Group #44480433 — subgroups

Subgroups — #1663×C₂₃₉ #44480433

Order 30592.

172 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 60 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	#564×C₂₃₉	C₂	1	1	yes	maximal, characteristic
2	#501×C₂₃₉	C₂	1	2	yes	maximal
3	#491×C₂₃₉	C₂	1	1	yes	maximal, characteristic
4	#330×C₂₃₉	C₂	1	2	yes	maximal
5	#330×C₂₃₉	C₂	1	1	yes	maximal, characteristic
6	C₄⋊Q₈×C₂₃₉	C₂²	1	1	yes	characteristic
7	#125×C₂₃₉	—	2	2	no	—
8	#125×C₂₃₉	—	2	2	no	—
9	#125×C₂₃₉	—	2	2	no	—
10	#125×C₂₃₉	C₂²	1	1	yes	characteristic
11	#125×C₂₃₉	C₂²	1	2	yes	—
12	#107×C₂₃₉	—	2	2	no	—
13	#106×C₂₃₉	—	2	2	no	—
14	#103×C₂₃₉	—	2	2	no	—
15	#97×C₂₃₉	C₂²	1	1	yes	characteristic
16	#97×C₂₃₉	C₂²	1	2	yes	—
17	C₂×Q₈×C₂₃₉	—	2	1	no	—
18	C₂×C₈×C₂₃₉	—	2	2	no	—
19	C₂×C₈×C₂₃₉	—	2	1	no	—
20	C₄⋊C₄×C₂₃₉	—	2	2	no	—
21	C₄⋊C₄×C₂₃₉	—	2	2	no	—
22	C₄⋊C₄×C₂₃₉	—	2	2	no	—
23	C₄⋊C₄×C₂₃₉	—	2	2	no	—
24	C₄⋊C₄×C₂₃₉	—	2	2	no	—
25	C₄⋊C₄×C₂₃₉	—	2	2	no	—
26	C₄⋊C₄×C₂₃₉	—	2	2	no	—
27	C₄⋊C₄×C₂₃₉	D₄	1	2	yes	—
28	C₄⋊C₄×C₂₃₉	D₄	1	2	yes	—
29	C₄⋊C₄×C₂₃₉	D₄	1	2	yes	—
30	C₄²×C₂₃₉	—	2	2	no	—
31	C₄²×C₂₃₉	C₂³	1	1	yes	characteristic
32	Q₈×C₂₃₉	—	4	2	no	—
33	C₂×C₄×C₂₃₉	—	2	2	no	—
34	C₂×C₄×C₂₃₉	—	2	2	no	—
35	C₂×C₄×C₂₃₉	—	2	2	no	—
36	C₂×C₄×C₂₃₉	—	4	1	no	—
37	C₂×C₄×C₂₃₉	C₂×D₄	1	2	yes	—
38	C₂×C₄×C₂₃₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₂₃₉	—	2	4	no	—
40	C₈×C₂₃₉	—	4	1	no	—
41	C₂²×C₂₃₉	#120	1	1	yes	characteristic
42	C₄×C₂₃₉	—	2	1	no	—
43	C₄×C₂₃₉	—	2	2	no	—
44	C₄×C₂₃₉	—	4	2	no	—
45	C₄×C₂₃₉	—	4	2	no	—
46	C₄×C₂₃₉	—	4	2	no	—
47	C₄×C₂₃₉	—	8	1	no	—
48	C₂×C₂₃₉	#454	1	1	yes	characteristic
49	C₂×C₂₃₉	#456	1	2	yes	—
50	C₂₃₉	#1663	1	1	yes	characteristic, direct product factor, Sylow
51	#1663	C₂₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	#564	C₂×C₂₃₉	1	1	yes	characteristic
53	#501	C₂×C₂₃₉	1	2	yes	—
54	#491	C₂×C₂₃₉	1	1	yes	characteristic
55	#330	C₂×C₂₃₉	1	2	yes	—
56	#330	C₂×C₂₃₉	1	1	yes	characteristic
57	C₄⋊Q₈	C₂²×C₂₃₉	1	1	yes	characteristic
58	#125	—	2	2	no	—
59	#125	—	2	2	no	—
60	#125	—	2	2	no	—
61	#125	C₂²×C₂₃₉	1	1	yes	characteristic
62	#125	C₂²×C₂₃₉	1	2	yes	—
63	#107	—	2	2	no	—
64	#106	—	2	2	no	—
65	#103	—	2	2	no	—
66	#97	C₂²×C₂₃₉	1	1	yes	characteristic
67	#97	C₂²×C₂₃₉	1	2	yes	—
68	C₂×Q₈	—	2	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	2	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	2	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	D₄×C₂₃₉	1	2	yes	—
79	C₄⋊C₄	D₄×C₂₃₉	1	2	yes	—
80	C₄⋊C₄	D₄×C₂₃₉	1	2	yes	—
81	C₄²	—	2	2	no	—
82	C₄²	C₂³×C₂₃₉	1	1	yes	characteristic
83	Q₈	—	4	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	C₂×D₄×C₂₃₉	1	2	yes	—
89	C₂×C₄	C₂×D₄×C₂₃₉	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	4	1	no	—
92	C₂²	#120×C₂₃₉	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	4	2	no	—
97	C₄	—	4	2	no	—
98	C₄	—	8	1	no	—
99	C₂	#454×C₂₃₉	1	1	yes	characteristic
100	C₂	#456×C₂₃₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#564×C₂₃₉

C₂

yes

maximal, characteristic

#501×C₂₃₉

C₂

yes

maximal

#491×C₂₃₉

C₂

yes

maximal, characteristic

#330×C₂₃₉

C₂

yes

maximal

#330×C₂₃₉

C₂

yes

maximal, characteristic

C₄⋊Q₈×C₂₃₉

C₂²

yes

characteristic

#125×C₂₃₉

—

#125×C₂₃₉

—

#125×C₂₃₉

—

#125×C₂₃₉

C₂²

yes

characteristic

#125×C₂₃₉

C₂²

yes

—

#107×C₂₃₉

—

#106×C₂₃₉

—

#103×C₂₃₉

—

#97×C₂₃₉

C₂²

yes

characteristic

#97×C₂₃₉

C₂²

yes

—

C₂×Q₈×C₂₃₉

—

C₂×C₈×C₂₃₉

—

C₂×C₈×C₂₃₉

—

C₄⋊C₄×C₂₃₉

—

C₄⋊C₄×C₂₃₉

—

C₄⋊C₄×C₂₃₉

—

C₄⋊C₄×C₂₃₉

—

C₄⋊C₄×C₂₃₉

—

C₄⋊C₄×C₂₃₉

—

C₄⋊C₄×C₂₃₉

—

C₄⋊C₄×C₂₃₉

D₄

yes

—

C₄⋊C₄×C₂₃₉

D₄

yes

—

C₄⋊C₄×C₂₃₉

D₄

yes

—

C₄²×C₂₃₉

—

C₄²×C₂₃₉

C₂³

yes

characteristic

Q₈×C₂₃₉

—

C₂×C₄×C₂₃₉

—

C₂×C₄×C₂₃₉

—

C₂×C₄×C₂₃₉

—

C₂×C₄×C₂₃₉

—

C₂×C₄×C₂₃₉

C₂×D₄

yes

—

C₂×C₄×C₂₃₉

C₂×D₄

yes

characteristic

C₈×C₂₃₉

—

C₈×C₂₃₉

—

C₂²×C₂₃₉

#120

yes

characteristic

C₄×C₂₃₉

—

C₄×C₂₃₉

—

C₄×C₂₃₉

—

C₄×C₂₃₉

—

C₄×C₂₃₉

—

C₄×C₂₃₉

—

C₂×C₂₃₉

#454

yes

characteristic

C₂×C₂₃₉

#456

yes

—

C₂₃₉

#1663

yes

characteristic, direct product factor, Sylow

#1663

C₂₃₉

yes

maximal, characteristic, direct product factor, Sylow

#564

C₂×C₂₃₉

yes

characteristic

#501

C₂×C₂₃₉

yes

—

#491

C₂×C₂₃₉

yes

characteristic

#330

C₂×C₂₃₉

yes

—

#330

C₂×C₂₃₉

yes

characteristic

C₄⋊Q₈

C₂²×C₂₃₉

yes

—

—

—

C₂²×C₂₃₉

yes

characteristic

#125

C₂²×C₂₃₉

yes

—

—

—

—

C₂²×C₂₃₉

yes

characteristic

#97

C₂²×C₂₃₉

yes

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₂₃₉

yes

—

C₄⋊C₄

D₄×C₂₃₉

yes

—

C₄⋊C₄

D₄×C₂₃₉

yes

—

C₄²

—

C₄²

C₂³×C₂₃₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₂₃₉

yes

—

C₂×C₄

C₂×D₄×C₂₃₉

yes

characteristic

C₈

—

C₈

—

C₂²

#120×C₂₃₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

#454×C₂₃₉

yes

characteristic

100

C₂

#456×C₂₃₉

yes

—

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃₉ ◁ C₄²×C₂₃₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₂₃₉

#120

commutator, Frattini, cosocle

C₄²

C₂³×C₂₃₉

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₂₃₉ ◁ C₄²×C₂₃₉ ◁ G

N	H ≅ G/N	type
50. C₂₃₉	#1663	direct (N × H)
51. #1663	C₂₃₉	direct (N × H)

H ≅ G/N

type

50. C₂₃₉

#1663

direct (N × H)

51. #1663

C₂₃₉

direct (N × H)

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

subgroup	index
#564×C₂₃₉	2
#501×C₂₃₉	2
#491×C₂₃₉	2
#330×C₂₃₉	2
#1663	239

subgroup

index

#564×C₂₃₉

#501×C₂₃₉

#491×C₂₃₉

#330×C₂₃₉

#1663

239

Subgroups — #1663×C₂₃₉ #44480433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1663×C239 #44480433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1663×C₂₃₉ #44480433