Subgroups — C₄₇×#24726 #26064424

Order 12032.

1222 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#459	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2067	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2041	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1879	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₇	C₂²	1	2	yes	—
16	C₂×#121×C₄₇	—	2	1	no	—
17	C₂×#121×C₄₇	—	2	1	no	—
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
22	C₄₇×#459	—	2	8	no	—
23	C₄₇×#459	—	2	4	no	—
24	C₄×D₈×C₄₇	—	2	4	no	—
25	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
28	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#102×C₄₇	C₂²	1	2	yes	—
30	C₂×#102×C₄₇	C₂²	1	2	yes	—
31	C₂×#102×C₄₇	C₂²	1	2	yes	—
32	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#102×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#392	—	2	2	no	—
36	C₄₇×#390	C₂²	1	2	yes	—
37	C₄₇×#389	C₂²	1	2	yes	—
38	C₄₇×#385	—	2	2	no	—
39	C₄₇×#384	C₂²	1	1	yes	characteristic
40	C₄₇×#380	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₄₇	—	2	1	no	—
45	C₂²×D₄×C₄₇	—	2	2	no	—
46	C₂²×D₄×C₄₇	—	2	2	no	—
47	C₂²×D₄×C₄₇	—	2	1	no	—
48	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
49	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	—	2	1	no	—
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂³×C₄×C₄₇	—	2	2	no	—
54	C₂×D₈×C₄₇	—	2	2	no	—
55	C₂×D₈×C₄₇	—	2	2	no	—
56	C₂×D₈×C₄₇	—	2	4	no	—
57	C₂×D₈×C₄₇	—	2	4	no	—
58	C₂×D₈×C₄₇	—	2	4	no	—
59	C₂×D₈×C₄₇	D₄	1	4	yes	complemented
60	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
61	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
63	#127×C₄₇	—	2	4	no	—
64	#127×C₄₇	—	2	2	no	—
65	#127×C₄₇	—	2	2	no	—
66	#127×C₄₇	—	4	2	no	—
67	#121×C₄₇	—	4	4	no	—
68	#121×C₄₇	—	4	4	no	—
69	C₄×D₄×C₄₇	—	2	4	no	—
70	C₄×D₄×C₄₇	—	2	2	no	—
71	C₄×D₄×C₄₇	—	2	2	no	—
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₄×D₄×C₄₇	—	4	2	no	—
74	C₄×D₄×C₄₇	D₄	1	4	yes	complemented
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
79	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
89	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	#107×C₄₇	—	2	2	no	—
92	C₄⋊C₈×C₄₇	—	2	4	no	—
93	C₄⋊C₈×C₄₇	—	2	2	no	—
94	#102×C₄₇	—	2	4	no	—
95	#102×C₄₇	—	2	2	no	—
96	#102×C₄₇	—	2	4	no	—
97	#102×C₄₇	—	2	4	no	—
98	#102×C₄₇	—	2	2	no	—
99	#102×C₄₇	—	4	2	no	—
100	C₄×C₈×C₄₇	—	2	2	no	—
101	#95×C₄₇	—	2	2	no	—
102	#95×C₄₇	D₄	1	2	yes	—
103	C₂⁴×C₄₇	—	2	1	no	—
104	C₂⁴×C₄₇	—	2	1	no	—
105	C₂⁴×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	1	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	—	2	1	no	—
116	C₂×D₄×C₄₇	—	2	2	no	—
117	C₂×D₄×C₄₇	—	2	1	no	—
118	C₂×D₄×C₄₇	—	2	1	no	—
119	C₂×D₄×C₄₇	—	2	2	no	—
120	C₂×D₄×C₄₇	—	4	4	no	—
121	C₂×D₄×C₄₇	—	4	4	no	—
122	C₂×D₄×C₄₇	—	4	4	no	—
123	C₂×D₄×C₄₇	—	4	2	no	—
124	C₂×D₄×C₄₇	—	4	2	no	—
125	C₂×D₄×C₄₇	—	4	4	no	—
126	C₂×D₄×C₄₇	—	4	2	no	—
127	C₂×D₄×C₄₇	—	4	2	no	—
128	C₂×D₄×C₄₇	—	8	1	no	—
129	C₂×D₄×C₄₇	—	8	2	no	—
130	C₂×D₄×C₄₇	—	8	1	no	—
131	C₂×D₄×C₄₇	—	8	2	no	—
132	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₄₇	#41	1	2	yes	—
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	4	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	4	4	no	—
141	C₂²×C₄×C₄₇	—	4	2	no	—
142	C₂²×C₄×C₄₇	—	4	2	no	—
143	C₂²×C₄×C₄₇	—	4	2	no	—
144	C₂²×C₄×C₄₇	—	4	4	no	—
145	C₂²×C₄×C₄₇	—	4	2	no	—
146	C₂²×C₄×C₄₇	—	4	2	no	—
147	C₂²×C₄×C₄₇	—	8	2	no	—
148	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
153	D₈×C₄₇	—	2	8	no	—
154	D₈×C₄₇	—	4	8	no	—
155	C₂×C₈×C₄₇	—	2	1	no	—
156	C₂×C₈×C₄₇	—	2	1	no	—
157	C₂×C₈×C₄₇	—	2	2	no	—
158	C₂×C₈×C₄₇	—	2	2	no	—
159	C₂×C₈×C₄₇	—	2	1	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	—	2	1	no	—
162	C₂×C₈×C₄₇	—	2	1	no	—
163	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	—	2	1	no	—
166	C₄⋊C₄×C₄₇	—	2	1	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	1	no	—
169	C₄⋊C₄×C₄₇	—	2	2	no	—
170	C₄⋊C₄×C₄₇	—	4	4	no	—
171	C₄⋊C₄×C₄₇	—	4	2	no	—
172	C₄⋊C₄×C₄₇	—	8	1	no	—
173	C₄⋊C₄×C₄₇	D₈	1	4	yes	complemented
174	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
175	C₂²⋊C₄×C₄₇	—	2	4	no	—
176	C₂²⋊C₄×C₄₇	—	4	4	no	—
177	C₂²⋊C₄×C₄₇	—	4	4	no	—
178	C₂²⋊C₄×C₄₇	—	4	2	no	—
179	C₂²⋊C₄×C₄₇	—	4	4	no	—
180	C₄²×C₄₇	—	2	2	no	—
181	C₄²×C₄₇	—	2	2	no	—
182	C₄²×C₄₇	C₂×D₄	1	2	yes	—
183	C₄²×C₄₇	#41	1	2	yes	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	2	no	—
186	C₂³×C₄₇	—	2	2	no	—
187	C₂³×C₄₇	—	2	2	no	—
188	C₂³×C₄₇	—	4	1	no	—
189	C₂³×C₄₇	—	4	1	no	—
190	C₂³×C₄₇	—	4	1	no	—
191	C₂³×C₄₇	—	4	1	no	—
192	C₂³×C₄₇	—	4	1	no	—
193	C₂³×C₄₇	—	4	1	no	—
194	C₂³×C₄₇	—	4	1	no	—
195	C₂³×C₄₇	—	4	1	no	—
196	C₂³×C₄₇	—	4	1	no	—
197	C₂³×C₄₇	—	4	1	no	—
198	C₂³×C₄₇	—	4	2	no	—
199	C₂³×C₄₇	—	4	2	no	—
200	C₂³×C₄₇	—	4	2	no	—
201	C₂³×C₄₇	—	4	2	no	—
202	C₂³×C₄₇	—	4	2	no	—
203	C₂³×C₄₇	—	4	2	no	—
204	C₂³×C₄₇	—	4	2	no	—
205	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
206	D₄×C₄₇	—	2	2	no	—
207	D₄×C₄₇	—	2	2	no	—
208	D₄×C₄₇	—	2	2	no	—
209	D₄×C₄₇	—	2	2	no	—
210	D₄×C₄₇	—	2	2	no	—
211	D₄×C₄₇	—	4	2	no	—
212	D₄×C₄₇	—	4	1	no	—
213	D₄×C₄₇	—	4	2	no	—
214	D₄×C₄₇	—	4	2	no	—
215	D₄×C₄₇	—	4	1	no	—
216	D₄×C₄₇	—	4	2	no	—
217	D₄×C₄₇	—	8	8	no	—
218	D₄×C₄₇	—	8	4	no	—
219	D₄×C₄₇	—	8	8	no	—
220	D₄×C₄₇	—	8	4	no	—
221	D₄×C₄₇	#121	1	4	yes	complemented
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	1	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	1	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	8	no	—
233	C₂×C₄×C₄₇	—	4	1	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	—	4	1	no	—
236	C₂×C₄×C₄₇	—	4	2	no	—
237	C₂×C₄×C₄₇	—	4	1	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	—	8	8	no	—
240	C₂×C₄×C₄₇	—	8	4	no	—
241	C₂×C₄×C₄₇	#121	1	2	yes	—
242	C₂×C₄×C₄₇	#121	1	2	yes	—
243	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
244	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
245	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
246	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
251	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
252	C₈×C₄₇	—	2	2	no	—
253	C₈×C₄₇	—	4	2	no	—
254	C₈×C₄₇	—	4	1	no	—
255	#24726	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₇	—	2	4	no	—
257	C₂²×C₄₇	—	4	2	no	—
258	C₂²×C₄₇	—	4	2	no	—
259	C₂²×C₄₇	—	4	2	no	—
260	C₂²×C₄₇	—	4	2	no	—
261	C₂²×C₄₇	—	4	2	no	—
262	C₂²×C₄₇	—	4	2	no	—
263	C₂²×C₄₇	—	4	2	no	—
264	C₂²×C₄₇	—	4	2	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	8	1	no	—
267	C₂²×C₄₇	—	8	1	no	—
268	C₂²×C₄₇	—	8	1	no	—
269	C₂²×C₄₇	—	8	1	no	—
270	C₂²×C₄₇	—	8	2	no	—
271	C₂²×C₄₇	—	8	2	no	—
272	C₂²×C₄₇	—	8	2	no	—
273	C₂²×C₄₇	—	8	2	no	—
274	C₂²×C₄₇	—	8	2	no	—
275	C₂²×C₄₇	—	8	2	no	—
276	C₂²×C₄₇	—	8	2	no	—
277	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
278	C₂²×C₄₇	D₄²	1	1	yes	characteristic
279	C₂²×C₄₇	#548	1	1	yes	characteristic
280	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
281	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₂²×C₄₇	#576	1	1	yes	characteristic
283	C₂²×C₄₇	#577	1	1	yes	characteristic
284	C₄×C₄₇	—	2	4	no	—
285	C₄×C₄₇	—	2	2	no	—
286	C₄×C₄₇	—	4	2	no	—
287	C₄×C₄₇	—	4	2	no	—
288	C₄×C₄₇	—	8	2	no	—
289	C₄×C₄₇	—	8	1	no	—
290	C₄×C₄₇	#459	1	4	yes	complemented
291	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
292	C₄×C₄₇	#537	1	1	yes	characteristic
293	C₄×C₄₇	#547	1	1	yes	characteristic
294	C₄×C₄₇	#553	1	1	yes	characteristic
295	C₂×#459	C₂×C₄₇	1	2	yes	complemented
296	C₂×#459	C₂×C₄₇	1	1	yes	characteristic, complemented
297	C₂×C₄×D₈	C₂×C₄₇	1	1	yes	characteristic, complemented
298	#2541	C₂×C₄₇	1	1	yes	characteristic, complemented
299	D₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
300	#2067	C₂×C₄₇	1	2	yes	complemented
301	#2041	C₂×C₄₇	1	2	yes	complemented
302	#1957	C₂×C₄₇	1	1	yes	characteristic, complemented
303	#1939	C₂×C₄₇	1	1	yes	characteristic, complemented
304	#1879	C₂×C₄₇	1	2	yes	complemented
305	#1802	C₂×C₄₇	1	1	yes	characteristic, complemented
306	C₂×C₄₇	—	4	4	no	—
307	C₂×C₄₇	—	8	2	no	—
308	C₂×C₄₇	—	16	2	no	—
309	C₂×C₄₇	#2416	1	1	yes	characteristic
310	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
311	C₂×C₄₇	#3045	1	1	yes	characteristic
312	C₂×C₄₇	#3272	1	1	yes	characteristic
313	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
314	C₂×C₄₇	#3358	1	1	yes	characteristic
315	C₂×C₄₇	#3366	1	1	yes	characteristic
316	C₂²×D₈	C₂²×C₄₇	1	2	yes	—
317	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
318	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
319	C₂×#127	C₂²×C₄₇	1	2	yes	—
320	C₂×#121	—	2	1	no	—
321	C₂×#121	—	2	1	no	—
322	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
324	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	—	2	1	no	—
326	#459	—	2	8	no	—
327	#459	—	2	4	no	—
328	C₄×D₈	—	2	4	no	—
329	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
330	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
331	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
332	C₂×#102	C₂²×C₄₇	1	2	yes	—
333	C₂×#102	C₂²×C₄₇	1	2	yes	—
334	C₂×#102	C₂²×C₄₇	1	2	yes	—
335	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
336	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
337	C₂×#102	C₂²×C₄₇	1	2	yes	—
338	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
339	#392	—	2	2	no	—
340	#390	C₂²×C₄₇	1	2	yes	—
341	#389	C₂²×C₄₇	1	2	yes	—
342	#385	—	2	2	no	—
343	#384	C₂²×C₄₇	1	1	yes	characteristic
344	#380	—	2	1	no	—
345	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
346	#340	C₂²×C₄₇	1	2	yes	—
347	#336	C₂²×C₄₇	1	2	yes	—
348	C₄₇	#24726	1	1	yes	characteristic, direct product factor, Sylow
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
354	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
355	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
356	C₂³×C₄	—	2	1	no	—
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	—	2	2	no	—
359	C₂×D₈	—	2	2	no	—
360	C₂×D₈	—	2	2	no	—
361	C₂×D₈	—	2	4	no	—
362	C₂×D₈	—	2	4	no	—
363	C₂×D₈	—	2	4	no	—
364	C₂×D₈	D₄×C₄₇	1	4	yes	complemented
365	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
366	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
368	#127	—	2	4	no	—
369	#127	—	2	2	no	—
370	#127	—	2	2	no	—
371	#127	—	4	2	no	—
372	#121	—	4	4	no	—
373	#121	—	4	4	no	—
374	C₄×D₄	—	2	4	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	4	2	no	—
379	C₄×D₄	D₄×C₄₇	1	4	yes	complemented
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	4	4	no	—
384	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
385	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
395	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
396	#107	—	2	2	no	—
397	C₄⋊C₈	—	2	4	no	—
398	C₄⋊C₈	—	2	2	no	—
399	#102	—	2	2	no	—
400	#102	—	2	4	no	—
401	#102	—	2	4	no	—
402	#102	—	2	2	no	—
403	#102	—	2	4	no	—
404	#102	—	4	2	no	—
405	C₄×C₈	—	2	2	no	—
406	#95	—	2	2	no	—
407	#95	D₄×C₄₇	1	2	yes	—
408	C₂⁴	—	2	1	no	—
409	C₂⁴	—	2	1	no	—
410	C₂⁴	—	2	2	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	4	2	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	8	1	no	—
434	C₂×D₄	—	8	2	no	—
435	C₂×D₄	—	8	1	no	—
436	C₂×D₄	—	8	2	no	—
437	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
438	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
439	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
440	C₂×D₄	#41×C₄₇	1	2	yes	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	8	2	no	—
453	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
458	D₈	—	2	8	no	—
459	D₈	—	4	8	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	—	4	2	no	—
477	C₄⋊C₄	—	8	1	no	—
478	C₄⋊C₄	D₈×C₄₇	1	4	yes	complemented
479	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	4	4	no	—
482	C₂²⋊C₄	—	4	4	no	—
483	C₂²⋊C₄	—	4	2	no	—
484	C₂²⋊C₄	—	4	4	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	C₂×D₄×C₄₇	1	2	yes	—
488	C₄²	#41×C₄₇	1	2	yes	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
511	D₄	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	2	no	—
522	D₄	—	8	8	no	—
523	D₄	—	8	4	no	—
524	D₄	—	8	8	no	—
525	D₄	—	8	4	no	—
526	D₄	#121×C₄₇	1	4	yes	complemented
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	8	8	no	—
545	C₂×C₄	—	8	4	no	—
546	C₂×C₄	#121×C₄₇	1	2	yes	—
547	C₂×C₄	#121×C₄₇	1	2	yes	—
548	C₂×C₄	C₂×D₈×C₄₇	1	4	yes	—
549	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
550	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
554	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
555	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
556	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
557	C₈	—	2	2	no	—
558	C₈	—	4	2	no	—
559	C₈	—	4	1	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	2	no	—
576	C₂²	—	8	2	no	—
577	C₂²	—	8	2	no	—
578	C₂²	—	8	2	no	—
579	C₂²	—	8	2	no	—
580	C₂²	—	8	2	no	—
581	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
582	C₂²	D₄²×C₄₇	1	1	yes	characteristic
583	C₂²	C₄₇×#548	1	1	yes	characteristic
584	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
585	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
586	C₂²	C₄₇×#576	1	1	yes	characteristic
587	C₂²	C₄₇×#577	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	4	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	8	2	no	—
593	C₄	—	8	1	no	—
594	C₄	C₄₇×#459	1	4	yes	complemented
595	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
596	C₄	C₄₇×#537	1	1	yes	characteristic
597	C₄	C₄₇×#547	1	1	yes	characteristic
598	C₄	C₄₇×#553	1	1	yes	characteristic
599	C₂	—	4	4	no	—
600	C₂	—	8	2	no	—
601	C₂	—	16	2	no	—
602	C₂	C₄₇×#2416	1	1	yes	characteristic
603	C₂	C₂×C₄₇×#459	1	1	yes	characteristic
604	C₂	C₄₇×#3045	1	1	yes	characteristic
605	C₂	C₄₇×#3272	1	1	yes	characteristic
606	C₂	D₄×D₈×C₄₇	1	1	yes	characteristic
607	C₂	C₄₇×#3358	1	1	yes	characteristic
608	C₂	C₄₇×#3366	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#459	C₂	semidirect
2. C₂×C₄₇×#459	C₂	semidirect
3. C₂×C₄×D₈×C₄₇	C₂	semidirect
4. C₄₇×#2541	C₂	semidirect
5. D₄×C₄⋊C₄×C₄₇	C₂	semidirect
6. C₄₇×#2067	C₂	semidirect
7. C₄₇×#2041	C₂	semidirect
8. C₄₇×#1957	C₂	semidirect
9. C₄₇×#1939	C₂	semidirect
10. C₄₇×#1879	C₂	semidirect
11. C₄₇×#1802	C₂	semidirect
59. C₂×D₈×C₄₇	D₄	semidirect
74. C₄×D₄×C₄₇	D₄	semidirect
173. C₄⋊C₄×C₄₇	D₈	semidirect
221. D₄×C₄₇	#121	semidirect
255. #24726	C₄₇	direct (N × H)
290. C₄×C₄₇	#459	semidirect
295. C₂×#459	C₂×C₄₇	semidirect
296. C₂×#459	C₂×C₄₇	semidirect
297. C₂×C₄×D₈	C₂×C₄₇	semidirect
298. #2541	C₂×C₄₇	semidirect
299. D₄×C₄⋊C₄	C₂×C₄₇	semidirect
300. #2067	C₂×C₄₇	semidirect
301. #2041	C₂×C₄₇	semidirect
302. #1957	C₂×C₄₇	semidirect
303. #1939	C₂×C₄₇	semidirect
304. #1879	C₂×C₄₇	semidirect
305. #1802	C₂×C₄₇	semidirect
348. C₄₇	#24726	direct (N × H)
364. C₂×D₈	D₄×C₄₇	semidirect
379. C₄×D₄	D₄×C₄₇	semidirect
478. C₄⋊C₄	D₈×C₄₇	semidirect
526. D₄	#121×C₄₇	semidirect
594. C₄	C₄₇×#459	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#459	2
C₂×C₄×D₈×C₄₇	2
C₄₇×#2541	2
D₄×C₄⋊C₄×C₄₇	2
C₄₇×#2067	2
C₄₇×#2041	2
C₄₇×#1957	2
C₄₇×#1939	2
C₄₇×#1879	2
C₄₇×#1802	2
#24726	47

Subgroups — C47×#24726 #26064424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24726 #26064424