Subgroups — #26234527

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20252120	C₂	1	1	yes	maximal, characteristic
3	C₂×(C₂²⋊D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#108×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244162	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244160	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243595	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243594	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243591	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243558	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243425	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243424	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243289	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
19	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
22	#15689199	—	2	1	no	—
23	#15689198	—	2	1	no	—
24	#15689197	—	2	1	no	—
25	#15689194	—	2	1	no	—
26	#15689192	—	2	1	no	—
27	#15689191	—	2	1	no	—
28	C₈×C₂²⋊D₄₇	—	2	1	no	—
29	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
30	(C₂²⋊D₄₇)⋊C₈	C₄	1	2	yes	—
31	(C₂²⋊D₄₇)⋊C₈	C₄	1	2	yes	—
32	(C₂²⋊D₄₇)⋊C₈	C₄	1	2	yes	—
33	(C₂²⋊D₄₇)⋊C₈	C₄	1	2	yes	—
34	C₂×#13093960	C₂²	1	1	yes	characteristic
35	C₂×#13093960	C₂²	1	1	yes	characteristic
36	C₂×#13093959	—	2	4	no	—
37	C₂×#13093959	C₂²	1	1	yes	characteristic
38	C₂×#13093959	C₂²	1	1	yes	characteristic
39	C₂×#13093959	C₂²	1	1	yes	characteristic
40	C₂×#13093959	C₂²	1	1	yes	characteristic
41	C₂×#13093959	C₂²	1	1	yes	characteristic
42	C₂×#13093959	C₂²	1	1	yes	characteristic
43	#108×D₄₇	—	2	4	no	—
44	#15689146	C₂²	1	1	yes	characteristic
45	#15689146	C₂²	1	1	yes	characteristic
46	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
47	#15689087	C₂²	1	1	yes	characteristic
48	#15689086	C₂²	1	1	yes	characteristic
49	#15689086	C₂²	1	1	yes	characteristic
50	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
51	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
52	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
54	#15688888	C₂²	1	1	yes	characteristic
55	#15688888	C₂²	1	1	yes	characteristic
56	#15688887	C₂²	1	1	yes	characteristic
57	#15688887	C₂²	1	1	yes	characteristic
58	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
59	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
60	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
61	C₄₇×#407	C₂²	1	1	yes	characteristic
62	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
63	C₄₇×#341	C₂²	1	1	yes	characteristic
64	C₄₇×#341	C₂²	1	1	yes	characteristic
65	C₂²×C₂²⋊D₄₇	Q₈	1	1	yes	characteristic
66	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
67	C₂×#10625329	—	2	1	no	—
68	C₂×#10625329	—	2	2	no	—
69	C₂×#10625329	—	4	1	no	—
70	C₂×#10625329	C₂³	1	1	yes	characteristic
71	C₂×#10625329	C₂³	1	1	yes	characteristic
72	C₂×#10625329	C₂³	1	1	yes	characteristic
73	C₂×#10625329	C₂³	1	1	yes	characteristic
74	C₂×#10625324	—	2	1	no	—
75	C₂×#10625324	—	2	1	no	—
76	M₁₆×D₄₇	—	2	2	no	—
77	M₁₆×D₄₇	—	2	2	no	—
78	M₁₆×D₄₇	—	4	1	no	—
79	M₁₆×D₄₇	—	4	1	no	—
80	C₂²×C₄₇⋊C₈	—	2	2	no	—
81	C₂²×C₄₇⋊C₈	—	2	2	no	—
82	C₂²×C₄₇⋊C₈	—	2	1	no	—
83	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
84	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
85	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₄₇	—	2	2	no	—
88	C₂×C₈×D₄₇	—	2	2	no	—
89	C₂×C₈×D₄₇	—	2	1	no	—
90	C₂×C₈×D₄₇	—	2	1	no	—
91	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
92	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
93	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
94	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
95	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
96	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
97	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
98	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
99	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
100	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
101	C₂×Dic₄₇⋊C₄	Q₈	1	1	yes	characteristic
102	C₂×C₂²⋊Dic₄₇	Q₈	1	1	yes	characteristic
103	C₂×(C₂×D₄₇)⋊C₄	Q₈	1	1	yes	characteristic
104	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
105	#13093960	—	2	2	no	—
106	#13093960	—	4	1	no	—
107	#13093959	—	2	2	no	—
108	#13093959	—	2	2	no	—
109	#13093959	—	2	2	no	—
110	#13093959	—	2	2	no	—
111	#13093959	—	2	2	no	—
112	#13093959	D₄	1	4	yes	complemented
113	Dic₄₇⋊C₈	—	2	1	no	—
114	Dic₄₇⋊C₈	—	2	1	no	—
115	Dic₄₇⋊C₈	—	2	1	no	—
116	Dic₄₇⋊C₈	—	2	1	no	—
117	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
118	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
119	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
120	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
121	(C₂×D₄₇)⋊C₈	—	2	1	no	—
122	(C₂×D₄₇)⋊C₈	—	2	1	no	—
123	(C₂×D₄₇)⋊C₈	—	2	1	no	—
124	(C₂×D₄₇)⋊C₈	—	2	1	no	—
125	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
126	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
127	#13093934	—	2	1	no	—
128	#13093934	—	2	1	no	—
129	C₈×Dic₄₇	—	2	1	no	—
130	C₈×Dic₄₇	—	2	1	no	—
131	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
132	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
133	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
134	C₂×M₁₆×C₄₇	—	2	1	no	—
135	C₂×M₁₆×C₄₇	—	2	2	no	—
136	C₂×M₁₆×C₄₇	—	4	1	no	—
137	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₄₇	—	2	1	no	—
142	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
144	#108×C₄₇	—	2	2	no	—
145	#108×C₄₇	—	4	1	no	—
146	C₂²⋊C₈×C₄₇	—	2	1	no	—
147	C₂²⋊C₈×C₄₇	—	2	1	no	—
148	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
149	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
150	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
151	C₂³×D₄₇	C₂×Q₈	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	—	2	1	no	—
156	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
162	C₂×C₂²⋊D₄₇	—	2	4	no	—
163	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
167	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
168	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
169	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
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	1	no	—
174	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
177	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
178	M₁₆×C₄₇	—	2	1	no	—
179	M₁₆×C₄₇	—	2	1	no	—
180	M₁₆×C₄₇	—	2	1	no	—
181	M₁₆×C₄₇	—	2	1	no	—
182	M₁₆×C₄₇	—	2	1	no	—
183	M₁₆×C₄₇	—	2	1	no	—
184	M₁₆×C₄₇	—	2	1	no	—
185	M₁₆×C₄₇	—	4	2	no	—
186	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₄₇	—	2	1	no	—
188	C₂×C₈×C₄₇	—	2	1	no	—
189	C₂×C₈×C₄₇	—	2	1	no	—
190	C₂×C₈×C₄₇	—	2	1	no	—
191	C₂×C₈×C₄₇	—	2	1	no	—
192	C₂×C₈×C₄₇	—	2	1	no	—
193	C₂×C₈×C₄₇	—	2	1	no	—
194	C₂×C₈×C₄₇	—	2	1	no	—
195	C₂×C₈×C₄₇	—	4	2	no	—
196	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
197	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
198	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
199	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
200	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
201	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
202	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
203	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
204	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
205	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
206	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
207	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
208	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
209	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
210	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
211	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
212	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
213	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
214	#10625329	—	2	1	no	—
215	#10625329	—	2	1	no	—
216	#10625329	—	2	1	no	—
217	#10625329	—	2	1	no	—
218	#10625329	—	2	1	no	—
219	#10625329	—	2	1	no	—
220	#10625329	—	2	1	no	—
221	#10625329	—	4	2	no	—
222	#10625329	C₂×D₄	1	2	yes	—
223	C₂×C₄₇⋊C₈	—	2	1	no	—
224	C₂×C₄₇⋊C₈	—	2	1	no	—
225	C₂×C₄₇⋊C₈	—	2	1	no	—
226	C₂×C₄₇⋊C₈	—	2	4	no	—
227	C₂×C₄₇⋊C₈	—	2	4	no	—
228	C₂×C₄₇⋊C₈	—	2	1	no	—
229	C₂×C₄₇⋊C₈	—	2	1	no	—
230	C₂×C₄₇⋊C₈	—	2	1	no	—
231	C₂×C₄₇⋊C₈	—	4	2	no	—
232	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
233	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
234	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
235	C₂×C₄₇⋊C₈	#41	1	2	yes	—
236	#10625324	—	4	2	no	—
237	#10625324	—	4	2	no	—
238	C₈×D₄₇	—	2	4	no	—
239	C₈×D₄₇	—	2	4	no	—
240	C₈×D₄₇	—	4	2	no	—
241	C₈×D₄₇	—	4	2	no	—
242	C₂³×C₄₇	—	2	1	no	—
243	C₂³×C₄₇	—	2	1	no	—
244	C₂³×C₄₇	—	2	2	no	—
245	C₂³×C₄₇	—	4	1	no	—
246	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
249	C₂²×D₄₇	—	2	1	no	—
250	C₂²×D₄₇	—	2	1	no	—
251	C₂²×D₄₇	—	2	2	no	—
252	C₂²×D₄₇	—	4	1	no	—
253	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	—	2	1	no	—
256	C₂×C₄×C₄₇	—	2	1	no	—
257	C₂×C₄×C₄₇	—	2	1	no	—
258	C₂×C₄×C₄₇	—	2	1	no	—
259	C₂×C₄×C₄₇	—	2	1	no	—
260	C₂×C₄×C₄₇	—	2	1	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	C₂×C₄⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
273	C₂²⋊D₄₇	—	2	2	no	—
274	C₂²⋊D₄₇	—	2	2	no	—
275	C₂²⋊D₄₇	—	2	2	no	—
276	C₂²⋊D₄₇	#108	1	4	yes	complemented
277	C₂×Dic₄₇	—	2	1	no	—
278	C₂×Dic₄₇	—	2	1	no	—
279	C₂×Dic₄₇	—	2	2	no	—
280	C₂×Dic₄₇	—	4	1	no	—
281	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
282	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
283	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
284	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
285	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
286	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
287	C₄×D₄₇	—	2	1	no	—
288	C₄×D₄₇	—	2	1	no	—
289	C₄×D₄₇	—	2	1	no	—
290	C₄×D₄₇	—	2	1	no	—
291	C₄×D₄₇	—	2	1	no	—
292	C₄×D₄₇	—	2	1	no	—
293	C₄×D₄₇	—	2	1	no	—
294	C₄×D₄₇	—	2	1	no	—
295	C₈×C₄₇	—	2	2	no	—
296	C₈×C₄₇	—	2	2	no	—
297	C₈×C₄₇	—	2	2	no	—
298	C₈×C₄₇	—	4	1	no	—
299	C₈×C₄₇	—	4	1	no	—
300	C₈×C₄₇	—	4	1	no	—
301	C₄₇⋊C₈	—	2	2	no	—
302	C₄₇⋊C₈	—	2	2	no	—
303	C₄₇⋊C₈	—	4	1	no	—
304	C₄₇⋊C₈	—	4	1	no	—
305	C₄₇⋊C₈	—	4	1	no	—
306	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
307	D₄×#108	—	47	1	no	maximal, Sylow
308	C₂²×C₄₇	—	2	1	no	—
309	C₂²×C₄₇	—	2	1	no	—
310	C₂²×C₄₇	—	2	1	no	—
311	C₂²×C₄₇	—	2	1	no	—
312	C₂²×C₄₇	—	2	1	no	—
313	C₂²×C₄₇	—	2	1	no	—
314	C₂²×C₄₇	—	2	1	no	—
315	C₂²×C₄₇	—	4	2	no	—
316	C₂²×C₄₇	—	4	2	no	—
317	C₂²×C₄₇	C₂×#108	1	2	yes	complemented
318	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
319	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
320	C₂²×C₄₇	#554	1	1	yes	characteristic
321	C₂×D₄₇	—	2	1	no	—
322	C₂×D₄₇	—	2	1	no	—
323	C₂×D₄₇	—	2	1	no	—
324	C₂×D₄₇	—	2	1	no	—
325	C₂×D₄₇	—	2	1	no	—
326	C₂×D₄₇	—	4	2	no	—
327	C₂×D₄₇	—	4	2	no	—
328	C₂×D₄₇	C₂×#108	1	2	yes	complemented
329	C₄×C₄₇	—	2	1	no	—
330	C₄×C₄₇	—	2	1	no	—
331	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
332	C₄×C₄₇	#520	1	1	yes	characteristic
333	C₄×C₄₇	D₄²	1	1	yes	characteristic
334	C₄×C₄₇	#547	1	1	yes	characteristic
335	Dic₄₇	—	2	1	no	—
336	Dic₄₇	—	2	1	no	—
337	Dic₄₇	—	2	1	no	—
338	Dic₄₇	—	2	1	no	—
339	Dic₄₇	—	2	1	no	—
340	Dic₄₇	C₂×#108	1	2	yes	complemented
341	D₄×M₁₆	—	47	1	no	—
342	D₄×M₁₆	—	47	1	no	—
343	C₂×C₈×D₄	—	47	1	no	—
344	C₂²×#108	—	47	1	no	—
345	C₂²×#108	—	47	1	no	—
346	#1950	—	47	1	no	—
347	#1950	—	47	1	no	—
348	#1855	—	47	1	no	—
349	#1855	—	47	1	no	—
350	#1855	—	47	1	no	—
351	#1855	D₄₇	1	1	yes	characteristic, complemented
352	#1848	—	47	1	no	—
353	#1810	—	47	1	no	—
354	#1810	—	47	1	no	—
355	C₄×#108	—	47	1	no	—
356	C₂×C₄₇	—	2	1	no	—
357	C₂×C₄₇	—	2	1	no	—
358	C₂×C₄₇	—	2	2	no	—
359	C₂×C₄₇	—	4	1	no	—
360	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
361	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
362	C₂×C₄₇	#2916	1	1	yes	characteristic
363	D₄₇	—	2	2	no	—
364	D₄₇	—	4	1	no	—
365	C₂²×M₁₆	—	47	1	no	—
366	C₂²×M₁₆	—	47	1	no	—
367	C₂²×M₁₆	—	47	1	no	—
368	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
369	C₂³×C₈	—	47	1	no	—
370	C₂³×C₈	—	47	1	no	—
371	C₂×C₄×D₄	—	47	1	no	—
372	#436	—	94	1	no	—
373	#436	—	94	1	no	—
374	#435	—	94	1	no	—
375	#435	—	94	1	no	—
376	#435	—	94	1	no	—
377	#435	—	94	1	no	—
378	C₈×D₄	—	47	2	no	—
379	C₈×D₄	—	47	2	no	—
380	C₈×D₄	—	47	2	no	—
381	C₈×D₄	—	47	2	no	—
382	C₈×D₄	—	94	1	no	—
383	C₈×D₄	—	94	1	no	—
384	C₂×#108	—	47	1	no	—
385	C₂×#108	—	47	1	no	—
386	C₂×#108	—	47	1	no	—
387	C₂×#108	—	47	1	no	—
388	C₂×#108	—	47	1	no	—
389	C₂×#108	—	47	1	no	—
390	C₂×#108	—	47	1	no	—
391	C₂×#108	—	47	1	no	—
392	C₂×#108	—	94	4	no	—
393	C₂×#108	—	94	4	no	—
394	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
395	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
396	#423	—	47	1	no	—
397	#423	—	47	1	no	—
398	C₂×C₄⋊C₈	—	47	1	no	—
399	#407	—	47	1	no	—
400	#407	—	47	1	no	—
401	#407	—	47	1	no	—
402	#407	C₂×D₄₇	1	1	yes	characteristic
403	C₂×C₂²⋊C₈	—	47	1	no	—
404	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
405	C₄×M₁₆	—	47	1	no	—
406	C₄×M₁₆	—	47	1	no	—
407	C₂×C₄×C₈	—	47	1	no	—
408	#341	—	47	1	no	—
409	#341	—	47	1	no	—
410	#341	—	47	1	no	—
411	#341	—	47	1	no	—
412	#341	C₂×D₄₇	1	1	yes	characteristic
413	#341	C₂×D₄₇	1	1	yes	characteristic
414	C₄₇	D₄×#108	1	1	yes	characteristic, complemented, Sylow
415	C₂²×D₄	—	47	1	no	—
416	C₂³×C₄	—	47	1	no	—
417	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
418	C₂×M₁₆	—	2	1	no	—
419	C₂×M₁₆	—	2	2	no	—
420	C₂×M₁₆	—	4	1	no	—
421	C₂×M₁₆	—	47	1	no	—
422	C₂×M₁₆	—	47	1	no	—
423	C₂×M₁₆	—	47	1	no	—
424	C₂×M₁₆	—	47	1	no	—
425	C₂×M₁₆	—	94	1	no	—
426	C₂×M₁₆	—	94	1	no	—
427	C₂×M₁₆	—	94	1	no	—
428	C₂×M₁₆	—	94	2	no	—
429	C₂×M₁₆	—	94	2	no	—
430	C₂×M₁₆	—	94	2	no	—
431	C₂×M₁₆	—	188	1	no	—
432	C₂×M₁₆	—	188	1	no	—
433	C₂×M₁₆	—	188	1	no	—
434	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
435	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
436	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
437	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
438	C₂²×C₈	—	2	1	no	—
439	C₂²×C₈	—	47	1	no	—
440	C₂²×C₈	—	47	2	no	—
441	C₂²×C₈	—	47	2	no	—
442	C₂²×C₈	—	47	1	no	—
443	C₂²×C₈	—	47	2	no	—
444	C₂²×C₈	—	47	2	no	—
445	C₂²×C₈	—	94	2	no	—
446	C₂²×C₈	—	94	2	no	—
447	C₂²×C₈	—	94	1	no	—
448	C₂²×C₈	—	94	1	no	—
449	C₂²×C₈	—	94	2	no	—
450	C₂²×C₈	—	94	2	no	—
451	C₂²×C₈	—	94	1	no	—
452	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
453	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
454	C₄×D₄	—	47	1	no	—
455	C₄×D₄	—	47	1	no	—
456	C₄×D₄	—	47	1	no	—
457	C₄×D₄	—	47	1	no	—
458	C₄×D₄	—	47	1	no	—
459	C₄×D₄	—	47	1	no	—
460	C₄×D₄	—	47	1	no	—
461	C₄×D₄	—	47	1	no	—
462	C₂×C₄⋊C₄	—	47	1	no	—
463	C₂×C₂²⋊C₄	—	47	1	no	—
464	C₂×C₂²⋊C₄	—	47	1	no	—
465	C₂×C₄²	—	47	1	no	—
466	#108	—	2	2	no	—
467	#108	—	4	1	no	—
468	#108	—	47	4	no	—
469	#108	—	94	2	no	—
470	#108	—	94	2	no	—
471	#108	—	94	2	no	—
472	#108	—	94	2	no	—
473	#108	—	94	2	no	—
474	#108	—	94	2	no	—
475	#108	—	188	1	no	—
476	C₄⋊C₈	—	47	2	no	—
477	C₄⋊C₈	—	47	2	no	—
478	C₄⋊C₈	—	94	1	no	—
479	C₄⋊C₈	—	94	1	no	—
480	C₄⋊C₈	—	94	1	no	—
481	C₄⋊C₈	—	94	1	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	C₂²⋊C₈	—	2	1	no	—
484	C₂²⋊C₈	—	47	2	no	—
485	C₂²⋊C₈	—	47	2	no	—
486	C₂²⋊C₈	—	94	1	no	—
487	C₂²⋊C₈	—	94	1	no	—
488	C₂²⋊C₈	—	94	1	no	—
489	C₂²⋊C₈	—	94	1	no	—
490	C₂²⋊C₈	—	94	1	no	—
491	C₂²⋊C₈	—	94	1	no	—
492	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
493	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
494	#97	—	94	1	no	—
495	#97	—	94	1	no	—
496	C₄×C₈	—	47	2	no	—
497	C₄×C₈	—	47	2	no	—
498	C₄×C₈	—	94	1	no	—
499	C₄×C₈	—	94	1	no	—
500	C₂⁴	—	47	1	no	—
501	C₂⁴	Q₈×D₄₇	1	1	yes	characteristic
502	C₂×D₄	—	47	1	no	—
503	C₂×D₄	—	47	1	no	—
504	C₂×D₄	—	47	1	no	—
505	C₂×D₄	—	47	1	no	—
506	C₂×D₄	—	94	4	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	47	1	no	—
512	C₂²×C₄	—	47	1	no	—
513	C₂²×C₄	—	47	1	no	—
514	C₂²×C₄	—	47	1	no	—
515	C₂²×C₄	—	47	1	no	—
516	C₂²×C₄	—	47	1	no	—
517	C₂²×C₄	—	47	1	no	—
518	C₂²×C₄	—	94	1	no	—
519	C₂²×C₄	—	94	1	no	—
520	C₂²×C₄	—	94	1	no	—
521	C₂²×C₄	—	94	1	no	—
522	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
524	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
525	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
526	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
527	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
528	M₁₆	—	2	1	no	—
529	M₁₆	—	2	1	no	—
530	M₁₆	—	2	1	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	4	2	no	—
536	M₁₆	—	47	2	no	—
537	M₁₆	—	94	1	no	—
538	M₁₆	—	94	1	no	—
539	M₁₆	—	94	1	no	—
540	M₁₆	—	94	1	no	—
541	M₁₆	—	94	1	no	—
542	M₁₆	—	94	1	no	—
543	M₁₆	—	94	1	no	—
544	M₁₆	—	188	2	no	—
545	M₁₆	—	188	2	no	—
546	M₁₆	—	188	2	no	—
547	M₁₆	D₄×D₄₇	1	2	yes	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	4	2	no	—
557	C₂×C₈	—	47	2	no	—
558	C₂×C₈	—	47	2	no	—
559	C₂×C₈	—	47	2	no	—
560	C₂×C₈	—	47	2	no	—
561	C₂×C₈	—	94	4	no	—
562	C₂×C₈	—	94	4	no	—
563	C₂×C₈	—	94	4	no	—
564	C₂×C₈	—	94	4	no	—
565	C₂×C₈	—	94	1	no	—
566	C₂×C₈	—	94	1	no	—
567	C₂×C₈	—	94	1	no	—
568	C₂×C₈	—	94	1	no	—
569	C₂×C₈	—	94	1	no	—
570	C₂×C₈	—	94	1	no	—
571	C₂×C₈	—	188	2	no	—
572	C₂×C₈	—	188	2	no	—
573	C₂×C₈	—	188	2	no	—
574	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
575	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
576	C₄⋊C₄	—	47	1	no	—
577	C₄⋊C₄	—	47	1	no	—
578	C₄⋊C₄	—	47	1	no	—
579	C₄⋊C₄	—	47	1	no	—
580	C₂²⋊C₄	—	47	1	no	—
581	C₂²⋊C₄	—	47	1	no	—
582	C₂²⋊C₄	—	47	1	no	—
583	C₂²⋊C₄	—	47	1	no	—
584	C₂²⋊C₄	—	47	1	no	—
585	C₂²⋊C₄	—	47	1	no	—
586	C₂²⋊C₄	—	47	1	no	—
587	C₂²⋊C₄	—	47	1	no	—
588	C₄²	—	47	1	no	—
589	C₄²	—	47	1	no	—
590	C₄²	—	47	1	no	—
591	C₄²	—	47	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	47	1	no	—
597	C₂³	—	47	1	no	—
598	C₂³	—	94	2	no	—
599	C₂³	—	94	1	no	—
600	C₂³	—	94	1	no	—
601	C₂³	—	188	1	no	—
602	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
603	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
604	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
605	D₄	—	47	4	no	—
606	D₄	—	94	2	no	—
607	D₄	—	94	2	no	—
608	D₄	—	94	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	47	1	no	—
620	C₂×C₄	—	47	1	no	—
621	C₂×C₄	—	47	1	no	—
622	C₂×C₄	—	47	1	no	—
623	C₂×C₄	—	47	1	no	—
624	C₂×C₄	—	47	1	no	—
625	C₂×C₄	—	94	2	no	—
626	C₂×C₄	—	94	1	no	—
627	C₂×C₄	—	94	1	no	—
628	C₂×C₄	—	94	1	no	—
629	C₂×C₄	—	94	1	no	—
630	C₂×C₄	—	94	1	no	—
631	C₂×C₄	—	94	1	no	—
632	C₂×C₄	—	94	1	no	—
633	C₂×C₄	—	94	1	no	—
634	C₂×C₄	—	94	1	no	—
635	C₂×C₄	—	94	1	no	—
636	C₂×C₄	—	188	1	no	—
637	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
638	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
639	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
640	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
641	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
642	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
643	C₂×C₄	#13094069	1	1	yes	characteristic
644	C₂×C₄	#13094071	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₈	—	47	4	no	—
652	C₈	—	94	2	no	—
653	C₈	—	94	2	no	—
654	C₈	—	188	1	no	—
655	C₈	—	188	1	no	—
656	C₈	—	188	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	47	2	no	—
667	C₂²	—	94	1	no	—
668	C₂²	—	94	1	no	—
669	C₂²	—	94	1	no	—
670	C₂²	—	94	1	no	—
671	C₂²	—	94	1	no	—
672	C₂²	—	188	2	no	—
673	C₂²	—	188	2	no	—
674	C₂²	#108×D₄₇	1	2	yes	complemented
675	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
676	C₂²	#15689786	1	1	yes	characteristic
677	C₂²	#15689827	1	1	yes	characteristic
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	47	2	no	—
681	C₄	—	94	1	no	—
682	C₄	—	94	1	no	—
683	C₄	—	94	1	no	—
684	C₄	—	94	1	no	—
685	C₄	—	94	1	no	—
686	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
687	C₄	#15689602	1	1	yes	characteristic
688	C₄	#15689755	1	1	yes	characteristic
689	C₄	#15689771	1	1	yes	characteristic
690	C₂	—	2	1	no	—
691	C₂	—	2	1	no	—
692	C₂	—	2	2	no	—
693	C₂	—	4	1	no	—
694	C₂	—	94	2	no	—
695	C₂	—	188	1	no	—
696	C₂	#20246286	1	1	yes	characteristic
697	C₂	C₂×#108×D₄₇	1	1	yes	characteristic
698	C₂	#20251998	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1855	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂²×C₂²⋊D₄₇	Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1855	D₄₇
hypocenter	C₄₇	D₄×#108
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1855

Complements

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

N	H ≅ G/N	type
4. C₂²×#13093959	C₂	semidirect
5. C₂×#108×D₄₇	C₂	semidirect
6. #20244162	C₂	semidirect
7. #20244160	C₂	semidirect
8. #20243595	C₂	semidirect
9. #20243594	C₂	semidirect
10. #20243591	C₂	semidirect
11. #20243558	C₂	semidirect
12. #20243425	C₂	semidirect
13. #20243424	C₂	semidirect
14. #20243289	C₂	semidirect
15. C₄₇×#1855	C₂	semidirect
112. #13093959	D₄	semidirect
276. C₂²⋊D₄₇	#108	semidirect
317. C₂²×C₄₇	C₂×#108	semidirect
328. C₂×D₄₇	C₂×#108	semidirect
340. Dic₄₇	C₂×#108	semidirect
351. #1855	D₄₇	semidirect
414. C₄₇	D₄×#108	semidirect
674. C₂²	#108×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×C₂²⋊D₄₇	2
#20252120	2
C₂×(C₂²⋊D₄₇)⋊C₈	2
C₂²×#13093959	2
C₂×#108×D₄₇	2
#20244162	2
#20244160	2
#20243595	2
#20243594	2
#20243591	2
#20243558	2
#20243425	2
#20243424	2
#20243289	2
C₄₇×#1855	2
D₄×#108	47