Subgroups — #1778

Order 128.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108	C₂	1	2	yes	maximal
2	C₄×M₁₆	C₂	1	2	yes	maximal
3	C₂×#97	C₂	1	1	yes	maximal, characteristic
4	#341	C₂	1	2	yes	maximal
5	C₂×M₁₆	C₂²	1	4	yes	—
6	C₂²×C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄²	C₂²	1	1	yes	characteristic
9	#108	C₄	1	8	yes	complemented
10	#97	—	2	2	no	—
11	#97	C₄	1	4	yes	—
12	C₄×C₈	—	2	2	no	—
13	C₂²×C₄	Q₈	1	2	yes	—
14	C₂²×C₄	C₂³	1	1	yes	characteristic
15	M₁₆	—	2	4	no	—
16	M₁₆	C₂×C₄	1	8	yes	—
17	C₂×C₈	—	2	4	no	—
18	C₂×C₈	—	2	2	no	—
19	C₂×C₈	C₂×C₄	1	2	yes	—
20	C₂×C₈	C₂×C₄	1	2	yes	—
21	C₂×C₈	C₂×C₄	1	4	yes	—
22	C₄²	C₂×C₄	1	2	yes	—
23	C₄²	D₄	1	2	yes	—
24	C₂³	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄	—	4	2	no	—
26	C₂×C₄	C₄⋊C₄	1	4	yes	—
27	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄	C₂²×C₄	1	2	yes	—
29	C₂×C₄	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄	#41	1	2	yes	—
31	C₈	—	2	2	no	—
32	C₈	—	2	8	no	—
33	C₈	C₄²	1	4	yes	—
34	C₂²	—	2	2	no	—
35	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²	C₄×Q₈	1	2	yes	—
37	C₄	—	2	4	no	—
38	C₄	C₂×C₄²	1	1	yes	characteristic
39	C₄	#117	1	1	yes	characteristic
40	C₄	C₄×D₄	1	2	yes	—
41	C₂	—	2	2	no	—
42	C₂	C₄×C₄⋊C₄	1	1	yes	characteristic
43	C₂	#430	1	2	yes	—

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

N	H ≅ G/N	type
9. #108	C₄	semidirect

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