Group #44574259 — subgroups

Subgroups — C₁₂₇×#10586 #44574259

Order 32512.

350 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇×#2845	C₂	1	1	yes	maximal, characteristic
2	C₁₂₇×#1836	C₂	1	3	yes	maximal
3	C₁₂₇×#1295	C₂	1	3	yes	maximal
4	C₂×#97×C₁₂₇	C₂²	1	3	yes	—
5	#398×C₁₂₇	—	2	6	no	—
6	#384×C₁₂₇	C₂²	1	1	yes	characteristic
7	#382×C₁₂₇	C₂²	1	3	yes	—
8	#340×C₁₂₇	—	2	6	no	—
9	C₂²×C₈×C₁₂₇	—	2	3	no	—
10	C₂×C₄⋊C₄×C₁₂₇	—	2	3	no	—
11	C₂×C₄⋊C₄×C₁₂₇	—	2	6	no	—
12	C₂×C₄⋊C₄×C₁₂₇	D₄	1	6	yes	—
13	C₂×C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
14	#97×C₁₂₇	—	2	3	no	—
15	#97×C₁₂₇	Q₈	1	6	yes	—
16	#95×C₁₂₇	—	2	2	no	—
17	#95×C₁₂₇	—	2	6	no	—
18	C₂²×C₄×C₁₂₇	—	2	6	no	—
19	C₂²×C₄×C₁₂₇	—	4	1	no	—
20	C₂²×C₄×C₁₂₇	C₂×D₄	1	3	yes	—
21	C₂×C₈×C₁₂₇	—	2	6	no	—
22	C₂×C₈×C₁₂₇	—	4	3	no	—
23	C₂×C₈×C₁₂₇	—	4	3	no	—
24	C₄⋊C₄×C₁₂₇	—	4	6	no	—
25	C₄⋊C₄×C₁₂₇	—	4	6	no	—
26	C₄⋊C₄×C₁₂₇	—	8	6	no	—
27	C₄²×C₁₂₇	C₂×Q₈	1	3	yes	—
28	C₄²×C₁₂₇	#41	1	1	yes	characteristic
29	C₂³×C₁₂₇	#120	1	1	yes	characteristic
30	C₂×C₄×C₁₂₇	—	2	3	no	—
31	C₂×C₄×C₁₂₇	—	2	3	no	—
32	C₂×C₄×C₁₂₇	—	4	6	no	—
33	C₂×C₄×C₁₂₇	—	4	6	no	—
34	C₂×C₄×C₁₂₇	—	4	6	no	—
35	C₂×C₄×C₁₂₇	—	8	3	no	—
36	C₂×C₄×C₁₂₇	C₂²⋊Q₈	1	3	yes	—
37	C₂×C₄×C₁₂₇	C₄⋊Q₈	1	3	yes	—
38	C₈×C₁₂₇	—	4	6	no	—
39	C₂²×C₁₂₇	#395	1	1	yes	characteristic
40	C₂²×C₁₂₇	#454	1	3	yes	—
41	C₂²×C₁₂₇	#455	1	3	yes	—
42	C₄×C₁₂₇	—	2	3	no	—
43	C₄×C₁₂₇	—	2	3	no	—
44	C₄×C₁₂₇	—	8	6	no	—
45	C₄×C₁₂₇	—	16	1	no	—
46	#10586	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×C₁₂₇	#1658	1	1	yes	characteristic
48	C₂×C₁₂₇	#1662	1	3	yes	—
49	C₂×C₁₂₇	#2061	1	3	yes	—
50	#2845	C₂×C₁₂₇	1	1	yes	characteristic
51	#1836	C₂×C₁₂₇	1	3	yes	—
52	#1295	C₂×C₁₂₇	1	3	yes	—
53	C₁₂₇	#10586	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×#97	C₂²×C₁₂₇	1	3	yes	—
55	#398	—	2	6	no	—
56	#384	C₂²×C₁₂₇	1	1	yes	characteristic
57	#382	C₂²×C₁₂₇	1	3	yes	—
58	#340	—	2	6	no	—
59	C₂²×C₈	—	2	3	no	—
60	C₂×C₄⋊C₄	—	2	3	no	—
61	C₂×C₄⋊C₄	—	2	6	no	—
62	C₂×C₄⋊C₄	D₄×C₁₂₇	1	6	yes	—
63	C₂×C₄²	C₂³×C₁₂₇	1	1	yes	characteristic
64	#97	—	2	3	no	—
65	#97	Q₈×C₁₂₇	1	6	yes	—
66	#95	—	2	2	no	—
67	#95	—	2	6	no	—
68	C₂²×C₄	—	2	6	no	—
69	C₂²×C₄	—	4	1	no	—
70	C₂²×C₄	C₂×D₄×C₁₂₇	1	3	yes	—
71	C₂×C₈	—	2	6	no	—
72	C₂×C₈	—	4	3	no	—
73	C₂×C₈	—	4	3	no	—
74	C₄⋊C₄	—	4	6	no	—
75	C₄⋊C₄	—	4	6	no	—
76	C₄⋊C₄	—	8	6	no	—
77	C₄²	C₂×Q₈×C₁₂₇	1	3	yes	—
78	C₄²	#41×C₁₂₇	1	1	yes	characteristic
79	C₂³	#120×C₁₂₇	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	8	3	no	—
86	C₂×C₄	C₂²⋊Q₈×C₁₂₇	1	3	yes	—
87	C₂×C₄	C₄⋊Q₈×C₁₂₇	1	3	yes	—
88	C₈	—	4	6	no	—
89	C₂²	#395×C₁₂₇	1	1	yes	characteristic
90	C₂²	#454×C₁₂₇	1	3	yes	—
91	C₂²	#455×C₁₂₇	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	16	1	no	—
96	C₂	C₁₂₇×#1658	1	1	yes	characteristic
97	C₂	C₁₂₇×#1662	1	3	yes	—
98	C₂	C₁₂₇×#2061	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₂₇×#2845

C₂

yes

maximal, characteristic

C₁₂₇×#1836

C₂

yes

maximal

C₁₂₇×#1295

C₂

yes

maximal

C₂×#97×C₁₂₇

C₂²

yes

—

#398×C₁₂₇

—

#384×C₁₂₇

C₂²

yes

characteristic

#382×C₁₂₇

C₂²

yes

—

#340×C₁₂₇

—

C₂²×C₈×C₁₂₇

—

C₂×C₄⋊C₄×C₁₂₇

—

C₂×C₄⋊C₄×C₁₂₇

—

C₂×C₄⋊C₄×C₁₂₇

D₄

yes

—

C₂×C₄²×C₁₂₇

C₂³

yes

characteristic

#97×C₁₂₇

—

#97×C₁₂₇

Q₈

yes

—

#95×C₁₂₇

—

#95×C₁₂₇

—

C₂²×C₄×C₁₂₇

—

C₂²×C₄×C₁₂₇

—

C₂²×C₄×C₁₂₇

C₂×D₄

yes

—

C₂×C₈×C₁₂₇

—

C₂×C₈×C₁₂₇

—

C₂×C₈×C₁₂₇

—

C₄⋊C₄×C₁₂₇

—

C₄⋊C₄×C₁₂₇

—

C₄⋊C₄×C₁₂₇

—

C₄²×C₁₂₇

C₂×Q₈

yes

—

C₄²×C₁₂₇

yes

C₂³×C₁₂₇

yes

C₂×C₄×C₁₂₇

—

C₂×C₄×C₁₂₇

—

C₂×C₄×C₁₂₇

—

C₂×C₄×C₁₂₇

—

C₂×C₄×C₁₂₇

—

C₂×C₄×C₁₂₇

—

C₂×C₄×C₁₂₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₂₇

C₄⋊Q₈

yes

—

C₈×C₁₂₇

—

C₂²×C₁₂₇

#395

yes

characteristic

C₂²×C₁₂₇

#454

yes

—

C₂²×C₁₂₇

#455

yes

—

C₄×C₁₂₇

—

C₄×C₁₂₇

—

C₄×C₁₂₇

—

C₄×C₁₂₇

—

#10586

C₁₂₇

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₁₂₇

#1658

yes

characteristic

C₂×C₁₂₇

#1662

yes

—

C₂×C₁₂₇

#2061

yes

—

#2845

C₂×C₁₂₇

yes

characteristic

#1836

C₂×C₁₂₇

yes

—

#1295

C₂×C₁₂₇

yes

—

C₁₂₇

#10586

yes

characteristic, direct product factor, Sylow

C₂×#97

C₂²×C₁₂₇

yes

—

#398

—

#384

C₂²×C₁₂₇

yes

characteristic

#382

C₂²×C₁₂₇

yes

—

#340

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₁₂₇

yes

—

C₂×C₄²

C₂³×C₁₂₇

yes

characteristic

#97

—

#97

Q₈×C₁₂₇

yes

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₂₇

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×Q₈×C₁₂₇

yes

—

C₄²

#41×C₁₂₇

yes

characteristic

C₂³

#120×C₁₂₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Q₈×C₁₂₇

yes

—

C₂×C₄

C₄⋊Q₈×C₁₂₇

yes

—

C₈

—

C₂²

#395×C₁₂₇

yes

characteristic

C₂²

#454×C₁₂₇

yes

—

C₂²

#455×C₁₂₇

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

C₁₂₇×#1658

yes

characteristic

C₂

C₁₂₇×#1662

yes

—

C₂

C₁₂₇×#2061

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₂₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₂₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₂₇ ◁ C₂×C₄²×C₁₂₇ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₂₇

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₂₇

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₂₇ ◁ C₂×C₄²×C₁₂₇ ◁ G

N	H ≅ G/N	type
46. #10586	C₁₂₇	direct (N × H)
53. C₁₂₇	#10586	direct (N × H)

H ≅ G/N

type

46. #10586

C₁₂₇

direct (N × H)

53. C₁₂₇

#10586

direct (N × H)

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

subgroup	index
C₁₂₇×#2845	2
C₁₂₇×#1836	2
C₁₂₇×#1295	2
#10586	127

subgroup

index

C₁₂₇×#2845

C₁₂₇×#1836

C₁₂₇×#1295

#10586

127

Subgroups — C₁₂₇×#10586 #44574259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C127×#10586 #44574259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#10586 #44574259