Subgroups — C₂²×C₄₇×AΣL(1,𝔽₁₆) #26073039

Order 12032.

2774 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#120×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#100×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#99×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×AΣL(1,𝔽₁₆)	C₂	1	12	yes	maximal, direct product factor
5	C₂⁶×C₄₇	C₄	1	1	yes	characteristic, complemented
6	C₂³×D₄×C₄₇	—	2	1	no	—
7	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₇	—	2	1	no	—
9	C₂×#120×C₄₇	—	2	3	no	—
10	C₂×#120×C₄₇	—	2	3	no	—
11	C₂×#120×C₄₇	C₄	1	6	yes	complemented
12	C₂×#120×C₄₇	C₂²	1	6	yes	—
13	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
14	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
15	C₂²×C₂²⋊C₄×C₄₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#100×C₄₇	—	2	3	no	—
17	C₂×#100×C₄₇	C₂²	1	6	yes	complemented
18	C₂×#99×C₄₇	—	2	3	no	—
19	C₂×#99×C₄₇	C₂²	1	6	yes	complemented
20	C₄₇×AΣL(1,𝔽₁₆)	C₂²	1	16	yes	direct product factor
21	C₂⁵×C₄₇	—	2	1	no	—
22	C₂⁵×C₄₇	—	2	3	no	—
23	C₂⁵×C₄₇	—	4	8	no	—
24	C₂⁵×C₄₇	—	4	3	no	—
25	C₂⁵×C₄₇	—	4	1	no	—
26	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂⁵×C₄₇	C₂×C₄	1	6	yes	complemented
28	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₄₇	—	2	6	no	—
30	C₂²×D₄×C₄₇	—	2	6	no	—
31	C₂²×D₄×C₄₇	—	4	3	no	—
32	C₂²×D₄×C₄₇	—	4	1	no	—
33	C₂²×D₄×C₄₇	—	4	8	no	—
34	C₂²×D₄×C₄₇	C₂×C₄	1	3	yes	—
35	C₂²×D₄×C₄₇	D₄	1	3	yes	—
36	C₂²×D₄×C₄₇	D₄	1	3	yes	—
37	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
38	C₂³×C₄×C₄₇	—	2	1	no	—
39	C₂³×C₄×C₄₇	—	4	1	no	—
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂×M₁₆×C₄₇	—	2	6	no	—
42	C₂×M₁₆×C₄₇	—	4	3	no	—
43	C₂²×C₈×C₄₇	—	4	1	no	—
44	#120×C₄₇	—	2	12	no	—
45	#120×C₄₇	—	2	6	no	—
46	#120×C₄₇	—	2	6	no	—
47	#120×C₄₇	C₂×C₄	1	12	yes	complemented
48	#120×C₄₇	C₂³	1	4	yes	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	3	no	—
50	C₂×C₂²⋊C₄×C₄₇	—	2	6	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	6	no	—
52	C₂×C₂²⋊C₄×C₄₇	—	2	6	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	4	3	no	—
54	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	6	yes	complemented
55	#100×C₄₇	—	2	6	no	—
56	#100×C₄₇	C₂³	1	4	yes	complemented
57	#99×C₄₇	—	2	6	no	—
58	#99×C₄₇	C₂³	1	4	yes	complemented
59	C₂⁴×C₄₇	—	2	8	no	—
60	C₂⁴×C₄₇	—	2	3	no	—
61	C₂⁴×C₄₇	—	2	1	no	—
62	C₂⁴×C₄₇	—	2	1	no	—
63	C₂⁴×C₄₇	—	2	6	no	—
64	C₂⁴×C₄₇	—	2	3	no	—
65	C₂⁴×C₄₇	—	2	6	no	—
66	C₂⁴×C₄₇	—	4	4	no	—
67	C₂⁴×C₄₇	—	4	24	no	—
68	C₂⁴×C₄₇	—	4	6	no	—
69	C₂⁴×C₄₇	—	4	6	no	—
70	C₂⁴×C₄₇	—	4	4	no	—
71	C₂⁴×C₄₇	—	4	24	no	—
72	C₂⁴×C₄₇	—	4	6	no	—
73	C₂⁴×C₄₇	—	4	6	no	—
74	C₂⁴×C₄₇	—	4	4	no	—
75	C₂⁴×C₄₇	—	4	48	no	—
76	C₂⁴×C₄₇	—	4	8	no	—
77	C₂⁴×C₄₇	—	4	3	no	—
78	C₂⁴×C₄₇	—	4	1	no	—
79	C₂⁴×C₄₇	—	4	8	no	—
80	C₂⁴×C₄₇	C₂²⋊C₄	1	3	yes	—
81	C₂⁴×C₄₇	C₂²⋊C₄	1	3	yes	—
82	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂⁴×C₄₇	C₂²×C₄	1	3	yes	—
84	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	complemented
85	C₂⁴×C₄₇	C₂×D₄	1	3	yes	—
86	C₂×D₄×C₄₇	—	2	12	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	4	3	no	—
89	C₂×D₄×C₄₇	—	4	3	no	—
90	C₂×D₄×C₄₇	—	4	3	no	—
91	C₂×D₄×C₄₇	—	4	3	no	—
92	C₂×D₄×C₄₇	—	4	3	no	—
93	C₂×D₄×C₄₇	—	4	3	no	—
94	C₂×D₄×C₄₇	—	4	3	no	—
95	C₂×D₄×C₄₇	—	4	3	no	—
96	C₂×D₄×C₄₇	—	4	24	no	—
97	C₂×D₄×C₄₇	—	4	24	no	—
98	C₂×D₄×C₄₇	C₂²⋊C₄	1	6	yes	—
99	C₂×D₄×C₄₇	C₂²×C₄	1	3	yes	—
100	C₂×D₄×C₄₇	C₂×D₄	1	3	yes	—
101	C₂×D₄×C₄₇	C₂×D₄	1	3	yes	—
102	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	—	2	3	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	6	no	—
106	C₂²×C₄×C₄₇	—	4	4	no	—
107	C₂²×C₄×C₄₇	—	4	6	no	—
108	C₂²×C₄×C₄₇	—	8	4	no	—
109	C₂²×C₄×C₄₇	C₂²⋊C₄	1	3	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
111	M₁₆×C₄₇	—	2	4	no	—
112	M₁₆×C₄₇	—	4	6	no	—
113	C₂×C₈×C₄₇	—	4	6	no	—
114	C₂²⋊C₄×C₄₇	—	2	6	no	—
115	C₂²⋊C₄×C₄₇	—	2	12	no	—
116	C₂²⋊C₄×C₄₇	—	2	4	no	—
117	C₂²⋊C₄×C₄₇	—	2	4	no	—
118	C₂²⋊C₄×C₄₇	—	4	6	no	—
119	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	complemented
120	C₂³×C₄₇	—	2	4	no	—
121	C₂³×C₄₇	—	2	24	no	—
122	C₂³×C₄₇	—	2	4	no	—
123	C₂³×C₄₇	—	2	3	no	—
124	C₂³×C₄₇	—	2	3	no	—
125	C₂³×C₄₇	—	2	3	no	—
126	C₂³×C₄₇	—	2	3	no	—
127	C₂³×C₄₇	—	2	3	no	—
128	C₂³×C₄₇	—	2	3	no	—
129	C₂³×C₄₇	—	2	3	no	—
130	C₂³×C₄₇	—	2	3	no	—
131	C₂³×C₄₇	—	4	6	no	—
132	C₂³×C₄₇	—	4	6	no	—
133	C₂³×C₄₇	—	4	8	no	—
134	C₂³×C₄₇	—	4	4	no	—
135	C₂³×C₄₇	—	4	12	no	—
136	C₂³×C₄₇	—	4	24	no	—
137	C₂³×C₄₇	—	4	12	no	—
138	C₂³×C₄₇	—	4	24	no	—
139	C₂³×C₄₇	—	4	12	no	—
140	C₂³×C₄₇	—	4	6	no	—
141	C₂³×C₄₇	—	4	6	no	—
142	C₂³×C₄₇	—	4	24	no	—
143	C₂³×C₄₇	—	4	48	no	—
144	C₂³×C₄₇	—	4	48	no	—
145	C₂³×C₄₇	—	4	48	no	—
146	C₂³×C₄₇	—	4	24	no	—
147	C₂³×C₄₇	—	4	4	no	—
148	C₂³×C₄₇	—	4	8	no	—
149	C₂³×C₄₇	—	4	4	no	—
150	C₂³×C₄₇	—	4	6	no	—
151	C₂³×C₄₇	—	4	6	no	—
152	C₂³×C₄₇	—	8	6	no	—
153	C₂³×C₄₇	#99	1	3	yes	—
154	C₂³×C₄₇	#99	1	1	yes	characteristic
155	C₂³×C₄₇	C₂×C₂²⋊C₄	1	3	yes	—
156	C₂³×C₄₇	C₂×C₂²⋊C₄	1	3	yes	—
157	C₂³×C₄₇	C₂×C₂²⋊C₄	1	3	yes	—
158	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₄₇	—	4	6	no	—
161	D₄×C₄₇	—	4	3	no	—
162	D₄×C₄₇	—	4	3	no	—
163	D₄×C₄₇	—	4	3	no	—
164	D₄×C₄₇	—	4	1	no	—
165	D₄×C₄₇	—	4	24	no	—
166	D₄×C₄₇	—	4	8	no	—
167	C₂×C₄×C₄₇	—	2	3	no	—
168	C₂×C₄×C₄₇	—	2	3	no	—
169	C₂×C₄×C₄₇	—	2	3	no	—
170	C₂×C₄×C₄₇	—	2	3	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	4	12	no	—
173	C₂×C₄×C₄₇	—	4	4	no	—
174	C₂×C₄×C₄₇	—	8	12	no	—
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	3	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₄₇	—	4	4	no	—
178	C₂²×AΣL(1,𝔽₁₆)	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₇	—	2	6	no	—
180	C₂²×C₄₇	—	2	6	no	—
181	C₂²×C₄₇	—	2	8	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	3	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	3	no	—
186	C₂²×C₄₇	—	4	3	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	3	no	—
189	C₂²×C₄₇	—	4	1	no	—
190	C₂²×C₄₇	—	4	4	no	—
191	C₂²×C₄₇	—	4	24	no	—
192	C₂²×C₄₇	—	4	6	no	—
193	C₂²×C₄₇	—	4	6	no	—
194	C₂²×C₄₇	—	4	8	no	—
195	C₂²×C₄₇	—	4	8	no	—
196	C₂²×C₄₇	—	4	48	no	—
197	C₂²×C₄₇	—	4	4	no	—
198	C₂²×C₄₇	—	4	6	no	—
199	C₂²×C₄₇	—	4	24	no	—
200	C₂²×C₄₇	—	4	6	no	—
201	C₂²×C₄₇	—	4	6	no	—
202	C₂²×C₄₇	—	4	6	no	—
203	C₂²×C₄₇	—	8	3	no	—
204	C₂²×C₄₇	—	8	3	no	—
205	C₂²×C₄₇	AΣL(1,𝔽₁₆)	1	4	yes	direct product factor
206	C₂²×C₄₇	C₂×#99	1	3	yes	—
207	C₂²×C₄₇	C₂×#99	1	3	yes	—
208	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	3	no	—
211	C₄×C₄₇	—	4	4	no	—
212	C₄×C₄₇	—	8	4	no	—
213	C₂²×#120	C₂×C₄₇	1	1	yes	characteristic
214	C₂²×#100	C₂×C₄₇	1	1	yes	characteristic, complemented
215	C₂²×#99	C₂×C₄₇	1	1	yes	characteristic, complemented
216	C₂×AΣL(1,𝔽₁₆)	C₂×C₄₇	1	12	yes	direct product factor
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	3	no	—
219	C₂×C₄₇	—	4	1	no	—
220	C₂×C₄₇	—	4	8	no	—
221	C₂×C₄₇	—	4	3	no	—
222	C₂×C₄₇	—	4	1	no	—
223	C₂×C₄₇	—	4	3	no	—
224	C₂×C₄₇	C₂×AΣL(1,𝔽₁₆)	1	6	yes	direct product factor
225	C₂×C₄₇	C₂²×#99	1	1	yes	characteristic
226	C₂⁶	C₄×C₄₇	1	1	yes	characteristic, complemented
227	C₂³×D₄	—	2	1	no	—
228	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
229	C₂²×M₁₆	—	2	1	no	—
230	C₂×#120	—	2	3	no	—
231	C₂×#120	—	2	3	no	—
232	C₂×#120	C₄×C₄₇	1	6	yes	complemented
233	C₂×#120	C₂²×C₄₇	1	6	yes	—
234	C₂²×C₂²⋊C₄	—	2	1	no	—
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	C₂²×C₂²⋊C₄	C₄×C₄₇	1	1	yes	characteristic, complemented
237	C₂×#100	—	2	3	no	—
238	C₂×#100	C₂²×C₄₇	1	6	yes	complemented
239	C₂×#99	—	2	3	no	—
240	C₂×#99	C₂²×C₄₇	1	6	yes	complemented
241	AΣL(1,𝔽₁₆)	C₂²×C₄₇	1	16	yes	direct product factor
242	C₄₇	C₂²×AΣL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁵	—	2	1	no	—
244	C₂⁵	—	2	3	no	—
245	C₂⁵	—	4	8	no	—
246	C₂⁵	—	4	1	no	—
247	C₂⁵	—	4	3	no	—
248	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
249	C₂⁵	C₂×C₄×C₄₇	1	6	yes	complemented
250	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
251	C₂²×D₄	—	2	6	no	—
252	C₂²×D₄	—	2	6	no	—
253	C₂²×D₄	—	4	1	no	—
254	C₂²×D₄	—	4	3	no	—
255	C₂²×D₄	—	4	8	no	—
256	C₂²×D₄	C₂×C₄×C₄₇	1	3	yes	—
257	C₂²×D₄	D₄×C₄₇	1	3	yes	—
258	C₂²×D₄	D₄×C₄₇	1	3	yes	—
259	C₂²×D₄	C₂³×C₄₇	1	3	yes	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	4	1	no	—
262	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
263	C₂×M₁₆	—	2	6	no	—
264	C₂×M₁₆	—	4	3	no	—
265	C₂²×C₈	—	4	1	no	—
266	#120	—	2	12	no	—
267	#120	—	2	6	no	—
268	#120	—	2	6	no	—
269	#120	C₂×C₄×C₄₇	1	12	yes	complemented
270	#120	C₂³×C₄₇	1	4	yes	—
271	C₂×C₂²⋊C₄	—	2	3	no	—
272	C₂×C₂²⋊C₄	—	2	6	no	—
273	C₂×C₂²⋊C₄	—	2	6	no	—
274	C₂×C₂²⋊C₄	—	2	6	no	—
275	C₂×C₂²⋊C₄	—	4	3	no	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	6	yes	complemented
277	#100	—	2	6	no	—
278	#100	C₂³×C₄₇	1	4	yes	complemented
279	#99	—	2	6	no	—
280	#99	C₂³×C₄₇	1	4	yes	complemented
281	C₂⁴	—	2	8	no	—
282	C₂⁴	—	2	6	no	—
283	C₂⁴	—	2	1	no	—
284	C₂⁴	—	2	3	no	—
285	C₂⁴	—	2	1	no	—
286	C₂⁴	—	2	3	no	—
287	C₂⁴	—	2	6	no	—
288	C₂⁴	—	4	4	no	—
289	C₂⁴	—	4	24	no	—
290	C₂⁴	—	4	6	no	—
291	C₂⁴	—	4	6	no	—
292	C₂⁴	—	4	4	no	—
293	C₂⁴	—	4	24	no	—
294	C₂⁴	—	4	6	no	—
295	C₂⁴	—	4	6	no	—
296	C₂⁴	—	4	4	no	—
297	C₂⁴	—	4	8	no	—
298	C₂⁴	—	4	48	no	—
299	C₂⁴	—	4	8	no	—
300	C₂⁴	—	4	3	no	—
301	C₂⁴	—	4	1	no	—
302	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
303	C₂⁴	C₂²⋊C₄×C₄₇	1	3	yes	—
304	C₂⁴	C₂²⋊C₄×C₄₇	1	3	yes	—
305	C₂⁴	C₂²×C₄×C₄₇	1	3	yes	—
306	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	complemented
307	C₂⁴	C₂×D₄×C₄₇	1	3	yes	—
308	C₂×D₄	—	2	12	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	4	3	no	—
311	C₂×D₄	—	4	3	no	—
312	C₂×D₄	—	4	3	no	—
313	C₂×D₄	—	4	3	no	—
314	C₂×D₄	—	4	3	no	—
315	C₂×D₄	—	4	3	no	—
316	C₂×D₄	—	4	3	no	—
317	C₂×D₄	—	4	3	no	—
318	C₂×D₄	—	4	24	no	—
319	C₂×D₄	—	4	24	no	—
320	C₂×D₄	C₂²⋊C₄×C₄₇	1	6	yes	—
321	C₂×D₄	C₂²×C₄×C₄₇	1	3	yes	—
322	C₂×D₄	C₂×D₄×C₄₇	1	3	yes	—
323	C₂×D₄	C₂×D₄×C₄₇	1	3	yes	—
324	C₂×D₄	C₂⁴×C₄₇	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	3	no	—
327	C₂²×C₄	—	2	6	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	6	no	—
330	C₂²×C₄	—	8	4	no	—
331	C₂²×C₄	C₂²⋊C₄×C₄₇	1	3	yes	—
332	C₂²×C₄	C₂×D₄×C₄₇	1	3	yes	—
333	M₁₆	—	2	4	no	—
334	M₁₆	—	4	6	no	—
335	C₂×C₈	—	4	6	no	—
336	C₂²⋊C₄	—	2	6	no	—
337	C₂²⋊C₄	—	2	12	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	6	no	—
341	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	complemented
342	C₂³	—	2	4	no	—
343	C₂³	—	2	24	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	3	no	—
346	C₂³	—	2	3	no	—
347	C₂³	—	2	3	no	—
348	C₂³	—	2	3	no	—
349	C₂³	—	2	3	no	—
350	C₂³	—	2	3	no	—
351	C₂³	—	2	3	no	—
352	C₂³	—	2	3	no	—
353	C₂³	—	4	6	no	—
354	C₂³	—	4	6	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	12	no	—
358	C₂³	—	4	24	no	—
359	C₂³	—	4	12	no	—
360	C₂³	—	4	24	no	—
361	C₂³	—	4	12	no	—
362	C₂³	—	4	6	no	—
363	C₂³	—	4	6	no	—
364	C₂³	—	4	24	no	—
365	C₂³	—	4	48	no	—
366	C₂³	—	4	48	no	—
367	C₂³	—	4	24	no	—
368	C₂³	—	4	48	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	8	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	6	no	—
373	C₂³	—	4	6	no	—
374	C₂³	—	8	6	no	—
375	C₂³	#99×C₄₇	1	3	yes	—
376	C₂³	#99×C₄₇	1	1	yes	characteristic
377	C₂³	C₂×C₂²⋊C₄×C₄₇	1	3	yes	—
378	C₂³	C₂×C₂²⋊C₄×C₄₇	1	3	yes	—
379	C₂³	C₂×C₂²⋊C₄×C₄₇	1	3	yes	—
380	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
381	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
382	D₄	—	4	6	no	—
383	D₄	—	4	3	no	—
384	D₄	—	4	3	no	—
385	D₄	—	4	3	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	24	no	—
388	D₄	—	4	8	no	—
389	C₂×C₄	—	2	3	no	—
390	C₂×C₄	—	2	3	no	—
391	C₂×C₄	—	2	3	no	—
392	C₂×C₄	—	2	3	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	4	12	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	8	12	no	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	3	yes	—
398	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
399	C₈	—	4	4	no	—
400	C₂²	—	2	6	no	—
401	C₂²	—	2	6	no	—
402	C₂²	—	2	8	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	3	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	3	no	—
407	C₂²	—	4	3	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	3	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	24	no	—
413	C₂²	—	4	6	no	—
414	C₂²	—	4	6	no	—
415	C₂²	—	4	8	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	48	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	6	no	—
420	C₂²	—	4	24	no	—
421	C₂²	—	4	6	no	—
422	C₂²	—	4	6	no	—
423	C₂²	—	4	6	no	—
424	C₂²	—	8	3	no	—
425	C₂²	—	8	3	no	—
426	C₂²	C₄₇×AΣL(1,𝔽₁₆)	1	4	yes	direct product factor
427	C₂²	C₂×#99×C₄₇	1	3	yes	—
428	C₂²	C₂×#99×C₄₇	1	3	yes	—
429	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	3	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	4	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	3	no	—
436	C₂	—	4	1	no	—
437	C₂	—	4	8	no	—
438	C₂	—	4	3	no	—
439	C₂	—	4	1	no	—
440	C₂	—	4	3	no	—
441	C₂	C₂×C₄₇×AΣL(1,𝔽₁₆)	1	6	yes	direct product factor
442	C₂	C₂²×#99×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	#99
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂×D₄	C₂⁴×C₄₇
prime radical	C₂²×#120×C₄₇	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁴×C₄₇ ◁ C₂³×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#100×C₄₇	C₂	semidirect
3. C₂²×#99×C₄₇	C₂	semidirect
4. C₂×C₄₇×AΣL(1,𝔽₁₆)	C₂	direct (N × H)
5. C₂⁶×C₄₇	C₄	semidirect
11. C₂×#120×C₄₇	C₄	semidirect
15. C₂²×C₂²⋊C₄×C₄₇	C₄	semidirect
17. C₂×#100×C₄₇	C₂²	semidirect
19. C₂×#99×C₄₇	C₂²	semidirect
20. C₄₇×AΣL(1,𝔽₁₆)	C₂²	direct (N × H)
27. C₂⁵×C₄₇	C₂×C₄	semidirect
47. #120×C₄₇	C₂×C₄	semidirect
54. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
56. #100×C₄₇	C₂³	semidirect
58. #99×C₄₇	C₂³	semidirect
84. C₂⁴×C₄₇	C₂²×C₄	semidirect
119. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
178. C₂²×AΣL(1,𝔽₁₆)	C₄₇	direct (N × H)
205. C₂²×C₄₇	AΣL(1,𝔽₁₆)	direct (N × H)
214. C₂²×#100	C₂×C₄₇	semidirect
215. C₂²×#99	C₂×C₄₇	semidirect
216. C₂×AΣL(1,𝔽₁₆)	C₂×C₄₇	direct (N × H)
224. C₂×C₄₇	C₂×AΣL(1,𝔽₁₆)	direct (N × H)
226. C₂⁶	C₄×C₄₇	semidirect
232. C₂×#120	C₄×C₄₇	semidirect
236. C₂²×C₂²⋊C₄	C₄×C₄₇	semidirect
238. C₂×#100	C₂²×C₄₇	semidirect
240. C₂×#99	C₂²×C₄₇	semidirect
241. AΣL(1,𝔽₁₆)	C₂²×C₄₇	direct (N × H)
242. C₄₇	C₂²×AΣL(1,𝔽₁₆)	direct (N × H)
249. C₂⁵	C₂×C₄×C₄₇	semidirect
269. #120	C₂×C₄×C₄₇	semidirect
276. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
278. #100	C₂³×C₄₇	semidirect
280. #99	C₂³×C₄₇	semidirect
306. C₂⁴	C₂²×C₄×C₄₇	semidirect
341. C₂²⋊C₄	C₂²×C₄×C₄₇	semidirect
426. C₂²	C₄₇×AΣL(1,𝔽₁₆)	direct (N × H)
441. C₂	C₂×C₄₇×AΣL(1,𝔽₁₆)	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×#120×C₄₇	2
C₂²×#100×C₄₇	2
C₂²×#99×C₄₇	2
C₂×C₄₇×AΣL(1,𝔽₁₆)	2
C₂²×AΣL(1,𝔽₁₆)	47

Subgroups — C22×C47×AΣL(1,𝔽16) #26073039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄₇×AΣL(1,𝔽₁₆) #26073039