Subgroups — #26182719

Order 12032.

1646 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252021	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252021	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241831	C₂	1	4	yes	maximal, complemented
4	#20241813	C₂	1	4	yes	maximal, complemented
5	#20241779	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
7	#15689180	—	2	1	no	—
8	#15689180	—	2	1	no	—
9	#15689180	—	2	1	no	—
10	#15689180	C₂²	1	2	yes	complemented
11	#15689176	—	2	1	no	—
12	#15689176	C₂²	1	2	yes	complemented
13	#15689176	C₂²	1	2	yes	complemented
14	#15689176	C₂²	1	2	yes	complemented
15	#15689147	—	2	1	no	—
16	#15689147	C₂²	1	2	yes	complemented
17	#15689087	—	2	1	no	—
18	#15689087	—	2	1	no	—
19	C₄×#10625329	—	2	1	no	—
20	C₄×#10625329	C₂²	1	2	yes	complemented
21	D₄⋊(C₄₇⋊C₈)	C₂²	1	16	yes	complemented
22	C₂³×D₄×C₄₇	C₄	1	1	yes	characteristic
23	C₂⁴×C₄×C₄₇	—	2	1	no	—
24	C₂×C₄×D₄×C₄₇	—	2	1	no	—
25	C₂×C₄×D₄×C₄₇	—	2	1	no	—
26	C₂×C₄×D₄×C₄₇	—	2	1	no	—
27	C₂×C₄×D₄×C₄₇	—	2	1	no	—
28	C₂×C₄×D₄×C₄₇	—	2	1	no	—
29	C₂×C₄×D₄×C₄₇	—	2	1	no	—
30	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
31	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
32	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
33	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
38	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#10625329	—	2	2	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
42	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
44	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	complemented
45	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
46	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
47	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
49	#13093935	—	2	2	no	—
50	#13093935	—	2	2	no	—
51	C₄×C₄₇⋊C₈	—	2	2	no	—
52	C₄×C₄₇⋊C₈	C₂³	1	4	yes	complemented
53	C₂⁵×C₄₇	—	2	1	no	—
54	C₂²×D₄×C₄₇	—	2	8	no	—
55	C₂²×D₄×C₄₇	—	2	1	no	—
56	C₂²×D₄×C₄₇	—	2	1	no	—
57	C₂²×D₄×C₄₇	—	2	1	no	—
58	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₄₇	—	2	1	no	—
62	C₂³×C₄×C₄₇	—	2	2	no	—
63	C₂³×C₄×C₄₇	—	2	2	no	—
64	C₂³×C₄×C₄₇	—	2	2	no	—
65	C₂³×C₄×C₄₇	—	2	2	no	—
66	C₂³×C₄×C₄₇	—	2	2	no	—
67	C₂³×C₄×C₄₇	—	2	2	no	—
68	C₂³×C₄×C₄₇	—	4	8	no	—
69	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₄×D₄×C₄₇	—	2	2	no	—
74	C₄×D₄×C₄₇	—	2	2	no	—
75	C₄×D₄×C₄₇	—	2	2	no	—
76	C₄×D₄×C₄₇	—	2	2	no	—
77	C₄×D₄×C₄₇	—	2	2	no	—
78	C₄×D₄×C₄₇	—	2	2	no	—
79	C₄×D₄×C₄₇	—	2	2	no	—
80	C₄×D₄×C₄₇	—	2	2	no	—
81	C₄×D₄×C₄₇	—	2	2	no	—
82	C₄×D₄×C₄₇	—	2	2	no	—
83	C₄×D₄×C₄₇	—	2	2	no	—
84	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
85	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
86	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
87	C₄×D₄×C₄₇	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
100	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
112	C₂⁴×C₄₇	—	2	8	no	—
113	C₂⁴×C₄₇	—	2	2	no	—
114	C₂⁴×C₄₇	—	2	2	no	—
115	C₂⁴×C₄₇	—	2	2	no	—
116	C₂⁴×C₄₇	—	4	4	no	—
117	C₂⁴×C₄₇	—	4	4	no	—
118	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×D₄×C₄₇	—	2	8	no	—
120	C₂×D₄×C₄₇	—	2	8	no	—
121	C₂×D₄×C₄₇	—	2	8	no	—
122	C₂×D₄×C₄₇	—	2	8	no	—
123	C₂×D₄×C₄₇	—	2	8	no	—
124	C₂×D₄×C₄₇	—	2	2	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	4	no	—
128	C₂×D₄×C₄₇	M₁₆	1	8	yes	complemented
129	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₄₇	—	2	4	no	—
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	4	no	—
136	C₂²×C₄×C₄₇	—	2	4	no	—
137	C₂²×C₄×C₄₇	—	2	4	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	—	4	2	no	—
140	C₂²×C₄×C₄₇	—	4	8	no	—
141	C₂²×C₄×C₄₇	—	4	8	no	—
142	C₂²×C₄×C₄₇	—	4	8	no	—
143	C₂²×C₄×C₄₇	—	4	8	no	—
144	C₂²×C₄×C₄₇	—	4	8	no	—
145	C₂²×C₄×C₄₇	—	4	4	no	—
146	C₂²×C₄×C₄₇	—	4	8	no	—
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	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	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₄⋊C₄×C₄₇	—	2	2	no	—
166	C₄⋊C₄×C₄₇	—	2	2	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
169	C₂²⋊C₄×C₄₇	—	2	4	no	—
170	C₂²⋊C₄×C₄₇	—	2	4	no	—
171	C₂²⋊C₄×C₄₇	—	2	4	no	—
172	C₂²⋊C₄×C₄₇	—	2	4	no	—
173	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
189	#10625329	—	4	4	no	—
190	#10625329	—	4	4	no	—
191	C₂×C₄₇⋊C₈	—	2	4	no	—
192	C₂×C₄₇⋊C₈	—	2	4	no	—
193	C₂³×C₄₇	—	2	2	no	—
194	C₂³×C₄₇	—	2	2	no	—
195	C₂³×C₄₇	—	2	2	no	—
196	C₂³×C₄₇	—	2	8	no	—
197	C₂³×C₄₇	—	2	8	no	—
198	C₂³×C₄₇	—	2	4	no	—
199	C₂³×C₄₇	—	2	8	no	—
200	C₂³×C₄₇	—	4	4	no	—
201	C₂³×C₄₇	—	4	4	no	—
202	C₂³×C₄₇	—	4	32	no	—
203	C₂³×C₄₇	—	4	4	no	—
204	C₂³×C₄₇	—	4	4	no	—
205	C₂³×C₄₇	—	4	4	no	—
206	C₂³×C₄₇	—	4	4	no	—
207	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	D₄×C₄₇	—	2	8	no	—
211	D₄×C₄₇	—	2	8	no	—
212	D₄×C₄₇	—	2	4	no	—
213	D₄×C₄₇	—	2	8	no	—
214	D₄×C₄₇	C₂×M₁₆	1	8	yes	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	4	no	—
228	C₂×C₄×C₄₇	—	4	1	no	—
229	C₂×C₄×C₄₇	—	4	1	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	8	no	—
233	C₂×C₄×C₄₇	—	4	8	no	—
234	C₂×C₄×C₄₇	—	4	4	no	—
235	C₂×C₄×C₄₇	—	4	4	no	—
236	C₂×C₄×C₄₇	—	4	4	no	—
237	C₂×C₄×C₄₇	—	4	8	no	—
238	C₂×C₄×C₄₇	—	4	8	no	—
239	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
249	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
250	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
253	C₄₇⋊C₈	—	4	4	no	—
254	C₄₇⋊C₈	—	4	4	no	—
255	#17448	—	47	1	no	maximal, Sylow
256	C₂²×C₄₇	—	2	8	no	—
257	C₂²×C₄₇	—	2	1	no	—
258	C₂²×C₄₇	—	2	1	no	—
259	C₂²×C₄₇	—	2	1	no	—
260	C₂²×C₄₇	—	2	1	no	—
261	C₂²×C₄₇	—	2	1	no	—
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	8	no	—
264	C₂²×C₄₇	—	4	16	no	—
265	C₂²×C₄₇	—	4	16	no	—
266	C₂²×C₄₇	—	4	16	no	—
267	C₂²×C₄₇	—	4	4	no	—
268	C₂²×C₄₇	—	4	4	no	—
269	C₂²×C₄₇	#407	1	2	yes	—
270	C₂²×C₄₇	#418	1	2	yes	—
271	C₂²×C₄₇	#421	1	2	yes	—
272	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₄×C₄₇	—	2	1	no	—
274	C₄×C₄₇	—	2	1	no	—
275	C₄×C₄₇	—	2	1	no	—
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	2	1	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	—	4	4	no	—
282	C₄×C₄₇	#407	1	2	yes	—
283	C₄×C₄₇	#418	1	2	yes	—
284	C₄×C₄₇	C₂²×M₁₆	1	2	yes	—
285	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
286	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
287	#2920	—	47	1	no	—
288	#2920	—	47	1	no	—
289	#1490	—	47	4	no	—
290	#1486	—	47	4	no	—
291	#1478	—	47	4	no	—
292	C₂×C₄₇	—	2	2	no	—
293	C₂×C₄₇	—	2	2	no	—
294	C₂×C₄₇	—	2	2	no	—
295	C₂×C₄₇	—	4	8	no	—
296	C₂×C₄₇	C₂×#407	1	1	yes	characteristic
297	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
298	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
299	C₂³×D₄	Dic₄₇	1	1	yes	characteristic
300	C₂⁴×C₄	—	2	1	no	—
301	C₂×C₄×D₄	—	2	1	no	—
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	—	2	1	no	—
304	C₂×C₄×D₄	—	2	1	no	—
305	C₂×C₄×D₄	—	2	1	no	—
306	C₂×C₄×D₄	—	2	1	no	—
307	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
308	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
309	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
310	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
311	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
312	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
313	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	—	2	1	no	—
315	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
316	#432	—	47	2	no	—
317	#432	—	94	1	no	—
318	#432	—	94	1	no	—
319	#432	—	94	1	no	—
320	#431	—	47	2	no	—
321	#431	—	47	2	no	—
322	#431	—	47	2	no	—
323	#431	—	94	1	no	—
324	#423	—	47	2	no	—
325	#423	—	94	1	no	—
326	#407	—	94	1	no	—
327	#407	—	94	1	no	—
328	C₄×M₁₆	—	47	2	no	—
329	C₄×M₁₆	—	94	1	no	—
330	D₄⋊C₈	—	47	16	no	—
331	C₄₇	#17448	1	1	yes	characteristic, complemented, Sylow
332	C₂⁵	—	2	1	no	—
333	C₂²×D₄	—	2	8	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
338	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
339	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
340	C₂³×C₄	—	2	1	no	—
341	C₂³×C₄	—	2	2	no	—
342	C₂³×C₄	—	2	2	no	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	—	2	2	no	—
346	C₂³×C₄	—	2	2	no	—
347	C₂³×C₄	—	4	8	no	—
348	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
349	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
350	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
351	C₂×M₁₆	—	94	2	no	—
352	C₂×M₁₆	—	94	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
366	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
367	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
368	C₄×D₄	C₂²×D₄₇	1	4	yes	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
373	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
374	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
382	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
383	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
384	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
385	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
386	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
387	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
388	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
390	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
391	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
392	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
393	C₄⋊C₈	—	47	4	no	—
394	C₄⋊C₈	—	94	2	no	—
395	C₄⋊C₈	—	94	2	no	—
396	C₄⋊C₈	—	94	2	no	—
397	C₂²⋊C₈	—	94	2	no	—
398	C₂²⋊C₈	—	94	2	no	—
399	C₂²⋊C₈	—	94	2	no	—
400	C₂²⋊C₈	—	94	2	no	—
401	#97	—	94	2	no	—
402	#97	—	94	2	no	—
403	C₄×C₈	—	47	4	no	—
404	C₄×C₈	—	94	2	no	—
405	C₂⁴	—	2	8	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	4	4	no	—
410	C₂⁴	—	4	4	no	—
411	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	#10625329	1	8	yes	complemented
422	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	8	no	—
434	C₂²×C₄	—	4	8	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	—	4	8	no	—
437	C₂²×C₄	—	4	8	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	8	no	—
440	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
441	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
442	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
443	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
444	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
445	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
446	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
447	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
448	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
449	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
450	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
451	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
458	M₁₆	—	188	4	no	—
459	M₁₆	—	188	4	no	—
460	C₂×C₈	—	94	4	no	—
461	C₂×C₈	—	94	4	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
471	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
472	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
473	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
474	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
475	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
476	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
477	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
478	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
479	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
480	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
481	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
482	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
483	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
484	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
485	C₄²	C₂³×D₄₇	1	1	yes	characteristic
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	8	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	8	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	32	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
501	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
502	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
503	D₄	—	2	8	no	—
504	D₄	—	2	8	no	—
505	D₄	—	2	8	no	—
506	D₄	—	2	4	no	—
507	D₄	C₂×#10625329	1	8	yes	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
533	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
534	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
535	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
536	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
537	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
539	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
540	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
541	C₂×C₄	C₂×#10625329	1	4	yes	—
542	C₂×C₄	#13094050	1	4	yes	—
543	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
544	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
545	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
546	C₈	—	188	4	no	—
547	C₈	—	188	4	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	8	no	—
556	C₂²	—	4	16	no	—
557	C₂²	—	4	16	no	—
558	C₂²	—	4	16	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	#15689087	1	2	yes	—
562	C₂²	#15689128	1	2	yes	—
563	C₂²	#15689140	1	2	yes	—
564	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	4	4	no	—
574	C₄	#15689087	1	2	yes	—
575	C₄	#15689128	1	2	yes	—
576	C₄	C₂²×#10625329	1	2	yes	—
577	C₄	C₂×#13094050	1	2	yes	—
578	C₂	—	2	2	no	—
579	C₂	—	2	2	no	—
580	C₂	—	2	2	no	—
581	C₂	—	4	8	no	—
582	C₂	C₂×#15689087	1	1	yes	characteristic
583	C₂	C₂×#15689128	1	1	yes	characteristic
584	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂³×D₄×C₄₇	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	#17448
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20252021	C₂	semidirect
2. #20252021	C₂	semidirect
3. #20241831	C₂	semidirect
4. #20241813	C₂	semidirect
5. #20241779	C₂	semidirect
10. #15689180	C₂²	semidirect
12. #15689176	C₂²	semidirect
13. #15689176	C₂²	semidirect
14. #15689176	C₂²	semidirect
16. #15689147	C₂²	semidirect
20. C₄×#10625329	C₂²	semidirect
21. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
44. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
52. C₄×C₄₇⋊C₈	C₂³	semidirect
128. C₂×D₄×C₄₇	M₁₆	semidirect
331. C₄₇	#17448	semidirect
421. C₂×D₄	#10625329	semidirect

Maximal subgroups

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

subgroup	index
#20252021	2
#20241831	2
#20241813	2
#20241779	2
C₂²×C₄×D₄×C₄₇	2
#17448	47