Subgroups — #2165

Order 128.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#364	C₂	1	2	yes	maximal, complemented
3	#349	C₂	1	2	yes	maximal
4	#347	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆	C₄	1	1	yes	characteristic
6	C₂×M₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄²	C₄	1	1	yes	characteristic
8	M₃₂	C₂²	1	4	yes	—
9	#97	C₄	1	1	yes	characteristic
10	#97	C₂²	1	1	yes	characteristic
11	C₄×C₈	C₄	1	1	yes	characteristic
12	C₄×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₄	—	2	1	no	—
14	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
15	M₁₆	—	2	2	no	—
16	M₁₆	—	2	2	no	—
17	C₂×C₈	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈	C₂³	1	1	yes	characteristic
21	C₄²	—	2	1	no	—
22	C₄²	C₂×C₄	1	1	yes	characteristic
23	C₄²	C₂×C₄	1	1	yes	characteristic
24	C₁₆	—	2	4	no	—
25	C₂³	M₁₆	1	1	yes	characteristic
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	—	4	2	no	—
31	C₂×C₄	M₁₆	1	1	yes	characteristic
32	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	2	1	no	—
35	C₈	M₁₆	1	2	yes	—
36	C₈	#41	1	2	yes	—
37	C₂²	—	2	1	no	—
38	C₂²	—	4	1	no	—
39	C₂²	C₂×M₁₆	1	1	yes	characteristic
40	C₄	—	2	2	no	—
41	C₄	—	2	1	no	—
42	C₄	—	4	1	no	—
43	C₄	#117	1	1	yes	characteristic
44	C₄	C₂×M₁₆	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	—	4	1	no	—
47	C₂	#432	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #364	C₂	semidirect
4. #347	C₂	semidirect

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