Subgroups — C₂²×#106 #2907

Order 128.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂×#106	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₄	—	2	2	no	—
5	C₂³×C₄	C₂²	1	1	yes	characteristic
6	C₂²×C₈	C₄	1	8	yes	complemented
7	C₂²×C₈	C₂²	1	6	yes	—
8	C₂×C₄⋊C₄	—	2	6	no	—
9	C₂×C₄⋊C₄	C₂²	1	12	yes	—
10	#106	C₂²	1	16	yes	direct product factor
11	C₂⁴	D₄	1	1	yes	characteristic
12	C₂²×C₄	—	2	12	no	—
13	C₂²×C₄	—	4	8	no	—
14	C₂²×C₄	C₂×C₄	1	4	yes	—
15	C₂²×C₄	D₄	1	3	yes	—
16	C₂²×C₄	Q₈	1	4	yes	—
17	C₂²×C₄	C₂³	1	3	yes	—
18	C₂×C₈	C₂×C₄	1	24	yes	complemented
19	C₂×C₈	C₂³	1	4	yes	—
20	C₄⋊C₄	—	2	12	no	—
21	C₄⋊C₄	C₂³	1	8	yes	—
22	C₂³	C₄⋊C₄	1	4	yes	—
23	C₂³	SD₁₆	1	8	yes	—
24	C₂³	C₂×D₄	1	3	yes	—
25	C₂×C₄	—	2	8	no	—
26	C₂×C₄	—	4	24	no	—
27	C₂×C₄	C₄⋊C₄	1	12	yes	—
28	C₂×C₄	C₂²×C₄	1	6	yes	—
29	C₂×C₄	C₂×D₄	1	3	yes	—
30	C₂×C₄	C₂×Q₈	1	6	yes	—
31	C₂×C₄	C₂⁴	1	1	yes	characteristic
32	C₈	C₂²×C₄	1	8	yes	complemented
33	C₂²	#106	1	16	yes	direct product factor
34	C₂²	C₂×C₄⋊C₄	1	6	yes	—
35	C₂²	C₂×SD₁₆	1	12	yes	—
36	C₂²	C₂²×D₄	1	1	yes	characteristic
37	C₄	—	4	8	no	—
38	C₄	C₂×C₄⋊C₄	1	6	yes	—
39	C₄	C₂³×C₄	1	1	yes	characteristic
40	C₄	C₂²×Q₈	1	1	yes	characteristic
41	C₂	C₂×#106	1	12	yes	direct product factor
42	C₂	C₂²×C₄⋊C₄	1	1	yes	characteristic
43	C₂	C₂²×SD₁₆	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.