Subgroups — C₂×C₁₆×Dic₃₇ #17996182

Order 4736.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10596925	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	C₁₆×Dic₃₇	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64436	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₃₇	C₄	1	1	yes	characteristic
7	C₂×#10596925	C₄	1	4	yes	complemented
8	C₂×#10596925	C₂²	1	2	yes	—
9	C₈×Dic₃₇	C₄	1	2	yes	—
10	C₈×Dic₃₇	C₂²	1	2	yes	—
11	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₃₇	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₃₇	C₈	1	2	yes	—
16	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
20	C₄×Dic₃₇	C₈	1	2	yes	—
21	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
22	C₂×#64436	C₈	1	4	yes	—
23	C₂×#64436	C₂×C₄	1	2	yes	—
24	C₁₆×C₃₇	C₂×C₄	1	4	yes	complemented
25	#10596925	C₂×C₄	1	4	yes	complemented
26	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₄²	1	2	yes	—
28	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₃₇	C₁₆	1	8	yes	direct product factor
32	C₂×Dic₃₇	C₂×C₈	1	4	yes	—
33	C₈×C₃₇	C₄²	1	2	yes	—
34	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
36	#64436	C₂×C₈	1	4	yes	—
37	C₂²×C₃₇	C₄×C₈	1	2	yes	—
38	C₂²×C₃₇	C₂×C₁₆	1	4	yes	—
39	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₃₇	C₄×C₈	1	2	yes	—
41	C₄×C₃₇	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
43	Dic₃₇	C₂×C₁₆	1	8	yes	direct product factor
44	C₂×C₄×C₁₆	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	C₄×C₁₆	1	4	yes	complemented
46	C₂×C₃₇	C₂×C₄×C₈	1	1	yes	characteristic
47	C₂×C₃₇	C₂²×C₁₆	1	2	yes	—
48	C₂²×C₁₆	—	37	1	no	—
49	C₂²×C₁₆	D₃₇	1	1	yes	characteristic
50	C₂×C₄×C₈	—	37	1	no	—
51	C₄×C₁₆	—	37	4	no	—
52	C₃₇	C₂×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₈	—	37	1	no	—
54	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
55	C₂×C₄²	—	37	1	no	—
56	C₂×C₁₆	—	37	4	no	—
57	C₂×C₁₆	—	37	2	no	—
58	C₂×C₁₆	Dic₃₇	1	4	yes	direct product factor
59	C₂×C₁₆	C₂×D₃₇	1	2	yes	—
60	C₄×C₈	—	37	2	no	—
61	C₄×C₈	—	37	2	no	—
62	C₂²×C₄	—	37	2	no	—
63	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
64	C₂×C₈	—	37	4	no	—
65	C₂×C₈	—	37	2	no	—
66	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
67	C₂×C₈	C₄×D₃₇	1	2	yes	—
68	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
69	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
70	C₄²	—	37	2	no	—
71	C₄²	—	37	2	no	—
72	C₁₆	—	37	4	no	—
73	C₁₆	C₂×Dic₃₇	1	4	yes	direct product factor
74	C₂³	C₈×D₃₇	1	1	yes	characteristic
75	C₂×C₄	—	37	4	no	—
76	C₂×C₄	—	37	8	no	—
77	C₂×C₄	C₈×D₃₇	1	2	yes	—
78	C₂×C₄	C₈×D₃₇	1	1	yes	characteristic
79	C₂×C₄	C₄×Dic₃₇	1	2	yes	—
80	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
81	C₈	—	37	4	no	—
82	C₈	C₄×Dic₃₇	1	2	yes	—
83	C₈	C₂×C₄×D₃₇	1	1	yes	characteristic
84	C₈	C₂²×Dic₃₇	1	1	yes	characteristic
85	C₂²	C₈×Dic₃₇	1	2	yes	—
86	C₂²	C₁₆×D₃₇	1	4	yes	—
87	C₂²	C₂×C₈×D₃₇	1	1	yes	characteristic
88	C₄	—	37	8	no	—
89	C₄	C₈×Dic₃₇	1	2	yes	—
90	C₄	C₂×C₄×Dic₃₇	1	1	yes	characteristic
91	C₄	C₂×C₈×D₃₇	1	1	yes	characteristic
92	C₂	C₁₆×Dic₃₇	1	4	yes	direct product factor
93	C₂	C₂×C₈×Dic₃₇	1	1	yes	characteristic
94	C₂	C₂×C₁₆×D₃₇	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂²×C₁₆	D₃₇
commutator, hypocenter	C₃₇	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₂²×C₁₆×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₂×C₈
cosocle	C₂×C₈×C₃₇	C₂³
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₁₆×Dic₃₇	C₂	direct (N × H)
7. C₂×#10596925	C₄	semidirect
12. C₂×C₁₆×C₃₇	C₄	semidirect
24. C₁₆×C₃₇	C₂×C₄	semidirect
25. #10596925	C₂×C₄	semidirect
31. C₂×Dic₃₇	C₁₆	direct (N × H)
43. Dic₃₇	C₂×C₁₆	direct (N × H)
45. C₂×C₃₇	C₄×C₁₆	semidirect
52. C₃₇	C₂×C₄×C₁₆	semidirect
58. C₂×C₁₆	Dic₃₇	direct (N × H)
73. C₁₆	C₂×Dic₃₇	direct (N × H)
92. C₂	C₁₆×Dic₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#10596925	2
C₂×C₈×Dic₃₇	2
C₁₆×Dic₃₇	2
C₂²×C₁₆×C₃₇	2
C₂×C₄×C₁₆	37

Subgroups — C2×C16×Dic37 #17996182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₆×Dic₃₇ #17996182