Subgroups — C₂×C₃⋊(C₃₇⋊#3874) #45686348

Order 33300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₇×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(C₃₇⋊#3874)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₅₅₅	—	3	1	no	maximal
4	C₂×C₃₇⋊#3874	—	3	3	no	maximal
5	C₃×C₃₇×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₅₅₅	—	3	2	no	—
7	C₂×C₃₇×C₅²⋊C₃	D₃	1	3	yes	complemented
8	C₃₇⋊#3874	—	3	6	no	—
9	C₂×C₃×C₅²×C₃₇	D₃	1	1	yes	characteristic, complemented
10	C₂×C₅×D₁₈₅	—	9	1	no	Hall
11	C₃₇×C₅²⋊C₃	C₂×D₃	1	3	yes	complemented
12	C₃×C₅²×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented
13	C₂×D₅₅₅	—	3	1	no	—
14	C₂×C₅×D₁₁₁	—	15	1	no	—
15	C₂×C₅²×C₃₇	C₃⋊D₃	1	1	yes	characteristic, complemented
16	C₅×D₁₈₅	—	9	2	no	—
17	C₂×C₃⋊D₁₁₁	—	25	1	no	maximal, Hall
18	C₂×C₃×C₅×C₃₇	—	3	1	no	—
19	C₂×C₃×C₅×C₃₇	—	3	1	no	—
20	D₅₅₅	—	3	2	no	—
21	C₅×D₁₁₁	—	15	2	no	—
22	C₅²×C₃₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃⋊#3874	—	37	1	no	maximal, Hall
24	C₂×D₁₈₅	—	9	1	no	—
25	C₂×C₅×D₃₇	—	45	1	no	—
26	C₂×C₃²×C₃₇	—	25	1	no	—
27	C₃⋊D₁₁₁	—	25	2	no	—
28	C₃×C₅×C₃₇	—	3	1	no	—
29	C₃×C₅×C₃₇	—	3	1	no	—
30	C₂×C₃×C₅²⋊C₃	D₃₇	1	1	yes	characteristic, complemented
31	C₃⋊#3874	—	37	2	no	—
32	C₂×D₁₁₁	—	15	1	no	—
33	C₂×D₁₁₁	—	75	3	no	—
34	C₂×C₅×C₃₇	—	3	1	no	—
35	C₂×C₅×C₃₇	—	3	1	no	—
36	D₁₈₅	—	9	2	no	—
37	C₅×D₃₇	—	45	2	no	—
38	C₃²×C₃₇	—	25	1	no	Hall
39	C₂×C₅×D₁₅	—	111	1	no	—
40	C₂×#3874	—	111	3	no	—
41	C₃×C₅²⋊C₃	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₃₇	—	25	3	no	—
43	C₂×C₃×C₃₇	#3874	1	1	yes	characteristic, complemented
44	D₁₁₁	—	15	2	no	—
45	D₁₁₁	—	75	6	no	—
46	C₅×C₃₇	—	3	1	no	—
47	C₅×C₃₇	—	3	1	no	—
48	C₂×C₃×C₅²	D₁₁₁	1	1	yes	characteristic, complemented
49	C₅×D₁₅	—	111	2	no	—
50	C₂×C₅²⋊C₃	D₁₁₁	1	3	yes	complemented
51	#3874	—	111	6	no	—
52	C₂×D₃₇	—	45	1	no	Hall
53	C₃×C₃₇	—	25	3	no	—
54	C₃×C₃₇	C₂×#3874	1	1	yes	characteristic, complemented
55	C₂×C₅×D₅	—	333	1	no	Hall
56	C₃×C₅²	C₂×D₁₁₁	1	1	yes	characteristic, complemented
57	C₅²⋊C₃	C₂×D₁₁₁	1	3	yes	complemented
58	C₂×C₃₇	C₃⋊#3874	1	1	yes	characteristic, complemented
59	D₃₇	—	45	2	no	—
60	C₂×D₁₅	—	111	1	no	—
61	C₂×C₅×D₃	—	555	1	no	—
62	C₂×C₅²	C₃⋊D₁₁₁	1	1	yes	characteristic, complemented
63	C₅×D₅	—	333	2	no	—
64	C₃₇	C₂×C₃⋊#3874	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃⋊D₃	—	925	1	no	Hall
66	C₂×C₃×C₅	—	3	1	no	—
67	C₂×C₃×C₅	—	3	1	no	—
68	D₁₅	—	111	2	no	—
69	C₅×D₃	—	555	2	no	—
70	C₅²	C₂×C₃⋊D₁₁₁	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₅	—	1665	1	no	—
72	C₂×D₅	—	333	1	no	—
73	C₂×C₃²	—	25	1	no	—
74	C₃⋊D₃	—	925	2	no	—
75	C₃×C₅	—	3	1	no	—
76	C₃×C₅	—	3	1	no	—
77	C₂×D₃	—	555	1	no	—
78	C₂×D₃	—	2775	3	no	—
79	C₂×C₅	—	3	1	no	—
80	C₂×C₅	—	3	1	no	—
81	C₂×C₅	—	1665	2	no	—
82	D₅	—	333	2	no	—
83	C₃²	—	25	1	no	Sylow
84	C₂×C₃	—	25	3	no	—
85	C₂×C₃	C₃₇⋊#3874	1	1	yes	characteristic, complemented
86	D₃	—	555	2	no	—
87	D₃	—	2775	6	no	—
88	C₅	—	3	1	no	—
89	C₅	—	3	1	no	—
90	C₂²	—	1665	1	no	Sylow
91	C₃	—	25	3	no	—
92	C₃	C₂×C₃₇⋊#3874	1	1	yes	characteristic, complemented
93	C₂	—	1665	2	no	—
94	C₂	C₃⋊(C₃₇⋊#3874)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₃₇⋊#3874)
commutator, cosocle, hypocenter	C₃×C₃₇×C₅²⋊C₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₃₇	D₃
LCS	G ▷ C₃×C₃₇×C₅²⋊C₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₃₇×C₅²⋊C₃	C₂	semidirect
2. C₃⋊(C₃₇⋊#3874)	C₂	direct (N × H)
5. C₃×C₃₇×C₅²⋊C₃	C₂²	semidirect
7. C₂×C₃₇×C₅²⋊C₃	D₃	semidirect
9. C₂×C₃×C₅²×C₃₇	D₃	semidirect
11. C₃₇×C₅²⋊C₃	C₂×D₃	semidirect
12. C₃×C₅²×C₃₇	C₂×D₃	semidirect
15. C₂×C₅²×C₃₇	C₃⋊D₃	semidirect
22. C₅²×C₃₇	C₂×C₃⋊D₃	semidirect
30. C₂×C₃×C₅²⋊C₃	D₃₇	semidirect
41. C₃×C₅²⋊C₃	C₂×D₃₇	semidirect
43. C₂×C₃×C₃₇	#3874	semidirect
48. C₂×C₃×C₅²	D₁₁₁	semidirect
50. C₂×C₅²⋊C₃	D₁₁₁	semidirect
54. C₃×C₃₇	C₂×#3874	semidirect
56. C₃×C₅²	C₂×D₁₁₁	semidirect
57. C₅²⋊C₃	C₂×D₁₁₁	semidirect
58. C₂×C₃₇	C₃⋊#3874	semidirect
62. C₂×C₅²	C₃⋊D₁₁₁	semidirect
64. C₃₇	C₂×C₃⋊#3874	semidirect
70. C₅²	C₂×C₃⋊D₁₁₁	semidirect
85. C₂×C₃	C₃₇⋊#3874	semidirect
92. C₃	C₂×C₃₇⋊#3874	semidirect
94. C₂	C₃⋊(C₃₇⋊#3874)	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×C₃×C₃₇×C₅²⋊C₃	2
C₃⋊(C₃₇⋊#3874)	2
C₂×C₅×D₅₅₅	3
C₂×C₃₇⋊#3874	3
C₂×C₃⋊D₁₁₁	25
C₂×C₃⋊#3874	37

Subgroups — C2×C3⋊(C37⋊#3874) #45686348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₃₇⋊#3874) #45686348