Subgroups — C₄₇×#18883 #26058581

Order 12032.

1096 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	C₄₇×#3499	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3076	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×#1637	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1635	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1477	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×#533	C₂²	1	1	yes	characteristic
22	C₄₇×#532	—	2	1	no	—
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×#487	C₂²	1	2	yes	—
29	C₄₇×#483	—	2	2	no	—
30	C₄₇×#479	—	2	1	no	—
31	C₄₇×#478	—	2	1	no	—
32	C₄₇×#477	C₂²	1	1	yes	characteristic
33	C₄₇×#476	C₂²	1	1	yes	characteristic
34	C₄₇×#476	C₂²	1	2	yes	—
35	C₄₇×#475	—	2	2	no	—
36	C₄₇×#475	—	2	1	no	—
37	C₄₇×#475	C₂²	1	1	yes	characteristic
38	C₄₇×#474	C₂²	1	1	yes	characteristic
39	C₄₇×#465	—	2	2	no	—
40	C₄₇×#461	C₂²	1	2	yes	—
41	C₄₇×#460	—	2	1	no	—
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₄₇×#427	—	2	1	no	—
44	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₄₇×#416	—	2	1	no	—
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	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₄₇	—	2	2	no	—
61	C₂²×Q₈×C₄₇	—	2	2	no	—
62	C₂²×Q₈×C₄₇	—	2	1	no	—
63	C₂×SD₁₆×C₄₇	—	2	2	no	—
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₂²×C₈×C₄₇	—	2	1	no	—
66	C₄⋊Q₈×C₄₇	—	2	2	no	—
67	C₄⋊Q₈×C₄₇	—	2	2	no	—
68	C₄⋊Q₈×C₄₇	—	2	2	no	—
69	C₄⋊Q₈×C₄₇	—	2	1	no	—
70	C₄⋊Q₈×C₄₇	—	2	1	no	—
71	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
72	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
73	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
76	#127×C₄₇	D₄	1	1	yes	characteristic
77	#125×C₄₇	—	2	1	no	—
78	#124×C₄₇	—	2	2	no	—
79	#124×C₄₇	—	2	1	no	—
80	#123×C₄₇	—	2	4	no	—
81	#123×C₄₇	—	2	4	no	—
82	#123×C₄₇	—	2	4	no	—
83	C₂²⋊Q₈×C₄₇	—	2	4	no	—
84	C₂²⋊Q₈×C₄₇	—	2	2	no	—
85	C₂²⋊Q₈×C₄₇	—	2	4	no	—
86	C₂²⋊Q₈×C₄₇	—	2	2	no	—
87	C₂²⋊Q₈×C₄₇	—	2	1	no	—
88	C₂²⋊Q₈×C₄₇	—	2	1	no	—
89	#121×C₄₇	—	2	2	no	—
90	#121×C₄₇	—	2	2	no	—
91	#121×C₄₇	—	2	1	no	—
92	#121×C₄₇	D₄	1	2	yes	—
93	C₄×Q₈×C₄₇	—	2	1	no	—
94	C₄×Q₈×C₄₇	—	2	1	no	—
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	D₄	1	1	yes	characteristic
103	C₄×D₄×C₄₇	C₂³	1	2	yes	—
104	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
105	#117×C₄₇	—	2	1	no	—
106	#117×C₄₇	—	2	1	no	—
107	#117×C₄₇	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
112	C₂×C₄²×C₄₇	—	2	1	no	—
113	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	#107×C₄₇	—	2	1	no	—
115	#107×C₄₇	—	2	1	no	—
116	#106×C₄₇	—	2	2	no	—
117	#106×C₄₇	—	2	4	no	—
118	#106×C₄₇	—	2	1	no	—
119	#106×C₄₇	—	2	1	no	—
120	C₄⋊C₈×C₄₇	—	2	1	no	—
121	C₄⋊C₈×C₄₇	—	2	1	no	—
122	C₄⋊C₈×C₄₇	—	2	1	no	—
123	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
124	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
126	#103×C₄₇	—	2	1	no	—
127	#103×C₄₇	—	2	1	no	—
128	#103×C₄₇	—	2	2	no	—
129	#103×C₄₇	—	2	4	no	—
130	#102×C₄₇	—	2	2	no	—
131	#102×C₄₇	—	2	1	no	—
132	#102×C₄₇	—	2	1	no	—
133	C₂²⋊C₈×C₄₇	—	2	1	no	—
134	C₄×C₈×C₄₇	C₂³	1	2	yes	—
135	#41×C₄₇	—	2	2	no	—
136	#41×C₄₇	—	4	8	no	—
137	#41×C₄₇	—	4	16	no	—
138	#41×C₄₇	—	4	4	no	—
139	#41×C₄₇	—	4	4	no	—
140	#41×C₄₇	—	4	2	no	—
141	#41×C₄₇	—	4	2	no	—
142	#41×C₄₇	SD₁₆	1	4	yes	complemented
143	C₂×Q₈×C₄₇	—	2	4	no	—
144	C₂×Q₈×C₄₇	—	2	2	no	—
145	C₂×Q₈×C₄₇	—	2	1	no	—
146	C₂×Q₈×C₄₇	—	2	2	no	—
147	C₂×Q₈×C₄₇	—	2	1	no	—
148	C₂×Q₈×C₄₇	—	2	1	no	—
149	C₂×Q₈×C₄₇	—	4	8	no	—
150	C₂×Q₈×C₄₇	—	4	4	no	—
151	C₂×Q₈×C₄₇	—	4	4	no	—
152	C₂×Q₈×C₄₇	—	4	2	no	—
153	C₂×Q₈×C₄₇	—	4	2	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	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	—	2	1	no	—
163	C₂²×C₄×C₄₇	—	2	4	no	—
164	C₂²×C₄×C₄₇	—	2	4	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	2	1	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
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	SD₁₆×C₄₇	—	8	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	4	2	no	—
178	C₂×C₈×C₄₇	—	8	1	no	—
179	C₄⋊C₄×C₄₇	—	2	4	no	—
180	C₄⋊C₄×C₄₇	—	2	4	no	—
181	C₄⋊C₄×C₄₇	—	2	1	no	—
182	C₄⋊C₄×C₄₇	—	2	2	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	1	no	—
187	C₄⋊C₄×C₄₇	—	2	1	no	—
188	C₄⋊C₄×C₄₇	—	2	1	no	—
189	C₄⋊C₄×C₄₇	—	2	1	no	—
190	C₄⋊C₄×C₄₇	—	2	1	no	—
191	C₄⋊C₄×C₄₇	—	4	1	no	—
192	C₄⋊C₄×C₄₇	—	4	1	no	—
193	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
195	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₄₇	—	2	4	no	—
198	C₂²⋊C₄×C₄₇	—	2	4	no	—
199	C₂²⋊C₄×C₄₇	—	2	1	no	—
200	C₂²⋊C₄×C₄₇	—	2	1	no	—
201	C₂²⋊C₄×C₄₇	—	2	2	no	—
202	C₂²⋊C₄×C₄₇	—	2	1	no	—
203	C₂²⋊C₄×C₄₇	—	2	2	no	—
204	C₂²⋊C₄×C₄₇	—	4	1	no	—
205	C₄²×C₄₇	—	2	1	no	—
206	C₄²×C₄₇	—	2	1	no	—
207	C₄²×C₄₇	—	2	1	no	—
208	C₄²×C₄₇	—	4	1	no	—
209	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
213	C₂³×C₄₇	—	2	1	no	—
214	C₂³×C₄₇	—	2	2	no	—
215	C₂³×C₄₇	#120	1	1	yes	characteristic
216	Q₈×C₄₇	—	2	1	no	—
217	Q₈×C₄₇	—	4	8	no	—
218	Q₈×C₄₇	—	4	2	no	—
219	Q₈×C₄₇	—	4	2	no	—
220	Q₈×C₄₇	—	4	2	no	—
221	Q₈×C₄₇	—	4	2	no	—
222	Q₈×C₄₇	—	4	4	no	—
223	Q₈×C₄₇	—	4	1	no	—
224	Q₈×C₄₇	—	4	1	no	—
225	Q₈×C₄₇	C₂×SD₁₆	1	2	yes	—
226	D₄×C₄₇	—	2	4	no	—
227	D₄×C₄₇	—	2	1	no	—
228	D₄×C₄₇	—	2	2	no	—
229	D₄×C₄₇	—	2	2	no	—
230	D₄×C₄₇	—	4	2	no	—
231	D₄×C₄₇	—	4	8	no	—
232	D₄×C₄₇	—	4	4	no	—
233	D₄×C₄₇	—	4	2	no	—
234	D₄×C₄₇	C₂×SD₁₆	1	2	yes	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	1	no	—
240	C₂×C₄×C₄₇	—	2	1	no	—
241	C₂×C₄×C₄₇	—	2	4	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	4	1	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	4	8	no	—
246	C₂×C₄×C₄₇	—	4	8	no	—
247	C₂×C₄×C₄₇	—	4	4	no	—
248	C₂×C₄×C₄₇	—	4	2	no	—
249	C₂×C₄×C₄₇	—	4	2	no	—
250	C₂×C₄×C₄₇	—	4	1	no	—
251	C₂×C₄×C₄₇	—	4	1	no	—
252	C₂×C₄×C₄₇	—	4	1	no	—
253	C₂×C₄×C₄₇	—	4	1	no	—
254	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
255	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
256	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
258	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
259	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
262	C₈×C₄₇	—	4	2	no	—
263	C₈×C₄₇	—	4	1	no	—
264	C₈×C₄₇	—	4	1	no	—
265	C₈×C₄₇	—	4	2	no	—
266	#18883	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂²×C₄₇	—	2	1	no	—
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	2	no	—
270	C₂²×C₄₇	—	4	1	no	—
271	C₂²×C₄₇	—	4	1	no	—
272	C₂²×C₄₇	—	4	2	no	—
273	C₂²×C₄₇	—	4	2	no	—
274	C₂²×C₄₇	—	4	2	no	—
275	C₂²×C₄₇	#450	1	2	yes	—
276	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
277	C₄×C₄₇	—	2	2	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	2	1	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	—	4	4	no	—
282	C₄×C₄₇	—	4	2	no	—
283	C₄×C₄₇	—	4	1	no	—
284	C₄×C₄₇	—	4	1	no	—
285	C₄×C₄₇	—	8	1	no	—
286	C₄×C₄₇	—	8	1	no	—
287	C₄×C₄₇	#450	1	2	yes	—
288	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
289	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₄×C₄₇	#577	1	1	yes	characteristic
291	C₄×C₄₇	#578	1	1	yes	characteristic
292	#3499	C₂×C₄₇	1	1	yes	characteristic
293	#3246	C₂×C₄₇	1	1	yes	characteristic, complemented
294	#3229	C₂×C₄₇	1	1	yes	characteristic, complemented
295	#3076	C₂×C₄₇	1	1	yes	characteristic, complemented
296	#1654	C₂×C₄₇	1	2	yes	complemented
297	#1651	C₂×C₄₇	1	2	yes	complemented
298	#1637	C₂×C₄₇	1	2	yes	complemented
299	#1635	C₂×C₄₇	1	2	yes	complemented
300	C₂×#332	C₂×C₄₇	1	1	yes	characteristic, complemented
301	#1480	C₂×C₄₇	1	1	yes	characteristic, complemented
302	#1477	C₂×C₄₇	1	1	yes	characteristic, complemented
303	C₂×C₄₇	—	2	2	no	—
304	C₂×C₄₇	—	4	2	no	—
305	C₂×C₄₇	—	8	2	no	—
306	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
307	C₂×C₄₇	#3013	1	1	yes	characteristic
308	C₂×C₄₇	#3020	1	1	yes	characteristic
309	C₂×2₋¹⁺⁴	—	2	1	no	—
310	D₄×Q₈	—	2	1	no	—
311	D₄×Q₈	C₂²×C₄₇	1	2	yes	—
312	#547	—	2	2	no	—
313	#547	—	2	1	no	—
314	#547	—	2	2	no	—
315	#547	C₂²×C₄₇	1	2	yes	—
316	#536	—	2	2	no	—
317	#536	—	2	1	no	—
318	#533	C₂²×C₄₇	1	1	yes	characteristic
319	#532	—	2	1	no	—
320	#532	C₂²×C₄₇	1	1	yes	characteristic
321	C₂×C₄⋊Q₈	—	2	1	no	—
322	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
323	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
324	#498	C₂²×C₄₇	1	2	yes	—
325	#487	C₂²×C₄₇	1	2	yes	—
326	#483	—	2	2	no	—
327	#479	—	2	1	no	—
328	#478	—	2	1	no	—
329	#477	C₂²×C₄₇	1	1	yes	characteristic
330	#476	C₂²×C₄₇	1	1	yes	characteristic
331	#476	C₂²×C₄₇	1	2	yes	—
332	#475	—	2	2	no	—
333	#475	—	2	1	no	—
334	#475	C₂²×C₄₇	1	1	yes	characteristic
335	#474	C₂²×C₄₇	1	1	yes	characteristic
336	#465	—	2	2	no	—
337	#461	C₂²×C₄₇	1	2	yes	—
338	#460	—	2	1	no	—
339	#431	C₂²×C₄₇	1	1	yes	characteristic
340	#427	—	2	1	no	—
341	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
342	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
343	#416	—	2	1	no	—
344	#332	C₂²×C₄₇	1	2	yes	—
345	#332	C₂²×C₄₇	1	2	yes	—
346	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
347	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
348	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
349	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
350	C₄₇	#18883	1	1	yes	characteristic, direct product factor, Sylow
351	2₋¹⁺⁴	—	4	4	no	—
352	2₋¹⁺⁴	—	4	4	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	4	no	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
358	C₂²×Q₈	—	2	2	no	—
359	C₂²×Q₈	—	2	2	no	—
360	C₂²×Q₈	—	2	1	no	—
361	C₂×SD₁₆	—	2	2	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	—	2	2	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	—	2	1	no	—
369	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
370	C₄⋊Q₈	D₄×C₄₇	1	2	yes	—
371	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
372	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
373	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
374	#127	D₄×C₄₇	1	1	yes	characteristic
375	#125	—	2	1	no	—
376	#124	—	2	2	no	—
377	#124	—	2	1	no	—
378	#123	—	2	4	no	—
379	#123	—	2	4	no	—
380	#123	—	2	4	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	4	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	—	2	1	no	—
390	#121	D₄×C₄₇	1	2	yes	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
394	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
401	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
402	C₄×D₄	C₂³×C₄₇	1	2	yes	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	D₄×C₄₇	1	1	yes	characteristic
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
412	#107	—	2	1	no	—
413	#107	—	2	1	no	—
414	#106	—	2	1	no	—
415	#106	—	2	1	no	—
416	#106	—	2	2	no	—
417	#106	—	2	4	no	—
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
422	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#103	—	2	2	no	—
427	#103	—	2	4	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	2	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₄×C₈	C₂³×C₄₇	1	2	yes	—
433	#41	—	2	2	no	—
434	#41	—	4	8	no	—
435	#41	—	4	16	no	—
436	#41	—	4	4	no	—
437	#41	—	4	4	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	SD₁₆×C₄₇	1	4	yes	complemented
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	4	8	no	—
448	C₂×Q₈	—	4	4	no	—
449	C₂×Q₈	—	4	4	no	—
450	C₂×Q₈	—	4	2	no	—
451	C₂×Q₈	—	4	2	no	—
452	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
459	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
470	SD₁₆	—	8	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	4	2	no	—
476	C₂×C₈	—	8	1	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
492	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
493	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
508	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
510	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	#120×C₄₇	1	1	yes	characteristic
514	Q₈	—	2	1	no	—
515	Q₈	—	4	8	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	4	4	no	—
519	Q₈	—	4	2	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	C₂×SD₁₆×C₄₇	1	2	yes	—
524	D₄	—	2	4	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	8	no	—
530	D₄	—	4	4	no	—
531	D₄	—	4	2	no	—
532	D₄	C₂×SD₁₆×C₄₇	1	2	yes	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	8	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
553	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
554	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
555	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
556	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
560	C₈	—	4	2	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	2	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	C₄₇×#450	1	2	yes	—
573	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	8	1	no	—
583	C₄	—	8	1	no	—
584	C₄	C₄₇×#450	1	2	yes	—
585	C₄	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
586	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
587	C₄	C₄₇×#577	1	1	yes	characteristic
588	C₄	C₄₇×#578	1	1	yes	characteristic
589	C₂	—	2	2	no	—
590	C₂	—	4	2	no	—
591	C₂	—	8	2	no	—
592	C₂	C₂×C₄₇×#450	1	1	yes	characteristic
593	C₂	C₄₇×#3013	1	1	yes	characteristic
594	C₂	C₄₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	C₄₇×#3499	C₂
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
2. C₄₇×#3246	C₂	semidirect
3. C₄₇×#3229	C₂	semidirect
4. C₄₇×#3076	C₂	semidirect
5. C₄₇×#1654	C₂	semidirect
6. C₄₇×#1651	C₂	semidirect
7. C₄₇×#1637	C₂	semidirect
8. C₄₇×#1635	C₂	semidirect
9. C₂×C₄₇×#332	C₂	semidirect
10. C₄₇×#1480	C₂	semidirect
11. C₄₇×#1477	C₂	semidirect
142. #41×C₄₇	SD₁₆	semidirect
266. #18883	C₄₇	direct (N × H)
293. #3246	C₂×C₄₇	semidirect
294. #3229	C₂×C₄₇	semidirect
295. #3076	C₂×C₄₇	semidirect
296. #1654	C₂×C₄₇	semidirect
297. #1651	C₂×C₄₇	semidirect
298. #1637	C₂×C₄₇	semidirect
299. #1635	C₂×C₄₇	semidirect
300. C₂×#332	C₂×C₄₇	semidirect
301. #1480	C₂×C₄₇	semidirect
302. #1477	C₂×C₄₇	semidirect
350. C₄₇	#18883	direct (N × H)
440. #41	SD₁₆×C₄₇	semidirect

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×#3246	2
C₄₇×#3229	2
C₄₇×#3076	2
C₄₇×#1654	2
C₄₇×#1651	2
C₄₇×#1637	2
C₄₇×#1635	2
C₂×C₄₇×#332	2
C₄₇×#1480	2
C₄₇×#1477	2
#18883	47

Subgroups — C47×#18883 #26058581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18883 #26058581