Group #31814786 — subgroups

Subgroups — #31814786

Order 17792.

408 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 165 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	#22580859	C₂	1	3	yes	maximal
2	#22580851	C₂	1	3	yes	maximal
3	#22580837	C₂	1	6	yes	maximal
4	#22580821	C₂	1	2	yes	maximal
5	C₄³×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₁₃₉	C₂²	1	3	yes	—
8	C₂×Dic₁₃₉⋊C₄	C₂²	1	6	yes	—
9	C₁₃₉⋊#95	C₂²	1	6	yes	—
10	C₁₃₉⋊#95	C₂²	1	6	yes	—
11	C₁₃₉⋊#95	C₂²	1	6	yes	—
12	C₂×C₄²×C₁₃₉	C₂²	1	3	yes	—
13	C₂×C₄²×C₁₃₉	C₂²	1	3	yes	—
14	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₂₇₈	—	2	6	no	—
16	C₂²×Dic₁₃₉	C₂³	1	6	yes	—
17	C₂²×Dic₁₃₉	C₂³	1	2	yes	—
18	C₄⋊Dic₁₃₉	—	2	6	no	—
19	Dic₁₃₉⋊C₄	—	2	12	no	—
20	C₂²×C₄×C₁₃₉	C₂³	1	3	yes	—
21	C₂²×C₄×C₁₃₉	C₂³	1	3	yes	—
22	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
23	C₄²×C₁₃₉	—	2	6	no	—
24	C₄²×C₁₃₉	—	2	6	no	—
25	C₄²×C₁₃₉	Q₈	1	4	yes	complemented
26	Dic₂₇₈	—	4	4	no	—
27	C₂×Dic₁₃₉	—	2	12	no	—
28	C₂×Dic₁₃₉	—	2	6	no	—
29	C₂×Dic₁₃₉	—	2	6	no	—
30	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₁₃₉	—	2	3	no	—
32	C₂×C₄×C₁₃₉	—	2	3	no	—
33	C₂×C₄×C₁₃₉	—	2	3	no	—
34	C₂×C₄×C₁₃₉	—	2	3	no	—
35	C₂×C₄×C₁₃₉	C₂×Q₈	1	6	yes	—
36	C₂×C₄×C₁₃₉	#41	1	6	yes	—
37	C₂×C₄×C₁₃₉	#41	1	6	yes	—
38	C₂²×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
39	C₂²×C₁₃₉	C₂×#41	1	3	yes	—
40	C₂²×C₁₃₉	C₂×#41	1	3	yes	—
41	C₄×C₁₃₉	—	2	6	no	—
42	C₄×C₁₃₉	—	2	6	no	—
43	C₄×C₁₃₉	#126	1	4	yes	—
44	Dic₁₃₉	—	4	2	no	—
45	Dic₁₃₉	—	4	6	no	—
46	C₂×C₁₃₉	C₂×#126	1	1	yes	characteristic
47	C₂×C₁₃₉	#529	1	3	yes	—
48	C₂×C₁₃₉	#533	1	3	yes	—
49	C₁₃₉	#2863	1	1	yes	characteristic, complemented, Sylow
50	#2863	—	139	1	no	maximal, Sylow
51	#391	—	139	3	no	—
52	#389	—	139	3	no	—
53	#387	—	139	6	no	—
54	#383	—	139	2	no	—
55	C₄³	D₁₃₉	1	1	yes	characteristic
56	C₂²×Q₈	—	139	1	no	—
57	C₂×C₄⋊C₄	—	139	6	no	—
58	C₂×C₄⋊C₄	—	139	3	no	—
59	C₂×C₄²	C₂×D₁₃₉	1	3	yes	—
60	C₂×C₄²	C₂×D₁₃₉	1	3	yes	—
61	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
62	#95	—	139	6	no	—
63	#95	—	139	6	no	—
64	#95	—	139	6	no	—
65	C₂×Q₈	—	278	6	no	—
66	C₂²×C₄	—	139	2	no	—
67	C₂²×C₄	—	139	6	no	—
68	C₂²×C₄	C₂²×D₁₃₉	1	3	yes	—
69	C₂²×C₄	C₂²×D₁₃₉	1	3	yes	—
70	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
71	C₄⋊C₄	—	278	12	no	—
72	C₄⋊C₄	—	278	6	no	—
73	C₄²	—	2	6	no	—
74	C₄²	—	2	6	no	—
75	C₄²	Dic₂₇₈	1	4	yes	complemented
76	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
77	Q₈	—	556	4	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	278	6	no	—
83	C₂×C₄	—	278	12	no	—
84	C₂×C₄	—	278	6	no	—
85	C₂×C₄	C₂×Dic₂₇₈	1	6	yes	—
86	C₂×C₄	#14555785	1	6	yes	—
87	C₂×C₄	#14555785	1	6	yes	—
88	C₂²	C₂²×Dic₂₇₈	1	1	yes	characteristic
89	C₂²	C₂×#14555785	1	3	yes	—
90	C₂²	C₂×#14555785	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	2	6	no	—
93	C₄	—	556	2	no	—
94	C₄	—	556	6	no	—
95	C₄	#17984836	1	4	yes	—
96	C₂	C₂×#17984836	1	1	yes	characteristic
97	C₂	#22581487	1	3	yes	—
98	C₂	#22581510	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22580859

C₂

yes

maximal

#22580851

C₂

yes

maximal

#22580837

C₂

yes

maximal

#22580821

C₂

yes

maximal

C₄³×C₁₃₉

C₂

yes

maximal, characteristic

C₂²×Dic₂₇₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃₉

C₂²

yes

—

C₂×Dic₁₃₉⋊C₄

C₂²

yes

—

C₁₃₉⋊#95

C₂²

yes

—

C₁₃₉⋊#95

C₂²

yes

—

C₁₃₉⋊#95

C₂²

yes

—

C₂×C₄²×C₁₃₉

C₂²

yes

—

C₂×C₄²×C₁₃₉

C₂²

yes

—

C₂×C₄²×C₁₃₉

C₂²

yes

characteristic

C₂×Dic₂₇₈

—

C₂²×Dic₁₃₉

C₂³

yes

—

C₂²×Dic₁₃₉

C₂³

yes

—

C₄⋊Dic₁₃₉

—

Dic₁₃₉⋊C₄

—

C₂²×C₄×C₁₃₉

C₂³

yes

—

C₂²×C₄×C₁₃₉

C₂³

yes

—

C₂²×C₄×C₁₃₉

C₂³

yes

characteristic

C₄²×C₁₃₉

—

C₄²×C₁₃₉

—

C₄²×C₁₃₉

Q₈

yes

complemented

Dic₂₇₈

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂³×C₁₃₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂×Q₈

yes

—

C₂×C₄×C₁₃₉

#41

yes

—

C₂×C₄×C₁₃₉

#41

yes

—

C₂²×C₁₃₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₃₉

C₂×#41

yes

—

C₂²×C₁₃₉

C₂×#41

yes

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

#126

yes

—

Dic₁₃₉

—

Dic₁₃₉

—

C₂×C₁₃₉

C₂×#126

yes

characteristic

C₂×C₁₃₉

#529

yes

—

C₂×C₁₃₉

#533

yes

—

C₁₃₉

#2863

yes

characteristic, complemented, Sylow

#2863

—

139

maximal, Sylow

#391

—

139

—

#389

—

139

—

#387

—

139

—

#383

—

139

—

C₄³

D₁₃₉

yes

characteristic

C₂²×Q₈

—

139

—

C₂×C₄⋊C₄

—

139

—

C₂×C₄⋊C₄

—

139

—

C₂×C₄²

C₂×D₁₃₉

yes

—

C₂×C₄²

C₂×D₁₃₉

yes

—

C₂×C₄²

C₂×D₁₃₉

yes

characteristic

#95

—

139

—

#95

—

139

—

#95

—

139

—

C₂×Q₈

—

278

—

C₂²×C₄

—

139

—

C₂²×C₄

—

139

—

C₂²×C₄

C₂²×D₁₃₉

yes

—

C₂²×C₄

C₂²×D₁₃₉

yes

—

C₂²×C₄

C₂²×D₁₃₉

yes

characteristic

C₄⋊C₄

—

278

—

C₄⋊C₄

—

278

—

C₄²

—

C₄²

—

C₄²

Dic₂₇₈

yes

complemented

C₂³

C₂³×D₁₃₉

yes

characteristic

Q₈

—

556

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

C₂×Dic₂₇₈

yes

—

C₂×C₄

#14555785

yes

—

C₂×C₄

#14555785

yes

—

C₂²

C₂²×Dic₂₇₈

yes

characteristic

C₂²

C₂×#14555785

yes

—

C₂²

C₂×#14555785

yes

—

C₄

—

C₄

—

C₄

—

556

—

C₄

—

556

—

C₄

#17984836

yes

—

C₂

C₂×#17984836

yes

characteristic

C₂

#22581487

yes

—

C₂

#22581510

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃₉
commutator, socle, prime radical, cosocle	C₂³×C₁₃₉	C₂⁴
Fitting	C₄³×C₁₃₉	C₂
hypercenter	C₄³	D₁₃₉
hypocenter	C₁₃₉	#2863
LCS	G ▷ C₂³×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃₉

commutator, socle, prime radical, cosocle

C₂³×C₁₃₉

C₂⁴

Fitting

C₄³×C₁₃₉

C₂

hypercenter

C₄³

D₁₃₉

C₁₃₉

G ▷ C₂³×C₁₃₉ ▷ C₁₃₉

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
25. C₄²×C₁₃₉	Q₈	semidirect
49. C₁₃₉	#2863	semidirect
75. C₄²	Dic₂₇₈	semidirect

H ≅ G/N

type

25. C₄²×C₁₃₉

Q₈

semidirect

49. C₁₃₉

#2863

semidirect

75. C₄²

Dic₂₇₈

semidirect

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

subgroup	index
#22580859	2
#22580851	2
#22580837	2
#22580821	2
C₄³×C₁₃₉	2
#2863	139

subgroup

index

C₄³×C₁₃₉

139

Subgroups — #31814786

Conjugacy classes of subgroups

Complements

Maximal subgroups