Subgroups — C₂×#368 #2160

Order 128.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#108	C₂	1	2	yes	maximal
3	#368	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₁₆	—	2	2	no	—
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₁₆	C₄	1	2	yes	—
7	C₂×C₁₆	C₄	1	2	yes	—
8	C₂×C₁₆	C₂²	1	2	yes	—
9	#108	—	2	2	no	—
10	#108	C₂²	1	4	yes	—
11	C₂²×C₄	D₄	1	1	yes	characteristic
12	M₁₆	—	2	4	no	—
13	M₁₆	—	4	2	no	—
14	C₂×C₈	—	4	2	no	—
15	C₂×C₈	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈	D₄	1	1	yes	characteristic
18	C₂×C₈	Q₈	1	1	yes	characteristic
19	C₂×C₈	Q₈	1	1	yes	characteristic
20	C₂×C₈	C₂³	1	1	yes	characteristic
21	C₁₆	C₂×C₄	1	4	yes	—
22	C₂³	Q₁₆	1	1	yes	characteristic
23	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄	D₈	1	1	yes	characteristic
26	C₂×C₄	D₈	1	1	yes	characteristic
27	C₂×C₄	Q₁₆	1	1	yes	characteristic
28	C₂×C₄	C₂×D₄	1	1	yes	characteristic
29	C₈	—	4	4	no	—
30	C₈	C₄⋊C₄	1	1	yes	characteristic
31	C₈	C₄⋊C₄	1	1	yes	characteristic
32	C₈	C₂²×C₄	1	1	yes	characteristic
33	C₈	C₂×Q₈	1	1	yes	characteristic
34	C₂²	—	2	2	no	—
35	C₂²	#107	1	1	yes	characteristic
36	C₂²	#107	1	1	yes	characteristic
37	C₂²	C₂×Q₁₆	1	1	yes	characteristic
38	C₄	#107	1	1	yes	characteristic
39	C₄	#107	1	1	yes	characteristic
40	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄	C₂×D₈	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	2	1	no	—
44	C₂	#368	1	2	yes	direct product factor
45	C₂	C₂×#107	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #368	C₂	direct (N × H)
44. C₂	#368	direct (N × H)

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