Subgroups — #26237161

Order 12032.

980 conjugacy classes of subgroups.

The subgroup lattice has 688 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×#15689176	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094007	C₂	1	1	yes	maximal, characteristic
4	#20244105	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243995	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243992	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243948	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243943	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243680	C₂	1	1	yes	maximal, characteristic
10	#20243567	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243566	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243158	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
17	C₂×#13094007	C₄	1	1	yes	characteristic
18	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
19	C₈×C₂²⋊D₄₇	—	2	4	no	—
20	#15689176	—	2	4	no	—
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₄₇⋊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×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₄₇⋊C₈	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	#15689014	C₄	1	1	yes	characteristic
37	#15689014	C₄	1	1	yes	characteristic
38	#15689007	C₄	1	1	yes	characteristic
39	#15689007	C₄	1	1	yes	characteristic
40	#15689002	C₄	1	1	yes	characteristic
41	#15688996	C₄	1	1	yes	characteristic
42	#15688986	C₄	1	1	yes	characteristic
43	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
63	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	C₂×C₈×D₄₇	—	2	2	no	—
68	C₂×C₈×D₄₇	—	2	2	no	—
69	C₂×C₈×D₄₇	—	4	1	no	—
70	#13094007	C₈	1	8	yes	complemented
71	C₄×C₂²⋊D₄₇	—	2	2	no	—
72	C₄×C₂²⋊D₄₇	—	2	2	no	—
73	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
90	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
91	Dic₄₇⋊C₈	—	2	2	no	—
92	Dic₄₇⋊C₈	—	2	2	no	—
93	Dic₄₇⋊C₈	—	4	1	no	—
94	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
95	C₂²⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
96	(C₂×D₄₇)⋊C₈	—	2	2	no	—
97	(C₂×D₄₇)⋊C₈	—	2	2	no	—
98	(C₂×D₄₇)⋊C₈	—	4	1	no	—
99	C₄×C₄₇⋊C₈	—	2	2	no	—
100	C₄×C₄₇⋊C₈	—	2	2	no	—
101	C₈×Dic₄₇	—	2	2	no	—
102	C₈×Dic₄₇	—	2	2	no	—
103	C₈×Dic₄₇	—	4	1	no	—
104	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
116	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₇	—	2	2	no	—
118	C₂²×C₈×C₄₇	—	2	2	no	—
119	C₂²×C₈×C₄₇	—	2	2	no	—
120	C₂²×C₈×C₄₇	—	2	2	no	—
121	C₂²×C₈×C₄₇	—	4	1	no	—
122	C₂²×C₈×C₄₇	—	4	1	no	—
123	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	—	2	2	no	—
128	C₂×C₄²×C₄₇	—	2	2	no	—
129	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
133	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	—	2	1	no	—
140	C₂²×C₄×C₄₇	—	2	1	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	2	2	no	—
143	C₂²×C₄×C₄₇	—	4	1	no	—
144	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	complemented
145	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₄₇	#41	1	2	yes	—
152	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
153	C₂×C₂²⋊D₄₇	—	2	2	no	—
154	C₂×C₂²⋊D₄₇	—	2	2	no	—
155	C₂×C₂²⋊D₄₇	C₂×C₈	1	4	yes	—
156	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₄₇	—	2	1	no	—
164	C₂×C₄×D₄₇	—	2	1	no	—
165	C₂×C₄×D₄₇	—	2	1	no	—
166	C₂×C₄×D₄₇	—	2	1	no	—
167	C₂×C₄×D₄₇	—	2	1	no	—
168	C₂×C₄×D₄₇	—	2	1	no	—
169	C₂×C₈×C₄₇	—	2	1	no	—
170	C₂×C₈×C₄₇	—	2	1	no	—
171	C₂×C₈×C₄₇	—	2	1	no	—
172	C₂×C₈×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	1	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	2	1	no	—
179	C₂×C₈×C₄₇	—	4	4	no	—
180	C₂×C₈×C₄₇	—	4	4	no	—
181	C₂×C₈×C₄₇	#41	1	2	yes	—
182	C₂×C₈×C₄₇	#41	1	2	yes	—
183	C₄²×C₄₇	—	2	2	no	—
184	C₄²×C₄₇	—	2	2	no	—
185	C₄²×C₄₇	—	2	1	no	—
186	C₄²×C₄₇	—	2	1	no	—
187	C₄²×C₄₇	—	2	1	no	—
188	C₄²×C₄₇	—	2	1	no	—
189	C₂²⋊Dic₄₇	—	2	2	no	—
190	C₂²⋊Dic₄₇	—	2	2	no	—
191	C₂²⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
192	(C₂×D₄₇)⋊C₄	—	2	2	no	—
193	(C₂×D₄₇)⋊C₄	—	2	2	no	—
194	(C₂×D₄₇)⋊C₄	—	4	1	no	—
195	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	complemented
196	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	complemented
197	Dic₄₇⋊C₄	—	2	2	no	—
198	Dic₄₇⋊C₄	—	2	2	no	—
199	Dic₄₇⋊C₄	—	4	1	no	—
200	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
201	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
202	C₄×Dic₄₇	—	2	1	no	—
203	C₄×Dic₄₇	—	2	1	no	—
204	C₄×Dic₄₇	—	2	1	no	—
205	C₄×Dic₄₇	—	2	1	no	—
206	C₄×Dic₄₇	—	2	1	no	—
207	C₄×Dic₄₇	—	2	1	no	—
208	C₂×C₄₇⋊C₈	—	2	1	no	—
209	C₂×C₄₇⋊C₈	—	2	1	no	—
210	C₂×C₄₇⋊C₈	—	2	1	no	—
211	C₂×C₄₇⋊C₈	—	2	1	no	—
212	C₂×C₄₇⋊C₈	—	2	1	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	1	no	—
215	C₂×C₄₇⋊C₈	—	2	1	no	—
216	C₂×C₄₇⋊C₈	—	2	1	no	—
217	C₂×C₄₇⋊C₈	—	2	1	no	—
218	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
219	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
220	C₈×D₄₇	—	4	4	no	—
221	C₂³×C₄₇	—	2	1	no	—
222	C₂³×C₄₇	—	2	1	no	—
223	C₂³×C₄₇	—	2	1	no	—
224	C₂³×C₄₇	—	2	1	no	—
225	C₂³×C₄₇	C₄×D₄	1	2	yes	—
226	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
227	C₂³×C₄₇	#131	1	2	yes	—
228	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
229	C₂²×D₄₇	—	2	1	no	—
230	C₂²×D₄₇	—	2	1	no	—
231	C₂²×D₄₇	—	2	1	no	—
232	C₂²×D₄₇	—	2	1	no	—
233	C₂²×D₄₇	—	2	1	no	—
234	C₂²×D₄₇	—	2	1	no	—
235	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	—	2	1	no	—
240	C₂×C₄×C₄₇	—	2	1	no	—
241	C₂×C₄×C₄₇	—	2	1	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	8	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	2	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	2	1	no	—
250	C₂×C₄×C₄₇	—	2	1	no	—
251	C₂×C₄×C₄₇	—	2	1	no	—
252	C₂×C₄×C₄₇	—	4	4	no	—
253	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
255	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
256	C₂×C₄×C₄₇	#131	1	2	yes	—
257	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
263	C₂²⋊D₄₇	—	2	8	no	—
264	C₂×Dic₄₇	—	2	1	no	—
265	C₂×Dic₄₇	—	2	1	no	—
266	C₂×Dic₄₇	—	2	1	no	—
267	C₂×Dic₄₇	—	2	1	no	—
268	C₂×Dic₄₇	—	2	1	no	—
269	C₂×Dic₄₇	—	2	1	no	—
270	C₂×Dic₄₇	—	2	1	no	—
271	C₂×Dic₄₇	—	2	1	no	—
272	C₂×Dic₄₇	—	2	1	no	—
273	C₂×Dic₄₇	—	2	1	no	—
274	C₂×Dic₄₇	—	2	1	no	—
275	C₂×Dic₄₇	—	2	1	no	—
276	C₂×Dic₄₇	—	2	1	no	—
277	C₂×Dic₄₇	—	2	1	no	—
278	C₂×Dic₄₇	—	2	1	no	—
279	C₂×Dic₄₇	—	2	1	no	—
280	C₂×Dic₄₇	—	2	1	no	—
281	C₂×Dic₄₇	—	2	1	no	—
282	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
283	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
284	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
285	C₄×D₄₇	—	4	1	no	—
286	C₄×D₄₇	—	4	1	no	—
287	C₄×D₄₇	—	4	1	no	—
288	C₄×D₄₇	—	4	1	no	—
289	C₈×C₄₇	—	2	2	no	—
290	C₈×C₄₇	—	2	2	no	—
291	C₈×C₄₇	—	4	1	no	—
292	C₈×C₄₇	—	4	1	no	—
293	C₄₇⋊C₈	—	2	2	no	—
294	C₄₇⋊C₈	—	2	2	no	—
295	C₄₇⋊C₈	—	4	1	no	—
296	C₄₇⋊C₈	—	4	1	no	—
297	#22900	—	47	1	no	maximal, Sylow
298	C₂²×C₄₇	—	2	2	no	—
299	C₂²×C₄₇	—	2	2	no	—
300	C₂²×C₄₇	—	2	2	no	—
301	C₂²×C₄₇	—	2	2	no	—
302	C₂²×C₄₇	—	2	2	no	—
303	C₂²×C₄₇	—	2	2	no	—
304	C₂²×C₄₇	C₈×D₄	1	4	yes	—
305	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
306	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
307	C₂²×C₄₇	#520	1	1	yes	characteristic
308	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
309	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
310	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
311	C₂²×C₄₇	#568	1	1	yes	characteristic
312	C₂×D₄₇	—	2	2	no	—
313	C₂×D₄₇	—	2	2	no	—
314	C₂×D₄₇	—	2	2	no	—
315	C₂×D₄₇	—	4	1	no	—
316	C₂×D₄₇	—	4	1	no	—
317	C₂×D₄₇	—	4	1	no	—
318	C₂×D₄₇	—	4	1	no	—
319	C₄×C₄₇	—	2	2	no	—
320	C₄×C₄₇	—	2	2	no	—
321	C₄×C₄₇	—	2	2	no	—
322	C₄×C₄₇	—	2	2	no	—
323	C₄×C₄₇	—	4	1	no	—
324	C₄×C₄₇	#546	1	1	yes	characteristic
325	C₄×C₄₇	#547	1	1	yes	characteristic
326	C₄×C₄₇	#551	1	1	yes	characteristic
327	C₄×C₄₇	#552	1	1	yes	characteristic
328	Dic₄₇	—	2	2	no	—
329	Dic₄₇	—	2	2	no	—
330	Dic₄₇	—	2	2	no	—
331	Dic₄₇	—	4	1	no	—
332	Dic₄₇	—	4	1	no	—
333	Dic₄₇	—	4	1	no	—
334	Dic₄₇	—	4	1	no	—
335	C₂×C₈×D₄	—	47	1	no	—
336	C₂×#431	—	47	1	no	—
337	C₄×#123	—	47	1	no	—
338	#1939	—	47	1	no	—
339	#1923	—	47	1	no	—
340	#1923	—	47	1	no	—
341	#1916	—	47	1	no	—
342	#1916	—	47	1	no	—
343	#1869	—	47	1	no	—
344	#1850	—	47	1	no	—
345	#1850	—	47	1	no	—
346	C₈×C₄⋊C₄	—	47	1	no	—
347	C₈×C₂²⋊C₄	—	47	1	no	—
348	C₈×C₂²⋊C₄	—	47	1	no	—
349	C₂×#336	D₄₇	1	1	yes	characteristic, complemented
350	C₂×C₄₇	—	2	4	no	—
351	C₂×C₄₇	#2359	1	1	yes	characteristic
352	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
353	C₂×C₄₇	#2933	1	1	yes	characteristic
354	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
355	C₂×C₄₇	#2968	1	1	yes	characteristic
356	C₂×C₄₇	#2988	1	1	yes	characteristic
357	C₂×C₄₇	#2994	1	1	yes	characteristic
358	D₄₇	—	4	2	no	—
359	C₂³×C₈	—	47	1	no	—
360	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
361	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
362	C₂×#123	—	47	1	no	—
363	C₂×C₄×D₄	—	47	1	no	—
364	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
365	C₈×D₄	—	94	4	no	—
366	#431	—	94	4	no	—
367	C₂×C₄⋊C₈	—	47	1	no	—
368	C₂×C₄⋊C₈	—	47	1	no	—
369	C₂×C₄⋊C₈	—	47	1	no	—
370	C₂×C₄⋊C₈	—	47	1	no	—
371	C₂×C₄⋊C₈	—	47	1	no	—
372	C₂×C₂²⋊C₈	—	47	1	no	—
373	C₂×C₂²⋊C₈	—	47	1	no	—
374	C₂×C₂²⋊C₈	—	47	1	no	—
375	C₂×C₂²⋊C₈	—	47	1	no	—
376	C₂×C₂²⋊C₈	—	47	1	no	—
377	C₂×C₄×C₈	—	47	1	no	—
378	C₂×C₄×C₈	—	47	1	no	—
379	C₂×C₄×C₈	—	47	1	no	—
380	C₂×C₄×C₈	—	47	1	no	—
381	C₂×C₄×C₈	—	47	1	no	—
382	#388	—	47	1	no	—
383	#388	—	47	1	no	—
384	#387	—	47	1	no	—
385	#387	—	47	1	no	—
386	#386	—	47	1	no	—
387	#385	—	47	1	no	—
388	#381	—	47	1	no	—
389	C₄×C₄⋊C₄	—	47	1	no	—
390	C₄×C₄⋊C₄	—	47	1	no	—
391	C₄×C₂²⋊C₄	—	47	1	no	—
392	C₄×C₂²⋊C₄	—	47	1	no	—
393	C₄×C₂²⋊C₄	—	47	1	no	—
394	#336	—	47	1	no	—
395	#336	—	47	1	no	—
396	#336	—	47	1	no	—
397	#336	—	47	1	no	—
398	#336	—	47	1	no	—
399	#336	—	47	1	no	—
400	#336	C₂×D₄₇	1	1	yes	characteristic
401	#336	C₂×D₄₇	1	1	yes	characteristic
402	#336	C₂×D₄₇	1	1	yes	characteristic
403	#336	C₂×D₄₇	1	1	yes	characteristic
404	C₄₇	#22900	1	1	yes	characteristic, complemented, Sylow
405	C₂²×D₄	—	47	1	no	—
406	C₂³×C₄	—	47	1	no	—
407	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
408	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
409	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
410	C₂²×C₈	—	2	2	no	—
411	C₂²×C₈	—	2	2	no	—
412	C₂²×C₈	—	2	2	no	—
413	C₂²×C₈	—	2	2	no	—
414	C₂²×C₈	—	4	1	no	—
415	C₂²×C₈	—	4	1	no	—
416	C₂²×C₈	—	47	1	no	—
417	C₂²×C₈	—	47	1	no	—
418	C₂²×C₈	—	47	1	no	—
419	C₂²×C₈	—	47	1	no	—
420	C₂²×C₈	—	94	2	no	—
421	C₂²×C₈	—	94	2	no	—
422	C₂²×C₈	—	188	1	no	—
423	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
424	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
425	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
426	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
427	#123	—	47	8	no	—
428	C₄×D₄	—	94	2	no	—
429	C₄×D₄	—	94	2	no	—
430	C₂×C₄⋊C₄	—	47	1	no	—
431	C₂×C₄⋊C₄	—	47	1	no	—
432	C₂×C₄⋊C₄	—	47	1	no	—
433	C₂×C₄⋊C₄	—	47	1	no	—
434	C₂×C₄⋊C₄	—	47	1	no	—
435	C₂×C₂²⋊C₄	—	47	1	no	—
436	C₂×C₂²⋊C₄	—	47	1	no	—
437	C₂×C₂²⋊C₄	—	47	1	no	—
438	C₂×C₂²⋊C₄	—	47	1	no	—
439	C₂×C₂²⋊C₄	—	47	1	no	—
440	C₂×C₂²⋊C₄	—	47	1	no	—
441	C₂×C₂²⋊C₄	—	47	1	no	—
442	C₂×C₂²⋊C₄	—	47	1	no	—
443	C₂×C₄²	—	2	2	no	—
444	C₂×C₄²	—	2	2	no	—
445	C₂×C₄²	—	47	1	no	—
446	C₂×C₄²	—	47	1	no	—
447	C₂×C₄²	—	47	1	no	—
448	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
449	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
450	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
451	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
452	C₄⋊C₈	—	94	2	no	—
453	C₄⋊C₈	—	94	2	no	—
454	C₄⋊C₈	—	94	2	no	—
455	C₄⋊C₈	—	94	2	no	—
456	C₄⋊C₈	—	188	1	no	—
457	C₂²⋊C₈	—	47	4	no	—
458	C₂²⋊C₈	—	94	2	no	—
459	C₂²⋊C₈	—	94	2	no	—
460	C₂²⋊C₈	—	94	2	no	—
461	C₂²⋊C₈	—	188	1	no	—
462	C₄×C₈	—	94	2	no	—
463	C₄×C₈	—	94	2	no	—
464	C₄×C₈	—	94	2	no	—
465	C₄×C₈	—	94	2	no	—
466	C₄×C₈	—	188	1	no	—
467	#95	—	47	1	no	—
468	#95	—	47	1	no	—
469	#95	—	47	1	no	—
470	#95	—	47	1	no	—
471	#95	—	47	1	no	—
472	#95	—	47	1	no	—
473	#95	—	47	1	no	—
474	#95	—	47	1	no	—
475	#95	—	47	1	no	—
476	#95	—	47	1	no	—
477	C₂⁴	—	47	1	no	—
478	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
479	C₂×D₄	—	47	4	no	—
480	C₂×D₄	—	94	2	no	—
481	C₂×D₄	—	94	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	—	47	1	no	—
492	C₂²×C₄	—	47	1	no	—
493	C₂²×C₄	—	47	1	no	—
494	C₂²×C₄	—	47	1	no	—
495	C₂²×C₄	—	47	1	no	—
496	C₂²×C₄	—	47	1	no	—
497	C₂²×C₄	—	47	1	no	—
498	C₂²×C₄	—	94	1	no	—
499	C₂²×C₄	—	94	1	no	—
500	C₂²×C₄	—	94	1	no	—
501	C₂²×C₄	—	94	1	no	—
502	C₂²×C₄	—	94	1	no	—
503	C₂²×C₄	—	94	1	no	—
504	C₂²×C₄	C₈×D₄₇	1	4	yes	complemented
505	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
508	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
509	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
510	C₂²×C₄	D₄×D₄₇	1	2	yes	—
511	C₂²×C₄	#10625352	1	2	yes	—
512	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	4	4	no	—
524	C₂×C₈	—	4	4	no	—
525	C₂×C₈	—	47	2	no	—
526	C₂×C₈	—	47	2	no	—
527	C₂×C₈	—	94	1	no	—
528	C₂×C₈	—	94	1	no	—
529	C₂×C₈	—	94	1	no	—
530	C₂×C₈	—	94	1	no	—
531	C₂×C₈	—	94	1	no	—
532	C₂×C₈	—	94	1	no	—
533	C₂×C₈	—	94	1	no	—
534	C₂×C₈	—	94	1	no	—
535	C₂×C₈	—	94	1	no	—
536	C₂×C₈	—	94	1	no	—
537	C₂×C₈	—	188	4	no	—
538	C₂×C₈	#10625350	1	2	yes	—
539	C₂×C₈	#10625350	1	2	yes	—
540	C₄⋊C₄	—	47	4	no	—
541	C₄⋊C₄	—	47	4	no	—
542	C₄⋊C₄	—	94	2	no	—
543	C₄⋊C₄	—	94	2	no	—
544	C₄⋊C₄	—	188	1	no	—
545	C₂²⋊C₄	—	47	4	no	—
546	C₂²⋊C₄	—	47	4	no	—
547	C₂²⋊C₄	—	47	4	no	—
548	C₂²⋊C₄	—	94	2	no	—
549	C₂²⋊C₄	—	94	2	no	—
550	C₂²⋊C₄	—	94	2	no	—
551	C₂²⋊C₄	—	94	2	no	—
552	C₂²⋊C₄	—	188	1	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	94	1	no	—
560	C₄²	—	94	1	no	—
561	C₄²	—	94	1	no	—
562	C₄²	—	94	1	no	—
563	C₄²	—	94	1	no	—
564	C₄²	—	94	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	47	2	no	—
570	C₂³	—	94	1	no	—
571	C₂³	—	94	1	no	—
572	C₂³	—	94	1	no	—
573	C₂³	—	94	1	no	—
574	C₂³	—	94	1	no	—
575	C₂³	—	94	1	no	—
576	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
577	C₂³	C₂×C₈×D₄₇	1	2	yes	—
578	C₂³	#13094032	1	2	yes	—
579	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
580	D₄	—	94	8	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	47	2	no	—
599	C₂×C₄	—	47	2	no	—
600	C₂×C₄	—	47	2	no	—
601	C₂×C₄	—	94	1	no	—
602	C₂×C₄	—	94	1	no	—
603	C₂×C₄	—	94	1	no	—
604	C₂×C₄	—	94	1	no	—
605	C₂×C₄	—	94	1	no	—
606	C₂×C₄	—	94	1	no	—
607	C₂×C₄	—	94	1	no	—
608	C₂×C₄	—	94	1	no	—
609	C₂×C₄	—	94	1	no	—
610	C₂×C₄	—	94	1	no	—
611	C₂×C₄	—	94	1	no	—
612	C₂×C₄	—	94	1	no	—
613	C₂×C₄	—	94	1	no	—
614	C₂×C₄	—	94	1	no	—
615	C₂×C₄	—	94	1	no	—
616	C₂×C₄	—	94	1	no	—
617	C₂×C₄	—	94	1	no	—
618	C₂×C₄	—	94	1	no	—
619	C₂×C₄	—	188	1	no	—
620	C₂×C₄	—	188	1	no	—
621	C₂×C₄	—	188	1	no	—
622	C₂×C₄	—	188	1	no	—
623	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
624	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
625	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
626	C₂×C₄	#13094030	1	2	yes	—
627	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
628	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
629	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
630	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
631	C₂×C₄	#13094069	1	1	yes	characteristic
632	C₂×C₄	#13094072	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	2	2	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₈	—	94	2	no	—
638	C₈	—	94	2	no	—
639	C₈	—	188	1	no	—
640	C₈	—	188	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	94	2	no	—
648	C₂²	—	94	2	no	—
649	C₂²	—	94	2	no	—
650	C₂²	—	188	1	no	—
651	C₂²	—	188	1	no	—
652	C₂²	—	188	1	no	—
653	C₂²	—	188	1	no	—
654	C₂²	(C₂²⋊D₄₇)⋊C₈	1	4	yes	—
655	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
656	C₂²	C₄×#10625350	1	1	yes	characteristic
657	C₂²	#15689604	1	1	yes	characteristic
658	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
659	C₂²	C₂×#13094030	1	1	yes	characteristic
660	C₂²	C₂×#13094032	1	1	yes	characteristic
661	C₂²	#15689889	1	1	yes	characteristic
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	94	2	no	—
668	C₄	—	94	2	no	—
669	C₄	—	94	2	no	—
670	C₄	—	188	1	no	—
671	C₄	—	188	1	no	—
672	C₄	—	188	1	no	—
673	C₄	—	188	1	no	—
674	C₄	#15689763	1	1	yes	characteristic
675	C₄	#15689774	1	1	yes	characteristic
676	C₄	#15689799	1	1	yes	characteristic
677	C₄	#15689808	1	1	yes	characteristic
678	C₂	—	2	4	no	—
679	C₂	—	188	2	no	—
680	C₂	#20246376	1	1	yes	characteristic
681	C₂	C₂×(C₂²⋊D₄₇)⋊C₈	1	1	yes	characteristic
682	C₂	#20252109	1	1	yes	characteristic
683	C₂	C₈×#10625350	1	1	yes	characteristic
684	C₂	#20252382	1	1	yes	characteristic
685	C₂	#20252497	1	1	yes	characteristic
686	C₂	#20252544	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₂×C₄₇×#336	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×C₂²⋊D₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#22900
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
2. C₂×#15689176	C₂	semidirect
4. #20244105	C₂	semidirect
5. #20243995	C₂	semidirect
6. #20243992	C₂	semidirect
7. #20243948	C₂	semidirect
8. #20243943	C₂	semidirect
10. #20243567	C₂	semidirect
11. #20243566	C₂	semidirect
12. #20243249	C₂	semidirect
13. C₈×C₂²⋊Dic₄₇	C₂	semidirect
14. #20243158	C₂	semidirect
15. C₂×C₄₇×#336	C₂	semidirect
70. #13094007	C₈	semidirect
144. C₂²×C₄×C₄₇	C₂×C₈	semidirect
191. C₂²⋊Dic₄₇	C₂×C₈	semidirect
195. (C₂×D₄₇)⋊C₄	C₂×C₈	semidirect
196. (C₂×D₄₇)⋊C₄	C₂×C₈	semidirect
200. Dic₄₇⋊C₄	C₂×C₈	semidirect
201. Dic₄₇⋊C₄	C₂×C₈	semidirect
349. C₂×#336	D₄₇	semidirect
404. C₄₇	#22900	semidirect
504. 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×#15689176	2
C₄×#13094007	2
#20244105	2
#20243995	2
#20243992	2
#20243948	2
#20243943	2
#20243680	2
#20243567	2
#20243566	2
#20243249	2
C₈×C₂²⋊Dic₄₇	2
#20243158	2
C₂×C₄₇×#336	2
#22900	47