Subgroups — #1360

Order 128.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#495	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#334	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₁₆	C₄	1	1	yes	characteristic
5	C₂×SD₁₆	—	2	1	no	—
6	C₂×D₈	C₄	1	1	yes	characteristic
7	#124	—	2	1	no	—
8	C₂×C₁₆	—	2	1	no	—
9	C₄⋊C₈	—	2	1	no	—
10	C₄×C₈	C₂²	1	1	yes	characteristic
11	C₂×Q₈	—	2	1	no	—
12	C₂×D₄	—	2	1	no	—
13	Q₁₆	—	4	1	no	—
14	SD₁₆	—	4	1	no	—
15	SD₁₆	—	4	1	no	—
16	D₈	—	4	1	no	—
17	C₂×C₈	—	4	1	no	—
18	C₂×C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈	D₄	1	1	yes	characteristic
20	C₂²⋊C₄	—	4	1	no	—
21	C₂²⋊C₄	—	4	1	no	—
22	C₄²	D₄	1	1	yes	characteristic
23	C₁₆	—	4	1	no	—
24	C₂³	—	4	1	no	—
25	Q₈	—	4	1	no	—
26	Q₈	—	4	1	no	—
27	D₄	—	4	1	no	—
28	D₄	—	4	1	no	—
29	C₂×C₄	—	4	1	no	—
30	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄	D₈	1	1	yes	characteristic
32	C₂×C₄	SD₁₆	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	8	1	no	—
35	C₈	D₈	1	1	yes	characteristic
36	C₈	SD₁₆	1	1	yes	characteristic
37	C₂²	—	8	1	no	—
38	C₂²	—	8	1	no	—
39	C₂²	—	8	1	no	—
40	C₂²	#102	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	—	2	1	no	—
43	C₄	—	8	1	no	—
44	C₄	#100	1	1	yes	characteristic
45	C₄	#102	1	1	yes	characteristic
46	C₂	—	16	1	no	—
47	C₂	#331	1	1	yes	characteristic
48	C₂	#359	1	1	yes	characteristic
49	C₂	#360	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₄⋊C₁₆	C₂	semidirect
3. #334	C₂	semidirect

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