Subgroups — C₁₂₇×#1358 #30634310

Order 16256.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	#364×C₁₂₇	C₂	1	2	yes	maximal
3	C₂×Q₁₆×C₁₂₇	—	2	2	no	—
4	C₄⋊Q₈×C₁₂₇	C₄	1	2	yes	—
5	M₃₂×C₁₂₇	—	2	2	no	—
6	C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₁₂₇	—	2	2	no	—
8	Q₁₆×C₁₂₇	—	4	2	no	—
9	Q₁₆×C₁₂₇	—	4	2	no	—
10	C₂×C₈×C₁₂₇	D₄	1	2	yes	—
11	C₄⋊C₄×C₁₂₇	—	4	2	no	—
12	C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₁₂₇	—	4	2	no	—
14	Q₈×C₁₂₇	—	4	4	no	—
15	C₂×C₄×C₁₂₇	—	2	1	no	—
16	C₂×C₄×C₁₂₇	—	4	2	no	—
17	C₂×C₄×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₈×C₁₂₇	D₈	1	2	yes	—
19	C₈×C₁₂₇	SD₁₆	1	2	yes	—
20	C₂²×C₁₂₇	#100	1	1	yes	characteristic
21	C₄×C₁₂₇	—	2	2	no	—
22	C₄×C₁₂₇	—	8	2	no	—
23	C₄×C₁₂₇	#102	1	2	yes	—
24	C₂×C₁₂₇	—	2	1	no	—
25	C₂×C₁₂₇	#331	1	1	yes	characteristic
26	#1358	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₁₂₇	#1358	1	1	yes	characteristic, direct product factor, Sylow
28	#494	C₂×C₁₂₇	1	1	yes	characteristic
29	#364	C₂×C₁₂₇	1	2	yes	—
30	C₂×Q₁₆	—	2	2	no	—
31	C₄⋊Q₈	C₄×C₁₂₇	1	2	yes	—
32	M₃₂	—	2	2	no	—
33	C₄×C₈	C₂²×C₁₂₇	1	1	yes	characteristic
34	C₂×Q₈	—	2	2	no	—
35	Q₁₆	—	4	2	no	—
36	Q₁₆	—	4	2	no	—
37	C₂×C₈	D₄×C₁₂₇	1	2	yes	—
38	C₄⋊C₄	—	4	2	no	—
39	C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
40	C₁₆	—	4	2	no	—
41	Q₈	—	4	4	no	—
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
45	C₈	D₈×C₁₂₇	1	2	yes	—
46	C₈	SD₁₆×C₁₂₇	1	2	yes	—
47	C₂²	#100×C₁₂₇	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	8	2	no	—
50	C₄	#102×C₁₂₇	1	2	yes	—
51	C₂	—	2	1	no	—
52	C₂	#331×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₂₇	#331
commutator	C₄²	C₂×C₄×C₁₂₇
Frattini, cosocle	C₄×C₈	C₂²×C₁₂₇
prime radical	C₂²×C₁₂₇	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₂₇ ◁ C₂×C₄×C₁₂₇ ◁ C₄×C₈×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
26. #1358	C₁₂₇	direct (N × H)
27. C₁₂₇	#1358	direct (N × H)

Maximal subgroups

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

subgroup	index
#494×C₁₂₇	2
#364×C₁₂₇	2
#1358	127

Subgroups — C127×#1358 #30634310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#1358 #30634310