Subgroups — C₂×C₄₇×#1517 #26057267

Order 12032.

1366 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1517	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇×#327	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₄₇	—	2	1	no	—
7	C₄₇×#532	—	2	2	no	—
8	C₄₇×#532	—	2	2	no	—
9	C₄₇×#532	C₄	1	4	yes	complemented
10	C₄₇×#532	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
12	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
13	C₂×#124×C₄₇	—	2	1	no	—
14	C₂×#121×C₄₇	—	2	1	no	—
15	C₂×#121×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₄₇	—	2	1	no	—
17	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	complemented
18	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#431	—	2	2	no	—
21	C₄₇×#431	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
23	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₄₇	—	2	1	no	—
25	C₄₇×#382	—	2	2	no	—
26	C₄₇×#382	C₂²	1	4	yes	complemented
27	C₂×#95×C₄₇	—	2	1	no	—
28	C₂×#95×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#327	C₂²	1	16	yes	complemented
30	C₂×#41×C₄₇	—	2	4	no	—
31	C₂×#41×C₄₇	—	2	4	no	—
32	C₂×#41×C₄₇	—	4	4	no	—
33	C₂×#41×C₄₇	—	4	4	no	—
34	C₂²×Q₈×C₄₇	—	2	1	no	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	—	2	1	no	—
37	C₂²×D₄×C₄₇	—	2	1	no	—
38	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₄₇	—	2	2	no	—
40	C₂³×C₄×C₄₇	—	2	2	no	—
41	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	—	2	2	no	—
45	C₄⋊Q₈×C₄₇	—	2	2	no	—
46	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
47	#127×C₄₇	—	2	2	no	—
48	#127×C₄₇	C₂×C₄	1	4	yes	complemented
49	#124×C₄₇	—	2	4	no	—
50	#124×C₄₇	—	2	4	no	—
51	#121×C₄₇	—	2	4	no	—
52	#121×C₄₇	—	2	4	no	—
53	#121×C₄₇	—	2	2	no	—
54	#121×C₄₇	—	2	2	no	—
55	#121×C₄₇	C₂×C₄	1	4	yes	—
56	#121×C₄₇	C₂³	1	4	yes	—
57	C₄×D₄×C₄₇	—	2	4	no	—
58	C₄×D₄×C₄₇	—	2	4	no	—
59	C₄×D₄×C₄₇	—	2	4	no	—
60	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₄₇	D₄	1	2	yes	—
71	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	D₄	1	2	yes	—
74	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
75	C₄⋊C₈×C₄₇	—	2	4	no	—
76	C₂²⋊C₈×C₄₇	—	2	2	no	—
77	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
78	C₄×C₈×C₄₇	—	2	4	no	—
79	#95×C₄₇	—	2	4	no	—
80	#95×C₄₇	—	2	2	no	—
81	#95×C₄₇	C₂³	1	4	yes	—
82	C₂⁴×C₄₇	—	2	2	no	—
83	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
84	#41×C₄₇	—	4	16	no	—
85	#41×C₄₇	—	4	8	no	—
86	#41×C₄₇	—	4	8	no	—
87	C₂×Q₈×C₄₇	—	2	4	no	—
88	C₂×Q₈×C₄₇	—	4	4	no	—
89	C₂×D₄×C₄₇	—	2	4	no	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	2	4	no	—
94	C₂×D₄×C₄₇	—	4	4	no	—
95	C₂×D₄×C₄₇	—	4	4	no	—
96	C₂×D₄×C₄₇	—	4	4	no	—
97	C₂×D₄×C₄₇	—	4	4	no	—
98	C₂×D₄×C₄₇	—	4	4	no	—
99	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	8	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	—	4	2	no	—
105	C₂²×C₄×C₄₇	—	4	8	no	—
106	C₂²×C₄×C₄₇	—	4	4	no	—
107	C₂²×C₄×C₄₇	—	4	4	no	—
108	C₂²×C₄×C₄₇	—	4	4	no	—
109	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	D₈	1	4	yes	—
116	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	4	4	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	4	8	no	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₂²⋊C₄×C₄₇	—	2	8	no	—
133	C₂²⋊C₄×C₄₇	—	2	4	no	—
134	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
136	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
137	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
138	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
140	C₄²×C₄₇	C₂×D₄	1	2	yes	—
141	C₄²×C₄₇	C₂×D₄	1	2	yes	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	—	4	4	no	—
146	C₂³×C₄₇	—	4	4	no	—
147	C₂³×C₄₇	—	4	4	no	—
148	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂³×C₄₇	C₂×D₈	1	2	yes	—
151	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
152	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₄₇	—	4	8	no	—
154	D₄×C₄₇	—	4	4	no	—
155	D₄×C₄₇	—	4	4	no	—
156	D₄×C₄₇	—	4	8	no	—
157	D₄×C₄₇	—	4	4	no	—
158	D₄×C₄₇	—	4	4	no	—
159	D₄×C₄₇	—	4	8	no	—
160	D₄×C₄₇	—	4	8	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	4	no	—
173	C₂×C₄×C₄₇	—	4	16	no	—
174	C₂×C₄×C₄₇	—	4	4	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	4	4	no	—
177	C₂×C₄×C₄₇	—	8	8	no	—
178	C₂×C₄×C₄₇	#102	1	4	yes	—
179	C₂×C₄×C₄₇	#102	1	4	yes	—
180	C₂×C₄×C₄₇	#102	1	8	yes	—
181	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
188	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
189	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₄₇	—	4	4	no	—
192	C₂×#1517	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	4	no	—
198	C₂²×C₄₇	—	2	4	no	—
199	C₂²×C₄₇	—	4	4	no	—
200	C₂²×C₄₇	—	4	4	no	—
201	C₂²×C₄₇	—	4	4	no	—
202	C₂²×C₄₇	—	8	8	no	—
203	C₂²×C₄₇	#410	1	2	yes	—
204	C₂²×C₄₇	C₂×#102	1	2	yes	—
205	C₂²×C₄₇	C₂×#102	1	2	yes	—
206	C₂²×C₄₇	#421	1	2	yes	—
207	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
209	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₄×C₄₇	—	8	4	no	—
218	C₄×C₄₇	C₂×#102	1	4	yes	—
219	C₄×C₄₇	C₂×#102	1	4	yes	—
220	C₂×#532	C₂×C₄₇	1	1	yes	characteristic
221	C₂×#431	C₂×C₄₇	1	1	yes	characteristic, complemented
222	C₂×#382	C₂×C₄₇	1	1	yes	characteristic, complemented
223	#1517	C₂×C₄₇	1	8	yes	direct product factor
224	C₂×#327	C₂×C₄₇	1	4	yes	complemented
225	C₂×C₄₇	—	2	1	no	—
226	C₂×C₄₇	—	2	1	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	8	4	no	—
229	C₂×C₄₇	#1517	1	4	yes	direct product factor
230	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
231	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
233	C₂²×#41	—	2	1	no	—
234	#532	—	2	2	no	—
235	#532	—	2	2	no	—
236	#532	C₄×C₄₇	1	4	yes	complemented
237	#532	C₂²×C₄₇	1	4	yes	—
238	C₂×C₄⋊Q₈	C₄×C₄₇	1	1	yes	characteristic, complemented
239	C₂×#127	C₄×C₄₇	1	1	yes	characteristic, complemented
240	C₂×#124	—	2	1	no	—
241	C₂×#121	—	2	1	no	—
242	C₂×#121	C₂²×C₄₇	1	2	yes	—
243	C₂×C₄×D₄	—	2	1	no	—
244	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	complemented
245	C₂²×C₄⋊C₄	—	2	1	no	—
246	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
247	#431	—	2	2	no	—
248	#431	C₂²×C₄₇	1	4	yes	complemented
249	C₂×C₄⋊C₈	—	2	1	no	—
250	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
251	C₂×C₄×C₈	—	2	1	no	—
252	#382	—	2	2	no	—
253	#382	C₂²×C₄₇	1	4	yes	complemented
254	C₂×#95	—	2	1	no	—
255	C₂×#95	C₂²×C₄₇	1	2	yes	—
256	#327	C₂²×C₄₇	1	16	yes	complemented
257	C₄₇	C₂×#1517	1	1	yes	characteristic, direct product factor, Sylow
258	C₂×#41	—	2	4	no	—
259	C₂×#41	—	2	4	no	—
260	C₂×#41	—	4	4	no	—
261	C₂×#41	—	4	4	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
270	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
272	C₂²×C₈	—	2	2	no	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	C₂×C₄×C₄₇	1	4	yes	complemented
275	#127	—	2	2	no	—
276	#127	C₂×C₄×C₄₇	1	4	yes	complemented
277	#124	—	2	4	no	—
278	#124	—	2	4	no	—
279	#121	—	2	4	no	—
280	#121	—	2	4	no	—
281	#121	—	2	2	no	—
282	#121	—	2	2	no	—
283	#121	C₂×C₄×C₄₇	1	4	yes	—
284	#121	C₂³×C₄₇	1	4	yes	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	C₂×C₄×C₄₇	1	8	yes	complemented
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	4	4	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
296	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
297	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
298	C₂×C₄²	D₄×C₄₇	1	2	yes	—
299	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
301	C₂×C₄²	D₄×C₄₇	1	2	yes	—
302	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
303	C₄⋊C₈	—	2	4	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
306	C₄×C₈	—	2	4	no	—
307	#95	—	2	4	no	—
308	#95	—	2	2	no	—
309	#95	C₂³×C₄₇	1	4	yes	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
312	#41	—	4	8	no	—
313	#41	—	4	8	no	—
314	#41	—	4	16	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	4	4	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	8	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
340	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
341	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
343	C₂²×C₄	D₈×C₄₇	1	4	yes	—
344	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	—
345	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	4	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	8	no	—
358	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
363	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
364	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
365	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
366	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
367	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
368	C₄²	C₂×D₄×C₄₇	1	2	yes	—
369	C₄²	C₂×D₄×C₄₇	1	2	yes	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	4	4	no	—
376	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
377	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
378	C₂³	C₂×D₈×C₄₇	1	2	yes	—
379	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
380	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
381	Q₈	—	4	8	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	8	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	8	no	—
388	D₄	—	4	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	16	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	#102×C₄₇	1	4	yes	—
407	C₂×C₄	#102×C₄₇	1	4	yes	—
408	C₂×C₄	#102×C₄₇	1	8	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
410	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
412	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
413	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
414	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
415	C₂×C₄	C₂×D₈×C₄₇	1	4	yes	—
416	C₂×C₄	C₂×SD₁₆×C₄₇	1	4	yes	—
417	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
419	C₈	—	4	4	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	8	8	no	—
430	C₂²	C₄₇×#410	1	2	yes	—
431	C₂²	C₂×#102×C₄₇	1	2	yes	—
432	C₂²	C₂×#102×C₄₇	1	2	yes	—
433	C₂²	C₄₇×#421	1	2	yes	—
434	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
435	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
436	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	4	no	—
445	C₄	C₂×#102×C₄₇	1	4	yes	—
446	C₄	C₂×#102×C₄₇	1	4	yes	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	2	no	—
450	C₂	—	8	4	no	—
451	C₂	C₄₇×#1517	1	4	yes	direct product factor
452	C₂	C₂×C₄₇×#410	1	1	yes	characteristic
453	C₂	C₂²×#102×C₄₇	1	1	yes	characteristic
454	C₂	C₂×C₄₇×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#431	C₂	semidirect
3. C₂×C₄₇×#382	C₂	semidirect
4. C₄₇×#1517	C₂	direct (N × H)
5. C₂×C₄₇×#327	C₂	semidirect
9. C₄₇×#532	C₄	semidirect
11. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
12. C₂×#127×C₄₇	C₄	semidirect
17. C₂×C₄×D₄×C₄₇	C₄	semidirect
21. C₄₇×#431	C₂²	semidirect
26. C₄₇×#382	C₂²	semidirect
29. C₄₇×#327	C₂²	semidirect
46. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
48. #127×C₄₇	C₂×C₄	semidirect
60. C₄×D₄×C₄₇	C₂×C₄	semidirect
192. C₂×#1517	C₄₇	direct (N × H)
221. C₂×#431	C₂×C₄₇	semidirect
222. C₂×#382	C₂×C₄₇	semidirect
223. #1517	C₂×C₄₇	direct (N × H)
224. C₂×#327	C₂×C₄₇	semidirect
229. C₂×C₄₇	#1517	direct (N × H)
236. #532	C₄×C₄₇	semidirect
238. C₂×C₄⋊Q₈	C₄×C₄₇	semidirect
239. C₂×#127	C₄×C₄₇	semidirect
244. C₂×C₄×D₄	C₄×C₄₇	semidirect
248. #431	C₂²×C₄₇	semidirect
253. #382	C₂²×C₄₇	semidirect
256. #327	C₂²×C₄₇	semidirect
257. C₄₇	C₂×#1517	direct (N × H)
274. C₄⋊Q₈	C₂×C₄×C₄₇	semidirect
276. #127	C₂×C₄×C₄₇	semidirect
288. C₄×D₄	C₂×C₄×C₄₇	semidirect
451. C₂	C₄₇×#1517	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#532	2
C₂×C₄₇×#431	2
C₂×C₄₇×#382	2
C₄₇×#1517	2
C₂×C₄₇×#327	2
C₂×#1517	47

Subgroups — C2×C47×#1517 #26057267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1517 #26057267