Subgroups — #1834

Order 128.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	#384	C₂	1	2	yes	maximal
3	#340	C₂	1	4	yes	maximal
4	C₂²×C₈	C₂²	1	2	yes	—
5	C₂×C₄⋊C₄	—	2	2	no	—
6	C₂×C₄⋊C₄	—	2	2	no	—
7	C₂×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₄²	C₂²	1	1	yes	characteristic
9	C₄×C₈	C₄	1	4	yes	complemented
10	C₂²×C₄	—	2	4	no	—
11	C₂²×C₄	D₄	1	1	yes	characteristic
12	C₂²×C₄	D₄	1	1	yes	characteristic
13	C₂²×C₄	C₂³	1	1	yes	characteristic
14	C₂×C₈	—	2	4	no	—
15	C₂×C₈	C₂×C₄	1	4	yes	—
16	C₄⋊C₄	—	2	8	no	—
17	C₄⋊C₄	—	4	4	no	—
18	C₄⋊C₄	—	4	4	no	—
19	C₄²	C₂×C₄	1	2	yes	—
20	C₄²	Q₈	1	2	yes	—
21	C₂³	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄	—	4	4	no	—
23	C₂×C₄	—	4	4	no	—
24	C₂×C₄	—	4	4	no	—
25	C₂×C₄	C₄⋊C₄	1	2	yes	—
26	C₂×C₄	C₄⋊C₄	1	2	yes	—
27	C₂×C₄	D₈	1	2	yes	—
28	C₂×C₄	SD₁₆	1	4	yes	—
29	C₂×C₄	Q₁₆	1	2	yes	—
30	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄	#41	1	4	yes	—
33	C₈	—	2	4	no	—
34	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²	#124	1	2	yes	—
36	C₂²	C₂×D₈	1	1	yes	characteristic
37	C₂²	C₂×SD₁₆	1	2	yes	—
38	C₂²	C₂×Q₁₆	1	1	yes	characteristic
39	C₄	—	8	4	no	—
40	C₄	#106	1	4	yes	—
41	C₄	#107	1	4	yes	—
42	C₄	#117	1	2	yes	—
43	C₄	#125	1	2	yes	—
44	C₂	#382	1	1	yes	characteristic
45	C₂	C₂×#106	1	1	yes	characteristic
46	C₂	C₂×#107	1	1	yes	characteristic
47	C₂	#486	1	2	yes	—
48	C₂	#487	1	2	yes	—

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

N	H ≅ G/N	type
9. C₄×C₈	C₄	semidirect

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