Subgroups — C₂×#347 #2109

Order 128.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	2	yes	maximal
2	C₂×#97	C₂	1	1	yes	maximal, characteristic
3	#347	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈	C₄	1	1	yes	characteristic
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₄²	C₄	1	1	yes	characteristic
7	M₃₂	C₄	1	4	yes	complemented
8	M₃₂	C₂²	1	4	yes	—
9	C₂×C₁₆	C₄	1	4	yes	complemented
10	#97	C₄	1	2	yes	—
11	#97	C₂²	1	2	yes	—
12	C₂²×C₄	—	2	1	no	—
13	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈	—	2	1	no	—
15	C₂×C₈	—	2	1	no	—
16	C₂×C₈	C₂×C₄	1	2	yes	—
17	C₂×C₈	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈	C₂×C₄	1	2	yes	—
19	C₂×C₈	C₂×C₄	1	2	yes	—
20	C₂×C₈	C₂³	1	1	yes	characteristic
21	C₄²	—	2	1	no	—
22	C₄²	C₂×C₄	1	2	yes	—
23	C₁₆	C₂×C₄	1	8	yes	complemented
24	C₂³	M₁₆	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	—	4	2	no	—
27	C₂×C₄	C₄²	1	1	yes	characteristic
28	C₂×C₄	C₄²	1	1	yes	characteristic
29	C₂×C₄	M₁₆	1	1	yes	characteristic
30	C₂×C₄	M₁₆	1	1	yes	characteristic
31	C₂×C₄	M₁₆	1	1	yes	characteristic
32	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
33	C₈	—	2	2	no	—
34	C₈	C₄²	1	2	yes	—
35	C₈	C₂²×C₄	1	2	yes	—
36	C₂²	—	2	2	no	—
37	C₂²	#97	1	1	yes	characteristic
38	C₂²	#97	1	1	yes	characteristic
39	C₂²	C₂×M₁₆	1	1	yes	characteristic
40	C₄	—	4	2	no	—
41	C₄	#97	1	1	yes	characteristic
42	C₄	#97	1	1	yes	characteristic
43	C₄	C₂×C₄²	1	1	yes	characteristic
44	C₄	C₂×M₁₆	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	—	2	1	no	—
47	C₂	#347	1	2	yes	direct product factor
48	C₂	C₂×#97	1	1	yes	characteristic

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.