Subgroups — C₄₇×#13819 #26053517

Order 12032.

1514 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#387	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1436	C₂	1	2	yes	maximal
4	C₄₇×#1436	C₂	1	2	yes	maximal
5	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic
8	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₄×#95×C₄₇	C₂	1	2	yes	maximal
11	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
21	C₄₇×#387	C₄	1	16	yes	complemented
22	C₄×C₄⋊C₄×C₄₇	C₄	1	8	yes	complemented
23	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#95×C₄₇	C₂²	1	2	yes	—
27	C₂×#95×C₄₇	C₂²	1	2	yes	—
28	C₂×#95×C₄₇	C₂²	1	2	yes	—
29	C₂×#95×C₄₇	C₂²	1	2	yes	—
30	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#95×C₄₇	C₂²	1	2	yes	—
33	C₂×#95×C₄₇	C₂²	1	2	yes	—
34	C₂×#95×C₄₇	C₂²	1	2	yes	—
35	C₂×#95×C₄₇	C₂²	1	2	yes	—
36	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
56	C₂×C₄²×C₄₇	—	2	4	no	—
57	C₂×C₄²×C₄₇	—	2	4	no	—
58	C₂×C₄²×C₄₇	—	2	4	no	—
59	C₂×C₄²×C₄₇	—	2	4	no	—
60	C₂×C₄²×C₄₇	—	2	4	no	—
61	C₂×C₄²×C₄₇	—	4	2	no	—
62	C₂×C₄²×C₄₇	—	4	2	no	—
63	C₂×C₄²×C₄₇	—	4	2	no	—
64	C₂×C₄²×C₄₇	—	4	2	no	—
65	C₂×C₄²×C₄₇	—	4	2	no	—
66	C₂×C₄²×C₄₇	—	4	2	no	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
71	#95×C₄₇	—	2	4	no	—
72	#95×C₄₇	—	2	4	no	—
73	#95×C₄₇	—	2	4	no	—
74	#95×C₄₇	—	2	2	no	—
75	#95×C₄₇	—	2	2	no	—
76	#95×C₄₇	—	2	2	no	—
77	#95×C₄₇	—	4	2	no	—
78	#95×C₄₇	C₂×C₄	1	4	yes	—
79	#95×C₄₇	C₂×C₄	1	4	yes	—
80	#95×C₄₇	C₂×C₄	1	8	yes	—
81	#95×C₄₇	C₂×C₄	1	8	yes	—
82	#95×C₄₇	C₂×C₄	1	8	yes	—
83	#95×C₄₇	C₂×C₄	1	8	yes	—
84	#95×C₄₇	Q₈	1	4	yes	—
85	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	2	no	—
128	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
144	C₂²×C₄×C₄₇	#41	1	2	yes	—
145	C₂²×C₄×C₄₇	#41	1	4	yes	—
146	C₂²×C₄×C₄₇	#41	1	2	yes	—
147	C₂²×C₄×C₄₇	#41	1	4	yes	—
148	C₂²×C₄×C₄₇	#41	1	2	yes	—
149	C₄⋊C₄×C₄₇	—	2	8	no	—
150	C₄⋊C₄×C₄₇	—	4	8	no	—
151	C₄⋊C₄×C₄₇	C₄²	1	16	yes	complemented
152	C₄²×C₄₇	—	2	8	no	—
153	C₄²×C₄₇	—	4	4	no	—
154	C₄²×C₄₇	—	4	4	no	—
155	C₄²×C₄₇	—	4	8	no	—
156	C₄²×C₄₇	—	4	8	no	—
157	C₄²×C₄₇	—	4	8	no	—
158	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
160	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
161	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂³×C₄₇	C₂×#41	1	2	yes	—
163	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂³×C₄₇	C₂×#41	1	2	yes	—
165	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
168	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	4	no	—
183	C₂×C₄×C₄₇	—	2	4	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	4	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	2	4	no	—
192	C₂×C₄×C₄₇	—	2	4	no	—
193	C₂×C₄×C₄₇	—	2	4	no	—
194	C₂×C₄×C₄₇	—	2	4	no	—
195	C₂×C₄×C₄₇	—	2	4	no	—
196	C₂×C₄×C₄₇	—	2	4	no	—
197	C₂×C₄×C₄₇	—	2	4	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	4	no	—
202	C₂×C₄×C₄₇	—	2	4	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	4	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	—	4	2	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	4	2	no	—
220	C₂×C₄×C₄₇	—	4	2	no	—
221	C₂×C₄×C₄₇	—	4	2	no	—
222	C₂×C₄×C₄₇	—	4	2	no	—
223	C₂×C₄×C₄₇	—	4	2	no	—
224	C₂×C₄×C₄₇	—	4	2	no	—
225	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
226	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
227	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
228	C₂×C₄×C₄₇	#117	1	4	yes	—
229	C₂×C₄×C₄₇	#117	1	4	yes	—
230	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
231	C₂×C₄×C₄₇	C₄×Q₈	1	8	yes	—
232	#13819	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
234	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
235	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
236	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
237	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
238	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
239	C₂²×C₄₇	C₄×#41	1	2	yes	—
240	C₂²×C₄₇	C₄×#41	1	2	yes	—
241	C₂²×C₄₇	C₄×#41	1	2	yes	—
242	C₂²×C₄₇	#518	1	1	yes	characteristic
243	C₂²×C₄₇	#518	1	2	yes	—
244	C₂²×C₄₇	#520	1	1	yes	characteristic
245	C₂²×C₄₇	#520	1	2	yes	—
246	C₂²×C₄₇	#551	1	2	yes	—
247	C₂²×C₄₇	#551	1	2	yes	—
248	C₂²×C₄₇	#552	1	2	yes	—
249	C₂²×C₄₇	#553	1	2	yes	—
250	C₂²×C₄₇	#553	1	2	yes	—
251	C₂²×C₄₇	#554	1	2	yes	—
252	C₂²×C₄₇	#554	1	1	yes	characteristic
253	C₂²×C₄₇	#556	1	1	yes	characteristic
254	C₂²×C₄₇	#557	1	1	yes	characteristic
255	C₂²×C₄₇	#559	1	1	yes	characteristic
256	C₄×C₄₇	—	2	4	no	—
257	C₄×C₄₇	—	2	4	no	—
258	C₄×C₄₇	—	2	4	no	—
259	C₄×C₄₇	—	2	8	no	—
260	C₄×C₄₇	—	2	4	no	—
261	C₄×C₄₇	—	2	4	no	—
262	C₄×C₄₇	—	2	4	no	—
263	C₄×C₄₇	—	4	2	no	—
264	C₄×C₄₇	—	4	4	no	—
265	C₄×C₄₇	—	4	4	no	—
266	C₄×C₄₇	—	4	4	no	—
267	C₂×#387	C₂×C₄₇	1	2	yes	—
268	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
269	#1436	C₂×C₄₇	1	2	yes	—
270	#1436	C₂×C₄₇	1	2	yes	—
271	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic
272	#1434	C₂×C₄₇	1	1	yes	characteristic
273	#1434	C₂×C₄₇	1	1	yes	characteristic
274	C₄×#95	C₂×C₄₇	1	1	yes	characteristic
275	C₄×#95	C₂×C₄₇	1	1	yes	characteristic
276	C₄×#95	C₂×C₄₇	1	1	yes	characteristic
277	C₄×#95	C₂×C₄₇	1	2	yes	—
278	C₂×C₄₇	C₄×#117	1	1	yes	characteristic
279	C₂×C₄₇	C₄²×Q₈	1	1	yes	characteristic
280	C₂×C₄₇	#2275	1	1	yes	characteristic
281	C₂×C₄₇	#2343	1	1	yes	characteristic
282	C₂×C₄₇	#2345	1	1	yes	characteristic
283	C₂×C₄₇	#2353	1	1	yes	characteristic
284	C₂×C₄₇	#2355	1	1	yes	characteristic
285	C₂×C₄₇	#2368	1	2	yes	—
286	C₂×C₄₇	#2370	1	2	yes	—
287	C₂×C₄₇	#2373	1	2	yes	—
288	C₂×C₄₇	#2374	1	2	yes	—
289	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
290	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
291	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
292	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
293	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
294	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
295	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
296	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
297	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
298	#387	C₄×C₄₇	1	16	yes	complemented
299	C₄×C₄⋊C₄	C₄×C₄₇	1	8	yes	complemented
300	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
301	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
302	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
303	C₂×#95	C₂²×C₄₇	1	2	yes	—
304	C₂×#95	C₂²×C₄₇	1	2	yes	—
305	C₂×#95	C₂²×C₄₇	1	2	yes	—
306	C₂×#95	C₂²×C₄₇	1	2	yes	—
307	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
308	C₂×#95	C₂²×C₄₇	1	2	yes	—
309	C₂×#95	C₂²×C₄₇	1	2	yes	—
310	C₂×#95	C₂²×C₄₇	1	2	yes	—
311	C₂×#95	C₂²×C₄₇	1	2	yes	—
312	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
313	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
314	C₄₇	#13819	1	1	yes	characteristic, direct product factor, Sylow
315	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
316	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
317	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
319	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
323	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	4	2	no	—
329	C₂×C₄⋊C₄	—	4	2	no	—
330	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
331	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
332	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
333	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	—	2	4	no	—
336	C₂×C₄²	—	2	4	no	—
337	C₂×C₄²	—	2	4	no	—
338	C₂×C₄²	—	2	4	no	—
339	C₂×C₄²	—	4	2	no	—
340	C₂×C₄²	—	4	2	no	—
341	C₂×C₄²	—	4	2	no	—
342	C₂×C₄²	—	4	2	no	—
343	C₂×C₄²	—	4	2	no	—
344	C₂×C₄²	—	4	2	no	—
345	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
346	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
347	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
348	C₂×C₄²	C₂×C₄×C₄₇	1	8	yes	—
349	#95	—	2	4	no	—
350	#95	—	2	4	no	—
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	4	no	—
355	#95	—	4	2	no	—
356	#95	C₂×C₄×C₄₇	1	4	yes	—
357	#95	C₂×C₄×C₄₇	1	4	yes	—
358	#95	C₂×C₄×C₄₇	1	8	yes	—
359	#95	C₂×C₄×C₄₇	1	8	yes	—
360	#95	C₂×C₄×C₄₇	1	8	yes	—
361	#95	C₂×C₄×C₄₇	1	8	yes	—
362	#95	Q₈×C₄₇	1	4	yes	—
363	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
407	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
408	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
409	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
410	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
411	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
412	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
413	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
414	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
415	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
416	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
417	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
418	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
419	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
420	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
421	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
422	C₂²×C₄	#41×C₄₇	1	2	yes	—
423	C₂²×C₄	#41×C₄₇	1	4	yes	—
424	C₂²×C₄	#41×C₄₇	1	2	yes	—
425	C₂²×C₄	#41×C₄₇	1	2	yes	—
426	C₂²×C₄	#41×C₄₇	1	4	yes	—
427	C₄⋊C₄	—	2	8	no	—
428	C₄⋊C₄	—	4	8	no	—
429	C₄⋊C₄	C₄²×C₄₇	1	16	yes	complemented
430	C₄²	—	2	8	no	—
431	C₄²	—	4	4	no	—
432	C₄²	—	4	4	no	—
433	C₄²	—	4	8	no	—
434	C₄²	—	4	8	no	—
435	C₄²	—	4	8	no	—
436	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
437	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
438	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
439	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
440	C₂³	C₂×#41×C₄₇	1	2	yes	—
441	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
442	C₂³	C₂×#41×C₄₇	1	2	yes	—
443	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
444	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
445	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
446	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
504	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
505	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
506	C₂×C₄	#117×C₄₇	1	4	yes	—
507	C₂×C₄	#117×C₄₇	1	4	yes	—
508	C₂×C₄	C₄×Q₈×C₄₇	1	4	yes	—
509	C₂×C₄	C₄×Q₈×C₄₇	1	8	yes	—
510	C₂²	C₂²×C₄²×C₄₇	1	1	yes	characteristic
511	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
512	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
513	C₂²	C₂×C₄×Q₈×C₄₇	1	1	yes	characteristic
514	C₂²	C₂×C₄×Q₈×C₄₇	1	2	yes	—
515	C₂²	C₄×#41×C₄₇	1	2	yes	—
516	C₂²	C₄×#41×C₄₇	1	2	yes	—
517	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
518	C₂²	C₄×#41×C₄₇	1	2	yes	—
519	C₂²	C₄₇×#518	1	1	yes	characteristic
520	C₂²	C₄₇×#518	1	2	yes	—
521	C₂²	C₄₇×#520	1	1	yes	characteristic
522	C₂²	C₄₇×#520	1	2	yes	—
523	C₂²	C₄₇×#551	1	2	yes	—
524	C₂²	C₄₇×#551	1	2	yes	—
525	C₂²	C₄₇×#552	1	2	yes	—
526	C₂²	C₄₇×#553	1	2	yes	—
527	C₂²	C₄₇×#553	1	2	yes	—
528	C₂²	C₄₇×#554	1	2	yes	—
529	C₂²	C₄₇×#554	1	1	yes	characteristic
530	C₂²	C₄₇×#556	1	1	yes	characteristic
531	C₂²	C₄₇×#557	1	1	yes	characteristic
532	C₂²	C₄₇×#559	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	2	4	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	4	no	—
537	C₄	—	2	4	no	—
538	C₄	—	2	4	no	—
539	C₄	—	2	8	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	4	no	—
544	C₂	C₄×#117×C₄₇	1	1	yes	characteristic
545	C₂	C₄²×Q₈×C₄₇	1	1	yes	characteristic
546	C₂	C₄₇×#2275	1	1	yes	characteristic
547	C₂	C₄₇×#2343	1	1	yes	characteristic
548	C₂	C₄₇×#2345	1	1	yes	characteristic
549	C₂	C₄₇×#2353	1	1	yes	characteristic
550	C₂	C₄₇×#2355	1	1	yes	characteristic
551	C₂	C₄₇×#2368	1	2	yes	—
552	C₂	C₄₇×#2370	1	2	yes	—
553	C₂	C₄₇×#2373	1	2	yes	—
554	C₂	C₄₇×#2374	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
21. C₄₇×#387	C₄	semidirect
22. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
151. C₄⋊C₄×C₄₇	C₄²	semidirect
232. #13819	C₄₇	direct (N × H)
298. #387	C₄×C₄₇	semidirect
299. C₄×C₄⋊C₄	C₄×C₄₇	semidirect
314. C₄₇	#13819	direct (N × H)
429. C₄⋊C₄	C₄²×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×#387	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1436	2
C₄₇×C₄⋊#95	2
C₄₇×#1434	2
C₄×#95×C₄₇	2
#13819	47

Subgroups — C47×#13819 #26053517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13819 #26053517