Subgroups — #26234811

Order 12032.

1108 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243566	C₂	1	2	yes	maximal, complemented
6	#20243565	C₂	1	2	yes	maximal, complemented
7	#20243504	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243366	C₂	1	2	yes	maximal, complemented
9	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688877	C₂	1	2	yes	maximal, complemented
11	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	C₄	1	1	yes	characteristic
14	C₂×D₄×Dic₄₇	C₄	1	1	yes	characteristic
15	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
16	D₄×C₄₇⋊C₈	—	2	4	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
25	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
26	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
28	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
29	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
30	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688877	C₂²	1	1	yes	characteristic
32	#15688877	C₂²	1	1	yes	characteristic
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₄₇	—	2	4	no	—
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
44	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
45	C₂²×C₄₇⋊C₈	—	2	4	no	—
46	C₂²×C₄₇⋊C₈	—	2	4	no	—
47	C₂²×C₄₇⋊C₈	—	4	2	no	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	D₄×Dic₄₇	—	2	4	no	—
52	D₄×Dic₄₇	C₈	1	8	yes	complemented
53	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₄₇	—	4	2	no	—
58	C₂×C₄×Dic₄₇	—	4	2	no	—
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
68	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
69	Dic₄₇⋊C₈	—	2	2	no	—
70	Dic₄₇⋊C₈	—	2	2	no	—
71	Dic₄₇⋊C₈	—	4	2	no	—
72	Dic₄₇⋊C₈	—	4	2	no	—
73	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
74	C₄×C₄₇⋊C₈	—	2	2	no	—
75	C₄₇⋊#95	C₂×C₄	1	2	yes	—
76	C₄₇⋊#95	C₂×C₄	1	2	yes	—
77	C₄₇⋊#95	C₂×C₄	1	2	yes	—
78	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₄₇	—	2	4	no	—
81	C₂²×C₈×C₄₇	—	2	4	no	—
82	C₂²×C₈×C₄₇	—	4	2	no	—
83	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₄₇	D₄	1	4	yes	—
87	C₄×D₄×C₄₇	Q₈	1	4	yes	—
88	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	—	2	2	no	—
92	C₂²⋊C₈×C₄₇	—	2	4	no	—
93	C₄×C₈×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
96	C₂×D₄×C₄₇	C₂×C₈	1	4	yes	—
97	C₂×D₄×C₄₇	M₁₆	1	4	yes	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₄₇	—	2	4	no	—
109	C₂²×Dic₄₇	—	2	4	no	—
110	C₂²×Dic₄₇	—	4	2	no	—
111	C₂²×Dic₄₇	—	4	2	no	—
112	C₂²×Dic₄₇	—	4	2	no	—
113	C₂²×Dic₄₇	C₂×C₈	1	8	yes	complemented
114	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
118	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	4	8	no	—
129	C₂×C₈×C₄₇	#41	1	2	yes	—
130	C₄⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
131	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
132	C₄²×C₄₇	C₂×D₄	1	2	yes	—
133	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
134	C₂²⋊Dic₄₇	—	2	4	no	—
135	C₂²⋊Dic₄₇	C₂×C₈	1	8	yes	complemented
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	1	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	4	2	no	—
147	C₄×Dic₄₇	—	4	2	no	—
148	C₄×Dic₄₇	—	4	1	no	—
149	C₄×Dic₄₇	C₂×C₈	1	4	yes	complemented
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	4	8	no	—
159	C₂×C₄₇⋊C₈	#41	1	2	yes	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	—	2	2	no	—
164	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
165	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
166	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
167	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	D₄×C₄₇	C₄⋊C₈	1	16	yes	complemented
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
179	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	2	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	2	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	C₂×Dic₄₇	—	2	2	no	—
200	C₂×Dic₄₇	—	2	2	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	4	8	no	—
203	C₂×Dic₄₇	—	4	8	no	—
204	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
205	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
206	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
207	C₂×Dic₄₇	#131	1	2	yes	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	—	4	1	no	—
210	C₈×C₄₇	—	4	2	no	—
211	C₄₇⋊C₈	—	2	2	no	—
212	C₄₇⋊C₈	—	4	1	no	—
213	C₄₇⋊C₈	—	4	2	no	—
214	#22696	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	—	2	4	no	—
216	C₂²×C₄₇	—	2	4	no	—
217	C₂²×C₄₇	—	2	4	no	—
218	C₂²×C₄₇	—	2	4	no	—
219	C₂²×C₄₇	—	2	4	no	—
220	C₂²×C₄₇	—	2	4	no	—
221	C₂²×C₄₇	C₂×C₄⋊C₈	1	8	yes	—
222	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
224	C₂²×C₄₇	#518	1	1	yes	characteristic
225	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
226	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
227	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
228	C₂²×C₄₇	#568	1	1	yes	characteristic
229	C₄×C₄₇	—	2	4	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	C₂×C₄⋊C₈	1	4	yes	—
232	C₄×C₄₇	#546	1	1	yes	characteristic
233	C₄×C₄₇	#546	1	1	yes	characteristic
234	C₄×C₄₇	#554	1	1	yes	characteristic
235	C₄×C₄₇	#554	1	1	yes	characteristic
236	Dic₄₇	—	2	2	no	—
237	Dic₄₇	—	2	2	no	—
238	Dic₄₇	—	2	4	no	—
239	Dic₄₇	—	2	2	no	—
240	Dic₄₇	—	4	1	no	—
241	Dic₄₇	—	4	2	no	—
242	C₂×C₈×D₄	—	47	1	no	—
243	C₂×C₈×D₄	D₄₇	1	1	yes	characteristic
244	C₄²×D₄	—	47	1	no	—
245	#1939	—	47	1	no	—
246	#1939	—	47	1	no	—
247	#1850	—	47	2	no	—
248	#1850	—	47	2	no	—
249	#1831	—	47	1	no	—
250	#1797	—	47	2	no	—
251	C₄×C₄⋊C₈	—	47	1	no	—
252	C₂×#336	—	47	2	no	—
253	C₂×C₄₇	—	2	8	no	—
254	C₂×C₄₇	#2349	1	1	yes	characteristic
255	C₂×C₄₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
256	C₂×C₄₇	#2906	1	1	yes	characteristic
257	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
258	C₂×C₄₇	#2970	1	1	yes	characteristic
259	C₂×C₄₇	#2972	1	1	yes	characteristic
260	C₂×C₄₇	#2974	1	1	yes	characteristic
261	C₂³×C₈	—	47	2	no	—
262	C₂³×C₈	C₂×D₄₇	1	2	yes	—
263	C₂×C₄×D₄	—	47	1	no	—
264	C₂×C₄×D₄	—	47	1	no	—
265	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
266	C₂²×C₄²	—	47	2	no	—
267	C₈×D₄	—	2	4	no	—
268	C₈×D₄	—	94	4	no	—
269	C₂×C₄⋊C₈	—	47	1	no	—
270	C₂×C₄⋊C₈	—	47	1	no	—
271	C₂×C₄⋊C₈	—	47	1	no	—
272	C₂×C₄⋊C₈	—	47	2	no	—
273	C₂×C₄⋊C₈	—	47	2	no	—
274	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	—	47	2	no	—
276	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
277	C₂×C₄×C₈	—	47	1	no	—
278	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
279	C₄×C₄⋊C₄	—	47	1	no	—
280	C₄×C₄⋊C₄	—	47	1	no	—
281	C₄×C₄⋊C₄	—	47	1	no	—
282	C₄×C₂²⋊C₄	—	47	2	no	—
283	C₄×C₂²⋊C₄	—	47	2	no	—
284	C₄×C₂²⋊C₄	—	47	2	no	—
285	C₄³	—	47	1	no	—
286	#336	—	47	1	no	—
287	#336	—	47	2	no	—
288	#336	—	47	2	no	—
289	#336	—	47	2	no	—
290	#336	—	47	2	no	—
291	#336	—	47	1	no	—
292	C₄₇	#22696	1	1	yes	characteristic, complemented, Sylow
293	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
294	C₂³×C₄	—	47	2	no	—
295	C₂³×C₄	—	47	2	no	—
296	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
297	C₂²×C₈	—	2	4	no	—
298	C₂²×C₈	—	2	4	no	—
299	C₂²×C₈	—	4	2	no	—
300	C₂²×C₈	—	47	1	no	—
301	C₂²×C₈	—	47	2	no	—
302	C₂²×C₈	—	47	1	no	—
303	C₂²×C₈	—	94	4	no	—
304	C₂²×C₈	—	94	4	no	—
305	C₂²×C₈	—	188	2	no	—
306	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
307	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
308	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₄×D₄	—	47	8	no	—
310	C₄×D₄	—	94	4	no	—
311	C₄×D₄	Dic₉₄	1	4	yes	—
312	C₄×D₄	C₂²⋊D₄₇	1	4	yes	—
313	C₂×C₄⋊C₄	—	47	1	no	—
314	C₂×C₄⋊C₄	—	47	1	no	—
315	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	47	2	no	—
317	C₂×C₂²⋊C₄	—	47	2	no	—
318	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	47	1	no	—
323	C₂×C₄²	—	47	1	no	—
324	C₂×C₄²	—	47	2	no	—
325	C₂×C₄²	—	47	1	no	—
326	C₂×C₄²	—	47	2	no	—
327	C₂×C₄²	—	47	2	no	—
328	C₂×C₄²	—	188	2	no	—
329	C₂×C₄²	—	188	2	no	—
330	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	94	2	no	—
333	C₄⋊C₈	—	94	2	no	—
334	C₄⋊C₈	—	94	2	no	—
335	C₄⋊C₈	—	188	2	no	—
336	C₄⋊C₈	—	188	2	no	—
337	C₂²⋊C₈	—	2	4	no	—
338	C₂²⋊C₈	—	94	4	no	—
339	C₄×C₈	—	2	2	no	—
340	C₄×C₈	—	94	2	no	—
341	#95	—	47	2	no	—
342	#95	—	47	2	no	—
343	#95	—	47	2	no	—
344	C₂⁴	C₂×C₄×D₄₇	1	2	yes	—
345	C₂×D₄	C₈×D₄₇	1	4	yes	—
346	C₂×D₄	#10625324	1	4	yes	—
347	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	47	1	no	—
353	C₂²×C₄	—	47	2	no	—
354	C₂²×C₄	—	47	1	no	—
355	C₂²×C₄	—	47	1	no	—
356	C₂²×C₄	—	47	8	no	—
357	C₂²×C₄	—	47	1	no	—
358	C₂²×C₄	—	47	2	no	—
359	C₂²×C₄	—	94	4	no	—
360	C₂²×C₄	—	94	4	no	—
361	C₂²×C₄	—	188	2	no	—
362	C₂²×C₄	—	188	2	no	—
363	C₂²×C₄	—	188	2	no	—
364	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
365	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
367	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
369	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	4	8	no	—
379	C₂×C₈	—	47	2	no	—
380	C₂×C₈	—	94	1	no	—
381	C₂×C₈	—	94	1	no	—
382	C₂×C₈	—	94	1	no	—
383	C₂×C₈	—	94	2	no	—
384	C₂×C₈	—	94	2	no	—
385	C₂×C₈	—	94	1	no	—
386	C₂×C₈	—	94	1	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	—	188	8	no	—
389	C₂×C₈	#10625352	1	2	yes	—
390	C₄⋊C₄	—	47	4	no	—
391	C₄⋊C₄	—	94	2	no	—
392	C₄⋊C₄	Dic₄₇⋊C₄	1	4	yes	—
393	C₂²⋊C₄	—	47	8	no	—
394	C₂²⋊C₄	—	94	4	no	—
395	C₂²⋊C₄	Dic₄₇⋊C₄	1	8	yes	—
396	C₄²	—	47	4	no	—
397	C₄²	—	94	2	no	—
398	C₄²	—	94	2	no	—
399	C₄²	—	94	1	no	—
400	C₄²	—	94	1	no	—
401	C₄²	—	94	2	no	—
402	C₄²	—	94	1	no	—
403	C₄²	—	94	2	no	—
404	C₄²	—	94	1	no	—
405	C₄²	—	188	1	no	—
406	C₄²	—	188	2	no	—
407	C₄²	—	188	2	no	—
408	C₄²	C₂×Dic₉₄	1	2	yes	—
409	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	C₂×Dic₄₇⋊C₄	1	4	yes	—
415	C₂³	C₂×C₈×D₄₇	1	4	yes	—
416	C₂³	C₂×#10625324	1	4	yes	—
417	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
418	D₄	Dic₄₇⋊C₈	1	16	yes	complemented
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	47	2	no	—
428	C₂×C₄	—	47	2	no	—
429	C₂×C₄	—	47	4	no	—
430	C₂×C₄	—	47	2	no	—
431	C₂×C₄	—	94	1	no	—
432	C₂×C₄	—	94	1	no	—
433	C₂×C₄	—	94	1	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	1	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	94	1	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	94	2	no	—
443	C₂×C₄	—	94	2	no	—
444	C₂×C₄	—	94	1	no	—
445	C₂×C₄	—	188	8	no	—
446	C₂×C₄	—	188	8	no	—
447	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
448	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
449	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
450	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
451	C₂×C₄	C₂×#10625324	1	2	yes	—
452	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
454	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
455	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
456	C₂×C₄	#13094069	1	1	yes	characteristic
457	C₂×C₄	#13094070	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	2	no	—
461	C₈	—	94	2	no	—
462	C₈	—	188	2	no	—
463	C₈	—	188	1	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	C₂×Dic₄₇⋊C₈	1	8	yes	—
471	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
472	C₂²	C₄×#10625352	1	1	yes	characteristic
473	C₂²	#15689595	1	1	yes	characteristic
474	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
475	C₂²	C₂²×#10625324	1	1	yes	characteristic
476	C₂²	#131×D₄₇	1	1	yes	characteristic
477	C₂²	#15689888	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	94	2	no	—
481	C₄	—	94	2	no	—
482	C₄	—	94	2	no	—
483	C₄	—	94	4	no	—
484	C₄	—	188	2	no	—
485	C₄	—	188	1	no	—
486	C₄	C₂×Dic₄₇⋊C₈	1	4	yes	—
487	C₄	#15689761	1	1	yes	characteristic
488	C₄	#15689767	1	1	yes	characteristic
489	C₄	#15689830	1	1	yes	characteristic
490	C₄	#15689832	1	1	yes	characteristic
491	C₂	—	2	8	no	—
492	C₂	#20246293	1	1	yes	characteristic
493	C₂	C₂²×Dic₄₇⋊C₈	1	1	yes	characteristic
494	C₂	#20251954	1	1	yes	characteristic
495	C₂	C₈×#10625352	1	1	yes	characteristic
496	C₂	#20252396	1	1	yes	characteristic
497	C₂	#20252409	1	1	yes	characteristic
498	C₂	#20252421	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₂×C₈×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₈×D₄	D₄₇
hypocenter	C₄₇	#22696
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
3. #20244106	C₂	semidirect
4. #20244104	C₂	semidirect
5. #20243566	C₂	semidirect
6. #20243565	C₂	semidirect
7. #20243504	C₂	semidirect
8. #20243366	C₂	semidirect
9. C₄×Dic₄₇⋊C₈	C₂	semidirect
10. C₂×#15688877	C₂	semidirect
52. D₄×Dic₄₇	C₈	semidirect
113. C₂²×Dic₄₇	C₂×C₈	semidirect
135. C₂²⋊Dic₄₇	C₂×C₈	semidirect
137. C₄⋊Dic₄₇	C₂×C₈	semidirect
149. C₄×Dic₄₇	C₂×C₈	semidirect
168. D₄×C₄₇	C₄⋊C₈	semidirect
292. C₄₇	#22696	semidirect
418. D₄	Dic₄₇⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
C₄×D₄×Dic₄₇	2
#20244106	2
#20244104	2
#20243566	2
#20243565	2
#20243504	2
#20243366	2
C₄×Dic₄₇⋊C₈	2
C₂×#15688877	2
C₂×C₈×D₄×C₄₇	2
#22696	47