Subgroups — #1848

Order 128.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108	C₂	1	4	yes	maximal
2	#423	C₂	1	2	yes	maximal
3	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆	C₂²	1	4	yes	—
5	C₂²×C₈	C₂²	1	2	yes	—
6	C₂×C₄²	C₂²	1	1	yes	characteristic
7	#108	—	2	8	no	—
8	C₄⋊C₈	—	2	4	no	—
9	C₄×C₈	C₄	1	2	yes	—
10	C₄×C₈	C₄	1	2	yes	—
11	C₂²×C₄	Q₈	1	2	yes	—
12	C₂²×C₄	C₂³	1	1	yes	characteristic
13	M₁₆	—	2	8	no	—
14	C₂×C₈	—	2	4	no	—
15	C₂×C₈	C₂×C₄	1	4	yes	—
16	C₂×C₈	D₄	1	4	yes	—
17	C₂×C₈	Q₈	1	4	yes	—
18	C₄²	C₂×C₄	1	1	yes	characteristic
19	C₄²	C₂×C₄	1	1	yes	characteristic
20	C₄²	D₄	1	2	yes	—
21	C₂³	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄	—	2	4	no	—
23	C₂×C₄	C₄⋊C₄	1	2	yes	—
24	C₂×C₄	C₄⋊C₄	1	2	yes	—
25	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄	C₂×D₄	1	2	yes	—
27	C₂×C₄	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄	C₂×Q₈	1	2	yes	—
29	C₈	—	4	4	no	—
30	C₈	C₄⋊C₄	1	8	yes	—
31	C₂²	—	2	2	no	—
32	C₂²	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂²	C₄⋊Q₈	1	2	yes	—
34	C₄	—	2	2	no	—
35	C₄	#108	1	4	yes	complemented
36	C₄	C₂×C₄⋊C₄	1	2	yes	—
37	C₄	#127	1	1	yes	characteristic
38	C₄	C₄⋊Q₈	1	1	yes	characteristic
39	C₂	—	2	2	no	—
40	C₂	#384	1	1	yes	characteristic
41	C₂	C₂×#108	1	2	yes	—

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

N	H ≅ G/N	type
35. C₄	#108	semidirect

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