Subgroups — C₂×#11757623 #14517686

Order 1944.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6903	C₂	1	1	yes	maximal, characteristic
2	#11757623	C₂	1	2	yes	maximal, direct product factor
3	C₂×#66410	C₃	1	1	yes	maximal, characteristic
4	C₂×Dic₃×C₂₇	—	3	4	no	maximal
5	C₂×#6903	C₄	1	2	yes	complemented
6	C₂×#6903	C₂²	1	1	yes	characteristic
7	C₂²×#737	C₂×C₃	1	1	yes	characteristic
8	#66410	C₂×C₃	1	2	yes	—
9	C₂²×C₂₇⋊C₃	—	2	4	no	—
10	C₂²×C₃×C₂₇	D₃	1	4	yes	—
11	Dic₃×C₂₇	—	3	8	no	—
12	#6903	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂×#1084	C₉	1	1	yes	characteristic
14	C₂×C₉×Dic₃	—	3	4	no	—
15	C₂×C₄×C₂₇	—	9	1	no	—
16	C₂×#737	C₃×C₄	1	2	yes	—
17	C₂×#737	C₂²×C₃	1	1	yes	characteristic
18	C₂×C₂₇⋊C₃	—	2	8	no	—
19	C₂×C₂₇⋊C₃	—	2	4	no	—
20	C₂×C₃×C₂₇	Dic₃	1	8	yes	complemented
21	C₂×C₃×C₂₇	C₂×D₃	1	4	yes	—
22	C₂²×3₋¹⁺²	—	2	4	no	—
23	C₂²×H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic
24	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
25	#1084	C₂×C₉	1	2	yes	—
26	C₉×Dic₃	—	3	8	no	—
27	C₂²×C₂₇	—	2	4	no	—
28	C₂²×C₂₇	C₃⋊D₃	1	1	yes	characteristic
29	C₄×C₂₇	—	9	2	no	—
30	#737	C₂×C₃×C₄	1	1	yes	characteristic
31	C₂₇⋊C₃	—	2	4	no	—
32	C₃×C₂₇	C₂×Dic₃	1	4	yes	complemented
33	C₂×C₃×Dic₃	—	3	4	no	—
34	C₂×C₄×C₉	—	9	1	no	—
35	C₂×3₋¹⁺²	—	2	8	no	—
36	C₂×3₋¹⁺²	—	2	4	no	—
37	C₂×H(3,𝔽₃)	C₄×C₉	1	2	yes	—
38	C₂×H(3,𝔽₃)	C₂²×C₉	1	1	yes	characteristic
39	C₂×C₃×C₉	C₃×Dic₃	1	8	yes	—
40	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
41	C₂×C₂₇	—	2	8	no	—
42	C₂×C₂₇	—	2	4	no	—
43	C₂×C₂₇	C₃⋊Dic₃	1	2	yes	—
44	C₂×C₂₇	C₂×C₃⋊D₃	1	1	yes	characteristic
45	C₂²×C₃²	D₃×C₉	1	4	yes	—
46	C₃×Dic₃	—	3	8	no	—
47	C₂²×C₉	—	2	4	no	—
48	C₂²×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
49	C₄×C₉	—	9	2	no	—
50	3₋¹⁺²	—	2	4	no	—
51	H(3,𝔽₃)	C₂×C₄×C₉	1	1	yes	characteristic
52	C₃×C₉	C₂×C₃×Dic₃	1	4	yes	—
53	C₂₇	—	2	4	no	—
54	C₂₇	C₂×C₃⋊Dic₃	1	1	yes	characteristic
55	C₂×C₃×C₄	—	9	1	no	—
56	C₂×Dic₃	—	3	4	no	—
57	C₂×C₃²	C₉×Dic₃	1	8	yes	—
58	C₂×C₃²	C₂×D₃×C₉	1	4	yes	—
59	C₂×C₉	—	2	8	no	—
60	C₂×C₉	—	2	4	no	—
61	C₂×C₉	C₃×C₃⋊Dic₃	1	2	yes	—
62	C₂×C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
63	C₂²×C₃	—	3	4	no	—
64	C₂²×C₃	C₉×C₃⋊D₃	1	1	yes	characteristic
65	C₃×C₄	—	9	2	no	—
66	Dic₃	—	3	8	no	—
67	C₃²	C₂×C₉×Dic₃	1	4	yes	—
68	C₉	—	2	4	no	—
69	C₉	C₂×C₃×C₃⋊Dic₃	1	1	yes	characteristic
70	C₂×C₄	—	9	1	no	Sylow
71	C₂×C₃	—	3	8	no	—
72	C₂×C₃	—	3	4	no	—
73	C₂×C₃	C₉×C₃⋊Dic₃	1	2	yes	—
74	C₂×C₃	C₂×C₉×C₃⋊D₃	1	1	yes	characteristic
75	C₂²	#92319	1	1	yes	characteristic
76	C₄	—	9	2	no	—
77	C₃	—	3	4	no	—
78	C₃	C₂×C₉×C₃⋊Dic₃	1	1	yes	characteristic
79	C₂	#11757623	1	2	yes	direct product factor
80	C₂	C₂×#92319	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₂₇	C₃⋊D₃
commutator, hypocenter	H(3,𝔽₃)	C₂×C₄×C₉
Frattini	C₂×C₉	C₂×C₃×C₃⋊D₃
Fitting	C₂²×#6903	C₂
socle	C₂²×C₃	C₉×C₃⋊D₃
prime radical	C₂²×H(3,𝔽₃)	C₂×C₉
cosocle	C₂×#737	C₂²×C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂²×C₂₇

Complements

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

N	H ≅ G/N	type
2. #11757623	C₂	direct (N × H)
5. C₂×#6903	C₄	semidirect
12. #6903	C₂×C₄	semidirect
20. C₂×C₃×C₂₇	Dic₃	semidirect
32. C₃×C₂₇	C₂×Dic₃	semidirect
79. C₂	#11757623	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×#6903	2
#11757623	2
C₂×#66410	3
C₂×Dic₃×C₂₇	3

Subgroups — C2×#11757623 #14517686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11757623 #14517686