Subgroups — #26232811

Order 12032.

1292 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689252	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689251	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244329	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244326	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244326	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244322	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244322	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243367	C₂	1	1	yes	maximal, characteristic
10	#20243367	C₂	1	1	yes	maximal, characteristic
11	#20243365	C₂	1	1	yes	maximal, characteristic
12	#20243151	C₂	1	1	yes	maximal, characteristic
13	#20243149	C₂	1	1	yes	maximal, characteristic
14	#20243145	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×D₄₇	C₄	1	1	yes	characteristic
17	C₂×Q₈×Dic₄₇	C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
21	C₂×#13093989	C₄	1	1	yes	characteristic
22	C₂×#13093989	C₄	1	1	yes	characteristic
23	C₂×#13093989	C₄	1	1	yes	characteristic
24	C₄×Q₈×D₄₇	—	2	4	no	—
25	C₄×Q₈×D₄₇	—	2	4	no	—
26	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
28	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
29	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
32	#15689252	—	2	4	no	—
33	#15689251	—	2	4	no	—
34	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×#13093935	C₂²	1	1	yes	characteristic
44	C₂×#13093934	C₂²	1	1	yes	characteristic
45	C₂×#13093934	C₂²	1	1	yes	characteristic
46	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
47	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
48	#15688878	C₂²	1	1	yes	characteristic
49	#15688878	C₂²	1	1	yes	characteristic
50	#15688878	C₂²	1	1	yes	characteristic
51	#15688878	C₂²	1	1	yes	characteristic
52	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	#15688877	C₂²	1	1	yes	characteristic
55	#15688877	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
58	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₄₇×#336	C₂²	1	1	yes	characteristic
62	C₄₇×#336	C₂²	1	1	yes	characteristic
63	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
64	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
65	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
66	C₂×Q₈×D₄₇	—	2	4	no	—
67	C₂×Q₈×D₄₇	—	2	4	no	—
68	C₂×Q₈×D₄₇	—	2	4	no	—
69	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	Q₈×Dic₄₇	—	2	4	no	—
81	C₄×Dic₉₄	—	2	2	no	—
82	C₄×Dic₉₄	—	2	2	no	—
83	C₄×Dic₉₄	—	2	2	no	—
84	C₄×Dic₉₄	—	2	2	no	—
85	C₄×Dic₉₄	D₄	1	4	yes	—
86	C₄×Dic₉₄	D₄	1	4	yes	—
87	#13093989	—	2	4	no	—
88	#13093989	—	2	4	no	—
89	#13093989	—	2	4	no	—
90	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₄⋊C₄×D₄₇	—	2	4	no	—
100	C₄⋊C₄×D₄₇	—	2	4	no	—
101	C₄⋊C₄×D₄₇	—	2	4	no	—
102	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
111	C₄²×D₄₇	—	2	2	no	—
112	C₄²×D₄₇	—	2	2	no	—
113	C₄²×D₄₇	—	2	2	no	—
114	C₄²×D₄₇	—	2	2	no	—
115	C₄²×D₄₇	—	2	2	no	—
116	C₄²×D₄₇	—	2	2	no	—
117	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
118	Dic₄₇⋊C₈	—	2	2	no	—
119	Dic₄₇⋊C₈	—	2	2	no	—
120	Dic₄₇⋊C₈	—	2	2	no	—
121	Dic₄₇⋊C₈	—	2	2	no	—
122	(C₂×D₄₇)⋊C₈	—	2	2	no	—
123	(C₂×D₄₇)⋊C₈	—	2	2	no	—
124	(C₂×D₄₇)⋊C₈	—	2	2	no	—
125	(C₂×D₄₇)⋊C₈	Q₈	1	4	yes	complemented
126	#13093935	—	2	2	no	—
127	#13093934	—	2	2	no	—
128	#13093934	—	2	2	no	—
129	C₈×Dic₄₇	—	2	2	no	—
130	C₈×Dic₄₇	—	2	2	no	—
131	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
132	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
136	C₄×Q₈×C₄₇	—	2	2	no	—
137	C₄×Q₈×C₄₇	—	2	2	no	—
138	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
141	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
144	C₄⋊C₈×C₄₇	—	2	2	no	—
145	#97×C₄₇	—	2	2	no	—
146	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₄₇	—	2	2	no	—
148	C₂×Q₈×C₄₇	—	2	2	no	—
149	C₂×Q₈×C₄₇	—	2	2	no	—
150	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂⁴	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	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
164	Q₈×D₄₇	—	2	32	no	—
165	C₂×C₄×D₄₇	—	2	2	no	—
166	C₂×C₄×D₄₇	—	2	2	no	—
167	C₂×C₄×D₄₇	—	2	2	no	—
168	C₂×C₄×D₄₇	—	2	2	no	—
169	C₂×C₄×D₄₇	—	2	1	no	—
170	C₂×C₄×D₄₇	—	2	1	no	—
171	C₂×C₄×D₄₇	—	2	1	no	—
172	C₂×C₄×D₄₇	—	2	1	no	—
173	C₂×C₄×D₄₇	—	2	2	no	—
174	C₂×C₄×D₄₇	—	2	2	no	—
175	C₂×C₄×D₄₇	—	2	2	no	—
176	C₂×C₄×D₄₇	—	2	2	no	—
177	C₂×C₄×D₄₇	—	2	2	no	—
178	C₂×C₄×D₄₇	—	2	2	no	—
179	C₂×C₄×D₄₇	—	2	2	no	—
180	C₂×C₄×D₄₇	—	2	2	no	—
181	C₂×C₄×D₄₇	—	2	2	no	—
182	C₂×C₄×D₄₇	—	2	2	no	—
183	C₂×C₄×D₄₇	—	4	1	no	—
184	C₂×C₄×D₄₇	—	4	1	no	—
185	C₂×C₄×D₄₇	—	4	1	no	—
186	C₂×C₄×D₄₇	M₁₆	1	4	yes	—
187	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
188	C₂×C₄×D₄₇	#41	1	2	yes	—
189	C₂×Dic₉₄	—	2	2	no	—
190	C₂×Dic₉₄	—	2	2	no	—
191	C₂×Dic₉₄	—	2	2	no	—
192	C₂×Dic₉₄	—	2	2	no	—
193	C₂×Dic₉₄	—	2	2	no	—
194	C₂×Dic₉₄	—	2	2	no	—
195	C₂×Dic₉₄	—	2	2	no	—
196	C₂×Dic₉₄	C₂²⋊C₄	1	4	yes	—
197	C₂×Dic₉₄	M₁₆	1	4	yes	—
198	C₂×C₈×C₄₇	—	2	1	no	—
199	C₂×C₈×C₄₇	—	2	1	no	—
200	C₂×C₈×C₄₇	—	2	1	no	—
201	C₂×C₈×C₄₇	—	2	1	no	—
202	C₂×C₈×C₄₇	—	2	1	no	—
203	C₂×C₈×C₄₇	—	2	1	no	—
204	C₂×C₈×C₄₇	—	2	1	no	—
205	C₂×C₈×C₄₇	—	2	1	no	—
206	C₂×C₈×C₄₇	—	2	1	no	—
207	C₂×C₈×C₄₇	—	2	1	no	—
208	C₂×C₈×C₄₇	—	2	1	no	—
209	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	complemented
210	C₄⋊C₄×C₄₇	—	2	2	no	—
211	C₄⋊C₄×C₄₇	—	2	2	no	—
212	C₄⋊C₄×C₄₇	—	2	2	no	—
213	C₄²×C₄₇	—	2	1	no	—
214	C₄²×C₄₇	—	2	1	no	—
215	C₄²×C₄₇	—	2	1	no	—
216	C₄²×C₄₇	—	2	1	no	—
217	C₄²×C₄₇	C₂×D₄	1	2	yes	—
218	C₄²×C₄₇	C₂×D₄	1	2	yes	—
219	C₄⋊Dic₄₇	—	2	2	no	—
220	C₄⋊Dic₄₇	—	2	2	no	—
221	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
222	Dic₄₇⋊C₄	—	2	2	no	—
223	Dic₄₇⋊C₄	—	2	2	no	—
224	Dic₄₇⋊C₄	—	2	2	no	—
225	Dic₄₇⋊C₄	—	2	2	no	—
226	Dic₄₇⋊C₄	C₂²⋊C₄	1	4	yes	—
227	Dic₄₇⋊C₄	C₂²⋊C₄	1	4	yes	—
228	C₄×Dic₄₇	—	2	2	no	—
229	C₄×Dic₄₇	—	2	2	no	—
230	C₄×Dic₄₇	—	2	1	no	—
231	C₄×Dic₄₇	—	2	1	no	—
232	C₄×Dic₄₇	—	2	2	no	—
233	C₄×Dic₄₇	—	2	2	no	—
234	C₄×Dic₄₇	—	2	2	no	—
235	C₄×Dic₄₇	—	2	2	no	—
236	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
237	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
238	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
239	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
240	C₂×C₄₇⋊C₈	—	2	1	no	—
241	C₂×C₄₇⋊C₈	—	2	1	no	—
242	C₂×C₄₇⋊C₈	—	2	1	no	—
243	C₂×C₄₇⋊C₈	—	2	1	no	—
244	C₂×C₄₇⋊C₈	—	2	1	no	—
245	C₂×C₄₇⋊C₈	—	2	1	no	—
246	C₂×C₄₇⋊C₈	—	2	1	no	—
247	C₂×C₄₇⋊C₈	—	2	1	no	—
248	C₂×C₄₇⋊C₈	—	2	1	no	—
249	C₂×C₄₇⋊C₈	—	2	1	no	—
250	C₂×C₄₇⋊C₈	—	2	1	no	—
251	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	complemented
252	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
253	C₂²×D₄₇	—	2	1	no	—
254	C₂²×D₄₇	—	2	1	no	—
255	C₂²×D₄₇	—	2	1	no	—
256	C₂²×D₄₇	—	2	1	no	—
257	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
258	C₂²×D₄₇	C₂×M₁₆	1	2	yes	—
259	C₂²×D₄₇	#131	1	2	yes	—
260	Q₈×C₄₇	—	2	8	no	—
261	C₂×C₄×C₄₇	—	2	1	no	—
262	C₂×C₄×C₄₇	—	2	1	no	—
263	C₂×C₄×C₄₇	—	2	1	no	—
264	C₂×C₄×C₄₇	—	2	1	no	—
265	C₂×C₄×C₄₇	—	2	1	no	—
266	C₂×C₄×C₄₇	—	2	1	no	—
267	C₂×C₄×C₄₇	—	2	1	no	—
268	C₂×C₄×C₄₇	—	2	1	no	—
269	C₂×C₄×C₄₇	—	2	1	no	—
270	C₂×C₄×C₄₇	—	2	1	no	—
271	C₂×C₄×C₄₇	—	2	1	no	—
272	C₂×C₄×C₄₇	—	2	1	no	—
273	C₂×C₄×C₄₇	—	2	1	no	—
274	C₂×C₄×C₄₇	—	2	1	no	—
275	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
278	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
279	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
282	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
284	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
285	C₂×Dic₄₇	—	2	1	no	—
286	C₂×Dic₄₇	—	2	1	no	—
287	C₂×Dic₄₇	—	2	1	no	—
288	C₂×Dic₄₇	—	2	1	no	—
289	C₂×Dic₄₇	—	2	1	no	—
290	C₂×Dic₄₇	—	2	1	no	—
291	C₂×Dic₄₇	—	2	1	no	—
292	C₂×Dic₄₇	—	2	1	no	—
293	C₂×Dic₄₇	—	2	1	no	—
294	C₂×Dic₄₇	—	2	1	no	—
295	C₂×Dic₄₇	—	2	1	no	—
296	C₂×Dic₄₇	—	2	1	no	—
297	C₂×Dic₄₇	—	2	1	no	—
298	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
300	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
301	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
303	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
304	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
305	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
306	C₄×D₄₇	—	2	8	no	—
307	C₄×D₄₇	—	2	8	no	—
308	C₄×D₄₇	—	2	2	no	—
309	C₄×D₄₇	—	2	2	no	—
310	C₄×D₄₇	—	2	2	no	—
311	C₄×D₄₇	—	2	2	no	—
312	C₄×D₄₇	—	2	8	no	—
313	C₄×D₄₇	—	4	4	no	—
314	C₄×D₄₇	—	4	4	no	—
315	C₄×D₄₇	—	4	4	no	—
316	Dic₉₄	—	2	8	no	—
317	Dic₉₄	—	2	8	no	—
318	Dic₉₄	—	2	8	no	—
319	C₈×C₄₇	—	2	2	no	—
320	C₈×C₄₇	—	4	1	no	—
321	C₈×C₄₇	—	4	1	no	—
322	C₈×C₄₇	—	4	1	no	—
323	C₄₇⋊C₈	—	2	2	no	—
324	C₄₇⋊C₈	—	4	1	no	—
325	C₄₇⋊C₈	—	4	1	no	—
326	C₄₇⋊C₈	—	4	1	no	—
327	#22510	—	47	1	no	maximal, Sylow
328	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
330	C₂²×C₄₇	#519	1	1	yes	characteristic
331	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
332	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
333	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
334	C₂²×C₄₇	#568	1	1	yes	characteristic
335	C₂×D₄₇	—	2	2	no	—
336	C₂×D₄₇	—	2	2	no	—
337	C₂×D₄₇	—	2	2	no	—
338	C₂×D₄₇	—	2	2	no	—
339	C₂×D₄₇	—	2	2	no	—
340	C₂×D₄₇	—	2	2	no	—
341	C₂×D₄₇	#446	1	4	yes	complemented
342	C₄×C₄₇	—	2	2	no	—
343	C₄×C₄₇	—	2	2	no	—
344	C₄×C₄₇	—	2	2	no	—
345	C₄×C₄₇	—	2	2	no	—
346	C₄×C₄₇	—	4	1	no	—
347	C₄×C₄₇	—	4	1	no	—
348	C₄×C₄₇	#548	1	1	yes	characteristic
349	C₄×C₄₇	#548	1	1	yes	characteristic
350	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
351	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
352	Dic₄₇	—	2	2	no	—
353	Dic₄₇	—	2	2	no	—
354	Dic₄₇	—	2	2	no	—
355	Dic₄₇	—	2	2	no	—
356	Dic₄₇	—	2	2	no	—
357	Dic₄₇	—	4	1	no	—
358	Dic₄₇	#407	1	4	yes	—
359	C₂²×C₄×Q₈	—	47	1	no	—
360	C₂×#446	—	47	1	no	—
361	C₂×#446	—	47	1	no	—
362	#1985	—	47	1	no	—
363	#1985	—	47	1	no	—
364	#1985	—	47	1	no	—
365	#1985	D₄₇	1	1	yes	characteristic, complemented
366	#1984	—	47	1	no	—
367	#1984	—	47	1	no	—
368	#1797	—	47	1	no	—
369	#1797	—	47	1	no	—
370	#1797	—	47	1	no	—
371	#1749	—	47	1	no	—
372	#1749	—	47	1	no	—
373	C₄×C₂²⋊C₈	—	47	1	no	—
374	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
375	C₂×C₄₇	C₂×#407	1	1	yes	characteristic
376	C₂×C₄₇	#2880	1	1	yes	characteristic
377	C₂×C₄₇	C₂×#446	1	1	yes	characteristic
378	C₂×C₄₇	Q₈×M₁₆	1	1	yes	characteristic
379	C₂×C₄₇	#2983	1	1	yes	characteristic
380	C₂×C₄₇	#2984	1	1	yes	characteristic
381	D₄₇	—	2	4	no	—
382	C₂³×Q₈	—	47	1	no	—
383	C₂×C₄×Q₈	—	47	1	no	—
384	C₂×C₄×Q₈	—	47	1	no	—
385	C₂×C₄×Q₈	—	47	1	no	—
386	C₂×C₄×Q₈	—	47	1	no	—
387	C₂×C₄×Q₈	—	47	1	no	—
388	C₂×C₄×Q₈	—	47	1	no	—
389	C₂×C₄×Q₈	—	47	1	no	—
390	C₂×C₄×Q₈	—	94	4	no	—
391	C₂×C₄×Q₈	—	94	4	no	—
392	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	—	47	1	no	—
394	C₂²×C₄⋊C₄	—	47	1	no	—
395	C₂²×C₄⋊C₄	—	47	1	no	—
396	C₂²×C₄²	—	47	1	no	—
397	C₂²×C₄²	—	47	1	no	—
398	C₂²×C₄²	—	47	1	no	—
399	#446	—	94	4	no	—
400	#446	—	94	4	no	—
401	C₂×C₄⋊C₈	—	47	1	no	—
402	C₂×C₄⋊C₈	—	47	1	no	—
403	C₂×C₄⋊C₈	—	47	1	no	—
404	C₂×C₄⋊C₈	—	47	1	no	—
405	C₂×C₄⋊C₈	—	47	1	no	—
406	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
407	C₂×C₂²⋊C₈	—	47	1	no	—
408	C₂×C₂²⋊C₈	—	47	1	no	—
409	C₂×C₂²⋊C₈	—	47	1	no	—
410	C₂×C₂²⋊C₈	—	47	1	no	—
411	C₂×#97	—	47	1	no	—
412	C₂×#97	—	47	1	no	—
413	C₂×#97	—	47	1	no	—
414	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
415	C₂×C₄×C₈	—	47	1	no	—
416	C₂×C₄×C₈	—	47	1	no	—
417	#336	—	47	1	no	—
418	#336	—	47	1	no	—
419	#336	—	47	1	no	—
420	#336	—	47	1	no	—
421	#336	—	47	1	no	—
422	#336	—	47	1	no	—
423	#336	—	47	1	no	—
424	#336	—	47	1	no	—
425	#336	C₂×D₄₇	1	1	yes	characteristic
426	#336	C₂×D₄₇	1	1	yes	characteristic
427	#336	C₂×D₄₇	1	1	yes	characteristic
428	#336	C₂×D₄₇	1	1	yes	characteristic
429	C₄₇	#22510	1	1	yes	characteristic, complemented, Sylow
430	C₂²×Q₈	—	47	1	no	—
431	C₂²×Q₈	—	47	1	no	—
432	C₂²×Q₈	—	47	1	no	—
433	C₂²×Q₈	—	94	4	no	—
434	C₂²×Q₈	—	94	4	no	—
435	C₂²×Q₈	—	94	4	no	—
436	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
437	C₂³×C₄	—	47	1	no	—
438	C₂³×C₄	—	47	1	no	—
439	C₂³×C₄	—	47	1	no	—
440	C₂³×C₄	—	47	1	no	—
441	C₂³×C₄	—	47	1	no	—
442	C₂³×C₄	—	47	1	no	—
443	C₂³×C₄	—	47	1	no	—
444	C₂²×C₈	—	47	1	no	—
445	C₂²×C₈	—	47	1	no	—
446	C₂²×C₈	—	47	1	no	—
447	C₂²×C₈	—	47	1	no	—
448	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
449	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
450	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
451	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
452	C₄×Q₈	—	2	2	no	—
453	C₄×Q₈	—	2	2	no	—
454	C₄×Q₈	—	47	4	no	—
455	C₄×Q₈	—	47	4	no	—
456	C₄×Q₈	—	94	2	no	—
457	C₄×Q₈	—	94	2	no	—
458	C₄×Q₈	—	94	2	no	—
459	C₄×Q₈	—	94	2	no	—
460	C₄×Q₈	—	94	4	no	—
461	C₄×Q₈	—	94	4	no	—
462	C₄×Q₈	—	94	4	no	—
463	C₄×Q₈	—	94	4	no	—
464	C₂×C₄⋊C₄	—	47	1	no	—
465	C₂×C₄⋊C₄	—	47	1	no	—
466	C₂×C₄⋊C₄	—	47	1	no	—
467	C₂×C₄⋊C₄	—	47	1	no	—
468	C₂×C₄⋊C₄	—	47	1	no	—
469	C₂×C₄⋊C₄	—	47	1	no	—
470	C₂×C₄⋊C₄	—	47	1	no	—
471	C₂×C₄⋊C₄	—	47	1	no	—
472	C₂×C₄⋊C₄	—	47	1	no	—
473	C₂×C₄⋊C₄	—	94	4	no	—
474	C₂×C₄⋊C₄	—	94	4	no	—
475	C₂×C₄⋊C₄	—	94	4	no	—
476	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
479	C₂×C₄²	—	47	1	no	—
480	C₂×C₄²	—	47	1	no	—
481	C₂×C₄²	—	47	1	no	—
482	C₂×C₄²	—	47	1	no	—
483	C₂×C₄²	—	47	1	no	—
484	C₂×C₄²	—	47	1	no	—
485	C₂×C₄²	—	47	1	no	—
486	C₂×C₄²	—	47	1	no	—
487	C₂×C₄²	—	47	1	no	—
488	C₂×C₄²	—	94	2	no	—
489	C₂×C₄²	—	94	2	no	—
490	C₂×C₄²	—	94	2	no	—
491	C₂×C₄²	—	94	2	no	—
492	C₂×C₄²	—	94	2	no	—
493	C₂×C₄²	—	94	2	no	—
494	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
495	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
496	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
497	C₄⋊C₈	—	2	2	no	—
498	C₄⋊C₈	—	94	2	no	—
499	C₄⋊C₈	—	94	2	no	—
500	C₄⋊C₈	—	94	2	no	—
501	C₄⋊C₈	—	94	2	no	—
502	C₄⋊C₈	—	94	2	no	—
503	C₂²⋊C₈	—	47	4	no	—
504	C₂²⋊C₈	—	94	2	no	—
505	C₂²⋊C₈	—	94	2	no	—
506	C₂²⋊C₈	—	94	2	no	—
507	#97	—	2	2	no	—
508	#97	—	94	2	no	—
509	#97	—	94	2	no	—
510	#97	—	94	2	no	—
511	C₄×C₈	—	94	2	no	—
512	C₄×C₈	—	94	2	no	—
513	C₂⁴	—	47	1	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	47	4	no	—
518	C₂×Q₈	—	47	4	no	—
519	C₂×Q₈	—	94	2	no	—
520	C₂×Q₈	—	94	2	no	—
521	C₂×Q₈	—	94	2	no	—
522	C₂×Q₈	—	94	2	no	—
523	C₂×Q₈	—	94	2	no	—
524	C₂×Q₈	—	94	2	no	—
525	C₂×Q₈	—	94	32	no	—
526	C₂×Q₈	—	94	2	no	—
527	C₂²×C₄	—	47	1	no	—
528	C₂²×C₄	—	47	1	no	—
529	C₂²×C₄	—	47	1	no	—
530	C₂²×C₄	—	47	1	no	—
531	C₂²×C₄	—	47	1	no	—
532	C₂²×C₄	—	47	1	no	—
533	C₂²×C₄	—	47	4	no	—
534	C₂²×C₄	—	47	2	no	—
535	C₂²×C₄	—	47	2	no	—
536	C₂²×C₄	—	47	1	no	—
537	C₂²×C₄	—	94	2	no	—
538	C₂²×C₄	—	94	2	no	—
539	C₂²×C₄	—	94	2	no	—
540	C₂²×C₄	—	94	2	no	—
541	C₂²×C₄	—	94	2	no	—
542	C₂²×C₄	—	94	2	no	—
543	C₂²×C₄	—	94	2	no	—
544	C₂²×C₄	—	94	2	no	—
545	C₂²×C₄	—	94	2	no	—
546	C₂²×C₄	—	94	2	no	—
547	C₂²×C₄	—	94	2	no	—
548	C₂²×C₄	—	94	2	no	—
549	C₂²×C₄	—	94	2	no	—
550	C₂²×C₄	—	94	1	no	—
551	C₂²×C₄	—	94	1	no	—
552	C₂²×C₄	—	94	1	no	—
553	C₂²×C₄	—	94	1	no	—
554	C₂²×C₄	—	94	2	no	—
555	C₂²×C₄	—	188	1	no	—
556	C₂²×C₄	—	188	1	no	—
557	C₂²×C₄	—	188	1	no	—
558	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
559	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
560	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
561	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
562	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
563	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
564	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	47	2	no	—
577	C₂×C₈	—	94	1	no	—
578	C₂×C₈	—	94	1	no	—
579	C₂×C₈	—	94	1	no	—
580	C₂×C₈	—	94	1	no	—
581	C₂×C₈	—	94	1	no	—
582	C₂×C₈	—	94	1	no	—
583	C₂×C₈	—	94	1	no	—
584	C₂×C₈	—	94	1	no	—
585	C₂×C₈	—	94	1	no	—
586	C₂×C₈	—	94	1	no	—
587	C₂×C₈	—	94	1	no	—
588	C₂×C₈	Q₈×D₄₇	1	2	yes	complemented
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	47	4	no	—
593	C₄⋊C₄	—	47	4	no	—
594	C₄⋊C₄	—	47	4	no	—
595	C₄⋊C₄	—	94	2	no	—
596	C₄⋊C₄	—	94	2	no	—
597	C₄⋊C₄	—	94	2	no	—
598	C₄⋊C₄	—	94	2	no	—
599	C₄⋊C₄	—	94	2	no	—
600	C₄⋊C₄	—	94	2	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	47	2	no	—
606	C₄²	—	47	2	no	—
607	C₄²	—	47	2	no	—
608	C₄²	—	47	2	no	—
609	C₄²	—	94	2	no	—
610	C₄²	—	94	2	no	—
611	C₄²	—	94	2	no	—
612	C₄²	—	94	2	no	—
613	C₄²	—	94	2	no	—
614	C₄²	—	94	2	no	—
615	C₄²	—	94	1	no	—
616	C₄²	—	94	1	no	—
617	C₄²	D₄×D₄₇	1	2	yes	—
618	C₄²	D₄×D₄₇	1	2	yes	—
619	C₂³	—	47	2	no	—
620	C₂³	—	47	2	no	—
621	C₂³	—	47	2	no	—
622	C₂³	—	94	1	no	—
623	C₂³	—	94	1	no	—
624	C₂³	—	94	1	no	—
625	C₂³	—	94	1	no	—
626	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
627	Q₈	—	2	8	no	—
628	Q₈	—	94	8	no	—
629	Q₈	—	94	8	no	—
630	Q₈	—	94	8	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	47	2	no	—
646	C₂×C₄	—	47	2	no	—
647	C₂×C₄	—	47	2	no	—
648	C₂×C₄	—	47	2	no	—
649	C₂×C₄	—	47	2	no	—
650	C₂×C₄	—	47	2	no	—
651	C₂×C₄	—	47	2	no	—
652	C₂×C₄	—	47	2	no	—
653	C₂×C₄	—	94	8	no	—
654	C₂×C₄	—	94	8	no	—
655	C₂×C₄	—	94	8	no	—
656	C₂×C₄	—	94	1	no	—
657	C₂×C₄	—	94	1	no	—
658	C₂×C₄	—	94	1	no	—
659	C₂×C₄	—	94	1	no	—
660	C₂×C₄	—	94	1	no	—
661	C₂×C₄	—	94	1	no	—
662	C₂×C₄	—	94	1	no	—
663	C₂×C₄	—	94	1	no	—
664	C₂×C₄	—	94	1	no	—
665	C₂×C₄	—	94	1	no	—
666	C₂×C₄	—	94	2	no	—
667	C₂×C₄	—	94	2	no	—
668	C₂×C₄	—	94	2	no	—
669	C₂×C₄	—	94	2	no	—
670	C₂×C₄	—	94	1	no	—
671	C₂×C₄	—	94	1	no	—
672	C₂×C₄	—	94	1	no	—
673	C₂×C₄	—	188	4	no	—
674	C₂×C₄	—	188	4	no	—
675	C₂×C₄	—	188	4	no	—
676	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
677	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
678	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
679	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
680	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
681	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
682	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
683	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
684	C₂×C₄	#13094071	1	1	yes	characteristic
685	C₂×C₄	#13094072	1	1	yes	characteristic
686	C₈	—	2	2	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	94	2	no	—
691	C₈	—	188	1	no	—
692	C₈	—	188	1	no	—
693	C₈	—	188	1	no	—
694	C₂²	—	47	4	no	—
695	C₂²	—	94	2	no	—
696	C₂²	—	94	2	no	—
697	C₂²	—	94	2	no	—
698	C₂²	—	94	2	no	—
699	C₂²	—	94	2	no	—
700	C₂²	—	94	2	no	—
701	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
702	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
703	C₂²	#15689599	1	1	yes	characteristic
704	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
705	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
706	C₂²	#131×D₄₇	1	1	yes	characteristic
707	C₂²	#15689888	1	1	yes	characteristic
708	C₄	—	2	2	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	47	4	no	—
715	C₄	—	94	2	no	—
716	C₄	—	94	2	no	—
717	C₄	—	94	2	no	—
718	C₄	—	94	2	no	—
719	C₄	—	94	2	no	—
720	C₄	—	188	1	no	—
721	C₄	#15689781	1	1	yes	characteristic
722	C₄	#15689783	1	1	yes	characteristic
723	C₄	#15689786	1	1	yes	characteristic
724	C₄	#15689788	1	1	yes	characteristic
725	C₂	—	94	4	no	—
726	C₂	#20246222	1	1	yes	characteristic
727	C₂	#407×D₄₇	1	1	yes	characteristic
728	C₂	#20251836	1	1	yes	characteristic
729	C₂	#446×D₄₇	1	1	yes	characteristic
730	C₂	#20252340	1	1	yes	characteristic
731	C₂	#20252470	1	1	yes	characteristic
732	C₂	#20252474	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1985	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1985	D₄₇
hypocenter	C₄₇	#22510
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1985

Complements

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

N	H ≅ G/N	type
2. C₂×#15689252	C₂	semidirect
3. C₂×#15689251	C₂	semidirect
4. #20244329	C₂	semidirect
5. #20244326	C₂	semidirect
6. #20244326	C₂	semidirect
7. #20244322	C₂	semidirect
8. #20244322	C₂	semidirect
15. C₄₇×#1985	C₂	semidirect
125. (C₂×D₄₇)⋊C₈	Q₈	semidirect
209. C₂×C₈×C₄₇	C₂×Q₈	semidirect
251. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
341. C₂×D₄₇	#446	semidirect
365. #1985	D₄₇	semidirect
429. C₄₇	#22510	semidirect
588. C₂×C₈	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₈×D₄₇	2
C₂×#15689252	2
C₂×#15689251	2
#20244329	2
#20244326	2
#20244322	2
#20243367	2
#20243365	2
#20243151	2
#20243149	2
#20243145	2
C₄₇×#1985	2
#22510	47