Subgroups — #20257793

Order 6016.

1258 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689865	C₂	1	4	yes	maximal, complemented
2	#15689839	C₂	1	2	yes	maximal, complemented
3	#15689838	C₂	1	4	yes	maximal, complemented
4	D₄×D₁₈₈	C₂	1	4	yes	maximal, complemented
5	#15689758	C₂	1	2	yes	maximal, complemented
6	#15689689	C₂	1	8	yes	maximal, complemented
7	#15689687	C₂	1	4	yes	maximal, complemented
8	#15689673	C₂	1	2	yes	maximal, complemented
9	C₄₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625350	C₂²	1	4	yes	complemented
11	C₂²×D₁₈₈	C₂²	1	4	yes	complemented
12	C₂×D₄×D₄₇	C₂²	1	8	yes	complemented
13	#13094024	C₂²	1	2	yes	complemented
14	#13094021	C₂²	1	2	yes	—
15	#13094020	C₂²	1	8	yes	complemented
16	#13094013	C₂²	1	8	yes	complemented
17	#13094012	C₂²	1	4	yes	complemented
18	#13094010	C₂²	1	16	yes	complemented
19	#13093999	C₂²	1	8	yes	complemented
20	#13093998	C₂²	1	8	yes	complemented
21	#13093998	C₂²	1	4	yes	complemented
22	#13093998	C₂²	1	4	yes	complemented
23	#13093995	C₂²	1	8	yes	complemented
24	#13093994	C₂²	1	16	yes	complemented
25	#13093992	C₂²	1	8	yes	complemented
26	#13093992	C₂²	1	8	yes	complemented
27	C₄×D₁₈₈	C₂²	1	4	yes	complemented
28	C₄×D₁₈₈	C₂²	1	4	yes	complemented
29	#13093983	C₂²	1	4	yes	complemented
30	#13093982	C₂²	1	8	yes	complemented
31	C₂×#41×C₄₇	C₂²	1	2	yes	complemented
32	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
33	#127×C₄₇	C₂²	1	1	yes	characteristic
34	#124×C₄₇	C₂²	1	2	yes	complemented
35	#121×C₄₇	C₂²	1	4	yes	complemented
36	C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
37	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
38	C₂³×D₄₇	C₂³	1	8	yes	—
39	#41×C₄₇	—	4	4	no	—
40	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
41	C₂×D₄×C₄₇	C₂³	1	4	yes	—
42	C₂×D₄×C₄₇	C₂³	1	4	yes	—
43	C₂×D₄×C₄₇	C₂³	1	2	yes	—
44	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
45	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
47	C₂×C₂²⋊D₄₇	C₂³	1	8	yes	—
48	C₂×C₂²⋊D₄₇	C₂³	1	16	yes	—
49	D₄×D₄₇	—	4	16	no	—
50	#10625350	—	4	8	no	—
51	C₂×D₁₈₈	—	4	8	no	—
52	C₂×D₁₈₈	C₂³	1	4	yes	—
53	C₂×D₁₈₈	C₂³	1	4	yes	—
54	C₂×D₁₈₈	C₂³	1	4	yes	—
55	C₂×D₁₈₈	C₂³	1	8	yes	—
56	C₂×C₄×D₄₇	C₂³	1	8	yes	—
57	C₂×Dic₉₄	C₂³	1	4	yes	—
58	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
59	C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
60	C₄²×C₄₇	C₂³	1	2	yes	—
61	C₄²×C₄₇	C₂³	1	1	yes	characteristic
62	C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	C₂²⋊Dic₄₇	C₂³	1	8	yes	—
64	(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
65	(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
66	(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
67	C₄⋊Dic₄₇	C₂³	1	4	yes	—
68	C₄⋊Dic₄₇	C₂³	1	4	yes	—
69	C₄×Dic₄₇	C₂³	1	8	yes	—
70	C₂³×C₄₇	C₂⁴	1	4	yes	—
71	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
72	C₂²×D₄₇	—	4	8	no	—
73	C₂²×D₄₇	—	4	16	no	—
74	C₂²×D₄₇	C₂⁴	1	8	yes	—
75	Q₈×C₄₇	—	4	2	no	—
76	D₄×C₄₇	—	2	8	no	—
77	D₄×C₄₇	—	4	4	no	—
78	D₄×C₄₇	—	4	2	no	—
79	C₂×C₄×C₄₇	—	2	8	no	—
80	C₂×C₄×C₄₇	—	2	4	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
83	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
84	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
85	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
87	C₂²⋊D₄₇	—	4	8	no	—
88	C₂²⋊D₄₇	—	4	16	no	—
89	C₂×Dic₄₇	C₂⁴	1	8	yes	—
90	D₁₈₈	—	2	8	no	—
91	D₁₈₈	—	2	8	no	—
92	D₁₈₈	—	4	8	no	—
93	D₁₈₈	—	4	4	no	—
94	C₄×D₄₇	—	2	16	no	—
95	Dic₉₄	—	4	4	no	—
96	C₂²×C₄₇	—	2	2	no	—
97	C₂²×C₄₇	—	2	8	no	—
98	C₂²×C₄₇	—	2	1	no	—
99	C₂²×C₄₇	—	2	4	no	—
100	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
101	C₂×D₄₇	—	2	8	no	—
102	C₂×D₄₇	—	2	8	no	—
103	C₂×D₄₇	—	2	8	no	—
104	C₂×D₄₇	—	8	16	no	—
105	C₄×C₄₇	—	2	2	no	—
106	C₄×C₄₇	—	2	4	no	—
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
109	C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
110	Dic₄₇	—	2	8	no	—
111	#3549	—	47	1	no	maximal, Sylow
112	C₂×C₄₇	—	4	4	no	—
113	C₂×C₄₇	—	4	1	no	—
114	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
115	C₂×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
116	D₄₇	—	4	8	no	—
117	H(3,𝔽₄)	—	47	4	no	—
118	#555	—	47	2	no	—
119	#555	—	47	4	no	—
120	D₄²	—	47	2	no	—
121	D₄²	—	47	4	no	—
122	#535	—	47	4	no	—
123	#535	—	47	8	no	—
124	#532	—	47	2	no	—
125	#532	D₄₇	1	1	yes	characteristic, complemented
126	C₄₇	#3549	1	1	yes	characteristic, complemented, Sylow
127	C₂×#41	—	47	4	no	—
128	C₂×#41	C₂×D₄₇	1	2	yes	complemented
129	C₂²×D₄	—	47	8	no	—
130	C₂²×D₄	—	47	4	no	—
131	C₄⋊Q₈	—	47	2	no	—
132	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
133	#127	—	47	8	no	—
134	#127	—	47	2	no	—
135	#127	C₂×D₄₇	1	1	yes	characteristic
136	#124	—	47	8	no	—
137	#124	—	47	16	no	—
138	#124	—	47	4	no	—
139	#124	C₂×D₄₇	1	2	yes	complemented
140	#121	—	47	8	no	—
141	#121	—	47	4	no	—
142	#121	—	47	4	no	—
143	#121	—	47	8	no	—
144	#121	—	47	8	no	—
145	#121	C₂×D₄₇	1	4	yes	complemented
146	#120	—	47	8	no	—
147	#120	—	47	8	no	—
148	#120	—	47	16	no	—
149	C₄×D₄	—	47	4	no	—
150	C₄×D₄	—	47	4	no	—
151	C₄×D₄	C₂×D₄₇	1	4	yes	complemented
152	#117	—	47	4	no	—
153	#117	—	47	8	no	—
154	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic, complemented
155	C₂⁴	—	47	8	no	—
156	#41	—	4	4	no	—
157	#41	—	188	8	no	—
158	C₂×Q₈	—	47	4	no	—
159	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
160	C₂×D₄	—	47	16	no	—
161	C₂×D₄	—	47	8	no	—
162	C₂×D₄	—	47	4	no	—
163	C₂×D₄	—	47	4	no	—
164	C₂×D₄	—	47	4	no	—
165	C₂×D₄	—	47	8	no	—
166	C₂×D₄	—	188	8	no	—
167	C₂×D₄	—	188	16	no	—
168	C₂×D₄	C₂²×D₄₇	1	4	yes	—
169	C₂×D₄	C₂²×D₄₇	1	2	yes	—
170	C₂×D₄	C₂²×D₄₇	1	4	yes	—
171	C₂²×C₄	—	47	8	no	—
172	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
173	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
174	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
175	C₄⋊C₄	—	47	4	no	—
176	C₄⋊C₄	—	47	4	no	—
177	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
178	C₂²⋊C₄	—	47	8	no	—
179	C₂²⋊C₄	—	47	16	no	—
180	C₂²⋊C₄	—	47	8	no	—
181	C₂²⋊C₄	—	47	8	no	—
182	C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
183	C₄²	—	47	8	no	—
184	C₄²	C₂²×D₄₇	1	1	yes	characteristic
185	C₄²	C₂²×D₄₇	1	2	yes	—
186	C₄²	C₂²×D₄₇	1	1	yes	characteristic
187	C₂³	—	47	8	no	—
188	C₂³	—	188	8	no	—
189	C₂³	—	188	16	no	—
190	C₂³	C₂³×D₄₇	1	4	yes	—
191	C₂³	C₂³×D₄₇	1	1	yes	characteristic
192	Q₈	—	4	2	no	—
193	Q₈	—	188	4	no	—
194	D₄	—	2	8	no	—
195	D₄	—	4	2	no	—
196	D₄	—	4	4	no	—
197	D₄	—	94	8	no	—
198	D₄	—	94	8	no	—
199	D₄	—	188	8	no	—
200	D₄	—	188	4	no	—
201	D₄	—	188	16	no	—
202	D₄	—	188	8	no	—
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	47	8	no	—
207	C₂×C₄	—	94	16	no	—
208	C₂×C₄	C₂³×D₄₇	1	4	yes	—
209	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
210	C₂×C₄	C₂³×D₄₇	1	2	yes	—
211	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
212	C₂×C₄	C₂³×D₄₇	1	2	yes	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	2	2	no	—
216	C₂²	—	2	8	no	—
217	C₂²	—	94	8	no	—
218	C₂²	—	94	8	no	—
219	C₂²	—	94	8	no	—
220	C₂²	—	376	16	no	—
221	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	4	no	—
224	C₄	—	2	2	no	—
225	C₄	—	94	8	no	—
226	C₄	#13094069	1	2	yes	—
227	C₄	#13094070	1	4	yes	—
228	C₂	—	4	4	no	—
229	C₂	—	4	1	no	—
230	C₂	—	188	8	no	—
231	C₂	C₂×#13094069	1	1	yes	characteristic
232	C₂	C₂×#13094070	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#532	C₂
hypercenter	#532	D₄₇
hypocenter	C₄₇	#3549
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #15689865	C₂	semidirect
2. #15689839	C₂	semidirect
3. #15689838	C₂	semidirect
4. D₄×D₁₈₈	C₂	semidirect
5. #15689758	C₂	semidirect
6. #15689689	C₂	semidirect
7. #15689687	C₂	semidirect
8. #15689673	C₂	semidirect
9. C₄₇×#532	C₂	semidirect
10. C₂×#10625350	C₂²	semidirect
11. C₂²×D₁₈₈	C₂²	semidirect
12. C₂×D₄×D₄₇	C₂²	semidirect
13. #13094024	C₂²	semidirect
15. #13094020	C₂²	semidirect
16. #13094013	C₂²	semidirect
17. #13094012	C₂²	semidirect
18. #13094010	C₂²	semidirect
19. #13093999	C₂²	semidirect
20. #13093998	C₂²	semidirect
21. #13093998	C₂²	semidirect
22. #13093998	C₂²	semidirect
23. #13093995	C₂²	semidirect
24. #13093994	C₂²	semidirect
25. #13093992	C₂²	semidirect
26. #13093992	C₂²	semidirect
27. C₄×D₁₈₈	C₂²	semidirect
28. C₄×D₁₈₈	C₂²	semidirect
29. #13093983	C₂²	semidirect
30. #13093982	C₂²	semidirect
31. C₂×#41×C₄₇	C₂²	semidirect
32. C₄⋊Q₈×C₄₇	C₂²	semidirect
34. #124×C₄₇	C₂²	semidirect
35. #121×C₄₇	C₂²	semidirect
36. C₄×D₄×C₄₇	C₂²	semidirect
37. C₂×C₄²×C₄₇	C₂²	semidirect
125. #532	D₄₇	semidirect
126. C₄₇	#3549	semidirect
128. C₂×#41	C₂×D₄₇	semidirect
132. C₄⋊Q₈	C₂×D₄₇	semidirect
139. #124	C₂×D₄₇	semidirect
145. #121	C₂×D₄₇	semidirect
151. C₄×D₄	C₂×D₄₇	semidirect
154. C₂×C₄²	C₂×D₄₇	semidirect