Subgroups — C₄₇×#15148 #26054846

Order 12032.

1922 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#399	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₇×#390	C₂	1	2	yes	maximal
3	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#389	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1439	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1439	C₂	1	4	yes	maximal, complemented
8	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
18	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#399	—	2	8	no	—
22	C₄₇×#390	—	2	8	no	—
23	C₄₇×#390	—	2	4	no	—
24	C₄₇×#389	—	2	8	no	—
25	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
26	C₂×#95×C₄₇	C₂²	1	2	yes	—
27	C₂×#95×C₄₇	C₂²	1	4	yes	—
28	C₂×#95×C₄₇	C₂²	1	2	yes	—
29	C₂×#95×C₄₇	C₂²	1	2	yes	—
30	C₂⁵×C₄₇	C₂³	1	2	yes	—
31	C₂²×D₄×C₄₇	—	2	2	no	—
32	C₂²×D₄×C₄₇	—	2	4	no	—
33	C₂²×D₄×C₄₇	—	2	4	no	—
34	C₂²×D₄×C₄₇	—	2	2	no	—
35	C₂²×D₄×C₄₇	Q₈	1	4	yes	—
36	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	4	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	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
53	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
54	C₂×C₄⋊C₄×C₄₇	D₄	1	8	yes	—
55	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	complemented
56	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
67	C₂×C₄²×C₄₇	—	2	4	no	—
68	C₂×C₄²×C₄₇	—	2	4	no	—
69	C₂×C₄²×C₄₇	—	2	4	no	—
70	C₂×C₄²×C₄₇	—	2	4	no	—
71	C₂×C₄²×C₄₇	D₄	1	4	yes	—
72	#95×C₄₇	—	2	4	no	—
73	#95×C₄₇	—	2	8	no	—
74	#95×C₄₇	—	2	4	no	—
75	#95×C₄₇	—	4	2	no	—
76	C₂⁴×C₄₇	—	2	2	no	—
77	C₂⁴×C₄₇	—	2	2	no	—
78	C₂⁴×C₄₇	—	2	4	no	—
79	C₂⁴×C₄₇	—	2	2	no	—
80	C₂⁴×C₄₇	—	2	4	no	—
81	C₂⁴×C₄₇	—	2	4	no	—
82	C₂⁴×C₄₇	—	2	2	no	—
83	C₂⁴×C₄₇	—	2	4	no	—
84	C₂⁴×C₄₇	—	2	2	no	—
85	C₂⁴×C₄₇	—	2	2	no	—
86	C₂⁴×C₄₇	C₂×Q₈	1	4	yes	—
87	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₂×D₄×C₄₇	—	2	8	no	—
89	C₂×D₄×C₄₇	—	2	16	no	—
90	C₂×D₄×C₄₇	—	4	4	no	—
91	C₂×D₄×C₄₇	—	4	8	no	—
92	C₂×D₄×C₄₇	—	4	4	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	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	2	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	4	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	4	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	2	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	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	4	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	4	no	—
122	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₄₇	#41	1	4	yes	—
131	C₂²×C₄×C₄₇	#41	1	2	yes	—
132	C₂²×C₄×C₄₇	#41	1	4	yes	—
133	C₂²×C₄×C₄₇	#41	1	2	yes	—
134	C₄⋊C₄×C₄₇	—	2	8	no	—
135	C₄⋊C₄×C₄₇	—	2	8	no	—
136	C₄⋊C₄×C₄₇	—	2	16	no	—
137	C₄⋊C₄×C₄₇	—	4	16	no	—
138	C₄⋊C₄×C₄₇	—	4	4	no	—
139	C₂²⋊C₄×C₄₇	—	4	16	no	—
140	C₂²⋊C₄×C₄₇	—	4	16	no	—
141	C₂²⋊C₄×C₄₇	—	4	8	no	—
142	C₂²⋊C₄×C₄₇	—	4	8	no	—
143	C₄²×C₄₇	—	2	8	no	—
144	C₄²×C₄₇	—	4	8	no	—
145	C₂³×C₄₇	—	2	4	no	—
146	C₂³×C₄₇	—	2	8	no	—
147	C₂³×C₄₇	—	2	4	no	—
148	C₂³×C₄₇	—	2	8	no	—
149	C₂³×C₄₇	—	2	4	no	—
150	C₂³×C₄₇	—	4	2	no	—
151	C₂³×C₄₇	—	4	2	no	—
152	C₂³×C₄₇	—	4	4	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	—	4	4	no	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	—	4	4	no	—
157	C₂³×C₄₇	—	4	2	no	—
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	—	4	4	no	—
160	C₂³×C₄₇	—	4	4	no	—
161	C₂³×C₄₇	—	4	4	no	—
162	C₂³×C₄₇	—	4	4	no	—
163	C₂³×C₄₇	—	4	4	no	—
164	C₂³×C₄₇	—	4	4	no	—
165	C₂³×C₄₇	—	4	2	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	4	no	—
168	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
171	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
172	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂³×C₄₇	C₂×#41	1	2	yes	—
174	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂³×C₄₇	C₂×#41	1	2	yes	—
176	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
177	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
179	D₄×C₄₇	—	4	16	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	4	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	8	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	2	8	no	—
192	C₂×C₄×C₄₇	—	2	4	no	—
193	C₂×C₄×C₄₇	—	2	4	no	—
194	C₂×C₄×C₄₇	—	2	8	no	—
195	C₂×C₄×C₄₇	—	2	4	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	4	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	4	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	4	no	—
207	C₂×C₄×C₄₇	—	4	2	no	—
208	C₂×C₄×C₄₇	—	4	2	no	—
209	C₂×C₄×C₄₇	—	4	4	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	4	no	—
214	C₂×C₄×C₄₇	—	4	4	no	—
215	C₂×C₄×C₄₇	#121	1	4	yes	—
216	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
217	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
218	C₂×C₄×C₄₇	#123	1	4	yes	—
219	C₂×C₄×C₄₇	#123	1	8	yes	—
220	C₂×C₄×C₄₇	#127	1	4	yes	—
221	#15148	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₄₇	—	4	4	no	—
223	C₂²×C₄₇	—	4	4	no	—
224	C₂²×C₄₇	—	4	8	no	—
225	C₂²×C₄₇	—	4	8	no	—
226	C₂²×C₄₇	—	4	4	no	—
227	C₂²×C₄₇	—	8	2	no	—
228	C₂²×C₄₇	—	8	2	no	—
229	C₂²×C₄₇	—	8	4	no	—
230	C₂²×C₄₇	—	8	4	no	—
231	C₂²×C₄₇	—	8	2	no	—
232	C₂²×C₄₇	—	8	2	no	—
233	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
234	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
236	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
237	C₂²×C₄₇	C₂×#123	1	2	yes	—
238	C₂²×C₄₇	#525	1	1	yes	characteristic
239	C₂²×C₄₇	#529	1	2	yes	—
240	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
241	C₂²×C₄₇	#532	1	2	yes	—
242	C₂²×C₄₇	#535	1	1	yes	characteristic
243	C₂²×C₄₇	#537	1	1	yes	characteristic
244	C₂²×C₄₇	#540	1	2	yes	—
245	C₂²×C₄₇	#542	1	2	yes	—
246	C₂²×C₄₇	D₄²	1	2	yes	—
247	C₂²×C₄₇	#546	1	2	yes	—
248	C₂²×C₄₇	#548	1	2	yes	—
249	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
250	C₂²×C₄₇	#550	1	1	yes	characteristic
251	C₂²×C₄₇	#550	1	2	yes	—
252	C₂²×C₄₇	#554	1	2	yes	—
253	C₂²×C₄₇	#554	1	1	yes	characteristic
254	C₂²×C₄₇	#556	1	1	yes	characteristic
255	C₂²×C₄₇	#559	1	2	yes	—
256	C₄×C₄₇	—	2	4	no	—
257	C₄×C₄₇	—	4	2	no	—
258	C₄×C₄₇	—	4	8	no	—
259	C₄×C₄₇	—	4	4	no	—
260	C₄×C₄₇	—	4	4	no	—
261	C₄×C₄₇	—	8	2	no	—
262	C₄×C₄₇	#399	1	8	yes	complemented
263	C₂×#399	C₂×C₄₇	1	2	yes	complemented
264	C₂×#390	C₂×C₄₇	1	1	yes	characteristic
265	C₂×#390	C₂×C₄₇	1	2	yes	—
266	C₂×#389	C₂×C₄₇	1	2	yes	complemented
267	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
268	#1439	C₂×C₄₇	1	2	yes	complemented
269	#1439	C₂×C₄₇	1	4	yes	complemented
270	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic, complemented
271	C₂×C₄₇	—	8	4	no	—
272	C₂×C₄₇	C₂×#399	1	1	yes	characteristic
273	C₂×C₄₇	#2445	1	2	yes	—
274	C₂×C₄₇	#2448	1	2	yes	—
275	C₂×C₄₇	#2452	1	2	yes	—
276	C₂×C₄₇	#2454	1	2	yes	—
277	C₂×C₄₇	#2538	1	1	yes	characteristic
278	C₂×C₄₇	#2540	1	1	yes	characteristic
279	C₂×C₄₇	#2541	1	1	yes	characteristic
280	C₂×C₄₇	#2580	1	1	yes	characteristic
281	C₂×C₄₇	#2624	1	1	yes	characteristic
282	C₂×C₄₇	#2854	1	1	yes	characteristic
283	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
287	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
288	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
289	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
290	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
291	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
292	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
293	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
294	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
295	#399	—	2	8	no	—
296	#390	—	2	8	no	—
297	#390	—	2	4	no	—
298	#389	—	2	8	no	—
299	C₄×C₄⋊C₄	—	2	4	no	—
300	C₂×#95	C₂²×C₄₇	1	2	yes	—
301	C₂×#95	C₂²×C₄₇	1	2	yes	—
302	C₂×#95	C₂²×C₄₇	1	4	yes	—
303	C₂×#95	C₂²×C₄₇	1	2	yes	—
304	C₄₇	#15148	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁵	C₂³×C₄₇	1	2	yes	—
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	4	no	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	Q₈×C₄₇	1	4	yes	—
311	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
312	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
313	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
314	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
316	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	4	no	—
324	C₂×C₄⋊C₄	—	2	8	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	8	no	—
328	C₂×C₄⋊C₄	—	4	4	no	—
329	C₂×C₄⋊C₄	D₄×C₄₇	1	8	yes	—
330	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	complemented
331	C₂×C₂²⋊C₄	—	2	8	no	—
332	C₂×C₂²⋊C₄	—	2	8	no	—
333	C₂×C₂²⋊C₄	—	2	4	no	—
334	C₂×C₂²⋊C₄	—	2	4	no	—
335	C₂×C₂²⋊C₄	—	2	8	no	—
336	C₂×C₂²⋊C₄	—	2	4	no	—
337	C₂×C₂²⋊C₄	—	2	8	no	—
338	C₂×C₂²⋊C₄	—	2	4	no	—
339	C₂×C₂²⋊C₄	—	4	4	no	—
340	C₂×C₂²⋊C₄	—	4	4	no	—
341	C₂×C₂²⋊C₄	—	4	4	no	—
342	C₂×C₄²	—	2	4	no	—
343	C₂×C₄²	—	2	4	no	—
344	C₂×C₄²	—	2	4	no	—
345	C₂×C₄²	—	2	4	no	—
346	C₂×C₄²	D₄×C₄₇	1	4	yes	—
347	#95	—	2	4	no	—
348	#95	—	2	8	no	—
349	#95	—	2	4	no	—
350	#95	—	4	2	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	—	2	2	no	—
355	C₂⁴	—	2	4	no	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	—	2	2	no	—
361	C₂⁴	C₂×Q₈×C₄₇	1	4	yes	—
362	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	16	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	4	8	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	4	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	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
399	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
400	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
404	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
405	C₂²×C₄	#41×C₄₇	1	4	yes	—
406	C₂²×C₄	#41×C₄₇	1	2	yes	—
407	C₂²×C₄	#41×C₄₇	1	4	yes	—
408	C₂²×C₄	#41×C₄₇	1	2	yes	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	16	no	—
412	C₄⋊C₄	—	4	16	no	—
413	C₄⋊C₄	—	4	4	no	—
414	C₂²⋊C₄	—	4	16	no	—
415	C₂²⋊C₄	—	4	16	no	—
416	C₂²⋊C₄	—	4	8	no	—
417	C₂²⋊C₄	—	4	8	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	4	8	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	8	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	4	4	no	—
436	C₂³	—	4	4	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	4	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	4	no	—
443	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
444	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
445	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
446	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
447	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
448	C₂³	C₂×#41×C₄₇	1	2	yes	—
449	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
450	C₂³	C₂×#41×C₄₇	1	2	yes	—
451	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
452	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
453	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
454	D₄	—	4	16	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	#121×C₄₇	1	4	yes	—
491	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
492	C₂×C₄	C₂²⋊Q₈×C₄₇	1	8	yes	—
493	C₂×C₄	#123×C₄₇	1	4	yes	—
494	C₂×C₄	#123×C₄₇	1	8	yes	—
495	C₂×C₄	#127×C₄₇	1	4	yes	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	8	no	—
500	C₂²	—	4	8	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	4	no	—
507	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
508	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
509	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
510	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
511	C₂²	C₂×#123×C₄₇	1	2	yes	—
512	C₂²	C₄₇×#525	1	1	yes	characteristic
513	C₂²	C₄₇×#529	1	2	yes	—
514	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
515	C₂²	C₄₇×#532	1	2	yes	—
516	C₂²	C₄₇×#535	1	1	yes	characteristic
517	C₂²	C₄₇×#537	1	1	yes	characteristic
518	C₂²	C₄₇×#540	1	2	yes	—
519	C₂²	C₄₇×#542	1	2	yes	—
520	C₂²	D₄²×C₄₇	1	2	yes	—
521	C₂²	C₄₇×#546	1	2	yes	—
522	C₂²	C₄₇×#548	1	2	yes	—
523	C₂²	D₄×Q₈×C₄₇	1	1	yes	characteristic
524	C₂²	C₄₇×#550	1	1	yes	characteristic
525	C₂²	C₄₇×#550	1	2	yes	—
526	C₂²	C₄₇×#554	1	1	yes	characteristic
527	C₂²	C₄₇×#554	1	2	yes	—
528	C₂²	C₄₇×#556	1	1	yes	characteristic
529	C₂²	C₄₇×#559	1	2	yes	—
530	C₄	—	2	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	8	no	—
535	C₄	—	8	2	no	—
536	C₄	C₄₇×#399	1	8	yes	complemented
537	C₂	—	8	4	no	—
538	C₂	C₂×C₄₇×#399	1	1	yes	characteristic
539	C₂	C₄₇×#2445	1	2	yes	—
540	C₂	C₄₇×#2448	1	2	yes	—
541	C₂	C₄₇×#2452	1	2	yes	—
542	C₂	C₄₇×#2454	1	2	yes	—
543	C₂	C₄₇×#2538	1	1	yes	characteristic
544	C₂	C₄₇×#2540	1	1	yes	characteristic
545	C₂	C₄₇×#2541	1	1	yes	characteristic
546	C₂	C₄₇×#2580	1	1	yes	characteristic
547	C₂	C₄₇×#2624	1	1	yes	characteristic
548	C₂	C₄₇×#2854	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#399	C₂	semidirect
4. C₂×C₄₇×#389	C₂	semidirect
5. C₂×C₄×C₄⋊C₄×C₄₇	C₂	semidirect
6. C₄₇×#1439	C₂	semidirect
7. C₄₇×#1439	C₂	semidirect
8. C₄₇×C₄⋊#95	C₂	semidirect
55. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
221. #15148	C₄₇	direct (N × H)
262. C₄×C₄₇	#399	semidirect
263. C₂×#399	C₂×C₄₇	semidirect
266. C₂×#389	C₂×C₄₇	semidirect
267. C₂×C₄×C₄⋊C₄	C₂×C₄₇	semidirect
268. #1439	C₂×C₄₇	semidirect
269. #1439	C₂×C₄₇	semidirect
270. C₄⋊#95	C₂×C₄₇	semidirect
304. C₄₇	#15148	direct (N × H)
330. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
536. C₄	C₄₇×#399	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#399	2
C₂×C₄₇×#390	2
C₂×C₄₇×#389	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1439	2
C₄₇×C₄⋊#95	2
#15148	47

Subgroups — C47×#15148 #26054846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15148 #26054846