Subgroups — C₂²×#334 #17783

Order 256.

471 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#334	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₈	—	2	2	no	—
5	C₂³×C₈	C₄	1	1	yes	characteristic
6	C₂³×C₈	C₄	1	1	yes	characteristic
7	C₂²×C₄²	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₈	—	2	6	no	—
9	C₂×C₄⋊C₈	C₂²	1	12	yes	—
10	C₂×C₄×C₈	C₄	1	6	yes	—
11	C₂×C₄×C₈	C₂²	1	6	yes	—
12	#334	C₂²	1	16	yes	direct product factor
13	C₂³×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄	D₄	1	1	yes	characteristic
15	C₂³×C₄	Q₈	1	1	yes	characteristic
16	C₂²×C₈	—	2	4	no	—
17	C₂²×C₈	—	2	12	no	—
18	C₂²×C₈	—	4	8	no	—
19	C₂²×C₈	C₈	1	8	yes	complemented
20	C₂²×C₈	C₂×C₄	1	6	yes	—
21	C₂²×C₈	C₂×C₄	1	6	yes	—
22	C₂×C₄²	C₂×C₄	1	3	yes	—
23	C₂×C₄²	D₄	1	3	yes	—
24	C₂×C₄²	Q₈	1	3	yes	—
25	C₂×C₄²	C₂³	1	3	yes	—
26	C₄⋊C₈	—	2	12	no	—
27	C₄⋊C₈	C₂³	1	8	yes	—
28	C₄×C₈	C₂×C₄	1	12	yes	—
29	C₄×C₈	C₂³	1	4	yes	—
30	C₂⁴	C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₄	—	2	4	no	—
32	C₂²×C₄	C₄⋊C₄	1	3	yes	—
33	C₂²×C₄	C₄⋊C₄	1	3	yes	—
34	C₂²×C₄	C₄⋊C₄	1	3	yes	—
35	C₂²×C₄	C₂×C₈	1	4	yes	—
36	C₂²×C₄	M₁₆	1	4	yes	—
37	C₂²×C₄	SD₁₆	1	8	yes	—
38	C₂²×C₄	C₂²×C₄	1	3	yes	—
39	C₂²×C₄	C₂×D₄	1	3	yes	—
40	C₂²×C₄	C₂×Q₈	1	3	yes	—
41	C₂×C₈	—	2	12	no	—
42	C₂×C₈	—	2	8	no	—
43	C₂×C₈	—	4	24	no	—
44	C₂×C₈	C₂×C₈	1	24	yes	complemented
45	C₂×C₈	C₂²×C₄	1	4	yes	—
46	C₂×C₈	C₂²×C₄	1	4	yes	—
47	C₄²	C₄⋊C₄	1	6	yes	—
48	C₄²	C₂²×C₄	1	3	yes	—
49	C₄²	C₂×D₄	1	3	yes	—
50	C₄²	C₂×Q₈	1	3	yes	—
51	C₄²	C₂⁴	1	1	yes	characteristic
52	C₂³	C₄⋊C₈	1	4	yes	—
53	C₂³	#106	1	4	yes	—
54	C₂³	#108	1	4	yes	—
55	C₂³	C₂×C₄⋊C₄	1	3	yes	—
56	C₂×C₄	—	2	6	no	—
57	C₂×C₄	—	2	6	no	—
58	C₂×C₄	C₄⋊C₈	1	12	yes	—
59	C₂×C₄	#106	1	12	yes	—
60	C₂×C₄	C₂×C₄⋊C₄	1	3	yes	—
61	C₂×C₄	C₂×C₄⋊C₄	1	3	yes	—
62	C₂×C₄	C₂×C₄⋊C₄	1	3	yes	—
63	C₂×C₄	C₂²×C₈	1	6	yes	—
64	C₂×C₄	C₂×M₁₆	1	6	yes	—
65	C₂×C₄	C₂×SD₁₆	1	12	yes	—
66	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
67	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
68	C₂×C₄	C₂²×Q₈	1	1	yes	characteristic
69	C₈	—	2	4	no	—
70	C₈	—	4	8	no	—
71	C₈	C₂²×C₈	1	8	yes	complemented
72	C₂²	#334	1	16	yes	direct product factor
73	C₂²	C₂×C₄⋊C₈	1	6	yes	—
74	C₂²	C₂×#106	1	6	yes	—
75	C₂²	C₂×#108	1	6	yes	—
76	C₂²	C₂²×C₄⋊C₄	1	1	yes	characteristic
77	C₄	—	2	3	no	—
78	C₄	—	2	1	no	—
79	C₄	C₂×C₄⋊C₈	1	6	yes	—
80	C₄	C₂×#106	1	6	yes	—
81	C₄	C₂³×C₈	1	1	yes	characteristic
82	C₄	C₂²×M₁₆	1	1	yes	characteristic
83	C₄	C₂²×SD₁₆	1	2	yes	—
84	C₂	C₂×#334	1	12	yes	direct product factor
85	C₂	C₂²×C₄⋊C₈	1	1	yes	characteristic
86	C₂	C₂²×#106	1	1	yes	characteristic
87	C₂	C₂²×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	D₄
commutator	C₄	C₂³×C₈
Frattini, cosocle	C₄²	C₂⁴
socle, prime radical	C₂⁴	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₂×#334	C₂	direct (N × H)
12. #334	C₂²	direct (N × H)
19. C₂²×C₈	C₈	semidirect
44. C₂×C₈	C₂×C₈	semidirect
71. C₈	C₂²×C₈	semidirect
72. C₂²	#334	direct (N × H)
84. C₂	C₂×#334	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×C₄⋊C₈	2
C₂²×C₄×C₈	2
C₂×#334	2

Subgroups — C22×#334 #17783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#334 #17783