Subgroups — #1348

Order 128.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#467	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#340	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆	C₄	1	1	yes	characteristic, complemented
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂²⋊Q₈	—	2	1	no	—
7	C₂×C₄⋊C₄	—	2	1	no	—
8	C₂×C₁₆	—	2	1	no	—
9	#107	C₄	1	1	yes	characteristic, complemented
10	#103	—	2	1	no	—
11	C₂×Q₈	—	2	1	no	—
12	C₂²×C₄	—	4	1	no	—
13	C₂²×C₄	D₄	1	1	yes	characteristic
14	Q₁₆	—	4	1	no	—
15	C₂×C₈	—	4	1	no	—
16	C₂×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈	D₄	1	1	yes	characteristic
18	C₄⋊C₄	—	2	2	no	—
19	C₄⋊C₄	—	2	1	no	—
20	C₄⋊C₄	—	4	1	no	—
21	C₄⋊C₄	—	4	1	no	—
22	C₂²⋊C₄	—	4	1	no	—
23	C₁₆	—	4	1	no	—
24	C₂³	D₈	1	1	yes	characteristic
25	Q₈	—	4	1	no	—
26	Q₈	—	4	1	no	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	4	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	4	1	no	—
32	C₂×C₄	—	8	1	no	—
33	C₂×C₄	—	8	1	no	—
34	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄	SD₁₆	1	1	yes	characteristic
36	C₈	—	2	1	no	—
37	C₈	—	2	1	no	—
38	C₂²	—	2	1	no	—
39	C₂²	—	2	1	no	—
40	C₂²	#102	1	1	yes	characteristic
41	C₂²	SD₃₂	1	1	yes	characteristic
42	C₂²	Q₃₂	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	8	2	no	—
45	C₄	—	8	1	no	—
46	C₄	—	8	1	no	—
47	C₄	#99	1	1	yes	characteristic
48	C₄	#104	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	—	2	1	no	—
51	C₂	#327	1	1	yes	characteristic
52	C₂	#358	1	1	yes	characteristic
53	C₂	#360	1	1	yes	characteristic

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

N	H ≅ G/N	type
4. C₂×Q₁₆	C₄	semidirect
9. #107	C₄	semidirect

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