Subgroups — C₂×#376 #2267

Order 128.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²	C₂	1	3	yes	maximal
2	#376	C₂	1	8	yes	maximal, direct product factor
3	C₂×#95	C₂	1	4	yes	maximal
4	C₂³×C₄	C₂²	1	6	yes	—
5	C₂³×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₄²	C₄	1	24	yes	complemented
7	C₂×C₄²	C₂²	1	12	yes	—
8	#95	C₂²	1	16	yes	—
9	C₂⁴	C₂³	1	1	yes	characteristic
10	C₂²×C₄	—	2	24	no	—
11	C₂²×C₄	C₂×C₄	1	24	yes	—
12	C₂²×C₄	C₂×C₄	1	12	yes	—
13	C₂²×C₄	C₂³	1	12	yes	—
14	C₂²×C₄	C₂³	1	2	yes	—
15	C₄²	C₂×C₄	1	48	yes	complemented
16	C₂³	C₂²×C₄	1	6	yes	—
17	C₂³	#41	1	8	yes	—
18	C₂³	C₂⁴	1	1	yes	characteristic
19	C₂×C₄	—	2	48	no	—
20	C₂×C₄	—	2	24	no	—
21	C₂×C₄	C₄²	1	16	yes	—
22	C₂×C₄	C₂²×C₄	1	24	yes	—
23	C₂×C₄	C₂²×C₄	1	12	yes	—
24	C₂²	C₂×C₄²	1	4	yes	—
25	C₂²	#117	1	24	yes	—
26	C₂²	C₂³×C₄	1	3	yes	—
27	C₂²	C₂×#41	1	4	yes	—
28	C₄	—	2	24	no	—
29	C₄	C₂×C₄²	1	8	yes	—
30	C₂	#376	1	8	yes	direct product factor
31	C₂	C₂²×C₄²	1	1	yes	characteristic
32	C₂	C₂×#117	1	6	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.