Subgroups — C₂×#15689784 #20256856

Order 6016.

1620 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10625354	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689784	C₂	1	16	yes	maximal, direct product factor
3	C₂×#13094013	C₂	1	3	yes	maximal, complemented
4	C₂×#13094000	C₂	1	3	yes	maximal, complemented
5	C₂×#13093998	C₂	1	3	yes	maximal, complemented
6	C₂×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₂²⋊D₄₇	C₂	1	3	yes	maximal, complemented
8	C₂³×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10625354	—	2	8	no	—
10	C₂×#10625354	C₂²	1	8	yes	complemented
11	C₂²×D₁₈₈	C₂²	1	3	yes	—
12	C₂²×C₂²⋊D₄₇	C₂²	1	3	yes	—
13	C₂²×C₄×D₄₇	C₂²	1	3	yes	—
14	#13094013	C₂²	1	24	yes	complemented
15	#13094000	C₂²	1	24	yes	complemented
16	#13093998	C₂²	1	24	yes	complemented
17	Q₈×Dic₄₇	C₂²	1	8	yes	complemented
18	C₄×C₂²⋊D₄₇	C₂²	1	24	yes	complemented
19	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
20	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
21	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
23	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	6	yes	—
24	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
25	C₂²×Q₈×C₄₇	—	2	8	no	—
26	C₂²×Q₈×C₄₇	C₂²	1	3	yes	—
27	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×Q₈×C₄₇	C₂²	1	8	yes	complemented
29	C₂³×C₄×C₄₇	C₂²	1	3	yes	—
30	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
31	C₂³×D₄₇	C₂³	1	3	yes	—
32	C₂×Q₈×C₄₇	—	2	32	no	—
33	C₂×Q₈×C₄₇	—	2	12	no	—
34	C₂×Q₈×C₄₇	D₄	1	8	yes	complemented
35	C₂×Q₈×C₄₇	C₂³	1	12	yes	—
36	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
37	C₂²×C₄×C₄₇	—	2	12	no	—
38	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
39	C₂²×C₄×C₄₇	C₂³	1	12	yes	—
40	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
41	C₂×C₂²⋊D₄₇	—	2	12	no	—
42	C₂×C₂²⋊D₄₇	C₂³	1	12	yes	—
43	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
44	C₂²×Dic₄₇	C₂³	1	3	yes	—
45	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
46	#10625354	—	2	32	no	—
47	C₂×D₁₈₈	—	2	12	no	—
48	C₂×D₁₈₈	C₂³	1	12	yes	—
49	C₂×C₄×D₄₇	—	2	12	no	—
50	C₂×C₄×D₄₇	C₂³	1	12	yes	—
51	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
52	(C₂×D₄₇)⋊C₄	C₂³	1	12	yes	—
53	(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
54	C₄⋊Dic₄₇	C₂³	1	12	yes	—
55	Dic₄₇⋊C₄	C₂³	1	12	yes	—
56	C₄×Dic₄₇	C₂³	1	12	yes	—
57	C₂³×C₄₇	—	2	2	no	—
58	C₂³×C₄₇	—	2	2	no	—
59	C₂³×C₄₇	#41	1	4	yes	complemented
60	C₂³×C₄₇	C₂⁴	1	2	yes	—
61	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
62	C₂²×D₄₇	—	2	6	no	—
63	C₂²×D₄₇	—	2	6	no	—
64	C₂²×D₄₇	—	2	6	no	—
65	C₂²×D₄₇	C₂⁴	1	6	yes	—
66	Q₈×C₄₇	—	2	24	no	—
67	Q₈×C₄₇	C₂×D₄	1	16	yes	complemented
68	C₂×C₄×C₄₇	—	2	6	no	—
69	C₂×C₄×C₄₇	—	2	24	no	—
70	C₂×C₄×C₄₇	C₂×D₄	1	12	yes	—
71	C₂×C₄×C₄₇	C₂⁴	1	6	yes	—
72	C₂×C₄×C₄₇	C₂⁴	1	6	yes	—
73	C₂²⋊D₄₇	—	2	24	no	—
74	C₂×Dic₄₇	—	2	2	no	—
75	C₂×Dic₄₇	—	2	6	no	—
76	C₂×Dic₄₇	—	2	2	no	—
77	C₂×Dic₄₇	C₂⁴	1	2	yes	—
78	C₂×Dic₄₇	C₂⁴	1	6	yes	—
79	C₂×Dic₄₇	C₂⁴	1	2	yes	—
80	D₁₈₈	—	2	24	no	—
81	C₄×D₄₇	—	2	24	no	—
82	C₂²×C₄₇	—	2	8	no	—
83	C₂²×C₄₇	—	2	2	no	—
84	C₂²×C₄₇	—	2	2	no	—
85	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
86	C₂²×C₄₇	C₂×#41	1	2	yes	—
87	C₂²×C₄₇	C₂×#41	1	4	yes	complemented
88	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
89	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
90	C₂×D₄₇	—	2	6	no	—
91	C₂×D₄₇	—	2	6	no	—
92	C₂×D₄₇	—	2	6	no	—
93	C₂×D₄₇	—	4	12	no	—
94	C₄×C₄₇	—	2	6	no	—
95	C₄×C₄₇	C₂²×D₄	1	12	yes	—
96	Dic₄₇	—	2	2	no	—
97	Dic₄₇	—	2	6	no	—
98	Dic₄₇	—	2	2	no	—
99	C₂×#548	—	47	1	no	maximal, Sylow
100	C₂×C₄₇	—	2	4	no	—
101	C₂×C₄₇	#548	1	4	yes	complemented
102	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
103	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
104	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
105	D₄₇	—	4	6	no	—
106	C₂²×#41	—	47	1	no	—
107	C₂³×Q₈	D₄₇	1	1	yes	characteristic, complemented
108	#548	—	47	16	no	—
109	C₂×#124	—	47	3	no	—
110	C₂×C₂²⋊Q₈	—	47	3	no	—
111	C₂×#121	—	47	3	no	—
112	C₂×C₄×Q₈	—	47	1	no	—
113	C₂×C₄×D₄	—	47	3	no	—
114	C₄₇	C₂×#548	1	1	yes	characteristic, complemented, Sylow
115	C₂×#41	—	47	8	no	—
116	C₂×#41	—	94	8	no	—
117	C₂²×Q₈	—	2	8	no	—
118	C₂²×Q₈	C₂×D₄₇	1	3	yes	—
119	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
120	C₂²×Q₈	C₂×D₄₇	1	8	yes	complemented
121	C₂²×D₄	—	47	3	no	—
122	C₂²×D₄	—	47	3	no	—
123	C₂³×C₄	—	47	3	no	—
124	C₂³×C₄	C₂×D₄₇	1	3	yes	—
125	#124	—	47	24	no	—
126	C₂²⋊Q₈	—	47	24	no	—
127	#121	—	47	24	no	—
128	C₄×Q₈	—	47	8	no	—
129	C₄×D₄	—	47	24	no	—
130	C₂×C₄⋊C₄	—	47	3	no	—
131	C₂×C₄⋊C₄	—	47	3	no	—
132	C₂×C₂²⋊C₄	—	47	1	no	—
133	C₂×C₂²⋊C₄	—	47	3	no	—
134	C₂×C₂²⋊C₄	—	47	6	no	—
135	C₂×C₄²	—	47	3	no	—
136	C₂⁴	—	47	3	no	—
137	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
138	#41	—	94	32	no	—
139	C₂×Q₈	—	2	32	no	—
140	C₂×Q₈	—	2	12	no	—
141	C₂×Q₈	C₂²⋊D₄₇	1	8	yes	complemented
142	C₂×Q₈	C₂²×D₄₇	1	12	yes	—
143	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
144	C₂×D₄	—	47	12	no	—
145	C₂×D₄	—	47	12	no	—
146	C₂×D₄	—	94	12	no	—
147	C₂×D₄	—	94	12	no	—
148	C₂²×C₄	—	2	12	no	—
149	C₂²×C₄	—	47	1	no	—
150	C₂²×C₄	—	47	3	no	—
151	C₂²×C₄	—	47	1	no	—
152	C₂²×C₄	—	47	12	no	—
153	C₂²×C₄	—	94	12	no	—
154	C₂²×C₄	C₂²×D₄₇	1	12	yes	—
155	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
156	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
157	C₄⋊C₄	—	47	12	no	—
158	C₄⋊C₄	—	47	12	no	—
159	C₂²⋊C₄	—	47	4	no	—
160	C₂²⋊C₄	—	47	12	no	—
161	C₂²⋊C₄	—	47	24	no	—
162	C₄²	—	47	12	no	—
163	C₂³	—	2	2	no	—
164	C₂³	—	2	2	no	—
165	C₂³	—	47	6	no	—
166	C₂³	—	94	6	no	—
167	C₂³	—	94	6	no	—
168	C₂³	—	94	6	no	—
169	C₂³	#10625354	1	4	yes	complemented
170	C₂³	C₂³×D₄₇	1	2	yes	—
171	C₂³	C₂³×D₄₇	1	1	yes	characteristic
172	Q₈	—	2	24	no	—
173	Q₈	C₂×C₂²⋊D₄₇	1	16	yes	complemented
174	D₄	—	94	24	no	—
175	D₄	—	94	24	no	—
176	C₂×C₄	—	2	6	no	—
177	C₂×C₄	—	2	24	no	—
178	C₂×C₄	—	47	2	no	—
179	C₂×C₄	—	47	6	no	—
180	C₂×C₄	—	47	2	no	—
181	C₂×C₄	—	94	2	no	—
182	C₂×C₄	—	94	6	no	—
183	C₂×C₄	—	94	2	no	—
184	C₂×C₄	—	94	24	no	—
185	C₂×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
186	C₂×C₄	C₂³×D₄₇	1	6	yes	—
187	C₂×C₄	C₂³×D₄₇	1	6	yes	—
188	C₂²	—	2	8	no	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	94	6	no	—
192	C₂²	—	94	6	no	—
193	C₂²	—	94	6	no	—
194	C₂²	—	188	12	no	—
195	C₂²	C₂²×C₂²⋊D₄₇	1	2	yes	—
196	C₂²	C₂×#10625354	1	2	yes	—
197	C₂²	C₂×#10625354	1	4	yes	complemented
198	C₂²	#13094072	1	2	yes	—
199	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
200	C₄	—	2	6	no	—
201	C₄	—	94	2	no	—
202	C₄	—	94	6	no	—
203	C₄	—	94	2	no	—
204	C₄	C₂²×C₂²⋊D₄₇	1	12	yes	—
205	C₂	—	2	4	no	—
206	C₂	—	188	6	no	—
207	C₂	#15689784	1	4	yes	direct product factor
208	C₂	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
209	C₂	C₂²×#10625354	1	1	yes	characteristic
210	C₂	C₂×#13094072	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₂³×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂³×Q₈	D₄₇
hypocenter	C₄₇	C₂×#548
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#10625354	C₂	semidirect
2. #15689784	C₂	direct (N × H)
3. C₂×#13094013	C₂	semidirect
4. C₂×#13094000	C₂	semidirect
5. C₂×#13093998	C₂	semidirect
6. C₂×Q₈×Dic₄₇	C₂	semidirect
7. C₂×C₄×C₂²⋊D₄₇	C₂	semidirect
8. C₂³×Q₈×C₄₇	C₂	semidirect
10. C₂×#10625354	C₂²	semidirect
14. #13094013	C₂²	semidirect
15. #13094000	C₂²	semidirect
16. #13093998	C₂²	semidirect
17. Q₈×Dic₄₇	C₂²	semidirect
18. C₄×C₂²⋊D₄₇	C₂²	semidirect
28. C₂²×Q₈×C₄₇	C₂²	semidirect
34. C₂×Q₈×C₄₇	D₄	semidirect
59. C₂³×C₄₇	#41	semidirect
67. Q₈×C₄₇	C₂×D₄	semidirect
87. C₂²×C₄₇	C₂×#41	semidirect
101. C₂×C₄₇	#548	semidirect
107. C₂³×Q₈	D₄₇	semidirect
114. C₄₇	C₂×#548	semidirect
120. C₂²×Q₈	C₂×D₄₇	semidirect
141. C₂×Q₈	C₂²⋊D₄₇	semidirect
169. C₂³	#10625354	semidirect
173. Q₈	C₂×C₂²⋊D₄₇	semidirect
197. C₂²	C₂×#10625354	semidirect
207. C₂	#15689784	direct (N × H)

Subgroups — C2×#15689784 #20256856

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689784 #20256856