Subgroups — C₂²×#108 #2914

Order 128.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆	C₂	1	2	yes	maximal
2	C₂³×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#108	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₄	C₂²	1	1	yes	characteristic
5	C₂×M₁₆	—	2	6	no	—
6	C₂×M₁₆	C₂²	1	12	yes	—
7	C₂²×C₈	—	2	2	no	—
8	C₂²×C₈	C₄	1	2	yes	—
9	C₂²×C₈	C₄	1	6	yes	—
10	C₂²×C₈	C₂²	1	6	yes	—
11	#108	C₂²	1	16	yes	direct product factor
12	C₂⁴	Q₈	1	1	yes	characteristic
13	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄	C₂×C₄	1	3	yes	—
15	C₂²×C₄	D₄	1	3	yes	—
16	C₂²×C₄	D₄	1	1	yes	characteristic
17	C₂²×C₄	Q₈	1	3	yes	—
18	C₂²×C₄	C₂³	1	3	yes	—
19	M₁₆	—	2	12	no	—
20	M₁₆	C₂³	1	8	yes	—
21	C₂×C₈	—	2	12	no	—
22	C₂×C₈	C₂×C₄	1	12	yes	—
23	C₂×C₈	C₂×C₄	1	12	yes	—
24	C₂×C₈	C₂³	1	4	yes	—
25	C₂³	—	2	4	no	—
26	C₂³	C₄⋊C₄	1	3	yes	—
27	C₂³	C₄⋊C₄	1	1	yes	characteristic
28	C₂³	C₂×Q₈	1	3	yes	—
29	C₂×C₄	C₄⋊C₄	1	6	yes	—
30	C₂×C₄	C₄⋊C₄	1	3	yes	—
31	C₂×C₄	C₄⋊C₄	1	3	yes	—
32	C₂×C₄	C₂²×C₄	1	3	yes	—
33	C₂×C₄	C₂²×C₄	1	3	yes	—
34	C₂×C₄	C₂×D₄	1	3	yes	—
35	C₂×C₄	C₂×D₄	1	3	yes	—
36	C₂×C₄	C₂×Q₈	1	3	yes	—
37	C₂×C₄	C₂⁴	1	1	yes	characteristic
38	C₈	—	2	8	no	—
39	C₈	C₂²×C₄	1	8	yes	—
40	C₂²	—	2	6	no	—
41	C₂²	—	2	6	no	—
42	C₂²	#108	1	4	yes	direct product factor
43	C₂²	C₂×C₄⋊C₄	1	3	yes	—
44	C₂²	C₂×C₄⋊C₄	1	3	yes	—
45	C₂²	C₂²×Q₈	1	1	yes	characteristic
46	C₄	C₂×C₄⋊C₄	1	3	yes	—
47	C₄	C₂×C₄⋊C₄	1	3	yes	—
48	C₄	C₂³×C₄	1	1	yes	characteristic
49	C₄	C₂²×D₄	1	1	yes	characteristic
50	C₂	—	2	3	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂×#108	1	6	yes	direct product factor
53	C₂	C₂²×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄
commutator	C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂³	C₄⋊C₄
prime radical	C₂⁴	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₂×#108	C₂	direct (N × H)
11. #108	C₂²	direct (N × H)
42. C₂²	#108	direct (N × H)
52. C₂	C₂×#108	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×M₁₆	2
C₂³×C₈	2
C₂×#108	2

Subgroups — C22×#108 #2914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#108 #2914