Subgroups — #12910

Order 256.

153 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#368	C₂	1	4	yes	maximal
2	C₂×#346	C₂	1	1	yes	maximal, characteristic
3	#1848	C₂	1	2	yes	maximal
4	C₂²×C₁₆	C₂²	1	2	yes	—
5	C₂×#108	—	2	2	no	—
6	C₂×#108	C₂²	1	4	yes	—
7	#423	—	2	2	no	—
8	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
9	#368	—	2	8	no	—
10	#346	C₄	1	4	yes	—
11	C₂×M₁₆	—	2	4	no	—
12	C₂²×C₈	D₄	1	1	yes	characteristic
13	C₂²×C₈	C₂³	1	1	yes	characteristic
14	C₂×C₄²	D₄	1	1	yes	characteristic
15	C₂×C₁₆	C₂×C₄	1	4	yes	—
16	C₂×C₁₆	D₄	1	4	yes	—
17	C₂×C₁₆	Q₈	1	4	yes	—
18	#108	—	2	8	no	—
19	#108	—	4	4	no	—
20	C₄⋊C₈	—	4	4	no	—
21	C₄×C₈	C₂×C₄	1	2	yes	—
22	C₄×C₈	Q₈	1	2	yes	—
23	C₂²×C₄	Q₁₆	1	2	yes	—
24	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
25	M₁₆	—	4	4	no	—
26	M₁₆	—	4	4	no	—
27	C₂×C₈	—	4	4	no	—
28	C₂×C₈	C₄⋊C₄	1	2	yes	—
29	C₂×C₈	D₈	1	2	yes	—
30	C₂×C₈	Q₁₆	1	2	yes	—
31	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₈	C₂×D₄	1	2	yes	—
33	C₂×C₈	C₂×Q₈	1	2	yes	—
34	C₂×C₈	C₂×Q₈	1	1	yes	characteristic
35	C₄²	C₄⋊C₄	1	2	yes	—
36	C₄²	D₈	1	2	yes	—
37	C₁₆	C₄⋊C₄	1	8	yes	—
38	C₂³	C₂×Q₁₆	1	1	yes	characteristic
39	C₂×C₄	—	4	2	no	—
40	C₂×C₄	#107	1	4	yes	—
41	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄	#127	1	1	yes	characteristic
43	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
44	C₂×C₄	C₂×D₈	1	1	yes	characteristic
45	C₂×C₄	C₂×D₈	1	1	yes	characteristic
46	C₂×C₄	C₂×Q₁₆	1	1	yes	characteristic
47	C₈	—	8	4	no	—
48	C₈	#107	1	4	yes	—
49	C₈	C₂×C₄⋊C₄	1	2	yes	—
50	C₈	C₄⋊Q₈	1	2	yes	—
51	C₂²	—	2	2	no	—
52	C₂²	C₂×#107	1	1	yes	characteristic
53	C₂²	#494	1	1	yes	characteristic
54	C₂²	#500	1	1	yes	characteristic
55	C₄	—	2	4	no	—
56	C₄	#384	1	1	yes	characteristic
57	C₄	C₂×#107	1	1	yes	characteristic
58	C₄	#493	1	1	yes	characteristic
59	C₄	#500	1	1	yes	characteristic
60	C₂	—	2	1	no	—
61	C₂	—	2	1	no	—
62	C₂	#1845	1	1	yes	characteristic
63	C₂	#2161	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₈
commutator	C₂×C₈	C₂²×C₄
Frattini, cosocle	C₂²×C₈	C₂³
socle	C₂²	C₂×#107
prime radical	C₂³	C₂×Q₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Maximal subgroups

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

subgroup	index
C₂×#368	2
C₂×#346	2
#1848	2