Subgroups — C₂×Q₈×D₁₂₇ #16861248

Order 4064.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₅₄	C₂	1	3	yes	maximal, complemented
2	Q₈×D₁₂₇	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₁₂₇	C₂	1	3	yes	maximal
4	C₂×Q₈×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₂₇	C₂²	1	1	yes	characteristic
6	Dic₂₅₄	C₂²	1	12	yes	complemented
7	C₂×Dic₁₂₇	C₂²	1	3	yes	—
8	C₄×D₁₂₇	C₂²	1	12	yes	—
9	Q₈×C₁₂₇	C₂²	1	4	yes	complemented
10	C₂×C₄×C₁₂₇	C₂²	1	3	yes	—
11	C₂²×C₁₂₇	C₂³	1	1	yes	characteristic
12	C₂×D₁₂₇	Q₈	1	4	yes	direct product factor
13	C₂×D₁₂₇	C₂³	1	2	yes	—
14	C₄×C₁₂₇	C₂³	1	6	yes	—
15	Dic₁₂₇	C₂³	1	6	yes	—
16	C₂×C₁₂₇	C₂×Q₈	1	2	yes	complemented
17	C₂×C₁₂₇	C₂⁴	1	1	yes	characteristic
18	D₁₂₇	C₂×Q₈	1	4	yes	direct product factor
19	C₁₂₇	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
20	C₂²×Q₈	—	127	1	no	maximal, Sylow
21	C₂×Q₈	—	127	8	no	—
22	C₂×Q₈	—	127	3	no	—
23	C₂×Q₈	D₁₂₇	1	1	yes	characteristic, direct product factor
24	C₂²×C₄	—	127	3	no	—
25	C₂³	—	127	1	no	—
26	Q₈	—	127	12	no	—
27	Q₈	C₂×D₁₂₇	1	4	yes	direct product factor
28	C₂×C₄	—	127	3	no	—
29	C₂×C₄	—	127	12	no	—
30	C₂×C₄	C₂×D₁₂₇	1	3	yes	—
31	C₂²	—	127	4	no	—
32	C₂²	—	127	2	no	—
33	C₂²	C₂²×D₁₂₇	1	1	yes	characteristic
34	C₄	—	127	6	no	—
35	C₄	C₂²×D₁₂₇	1	6	yes	—
36	C₂	—	127	4	no	—
37	C₂	Q₈×D₁₂₇	1	2	yes	direct product factor
38	C₂	C₂³×D₁₂₇	1	1	yes	characteristic

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

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