Subgroups — C₂×#15689673 #20256671

Order 6016.

1728 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	C₂²×#10625350	C₂	1	2	yes	maximal, complemented
2	#15689673	C₂	1	16	yes	maximal, direct product factor
3	C₂×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13094021	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13094012	C₂	1	2	yes	maximal, complemented
6	C₂×#13093998	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×D₁₈₈	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10625350	—	2	16	no	—
10	C₂×#10625350	C₂²	1	16	yes	complemented
11	C₂²×Dic₉₄	C₂²	1	2	yes	—
12	C₂²×D₁₈₈	C₂²	1	4	yes	—
13	C₂²×D₁₈₈	C₂²	1	2	yes	—
14	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	—
15	C₂²×C₄×D₄₇	C₂²	1	4	yes	—
16	#13094024	C₂²	1	8	yes	complemented
17	#13094021	C₂²	1	8	yes	complemented
18	#13094012	C₂²	1	16	yes	complemented
19	#13093998	C₂²	1	32	yes	complemented
20	C₄×D₁₈₈	C₂²	1	32	yes	complemented
21	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
22	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	8	yes	—
23	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
24	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
26	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₄₇	C₂²	1	8	yes	complemented
29	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
30	C₂³×D₄₇	C₂³	1	4	yes	—
31	C₂²×C₄×C₄₇	—	2	8	no	—
32	C₂²×C₄×C₄₇	D₄	1	8	yes	complemented
33	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
34	C₂²×C₄×C₄₇	C₂³	1	8	yes	—
35	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
38	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂×C₂²⋊D₄₇	—	2	16	no	—
40	C₂×C₂²⋊D₄₇	C₂³	1	16	yes	—
41	C₂²×Dic₄₇	C₂³	1	4	yes	—
42	#10625350	—	2	64	no	—
43	C₂×D₁₈₈	—	2	8	no	—
44	C₂×D₁₈₈	—	2	16	no	—
45	C₂×D₁₈₈	C₂³	1	16	yes	—
46	C₂×D₁₈₈	C₂³	1	8	yes	—
47	C₂×C₄×D₄₇	—	2	16	no	—
48	C₂×C₄×D₄₇	C₂³	1	16	yes	—
49	C₂×Dic₉₄	—	2	8	no	—
50	C₂×Dic₉₄	C₂³	1	8	yes	—
51	C₄²×C₄₇	C₂³	1	8	yes	—
52	C₄²×C₄₇	C₂³	1	4	yes	—
53	C₄²×C₄₇	C₂³	1	4	yes	—
54	(C₂×D₄₇)⋊C₄	C₂³	1	32	yes	—
55	C₄⋊Dic₄₇	C₂³	1	16	yes	—
56	C₂³×C₄₇	—	2	4	no	—
57	C₂³×C₄₇	C₂×D₄	1	4	yes	—
58	C₂³×C₄₇	C₂⁴	1	2	yes	—
59	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
60	C₂²×D₄₇	—	2	8	no	—
61	C₂²×D₄₇	—	2	16	no	—
62	C₂²×D₄₇	C₂⁴	1	8	yes	—
63	C₂×C₄×C₄₇	—	2	4	no	—
64	C₂×C₄×C₄₇	—	2	16	no	—
65	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
66	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
67	C₂×C₄×C₄₇	C₂×D₄	1	16	yes	complemented
68	C₂×C₄×C₄₇	#41	1	8	yes	complemented
69	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
70	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
71	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
72	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
73	C₂²⋊D₄₇	—	2	32	no	—
74	C₂×Dic₄₇	—	2	8	no	—
75	C₂×Dic₄₇	C₂⁴	1	8	yes	—
76	D₁₈₈	—	2	16	no	—
77	D₁₈₈	—	2	32	no	—
78	C₄×D₄₇	—	2	32	no	—
79	Dic₉₄	—	2	16	no	—
80	C₂²×C₄₇	—	2	8	no	—
81	C₂²×C₄₇	—	2	4	no	—
82	C₂²×C₄₇	C₂²×D₄	1	4	yes	—
83	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
84	C₂²×C₄₇	C₂×#41	1	4	yes	—
85	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
86	C₂×D₄₇	—	2	8	no	—
87	C₂×D₄₇	—	2	16	no	—
88	C₂×D₄₇	—	4	16	no	—
89	C₄×C₄₇	—	2	4	no	—
90	C₄×C₄₇	C₂²×D₄	1	4	yes	—
91	C₄×C₄₇	C₂²×D₄	1	4	yes	—
92	C₄×C₄₇	C₂×#41	1	8	yes	complemented
93	Dic₄₇	—	2	8	no	—
94	C₂×#532	—	47	1	no	maximal, Sylow
95	C₂×C₄₇	—	2	4	no	—
96	C₂×C₄₇	#532	1	4	yes	complemented
97	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
98	C₂×C₄₇	C₂²×#41	1	2	yes	—
99	D₄₇	—	4	8	no	—
100	C₂²×#41	—	47	2	no	—
101	#532	—	47	16	no	—
102	C₂×C₄⋊Q₈	—	47	1	no	—
103	C₂×#127	—	47	1	no	—
104	C₂×#124	—	47	2	no	—
105	C₂×#121	—	47	4	no	—
106	C₂×C₄×D₄	—	47	4	no	—
107	C₂²×C₄²	D₄₇	1	1	yes	characteristic, complemented
108	C₄₇	C₂×#532	1	1	yes	characteristic, complemented, Sylow
109	C₂×#41	—	47	16	no	—
110	C₂×#41	—	94	16	no	—
111	C₂²×Q₈	—	47	2	no	—
112	C₂²×D₄	—	47	4	no	—
113	C₂²×D₄	—	47	4	no	—
114	C₂²×D₄	—	47	2	no	—
115	C₂³×C₄	—	47	4	no	—
116	C₂³×C₄	C₂×D₄₇	1	2	yes	—
117	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
118	C₄⋊Q₈	—	47	8	no	—
119	#127	—	47	8	no	—
120	#124	—	47	16	no	—
121	#121	—	47	32	no	—
122	C₄×D₄	—	47	32	no	—
123	C₂×C₄⋊C₄	—	47	4	no	—
124	C₂×C₂²⋊C₄	—	47	8	no	—
125	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
126	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
127	C₂×C₄²	C₂×D₄₇	1	2	yes	—
128	C₂×C₄²	C₂×D₄₇	1	8	yes	complemented
129	C₂⁴	—	47	4	no	—
130	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
131	#41	—	94	64	no	—
132	C₂×Q₈	—	47	8	no	—
133	C₂×Q₈	—	94	8	no	—
134	C₂×D₄	—	47	16	no	—
135	C₂×D₄	—	47	16	no	—
136	C₂×D₄	—	47	8	no	—
137	C₂×D₄	—	94	16	no	—
138	C₂×D₄	—	94	8	no	—
139	C₂×D₄	—	94	16	no	—
140	C₂²×C₄	—	2	8	no	—
141	C₂²×C₄	—	47	4	no	—
142	C₂²×C₄	—	47	16	no	—
143	C₂²×C₄	—	94	16	no	—
144	C₂²×C₄	D₁₈₈	1	8	yes	complemented
145	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
146	C₂²×C₄	C₂²×D₄₇	1	8	yes	—
147	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
148	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
149	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
150	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
151	C₄⋊C₄	—	47	16	no	—
152	C₂²⋊C₄	—	47	32	no	—
153	C₄²	C₂²×D₄₇	1	8	yes	—
154	C₄²	C₂²×D₄₇	1	4	yes	—
155	C₄²	C₂²×D₄₇	1	4	yes	—
156	C₂³	—	2	4	no	—
157	C₂³	—	47	8	no	—
158	C₂³	—	94	8	no	—
159	C₂³	—	94	16	no	—
160	C₂³	C₂×D₁₈₈	1	4	yes	—
161	C₂³	C₂³×D₄₇	1	2	yes	—
162	C₂³	C₂³×D₄₇	1	1	yes	characteristic
163	Q₈	—	94	16	no	—
164	D₄	—	94	32	no	—
165	D₄	—	94	16	no	—
166	D₄	—	94	32	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	16	no	—
169	C₂×C₄	—	47	8	no	—
170	C₂×C₄	—	94	8	no	—
171	C₂×C₄	—	94	32	no	—
172	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
173	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
174	C₂×C₄	C₂×D₁₈₈	1	16	yes	complemented
175	C₂×C₄	#10625350	1	8	yes	complemented
176	C₂×C₄	C₂³×D₄₇	1	4	yes	—
177	C₂×C₄	C₂³×D₄₇	1	2	yes	—
178	C₂×C₄	C₂³×D₄₇	1	2	yes	—
179	C₂×C₄	C₂³×D₄₇	1	4	yes	—
180	C₂²	—	2	8	no	—
181	C₂²	—	2	4	no	—
182	C₂²	—	94	8	no	—
183	C₂²	—	94	16	no	—
184	C₂²	—	188	16	no	—
185	C₂²	C₂²×D₁₈₈	1	4	yes	—
186	C₂²	C₂²×D₁₈₈	1	2	yes	—
187	C₂²	C₂×#10625350	1	4	yes	—
188	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
189	C₄	—	2	4	no	—
190	C₄	—	94	8	no	—
191	C₄	C₂²×D₁₈₈	1	4	yes	—
192	C₄	C₂²×D₁₈₈	1	4	yes	—
193	C₄	C₂×#10625350	1	8	yes	complemented
194	C₂	—	2	4	no	—
195	C₂	—	188	8	no	—
196	C₂	#15689673	1	4	yes	direct product factor
197	C₂	C₂³×D₁₈₈	1	1	yes	characteristic
198	C₂	C₂²×#10625350	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₂²×C₄²×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂²×C₄²	D₄₇
hypocenter	C₄₇	C₂×#532
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×#10625350	C₂	semidirect
2. #15689673	C₂	direct (N × H)
3. C₂×#13094024	C₂	semidirect
4. C₂×#13094021	C₂	semidirect
5. C₂×#13094012	C₂	semidirect
6. C₂×#13093998	C₂	semidirect
7. C₂×C₄×D₁₈₈	C₂	semidirect
8. C₂²×C₄²×C₄₇	C₂	semidirect
10. C₂×#10625350	C₂²	semidirect
16. #13094024	C₂²	semidirect
17. #13094021	C₂²	semidirect
18. #13094012	C₂²	semidirect
19. #13093998	C₂²	semidirect
20. C₄×D₁₈₈	C₂²	semidirect
28. C₂×C₄²×C₄₇	C₂²	semidirect
32. C₂²×C₄×C₄₇	D₄	semidirect
67. C₂×C₄×C₄₇	C₂×D₄	semidirect
68. C₂×C₄×C₄₇	#41	semidirect
92. C₄×C₄₇	C₂×#41	semidirect
96. C₂×C₄₇	#532	semidirect
107. C₂²×C₄²	D₄₇	semidirect
108. C₄₇	C₂×#532	semidirect
128. C₂×C₄²	C₂×D₄₇	semidirect
144. C₂²×C₄	D₁₈₈	semidirect
174. C₂×C₄	C₂×D₁₈₈	semidirect
175. C₂×C₄	#10625350	semidirect
193. C₄	C₂×#10625350	semidirect
196. C₂	#15689673	direct (N × H)

Subgroups — C2×#15689673 #20256671

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689673 #20256671