Subgroups — C₂×#4937 #82059

Order 384.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#95	C₂	1	6	yes	maximal
3	#4937	C₂	1	8	yes	maximal, direct product factor
4	C₂×#383	—	3	1	no	maximal, Sylow
5	C₂³×C₃×C₄	C₂²	1	3	yes	—
6	C₂³×Dic₃	C₂²	1	4	yes	—
7	C₂×C₃×C₄²	C₄	1	8	yes	complemented
8	C₂×C₃×C₄²	C₂²	1	4	yes	—
9	C₃⋊#95	C₂²	1	24	yes	—
10	C₂²×C₄²	D₃	1	1	yes	characteristic
11	#383	—	3	8	no	—
12	C₂×#95	—	3	6	no	—
13	C₂⁴×C₃	C₂³	1	1	yes	characteristic
14	C₂²×C₃×C₄	—	2	12	no	—
15	C₂²×C₃×C₄	C₂×C₄	1	12	yes	—
16	C₂²×C₃×C₄	C₂³	1	6	yes	—
17	C₂²×Dic₃	—	2	24	no	—
18	C₂²×Dic₃	C₂³	1	8	yes	—
19	C₃×C₄²	C₂×C₄	1	16	yes	complemented
20	C₂³×C₄	—	3	4	no	—
21	C₂³×C₄	C₂×D₃	1	3	yes	—
22	C₂×C₄²	Dic₃	1	8	yes	complemented
23	C₂×C₄²	C₂×D₃	1	4	yes	—
24	#95	—	3	24	no	—
25	C₂³×C₃	C₂²×C₄	1	2	yes	—
26	C₂³×C₃	#41	1	12	yes	—
27	C₂³×C₃	C₂⁴	1	1	yes	characteristic
28	C₂×C₃×C₄	—	2	24	no	—
29	C₂×C₃×C₄	—	2	12	no	—
30	C₂×C₃×C₄	C₂²×C₄	1	12	yes	—
31	C₂×Dic₃	—	2	24	no	—
32	C₂×Dic₃	—	4	16	no	—
33	C₂⁴	C₂²×D₃	1	1	yes	characteristic
34	C₂²×C₄	—	2	12	no	—
35	C₂²×C₄	—	3	8	no	—
36	C₂²×C₄	—	6	24	no	—
37	C₂²×C₄	C₂×Dic₃	1	12	yes	—
38	C₂²×C₄	C₂²×D₃	1	6	yes	—
39	C₄²	C₂×Dic₃	1	16	yes	complemented
40	C₂²×C₃	#117	1	12	yes	—
41	C₂²×C₃	#126	1	16	yes	—
42	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
43	C₂²×C₃	C₂×#41	1	6	yes	—
44	C₃×C₄	—	2	12	no	—
45	Dic₃	—	4	8	no	—
46	C₂³	#235	1	12	yes	—
47	C₂³	C₂²×Dic₃	1	2	yes	—
48	C₂³	C₂³×D₃	1	1	yes	characteristic
49	C₂×C₄	—	2	24	no	—
50	C₂×C₄	—	2	12	no	—
51	C₂×C₄	—	6	24	no	—
52	C₂×C₄	—	12	16	no	—
53	C₂×C₄	C₂²×Dic₃	1	12	yes	—
54	C₂×C₃	#383	1	8	yes	complemented
55	C₂×C₃	C₂×#117	1	3	yes	—
56	C₂×C₃	C₂×#126	1	4	yes	—
57	C₂²	#876	1	16	yes	—
58	C₂²	#926	1	12	yes	—
59	C₂²	C₂×#235	1	6	yes	—
60	C₂²	C₂³×Dic₃	1	1	yes	characteristic
61	C₄	—	2	12	no	—
62	C₄	—	12	8	no	—
63	C₃	C₂×#383	1	1	yes	characteristic, complemented, Sylow
64	C₂	#4937	1	8	yes	direct product factor
65	C₂	C₂×#876	1	4	yes	—
66	C₂	C₂×#926	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄
Frattini	C₂³	C₂³×D₃
Fitting	C₂²×C₃×C₄²	C₂
socle, prime radical	C₂⁴×C₃	C₂³
cosocle	C₂³×C₃	C₂⁴
hypercenter	C₂²×C₄²	D₃
hypocenter	C₃	C₂×#383
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
3. #4937	C₂	direct (N × H)
7. C₂×C₃×C₄²	C₄	semidirect
19. C₃×C₄²	C₂×C₄	semidirect
22. C₂×C₄²	Dic₃	semidirect
39. C₄²	C₂×Dic₃	semidirect
54. C₂×C₃	#383	semidirect
63. C₃	C₂×#383	semidirect
64. C₂	#4937	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×C₃×C₄²	2
C₂×C₃⋊#95	2
#4937	2
C₂×#383	3

Subgroups — C2×#4937 #82059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4937 #82059