Subgroups — C₂×#13094047 #15689906

Order 3008.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625354	C₂	1	2	yes	maximal, complemented
2	#13094047	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10625336	C₂	1	2	yes	maximal, complemented
4	C₂×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Q₈×C₄₇	C₂²	1	2	yes	—
8	#10625354	—	2	4	no	—
9	#10625354	C₂²	1	8	yes	complemented
10	C₂×D₁₈₈	—	2	2	no	—
11	C₂×D₁₈₈	C₂²	1	2	yes	—
12	C₂×C₄×D₄₇	—	2	2	no	—
13	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
14	Q₁₆×C₄₇	C₂²	1	4	yes	complemented
15	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	#10625336	C₂²	1	8	yes	complemented
17	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	D₃₇₆	C₂²	1	4	yes	complemented
19	C₈×D₄₇	C₂²	1	4	yes	complemented
20	C₂²×D₄₇	—	2	2	no	—
21	C₂²×D₄₇	D₄	1	1	yes	characteristic
22	Q₈×C₄₇	—	2	2	no	—
23	Q₈×C₄₇	C₂³	1	4	yes	—
24	C₂×C₄×C₄₇	—	2	2	no	—
25	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
26	C₂×Dic₄₇	D₄	1	1	yes	characteristic
27	D₁₈₈	—	2	8	no	—
28	D₁₈₈	—	2	2	no	—
29	D₁₈₈	C₂³	1	4	yes	—
30	C₄×D₄₇	—	2	8	no	—
31	C₄×D₄₇	D₄	1	2	yes	—
32	C₄×D₄₇	C₂³	1	2	yes	—
33	C₈×C₄₇	C₂³	1	2	yes	—
34	C₄₇⋊C₈	C₂³	1	2	yes	—
35	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
36	C₂×D₄₇	—	2	2	no	—
37	C₂×D₄₇	—	2	4	no	—
38	C₂×D₄₇	—	4	4	no	—
39	C₂×D₄₇	C₂×D₄	1	2	yes	—
40	C₄×C₄₇	—	2	4	no	—
41	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₄×C₄₇	C₂⁴	1	1	yes	characteristic
43	Dic₄₇	C₂×D₄	1	2	yes	—
44	C₂×C₄₇	#135	1	2	yes	complemented
45	C₂×C₄₇	C₂²×D₄	1	1	yes	characteristic
46	D₄₇	—	2	2	no	—
47	D₄₇	—	4	4	no	—
48	C₂×#135	—	47	1	no	maximal, Sylow
49	C₄₇	C₂×#135	1	1	yes	characteristic, complemented, Sylow
50	C₂×#41	—	47	2	no	—
51	#135	—	47	8	no	—
52	C₂×Q₁₆	D₄₇	1	1	yes	characteristic, complemented
53	C₂×SD₁₆	—	47	2	no	—
54	C₂×D₈	—	47	1	no	—
55	C₂²×C₈	—	47	1	no	—
56	#41	—	47	8	no	—
57	#41	—	94	4	no	—
58	C₂×Q₈	C₂×D₄₇	1	2	yes	—
59	C₂×D₄	—	47	2	no	—
60	C₂×D₄	—	94	2	no	—
61	C₂²×C₄	—	47	1	no	—
62	C₂²×C₄	—	94	2	no	—
63	Q₁₆	C₂×D₄₇	1	4	yes	complemented
64	SD₁₆	—	47	8	no	—
65	D₈	—	47	4	no	—
66	C₂×C₈	—	47	1	no	—
67	C₂×C₈	—	47	4	no	—
68	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
69	C₂³	—	47	1	no	—
70	C₂³	—	94	2	no	—
71	Q₈	—	2	2	no	—
72	Q₈	C₂²×D₄₇	1	4	yes	—
73	D₄	—	47	4	no	—
74	D₄	—	94	8	no	—
75	D₄	—	94	2	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	47	1	no	—
78	C₂×C₄	—	47	2	no	—
79	C₂×C₄	—	47	2	no	—
80	C₂×C₄	—	94	8	no	—
81	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
82	C₈	—	47	2	no	—
83	C₈	C₂²×D₄₇	1	2	yes	—
84	C₂²	—	47	2	no	—
85	C₂²	—	94	2	no	—
86	C₂²	—	94	4	no	—
87	C₂²	—	188	4	no	—
88	C₂²	D₄×D₄₇	1	1	yes	characteristic
89	C₄	—	2	4	no	—
90	C₄	—	47	2	no	—
91	C₄	D₄×D₄₇	1	1	yes	characteristic
92	C₄	C₂³×D₄₇	1	1	yes	characteristic
93	C₂	—	94	2	no	—
94	C₂	—	188	4	no	—
95	C₂	#13094047	1	2	yes	direct product factor
96	C₂	C₂×D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₄×C₄₇	C₂⁴
Frattini	C₄	C₂³×D₄₇
Fitting	C₂×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
hypercenter	C₂×Q₁₆	D₄₇
hypocenter	C₄₇	C₂×#135
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#10625354	C₂	semidirect
2. #13094047	C₂	direct (N × H)
3. C₂×#10625336	C₂	semidirect
4. C₂×D₃₇₆	C₂	semidirect
5. C₂×C₈×D₄₇	C₂	semidirect
6. C₂×Q₁₆×C₄₇	C₂	semidirect
9. #10625354	C₂²	semidirect
14. Q₁₆×C₄₇	C₂²	semidirect
16. #10625336	C₂²	semidirect
18. D₃₇₆	C₂²	semidirect
19. C₈×D₄₇	C₂²	semidirect
44. C₂×C₄₇	#135	semidirect
49. C₄₇	C₂×#135	semidirect
52. C₂×Q₁₆	D₄₇	semidirect
63. Q₁₆	C₂×D₄₇	semidirect
95. C₂	#13094047	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10625354	2
#13094047	2
C₂×#10625336	2
C₂×D₃₇₆	2
C₂×C₈×D₄₇	2
C₂×Q₁₆×C₄₇	2
C₂×#135	47

Subgroups — C2×#13094047 #15689906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13094047 #15689906