Subgroups — #26232219

Order 12032.

1312 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252305	C₂	1	2	yes	maximal, complemented
2	#20251871	C₂	1	1	yes	maximal, characteristic, complemented
3	#20251867	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244293	C₂	1	2	yes	maximal, complemented
5	#20243870	C₂	1	2	yes	maximal, complemented
6	#20243863	C₂	1	2	yes	maximal, complemented
7	#20243438	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243363	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243358	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243188	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#577	C₂	1	1	yes	maximal, characteristic
12	#15689890	C₂²	1	2	yes	—
13	#15689890	C₂²	1	2	yes	complemented
14	#15689245	—	2	4	no	—
15	#15689240	—	2	4	no	—
16	C₂×#13093960	C₂²	1	2	yes	complemented
17	#15689140	C₂²	1	2	yes	—
18	#15689140	C₂²	1	2	yes	complemented
19	#15689132	C₂²	1	2	yes	complemented
20	#15689128	C₂²	1	2	yes	—
21	#15689107	—	2	2	no	—
22	#15689107	—	2	2	no	—
23	#15689107	C₂²	1	1	yes	characteristic
24	#15689107	C₂²	1	1	yes	characteristic
25	#15689107	C₂²	1	1	yes	characteristic
26	C₂×#13093943	—	2	2	no	—
27	C₂×#13093943	C₂²	1	2	yes	complemented
28	C₂×#13093941	—	2	2	no	—
29	C₂×#13093941	C₂²	1	2	yes	—
30	#15689097	C₂²	1	1	yes	characteristic
31	#15689078	C₂²	1	2	yes	complemented
32	#15688894	C₂²	1	2	yes	complemented
33	C₄₇⋊#338	C₂²	1	2	yes	complemented
34	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#577	—	2	4	no	—
37	C₄₇×#577	—	2	4	no	—
38	C₂×#137×C₄₇	C₄	1	2	yes	complemented
39	C₂×#137×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×AGL(1,ℤ/8)×C₄₇	C₄	1	2	yes	complemented
41	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#135×C₄₇	C₄	1	2	yes	complemented
43	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×SD₁₆×C₄₇	C₄	1	2	yes	complemented
45	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
47	#13094031	—	2	4	no	—
48	#13094031	—	2	4	no	—
49	#13094031	—	4	2	no	—
50	#13094031	—	4	2	no	—
51	C₂×#10625329	—	2	4	no	—
52	C₂×#10625329	—	2	4	no	—
53	C₂×#10625329	C₂³	1	2	yes	—
54	C₂×#10625329	C₂³	1	2	yes	—
55	C₂×#10625329	C₂³	1	2	yes	—
56	#13093983	C₂³	1	2	yes	—
57	#13093960	—	2	2	no	—
58	#13093960	—	2	2	no	—
59	#13093951	—	2	4	no	—
60	#13093951	—	2	4	no	—
61	#13093948	—	4	2	no	—
62	#13093945	—	4	2	no	—
63	#13093943	—	2	1	no	—
64	#13093943	—	2	1	no	—
65	#13093943	—	2	4	no	—
66	#13093943	D₄	1	2	yes	—
67	#13093941	—	2	1	no	—
68	#13093941	—	2	1	no	—
69	#13093941	—	2	4	no	—
70	#13093941	D₄	1	2	yes	—
71	#13093939	—	2	2	no	—
72	#13093934	—	2	2	no	—
73	C₈×Dic₄₇	—	2	2	no	—
74	2₋¹⁺⁴×C₄₇	—	2	4	no	—
75	2₋¹⁺⁴×C₄₇	—	4	2	no	—
76	H(5,𝔽₂)×C₄₇	—	2	4	no	—
77	H(5,𝔽₂)×C₄₇	—	4	2	no	—
78	C₂×#41×C₄₇	—	2	1	no	—
79	C₂×#41×C₄₇	—	2	1	no	—
80	C₂×#41×C₄₇	—	2	2	no	—
81	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₄₇	—	2	1	no	—
87	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
88	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₄₇	—	2	1	no	—
90	C₂²×D₄×C₄₇	—	2	2	no	—
91	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
92	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
93	#137×C₄₇	—	2	4	no	—
94	#137×C₄₇	—	2	8	no	—
95	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
96	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
97	#135×C₄₇	—	2	4	no	—
98	#135×C₄₇	—	2	4	no	—
99	#135×C₄₇	D₄	1	4	yes	—
100	#135×C₄₇	D₄	1	4	yes	—
101	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
102	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂×SD₁₆×C₄₇	—	2	4	no	—
104	C₂×SD₁₆×C₄₇	—	2	4	no	—
105	C₂×SD₁₆×C₄₇	—	2	2	no	—
106	C₂×SD₁₆×C₄₇	—	2	2	no	—
107	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
108	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
109	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
110	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
111	C₂×SD₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₂×SD₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
114	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
115	#131×C₄₇	—	2	2	no	—
116	#131×C₄₇	—	2	2	no	—
117	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
118	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
120	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
121	C₂⁴×C₄₇	—	2	2	no	—
122	C₂⁴×C₄₇	—	2	1	no	—
123	#41×C₄₇	—	2	2	no	—
124	#41×C₄₇	—	2	2	no	—
125	#41×C₄₇	—	2	2	no	—
126	#41×C₄₇	—	2	2	no	—
127	#41×C₄₇	—	2	4	no	—
128	#41×C₄₇	—	2	4	no	—
129	#41×C₄₇	—	4	2	no	—
130	#41×C₄₇	—	4	2	no	—
131	#41×C₄₇	—	4	4	no	—
132	#41×C₄₇	—	4	4	no	—
133	#41×C₄₇	—	4	8	no	—
134	#41×C₄₇	C₂×D₄	1	4	yes	—
135	#41×C₄₇	C₂×D₄	1	4	yes	—
136	C₂×Q₈×C₄₇	—	2	2	no	—
137	C₂×Q₈×C₄₇	—	2	1	no	—
138	C₂×Q₈×C₄₇	—	2	4	no	—
139	C₂×Q₈×C₄₇	—	2	2	no	—
140	C₂×Q₈×C₄₇	—	2	2	no	—
141	C₂×Q₈×C₄₇	—	4	2	no	—
142	C₂×Q₈×C₄₇	—	4	4	no	—
143	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₄₇	—	2	1	no	—
148	C₂×D₄×C₄₇	—	2	1	no	—
149	C₂×D₄×C₄₇	—	2	4	no	—
150	C₂×D₄×C₄₇	—	2	2	no	—
151	C₂×D₄×C₄₇	—	2	2	no	—
152	C₂×D₄×C₄₇	—	2	2	no	—
153	C₂×D₄×C₄₇	—	2	2	no	—
154	C₂×D₄×C₄₇	—	2	1	no	—
155	C₂×D₄×C₄₇	—	2	2	no	—
156	C₂×D₄×C₄₇	—	4	2	no	—
157	C₂×D₄×C₄₇	—	4	4	no	—
158	C₂×D₄×C₄₇	—	4	8	no	—
159	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₄₇	#41	1	2	yes	—
164	C₂²×C₄×C₄₇	—	2	1	no	—
165	C₂²×C₄×C₄₇	—	2	1	no	—
166	C₂²×C₄×C₄₇	—	2	2	no	—
167	C₂²×C₄×C₄₇	—	2	1	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	2	2	no	—
170	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
172	Q₁₆×C₄₇	—	2	4	no	—
173	Q₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
174	SD₁₆×C₄₇	—	2	4	no	—
175	SD₁₆×C₄₇	—	2	4	no	—
176	SD₁₆×C₄₇	—	2	2	no	—
177	SD₁₆×C₄₇	—	2	2	no	—
178	SD₁₆×C₄₇	—	2	4	no	—
179	SD₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
180	SD₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
181	SD₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
182	SD₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
183	D₈×C₄₇	—	2	4	no	—
184	D₈×C₄₇	C₂²⋊C₄	1	4	yes	—
185	M₁₆×C₄₇	—	2	2	no	—
186	M₁₆×C₄₇	—	2	4	no	—
187	C₂×C₈×C₄₇	—	2	2	no	—
188	C₂×C₈×C₄₇	—	2	2	no	—
189	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
190	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
194	C₂²⋊Dic₄₇	—	2	2	no	—
195	C₄⋊Dic₄₇	—	2	2	no	—
196	C₄×Dic₄₇	—	2	2	no	—
197	#10625329	—	2	2	no	—
198	#10625329	—	2	2	no	—
199	#10625329	—	2	2	no	—
200	#10625329	—	2	2	no	—
201	#10625329	—	2	2	no	—
202	#10625329	—	4	4	no	—
203	#10625329	—	4	4	no	—
204	#10625329	C₂×D₄	1	4	yes	—
205	C₂×C₄₇⋊C₈	—	2	2	no	—
206	C₂×C₄₇⋊C₈	—	2	2	no	—
207	C₂×C₄₇⋊C₈	—	2	2	no	—
208	C₂×C₄₇⋊C₈	—	4	4	no	—
209	C₂×C₄₇⋊C₈	—	4	4	no	—
210	C₂³×C₄₇	—	2	1	no	—
211	C₂³×C₄₇	—	2	1	no	—
212	C₂³×C₄₇	—	2	2	no	—
213	C₂³×C₄₇	—	4	4	no	—
214	C₂³×C₄₇	—	4	2	no	—
215	C₂³×C₄₇	—	16	1	no	—
216	C₂³×C₄₇	—	16	2	no	—
217	C₂³×C₄₇	C₄×D₄	1	2	yes	—
218	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
219	Q₈×C₄₇	—	2	1	no	—
220	Q₈×C₄₇	—	2	1	no	—
221	Q₈×C₄₇	—	2	2	no	—
222	Q₈×C₄₇	—	2	2	no	—
223	Q₈×C₄₇	—	2	2	no	—
224	Q₈×C₄₇	—	4	4	no	—
225	Q₈×C₄₇	—	4	2	no	—
226	Q₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
227	Q₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
228	D₄×C₄₇	—	2	4	no	—
229	D₄×C₄₇	—	2	4	no	—
230	D₄×C₄₇	—	2	4	no	—
231	D₄×C₄₇	—	2	2	no	—
232	D₄×C₄₇	—	2	1	no	—
233	D₄×C₄₇	—	2	1	no	—
234	D₄×C₄₇	—	2	2	no	—
235	D₄×C₄₇	—	2	2	no	—
236	D₄×C₄₇	—	4	4	no	—
237	D₄×C₄₇	—	4	4	no	—
238	D₄×C₄₇	—	4	4	no	—
239	D₄×C₄₇	—	4	2	no	—
240	D₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
241	D₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	4	no	—
247	C₂×C₄×C₄₇	—	2	4	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	4	4	no	—
250	C₂×C₄×C₄₇	—	4	4	no	—
251	C₂×C₄×C₄₇	—	4	4	no	—
252	C₂×C₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
258	C₂×Dic₄₇	—	4	2	no	—
259	C₈×C₄₇	—	2	2	no	—
260	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
263	C₄₇⋊C₈	—	2	4	no	—
264	C₄₇⋊C₈	—	4	2	no	—
265	C₄₇⋊C₈	—	4	2	no	—
266	#22459	—	47	1	no	maximal, Sylow
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	2	2	no	—
269	C₂²×C₄₇	—	2	2	no	—
270	C₂²×C₄₇	—	4	1	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	—	4	2	no	—
273	C₂²×C₄₇	—	8	1	no	—
274	C₂²×C₄₇	—	8	1	no	—
275	C₂²×C₄₇	—	8	2	no	—
276	C₂²×C₄₇	—	16	2	no	—
277	C₂²×C₄₇	—	16	4	no	—
278	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₄₇	#546	1	2	yes	—
280	C₄×C₄₇	—	2	2	no	—
281	C₄×C₄₇	—	2	2	no	—
282	C₄×C₄₇	—	2	2	no	—
283	C₄×C₄₇	—	4	2	no	—
284	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₄×C₄₇	#518	1	1	yes	characteristic
286	C₄×C₄₇	D₄²	1	2	yes	—
287	Dic₄₇	—	8	2	no	—
288	C₂×#577	D₄₇	1	1	yes	characteristic
289	#2957	—	47	2	no	—
290	#2889	—	47	1	no	—
291	#2888	—	47	1	no	—
292	#1977	—	47	2	no	—
293	#1903	—	47	2	no	—
294	#1902	—	47	2	no	—
295	#1813	—	47	1	no	—
296	#1796	—	47	1	no	—
297	#1795	—	47	1	no	—
298	#1757	—	47	1	no	—
299	C₂×C₄₇	—	2	2	no	—
300	C₂×C₄₇	—	2	1	no	—
301	C₂×C₄₇	—	4	2	no	—
302	C₂×C₄₇	—	4	2	no	—
303	C₂×C₄₇	—	4	2	no	—
304	C₂×C₄₇	—	8	2	no	—
305	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic
307	C₂×H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic
308	#577	—	2	4	no	—
309	#577	—	2	4	no	—
310	C₂×#137	Dic₄₇	1	2	yes	complemented
311	C₂×#137	C₂×D₄₇	1	1	yes	characteristic
312	C₂×AGL(1,ℤ/8)	Dic₄₇	1	2	yes	complemented
313	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	1	yes	characteristic
314	C₂×#135	Dic₄₇	1	2	yes	complemented
315	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
316	C₂²×SD₁₆	Dic₄₇	1	2	yes	complemented
317	C₂²×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
318	#568	—	47	2	no	—
319	#568	—	47	2	no	—
320	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
321	#444	—	94	4	no	—
322	#443	—	94	4	no	—
323	C₂×#108	—	47	2	no	—
324	#421	—	47	2	no	—
325	#421	—	47	2	no	—
326	#419	—	47	2	no	—
327	#418	—	47	2	no	—
328	#413	—	47	1	no	—
329	#413	—	47	1	no	—
330	#413	—	47	1	no	—
331	#413	—	94	2	no	—
332	#413	—	94	2	no	—
333	C₂×#101	—	47	2	no	—
334	C₂×#101	—	94	2	no	—
335	C₂×#100	—	47	2	no	—
336	C₂×#100	—	94	2	no	—
337	#410	—	47	1	no	—
338	#405	—	47	2	no	—
339	#344	—	47	2	no	—
340	#338	—	47	2	no	—
341	C₄₇	#22459	1	1	yes	characteristic, complemented, Sylow
342	2₋¹⁺⁴	—	2	4	no	—
343	2₋¹⁺⁴	—	4	2	no	—
344	H(5,𝔽₂)	—	2	4	no	—
345	H(5,𝔽₂)	—	4	2	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	C₂×Dic₄₇	1	2	yes	—
350	C₂×#41	C₂×Dic₄₇	1	2	yes	—
351	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
352	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
353	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
354	C₂²×Q₈	—	2	1	no	—
355	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
356	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
360	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
361	#137	—	2	4	no	—
362	#137	—	2	8	no	—
363	AGL(1,ℤ/8)	—	2	4	no	—
364	AGL(1,ℤ/8)	—	2	8	no	—
365	#135	—	2	4	no	—
366	#135	—	2	4	no	—
367	#135	C₂²⋊D₄₇	1	4	yes	—
368	#135	C₂²⋊D₄₇	1	4	yes	—
369	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
370	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
371	C₂×SD₁₆	—	2	4	no	—
372	C₂×SD₁₆	—	2	4	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
376	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
377	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
378	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
379	C₂×SD₁₆	C₂×Dic₄₇	1	1	yes	characteristic
380	C₂×SD₁₆	C₂×Dic₄₇	1	1	yes	characteristic
381	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
382	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
383	#131	—	2	2	no	—
384	#131	—	2	2	no	—
385	#131	—	94	4	no	—
386	#131	—	94	4	no	—
387	#131	—	188	2	no	—
388	#131	—	188	2	no	—
389	C₂×M₁₆	—	47	2	no	—
390	C₂×M₁₆	—	47	2	no	—
391	C₂×M₁₆	—	47	2	no	—
392	C₂×M₁₆	—	94	4	no	—
393	C₂×M₁₆	—	94	4	no	—
394	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
395	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
396	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
397	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
398	#117	—	47	2	no	—
399	#108	—	94	2	no	—
400	#108	—	94	2	no	—
401	#104	—	94	4	no	—
402	#104	—	94	4	no	—
403	#103	—	188	2	no	—
404	#102	—	188	2	no	—
405	#101	—	47	2	no	—
406	#101	—	94	4	no	—
407	#101	—	94	1	no	—
408	#101	—	94	1	no	—
409	#100	—	47	2	no	—
410	#100	—	94	4	no	—
411	#100	—	94	1	no	—
412	#100	—	94	1	no	—
413	#99	—	94	2	no	—
414	#97	—	94	2	no	—
415	C₄×C₈	—	94	2	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	—	2	1	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	4	no	—
423	#41	—	2	4	no	—
424	#41	—	4	2	no	—
425	#41	—	4	2	no	—
426	#41	—	4	4	no	—
427	#41	—	4	4	no	—
428	#41	—	4	8	no	—
429	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
430	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	4	2	no	—
437	C₂×Q₈	—	4	4	no	—
438	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
439	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
440	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
441	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
455	C₂×D₄	#10625352	1	2	yes	—
456	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
457	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
458	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
466	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
467	Q₁₆	—	2	4	no	—
468	Q₁₆	C₂²⋊Dic₄₇	1	4	yes	—
469	SD₁₆	—	2	4	no	—
470	SD₁₆	—	2	4	no	—
471	SD₁₆	—	2	2	no	—
472	SD₁₆	—	2	2	no	—
473	SD₁₆	—	2	4	no	—
474	SD₁₆	C₂²⋊Dic₄₇	1	2	yes	—
475	SD₁₆	C₂²⋊Dic₄₇	1	2	yes	—
476	SD₁₆	C₂²⋊Dic₄₇	1	2	yes	—
477	SD₁₆	C₂²⋊Dic₄₇	1	2	yes	—
478	D₈	—	2	4	no	—
479	D₈	C₂²⋊Dic₄₇	1	4	yes	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	4	no	—
482	M₁₆	—	47	4	no	—
483	M₁₆	—	94	2	no	—
484	M₁₆	—	94	2	no	—
485	M₁₆	—	94	2	no	—
486	M₁₆	—	94	2	no	—
487	M₁₆	—	94	2	no	—
488	M₁₆	—	188	4	no	—
489	M₁₆	—	188	4	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	94	2	no	—
493	C₂×C₈	—	94	2	no	—
494	C₂×C₈	—	94	2	no	—
495	C₂×C₈	—	188	4	no	—
496	C₂×C₈	—	188	4	no	—
497	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
498	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
499	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
500	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
501	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
502	C₄⋊C₄	—	94	2	no	—
503	C₂²⋊C₄	—	94	2	no	—
504	C₄²	—	94	2	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	16	1	no	—
511	C₂³	—	16	2	no	—
512	C₂³	D₄×Dic₄₇	1	2	yes	—
513	C₂³	C₂×#10625352	1	1	yes	characteristic
514	Q₈	—	2	2	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	4	no	—
520	Q₈	—	4	2	no	—
521	Q₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
522	Q₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
523	D₄	—	2	4	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	2	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	2	no	—
535	D₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
536	D₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	188	2	no	—
549	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
550	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
551	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
553	C₂×C₄	#13094069	1	2	yes	—
554	C₈	—	2	2	no	—
555	C₈	—	94	4	no	—
556	C₈	—	188	2	no	—
557	C₈	—	188	2	no	—
558	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
559	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
560	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	16	2	no	—
571	C₂²	—	16	4	no	—
572	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
573	C₂²	#15689767	1	2	yes	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	376	2	no	—
579	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
580	C₄	#15689598	1	1	yes	characteristic
581	C₄	D₄×C₂²⋊D₄₇	1	2	yes	—
582	C₂	—	2	2	no	—
583	C₂	—	2	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	2	no	—
586	C₂	—	4	2	no	—
587	C₂	—	8	2	no	—
588	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#577	C₂
socle	C₂×C₄₇	D₄×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#577	D₄₇
hypocenter	C₄₇	#22459
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#577

Complements

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

N	H ≅ G/N	type
1. #20252305	C₂	semidirect
2. #20251871	C₂	semidirect
3. #20251867	C₂	semidirect
4. #20244293	C₂	semidirect
5. #20243870	C₂	semidirect
6. #20243863	C₂	semidirect
7. #20243438	C₂	semidirect
8. #20243363	C₂	semidirect
9. #20243358	C₂	semidirect
10. #20243188	C₂	semidirect
13. #15689890	C₂²	semidirect
16. C₂×#13093960	C₂²	semidirect
18. #15689140	C₂²	semidirect
19. #15689132	C₂²	semidirect
27. C₂×#13093943	C₂²	semidirect
31. #15689078	C₂²	semidirect
32. #15688894	C₂²	semidirect
33. C₄₇⋊#338	C₂²	semidirect
38. C₂×#137×C₄₇	C₄	semidirect
40. C₂×AGL(1,ℤ/8)×C₄₇	C₄	semidirect
42. C₂×#135×C₄₇	C₄	semidirect
44. C₂²×SD₁₆×C₄₇	C₄	semidirect
310. C₂×#137	Dic₄₇	semidirect
312. C₂×AGL(1,ℤ/8)	Dic₄₇	semidirect
314. C₂×#135	Dic₄₇	semidirect
316. C₂²×SD₁₆	Dic₄₇	semidirect
341. C₄₇	#22459	semidirect

Maximal subgroups

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

subgroup	index
#20252305	2
#20251871	2
#20251867	2
#20244293	2
#20243870	2
#20243863	2
#20243438	2
#20243363	2
#20243358	2
#20243188	2
C₂×C₄₇×#577	2
#22459	47