Subgroups — #26232260

Order 12032.

1380 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689245	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252272	C₂	1	1	yes	maximal, characteristic, complemented
3	#20251914	C₂	1	2	yes	maximal, complemented
4	#20244299	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244265	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243898	C₂	1	2	yes	maximal, complemented
7	#20243766	C₂	1	2	yes	maximal, complemented
8	#20243447	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243342	C₂	1	2	yes	maximal, complemented
10	#20243230	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#576	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	complemented
13	#15689606	C₂²	1	2	yes	complemented
14	#15689245	—	2	4	no	—
15	#15689235	—	2	1	no	—
16	#15689230	—	2	1	no	—
17	SD₁₆×Dic₄₇	—	2	2	no	—
18	C₂×#13093960	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13093956	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13093951	C₂²	1	1	yes	characteristic
21	C₂×#13093951	C₂²	1	2	yes	complemented
22	#15689128	—	2	2	no	—
23	#15689128	C₂²	1	2	yes	complemented
24	#15689124	—	2	2	no	—
25	#15689124	C₂²	1	2	yes	—
26	#15689124	C₂²	1	2	yes	complemented
27	#15689119	—	2	2	no	—
28	#15689119	C₂²	1	1	yes	characteristic
29	C₂×#13093945	—	2	2	no	—
30	C₂×#13093945	C₂²	1	2	yes	complemented
31	C₂×#13093941	C₂²	1	2	yes	complemented
32	#15689078	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13093934	C₂²	1	1	yes	characteristic, complemented
34	#15689026	C₂²	1	2	yes	complemented
35	#15688891	C₂²	1	2	yes	complemented
36	#15688887	C₂²	1	1	yes	characteristic, complemented
37	#15688884	C₂²	1	1	yes	characteristic, complemented
38	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#576	—	2	4	no	—
40	C₄₇×#576	C₄	1	8	yes	complemented
41	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
42	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
43	C₂×#135×C₄₇	—	2	1	no	—
44	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×D₈×C₄₇	—	2	1	no	—
46	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
48	#13094031	—	2	4	no	—
49	#13094031	—	4	2	no	—
50	C₂×#10625329	—	2	2	no	—
51	C₂×#10625329	C₂³	1	1	yes	characteristic
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	Q₈×Dic₄₇	—	2	2	no	—
56	D₄×Dic₄₇	—	2	2	no	—
57	D₄×Dic₄₇	—	4	2	no	—
58	#13093983	—	2	2	no	—
59	#13093983	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊Dic₄₇	—	2	2	no	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
62	C₂×C₂²⋊Dic₄₇	—	4	2	no	—
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	#13093960	—	2	2	no	—
65	#13093956	—	2	1	no	—
66	#13093956	—	2	1	no	—
67	#13093951	—	2	4	no	—
68	#13093951	—	2	2	no	—
69	#13093948	—	2	2	no	—
70	#13093948	—	2	2	no	—
71	#13093948	D₄	1	2	yes	—
72	#13093945	—	2	2	no	—
73	#13093945	—	2	2	no	—
74	#13093945	—	2	2	no	—
75	#13093945	—	2	2	no	—
76	#13093945	—	2	2	no	—
77	#13093945	—	2	2	no	—
78	#13093945	D₄	1	2	yes	—
79	#13093941	—	4	2	no	—
80	#13093934	—	2	1	no	—
81	#13093934	—	2	2	no	—
82	C₈×Dic₄₇	—	2	1	no	—
83	H(5,𝔽₂)×C₄₇	—	2	4	no	—
84	H(5,𝔽₂)×C₄₇	—	2	4	no	—
85	H(5,𝔽₂)×C₄₇	—	4	2	no	—
86	H(5,𝔽₂)×C₄₇	C₂×C₄	1	8	yes	complemented
87	C₂×#41×C₄₇	—	2	2	no	—
88	C₂×#41×C₄₇	—	2	2	no	—
89	C₂×#41×C₄₇	C₂³	1	2	yes	—
90	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₄₇	—	2	2	no	—
92	C₂²×D₄×C₄₇	—	2	2	no	—
93	C₂²×D₄×C₄₇	—	4	2	no	—
94	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
95	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
96	AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
97	AGL(1,ℤ/8)×C₄₇	C₂×C₄	1	8	yes	complemented
98	#135×C₄₇	—	2	8	no	—
99	#135×C₄₇	C₂×C₄	1	4	yes	—
100	#135×C₄₇	D₄	1	4	yes	—
101	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
102	C₂×SD₁₆×C₄₇	—	2	2	no	—
103	C₂×SD₁₆×C₄₇	D₄	1	2	yes	—
104	C₂×D₈×C₄₇	—	2	2	no	—
105	C₂×D₈×C₄₇	—	2	8	no	—
106	C₂×D₈×C₄₇	—	2	1	no	—
107	C₂×D₈×C₄₇	—	2	1	no	—
108	C₂×D₈×C₄₇	—	2	2	no	—
109	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
110	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic
111	#131×C₄₇	—	2	2	no	—
112	#131×C₄₇	C₂×C₄	1	4	yes	complemented
113	C₂×M₁₆×C₄₇	—	2	1	no	—
114	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	—	2	1	no	—
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₂⁴×C₄₇	—	2	2	no	—
118	C₂⁴×C₄₇	—	4	2	no	—
119	#41×C₄₇	—	2	1	no	—
120	#41×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	1	no	—
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	8	no	—
124	#41×C₄₇	—	2	8	no	—
125	#41×C₄₇	—	4	4	no	—
126	#41×C₄₇	—	4	4	no	—
127	#41×C₄₇	C₂²×C₄	1	4	yes	—
128	#41×C₄₇	C₂²×C₄	1	2	yes	—
129	#41×C₄₇	C₂×D₄	1	4	yes	—
130	#41×C₄₇	#41	1	2	yes	—
131	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂×D₄×C₄₇	—	2	1	no	—
134	C₂×D₄×C₄₇	—	2	2	no	—
135	C₂×D₄×C₄₇	—	2	8	no	—
136	C₂×D₄×C₄₇	—	2	8	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	2	no	—
142	C₂×D₄×C₄₇	—	4	4	no	—
143	C₂×D₄×C₄₇	—	4	4	no	—
144	C₂×D₄×C₄₇	—	4	2	no	—
145	C₂×D₄×C₄₇	—	4	2	no	—
146	C₂×D₄×C₄₇	—	4	8	no	—
147	C₂×D₄×C₄₇	—	4	8	no	—
148	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
149	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	4	2	no	—
154	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
155	C₂²×Dic₄₇	—	2	1	no	—
156	C₂²×Dic₄₇	—	2	2	no	—
157	C₂²×Dic₄₇	—	4	2	no	—
158	Q₁₆×C₄₇	C₂²⋊C₄	1	4	yes	complemented
159	SD₁₆×C₄₇	—	2	8	no	—
160	SD₁₆×C₄₇	C₂²⋊C₄	1	8	yes	complemented
161	D₈×C₄₇	—	2	8	no	—
162	D₈×C₄₇	—	2	4	no	—
163	D₈×C₄₇	—	2	4	no	—
164	D₈×C₄₇	C₂²⋊C₄	1	4	yes	complemented
165	M₁₆×C₄₇	—	2	1	no	—
166	M₁₆×C₄₇	—	2	4	no	—
167	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₄₇	—	2	1	no	—
169	C₂×C₈×C₄₇	—	2	4	no	—
170	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
171	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
174	C₂²⋊Dic₄₇	—	2	1	no	—
175	C₂²⋊Dic₄₇	—	4	2	no	—
176	C₂²⋊Dic₄₇	—	8	4	no	—
177	C₄⋊Dic₄₇	—	2	2	no	—
178	C₄⋊Dic₄₇	—	2	2	no	—
179	C₄⋊Dic₄₇	—	4	2	no	—
180	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
181	C₄×Dic₄₇	—	2	1	no	—
182	C₄×Dic₄₇	—	2	1	no	—
183	C₄×Dic₄₇	—	2	1	no	—
184	C₄×Dic₄₇	—	4	2	no	—
185	#10625329	—	2	2	no	—
186	#10625329	—	2	1	no	—
187	#10625329	—	2	1	no	—
188	#10625329	—	2	2	no	—
189	#10625329	—	4	4	no	—
190	C₂×C₄₇⋊C₈	—	2	1	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	1	no	—
193	C₂×C₄₇⋊C₈	—	2	2	no	—
194	C₂×C₄₇⋊C₈	—	4	4	no	—
195	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
196	C₂³×C₄₇	—	2	2	no	—
197	C₂³×C₄₇	—	2	1	no	—
198	C₂³×C₄₇	—	2	4	no	—
199	C₂³×C₄₇	—	4	8	no	—
200	C₂³×C₄₇	—	4	2	no	—
201	C₂³×C₄₇	—	4	2	no	—
202	C₂³×C₄₇	—	8	2	no	—
203	C₂³×C₄₇	—	8	2	no	—
204	C₂³×C₄₇	—	16	2	no	—
205	C₂³×C₄₇	—	16	2	no	—
206	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
207	Q₈×C₄₇	—	2	1	no	—
208	Q₈×C₄₇	—	2	2	no	—
209	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
210	Q₈×C₄₇	C₄×D₄	1	2	yes	—
211	D₄×C₄₇	—	2	2	no	—
212	D₄×C₄₇	—	2	4	no	—
213	D₄×C₄₇	—	2	2	no	—
214	D₄×C₄₇	—	2	4	no	—
215	D₄×C₄₇	—	2	4	no	—
216	D₄×C₄₇	—	2	4	no	—
217	D₄×C₄₇	—	2	1	no	—
218	D₄×C₄₇	—	2	2	no	—
219	D₄×C₄₇	—	4	8	no	—
220	D₄×C₄₇	—	4	8	no	—
221	D₄×C₄₇	—	4	2	no	—
222	D₄×C₄₇	—	4	2	no	—
223	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
224	D₄×C₄₇	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	1	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	4	no	—
229	C₂×C₄×C₄₇	—	2	4	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	4	8	no	—
232	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×Dic₄₇	—	2	2	no	—
239	C₂×Dic₄₇	—	4	2	no	—
240	C₂×Dic₄₇	—	4	2	no	—
241	C₂×Dic₄₇	—	4	1	no	—
242	C₂×Dic₄₇	—	8	2	no	—
243	C₂×Dic₄₇	—	16	2	no	—
244	C₈×C₄₇	—	2	2	no	—
245	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
246	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
247	C₄₇⋊C₈	—	2	2	no	—
248	C₄₇⋊C₈	—	4	2	no	—
249	C₄₇⋊C₈	—	4	1	no	—
250	#22463	—	47	1	no	maximal, Sylow
251	C₂²×C₄₇	—	2	2	no	—
252	C₂²×C₄₇	—	2	2	no	—
253	C₂²×C₄₇	—	2	4	no	—
254	C₂²×C₄₇	—	4	2	no	—
255	C₂²×C₄₇	—	4	2	no	—
256	C₂²×C₄₇	—	4	2	no	—
257	C₂²×C₄₇	—	4	4	no	—
258	C₂²×C₄₇	—	8	4	no	—
259	C₂²×C₄₇	—	8	2	no	—
260	C₂²×C₄₇	—	8	2	no	—
261	C₂²×C₄₇	—	16	2	no	—
262	C₂²×C₄₇	—	16	8	no	—
263	C₂²×C₄₇	#518	1	1	yes	characteristic
264	C₂²×C₄₇	D₄²	1	1	yes	characteristic
265	C₂²×C₄₇	#546	1	1	yes	characteristic
266	C₄×C₄₇	—	2	2	no	—
267	C₄×C₄₇	—	2	4	no	—
268	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
269	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₄₇	D₄²	1	1	yes	characteristic
271	C₄×C₄₇	#546	1	1	yes	characteristic
272	Dic₄₇	—	4	2	no	—
273	Dic₄₇	—	8	1	no	—
274	Dic₄₇	—	8	2	no	—
275	C₂×#576	D₄₇	1	1	yes	characteristic
276	C₂×#444	—	47	1	no	—
277	#2952	—	47	1	no	—
278	#2897	—	47	2	no	—
279	#1978	—	47	1	no	—
280	#1972	—	47	1	no	—
281	#1907	—	47	2	no	—
282	#1883	—	47	2	no	—
283	#1815	—	47	1	no	—
284	#1792	—	47	2	no	—
285	#1765	—	47	1	no	—
286	C₂×C₄₇	—	2	1	no	—
287	C₂×C₄₇	—	2	1	no	—
288	C₂×C₄₇	—	4	4	no	—
289	C₂×C₄₇	—	4	2	no	—
290	C₂×C₄₇	—	8	4	no	—
291	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₄₇	#3288	1	2	yes	—
293	C₂×H(5,𝔽₂)	C₂×D₄₇	1	2	yes	—
294	#576	—	2	4	no	—
295	#576	Dic₄₇	1	8	yes	complemented
296	C₂×AGL(1,ℤ/8)	—	2	2	no	—
297	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	2	yes	—
298	C₂×#135	—	2	1	no	—
299	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
300	C₂²×D₈	—	2	1	no	—
301	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
302	C₂×#131	—	47	2	no	—
303	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
304	#520	—	47	2	no	—
305	#444	—	94	4	no	—
306	#442	—	94	1	no	—
307	#441	—	94	1	no	—
308	C₄×SD₁₆	—	94	2	no	—
309	C₂×#108	—	47	1	no	—
310	C₂×#106	—	47	1	no	—
311	C₂×#104	—	47	1	no	—
312	C₂×#104	—	47	2	no	—
313	#418	—	47	2	no	—
314	#418	—	94	2	no	—
315	#417	—	47	2	no	—
316	#417	—	47	2	no	—
317	#417	—	94	2	no	—
318	#416	—	47	1	no	—
319	#416	—	94	2	no	—
320	C₂×#102	—	47	2	no	—
321	C₂×#102	—	94	2	no	—
322	C₂×#100	—	47	2	no	—
323	#405	—	47	1	no	—
324	C₂×#97	—	47	1	no	—
325	#390	—	47	2	no	—
326	#343	—	47	2	no	—
327	#341	—	47	1	no	—
328	#339	—	47	1	no	—
329	C₄₇	#22463	1	1	yes	characteristic, complemented, Sylow
330	H(5,𝔽₂)	—	2	4	no	—
331	H(5,𝔽₂)	—	2	4	no	—
332	H(5,𝔽₂)	—	4	2	no	—
333	H(5,𝔽₂)	C₂×Dic₄₇	1	8	yes	complemented
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
337	C₂×#41	C₂²×D₄₇	1	2	yes	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	4	2	no	—
341	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
342	AGL(1,ℤ/8)	—	2	4	no	—
343	AGL(1,ℤ/8)	—	2	16	no	—
344	AGL(1,ℤ/8)	C₂×Dic₄₇	1	8	yes	complemented
345	#135	—	2	8	no	—
346	#135	C₂×Dic₄₇	1	4	yes	—
347	#135	C₂²⋊D₄₇	1	4	yes	—
348	C₂×Q₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
349	C₂×SD₁₆	—	2	2	no	—
350	C₂×SD₁₆	C₂²⋊D₄₇	1	2	yes	—
351	C₂×D₈	—	2	2	no	—
352	C₂×D₈	—	2	8	no	—
353	C₂×D₈	—	2	1	no	—
354	C₂×D₈	—	2	1	no	—
355	C₂×D₈	—	2	2	no	—
356	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
357	C₂×D₈	C₂²⋊D₄₇	1	1	yes	characteristic
358	#131	—	2	2	no	—
359	#131	—	94	4	no	—
360	#131	—	188	2	no	—
361	#131	C₂×Dic₄₇	1	4	yes	complemented
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	47	2	no	—
364	C₂×M₁₆	—	47	1	no	—
365	C₂×M₁₆	—	94	2	no	—
366	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	47	1	no	—
369	C₂²×C₈	—	94	2	no	—
370	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
371	C₄×Q₈	—	94	2	no	—
372	C₄×D₄	—	94	2	no	—
373	C₄×D₄	—	188	2	no	—
374	#117	—	47	1	no	—
375	#117	—	94	2	no	—
376	C₂×C₄⋊C₄	—	47	2	no	—
377	C₂×C₄⋊C₄	—	94	2	no	—
378	C₂×C₂²⋊C₄	—	188	2	no	—
379	C₂×C₄²	—	47	1	no	—
380	#108	—	94	2	no	—
381	#106	—	94	1	no	—
382	#106	—	94	1	no	—
383	#104	—	94	2	no	—
384	#104	—	94	4	no	—
385	#103	—	47	2	no	—
386	#103	—	94	2	no	—
387	#103	—	94	2	no	—
388	#102	—	47	2	no	—
389	#102	—	94	2	no	—
390	#102	—	94	2	no	—
391	#102	—	94	2	no	—
392	#102	—	94	2	no	—
393	#102	—	94	2	no	—
394	#102	—	94	2	no	—
395	#100	—	188	2	no	—
396	#97	—	94	2	no	—
397	#97	—	94	1	no	—
398	C₄×C₈	—	94	1	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	4	2	no	—
401	#41	—	2	1	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	1	no	—
405	#41	—	2	8	no	—
406	#41	—	2	8	no	—
407	#41	—	4	4	no	—
408	#41	—	4	4	no	—
409	#41	#10625352	1	2	yes	—
410	#41	C₂²×Dic₄₇	1	4	yes	—
411	#41	C₂²×Dic₄₇	1	2	yes	—
412	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
413	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
414	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	—	4	2	no	—
428	C₂×D₄	—	4	8	no	—
429	C₂×D₄	—	4	8	no	—
430	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
431	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
432	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	94	2	no	—
437	C₂²×C₄	—	94	1	no	—
438	C₂²×C₄	—	188	2	no	—
439	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
440	Q₁₆	C₂²⋊Dic₄₇	1	4	yes	complemented
441	SD₁₆	—	2	8	no	—
442	SD₁₆	C₂²⋊Dic₄₇	1	8	yes	complemented
443	D₈	—	2	8	no	—
444	D₈	—	2	4	no	—
445	D₈	—	2	4	no	—
446	D₈	C₂²⋊Dic₄₇	1	4	yes	complemented
447	M₁₆	—	2	1	no	—
448	M₁₆	—	2	4	no	—
449	M₁₆	—	94	2	no	—
450	M₁₆	—	94	1	no	—
451	M₁₆	—	94	1	no	—
452	M₁₆	—	94	2	no	—
453	M₁₆	—	188	4	no	—
454	M₁₆	C₂²×Dic₄₇	1	2	yes	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	4	no	—
457	C₂×C₈	—	47	2	no	—
458	C₂×C₈	—	94	1	no	—
459	C₂×C₈	—	94	1	no	—
460	C₂×C₈	—	94	2	no	—
461	C₂×C₈	—	94	1	no	—
462	C₂×C₈	—	188	4	no	—
463	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
464	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
465	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
466	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
467	C₄⋊C₄	—	47	2	no	—
468	C₄⋊C₄	—	94	2	no	—
469	C₄⋊C₄	—	94	2	no	—
470	C₄⋊C₄	—	188	2	no	—
471	C₂²⋊C₄	—	94	1	no	—
472	C₂²⋊C₄	—	376	4	no	—
473	C₂²⋊C₄	—	188	2	no	—
474	C₄²	—	94	1	no	—
475	C₄²	—	94	1	no	—
476	C₄²	—	94	1	no	—
477	C₄²	—	188	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	8	2	no	—
485	C₂³	—	8	2	no	—
486	C₂³	—	16	2	no	—
487	C₂³	—	16	2	no	—
488	C₂³	#13094069	1	1	yes	characteristic
489	Q₈	—	2	1	no	—
490	Q₈	—	2	2	no	—
491	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
492	Q₈	D₄×Dic₄₇	1	2	yes	—
493	D₄	—	2	2	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	1	no	—
498	D₄	—	2	2	no	—
499	D₄	—	2	4	no	—
500	D₄	—	2	4	no	—
501	D₄	—	4	8	no	—
502	D₄	—	4	8	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
506	D₄	D₄×Dic₄₇	1	2	yes	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	94	2	no	—
515	C₂×C₄	—	376	2	no	—
516	C₂×C₄	—	188	2	no	—
517	C₂×C₄	—	188	2	no	—
518	C₂×C₄	—	188	1	no	—
519	C₂×C₄	—	752	2	no	—
520	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
521	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
524	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
525	C₂×C₄	#13094069	1	1	yes	characteristic
526	C₈	—	2	2	no	—
527	C₈	—	94	2	no	—
528	C₈	—	188	2	no	—
529	C₈	—	188	1	no	—
530	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
531	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	8	4	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	16	2	no	—
543	C₂²	—	16	8	no	—
544	C₂²	#15689598	1	1	yes	characteristic
545	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
546	C₂²	#15689767	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	2	4	no	—
549	C₄	—	376	1	no	—
550	C₄	—	376	2	no	—
551	C₄	—	188	2	no	—
552	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
553	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
554	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
555	C₄	#15689767	1	1	yes	characteristic
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	4	2	no	—
559	C₂	—	4	4	no	—
560	C₂	—	8	4	no	—
561	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
562	C₂	#20255152	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#576	C₂
socle	C₂²×C₄₇	D₄²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#576	D₄₇
hypocenter	C₄₇	#22463
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. C₂×#15689245	C₂	semidirect
2. #20252272	C₂	semidirect
3. #20251914	C₂	semidirect
4. #20244299	C₂	semidirect
5. #20244265	C₂	semidirect
6. #20243898	C₂	semidirect
7. #20243766	C₂	semidirect
8. #20243447	C₂	semidirect
9. #20243342	C₂	semidirect
10. #20243230	C₂	semidirect
12. C₂×#13094031	C₂²	semidirect
13. #15689606	C₂²	semidirect
18. C₂×#13093960	C₂²	semidirect
19. C₂×#13093956	C₂²	semidirect
21. C₂×#13093951	C₂²	semidirect
23. #15689128	C₂²	semidirect
26. #15689124	C₂²	semidirect
30. C₂×#13093945	C₂²	semidirect
31. C₂×#13093941	C₂²	semidirect
32. #15689078	C₂²	semidirect
33. C₂×#13093934	C₂²	semidirect
34. #15689026	C₂²	semidirect
35. #15688891	C₂²	semidirect
36. #15688887	C₂²	semidirect
37. #15688884	C₂²	semidirect
40. C₄₇×#576	C₄	semidirect
86. H(5,𝔽₂)×C₄₇	C₂×C₄	semidirect
97. AGL(1,ℤ/8)×C₄₇	C₂×C₄	semidirect
109. C₂×D₈×C₄₇	C₂×C₄	semidirect
112. #131×C₄₇	C₂×C₄	semidirect
158. Q₁₆×C₄₇	C₂²⋊C₄	semidirect
160. SD₁₆×C₄₇	C₂²⋊C₄	semidirect
164. D₈×C₄₇	C₂²⋊C₄	semidirect
295. #576	Dic₄₇	semidirect
329. C₄₇	#22463	semidirect
333. H(5,𝔽₂)	C₂×Dic₄₇	semidirect
344. AGL(1,ℤ/8)	C₂×Dic₄₇	semidirect
356. C₂×D₈	C₂×Dic₄₇	semidirect
361. #131	C₂×Dic₄₇	semidirect
440. Q₁₆	C₂²⋊Dic₄₇	semidirect
442. SD₁₆	C₂²⋊Dic₄₇	semidirect
446. D₈	C₂²⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689245	2
#20252272	2
#20251914	2
#20244299	2
#20244265	2
#20243898	2
#20243766	2
#20243447	2
#20243342	2
#20243230	2
C₂×C₄₇×#576	2
#22463	47