Subgroups — C₄₇×#21614 #26061312

Order 12032.

988 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#476	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1919	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1862	C₂	1	2	yes	maximal
8	C₄₇×#1802	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1776	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1762	C₂	1	2	yes	maximal
12	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
14	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	—	2	1	no	—
18	C₄₇×#476	C₄	1	8	yes	complemented
19	C₂×#107×C₄₇	C₂²	1	2	yes	—
20	C₂×#106×C₄₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#102×C₄₇	C₂²	1	2	yes	—
24	C₂×#102×C₄₇	C₂²	1	2	yes	—
25	C₂×#97×C₄₇	C₂²	1	2	yes	—
26	C₄₇×#391	—	2	1	no	—
27	C₄₇×#389	—	2	1	no	—
28	C₄₇×#389	C₂²	1	2	yes	—
29	C₄₇×#384	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
31	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
38	C₄³×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₇	—	2	1	no	—
45	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	—	2	1	no	—
47	C₂³×C₄×C₄₇	—	2	1	no	—
48	C₂³×C₄×C₄₇	—	2	1	no	—
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₄₇	—	2	2	no	—
52	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
53	C₄×Q₈×C₄₇	—	4	4	no	—
54	C₄×D₄×C₄₇	—	2	2	no	—
55	C₄×D₄×C₄₇	—	2	2	no	—
56	C₄×D₄×C₄₇	—	2	2	no	—
57	C₄×D₄×C₄₇	—	2	2	no	—
58	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₄×D₄×C₄₇	Q₈	1	4	yes	complemented
60	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄²×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	—	2	1	no	—
74	C₂×C₄²×C₄₇	—	2	1	no	—
75	C₂×C₄²×C₄₇	—	2	2	no	—
76	C₂×C₄²×C₄₇	—	4	4	no	—
77	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#107×C₄₇	—	2	4	no	—
85	#106×C₄₇	C₂×C₄	1	8	yes	complemented
86	C₄⋊C₈×C₄₇	—	2	2	no	—
87	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
88	#102×C₄₇	—	2	4	no	—
89	#102×C₄₇	C₂×C₄	1	8	yes	—
90	#97×C₄₇	—	2	4	no	—
91	#95×C₄₇	—	2	1	no	—
92	#95×C₄₇	—	2	1	no	—
93	#95×C₄₇	—	2	1	no	—
94	#95×C₄₇	—	2	2	no	—
95	#95×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	4	no	—
98	C₂×Q₈×C₄₇	—	4	2	no	—
99	C₂×Q₈×C₄₇	—	4	2	no	—
100	C₂×D₄×C₄₇	—	2	1	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	2	1	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
105	C₂×D₄×C₄₇	#41	1	2	yes	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	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	—	4	2	no	—
115	C₂²×C₄×C₄₇	—	4	2	no	—
116	C₂²×C₄×C₄₇	—	4	2	no	—
117	C₂²×C₄×C₄₇	—	4	2	no	—
118	C₂²×C₄×C₄₇	—	4	2	no	—
119	C₂²×C₄×C₄₇	—	4	2	no	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₄₇	—	2	4	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	4	2	no	—
141	C₄⋊C₄×C₄₇	—	4	2	no	—
142	C₄⋊C₄×C₄₇	—	4	4	no	—
143	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
145	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
146	C₄⋊C₄×C₄₇	#41	1	2	yes	—
147	C₂²⋊C₄×C₄₇	—	2	4	no	—
148	C₂²⋊C₄×C₄₇	—	2	4	no	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₄²×C₄₇	—	2	2	no	—
151	C₄²×C₄₇	—	2	2	no	—
152	C₄²×C₄₇	—	2	2	no	—
153	C₄²×C₄₇	—	2	1	no	—
154	C₄²×C₄₇	—	2	1	no	—
155	C₄²×C₄₇	—	4	1	no	—
156	C₄²×C₄₇	—	4	2	no	—
157	C₄²×C₄₇	—	4	2	no	—
158	C₄²×C₄₇	—	4	4	no	—
159	C₄²×C₄₇	—	4	2	no	—
160	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
161	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
162	C₄²×C₄₇	#41	1	2	yes	—
163	C₄²×C₄₇	#41	1	2	yes	—
164	C₂³×C₄₇	—	2	2	no	—
165	C₂³×C₄₇	—	2	2	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	—	4	1	no	—
168	C₂³×C₄₇	—	4	1	no	—
169	C₂³×C₄₇	—	4	1	no	—
170	C₂³×C₄₇	—	4	1	no	—
171	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₄₇	—	4	8	no	—
173	D₄×C₄₇	—	2	2	no	—
174	D₄×C₄₇	—	2	2	no	—
175	D₄×C₄₇	—	2	2	no	—
176	D₄×C₄₇	C₄×Q₈	1	4	yes	complemented
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	4	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	1	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	4	8	no	—
193	C₂×C₄×C₄₇	—	4	8	no	—
194	C₂×C₄×C₄₇	—	4	1	no	—
195	C₂×C₄×C₄₇	—	4	1	no	—
196	C₂×C₄×C₄₇	—	4	1	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	1	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	8	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	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
210	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
211	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₄₇	#137	1	2	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
219	C₈×C₄₇	—	2	4	no	—
220	C₈×C₄₇	—	4	2	no	—
221	#21614	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₄₇	—	2	4	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	—	4	2	no	—
225	C₂²×C₄₇	—	4	2	no	—
226	C₂²×C₄₇	—	4	2	no	—
227	C₂²×C₄₇	—	4	2	no	—
228	C₂²×C₄₇	—	4	2	no	—
229	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
231	C₂²×C₄₇	#525	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
235	C₂²×C₄₇	#575	1	1	yes	characteristic
236	C₄×C₄₇	—	2	2	no	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	—	2	2	no	—
240	C₄×C₄₇	—	4	2	no	—
241	C₄×C₄₇	—	4	2	no	—
242	C₄×C₄₇	—	4	1	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	—	4	4	no	—
245	C₄×C₄₇	—	8	2	no	—
246	C₄×C₄₇	#440	1	4	yes	—
247	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
248	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
249	C₄×C₄₇	#529	1	1	yes	characteristic
250	C₄×C₄₇	#533	1	1	yes	characteristic
251	C₂×#476	C₂×C₄₇	1	1	yes	characteristic
252	C₄×C₄⋊Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
253	C₄²×D₄	C₂×C₄₇	1	1	yes	characteristic
254	#1987	C₂×C₄₇	1	1	yes	characteristic, complemented
255	#1947	C₂×C₄₇	1	1	yes	characteristic, complemented
256	#1919	C₂×C₄₇	1	2	yes	complemented
257	#1862	C₂×C₄₇	1	2	yes	—
258	#1802	C₂×C₄₇	1	1	yes	characteristic
259	#1776	C₂×C₄₇	1	2	yes	complemented
260	#1767	C₂×C₄₇	1	1	yes	characteristic, complemented
261	#1762	C₂×C₄₇	1	2	yes	—
262	C₂×C₄₇	—	4	4	no	—
263	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
265	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂×C₄₇	#3077	1	1	yes	characteristic
267	C₂×C₄₇	#3079	1	1	yes	characteristic
268	C₂×C₄₇	#3109	1	1	yes	characteristic
269	C₂×C₄₇	#3116	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
271	C₂×C₄×Q₈	—	2	1	no	—
272	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
275	C₂²×C₄²	—	2	1	no	—
276	#476	C₄×C₄₇	1	8	yes	complemented
277	C₂×#107	C₂²×C₄₇	1	2	yes	—
278	C₂×#106	C₂²×C₄₇	1	2	yes	—
279	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
281	C₂×#102	C₂²×C₄₇	1	2	yes	—
282	C₂×#102	C₂²×C₄₇	1	2	yes	—
283	C₂×#97	C₂²×C₄₇	1	2	yes	—
284	#391	—	2	1	no	—
285	#389	—	2	1	no	—
286	#389	C₂²×C₄₇	1	2	yes	—
287	#384	C₂²×C₄₇	1	1	yes	characteristic
288	C₄×C₄⋊C₄	—	2	1	no	—
289	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
290	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
292	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
293	C₄×C₂²⋊C₄	—	2	1	no	—
294	C₄×C₂²⋊C₄	—	2	1	no	—
295	C₄×C₂²⋊C₄	—	2	1	no	—
296	C₄³	C₂²×C₄₇	1	1	yes	characteristic
297	#340	C₂²×C₄₇	1	2	yes	—
298	#340	C₂²×C₄₇	1	2	yes	—
299	#340	C₂²×C₄₇	1	2	yes	—
300	#340	C₂²×C₄₇	1	2	yes	—
301	#336	C₂²×C₄₇	1	2	yes	—
302	C₄₇	#21614	1	1	yes	characteristic, direct product factor, Sylow
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
309	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	C₂×C₄×C₄₇	1	4	yes	complemented
312	C₄×Q₈	—	4	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
318	C₄×D₄	Q₈×C₄₇	1	4	yes	complemented
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	4	4	no	—
336	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
337	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
338	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
339	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
343	#107	—	2	4	no	—
344	#106	C₂×C₄×C₄₇	1	8	yes	complemented
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	C₂×C₄×C₄₇	1	4	yes	complemented
347	#102	—	2	4	no	—
348	#102	C₂×C₄×C₄₇	1	8	yes	—
349	#97	—	2	4	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	C₂⁴	—	2	1	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
363	C₂×D₄	C₂×Q₈×C₄₇	1	2	yes	—
364	C₂×D₄	#41×C₄₇	1	2	yes	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	4	no	—
402	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
403	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
404	C₄⋊C₄	C₂×Q₈×C₄₇	1	2	yes	—
405	C₄⋊C₄	#41×C₄₇	1	2	yes	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	4	1	no	—
415	C₄²	—	4	2	no	—
416	C₄²	—	4	2	no	—
417	C₄²	—	4	4	no	—
418	C₄²	—	4	2	no	—
419	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
420	C₄²	C₂×Q₈×C₄₇	1	2	yes	—
421	C₄²	#41×C₄₇	1	2	yes	—
422	C₄²	#41×C₄₇	1	2	yes	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
431	Q₈	—	4	8	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	C₄×Q₈×C₄₇	1	4	yes	complemented
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
466	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
467	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
468	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
469	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
470	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
471	C₂×C₄	#137×C₄₇	1	2	yes	—
472	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
478	C₈	—	2	4	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
488	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
489	C₂²	C₄₇×#525	1	1	yes	characteristic
490	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
491	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
492	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
493	C₂²	C₄₇×#575	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	4	no	—
503	C₄	—	8	2	no	—
504	C₄	C₄₇×#440	1	4	yes	—
505	C₄	C₂×C₄×Q₈×C₄₇	1	1	yes	characteristic
506	C₄	C₄×#41×C₄₇	1	1	yes	characteristic
507	C₄	C₄₇×#529	1	1	yes	characteristic
508	C₄	C₄₇×#533	1	1	yes	characteristic
509	C₂	—	4	4	no	—
510	C₂	C₄×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
511	C₂	C₂×C₄₇×#440	1	1	yes	characteristic
512	C₂	C₄×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
513	C₂	C₄₇×#3077	1	1	yes	characteristic
514	C₂	C₄₇×#3079	1	1	yes	characteristic
515	C₂	C₄₇×#3109	1	1	yes	characteristic
516	C₂	C₄₇×#3116	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×D₄×C₄₇	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₄³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊Q₈×C₄₇	C₂	semidirect
4. C₄₇×#1987	C₂	semidirect
5. C₄₇×#1947	C₂	semidirect
6. C₄₇×#1919	C₂	semidirect
9. C₄₇×#1776	C₂	semidirect
10. C₄₇×#1767	C₂	semidirect
18. C₄₇×#476	C₄	semidirect
52. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
59. C₄×D₄×C₄₇	Q₈	semidirect
85. #106×C₄₇	C₂×C₄	semidirect
87. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
176. D₄×C₄₇	C₄×Q₈	semidirect
221. #21614	C₄₇	direct (N × H)
252. C₄×C₄⋊Q₈	C₂×C₄₇	semidirect
254. #1987	C₂×C₄₇	semidirect
255. #1947	C₂×C₄₇	semidirect
256. #1919	C₂×C₄₇	semidirect
259. #1776	C₂×C₄₇	semidirect
260. #1767	C₂×C₄₇	semidirect
276. #476	C₄×C₄₇	semidirect
302. C₄₇	#21614	direct (N × H)
311. C₄⋊Q₈	C₂×C₄×C₄₇	semidirect
318. C₄×D₄	Q₈×C₄₇	semidirect
344. #106	C₂×C₄×C₄₇	semidirect
346. C₄⋊C₈	C₂×C₄×C₄₇	semidirect
435. D₄	C₄×Q₈×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×#476	2
C₄×C₄⋊Q₈×C₄₇	2
C₄²×D₄×C₄₇	2
C₄₇×#1987	2
C₄₇×#1947	2
C₄₇×#1919	2
C₄₇×#1862	2
C₄₇×#1802	2
C₄₇×#1776	2
C₄₇×#1767	2
C₄₇×#1762	2
#21614	47

Subgroups — C47×#21614 #26061312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21614 #26061312