Subgroups — #20256597

Order 6016.

1492 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094072	C₂	1	1	yes	maximal, characteristic
2	#15689605	C₂	1	4	yes	maximal, complemented
3	#15689603	C₂	1	6	yes	maximal, complemented
4	#15689599	C₂	1	4	yes	maximal, complemented
5	C₄×#10625354	C₂	1	4	yes	maximal, complemented
6	#15689591	C₂	1	6	yes	maximal, complemented
7	C₂×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×Q₈×D₄₇	C₂	1	4	yes	maximal, complemented
9	C₄₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
10	#13094072	C₄	1	16	yes	complemented
11	C₂×#10625354	C₂²	1	4	yes	—
12	C₂×#10625350	C₂²	1	6	yes	—
13	C₂×Q₈×D₄₇	C₂²	1	4	yes	—
14	Q₈×Dic₄₇	C₂²	1	4	yes	—
15	Q₈×Dic₄₇	C₂²	1	4	yes	—
16	C₄×Dic₉₄	C₂²	1	12	yes	—
17	#13093989	C₂²	1	6	yes	—
18	#13093989	C₂²	1	6	yes	—
19	C₄×D₁₈₈	C₂²	1	12	yes	—
20	#13093986	C₂²	1	6	yes	—
21	#13093986	C₂²	1	6	yes	—
22	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
23	(C₂²⋊D₄₇)⋊C₄	C₂²	1	12	yes	—
24	#13093982	C₂²	1	12	yes	—
25	#13093981	C₂²	1	12	yes	—
26	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
27	C₄⋊C₄×D₄₇	C₂²	1	12	yes	—
28	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
29	C₄²×D₄₇	C₂²	1	12	yes	—
30	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄×Q₈×C₄₇	C₂²	1	4	yes	—
32	C₄×Q₈×C₄₇	C₂²	1	4	yes	—
33	#117×C₄₇	C₂²	1	6	yes	—
34	C₂×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
35	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
36	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
37	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
38	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
39	C₂²×Dic₄₇	C₂³	1	3	yes	—
40	#10625354	C₂×C₄	1	32	yes	complemented
41	Q₈×D₄₇	C₂×C₄	1	32	yes	complemented
42	#10625350	C₂×C₄	1	48	yes	complemented
43	C₂×D₁₈₈	C₂³	1	6	yes	—
44	C₂×C₄×D₄₇	C₂³	1	4	yes	—
45	C₂×C₄×D₄₇	C₂³	1	12	yes	—
46	C₂×C₄×D₄₇	C₂³	1	12	yes	—
47	C₂×Dic₉₄	C₂³	1	6	yes	—
48	C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
49	C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
50	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
51	C₄²×C₄₇	C₂³	1	12	yes	—
52	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
53	(C₂×D₄₇)⋊C₄	C₂³	1	12	yes	—
54	C₄⋊Dic₄₇	C₂³	1	12	yes	—
55	Dic₄₇⋊C₄	C₂³	1	12	yes	—
56	Dic₄₇⋊C₄	C₂³	1	4	yes	—
57	C₄×Dic₄₇	C₂³	1	4	yes	—
58	C₄×Dic₄₇	C₂³	1	6	yes	—
59	C₄×Dic₄₇	C₂³	1	12	yes	—
60	C₄×Dic₄₇	C₂³	1	6	yes	—
61	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
62	C₂²×D₄₇	C₂⁴	1	4	yes	—
63	Q₈×C₄₇	C₂²×C₄	1	16	yes	—
64	C₂×C₄×C₄₇	C₂²×C₄	1	12	yes	—
65	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
66	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
67	C₂×C₄×C₄₇	C₂⁴	1	6	yes	—
68	C₂²⋊D₄₇	C₂²×C₄	1	16	yes	—
69	C₂×Dic₄₇	—	2	2	no	—
70	C₂×Dic₄₇	—	4	3	no	—
71	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
72	C₂×Dic₄₇	C₂⁴	1	6	yes	—
73	C₂×Dic₄₇	C₂⁴	1	4	yes	—
74	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
75	D₁₈₈	C₂²×C₄	1	24	yes	—
76	C₄×D₄₇	—	2	8	no	—
77	C₄×D₄₇	—	4	12	no	—
78	C₄×D₄₇	C₂²×C₄	1	48	yes	—
79	Dic₉₄	C₂²×C₄	1	24	yes	—
80	C₂²×C₄₇	—	2	1	no	—
81	C₂²×C₄₇	—	2	1	no	—
82	C₂²×C₄₇	C₂³×C₄	1	2	yes	—
83	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
84	C₂×D₄₇	—	2	4	no	—
85	C₂×D₄₇	—	2	4	no	—
86	C₂×D₄₇	C₂³×C₄	1	8	yes	—
87	C₄×C₄₇	—	2	4	no	—
88	C₄×C₄₇	—	2	4	no	—
89	C₄×C₄₇	C₂³×C₄	1	12	yes	—
90	Dic₄₇	—	2	1	no	—
91	Dic₄₇	—	2	6	no	—
92	Dic₄₇	C₂³×C₄	1	8	yes	—
93	Dic₄₇	2₋¹⁺⁴	1	2	yes	complemented
94	C₄×2₋¹⁺⁴	—	47	1	no	maximal, Sylow
95	C₂×C₄₇	—	2	2	no	—
96	C₂×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
97	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
98	C₂×C₄₇	#585	1	1	yes	characteristic
99	D₄₇	—	2	8	no	—
100	C₂×2₋¹⁺⁴	—	47	1	no	—
101	#520	—	47	4	no	—
102	#520	—	47	6	no	—
103	#519	—	47	4	no	—
104	#519	D₄₇	1	1	yes	characteristic, complemented
105	C₄×#41	—	47	4	no	—
106	C₄×#41	—	47	6	no	—
107	C₂×C₄×Q₈	—	47	1	no	—
108	C₂×C₄×Q₈	—	47	4	no	—
109	C₄₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
110	2₋¹⁺⁴	—	47	16	no	—
111	C₂×#41	—	47	4	no	—
112	C₂×#41	—	47	6	no	—
113	C₂²×Q₈	—	47	4	no	—
114	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
115	C₄×Q₈	—	47	4	no	—
116	C₄×Q₈	—	47	4	no	—
117	C₄×Q₈	—	47	6	no	—
118	C₄×Q₈	—	47	6	no	—
119	C₄×Q₈	—	47	12	no	—
120	C₄×Q₈	C₂×D₄₇	1	4	yes	—
121	C₄×Q₈	C₂×D₄₇	1	4	yes	—
122	C₄×D₄	—	47	6	no	—
123	C₄×D₄	—	47	6	no	—
124	C₄×D₄	—	47	4	no	—
125	C₄×D₄	—	47	12	no	—
126	C₄×D₄	—	47	12	no	—
127	#117	—	47	12	no	—
128	#117	—	47	12	no	—
129	#117	C₂×D₄₇	1	6	yes	—
130	C₂×C₄⋊C₄	—	47	3	no	—
131	C₂×C₄⋊C₄	—	47	12	no	—
132	C₂×C₄²	—	47	3	no	—
133	C₂×C₄²	—	47	12	no	—
134	#41	—	47	32	no	—
135	#41	—	47	48	no	—
136	C₂×Q₈	—	47	32	no	—
137	C₂×Q₈	—	47	6	no	—
138	C₂×Q₈	C₄×D₄₇	1	8	yes	complemented
139	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
140	C₂×D₄	—	47	4	no	—
141	C₂×D₄	—	47	6	no	—
142	C₂²×C₄	—	47	12	no	—
143	C₂²×C₄	—	47	1	no	—
144	C₂²×C₄	—	47	3	no	—
145	C₂²×C₄	—	47	4	no	—
146	C₂²×C₄	—	47	12	no	—
147	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
148	C₄⋊C₄	—	47	12	no	—
149	C₄⋊C₄	—	47	4	no	—
150	C₄⋊C₄	—	47	12	no	—
151	C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
152	C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
153	C₂²⋊C₄	—	47	4	no	—
154	C₂²⋊C₄	—	47	12	no	—
155	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
156	C₄²	—	47	4	no	—
157	C₄²	—	47	6	no	—
158	C₄²	—	47	12	no	—
159	C₄²	—	47	6	no	—
160	C₄²	C₂²×D₄₇	1	12	yes	—
161	C₂³	—	47	4	no	—
162	C₂³	C₂³×D₄₇	1	1	yes	characteristic
163	Q₈	—	47	24	no	—
164	Q₈	C₂×C₄×D₄₇	1	16	yes	—
165	D₄	—	47	16	no	—
166	D₄	—	47	24	no	—
167	C₂×C₄	—	47	1	no	—
168	C₂×C₄	—	47	4	no	—
169	C₂×C₄	—	47	48	no	—
170	C₂×C₄	—	47	1	no	—
171	C₂×C₄	—	47	6	no	—
172	C₂×C₄	—	94	8	no	—
173	C₂×C₄	—	94	2	no	—
174	C₂×C₄	—	188	12	no	—
175	C₂×C₄	—	188	3	no	—
176	C₂×C₄	C₂×C₄×D₄₇	1	12	yes	—
177	C₂×C₄	C₂³×D₄₇	1	4	yes	—
178	C₂×C₄	C₂³×D₄₇	1	4	yes	—
179	C₂×C₄	C₂³×D₄₇	1	6	yes	—
180	C₂²	—	2	1	no	—
181	C₂²	—	2	1	no	—
182	C₂²	—	47	8	no	—
183	C₂²	—	94	4	no	—
184	C₂²	—	94	4	no	—
185	C₂²	C₂²×C₄×D₄₇	1	2	yes	—
186	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
187	C₄	—	2	4	no	—
188	C₄	—	2	4	no	—
189	C₄	—	47	8	no	—
190	C₄	—	47	2	no	—
191	C₄	—	94	1	no	—
192	C₄	—	94	6	no	—
193	C₄	C₂²×C₄×D₄₇	1	12	yes	—
194	C₂	—	2	2	no	—
195	C₂	—	94	8	no	—
196	C₂	C₂³×C₄×D₄₇	1	1	yes	characteristic
197	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
198	C₂	#15689960	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator	C₂×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#519	C₂
socle	C₂²×C₄₇	C₂⁵
hypercenter	#519	D₄₇
hypocenter	C₄₇	C₄×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #519

Complements

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

N	H ≅ G/N	type
2. #15689605	C₂	semidirect
3. #15689603	C₂	semidirect
4. #15689599	C₂	semidirect
5. C₄×#10625354	C₂	semidirect
6. #15689591	C₂	semidirect
7. C₂×Q₈×Dic₄₇	C₂	semidirect
8. C₄×Q₈×D₄₇	C₂	semidirect
9. C₄₇×#519	C₂	semidirect
10. #13094072	C₄	semidirect
34. C₂×Q₈×C₄₇	C₂×C₄	semidirect
40. #10625354	C₂×C₄	semidirect
41. Q₈×D₄₇	C₂×C₄	semidirect
42. #10625350	C₂×C₄	semidirect
93. Dic₄₇	2₋¹⁺⁴	semidirect
104. #519	D₄₇	semidirect
109. C₄₇	C₄×2₋¹⁺⁴	semidirect
138. C₂×Q₈	C₄×D₄₇	semidirect