Subgroups — #1745

Order 128.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#97	C₂	1	2	yes	maximal
2	C₄³	C₂	1	1	yes	maximal, characteristic
3	#336	C₂	1	4	yes	maximal
4	C₂²×C₈	C₂²	1	4	yes	—
5	C₂×C₄²	C₄	1	4	yes	—
6	C₂×C₄²	C₂²	1	2	yes	—
7	C₂×C₄²	C₂²	1	1	yes	characteristic
8	#97	C₄	1	8	yes	complemented
9	C₂²×C₄	C₂×C₄	1	2	yes	—
10	C₂²×C₄	C₂×C₄	1	4	yes	—
11	C₂²×C₄	C₂³	1	1	yes	characteristic
12	C₂×C₈	—	2	8	no	—
13	C₂×C₈	C₂×C₄	1	8	yes	—
14	C₄²	—	2	8	no	—
15	C₄²	—	2	4	no	—
16	C₄²	C₂×C₄	1	4	yes	—
17	C₂³	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄	—	2	4	no	—
19	C₂×C₄	—	2	4	no	—
20	C₂×C₄	—	2	4	no	—
21	C₂×C₄	C₄²	1	4	yes	—
22	C₂×C₄	M₁₆	1	8	yes	—
23	C₂×C₄	C₂²×C₄	1	2	yes	—
24	C₂×C₄	#41	1	4	yes	—
25	C₈	—	2	8	no	—
26	C₂²	C₂×C₄²	1	1	yes	characteristic
27	C₂²	#117	1	2	yes	—
28	C₂²	C₂×M₁₆	1	4	yes	—
29	C₄	—	2	4	no	—
30	C₄	—	2	8	no	—
31	C₄	#117	1	4	yes	—
32	C₂	#376	1	1	yes	characteristic
33	C₂	C₄×M₁₆	1	2	yes	—
34	C₂	#432	1	4	yes	—

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

N	H ≅ G/N	type
8. #97	C₄	semidirect

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