Subgroups — #1835

Order 128.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	#382	C₂	1	2	yes	maximal
3	#340	C₂	1	4	yes	maximal
4	C₂²×C₈	C₂²	1	2	yes	—
5	C₂×C₄⋊C₄	C₂²	1	4	yes	—
6	C₂×C₄²	C₂²	1	1	yes	characteristic
7	C₄×C₈	C₄	1	4	yes	complemented
8	#95	—	2	4	no	—
9	C₂²×C₄	—	2	4	no	—
10	C₂²×C₄	D₄	1	2	yes	—
11	C₂²×C₄	C₂³	1	1	yes	characteristic
12	C₂×C₈	—	2	4	no	—
13	C₂×C₈	C₂×C₄	1	4	yes	—
14	C₄⋊C₄	—	2	8	no	—
15	C₄²	C₂×C₄	1	2	yes	—
16	C₄²	Q₈	1	2	yes	—
17	C₂³	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄	—	2	4	no	—
19	C₂×C₄	—	4	4	no	—
20	C₂×C₄	—	4	8	no	—
21	C₂×C₄	C₄⋊C₄	1	4	yes	—
22	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄	#41	1	4	yes	—
25	C₈	—	2	4	no	—
26	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²	#124	1	2	yes	—
28	C₂²	#135	1	4	yes	—
29	C₄	—	2	4	no	—
30	C₄	—	8	4	no	—
31	C₄	#117	1	2	yes	—
32	C₄	#125	1	2	yes	—
33	C₂	#382	1	1	yes	characteristic
34	C₂	#427	1	2	yes	—
35	C₂	#488	1	4	yes	—

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

N	H ≅ G/N	type
7. C₄×C₈	C₄	semidirect

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