Subgroups — #20252133

Order 6016.

492 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094032	C₂	1	2	yes	maximal, complemented
2	#15689670	C₂	1	1	yes	maximal, characteristic
3	#15689200	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689192	C₂	1	2	yes	maximal, complemented
5	#15689191	C₂	1	2	yes	maximal, complemented
6	C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689088	C₂	1	2	yes	maximal, complemented
10	C₄×#10625324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625350	C₂²	1	2	yes	—
13	#13094032	—	2	8	no	—
14	C₂×#10625324	C₂²	1	1	yes	characteristic
15	C₂×#10625324	C₂²	1	2	yes	—
16	C₂×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×C₈×D₄₇	C₂²	1	2	yes	—
19	C₂×C₈×D₄₇	C₂²	1	2	yes	—
20	#13094023	C₄	1	1	yes	characteristic
21	#13094020	C₄	1	1	yes	characteristic
22	#13094010	C₄	1	2	yes	—
23	#13093999	C₄	1	1	yes	characteristic
24	#13093997	C₄	1	2	yes	—
25	#13093995	C₄	1	1	yes	characteristic
26	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
28	C₄²×D₄₇	C₂²	1	1	yes	characteristic
29	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	Dic₄₇⋊C₈	C₂²	1	2	yes	—
31	C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
32	(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
33	(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
34	#13093934	C₂²	1	1	yes	characteristic
35	#13093934	C₂²	1	1	yes	characteristic
36	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
38	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
41	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
47	#10625350	—	2	4	no	—
48	#10625350	—	2	4	no	—
49	C₂×D₁₈₈	C₂×C₄	1	1	yes	characteristic
50	C₂×D₁₈₈	C₂×C₄	1	2	yes	—
51	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×D₄₇	C₂³	1	2	yes	—
54	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
55	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
56	M₁₆×C₄₇	—	2	4	no	—
57	C₂×C₈×C₄₇	C₂³	1	2	yes	—
58	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
60	C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
64	(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
65	(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
66	C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
68	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄₇⋊C₈	—	2	4	no	—
72	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
74	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	#10625324	—	2	2	no	—
76	#10625324	—	2	4	no	—
77	#10625324	D₄	1	4	yes	complemented
78	C₈×D₄₇	—	2	4	no	—
79	C₈×D₄₇	—	2	4	no	—
80	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
81	C₂²×D₄₇	C₂²×C₄	1	2	yes	—
82	C₂²×D₄₇	C₂²×C₄	1	1	yes	characteristic
83	D₄×C₄₇	—	2	2	no	—
84	C₂×C₄×C₄₇	—	2	2	no	—
85	C₂×C₄×C₄₇	—	2	2	no	—
86	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²⋊D₄₇	—	2	4	no	—
91	C₂²⋊D₄₇	—	2	4	no	—
92	C₂²⋊D₄₇	—	4	2	no	—
93	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
96	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
97	D₁₈₈	—	2	4	no	—
98	D₁₈₈	—	2	2	no	—
99	C₄×D₄₇	—	2	2	no	—
100	C₄×D₄₇	—	2	2	no	—
101	C₄×D₄₇	—	2	2	no	—
102	C₄×D₄₇	—	4	1	no	—
103	C₄×D₄₇	C₂×D₄	1	2	yes	—
104	C₄×D₄₇	#41	1	2	yes	—
105	Dic₉₄	—	2	4	no	—
106	C₈×C₄₇	—	2	2	no	—
107	C₈×C₄₇	—	2	1	no	—
108	C₈×C₄₇	C₂×D₄	1	2	yes	—
109	C₄₇⋊C₈	—	2	2	no	—
110	C₄₇⋊C₈	—	2	1	no	—
111	C₄₇⋊C₈	C₂×D₄	1	2	yes	—
112	C₂²×C₄₇	—	2	2	no	—
113	C₂²×C₄₇	—	2	2	no	—
114	C₂²×C₄₇	—	2	2	no	—
115	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
116	C₂×D₄₇	—	2	1	no	—
117	C₂×D₄₇	—	2	1	no	—
118	C₂×D₄₇	—	2	2	no	—
119	C₂×D₄₇	—	2	2	no	—
120	C₂×D₄₇	—	2	2	no	—
121	C₂×D₄₇	C₄×D₄	1	2	yes	—
122	C₄×C₄₇	—	2	2	no	—
123	C₄×C₄₇	—	2	1	no	—
124	C₄×C₄₇	#131	1	2	yes	complemented
125	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
126	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
127	Dic₄₇	—	2	2	no	—
128	Dic₄₇	—	2	1	no	—
129	Dic₄₇	—	2	1	no	—
130	Dic₄₇	C₄×D₄	1	2	yes	—
131	#2935	—	47	1	no	maximal, Sylow
132	C₂×C₄₇	—	4	2	no	—
133	C₂×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
134	C₂×C₄₇	C₂×#131	1	1	yes	characteristic
135	C₂×C₄₇	#568	1	1	yes	characteristic
136	D₄₇	—	2	2	no	—
137	D₄₇	—	4	2	no	—
138	C₂×#131	—	47	2	no	—
139	#532	—	47	1	no	—
140	#436	—	47	1	no	—
141	#436	D₄₇	1	1	yes	characteristic, complemented
142	#435	—	47	2	no	—
143	#435	—	47	2	no	—
144	C₈×D₄	—	47	1	no	—
145	C₈×D₄	—	47	1	no	—
146	C₂×C₄⋊C₈	—	47	1	no	—
147	#408	—	47	2	no	—
148	C₄×M₁₆	—	47	1	no	—
149	C₄₇	#2935	1	1	yes	characteristic, complemented, Sylow
150	C₂×#41	—	47	2	no	—
151	#131	—	94	8	no	—
152	C₂×M₁₆	—	47	1	no	—
153	C₂×M₁₆	—	47	2	no	—
154	C₂×M₁₆	—	47	1	no	—
155	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
156	C₂²×C₈	—	47	2	no	—
157	C₂²×C₈	—	47	2	no	—
158	C₂²×C₈	—	47	2	no	—
159	C₄⋊Q₈	—	47	1	no	—
160	#127	—	47	1	no	—
161	#124	—	47	2	no	—
162	#121	—	47	1	no	—
163	#121	—	47	1	no	—
164	#121	—	47	2	no	—
165	C₄×D₄	—	47	2	no	—
166	C₄×D₄	—	47	1	no	—
167	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
168	C₂×C₄²	—	47	1	no	—
169	C₄⋊C₈	—	47	2	no	—
170	C₄⋊C₈	—	47	1	no	—
171	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
172	C₂²⋊C₈	—	47	2	no	—
173	C₂²⋊C₈	—	47	2	no	—
174	C₂²⋊C₈	—	47	2	no	—
175	C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
176	#97	—	47	1	no	—
177	#97	—	47	1	no	—
178	C₄×C₈	—	47	1	no	—
179	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
180	#41	—	94	4	no	—
181	#41	—	94	4	no	—
182	C₂×Q₈	—	47	2	no	—
183	C₂×D₄	—	47	2	no	—
184	C₂×D₄	—	47	2	no	—
185	C₂×D₄	—	47	2	no	—
186	C₂×D₄	—	47	1	no	—
187	C₂×D₄	—	47	2	no	—
188	C₂×D₄	C₄×D₄₇	1	1	yes	characteristic
189	C₂²×C₄	—	47	1	no	—
190	C₂²×C₄	—	47	1	no	—
191	C₂²×C₄	—	47	2	no	—
192	C₂²×C₄	—	47	1	no	—
193	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
194	M₁₆	—	2	4	no	—
195	M₁₆	—	47	4	no	—
196	M₁₆	—	94	4	no	—
197	M₁₆	—	94	2	no	—
198	C₂×C₈	—	47	1	no	—
199	C₂×C₈	—	47	1	no	—
200	C₂×C₈	—	47	2	no	—
201	C₂×C₈	—	94	4	no	—
202	C₂×C₈	—	94	4	no	—
203	C₂×C₈	—	94	4	no	—
204	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
205	C₂×C₈	C₂²×D₄₇	1	2	yes	—
206	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
207	C₄⋊C₄	—	47	2	no	—
208	C₄⋊C₄	—	47	1	no	—
209	C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
210	C₂²⋊C₄	—	47	2	no	—
211	C₂²⋊C₄	—	47	2	no	—
212	C₂²⋊C₄	—	47	2	no	—
213	C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
214	C₄²	—	47	1	no	—
215	C₄²	—	47	1	no	—
216	C₄²	—	47	1	no	—
217	C₄²	C₂²×D₄₇	1	1	yes	characteristic
218	C₂³	—	47	1	no	—
219	C₂³	—	47	2	no	—
220	C₂³	C₂×C₄×D₄₇	1	2	yes	—
221	Q₈	—	94	4	no	—
222	D₄	—	2	2	no	—
223	D₄	—	94	4	no	—
224	D₄	—	94	4	no	—
225	D₄	—	94	4	no	—
226	D₄	—	94	2	no	—
227	D₄	—	188	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	47	1	no	—
231	C₂×C₄	—	47	2	no	—
232	C₂×C₄	—	47	2	no	—
233	C₂×C₄	—	47	1	no	—
234	C₂×C₄	—	47	1	no	—
235	C₂×C₄	—	47	2	no	—
236	C₂×C₄	—	94	2	no	—
237	C₂×C₄	—	94	2	no	—
238	C₂×C₄	—	94	2	no	—
239	C₂×C₄	—	188	1	no	—
240	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
241	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
242	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
243	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
244	C₈	—	2	2	no	—
245	C₈	—	2	1	no	—
246	C₈	—	47	2	no	—
247	C₈	—	94	2	no	—
248	C₈	—	94	1	no	—
249	C₈	D₄×D₄₇	1	2	yes	—
250	C₂²	—	2	2	no	—
251	C₂²	—	2	2	no	—
252	C₂²	—	2	2	no	—
253	C₂²	—	47	2	no	—
254	C₂²	—	94	1	no	—
255	C₂²	—	94	1	no	—
256	C₂²	—	94	2	no	—
257	C₂²	—	94	2	no	—
258	C₂²	—	94	2	no	—
259	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
260	C₄	—	2	2	no	—
261	C₄	—	2	1	no	—
262	C₄	—	47	2	no	—
263	C₄	—	94	2	no	—
264	C₄	—	94	1	no	—
265	C₄	—	94	1	no	—
266	C₄	#13094032	1	2	yes	complemented
267	C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
268	C₄	#41×D₄₇	1	1	yes	characteristic
269	C₂	—	4	2	no	—
270	C₂	—	94	2	no	—
271	C₂	—	188	2	no	—
272	C₂	C₄×D₄×D₄₇	1	1	yes	characteristic
273	C₂	C₂×#13094032	1	1	yes	characteristic
274	C₂	#15689888	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₄
Fitting	C₄₇×#436	C₂
hypercenter	#436	D₄₇
hypocenter	C₄₇	#2935
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #436

Complements

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

N	H ≅ G/N	type
1. C₂×#13094032	C₂	semidirect
3. #15689200	C₂	semidirect
4. #15689192	C₂	semidirect
5. #15689191	C₂	semidirect
6. C₈×D₁₈₈	C₂	semidirect
7. D₄×C₄₇⋊C₈	C₂	semidirect
8. C₄⋊C₈×D₄₇	C₂	semidirect
9. #15689088	C₂	semidirect
10. C₄×#10625324	C₂	semidirect
11. C₄₇×#436	C₂	semidirect
77. #10625324	D₄	semidirect
124. C₄×C₄₇	#131	semidirect
141. #436	D₄₇	semidirect
149. C₄₇	#2935	semidirect
266. C₄	#13094032	semidirect