4	2	no	—
178	SD₁₆×C₄₇	—	8	2	no	—
179	D₈×C₄₇	—	4	2	no	—
180	D₈×C₄₇	—	8	2	no	—
181	C₂×C₈×C₄₇	—	2	1	no	—
182	C₂×C₈×C₄₇	—	2	2	no	—
183	C₂×C₈×C₄₇	—	2	2	no	—
184	C₂×C₈×C₄₇	—	2	1	no	—
185	C₄⋊C₄×C₄₇	—	2	4	no	—
186	C₄⋊C₄×C₄₇	—	2	4	no	—
187	C₄⋊C₄×C₄₇	—	2	1	no	—
188	C₄⋊C₄×C₄₇	—	2	2	no	—
189	C₄⋊C₄×C₄₇	—	2	2	no	—
190	C₄⋊C₄×C₄₇	—	2	1	no	—
191	C₄⋊C₄×C₄₇	—	2	2	no	—
192	C₄⋊C₄×C₄₇	—	2	1	no	—
193	C₄⋊C₄×C₄₇	—	2	1	no	—
194	C₄⋊C₄×C₄₇	—	2	1	no	—
195	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
196	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
197	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₄₇	—	2	4	no	—
200	C₂²⋊C₄×C₄₇	—	2	4	no	—
201	C₂²⋊C₄×C₄₇	—	2	1	no	—
202	C₂²⋊C₄×C₄₇	—	2	1	no	—
203	C₂²⋊C₄×C₄₇	—	2	2	no	—
204	C₂²⋊C₄×C₄₇	—	2	1	no	—
205	C₂²⋊C₄×C₄₇	—	2	2	no	—
206	C₂²⋊C₄×C₄₇	—	4	1	no	—
207	C₂²⋊C₄×C₄₇	—	4	1	no	—
208	C₄²×C₄₇	—	2	1	no	—
209	C₄²×C₄₇	—	2	1	no	—
210	C₄²×C₄₇	—	2	1	no	—
211	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
215	C₂³×C₄₇	—	2	1	no	—
216	C₂³×C₄₇	—	2	2	no	—
217	C₂³×C₄₇	—	4	1	no	—
218	C₂³×C₄₇	#120	1	1	yes	characteristic
219	Q₈×C₄₇	—	2	1	no	—
220	Q₈×C₄₇	—	4	4	no	—
221	Q₈×C₄₇	—	4	2	no	—
222	Q₈×C₄₇	—	4	8	no	—
223	Q₈×C₄₇	—	4	2	no	—
224	Q₈×C₄₇	—	4	2	no	—
225	Q₈×C₄₇	—	4	2	no	—
226	Q₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
227	D₄×C₄₇	—	2	4	no	—
228	D₄×C₄₇	—	2	1	no	—
229	D₄×C₄₇	—	2	2	no	—
230	D₄×C₄₇	—	2	2	no	—
231	D₄×C₄₇	—	4	2	no	—
232	D₄×C₄₇	—	4	2	no	—
233	D₄×C₄₇	—	4	2	no	—
234	D₄×C₄₇	—	4	4	no	—
235	D₄×C₄₇	—	4	8	no	—
236	D₄×C₄₇	—	4	1	no	—
237	D₄×C₄₇	—	4	1	no	—
238	D₄×C₄₇	—	4	2	no	—
239	D₄×C₄₇	—	8	2	no	—
240	D₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
241	C₂×C₄×C₄₇	—	2	4	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	1	no	—
247	C₂×C₄×C₄₇	—	2	1	no	—
248	C₂×C₄×C₄₇	—	2	4	no	—
249	C₂×C₄×C₄₇	—	2	2	no	—
250	C₂×C₄×C₄₇	—	4	1	no	—
251	C₂×C₄×C₄₇	—	4	2	no	—
252	C₂×C₄×C₄₇	—	4	8	no	—
253	C₂×C₄×C₄₇	—	4	4	no	—
254	C₂×C₄×C₄₇	—	4	8	no	—
255	C₂×C₄×C₄₇	—	4	2	no	—
256	C₂×C₄×C₄₇	—	4	2	no	—
257	C₂×C₄×C₄₇	—	4	2	no	—
258	C₂×C₄×C₄₇	—	4	1	no	—
259	C₂×C₄×C₄₇	—	8	2	no	—
260	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
261	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
262	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
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	C₈×C₄₇	—	4	2	no	—
267	C₈×C₄₇	—	4	1	no	—
268	C₈×C₄₇	—	4	1	no	—
269	C₈×C₄₇	—	4	2	no	—
270	#18826	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	2	2	no	—
273	C₂²×C₄₇	—	2	1	no	—
274	C₂²×C₄₇	—	2	1	no	—
275	C₂²×C₄₇	—	4	1	no	—
276	C₂²×C₄₇	—	4	1	no	—
277	C₂²×C₄₇	—	4	2	no	—
278	C₂²×C₄₇	—	4	2	no	—
279	C₂²×C₄₇	—	4	2	no	—
280	C₂²×C₄₇	—	8	1	no	—
281	C₂²×C₄₇	—	8	1	no	—
282	C₂²×C₄₇	—	8	1	no	—
283	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
284	C₄×C₄₇	—	2	1	no	—
285	C₄×C₄₇	—	2	2	no	—
286	C₄×C₄₇	—	2	1	no	—
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	4	4	no	—
290	C₄×C₄₇	—	4	2	no	—
291	C₄×C₄₇	—	4	1	no	—
292	C₄×C₄₇	—	4	1	no	—
293	C₄×C₄₇	—	8	1	no	—
294	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	C₄×C₄₇	#577	1	2	yes	—
297	#3499	C₂×C₄₇	1	1	yes	characteristic, complemented
298	#3227	C₂×C₄₇	1	1	yes	characteristic, complemented
299	#3214	C₂×C₄₇	1	1	yes	characteristic, complemented
300	#3115	C₂×C₄₇	1	1	yes	characteristic, complemented
301	#1654	C₂×C₄₇	1	2	yes	complemented
302	#1651	C₂×C₄₇	1	2	yes	complemented
303	#1627	C₂×C₄₇	1	2	yes	complemented
304	#1625	C₂×C₄₇	1	2	yes	complemented
305	#1556	C₂×C₄₇	1	1	yes	characteristic, complemented
306	#1496	C₂×C₄₇	1	1	yes	characteristic, complemented
307	#1488	C₂×C₄₇	1	1	yes	characteristic, complemented
308	C₂×C₄₇	—	4	1	no	—
309	C₂×C₄₇	—	4	2	no	—
310	C₂×C₄₇	—	8	2	no	—
311	C₂×C₄₇	—	16	1	no	—
312	C₂×C₄₇	#3003	1	1	yes	characteristic
313	C₂×C₄₇	#3010	1	1	yes	characteristic
314	C₂×C₄₇	#3020	1	1	yes	characteristic
315	C₂×2₋¹⁺⁴	—	2	1	no	—
316	D₄×Q₈	—	2	1	no	—
317	D₄×Q₈	C₂²×C₄₇	1	2	yes	—
318	#547	—	2	2	no	—
319	#547	—	2	1	no	—
320	#547	—	2	2	no	—
321	#547	C₂²×C₄₇	1	2	yes	—
322	#536	—	2	2	no	—
323	#536	—	2	1	no	—
324	#532	—	2	1	no	—
325	#532	C₂²×C₄₇	1	1	yes	characteristic
326	#532	C₂²×C₄₇	1	1	yes	characteristic
327	C₂×C₄⋊Q₈	—	2	1	no	—
328	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
329	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
330	#498	C₂²×C₄₇	1	2	yes	—
331	#496	—	2	1	no	—
332	#489	—	2	1	no	—
333	#486	C₂²×C₄₇	1	2	yes	—
334	#482	—	2	1	no	—
335	#481	—	2	2	no	—
336	#476	—	2	2	no	—
337	#475	C₂²×C₄₇	1	1	yes	characteristic
338	#474	C₂²×C₄₇	1	1	yes	characteristic
339	#461	C₂²×C₄₇	1	2	yes	—
340	#460	C₂²×C₄₇	1	1	yes	characteristic
341	#459	C₂²×C₄₇	1	1	yes	characteristic
342	#459	C₂²×C₄₇	1	2	yes	—
343	#449	—	2	1	no	—
344	#449	—	2	2	no	—
345	#442	—	2	1	no	—
346	#440	—	2	1	no	—
347	#432	C₂²×C₄₇	1	1	yes	characteristic
348	#432	C₂²×C₄₇	1	1	yes	characteristic
349	#431	C₂²×C₄₇	1	1	yes	characteristic
350	#332	C₂²×C₄₇	1	2	yes	—
351	#332	C₂²×C₄₇	1	2	yes	—
352	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
353	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
354	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
355	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
356	C₄₇	#18826	1	1	yes	characteristic, direct product factor, Sylow
357	2₋¹⁺⁴	—	4	4	no	—
358	2₋¹⁺⁴	—	4	4	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	4	no	—
361	C₂×#41	—	2	2	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
365	C₂²×Q₈	—	2	2	no	—
366	C₂²×Q₈	—	2	2	no	—
367	C₂²×Q₈	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×D₈	—	2	1	no	—
371	C₂×D₈	—	2	2	no	—
372	C₄⋊Q₈	—	2	2	no	—
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	—	2	2	no	—
375	C₄⋊Q₈	—	2	1	no	—
376	C₄⋊Q₈	—	2	1	no	—
377	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
378	C₄⋊Q₈	D₄×C₄₇	1	2	yes	—
379	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
380	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
381	#127	D₄×C₄₇	1	1	yes	characteristic
382	#127	C₂³×C₄₇	1	1	yes	characteristic
383	#124	—	2	2	no	—
384	#124	—	2	1	no	—
385	#124	—	2	1	no	—
386	#123	—	2	4	no	—
387	#123	—	2	4	no	—
388	#123	—	2	4	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	—	2	4	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	#121	—	2	2	no	—
394	#121	—	2	2	no	—
395	#121	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	D₄×C₄₇	1	2	yes	—
399	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
400	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
409	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
410	C₄×D₄	C₂³×C₄₇	1	2	yes	—
411	#117	—	2	1	no	—
412	#117	D₄×C₄₇	1	1	yes	characteristic
413	C₂×C₄⋊C₄	—	2	2	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	2	no	—
416	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
419	#107	—	2	1	no	—
420	#106	—	2	1	no	—
421	#106	—	2	4	no	—
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
424	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
425	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
426	#103	—	2	1	no	—
427	#103	—	2	2	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	2	no	—
432	#102	—	2	4	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	#97	—	2	1	no	—
437	#97	—	2	1	no	—
438	C₄×C₈	C₂³×C₄₇	1	2	yes	—
439	#41	—	2	2	no	—
440	#41	—	2	2	no	—
441	#41	—	4	8	no	—
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	4	16	no	—
445	#41	—	4	4	no	—
446	#41	—	4	4	no	—
447	#41	—	8	2	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	4	8	no	—
454	C₂×Q₈	—	4	2	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	4	4	no	—
457	C₂×Q₈	—	4	4	no	—
458	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
469	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	4	1	no	—
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	SD₁₆	—	4	2	no	—
482	SD₁₆	—	8	2	no	—
483	D₈	—	4	2	no	—
484	D₈	—	8	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
500	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
501	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
517	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
518	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
519	C₂³	—	2	1	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	#120×C₄₇	1	1	yes	characteristic
523	Q₈	—	2	1	no	—
524	Q₈	—	4	4	no	—
525	Q₈	—	4	2	no	—
526	Q₈	—	4	8	no	—
527	Q₈	—	4	2	no	—
528	Q₈	—	4	2	no	—
529	Q₈	—	4	2	no	—
530	Q₈	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
531	D₄	—	2	4	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	8	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	2	no	—
543	D₄	—	8	2	no	—
544	D₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	8	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	8	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
565	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
566	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
570	C₈	—	4	2	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	4	4	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
598	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
599	C₄	C₄₇×#577	1	2	yes	—
600	C₂	—	4	1	no	—
601	C₂	—	4	2	no	—
602	C₂	—	8	2	no	—
603	C₂	—	16	1	no	—
604	C₂	C₄₇×#3003	1	1	yes	characteristic
605	C₂	C₄₇×#3010	1	1	yes	characteristic
606	C₂	C₄₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3499	C₂	semidirect
2. C₄₇×#3227	C₂	semidirect
3. C₄₇×#3214	C₂	semidirect
4. C₄₇×#3115	C₂	semidirect
5. C₄₇×#1654	C₂	semidirect
6. C₄₇×#1651	C₂	semidirect
7. C₄₇×#1627	C₂	semidirect
8. C₄₇×#1625	C₂	semidirect
9. C₄₇×#1556	C₂	semidirect
10. C₄₇×#1496	C₂	semidirect
11. C₄₇×#1488	C₂	semidirect
270. #18826	C₄₇	direct (N × H)
297. #3499	C₂×C₄₇	semidirect
298. #3227	C₂×C₄₇	semidirect
299. #3214	C₂×C₄₇	semidirect
300. #3115	C₂×C₄₇	semidirect
301. #1654	C₂×C₄₇	semidirect
302. #1651	C₂×C₄₇	semidirect
303. #1627	C₂×C₄₇	semidirect
304. #1625	C₂×C₄₇	semidirect
305. #1556	C₂×C₄₇	semidirect
306. #1496	C₂×C₄₇	semidirect
307. #1488	C₂×C₄₇	semidirect
356. C₄₇	#18826	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3499	2
C₄₇×#3227	2
C₄₇×#3214	2
C₄₇×#3115	2
C₄₇×#1654	2
C₄₇×#1651	2
C₄₇×#1627	2
C₄₇×#1625	2
C₄₇×#1556	2
C₄₇×#1496	2
C₄₇×#1488	2
#18826	47

Subgroups — C47×#18826 #26058524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18826 #26058524