Subgroups — C₂×#338 #1731

Order 128.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆	C₂	1	3	yes	maximal
2	#338	C₂	1	4	yes	maximal, direct product factor
3	C₂³×C₄	C₂²	1	1	yes	characteristic
4	C₂×M₁₆	—	2	6	no	—
5	C₂×M₁₆	—	2	6	no	—
6	C₂×M₁₆	C₄	1	6	yes	—
7	C₂×M₁₆	C₂²	1	6	yes	—
8	C₂²×C₈	C₄	1	6	yes	—
9	C₂⁴	Q₈	1	1	yes	characteristic
10	C₂²×C₄	C₂×C₄	1	3	yes	—
11	C₂²×C₄	C₂×C₄	1	3	yes	—
12	C₂²×C₄	D₄	1	3	yes	—
13	C₂²×C₄	D₄	1	3	yes	—
14	C₂²×C₄	Q₈	1	1	yes	characteristic
15	C₂²×C₄	C₂³	1	1	yes	characteristic
16	M₁₆	—	2	12	no	—
17	M₁₆	—	2	12	no	—
18	C₂×C₈	—	2	6	no	—
19	C₂×C₈	—	2	6	no	—
20	C₂×C₈	C₂×C₄	1	12	yes	—
21	C₂³	—	4	2	no	—
22	C₂³	C₄⋊C₄	1	3	yes	—
23	C₂³	C₄⋊C₄	1	3	yes	—
24	C₂³	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄	C₄²	1	3	yes	—
26	C₂×C₄	C₄²	1	1	yes	characteristic
27	C₂×C₄	C₂²⋊C₄	1	3	yes	—
28	C₂×C₄	C₂²⋊C₄	1	3	yes	—
29	C₂×C₄	C₂²⋊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	C₂×D₄	1	3	yes	—
34	C₈	—	2	12	no	—
35	C₂²	—	2	6	no	—
36	C₂²	—	4	3	no	—
37	C₂²	—	4	1	no	—
38	C₂²	#95	1	3	yes	—
39	C₂²	#95	1	1	yes	characteristic
40	C₂²	C₂×C₄⋊C₄	1	3	yes	—
41	C₄	#95	1	3	yes	—
42	C₄	#95	1	1	yes	characteristic
43	C₄	C₂×C₄²	1	1	yes	characteristic
44	C₄	C₂×C₂²⋊C₄	1	3	yes	—
45	C₂	—	2	3	no	—
46	C₂	—	2	3	no	—
47	C₂	#338	1	2	yes	direct product factor
48	C₂	C₂×#95	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #338	C₂	direct (N × H)
47. C₂	#338	direct (N × H)

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

subgroup	index
C₂²×M₁₆	2
#338	2