Subgroups — C₂×C₄×M₁₆×D₄₇ #27079662

Order 12032.

3950 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆×D₄₇	C₂	1	2	yes	maximal
2	C₂²×C₄²×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689075	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×Dic₄₇	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#10625324	C₂	1	2	yes	maximal, complemented
7	C₄×M₁₆×D₄₇	C₂	1	16	yes	maximal, direct product factor
8	C₂×#97×D₄₇	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₈×D₄₇	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₄×D₄₇	C₄	1	2	yes	—
12	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	2	yes	—
14	C₂²×#10625324	C₂²	1	4	yes	—
15	C₂×M₁₆×D₄₇	C₄	1	32	yes	direct product factor
16	C₂×M₁₆×D₄₇	C₂²	1	16	yes	—
17	C₂²×C₈×D₄₇	C₂²	1	4	yes	—
18	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
19	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄²×D₄₇	C₄	1	8	yes	—
21	C₂×C₄²×D₄₇	C₄	1	2	yes	—
22	C₂×C₄²×D₄₇	C₄	1	2	yes	—
23	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄²×D₄₇	C₂²	1	8	yes	—
26	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
28	C₄×#10625329	C₂²	1	8	yes	complemented
29	#15689075	C₂²	1	16	yes	complemented
30	M₁₆×Dic₄₇	C₂²	1	16	yes	complemented
31	C₄×#10625324	C₂²	1	16	yes	complemented
32	C₂×#13093935	C₂²	1	2	yes	complemented
33	C₂×#13093934	C₂²	1	4	yes	complemented
34	#97×D₄₇	C₂²	1	16	yes	complemented
35	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
36	C₂×C₈×Dic₄₇	C₂²	1	4	yes	complemented
37	C₄×C₈×D₄₇	C₂²	1	16	yes	complemented
38	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
39	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₄₇	C₂²	1	8	yes	complemented
41	C₂×#97×C₄₇	C₂²	1	2	yes	complemented
42	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
43	C₂⁴×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
45	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	—	2	16	no	—
47	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
48	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
49	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
50	C₂²×C₄×D₄₇	C₂×C₄	1	16	yes	—
51	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₄₇	C₂×C₄	1	4	yes	—
53	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄×D₄₇	C₂×C₄	1	16	yes	—
55	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
56	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
57	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
58	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
59	C₂×#10625329	C₂×C₄	1	16	yes	complemented
60	C₂×#10625329	C₂³	1	8	yes	—
61	C₂×#10625324	C₂×C₄	1	32	yes	complemented
62	C₂×#10625324	C₂³	1	16	yes	—
63	M₁₆×D₄₇	C₂×C₄	1	128	yes	direct product factor
64	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
65	C₂×C₈×D₄₇	C₂×C₄	1	32	yes	complemented
66	C₂×C₈×D₄₇	C₂³	1	16	yes	—
67	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
68	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₄₇	C₂×C₄	1	16	yes	—
71	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
77	C₄²×D₄₇	C₂×C₄	1	4	yes	—
78	C₄²×D₄₇	C₂×C₄	1	16	yes	—
79	C₄²×D₄₇	C₂×C₄	1	4	yes	—
80	C₄²×D₄₇	C₂×C₄	1	4	yes	—
81	C₄²×D₄₇	C₂×C₄	1	16	yes	—
82	C₄²×D₄₇	C₂×C₄	1	4	yes	—
83	C₄²×D₄₇	C₂³	1	4	yes	—
84	C₄²×D₄₇	C₂³	1	4	yes	—
85	C₄²×D₄₇	C₂³	1	4	yes	—
86	C₄²×D₄₇	C₂³	1	4	yes	—
87	#13093935	C₂³	1	8	yes	complemented
88	#13093934	C₂³	1	16	yes	complemented
89	C₄×C₄₇⋊C₈	C₂³	1	8	yes	complemented
90	C₈×Dic₄₇	C₂³	1	16	yes	complemented
91	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
92	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
94	C₂×M₁₆×C₄₇	C₂³	1	8	yes	—
95	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
96	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
97	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	#97×C₄₇	C₂³	1	8	yes	complemented
102	C₄×C₈×C₄₇	C₂³	1	8	yes	complemented
103	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂³×D₄₇	—	2	8	no	—
105	C₂³×D₄₇	C₄²	1	8	yes	—
106	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂³×D₄₇	C₂²×C₄	1	4	yes	—
108	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	—	2	8	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	8	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	8	yes	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
118	C₂²×Dic₄₇	—	2	8	no	—
119	C₂²×Dic₄₇	C₄²	1	8	yes	—
120	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
122	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
123	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
126	C₂×C₄×D₄₇	—	2	8	no	—
127	C₂×C₄×D₄₇	—	2	8	no	—
128	C₂×C₄×D₄₇	—	2	8	no	—
129	C₂×C₄×D₄₇	—	2	64	no	—
130	C₂×C₄×D₄₇	C₄²	1	8	yes	—
131	C₂×C₄×D₄₇	C₄²	1	32	yes	—
132	C₂×C₄×D₄₇	C₄²	1	8	yes	—
133	C₂×C₄×D₄₇	M₁₆	1	16	yes	direct product factor
134	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
135	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
136	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
137	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
138	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
139	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
140	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
141	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
142	C₂×C₄×D₄₇	C₂²×C₄	1	32	yes	—
143	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
144	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
145	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
146	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
147	M₁₆×C₄₇	C₂²×C₄	1	32	yes	complemented
148	C₂×C₈×C₄₇	C₂²×C₄	1	16	yes	complemented
149	C₂×C₈×C₄₇	C₂⁴	1	8	yes	—
150	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
152	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
153	C₄²×C₄₇	C₂⁴	1	2	yes	—
154	C₄²×C₄₇	C₂⁴	1	2	yes	—
155	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
156	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
157	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
158	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
159	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
160	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
161	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
162	C₄×Dic₄₇	C₂⁴	1	2	yes	—
163	C₄×Dic₄₇	C₂⁴	1	2	yes	—
164	#10625329	C₂²×C₄	1	32	yes	complemented
165	C₂×C₄₇⋊C₈	C₂²×C₄	1	16	yes	complemented
166	C₂×C₄₇⋊C₈	C₂⁴	1	8	yes	—
167	#10625324	C₂²×C₄	1	64	yes	complemented
168	C₈×D₄₇	C₂²×C₄	1	64	yes	complemented
169	C₂³×C₄₇	—	2	4	no	—
170	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
171	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
172	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂²×D₄₇	—	2	4	no	—
174	C₂²×D₄₇	—	2	16	no	—
175	C₂²×D₄₇	—	2	32	no	—
176	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
177	C₂²×D₄₇	C₂×C₄²	1	16	yes	—
178	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
179	C₂²×D₄₇	C₂×M₁₆	1	8	yes	—
180	C₂²×D₄₇	C₂³×C₄	1	2	yes	—
181	C₂²×D₄₇	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₄₇	—	2	4	no	—
183	C₂×C₄×C₄₇	—	2	16	no	—
184	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
185	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
186	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	complemented
187	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
188	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
189	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
194	C₂×Dic₄₇	—	2	4	no	—
195	C₂×Dic₄₇	—	2	16	no	—
196	C₂×Dic₄₇	C₂×C₄²	1	16	yes	—
197	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
198	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
199	C₂×Dic₄₇	C₂×M₁₆	1	8	yes	complemented
200	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
201	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
202	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
203	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
204	C₄×D₄₇	—	2	16	no	—
205	C₄×D₄₇	—	2	16	no	—
206	C₄×D₄₇	—	2	16	no	—
207	C₄×D₄₇	C₂×C₄²	1	16	yes	—
208	C₄×D₄₇	C₂×C₄²	1	8	yes	—
209	C₄×D₄₇	C₂×C₄²	1	8	yes	—
210	C₄×D₄₇	C₂×C₄²	1	16	yes	—
211	C₄×D₄₇	C₂×M₁₆	1	32	yes	direct product factor
212	C₄×D₄₇	C₂³×C₄	1	8	yes	—
213	C₄×D₄₇	C₂³×C₄	1	8	yes	—
214	C₈×C₄₇	C₂³×C₄	1	16	yes	complemented
215	C₄₇⋊C₈	C₂³×C₄	1	16	yes	complemented
216	C₂²×C₄×M₁₆	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	—	2	8	no	—
218	C₂²×C₄₇	—	2	4	no	—
219	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
220	C₂²×C₄₇	C₂²×C₄²	1	2	yes	—
221	C₂²×C₄₇	C₂²×M₁₆	1	4	yes	—
222	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
223	C₂×D₄₇	—	2	8	no	—
224	C₂×D₄₇	—	2	4	no	—
225	C₂×D₄₇	—	2	32	no	—
226	C₂×D₄₇	C₄×M₁₆	1	16	yes	direct product factor
227	C₂×D₄₇	C₂²×C₄²	1	4	yes	—
228	C₂×D₄₇	C₂²×C₄²	1	4	yes	—
229	C₂×D₄₇	C₂²×M₁₆	1	8	yes	—
230	C₄×C₄₇	—	2	4	no	—
231	C₄×C₄₇	C₂²×C₄²	1	2	yes	—
232	C₄×C₄₇	C₂²×C₄²	1	4	yes	—
233	C₄×C₄₇	C₂²×M₁₆	1	8	yes	complemented
234	C₄×C₄₇	C₂⁴×C₄	1	2	yes	—
235	Dic₄₇	—	2	4	no	—
236	Dic₄₇	C₂²×C₄²	1	4	yes	—
237	Dic₄₇	C₂²×C₄²	1	4	yes	—
238	Dic₄₇	C₂²×M₁₆	1	8	yes	complemented
239	C₂³×M₁₆	—	47	2	no	—
240	C₂³×C₄²	—	47	1	no	—
241	C₂×C₄×M₁₆	—	47	1	no	—
242	C₂×C₄×M₁₆	—	47	16	no	—
243	C₂×C₄×M₁₆	—	47	2	no	—
244	C₂×C₄×M₁₆	—	47	2	no	—
245	C₂×C₄×M₁₆	—	47	2	no	—
246	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic, direct product factor
247	C₂²×#97	—	47	2	no	—
248	C₂²×C₄×C₈	—	47	2	no	—
249	C₂×C₄₇	—	2	4	no	—
250	C₂×C₄₇	C₂×C₄×M₁₆	1	4	yes	complemented
251	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
252	C₂×C₄₇	C₂³×M₁₆	1	2	yes	—
253	D₄₇	—	2	4	no	—
254	D₄₇	C₂×C₄×M₁₆	1	8	yes	direct product factor
255	C₂⁴×C₄	—	47	1	no	—
256	C₂⁴×C₄	—	47	2	no	—
257	C₂²×M₁₆	—	47	2	no	—
258	C₂²×M₁₆	—	47	32	no	—
259	C₂²×M₁₆	—	47	16	no	—
260	C₂²×M₁₆	—	47	4	no	—
261	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
262	C₂³×C₈	—	47	4	no	—
263	C₂²×C₄²	—	47	2	no	—
264	C₂²×C₄²	—	47	1	no	—
265	C₂²×C₄²	—	47	2	no	—
266	C₂²×C₄²	—	47	2	no	—
267	C₂²×C₄²	—	47	8	no	—
268	C₂²×C₄²	—	47	1	no	—
269	C₂²×C₄²	—	47	1	no	—
270	C₂²×C₄²	—	47	8	no	—
271	C₂²×C₄²	—	47	1	no	—
272	C₂²×C₄²	—	47	1	no	—
273	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
274	C₄×M₁₆	—	47	16	no	—
275	C₄×M₁₆	—	47	8	no	—
276	C₄×M₁₆	—	47	16	no	—
277	C₄×M₁₆	—	47	16	no	—
278	C₄×M₁₆	C₂×D₄₇	1	8	yes	direct product factor
279	C₂×#97	—	47	4	no	—
280	C₂×#97	—	47	2	no	—
281	C₂×#97	—	47	16	no	—
282	C₂×#97	C₂×D₄₇	1	2	yes	complemented
283	C₂×C₄×C₈	—	47	4	no	—
284	C₂×C₄×C₈	—	47	2	no	—
285	C₂×C₄×C₈	—	47	16	no	—
286	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	complemented
287	C₄₇	C₂²×C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
288	C₂⁵	—	47	1	no	—
289	C₂³×C₄	—	47	1	no	—
290	C₂³×C₄	—	47	16	no	—
291	C₂³×C₄	—	47	1	no	—
292	C₂³×C₄	—	47	4	no	—
293	C₂³×C₄	—	47	1	no	—
294	C₂³×C₄	—	47	2	no	—
295	C₂³×C₄	—	47	1	no	—
296	C₂³×C₄	—	47	4	no	—
297	C₂³×C₄	—	47	1	no	—
298	C₂³×C₄	—	47	2	no	—
299	C₂³×C₄	—	47	2	no	—
300	C₂³×C₄	—	47	16	no	—
301	C₂³×C₄	—	47	2	no	—
302	C₂³×C₄	—	47	2	no	—
303	C₂³×C₄	—	94	16	no	—
304	C₂³×C₄	C₄×D₄₇	1	2	yes	—
305	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
306	C₂×M₁₆	—	47	16	no	—
307	C₂×M₁₆	—	47	8	no	—
308	C₂×M₁₆	—	47	128	no	—
309	C₂×M₁₆	—	47	32	no	—
310	C₂×M₁₆	—	47	16	no	—
311	C₂×M₁₆	C₄×D₄₇	1	16	yes	direct product factor
312	C₂×M₁₆	C₂²×D₄₇	1	8	yes	—
313	C₂²×C₈	—	47	4	no	—
314	C₂²×C₈	—	47	32	no	—
315	C₂²×C₈	—	47	16	no	—
316	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
317	C₂×C₄²	—	47	2	no	—
318	C₂×C₄²	—	47	2	no	—
319	C₂×C₄²	—	47	2	no	—
320	C₂×C₄²	—	47	16	no	—
321	C₂×C₄²	—	47	2	no	—
322	C₂×C₄²	—	47	2	no	—
323	C₂×C₄²	—	47	4	no	—
324	C₂×C₄²	—	47	1	no	—
325	C₂×C₄²	—	47	1	no	—
326	C₂×C₄²	—	47	4	no	—
327	C₂×C₄²	—	47	16	no	—
328	C₂×C₄²	—	47	4	no	—
329	C₂×C₄²	—	47	4	no	—
330	C₂×C₄²	—	47	16	no	—
331	C₂×C₄²	—	47	4	no	—
332	C₂×C₄²	—	47	4	no	—
333	C₂×C₄²	—	47	4	no	—
334	C₂×C₄²	—	47	4	no	—
335	C₂×C₄²	—	47	4	no	—
336	C₂×C₄²	—	47	4	no	—
337	C₂×C₄²	C₄×D₄₇	1	2	yes	—
338	C₂×C₄²	C₄×D₄₇	1	4	yes	—
339	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
340	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
341	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
342	#97	—	47	16	no	—
343	#97	—	47	8	no	—
344	#97	C₂²×D₄₇	1	8	yes	complemented
345	C₄×C₈	—	47	16	no	—
346	C₄×C₈	—	47	8	no	—
347	C₄×C₈	C₂²×D₄₇	1	8	yes	complemented
348	C₂⁴	—	47	1	no	—
349	C₂⁴	—	47	8	no	—
350	C₂⁴	—	47	4	no	—
351	C₂⁴	—	47	1	no	—
352	C₂⁴	—	94	8	no	—
353	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	47	8	no	—
356	C₂²×C₄	—	47	4	no	—
357	C₂²×C₄	—	47	1	no	—
358	C₂²×C₄	—	47	1	no	—
359	C₂²×C₄	—	47	2	no	—
360	C₂²×C₄	—	47	8	no	—
361	C₂²×C₄	—	47	32	no	—
362	C₂²×C₄	—	47	8	no	—
363	C₂²×C₄	—	47	16	no	—
364	C₂²×C₄	—	47	2	no	—
365	C₂²×C₄	—	47	4	no	—
366	C₂²×C₄	—	47	4	no	—
367	C₂²×C₄	—	47	2	no	—
368	C₂²×C₄	—	47	8	no	—
369	C₂²×C₄	—	47	8	no	—
370	C₂²×C₄	—	47	32	no	—
371	C₂²×C₄	—	47	8	no	—
372	C₂²×C₄	—	47	2	no	—
373	C₂²×C₄	—	47	2	no	—
374	C₂²×C₄	—	47	8	no	—
375	C₂²×C₄	—	47	2	no	—
376	C₂²×C₄	—	47	8	no	—
377	C₂²×C₄	—	47	8	no	—
378	C₂²×C₄	—	47	8	no	—
379	C₂²×C₄	—	94	8	no	—
380	C₂²×C₄	—	94	64	no	—
381	C₂²×C₄	—	94	8	no	—
382	C₂²×C₄	—	94	8	no	—
383	C₂²×C₄	—	94	8	no	—
384	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
385	C₂²×C₄	C₂×C₄×D₄₇	1	8	yes	—
386	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
387	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₄₇	1	8	yes	—
389	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
390	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
391	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	M₁₆	—	47	32	no	—
393	M₁₆	—	47	64	no	—
394	M₁₆	C₂×C₄×D₄₇	1	32	yes	direct product factor
395	C₂×C₈	—	47	16	no	—
396	C₂×C₈	—	47	8	no	—
397	C₂×C₈	—	47	64	no	—
398	C₂×C₈	C₂×C₄×D₄₇	1	16	yes	complemented
399	C₂×C₈	C₂³×D₄₇	1	8	yes	—
400	C₄²	—	47	8	no	—
401	C₄²	—	47	2	no	—
402	C₄²	—	47	8	no	—
403	C₄²	—	47	8	no	—
404	C₄²	—	47	8	no	—
405	C₄²	—	47	8	no	—
406	C₄²	—	47	2	no	—
407	C₄²	—	47	2	no	—
408	C₄²	—	47	2	no	—
409	C₄²	C₂×C₄×D₄₇	1	2	yes	—
410	C₄²	C₂×C₄×D₄₇	1	8	yes	—
411	C₄²	C₂×C₄×D₄₇	1	2	yes	—
412	C₄²	C₂³×D₄₇	1	2	yes	—
413	C₄²	C₂³×D₄₇	1	2	yes	—
414	C₂³	—	2	4	no	—
415	C₂³	—	47	4	no	—
416	C₂³	—	47	8	no	—
417	C₂³	—	47	2	no	—
418	C₂³	—	47	16	no	—
419	C₂³	—	47	4	no	—
420	C₂³	—	47	2	no	—
421	C₂³	—	94	16	no	—
422	C₂³	—	94	32	no	—
423	C₂³	—	94	4	no	—
424	C₂³	C₄²×D₄₇	1	4	yes	—
425	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
426	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	16	no	—
429	C₂×C₄	—	47	16	no	—
430	C₂×C₄	—	47	4	no	—
431	C₂×C₄	—	47	4	no	—
432	C₂×C₄	—	47	8	no	—
433	C₂×C₄	—	47	2	no	—
434	C₂×C₄	—	47	2	no	—
435	C₂×C₄	—	47	4	no	—
436	C₂×C₄	—	47	8	no	—
437	C₂×C₄	—	47	16	no	—
438	C₂×C₄	—	47	16	no	—
439	C₂×C₄	—	47	8	no	—
440	C₂×C₄	—	47	32	no	—
441	C₂×C₄	—	47	8	no	—
442	C₂×C₄	—	47	8	no	—
443	C₂×C₄	—	47	4	no	—
444	C₂×C₄	—	94	16	no	—
445	C₂×C₄	—	94	16	no	—
446	C₂×C₄	—	94	16	no	—
447	C₂×C₄	—	94	4	no	—
448	C₂×C₄	—	94	16	no	—
449	C₂×C₄	C₄²×D₄₇	1	8	yes	—
450	C₂×C₄	C₄²×D₄₇	1	4	yes	—
451	C₂×C₄	M₁₆×D₄₇	1	8	yes	direct product factor
452	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
453	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
454	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
455	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
456	C₂×C₄	C₂²×C₄×D₄₇	1	8	yes	—
457	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
458	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
459	C₈	—	47	16	no	—
460	C₈	C₂²×C₄×D₄₇	1	16	yes	complemented
461	C₂²	—	2	4	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	47	4	no	—
464	C₂²	—	47	8	no	—
465	C₂²	—	47	16	no	—
466	C₂²	—	47	4	no	—
467	C₂²	—	94	32	no	—
468	C₂²	—	94	4	no	—
469	C₂²	—	94	8	no	—
470	C₂²	C₂×C₄²×D₄₇	1	4	yes	—
471	C₂²	C₂×C₄²×D₄₇	1	2	yes	—
472	C₂²	C₂×M₁₆×D₄₇	1	4	yes	—
473	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
474	C₄	—	2	4	no	—
475	C₄	—	47	4	no	—
476	C₄	—	47	4	no	—
477	C₄	—	47	8	no	—
478	C₄	—	94	4	no	—
479	C₄	C₂×C₄²×D₄₇	1	2	yes	—
480	C₄	C₂×C₄²×D₄₇	1	4	yes	—
481	C₄	C₂×M₁₆×D₄₇	1	8	yes	direct product factor
482	C₄	C₂³×C₄×D₄₇	1	2	yes	—
483	C₂	—	2	4	no	—
484	C₂	—	47	8	no	—
485	C₂	—	94	4	no	—
486	C₂	C₄×M₁₆×D₄₇	1	4	yes	direct product factor
487	C₂	C₂²×C₄²×D₄₇	1	1	yes	characteristic
488	C₂	C₂²×M₁₆×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×D₄₇	C₂×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	C₂²×C₄×M₁₆
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×#10625329	C₂	semidirect
4. C₂×#15689075	C₂	semidirect
5. C₂×M₁₆×Dic₄₇	C₂	semidirect
6. C₂×C₄×#10625324	C₂	semidirect
7. C₄×M₁₆×D₄₇	C₂	direct (N × H)
8. C₂×#97×D₄₇	C₂	semidirect
9. C₂×C₄×C₈×D₄₇	C₂	semidirect
10. C₂×C₄×M₁₆×C₄₇	C₂	semidirect
15. C₂×M₁₆×D₄₇	C₄	direct (N × H)
28. C₄×#10625329	C₂²	semidirect
29. #15689075	C₂²	semidirect
30. M₁₆×Dic₄₇	C₂²	semidirect
31. C₄×#10625324	C₂²	semidirect
32. C₂×#13093935	C₂²	semidirect
33. C₂×#13093934	C₂²	semidirect
34. #97×D₄₇	C₂²	semidirect
35. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
36. C₂×C₈×Dic₄₇	C₂²	semidirect
37. C₄×C₈×D₄₇	C₂²	semidirect
40. C₄×M₁₆×C₄₇	C₂²	semidirect
41. C₂×#97×C₄₇	C₂²	semidirect
42. C₂×C₄×C₈×C₄₇	C₂²	semidirect
59. C₂×#10625329	C₂×C₄	semidirect
61. C₂×#10625324	C₂×C₄	semidirect
63. M₁₆×D₄₇	C₂×C₄	direct (N × H)
65. C₂×C₈×D₄₇	C₂×C₄	semidirect
87. #13093935	C₂³	semidirect
88. #13093934	C₂³	semidirect
89. C₄×C₄₇⋊C₈	C₂³	semidirect
90. C₈×Dic₄₇	C₂³	semidirect
93. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
101. #97×C₄₇	C₂³	semidirect
102. C₄×C₈×C₄₇	C₂³	semidirect
133. C₂×C₄×D₄₇	M₁₆	direct (N × H)
147. M₁₆×C₄₇	C₂²×C₄	semidirect
148. C₂×C₈×C₄₇	C₂²×C₄	semidirect
164. #10625329	C₂²×C₄	semidirect
165. C₂×C₄₇⋊C₈	C₂²×C₄	semidirect
167. #10625324	C₂²×C₄	semidirect
168. C₈×D₄₇	C₂²×C₄	semidirect
186. C₂×C₄×C₄₇	C₂×M₁₆	semidirect
199. C₂×Dic₄₇	C₂×M₁₆	semidirect
211. C₄×D₄₇	C₂×M₁₆	direct (N × H)
214. C₈×C₄₇	C₂³×C₄	semidirect
215. C₄₇⋊C₈	C₂³×C₄	semidirect
226. C₂×D₄₇	C₄×M₁₆	direct (N × H)
233. C₄×C₄₇	C₂²×M₁₆	semidirect
238. Dic₄₇	C₂²×M₁₆	semidirect
246. C₂×C₄×M₁₆	D₄₇	direct (N × H)
250. C₂×C₄₇	C₂×C₄×M₁₆	semidirect
254. D₄₇	C₂×C₄×M₁₆	direct (N × H)
278. C₄×M₁₆	C₂×D₄₇	direct (N × H)
282. C₂×#97	C₂×D₄₇	semidirect
286. C₂×C₄×C₈	C₂×D₄₇	semidirect
287. C₄₇	C₂²×C₄×M₁₆	semidirect
311. C₂×M₁₆	C₄×D₄₇	direct (N × H)
344. #97	C₂²×D₄₇	semidirect
347. C₄×C₈	C₂²×D₄₇	semidirect
394. M₁₆	C₂×C₄×D₄₇	direct (N × H)
398. C₂×C₈	C₂×C₄×D₄₇	semidirect
451. C₂×C₄	M₁₆×D₄₇	direct (N × H)
460. C₈	C₂²×C₄×D₄₇	semidirect
481. C₄	C₂×M₁₆×D₄₇	direct (N × H)
486. C₂	C₄×M₁₆×D₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×M₁₆×D₄₇	2
C₂²×C₄²×D₄₇	2
C₂×C₄×#10625329	2
C₂×#15689075	2
C₂×M₁₆×Dic₄₇	2
C₂×C₄×#10625324	2
C₄×M₁₆×D₄₇	2
C₂×#97×D₄₇	2
C₂×C₄×C₈×D₄₇	2
C₂×C₄×M₁₆×C₄₇	2
C₂²×C₄×M₁₆	47

Subgroups — C2×C4×M16×D47 #27079662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×M₁₆×D₄₇ #27079662