Subgroups — #26223236

Order 12032.

1034 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×#15689188	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094009	C₂	1	1	yes	maximal, characteristic
4	#20243995	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243994	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243942	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243679	C₂	1	1	yes	maximal, characteristic
8	#20243567	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243455	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243249	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243158	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243158	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243158	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₄₇	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×#13094009	C₄	1	1	yes	characteristic
20	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
21	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
22	#15689188	—	2	4	no	—
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊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×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	C₄×C₈×D₄₇	—	2	4	no	—
37	#15689013	C₄	1	1	yes	characteristic
38	#15689012	C₄	1	1	yes	characteristic
39	#15689010	C₄	1	1	yes	characteristic
40	#15689009	C₄	1	1	yes	characteristic
41	#15689001	C₄	1	1	yes	characteristic
42	#15688994	C₄	1	1	yes	characteristic
43	#15688985	C₄	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×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
48	#15688878	C₂²	1	1	yes	characteristic
49	#15688878	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	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×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×D₁₈₈	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
65	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₄₇	—	2	2	no	—
71	C₂×C₈×D₄₇	—	2	2	no	—
72	C₂×C₈×D₄₇	—	2	2	no	—
73	C₂×C₈×D₄₇	—	2	2	no	—
74	C₂×C₈×D₄₇	—	2	2	no	—
75	C₂×C₈×D₄₇	—	2	2	no	—
76	C₂×C₈×D₄₇	—	2	2	no	—
77	C₂×C₈×D₄₇	—	2	2	no	—
78	C₂×C₈×D₄₇	D₄	1	4	yes	—
79	#13094009	C₈	1	8	yes	complemented
80	C₄×D₁₈₈	—	2	2	no	—
81	C₄×D₁₈₈	—	2	2	no	—
82	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
97	C₄²×D₄₇	—	2	2	no	—
98	C₄²×D₄₇	—	2	2	no	—
99	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
100	Dic₄₇⋊C₈	—	2	2	no	—
101	(C₂×D₄₇)⋊C₈	—	2	2	no	—
102	(C₂×D₄₇)⋊C₈	—	2	2	no	—
103	(C₂×D₄₇)⋊C₈	—	2	2	no	—
104	(C₂×D₄₇)⋊C₈	—	2	2	no	—
105	(C₂×D₄₇)⋊C₈	—	2	2	no	—
106	C₄×C₄₇⋊C₈	—	2	2	no	—
107	C₄×C₄₇⋊C₈	—	2	2	no	—
108	C₄×C₄₇⋊C₈	—	2	2	no	—
109	C₈×Dic₄₇	—	2	2	no	—
110	C₈×Dic₄₇	—	2	2	no	—
111	C₈×Dic₄₇	—	2	2	no	—
112	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
115	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
116	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
117	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
118	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
119	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
120	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₄₇	—	2	2	no	—
130	C₄×C₈×C₄₇	—	2	2	no	—
131	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
132	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
133	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₁₈₈	—	2	2	no	—
149	C₂×D₁₈₈	—	2	2	no	—
150	C₂×D₁₈₈	C₂×C₈	1	4	yes	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×C₄×D₄₇	—	2	2	no	—
153	C₂×C₄×D₄₇	—	2	2	no	—
154	C₂×C₄×D₄₇	—	2	2	no	—
155	C₂×C₄×D₄₇	—	2	1	no	—
156	C₂×C₄×D₄₇	—	2	1	no	—
157	C₂×C₄×D₄₇	—	2	1	no	—
158	C₂×C₄×D₄₇	—	2	1	no	—
159	C₂×C₄×D₄₇	—	2	2	no	—
160	C₂×C₄×D₄₇	—	2	1	no	—
161	C₂×C₄×D₄₇	—	2	1	no	—
162	C₂×C₄×D₄₇	—	2	1	no	—
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	C₂×C₈	1	4	yes	complemented
167	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
168	C₂×C₄×D₄₇	#41	1	2	yes	—
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	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₄₇	#41	1	2	yes	—
181	C₄⋊C₄×C₄₇	—	2	2	no	—
182	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
183	C₄²×C₄₇	—	2	1	no	—
184	C₄²×C₄₇	—	2	1	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	(C₂×D₄₇)⋊C₄	—	2	2	no	—
190	(C₂×D₄₇)⋊C₄	—	2	2	no	—
191	(C₂×D₄₇)⋊C₄	—	2	2	no	—
192	(C₂×D₄₇)⋊C₄	—	2	2	no	—
193	(C₂×D₄₇)⋊C₄	—	2	2	no	—
194	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	complemented
195	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	complemented
196	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	complemented
197	C₄⋊Dic₄₇	—	2	2	no	—
198	Dic₄₇⋊C₄	—	2	2	no	—
199	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
200	C₄×Dic₄₇	—	2	1	no	—
201	C₄×Dic₄₇	—	2	1	no	—
202	C₄×Dic₄₇	—	2	1	no	—
203	C₄×Dic₄₇	—	2	1	no	—
204	C₄×Dic₄₇	—	2	2	no	—
205	C₄×Dic₄₇	—	2	2	no	—
206	C₂×C₄₇⋊C₈	—	2	1	no	—
207	C₂×C₄₇⋊C₈	—	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	C₂×D₄	1	2	yes	—
215	C₂×C₄₇⋊C₈	#41	1	2	yes	—
216	C₂×C₄₇⋊C₈	#41	1	2	yes	—
217	C₂×C₄₇⋊C₈	#41	1	2	yes	—
218	C₈×D₄₇	—	2	8	no	—
219	C₈×D₄₇	—	2	8	no	—
220	C₈×D₄₇	—	4	4	no	—
221	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
222	C₂²×D₄₇	—	2	1	no	—
223	C₂²×D₄₇	—	2	1	no	—
224	C₂²×D₄₇	—	2	1	no	—
225	C₂²×D₄₇	—	2	1	no	—
226	C₂²×D₄₇	—	2	1	no	—
227	C₂²×D₄₇	—	2	1	no	—
228	C₂²×D₄₇	—	2	1	no	—
229	C₂²×D₄₇	—	2	1	no	—
230	C₂²×D₄₇	—	2	1	no	—
231	C₂²×D₄₇	—	2	1	no	—
232	C₂²×D₄₇	C₄×D₄	1	2	yes	—
233	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
234	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
235	C₂²×D₄₇	#131	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	1	no	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	—	2	1	no	—
247	C₂×C₄×C₄₇	—	2	1	no	—
248	C₂×C₄×C₄₇	—	2	1	no	—
249	C₂×C₄×C₄₇	—	2	1	no	—
250	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
251	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
252	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
253	C₂×C₄×C₄₇	#131	1	2	yes	—
254	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂×#41	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×Dic₄₇	—	2	1	no	—
261	C₂×Dic₄₇	—	2	1	no	—
262	C₂×Dic₄₇	—	2	1	no	—
263	C₂×Dic₄₇	—	2	1	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	C₄×D₄	1	2	yes	—
275	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
276	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
277	C₂×Dic₄₇	#131	1	2	yes	—
278	D₁₈₈	—	2	8	no	—
279	C₄×D₄₇	—	2	8	no	—
280	C₄×D₄₇	—	2	8	no	—
281	C₄×D₄₇	—	2	2	no	—
282	C₄×D₄₇	—	2	2	no	—
283	C₄×D₄₇	—	2	2	no	—
284	C₄×D₄₇	—	2	2	no	—
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	—	4	1	no	—
295	C₄₇⋊C₈	—	4	1	no	—
296	C₄₇⋊C₈	#123	1	4	yes	complemented
297	C₈×#123	—	47	1	no	maximal, Sylow
298	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
300	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
301	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
302	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
303	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
304	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
305	C₂×D₄₇	—	2	2	no	—
306	C₂×D₄₇	—	2	2	no	—
307	C₂×D₄₇	—	2	2	no	—
308	C₂×D₄₇	—	2	2	no	—
309	C₂×D₄₇	—	2	2	no	—
310	C₂×D₄₇	—	2	2	no	—
311	C₂×D₄₇	—	2	2	no	—
312	C₂×D₄₇	—	2	2	no	—
313	C₂×D₄₇	—	2	2	no	—
314	C₂×D₄₇	—	4	1	no	—
315	C₂×D₄₇	—	4	1	no	—
316	C₂×D₄₇	—	4	1	no	—
317	C₂×D₄₇	—	4	1	no	—
318	C₂×D₄₇	C₈×D₄	1	4	yes	—
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	—	4	1	no	—
325	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
326	C₄×C₄₇	#525	1	1	yes	characteristic
327	C₄×C₄₇	#529	1	1	yes	characteristic
328	C₄×C₄₇	#529	1	1	yes	characteristic
329	Dic₄₇	—	2	2	no	—
330	Dic₄₇	—	2	2	no	—
331	Dic₄₇	—	2	2	no	—
332	Dic₄₇	—	2	2	no	—
333	Dic₄₇	—	4	1	no	—
334	Dic₄₇	—	4	1	no	—
335	C₂×C₈×D₄	—	47	1	no	—
336	C₂²×C₄×C₈	—	47	1	no	—
337	C₄×#123	—	47	1	no	—
338	#1923	—	47	1	no	—
339	#1923	—	47	1	no	—
340	#1916	—	47	1	no	—
341	#1916	D₄₇	1	1	yes	characteristic, complemented
342	#1869	—	47	1	no	—
343	#1850	—	47	1	no	—
344	#1817	—	47	1	no	—
345	C₈×C₄⋊C₄	—	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	C₈×C₂²⋊C₄	—	47	1	no	—
350	C₂×C₄₇	C₄×#123	1	1	yes	characteristic
351	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
352	C₂×C₄₇	#2929	1	1	yes	characteristic
353	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
354	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
355	C₂×C₄₇	#2966	1	1	yes	characteristic
356	C₂×C₄₇	#2966	1	1	yes	characteristic
357	D₄₇	—	2	4	no	—
358	D₄₇	—	4	2	no	—
359	C₂³×C₈	—	47	1	no	—
360	C₂³×C₈	—	47	1	no	—
361	C₂³×C₈	—	47	1	no	—
362	C₂×#123	—	47	1	no	—
363	C₂×C₄×D₄	—	47	1	no	—
364	C₂²×C₄²	—	47	1	no	—
365	C₈×D₄	—	94	4	no	—
366	C₂×C₄⋊C₈	—	47	1	no	—
367	C₂×C₄⋊C₈	—	47	1	no	—
368	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	—	47	1	no	—
370	C₂×C₂²⋊C₈	—	47	1	no	—
371	C₂×C₂²⋊C₈	—	47	1	no	—
372	C₂×C₂²⋊C₈	—	47	1	no	—
373	C₂×C₂²⋊C₈	—	47	1	no	—
374	C₂×C₄×C₈	—	47	1	no	—
375	C₂×C₄×C₈	—	47	1	no	—
376	C₂×C₄×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	—	94	4	no	—
381	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
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	C₂×D₄₇	1	1	yes	characteristic
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	C₈×#123	1	1	yes	characteristic, complemented, Sylow
405	C₂²×D₄	—	47	1	no	—
406	C₂³×C₄	—	47	1	no	—
407	C₂³×C₄	—	47	1	no	—
408	C₂³×C₄	—	47	1	no	—
409	C₂³×C₄	—	47	1	no	—
410	C₂²×C₈	—	47	1	no	—
411	C₂²×C₈	—	47	1	no	—
412	C₂²×C₈	—	47	4	no	—
413	C₂²×C₈	—	47	1	no	—
414	C₂²×C₈	—	47	1	no	—
415	C₂²×C₈	—	94	2	no	—
416	C₂²×C₈	—	94	2	no	—
417	C₂²×C₈	—	94	2	no	—
418	C₂²×C₈	—	94	2	no	—
419	C₂²×C₈	—	94	2	no	—
420	C₂²×C₈	—	94	2	no	—
421	C₂²×C₈	—	94	2	no	—
422	C₂²×C₈	—	94	2	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	C₄×D₄₇	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
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	—	47	1	no	—
444	C₂×C₄²	—	47	1	no	—
445	C₂×C₄²	—	47	1	no	—
446	C₂×C₄²	—	47	1	no	—
447	C₂×C₄²	—	94	2	no	—
448	C₂×C₄²	—	94	2	no	—
449	C₂×C₄²	C₂²×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	—	2	2	no	—
453	C₄⋊C₈	—	94	2	no	—
454	C₄⋊C₈	—	94	2	no	—
455	C₂²⋊C₈	—	94	2	no	—
456	C₂²⋊C₈	—	94	2	no	—
457	C₂²⋊C₈	—	94	2	no	—
458	C₂²⋊C₈	—	94	2	no	—
459	C₂²⋊C₈	—	94	2	no	—
460	C₄×C₈	—	2	2	no	—
461	C₄×C₈	—	94	2	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	—	94	2	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	C₄×D₄₇	1	1	yes	characteristic
476	#95	C₄×D₄₇	1	1	yes	characteristic
477	C₂⁴	—	47	1	no	—
478	C₂⁴	—	47	1	no	—
479	C₂×D₄	—	47	4	no	—
480	C₂×D₄	—	94	2	no	—
481	C₂×D₄	—	94	2	no	—
482	C₂²×C₄	—	47	1	no	—
483	C₂²×C₄	—	47	1	no	—
484	C₂²×C₄	—	47	1	no	—
485	C₂²×C₄	—	47	1	no	—
486	C₂²×C₄	—	47	4	no	—
487	C₂²×C₄	—	47	2	no	—
488	C₂²×C₄	—	47	2	no	—
489	C₂²×C₄	—	47	1	no	—
490	C₂²×C₄	—	47	1	no	—
491	C₂²×C₄	—	94	2	no	—
492	C₂²×C₄	—	94	2	no	—
493	C₂²×C₄	—	94	2	no	—
494	C₂²×C₄	—	94	2	no	—
495	C₂²×C₄	—	94	2	no	—
496	C₂²×C₄	—	94	1	no	—
497	C₂²×C₄	—	94	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	—	94	1	no	—
505	C₂²×C₄	—	94	1	no	—
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	C₂×C₄×D₄₇	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
524	C₂×C₈	—	47	2	no	—
525	C₂×C₈	—	47	2	no	—
526	C₂×C₈	—	47	2	no	—
527	C₂×C₈	—	94	8	no	—
528	C₂×C₈	—	94	8	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	D₄×D₄₇	1	2	yes	—
539	C₂×C₈	#10625354	1	2	yes	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	47	4	no	—
542	C₄⋊C₄	—	94	2	no	—
543	C₄⋊C₄	—	94	2	no	—
544	C₄⋊C₄	C₈×D₄₇	1	4	yes	complemented
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	—	94	2	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	94	2	no	—
560	C₄²	—	94	2	no	—
561	C₄²	—	94	1	no	—
562	C₄²	—	94	1	no	—
563	C₄²	—	94	1	no	—
564	C₄²	—	94	1	no	—
565	C₂³	—	47	2	no	—
566	C₂³	—	47	2	no	—
567	C₂³	—	47	2	no	—
568	C₂³	—	47	2	no	—
569	C₂³	—	94	1	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	—	94	1	no	—
577	C₂³	—	94	1	no	—
578	C₂³	—	94	1	no	—
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	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	47	2	no	—
596	C₂×C₄	—	47	2	no	—
597	C₂×C₄	—	47	2	no	—
598	C₂×C₄	—	47	2	no	—
599	C₂×C₄	—	94	8	no	—
600	C₂×C₄	—	94	8	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	2	no	—
610	C₂×C₄	—	94	2	no	—
611	C₂×C₄	—	94	2	no	—
612	C₂×C₄	—	94	2	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	C₂×C₈×D₄₇	1	2	yes	—
624	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
625	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
626	C₂×C₄	#13094032	1	2	yes	—
627	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
628	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
629	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
630	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
631	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
632	C₂×C₄	C₂×#10625354	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	—	47	4	no	—
638	C₈	—	94	2	no	—
639	C₈	—	188	1	no	—
640	C₈	—	188	1	no	—
641	C₂²	—	47	4	no	—
642	C₂²	—	94	2	no	—
643	C₂²	—	94	2	no	—
644	C₂²	—	94	2	no	—
645	C₂²	—	94	2	no	—
646	C₂²	—	94	2	no	—
647	C₂²	—	94	2	no	—
648	C₂²	—	94	2	no	—
649	C₂²	—	94	2	no	—
650	C₂²	—	94	2	no	—
651	C₂²	—	188	1	no	—
652	C₂²	—	188	1	no	—
653	C₂²	—	188	1	no	—
654	C₂²	—	188	1	no	—
655	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
656	C₂²	#15689591	1	1	yes	characteristic
657	C₂²	C₄×#10625354	1	1	yes	characteristic
658	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
659	C₂²	#131×D₄₇	1	1	yes	characteristic
660	C₂²	#131×D₄₇	1	1	yes	characteristic
661	C₂²	C₂×#13094032	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	—	4	1	no	—
668	C₄	—	94	2	no	—
669	C₄	—	94	2	no	—
670	C₄	—	94	2	no	—
671	C₄	—	94	2	no	—
672	C₄	—	188	1	no	—
673	C₄	—	188	1	no	—
674	C₄	#123×D₄₇	1	1	yes	characteristic
675	C₄	#15689636	1	1	yes	characteristic
676	C₄	#15689656	1	1	yes	characteristic
677	C₄	#15689658	1	1	yes	characteristic
678	C₂	—	94	4	no	—
679	C₂	—	188	2	no	—
680	C₂	#20245909	1	1	yes	characteristic
681	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
682	C₂	#20252079	1	1	yes	characteristic
683	C₂	#20252344	1	1	yes	characteristic
684	C₂	C₈×#10625354	1	1	yes	characteristic
685	C₂	#20252361	1	1	yes	characteristic
686	C₂	#20252362	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1916	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1916	D₄₇
hypocenter	C₄₇	C₈×#123
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1916

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₈×D₄₇	C₂	semidirect
4. #20243995	C₂	semidirect
5. #20243994	C₂	semidirect
6. #20243942	C₂	semidirect
8. #20243567	C₂	semidirect
9. #20243455	C₂	semidirect
10. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
11. #20243249	C₂	semidirect
12. #20243158	C₂	semidirect
13. #20243158	C₂	semidirect
14. #20243158	C₂	semidirect
15. C₄₇×#1916	C₂	semidirect
79. #13094009	C₈	semidirect
166. C₂×C₄×D₄₇	C₂×C₈	semidirect
182. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
194. (C₂×D₄₇)⋊C₄	C₂×C₈	semidirect
195. (C₂×D₄₇)⋊C₄	C₂×C₈	semidirect
196. (C₂×D₄₇)⋊C₄	C₂×C₈	semidirect
199. Dic₄₇⋊C₄	C₂×C₈	semidirect
296. C₄₇⋊C₈	#123	semidirect
341. #1916	D₄₇	semidirect
404. C₄₇	C₈×#123	semidirect
544. C₄⋊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×#15689188	2
C₂×C₄×C₈×D₄₇	2
C₄×#13094009	2
#20243995	2
#20243994	2
#20243942	2
#20243679	2
#20243567	2
#20243455	2
C₄⋊C₄×C₄₇⋊C₈	2
#20243249	2
#20243158	2
C₄₇×#1916	2
C₈×#123	47