Subgroups — #1746

Order 128.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#376	C₂	1	1	yes	maximal, characteristic
4	#336	C₂	1	4	yes	maximal
5	C₂²×C₈	C₂²	1	2	yes	—
6	C₂²×C₈	C₂²	1	2	yes	—
7	C₂×C₄²	C₂²	1	2	yes	—
8	C₂×C₄²	C₂²	1	1	yes	characteristic
9	#97	C₄	1	4	yes	complemented
10	C₄×C₈	C₄	1	4	yes	complemented
11	#95	C₄	1	4	yes	—
12	C₂²×C₄	C₂×C₄	1	4	yes	—
13	C₂²×C₄	C₂×C₄	1	2	yes	—
14	C₂²×C₄	C₂³	1	1	yes	characteristic
15	C₂×C₈	—	2	4	no	—
16	C₂×C₈	—	2	4	no	—
17	C₂×C₈	C₂×C₄	1	4	yes	—
18	C₂×C₈	C₂×C₄	1	4	yes	—
19	C₄²	—	2	4	no	—
20	C₄²	C₂×C₄	1	2	yes	—
21	C₄²	C₂×C₄	1	2	yes	—
22	C₂³	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄	—	2	4	no	—
24	C₂×C₄	—	2	4	no	—
25	C₂×C₄	—	2	8	no	—
26	C₂×C₄	C₄²	1	4	yes	—
27	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄	#41	1	4	yes	—
30	C₈	—	2	4	no	—
31	C₈	—	2	4	no	—
32	C₂²	C₂×C₄²	1	1	yes	characteristic
33	C₂²	#117	1	2	yes	—
34	C₂²	#131	1	4	yes	—
35	C₄	—	2	4	no	—
36	C₄	—	4	4	no	—
37	C₄	#117	1	2	yes	—
38	C₄	#117	1	2	yes	—
39	C₂	#376	1	1	yes	characteristic
40	C₂	#405	1	2	yes	—
41	C₂	#433	1	4	yes	—

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

N	H ≅ G/N	type
9. #97	C₄	semidirect
10. C₄×C₈	C₄	semidirect

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