Subgroups — #1844

Order 128.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#106	C₂	1	4	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#384	C₂	1	2	yes	maximal
4	C₂²×C₈	C₂²	1	2	yes	—
5	C₂×C₄⋊C₄	—	2	4	no	—
6	C₂×C₄⋊C₄	C₂²	1	4	yes	—
7	C₂×C₄²	C₂²	1	1	yes	characteristic
8	#106	—	2	8	no	—
9	C₄×C₈	C₄	1	4	yes	complemented
10	C₂²×C₄	—	2	4	no	—
11	C₂²×C₄	D₄	1	2	yes	—
12	C₂²×C₄	C₂³	1	1	yes	characteristic
13	C₂×C₈	C₂×C₄	1	4	yes	—
14	C₂×C₈	D₄	1	4	yes	—
15	C₂×C₈	Q₈	1	4	yes	—
16	C₄⋊C₄	—	2	8	no	—
17	C₄⋊C₄	—	4	8	no	—
18	C₄²	C₂×C₄	1	2	yes	—
19	C₄²	Q₈	1	2	yes	—
20	C₂³	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄	—	4	4	no	—
22	C₂×C₄	—	4	8	no	—
23	C₂×C₄	C₄⋊C₄	1	4	yes	—
24	C₂×C₄	SD₁₆	1	8	yes	—
25	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄	C₂×D₄	1	2	yes	—
27	C₂×C₄	C₂×Q₈	1	2	yes	—
28	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
29	C₈	C₄⋊C₄	1	8	yes	complemented
30	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂²	#127	1	1	yes	characteristic
32	C₂²	C₄⋊Q₈	1	1	yes	characteristic
33	C₂²	C₂×SD₁₆	1	4	yes	—
34	C₄	—	8	4	no	—
35	C₄	#106	1	8	yes	complemented
36	C₄	C₂×C₄⋊C₄	1	2	yes	—
37	C₄	C₄⋊Q₈	1	2	yes	—
38	C₂	#384	1	1	yes	characteristic
39	C₂	C₂×#106	1	2	yes	—
40	C₂	#492	1	2	yes	—
41	C₂	#498	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.