Subgroups — C₂×#396 #2389

Order 128.

454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₄	C₂	1	3	yes	maximal, complemented
2	C₂²×C₂²⋊C₄	C₂	1	3	yes	maximal
3	#396	C₂	1	8	yes	maximal, direct product factor
4	C₂×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵	C₂²	1	1	yes	characteristic
6	C₂³×C₄	C₂²	1	3	yes	—
7	C₂³×C₄	C₂²	1	3	yes	—
8	C₂×C₄⋊C₄	—	2	12	no	—
9	C₂×C₄⋊C₄	C₂²	1	12	yes	complemented
10	C₂×C₂²⋊C₄	—	2	12	no	—
11	C₂×C₂²⋊C₄	C₂²	1	12	yes	—
12	#95	C₂²	1	4	yes	complemented
13	C₂⁴	—	2	6	no	—
14	C₂⁴	—	2	6	no	—
15	C₂⁴	Q₈	1	4	yes	—
16	C₂⁴	C₂³	1	2	yes	—
17	C₂⁴	C₂³	1	1	yes	characteristic
18	C₂²×C₄	—	2	6	no	—
19	C₂²×C₄	—	2	6	no	—
20	C₂²×C₄	—	2	6	no	—
21	C₂²×C₄	—	2	6	no	—
22	C₂²×C₄	—	2	6	no	—
23	C₂²×C₄	D₄	1	12	yes	—
24	C₂²×C₄	C₂³	1	6	yes	—
25	C₂²×C₄	C₂³	1	6	yes	—
26	C₄⋊C₄	—	2	24	no	—
27	C₂²⋊C₄	—	2	24	no	—
28	C₂³	—	2	24	no	—
29	C₂³	—	2	6	no	—
30	C₂³	—	2	6	no	—
31	C₂³	—	4	12	no	—
32	C₂³	—	4	4	no	—
33	C₂³	C₂×D₄	1	6	yes	—
34	C₂³	C₂×Q₈	1	4	yes	—
35	C₂³	C₂×Q₈	1	2	yes	—
36	C₂³	#41	1	6	yes	—
37	C₂³	C₂⁴	1	1	yes	characteristic
38	C₂×C₄	—	2	24	no	—
39	C₂×C₄	—	2	6	no	—
40	C₂×C₄	—	2	6	no	—
41	C₂×C₄	—	2	6	no	—
42	C₂×C₄	—	2	6	no	—
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	—	4	12	no	—
45	C₂×C₄	C₂×D₄	1	12	yes	—
46	C₂²	—	2	12	no	—
47	C₂²	—	4	6	no	—
48	C₂²	—	4	2	no	—
49	C₂²	—	4	16	no	—
50	C₂²	#121	1	12	yes	—
51	C₂²	C₂²⋊Q₈	1	12	yes	—
52	C₂²	#126	1	4	yes	—
53	C₂²	C₂²×D₄	1	3	yes	—
54	C₂²	C₂²×Q₈	1	1	yes	characteristic
55	C₂²	C₂×#41	1	3	yes	—
56	C₄	—	2	12	no	—
57	C₄	—	4	6	no	—
58	C₂	—	4	4	no	—
59	C₂	#396	1	8	yes	direct product factor
60	C₂	C₂×#121	1	3	yes	—
61	C₂	C₂×C₂²⋊Q₈	1	3	yes	—
62	C₂	C₂×#126	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴
prime radical	C₂⁵	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊C₄	C₂	semidirect
3. #396	C₂	direct (N × H)
4. C₂×#95	C₂	semidirect
9. C₂×C₄⋊C₄	C₂²	semidirect
12. #95	C₂²	semidirect
59. C₂	#396	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⋊C₄	2
C₂²×C₂²⋊C₄	2
#396	2
C₂×#95	2

Subgroups — C2×#396 #2389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#396 #2389