Subgroups — C₄₇×#21244 #26060942

Order 12032.

1460 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#575	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#421	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#410	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1976	C₂	1	8	yes	maximal, complemented
7	C₂²×#41×C₄₇	C₂²	1	2	yes	—
8	C₄₇×#575	—	2	2	no	—
9	C₄₇×#575	—	2	2	no	—
10	C₄₇×#575	—	2	4	no	—
11	C₂×#137×C₄₇	C₄	1	4	yes	complemented
12	C₂×AGL(1,ℤ/8)×C₄₇	C₄	1	4	yes	complemented
13	C₂×#135×C₄₇	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	C₂²	1	2	yes	—
17	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#428	—	2	4	no	—
19	C₄₇×#427	C₂²	1	4	yes	complemented
20	C₄₇×#421	—	2	4	no	—
21	C₄₇×#421	C₂²	1	8	yes	complemented
22	C₂×#104×C₄₇	—	2	4	no	—
23	C₄₇×#410	—	2	4	no	—
24	C₄₇×#410	C₂²	1	8	yes	complemented
25	C₂×#99×C₄₇	—	2	4	no	—
26	C₄₇×#405	—	2	2	no	—
27	C₄₇×#405	C₂²	1	4	yes	complemented
28	C₄×M₁₆×C₄₇	—	2	2	no	—
29	C₂×#41×C₄₇	—	2	2	no	—
30	C₂×#41×C₄₇	—	2	2	no	—
31	C₂×#41×C₄₇	—	2	2	no	—
32	C₂×#41×C₄₇	—	2	2	no	—
33	C₂×#41×C₄₇	—	2	2	no	—
34	C₂×#41×C₄₇	—	2	2	no	—
35	C₂×#41×C₄₇	—	2	2	no	—
36	C₂×#41×C₄₇	—	2	2	no	—
37	C₂×#41×C₄₇	—	2	2	no	—
38	C₂×#41×C₄₇	—	2	2	no	—
39	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
40	C₂×#41×C₄₇	C₂³	1	4	yes	—
41	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
42	C₂²×D₄×C₄₇	—	2	2	no	—
43	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	#137×C₄₇	—	2	8	no	—
47	#137×C₄₇	—	2	8	no	—
48	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
49	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
50	#135×C₄₇	—	2	8	no	—
51	#135×C₄₇	—	2	8	no	—
52	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
53	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
54	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
55	C₂×M₁₆×C₄₇	—	2	1	no	—
56	C₂×M₁₆×C₄₇	—	2	2	no	—
57	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
58	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
59	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
60	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
61	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
62	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
63	C₂²×C₈×C₄₇	—	2	1	no	—
64	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
65	#117×C₄₇	—	2	1	no	—
66	#117×C₄₇	—	2	1	no	—
67	#117×C₄₇	—	2	2	no	—
68	#117×C₄₇	—	2	2	no	—
69	#117×C₄₇	—	2	2	no	—
70	#117×C₄₇	D₄	1	2	yes	—
71	#117×C₄₇	C₂³	1	4	yes	—
72	#117×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
77	C₂×C₄²×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	#107×C₄₇	—	2	4	no	—
80	#106×C₄₇	—	2	4	no	—
81	#104×C₄₇	—	2	16	no	—
82	#99×C₄₇	—	2	16	no	—
83	#97×C₄₇	—	2	4	no	—
84	C₄×C₈×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	—	2	2	no	—
86	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
87	#41×C₄₇	—	2	4	no	—
88	#41×C₄₇	—	2	4	no	—
89	#41×C₄₇	—	2	4	no	—
90	#41×C₄₇	—	2	4	no	—
91	#41×C₄₇	—	2	4	no	—
92	#41×C₄₇	—	2	4	no	—
93	#41×C₄₇	—	2	4	no	—
94	#41×C₄₇	—	2	4	no	—
95	#41×C₄₇	—	4	2	no	—
96	#41×C₄₇	—	4	2	no	—
97	#41×C₄₇	—	4	2	no	—
98	#41×C₄₇	—	4	2	no	—
99	#41×C₄₇	—	4	2	no	—
100	#41×C₄₇	—	4	2	no	—
101	#41×C₄₇	—	4	2	no	—
102	#41×C₄₇	—	4	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂×D₄×C₄₇	—	2	4	no	—
110	C₂×D₄×C₄₇	—	2	4	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	4	2	no	—
117	C₂×D₄×C₄₇	—	4	2	no	—
118	C₂×D₄×C₄₇	—	4	2	no	—
119	C₂×D₄×C₄₇	—	4	2	no	—
120	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	4	no	—
124	C₂²×C₄×C₄₇	—	2	4	no	—
125	C₂²×C₄×C₄₇	—	4	2	no	—
126	C₂²×C₄×C₄₇	—	4	2	no	—
127	C₂²×C₄×C₄₇	—	4	2	no	—
128	C₂²×C₄×C₄₇	—	4	2	no	—
129	C₂²×C₄×C₄₇	—	4	2	no	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	#41	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₄₇	—	2	8	no	—
141	SD₁₆×C₄₇	—	2	16	no	—
142	D₈×C₄₇	—	2	8	no	—
143	M₁₆×C₄₇	—	2	4	no	—
144	M₁₆×C₄₇	—	2	2	no	—
145	M₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
146	M₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
147	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₄₇	—	2	4	no	—
149	C₂×C₈×C₄₇	—	2	2	no	—
150	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
151	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
152	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
153	C₄⋊C₄×C₄₇	—	2	2	no	—
154	C₄⋊C₄×C₄₇	—	2	2	no	—
155	C₄⋊C₄×C₄₇	—	2	4	no	—
156	C₄⋊C₄×C₄₇	—	4	2	no	—
157	C₂²⋊C₄×C₄₇	—	2	2	no	—
158	C₂²⋊C₄×C₄₇	—	2	4	no	—
159	C₂²⋊C₄×C₄₇	—	4	2	no	—
160	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
161	C₄²×C₄₇	—	2	2	no	—
162	C₄²×C₄₇	—	2	2	no	—
163	C₄²×C₄₇	—	2	4	no	—
164	C₄²×C₄₇	—	4	2	no	—
165	C₂³×C₄₇	—	2	4	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	8	1	no	—
169	C₂³×C₄₇	—	8	4	no	—
170	C₂³×C₄₇	C₄×D₄	1	2	yes	—
171	C₂³×C₄₇	#121	1	1	yes	characteristic
172	C₂³×C₄₇	#121	1	1	yes	characteristic
173	C₂³×C₄₇	#127	1	2	yes	—
174	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₄₇	—	2	4	no	—
176	Q₈×C₄₇	—	2	4	no	—
177	Q₈×C₄₇	—	4	2	no	—
178	Q₈×C₄₇	—	4	2	no	—
179	D₄×C₄₇	—	2	4	no	—
180	D₄×C₄₇	—	2	4	no	—
181	D₄×C₄₇	—	4	4	no	—
182	D₄×C₄₇	—	4	4	no	—
183	D₄×C₄₇	—	4	4	no	—
184	D₄×C₄₇	—	4	4	no	—
185	D₄×C₄₇	—	4	2	no	—
186	D₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	4	no	—
192	C₂×C₄×C₄₇	—	4	4	no	—
193	C₂×C₄×C₄₇	—	4	4	no	—
194	C₂×C₄×C₄₇	—	4	4	no	—
195	C₂×C₄×C₄₇	—	4	4	no	—
196	C₂×C₄×C₄₇	—	8	2	no	—
197	C₂×C₄×C₄₇	—	8	4	no	—
198	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₄₇	#121	1	2	yes	—
204	C₂×C₄×C₄₇	#121	1	2	yes	—
205	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
206	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
207	C₂×C₄×C₄₇	#124	1	2	yes	—
208	C₂×C₄×C₄₇	#124	1	2	yes	—
209	C₂×C₄×C₄₇	#127	1	2	yes	—
210	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₈×C₄₇	—	2	4	no	—
217	C₈×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
218	#21244	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₄₇	—	4	1	no	—
220	C₂²×C₄₇	—	4	2	no	—
221	C₂²×C₄₇	—	4	2	no	—
222	C₂²×C₄₇	—	4	1	no	—
223	C₂²×C₄₇	—	4	1	no	—
224	C₂²×C₄₇	—	4	4	no	—
225	C₂²×C₄₇	—	8	4	no	—
226	C₂²×C₄₇	—	8	4	no	—
227	C₂²×C₄₇	—	8	4	no	—
228	C₂²×C₄₇	#390	1	2	yes	—
229	C₂²×C₄₇	#390	1	2	yes	—
230	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
233	C₄×C₄₇	—	4	4	no	—
234	C₄×C₄₇	—	4	4	no	—
235	C₄×C₄₇	—	8	4	no	—
236	C₄×C₄₇	#390	1	2	yes	—
237	C₄×C₄₇	#390	1	2	yes	—
238	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
239	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
241	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
242	C₂×#575	C₂×C₄₇	1	1	yes	characteristic
243	#2911	C₂×C₄₇	1	1	yes	characteristic, complemented
244	C₂×#421	C₂×C₄₇	1	2	yes	complemented
245	C₂×#410	C₂×C₄₇	1	2	yes	complemented
246	#2873	C₂×C₄₇	1	1	yes	characteristic, complemented
247	#1976	C₂×C₄₇	1	8	yes	complemented
248	C₂×C₄₇	—	2	1	no	—
249	C₂×C₄₇	—	2	1	no	—
250	C₂×C₄₇	—	2	1	no	—
251	C₂×C₄₇	—	2	2	no	—
252	C₂×C₄₇	—	2	2	no	—
253	C₂×C₄₇	—	8	4	no	—
254	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
255	C₂²×#41	C₂²×C₄₇	1	2	yes	—
256	#575	—	2	2	no	—
257	#575	—	2	2	no	—
258	#575	—	2	4	no	—
259	C₂×#137	C₄×C₄₇	1	4	yes	complemented
260	C₂×AGL(1,ℤ/8)	C₄×C₄₇	1	4	yes	complemented
261	C₂×#135	C₂²×C₄₇	1	4	yes	—
262	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
264	C₂×#117	C₂²×C₄₇	1	2	yes	—
265	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
266	#428	—	2	4	no	—
267	#427	C₂²×C₄₇	1	4	yes	complemented
268	#421	—	2	4	no	—
269	#421	C₂²×C₄₇	1	8	yes	complemented
270	C₂×#104	—	2	4	no	—
271	#410	—	2	4	no	—
272	#410	C₂²×C₄₇	1	8	yes	complemented
273	C₂×#99	—	2	4	no	—
274	#405	—	2	2	no	—
275	#405	C₂²×C₄₇	1	4	yes	complemented
276	C₄×M₁₆	—	2	2	no	—
277	C₄₇	#21244	1	1	yes	characteristic, direct product factor, Sylow
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
289	C₂×#41	C₂³×C₄₇	1	4	yes	—
290	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
295	#137	—	2	8	no	—
296	#137	—	2	8	no	—
297	AGL(1,ℤ/8)	—	2	8	no	—
298	AGL(1,ℤ/8)	—	2	8	no	—
299	#135	—	2	8	no	—
300	#135	—	2	8	no	—
301	C₂×Q₁₆	C₂×C₄×C₄₇	1	4	yes	complemented
302	C₂×SD₁₆	C₂×C₄×C₄₇	1	8	yes	complemented
303	C₂×D₈	C₂×C₄×C₄₇	1	4	yes	complemented
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
307	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
308	C₂×M₁₆	D₄×C₄₇	1	2	yes	—
309	C₂×M₁₆	D₄×C₄₇	1	2	yes	—
310	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
311	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
314	#117	—	2	1	no	—
315	#117	—	2	1	no	—
316	#117	—	2	2	no	—
317	#117	—	2	2	no	—
318	#117	—	2	2	no	—
319	#117	D₄×C₄₇	1	2	yes	—
320	#117	C₂³×C₄₇	1	4	yes	—
321	#117	C₂³×C₄₇	1	2	yes	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	2	no	—
328	#107	—	2	4	no	—
329	#106	—	2	4	no	—
330	#104	—	2	16	no	—
331	#99	—	2	16	no	—
332	#97	—	2	4	no	—
333	C₄×C₈	—	2	4	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	2	4	no	—
339	#41	—	2	4	no	—
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	#41	—	4	2	no	—
349	#41	—	4	2	no	—
350	#41	—	4	2	no	—
351	#41	—	4	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
383	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
385	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
386	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
387	C₂²×C₄	#41×C₄₇	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
389	Q₁₆	—	2	8	no	—
390	SD₁₆	—	2	16	no	—
391	D₈	—	2	8	no	—
392	M₁₆	—	2	4	no	—
393	M₁₆	—	2	2	no	—
394	M₁₆	C₂²⋊C₄×C₄₇	1	8	yes	—
395	M₁₆	C₂²⋊C₄×C₄₇	1	8	yes	—
396	M₁₆	C₂×D₄×C₄₇	1	4	yes	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	—
400	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
401	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	4	no	—
413	C₄²	—	4	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	8	1	no	—
418	C₂³	—	8	4	no	—
419	C₂³	C₄×D₄×C₄₇	1	2	yes	—
420	C₂³	#121×C₄₇	1	1	yes	characteristic
421	C₂³	#121×C₄₇	1	1	yes	characteristic
422	C₂³	#127×C₄₇	1	2	yes	—
423	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
424	Q₈	—	2	4	no	—
425	Q₈	—	2	4	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	4	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	4	no	—
433	D₄	—	4	4	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	8	2	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
448	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
449	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
450	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
451	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
452	C₂×C₄	#121×C₄₇	1	2	yes	—
453	C₂×C₄	#121×C₄₇	1	2	yes	—
454	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
455	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
456	C₂×C₄	#124×C₄₇	1	2	yes	—
457	C₂×C₄	#124×C₄₇	1	2	yes	—
458	C₂×C₄	#127×C₄₇	1	2	yes	—
459	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
465	C₈	—	2	4	no	—
466	C₈	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	8	4	no	—
474	C₂²	—	8	4	no	—
475	C₂²	—	8	4	no	—
476	C₂²	C₄₇×#390	1	2	yes	—
477	C₂²	C₄₇×#390	1	2	yes	—
478	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
479	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
480	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
481	C₄	—	4	4	no	—
482	C₄	—	4	4	no	—
483	C₄	—	8	4	no	—
484	C₄	C₄₇×#390	1	2	yes	—
485	C₄	C₄₇×#390	1	2	yes	—
486	C₄	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
487	C₄	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
488	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
489	C₄	C₂×#124×C₄₇	1	1	yes	characteristic
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	8	4	no	—
496	C₂	C₂×C₄₇×#390	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₇	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂×C₄₇	C₂×#390
prime radical	C₂×C₄₇×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×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. C₂×C₄₇×#410	C₂	semidirect
5. C₄₇×#2873	C₂	semidirect
6. C₄₇×#1976	C₂	semidirect
11. C₂×#137×C₄₇	C₄	semidirect
12. C₂×AGL(1,ℤ/8)×C₄₇	C₄	semidirect
19. C₄₇×#427	C₂²	semidirect
21. C₄₇×#421	C₂²	semidirect
24. C₄₇×#410	C₂²	semidirect
27. C₄₇×#405	C₂²	semidirect
52. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
53. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
54. C₂×D₈×C₄₇	C₂×C₄	semidirect
218. #21244	C₄₇	direct (N × H)
243. #2911	C₂×C₄₇	semidirect
244. C₂×#421	C₂×C₄₇	semidirect
245. C₂×#410	C₂×C₄₇	semidirect
246. #2873	C₂×C₄₇	semidirect
247. #1976	C₂×C₄₇	semidirect
259. C₂×#137	C₄×C₄₇	semidirect
260. C₂×AGL(1,ℤ/8)	C₄×C₄₇	semidirect
267. #427	C₂²×C₄₇	semidirect
269. #421	C₂²×C₄₇	semidirect
272. #410	C₂²×C₄₇	semidirect
275. #405	C₂²×C₄₇	semidirect
277. C₄₇	#21244	direct (N × H)
301. C₂×Q₁₆	C₂×C₄×C₄₇	semidirect
302. C₂×SD₁₆	C₂×C₄×C₄₇	semidirect
303. C₂×D₈	C₂×C₄×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×#575	2
C₄₇×#2911	2
C₂×C₄₇×#421	2
C₂×C₄₇×#410	2
C₄₇×#2873	2
C₄₇×#1976	2
#21244	47

Subgroups — C47×#21244 #26060942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21244 #26060942