Subgroups — C₂×#338⋊C₃ #68022

Order 384.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#338⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×#338	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂×C₄×A₄	—	4	1	no	maximal
4	C₂²×M₁₆	—	3	1	no	—
5	#338	—	3	1	no	—
6	#338	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×A₄	—	4	1	no	—
8	C₄×A₄	—	4	1	no	—
9	C₄×A₄	—	4	1	no	—
10	C₂³×C₄	A₄	1	1	yes	characteristic
11	C₂×M₁₆	—	3	2	no	—
12	C₂×M₁₆	—	3	1	no	—
13	C₂×M₁₆	—	3	1	no	—
14	C₂×M₁₆	—	6	2	no	—
15	C₂×M₁₆	—	6	2	no	—
16	C₂²×C₈	—	3	2	no	—
17	C₂×A₄	—	4	2	no	—
18	C₂×A₄	—	4	1	no	—
19	C₂×C₃×C₄	—	16	1	no	—
20	C₂⁴	SL(2,𝔽₃)	1	1	yes	characteristic
21	C₂²×C₄	—	3	1	no	—
22	C₂²×C₄	—	3	1	no	—
23	C₂²×C₄	—	3	1	no	—
24	C₂²×C₄	—	3	1	no	—
25	C₂²×C₄	SL(2,𝔽₃)	1	1	yes	characteristic
26	C₂²×C₄	C₂×A₄	1	1	yes	characteristic
27	M₁₆	—	6	4	no	—
28	M₁₆	—	6	2	no	—
29	M₁₆	—	6	2	no	—
30	C₂×C₈	—	3	2	no	—
31	C₂×C₈	—	3	2	no	—
32	C₂×C₈	—	6	2	no	—
33	C₂×C₈	—	6	2	no	—
34	C₂²×C₃	—	16	1	no	—
35	A₄	—	4	1	no	—
36	C₃×C₄	—	16	1	no	—
37	C₃×C₄	—	16	1	no	—
38	C₂³	—	3	1	no	—
39	C₂³	—	3	1	no	—
40	C₂³	—	4	2	no	—
41	C₂³	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
42	C₂×C₄	—	3	2	no	—
43	C₂×C₄	—	3	1	no	—
44	C₂×C₄	—	3	1	no	—
45	C₂×C₄	—	3	1	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₄	—	3	1	no	—
48	C₂×C₄	—	3	1	no	—
49	C₂×C₄	—	3	1	no	—
50	C₂×C₄	C₄²⋊C₃	1	1	yes	characteristic
51	C₈	—	6	2	no	—
52	C₈	—	6	2	no	—
53	C₂×C₃	—	16	1	no	—
54	C₂×C₃	—	16	2	no	—
55	C₂²	—	3	1	no	—
56	C₂²	—	3	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	—	6	2	no	—
59	C₂²	—	12	1	no	—
60	C₂²	#95⋊C₃	1	1	yes	characteristic
61	C₄	—	3	1	no	—
62	C₄	—	3	1	no	—
63	C₄	#95⋊C₃	1	1	yes	characteristic
64	C₄	C₂×C₄²⋊C₃	1	1	yes	characteristic
65	C₃	—	16	1	no	Sylow
66	C₂	—	6	1	no	—
67	C₂	—	6	1	no	—
68	C₂	#338⋊C₃	1	2	yes	direct product factor
69	C₂	C₂×#95⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	C₄²⋊C₃
commutator, cosocle, hypocenter	#338	C₂×C₃
Frattini	C₂²×C₄	C₂×A₄
Fitting	C₂×#338	C₃
socle	C₂²	#95⋊C₃
LCS	G ▷ #338
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #338⋊C₃	C₂	direct (N × H)
2. C₂×#338	C₃	semidirect
6. #338	C₂×C₃	semidirect
68. C₂	#338⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
#338⋊C₃	2
C₂×#338	3
C₂×C₄×A₄	4

Subgroups — C2×#338⋊C3 #68022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#338⋊C₃ #68022