Subgroups — #26215164

Order 12032.

1222 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₂²⋊D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂²⋊D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243249	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243158	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×(C₂×D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243132	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15688877	C₂	1	1	yes	maximal, characteristic, complemented
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
20	C₂×(C₂²⋊D₄₇)⋊C₄	C₄	1	2	yes	—
21	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₄₇	C₄	1	8	yes	complemented
24	(C₂²⋊D₄₇)⋊C₈	C₄	1	8	yes	complemented
25	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
37	#15688974	C₄	1	2	yes	—
38	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
39	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
40	#15688970	C₄	1	2	yes	—
41	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
42	#15688878	C₂²	1	1	yes	characteristic
43	#15688878	C₂²	1	1	yes	characteristic
44	#15688877	C₂²	1	1	yes	characteristic
45	#15688877	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₂²×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
59	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
60	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	—	4	1	no	—
62	C₂²×C₄₇⋊C₈	—	4	1	no	—
63	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
64	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₄₇	—	4	1	no	—
69	C₂×C₈×D₄₇	—	4	1	no	—
70	C₂×C₈×D₄₇	—	4	1	no	—
71	C₂×C₈×D₄₇	—	4	1	no	—
72	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	complemented
73	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	complemented
74	C₄×C₂²⋊D₄₇	C₂×C₄	1	4	yes	—
75	C₄×C₂²⋊D₄₇	C₂×C₄	1	4	yes	—
76	(C₂²⋊D₄₇)⋊C₄	C₈	1	16	yes	complemented
77	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₄×Dic₄₇	—	4	1	no	—
83	C₂×C₄×Dic₄₇	—	4	1	no	—
84	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
86	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
87	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
88	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₄²×D₄₇	—	4	1	no	—
92	C₄²×D₄₇	—	4	1	no	—
93	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
94	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
95	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
96	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	complemented
97	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	complemented
98	C₄×C₄₇⋊C₈	—	4	1	no	—
99	C₄×C₄₇⋊C₈	—	4	1	no	—
100	C₈×Dic₄₇	—	4	1	no	—
101	C₈×Dic₄₇	—	4	1	no	—
102	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
103	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
104	C₄₇⋊#95	C₂×C₄	1	2	yes	—
105	C₄₇⋊#95	C₂×C₄	1	2	yes	—
106	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₇	—	4	1	no	—
108	C₂²×C₈×C₄₇	—	4	1	no	—
109	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
110	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
115	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
118	C₄×C₈×C₄₇	—	4	1	no	—
119	C₄×C₈×C₄₇	—	4	1	no	—
120	#95×C₄₇	C₂×C₄	1	2	yes	—
121	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
134	C₂×C₂²⋊D₄₇	C₂×C₈	1	8	yes	—
135	C₂²×Dic₄₇	—	4	2	no	—
136	C₂²×Dic₄₇	—	4	2	no	—
137	C₂²×Dic₄₇	C₂×C₈	1	8	yes	complemented
138	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
141	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄×D₄₇	—	2	1	no	—
144	C₂×C₄×D₄₇	—	2	1	no	—
145	C₂×C₄×D₄₇	—	2	1	no	—
146	C₂×C₄×D₄₇	—	2	1	no	—
147	C₂×C₄×D₄₇	—	4	2	no	—
148	C₂×C₄×D₄₇	—	4	2	no	—
149	C₂×C₄×D₄₇	C₂×C₈	1	8	yes	complemented
150	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
151	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₄₇	—	2	1	no	—
153	C₂×C₈×C₄₇	—	2	1	no	—
154	C₂×C₈×C₄₇	—	2	1	no	—
155	C₂×C₈×C₄₇	—	2	1	no	—
156	C₂×C₈×C₄₇	—	2	1	no	—
157	C₂×C₈×C₄₇	—	2	1	no	—
158	C₂×C₈×C₄₇	—	2	1	no	—
159	C₂×C₈×C₄₇	—	2	1	no	—
160	C₂×C₈×C₄₇	—	4	4	no	—
161	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
163	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
165	C₂²⋊C₄×C₄₇	C₂×C₈	1	8	yes	complemented
166	C₄²×C₄₇	—	2	1	no	—
167	C₄²×C₄₇	—	2	1	no	—
168	C₄²×C₄₇	—	2	1	no	—
169	C₄²×C₄₇	—	2	1	no	—
170	C₂²⋊Dic₄₇	C₄²	1	4	yes	—
171	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
172	(C₂×D₄₇)⋊C₄	C₂×C₈	1	8	yes	complemented
173	Dic₄₇⋊C₄	C₄²	1	4	yes	—
174	Dic₄₇⋊C₄	C₂×C₈	1	8	yes	complemented
175	C₄×Dic₄₇	—	2	1	no	—
176	C₄×Dic₄₇	—	2	1	no	—
177	C₄×Dic₄₇	—	2	1	no	—
178	C₄×Dic₄₇	—	2	1	no	—
179	C₄×Dic₄₇	—	4	2	no	—
180	C₄×Dic₄₇	—	4	2	no	—
181	C₄×Dic₄₇	—	4	2	no	—
182	C₄×Dic₄₇	C₂×C₈	1	8	yes	complemented
183	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
184	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
185	C₂×C₄₇⋊C₈	—	2	1	no	—
186	C₂×C₄₇⋊C₈	—	2	1	no	—
187	C₂×C₄₇⋊C₈	—	2	1	no	—
188	C₂×C₄₇⋊C₈	—	2	1	no	—
189	C₂×C₄₇⋊C₈	—	2	1	no	—
190	C₂×C₄₇⋊C₈	—	2	1	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	1	no	—
193	C₂×C₄₇⋊C₈	—	4	4	no	—
194	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
195	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
196	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
197	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
198	C₈×D₄₇	—	4	4	no	—
199	C₈×D₄₇	—	4	4	no	—
200	C₂³×C₄₇	—	2	1	no	—
201	C₂³×C₄₇	—	2	1	no	—
202	C₂³×C₄₇	—	2	2	no	—
203	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
204	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
205	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
206	C₂²×D₄₇	—	2	1	no	—
207	C₂²×D₄₇	—	2	1	no	—
208	C₂²×D₄₇	—	2	2	no	—
209	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
210	C₂²×D₄₇	C₂²×C₈	1	4	yes	—
211	C₂×C₄×C₄₇	—	2	1	no	—
212	C₂×C₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	1	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
222	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
223	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
224	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
230	C₂²⋊D₄₇	C₄×C₈	1	16	yes	complemented
231	C₂×Dic₄₇	—	2	2	no	—
232	C₂×Dic₄₇	—	2	2	no	—
233	C₂×Dic₄₇	—	2	1	no	—
234	C₂×Dic₄₇	—	2	1	no	—
235	C₂×Dic₄₇	—	2	2	no	—
236	C₂×Dic₄₇	—	2	2	no	—
237	C₂×Dic₄₇	—	2	2	no	—
238	C₂×Dic₄₇	—	4	8	no	—
239	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
240	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
241	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
242	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
243	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
244	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
245	C₄×D₄₇	—	2	2	no	—
246	C₄×D₄₇	—	2	2	no	—
247	C₄×D₄₇	—	2	2	no	—
248	C₄×D₄₇	—	2	2	no	—
249	C₄×D₄₇	—	4	8	no	—
250	C₈×C₄₇	—	2	2	no	—
251	C₈×C₄₇	—	2	2	no	—
252	C₈×C₄₇	—	2	2	no	—
253	C₈×C₄₇	—	2	2	no	—
254	C₄₇⋊C₈	—	2	2	no	—
255	C₄₇⋊C₈	—	2	2	no	—
256	C₄₇⋊C₈	—	2	2	no	—
257	C₄₇⋊C₈	—	2	2	no	—
258	#20555	—	47	1	no	maximal, Sylow
259	C₂²×C₄₇	—	2	2	no	—
260	C₂²×C₄₇	—	2	4	no	—
261	C₂²×C₄₇	—	2	4	no	—
262	C₂²×C₄₇	—	2	2	no	—
263	C₂²×C₄₇	C₂×C₄×C₈	1	4	yes	—
264	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
265	C₂²×C₄₇	#518	1	1	yes	characteristic
266	C₂²×C₄₇	#520	1	1	yes	characteristic
267	C₂²×C₄₇	C₂³×C₈	1	2	yes	—
268	C₂²×C₄₇	#568	1	2	yes	—
269	C₂×D₄₇	—	2	2	no	—
270	C₂×D₄₇	—	2	4	no	—
271	C₂×D₄₇	—	2	4	no	—
272	C₂×D₄₇	—	2	2	no	—
273	C₂×D₄₇	C₂×C₄×C₈	1	4	yes	—
274	C₄×C₄₇	—	2	4	no	—
275	C₄×C₄₇	—	2	4	no	—
276	C₄×C₄₇	—	2	2	no	—
277	C₄×C₄₇	#518	1	1	yes	characteristic
278	C₄×C₄₇	#518	1	1	yes	characteristic
279	C₄×C₄₇	#520	1	1	yes	characteristic
280	C₄×C₄₇	#520	1	1	yes	characteristic
281	Dic₄₇	—	2	2	no	—
282	Dic₄₇	—	2	4	no	—
283	Dic₄₇	—	2	4	no	—
284	Dic₄₇	—	2	2	no	—
285	Dic₄₇	C₂×C₄×C₈	1	4	yes	—
286	C₂×C₈×D₄	—	47	1	no	—
287	C₂×C₈×D₄	—	47	1	no	—
288	C₄²×D₄	—	47	1	no	—
289	C₈×C₄⋊C₄	—	47	1	no	—
290	C₈×C₄⋊C₄	—	47	1	no	—
291	C₄×C₄⋊C₈	—	47	1	no	—
292	C₈×C₂²⋊C₄	—	47	1	no	—
293	C₈×C₂²⋊C₄	—	47	1	no	—
294	C₈×C₂²⋊C₄	—	47	1	no	—
295	C₈×C₂²⋊C₄	D₄₇	1	1	yes	characteristic, complemented
296	C₄×C₂²⋊C₈	—	47	1	no	—
297	C₄×C₂²⋊C₈	—	47	1	no	—
298	#1744	—	47	1	no	—
299	C₂×#336	—	47	1	no	—
300	C₂×#336	—	47	1	no	—
301	C₂×C₄₇	—	2	4	no	—
302	C₂×C₄₇	#2275	1	1	yes	characteristic
303	C₂×C₄₇	C₂²×C₄×C₈	1	1	yes	characteristic
304	C₂×C₄₇	#2875	1	1	yes	characteristic
305	C₂×C₄₇	#2972	1	2	yes	—
306	C₂×C₄₇	#2988	1	2	yes	—
307	D₄₇	—	2	4	no	—
308	C₂³×C₈	—	47	1	no	—
309	C₂³×C₈	—	47	1	no	—
310	C₂³×C₈	—	47	1	no	—
311	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
312	C₂×C₄×D₄	—	47	1	no	—
313	C₂×C₄×D₄	—	47	2	no	—
314	C₂²×C₄²	—	47	1	no	—
315	C₂²×C₄²	—	47	1	no	—
316	C₈×D₄	—	47	8	no	—
317	C₈×D₄	—	47	8	no	—
318	C₂×C₄⋊C₈	—	47	1	no	—
319	C₂×C₄⋊C₈	—	47	1	no	—
320	C₂×C₂²⋊C₈	—	47	1	no	—
321	C₂×C₂²⋊C₈	—	47	1	no	—
322	C₂×C₂²⋊C₈	—	47	1	no	—
323	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
324	C₂×C₄×C₈	—	47	1	no	—
325	C₂×C₄×C₈	—	47	1	no	—
326	C₂×C₄×C₈	—	47	1	no	—
327	C₂×C₄×C₈	—	47	1	no	—
328	C₂×C₄×C₈	—	47	1	no	—
329	C₂×C₄×C₈	—	47	1	no	—
330	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
332	C₄×C₄⋊C₄	—	47	1	no	—
333	C₄×C₄⋊C₄	—	47	2	no	—
334	C₄×C₂²⋊C₄	—	47	2	no	—
335	C₄×C₂²⋊C₄	—	47	1	no	—
336	C₄×C₂²⋊C₄	—	47	2	no	—
337	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
338	C₄³	—	47	1	no	—
339	#336	—	47	1	no	—
340	#336	—	47	1	no	—
341	#336	—	47	1	no	—
342	#336	—	47	1	no	—
343	#336	—	47	1	no	—
344	#336	—	47	1	no	—
345	#336	—	47	1	no	—
346	#336	—	47	1	no	—
347	#336	C₂×D₄₇	1	1	yes	characteristic
348	#336	C₂×D₄₇	1	1	yes	characteristic
349	C₄₇	#20555	1	1	yes	characteristic, complemented, Sylow
350	C₂²×D₄	—	47	1	no	—
351	C₂³×C₄	—	47	2	no	—
352	C₂³×C₄	—	47	1	no	—
353	C₂³×C₄	—	47	2	no	—
354	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
355	C₂²×C₈	—	4	1	no	—
356	C₂²×C₈	—	4	1	no	—
357	C₂²×C₈	—	47	1	no	—
358	C₂²×C₈	—	47	1	no	—
359	C₂²×C₈	—	47	1	no	—
360	C₂²×C₈	—	47	1	no	—
361	C₂²×C₈	—	47	4	no	—
362	C₂²×C₈	—	47	4	no	—
363	C₂²×C₈	—	47	4	no	—
364	C₂²×C₈	—	188	1	no	—
365	C₂²×C₈	—	188	1	no	—
366	C₂²×C₈	—	188	1	no	—
367	C₂²×C₈	—	188	1	no	—
368	C₂²×C₈	—	188	1	no	—
369	C₂²×C₈	—	188	1	no	—
370	C₂²×C₈	C₄×D₄₇	1	4	yes	complemented
371	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
372	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
373	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
374	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
375	C₄×D₄	—	47	4	no	—
376	C₄×D₄	—	47	4	no	—
377	C₄×D₄	—	47	16	no	—
378	C₂×C₄⋊C₄	—	47	1	no	—
379	C₂×C₄⋊C₄	—	47	2	no	—
380	C₂×C₂²⋊C₄	—	47	1	no	—
381	C₂×C₂²⋊C₄	—	47	1	no	—
382	C₂×C₂²⋊C₄	—	47	2	no	—
383	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
384	C₂×C₄²	—	47	2	no	—
385	C₂×C₄²	—	47	1	no	—
386	C₂×C₄²	—	47	1	no	—
387	C₂×C₄²	—	47	1	no	—
388	C₂×C₄²	—	47	2	no	—
389	C₂×C₄²	—	47	2	no	—
390	C₂×C₄²	—	47	2	no	—
391	C₂×C₄²	—	188	1	no	—
392	C₂×C₄²	—	188	1	no	—
393	C₂×C₄²	—	188	1	no	—
394	C₂×C₄²	—	188	1	no	—
395	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
396	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
397	C₄⋊C₈	—	47	4	no	—
398	C₄⋊C₈	—	47	4	no	—
399	C₂²⋊C₈	—	47	4	no	—
400	C₂²⋊C₈	—	47	4	no	—
401	C₂²⋊C₈	—	47	4	no	—
402	C₂²⋊C₈	C₄×D₄₇	1	4	yes	complemented
403	C₄×C₈	—	4	1	no	—
404	C₄×C₈	—	4	1	no	—
405	C₄×C₈	—	47	4	no	—
406	C₄×C₈	—	47	4	no	—
407	C₄×C₈	—	188	1	no	—
408	C₄×C₈	—	188	1	no	—
409	C₄×C₈	—	188	1	no	—
410	C₄×C₈	—	188	1	no	—
411	#95	—	47	2	no	—
412	#95	—	47	2	no	—
413	#95	C₄×D₄₇	1	2	yes	—
414	C₂⁴	—	47	1	no	—
415	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
416	C₂×D₄	—	47	4	no	—
417	C₂×D₄	—	47	8	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	47	1	no	—
423	C₂²×C₄	—	47	1	no	—
424	C₂²×C₄	—	47	1	no	—
425	C₂²×C₄	—	47	2	no	—
426	C₂²×C₄	—	47	2	no	—
427	C₂²×C₄	—	47	8	no	—
428	C₂²×C₄	—	47	2	no	—
429	C₂²×C₄	—	47	2	no	—
430	C₂²×C₄	—	47	8	no	—
431	C₂²×C₄	—	94	1	no	—
432	C₂²×C₄	—	94	1	no	—
433	C₂²×C₄	—	94	1	no	—
434	C₂²×C₄	—	94	1	no	—
435	C₂²×C₄	—	188	2	no	—
436	C₂²×C₄	—	188	2	no	—
437	C₂²×C₄	—	188	2	no	—
438	C₂²×C₄	—	188	2	no	—
439	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
441	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
442	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
443	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
444	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	4	4	no	—
454	C₂×C₈	—	47	2	no	—
455	C₂×C₈	—	47	2	no	—
456	C₂×C₈	—	47	2	no	—
457	C₂×C₈	—	47	2	no	—
458	C₂×C₈	—	94	1	no	—
459	C₂×C₈	—	94	1	no	—
460	C₂×C₈	—	94	1	no	—
461	C₂×C₈	—	94	1	no	—
462	C₂×C₈	—	94	1	no	—
463	C₂×C₈	—	94	1	no	—
464	C₂×C₈	—	94	1	no	—
465	C₂×C₈	—	94	1	no	—
466	C₂×C₈	—	188	4	no	—
467	C₂×C₈	—	188	4	no	—
468	C₂×C₈	—	188	4	no	—
469	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
470	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
471	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
472	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
473	C₄⋊C₄	—	47	4	no	—
474	C₄⋊C₄	—	47	8	no	—
475	C₂²⋊C₄	—	47	4	no	—
476	C₂²⋊C₄	—	47	4	no	—
477	C₂²⋊C₄	—	47	8	no	—
478	C₂²⋊C₄	C₈×D₄₇	1	8	yes	complemented
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	47	8	no	—
484	C₄²	—	47	2	no	—
485	C₄²	—	47	2	no	—
486	C₄²	—	94	1	no	—
487	C₄²	—	94	1	no	—
488	C₄²	—	94	1	no	—
489	C₄²	—	94	1	no	—
490	C₄²	—	188	2	no	—
491	C₄²	—	188	2	no	—
492	C₄²	—	188	2	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	47	2	no	—
497	C₂³	—	47	4	no	—
498	C₂³	—	94	1	no	—
499	C₂³	—	94	1	no	—
500	C₂³	—	94	2	no	—
501	C₂³	C₄²×D₄₇	1	2	yes	—
502	C₂³	C₂×C₈×D₄₇	1	4	yes	—
503	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
504	D₄	—	47	16	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	47	2	no	—
516	C₂×C₄	—	47	4	no	—
517	C₂×C₄	—	47	2	no	—
518	C₂×C₄	—	47	2	no	—
519	C₂×C₄	—	47	4	no	—
520	C₂×C₄	—	47	4	no	—
521	C₂×C₄	—	94	2	no	—
522	C₂×C₄	—	94	2	no	—
523	C₂×C₄	—	94	1	no	—
524	C₂×C₄	—	94	1	no	—
525	C₂×C₄	—	94	2	no	—
526	C₂×C₄	—	94	2	no	—
527	C₂×C₄	—	94	2	no	—
528	C₂×C₄	—	94	2	no	—
529	C₂×C₄	—	94	2	no	—
530	C₂×C₄	—	94	2	no	—
531	C₂×C₄	—	94	2	no	—
532	C₂×C₄	—	188	8	no	—
533	C₂×C₄	—	188	8	no	—
534	C₂×C₄	C₄²×D₄₇	1	2	yes	—
535	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
536	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
537	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
539	C₂×C₄	#13094069	1	1	yes	characteristic
540	C₂×C₄	#13094069	1	1	yes	characteristic
541	C₂×C₄	#13094070	1	1	yes	characteristic
542	C₂×C₄	#13094071	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	2	2	no	—
547	C₈	—	94	2	no	—
548	C₈	—	94	2	no	—
549	C₈	—	94	2	no	—
550	C₈	—	94	2	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	47	4	no	—
556	C₂²	—	94	4	no	—
557	C₂²	—	94	2	no	—
558	C₂²	—	94	2	no	—
559	C₂²	—	94	4	no	—
560	C₂²	C₄×C₈×D₄₇	1	4	yes	—
561	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
562	C₂²	#15689595	1	1	yes	characteristic
563	C₂²	#15689602	1	1	yes	characteristic
564	C₂²	C₂²×C₈×D₄₇	1	2	yes	—
565	C₂²	#15689888	1	2	yes	—
566	C₄	—	2	4	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	47	4	no	—
570	C₄	—	94	2	no	—
571	C₄	—	94	2	no	—
572	C₄	—	94	4	no	—
573	C₄	—	94	4	no	—
574	C₄	#15689595	1	1	yes	characteristic
575	C₄	#15689596	1	1	yes	characteristic
576	C₄	#15689602	1	1	yes	characteristic
577	C₄	#15689603	1	1	yes	characteristic
578	C₂	—	2	4	no	—
579	C₂	—	94	4	no	—
580	C₂	#20245747	1	1	yes	characteristic
581	C₂	C₂×C₄×C₈×D₄₇	1	1	yes	characteristic
582	C₂	#20251815	1	1	yes	characteristic
583	C₂	#20252409	1	2	yes	—
584	C₂	#20252495	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂×C₄₇	C₂²×C₄×C₈
Fitting	C₈×C₂²⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×C₂²⋊D₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	#20555
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₈×Dic₄₇⋊C₄	C₂	semidirect
5. #20243249	C₂	semidirect
6. C₄×Dic₄₇⋊C₈	C₂	semidirect
7. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
8. C₈×(C₂×D₄₇)⋊C₄	C₂	semidirect
9. #20243158	C₂	semidirect
10. C₂²⋊C₈×Dic₄₇	C₂	semidirect
11. C₄×(C₂×D₄₇)⋊C₈	C₂	semidirect
12. #20243132	C₂	semidirect
13. C₂×#15688877	C₂	semidirect
14. #336×D₄₇	C₂	semidirect
15. C₈×C₂²⋊C₄×C₄₇	C₂	semidirect
23. C₈×C₂²⋊D₄₇	C₄	semidirect
24. (C₂²⋊D₄₇)⋊C₈	C₄	semidirect
63. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
72. C₂×C₈×D₄₇	C₂×C₄	semidirect
73. C₂×C₈×D₄₇	C₂×C₄	semidirect
76. (C₂²⋊D₄₇)⋊C₄	C₈	semidirect
93. Dic₄₇⋊C₈	C₂×C₄	semidirect
94. Dic₄₇⋊C₈	C₂×C₄	semidirect
95. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
96. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
97. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
102. C₈×Dic₄₇	C₂×C₄	semidirect
103. C₈×Dic₄₇	C₂×C₄	semidirect
109. C₂²×C₈×C₄₇	C₂×C₄	semidirect
117. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
137. C₂²×Dic₄₇	C₂×C₈	semidirect
149. C₂×C₄×D₄₇	C₂×C₈	semidirect
165. C₂²⋊C₄×C₄₇	C₂×C₈	semidirect
172. (C₂×D₄₇)⋊C₄	C₂×C₈	semidirect
174. Dic₄₇⋊C₄	C₂×C₈	semidirect
182. C₄×Dic₄₇	C₂×C₈	semidirect
230. C₂²⋊D₄₇	C₄×C₈	semidirect
295. C₈×C₂²⋊C₄	D₄₇	semidirect
349. C₄₇	#20555	semidirect
370. C₂²×C₈	C₄×D₄₇	semidirect
402. C₂²⋊C₈	C₄×D₄₇	semidirect
478. C₂²⋊C₄	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₂²⋊D₄₇	2
C₂×(C₂²⋊D₄₇)⋊C₈	2
C₄×(C₂²⋊D₄₇)⋊C₄	2
C₈×Dic₄₇⋊C₄	2
#20243249	2
C₄×Dic₄₇⋊C₈	2
C₂²⋊C₄×C₄₇⋊C₈	2
C₈×(C₂×D₄₇)⋊C₄	2
#20243158	2
C₂²⋊C₈×Dic₄₇	2
C₄×(C₂×D₄₇)⋊C₈	2
#20243132	2
C₂×#15688877	2
#336×D₄₇	2
C₈×C₂²⋊C₄×C₄₇	2
#20555	47