Subgroups — C₂×#322 #1448

Order 128.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#322	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈	C₄	1	4	yes	—
5	C₂²×C₈	C₄	1	2	yes	—
6	C₂×C₄²	C₂²	1	1	yes	characteristic
7	C₄×C₈	C₄	1	4	yes	—
8	C₄×C₈	C₄	1	2	yes	—
9	C₄×C₈	C₂²	1	4	yes	—
10	C₄×C₈	C₂²	1	2	yes	—
11	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄	C₂×C₄	1	2	yes	—
13	C₂×C₈	—	2	8	no	—
14	C₂×C₈	C₈	1	8	yes	complemented
15	C₂×C₈	C₂×C₄	1	8	yes	—
16	C₂×C₈	C₂×C₄	1	4	yes	—
17	C₄²	C₂×C₄	1	2	yes	—
18	C₄²	C₂×C₄	1	1	yes	characteristic
19	C₄²	C₂³	1	1	yes	characteristic
20	C₂³	C₄²	1	1	yes	characteristic
21	C₂×C₄	C₄²	1	1	yes	characteristic
22	C₂×C₄	C₄²	1	2	yes	—
23	C₂×C₄	C₂×C₈	1	4	yes	—
24	C₂×C₄	M₁₆	1	8	yes	—
25	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄	C₂²×C₄	1	2	yes	—
27	C₈	—	2	8	no	—
28	C₈	C₂×C₈	1	8	yes	complemented
29	C₂²	C₄×C₈	1	2	yes	—
30	C₂²	#97	1	4	yes	—
31	C₂²	C₂×C₄²	1	1	yes	characteristic
32	C₄	C₄×C₈	1	2	yes	—
33	C₄	#97	1	4	yes	—
34	C₄	C₂²×C₈	1	2	yes	—
35	C₄	C₂×M₁₆	1	4	yes	—
36	C₂	#322	1	4	yes	direct product factor
37	C₂	C₂×C₄×C₈	1	1	yes	characteristic
38	C₂	C₂×#97	1	2	yes	—

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

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

subgroup	index
C₂×C₄×C₈	2
#322	2