Subgroups — #1296

Order 128.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈	C₂	1	2	yes	maximal
2	#384	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈	—	2	2	no	—
4	C₂×C₄⋊C₄	—	2	2	no	—
5	C₂×C₄⋊C₄	C₄	1	2	yes	—
6	C₂×C₄²	C₂²	1	1	yes	characteristic
7	C₄⋊C₈	—	2	2	no	—
8	C₄⋊C₈	C₄	1	4	yes	complemented
9	C₂²×C₄	—	2	2	no	—
10	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄	D₄	1	2	yes	—
12	C₂×C₈	—	2	4	no	—
13	C₂×C₈	—	4	2	no	—
14	C₂×C₈	—	4	2	no	—
15	C₄⋊C₄	—	4	2	no	—
16	C₄⋊C₄	—	4	2	no	—
17	C₄⋊C₄	—	4	2	no	—
18	C₄²	C₂×C₄	1	2	yes	—
19	C₄²	D₄	1	1	yes	characteristic
20	C₄²	Q₈	1	1	yes	characteristic
21	C₂³	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	—	2	1	no	—
24	C₂×C₄	—	4	2	no	—
25	C₂×C₄	—	4	4	no	—
26	C₂×C₄	C₄²	1	1	yes	characteristic
27	C₂×C₄	C₂²⋊C₄	1	2	yes	—
28	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄	C₄⋊C₄	1	2	yes	—
30	C₂×C₄	D₈	1	2	yes	—
31	C₂×C₄	SD₁₆	1	2	yes	—
32	C₂×C₄	SD₁₆	1	2	yes	—
33	C₂×C₄	Q₁₆	1	2	yes	—
34	C₈	—	4	4	no	—
35	C₂²	#95	1	1	yes	characteristic
36	C₂²	#100	1	1	yes	characteristic
37	C₂²	#101	1	1	yes	characteristic
38	C₂²	#102	1	2	yes	—
39	C₂²	#103	1	2	yes	—
40	C₄	—	2	1	no	—
41	C₄	—	2	1	no	—
42	C₄	—	8	2	no	—
43	C₄	#102	1	2	yes	—
44	C₄	#103	1	2	yes	—
45	C₄	#106	1	2	yes	—
46	C₄	#107	1	2	yes	—
47	C₂	#331	1	1	yes	characteristic
48	C₂	#332	1	2	yes	—
49	C₂	#333	1	1	yes	characteristic
50	C₂	#340	1	2	yes	—
51	C₂	#343	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₄⋊C₈	C₄	semidirect

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

subgroup	index
C₂×C₄⋊C₈	2
#384	2