Subgroups — C₁₂₇×#1355 #30634307

Order 16256.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#490×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	#347×C₁₂₇	C₂	1	2	yes	maximal, complemented
3	#127×C₁₂₇	C₄	1	1	yes	characteristic
4	#125×C₁₂₇	C₄	1	1	yes	characteristic
5	M₃₂×C₁₂₇	—	2	2	no	—
6	#102×C₁₂₇	—	2	2	no	—
7	#97×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₂×D₄×C₁₂₇	—	2	1	no	—
9	C₂×D₄×C₁₂₇	—	4	1	no	—
10	C₂×C₈×C₁₂₇	D₄	1	2	yes	—
11	C₄⋊C₄×C₁₂₇	—	2	1	no	—
12	C₄⋊C₄×C₁₂₇	—	4	1	no	—
13	C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₁₂₇	—	2	4	no	—
15	C₂³×C₁₂₇	—	4	1	no	—
16	D₄×C₁₂₇	—	4	2	no	—
17	D₄×C₁₂₇	—	8	2	no	—
18	C₂×C₄×C₁₂₇	—	2	1	no	—
19	C₂×C₄×C₁₂₇	—	4	1	no	—
20	C₂×C₄×C₁₂₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₁₂₇	—	2	2	no	—
22	C₂²×C₁₂₇	—	8	2	no	—
23	C₂²×C₁₂₇	—	8	1	no	—
24	C₂²×C₁₂₇	#100	1	1	yes	characteristic
25	C₄×C₁₂₇	—	4	1	no	—
26	C₄×C₁₂₇	—	8	1	no	—
27	C₄×C₁₂₇	#104	1	2	yes	—
28	C₂×C₁₂₇	—	2	1	no	—
29	C₂×C₁₂₇	—	16	1	no	—
30	C₂×C₁₂₇	#329	1	1	yes	characteristic
31	#1355	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₁₂₇	#1355	1	1	yes	characteristic, direct product factor, Sylow
33	#490	C₂×C₁₂₇	1	1	yes	characteristic
34	#347	C₂×C₁₂₇	1	2	yes	complemented
35	#127	C₄×C₁₂₇	1	1	yes	characteristic
36	#125	C₄×C₁₂₇	1	1	yes	characteristic
37	M₃₂	—	2	2	no	—
38	#102	—	2	2	no	—
39	#97	C₂²×C₁₂₇	1	1	yes	characteristic
40	C₂×D₄	—	2	1	no	—
41	C₂×D₄	—	4	1	no	—
42	C₂×C₈	D₄×C₁₂₇	1	2	yes	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×C₄×C₁₂₇	1	1	yes	characteristic
46	C₁₆	—	2	4	no	—
47	C₂³	—	4	1	no	—
48	D₄	—	4	2	no	—
49	D₄	—	8	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊C₄×C₁₂₇	1	1	yes	characteristic
53	C₈	—	2	2	no	—
54	C₂²	—	8	2	no	—
55	C₂²	—	8	1	no	—
56	C₂²	#100×C₁₂₇	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#104×C₁₂₇	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	16	1	no	—
62	C₂	#329×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₂₇	#329
commutator	C₄²	C₂×C₄×C₁₂₇
Frattini, cosocle	#97	C₂²×C₁₂₇
prime radical	#127×C₁₂₇	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₂₇ ◁ C₂×C₄×C₁₂₇ ◁ #97×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #347×C₁₂₇	C₂	semidirect
31. #1355	C₁₂₇	direct (N × H)
32. C₁₂₇	#1355	direct (N × H)
34. #347	C₂×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#490×C₁₂₇	2
#347×C₁₂₇	2
#1355	127

Subgroups — C127×#1355 #30634307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#1355 #30634307