Subgroups — C₂×#13094046 #15689905

Order 3008.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625350	C₂	1	2	yes	maximal, complemented
2	#13094046	C₂	1	8	yes	maximal, direct product factor
3	C₂×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625325	C₂	1	2	yes	maximal, complemented
5	C₂×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₄₇	—	2	2	no	—
9	#10625350	—	2	4	no	—
10	#10625350	C₂²	1	8	yes	complemented
11	C₂×D₁₈₈	C₂²	1	2	yes	—
12	C₂×C₄×D₄₇	—	2	2	no	—
13	C₂×Dic₉₄	C₂²	1	2	yes	—
14	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₄₇	C₂²	1	4	yes	complemented
17	Dic₁₈₈	C₂²	1	4	yes	complemented
18	D₃₇₆	C₂²	1	4	yes	complemented
19	#10625325	C₂²	1	8	yes	complemented
20	C₂³×C₄₇	D₄	1	1	yes	characteristic
21	C₂²×D₄₇	—	2	2	no	—
22	C₂×C₄×C₄₇	D₄	1	2	yes	—
23	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₂³	1	2	yes	—
26	C₂²⋊D₄₇	—	2	8	no	—
27	C₂×Dic₄₇	—	2	2	no	—
28	D₁₈₈	—	2	2	no	—
29	D₁₈₈	C₂³	1	4	yes	—
30	C₄×D₄₇	—	2	8	no	—
31	Dic₉₄	—	2	2	no	—
32	Dic₉₄	C₂³	1	4	yes	—
33	C₈×C₄₇	C₂³	1	2	yes	—
34	C₈×C₄₇	C₂³	1	2	yes	—
35	C₂²×C₄₇	—	2	2	no	—
36	C₂²×C₄₇	C₂×D₄	1	2	yes	—
37	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×D₄₇	—	2	4	no	—
39	C₂×D₄₇	—	4	4	no	—
40	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
41	C₄×C₄₇	C₂×D₄	1	2	yes	—
42	C₄×C₄₇	C₂⁴	1	1	yes	characteristic
43	Dic₄₇	—	2	4	no	—
44	C₂×C₄₇	—	2	2	no	—
45	C₂×C₄₇	#135	1	2	yes	complemented
46	C₂×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	—	47	1	no	—
53	C₂×SD₁₆	—	47	2	no	—
54	C₂×D₈	—	47	1	no	—
55	C₂²×C₈	D₄₇	1	1	yes	characteristic, complemented
56	#41	—	47	8	no	—
57	#41	—	94	4	no	—
58	C₂×Q₈	—	47	2	no	—
59	C₂×D₄	—	47	2	no	—
60	C₂×D₄	—	94	2	no	—
61	C₂²×C₄	—	94	2	no	—
62	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
63	Q₁₆	—	47	4	no	—
64	SD₁₆	—	47	8	no	—
65	D₈	—	47	4	no	—
66	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
67	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
68	C₂×C₈	C₂×D₄₇	1	4	yes	complemented
69	C₂³	—	94	2	no	—
70	C₂³	D₁₈₈	1	1	yes	characteristic
71	Q₈	—	47	4	no	—
72	Q₈	—	94	2	no	—
73	D₄	—	47	4	no	—
74	D₄	—	94	8	no	—
75	D₄	—	94	2	no	—
76	C₂×C₄	—	94	2	no	—
77	C₂×C₄	—	94	8	no	—
78	C₂×C₄	D₁₈₈	1	2	yes	—
79	C₂×C₄	D₁₈₈	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
81	C₂×C₄	C₂²×D₄₇	1	2	yes	—
82	C₈	C₂²×D₄₇	1	2	yes	—
83	C₈	C₂²×D₄₇	1	2	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	—	94	4	no	—
86	C₂²	—	188	4	no	—
87	C₂²	C₂×D₁₈₈	1	2	yes	—
88	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
89	C₄	—	94	4	no	—
90	C₄	C₂×D₁₈₈	1	2	yes	—
91	C₄	C₂×D₁₈₈	1	1	yes	characteristic
92	C₄	C₂³×D₄₇	1	1	yes	characteristic
93	C₂	—	2	2	no	—
94	C₂	—	188	4	no	—
95	C₂	#13094046	1	2	yes	direct product factor
96	C₂	C₂²×D₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₈₈
commutator, cosocle	C₄×C₄₇	C₂⁴
Frattini	C₄	C₂³×D₄₇
Fitting	C₂²×C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
hypercenter	C₂²×C₈	D₄₇
hypocenter	C₄₇	C₂×#135
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10625350	C₂	semidirect
2. #13094046	C₂	direct (N × H)
3. C₂×Dic₁₈₈	C₂	semidirect
4. C₂×#10625325	C₂	semidirect
5. C₂×D₃₇₆	C₂	semidirect
6. C₂²×C₈×C₄₇	C₂	semidirect
10. #10625350	C₂²	semidirect
16. C₂×C₈×C₄₇	C₂²	semidirect
17. Dic₁₈₈	C₂²	semidirect
18. D₃₇₆	C₂²	semidirect
19. #10625325	C₂²	semidirect
45. C₂×C₄₇	#135	semidirect
49. C₄₇	C₂×#135	semidirect
55. C₂²×C₈	D₄₇	semidirect
68. C₂×C₈	C₂×D₄₇	semidirect
95. C₂	#13094046	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×#10625350	2
#13094046	2
C₂×Dic₁₈₈	2
C₂×#10625325	2
C₂×D₃₇₆	2
C₂²×C₈×C₄₇	2
C₂×#135	47

Subgroups — C2×#13094046 #15689905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13094046 #15689905