Group #23765191 — subgroups

Subgroups — C₂×#19098392 #23765191

Order 10112.

144 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579097	C₂	1	1	yes	maximal, characteristic
3	#19098392	C₂	1	4	yes	maximal, direct product factor
4	C₂×#108×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#11929608	—	2	1	no	—
6	C₂×C₇₉⋊C₁₆	C₄	1	2	yes	—
7	C₂×C₇₉⋊C₁₆	C₄	1	2	yes	—
8	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
9	#14579097	—	2	1	no	—
10	#14579097	C₂²	1	2	yes	—
11	C₂×M₁₆×C₇₉	—	2	1	no	—
12	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	#108×C₇₉	—	2	1	no	—
14	#108×C₇₉	C₂²	1	2	yes	—
15	#11929608	—	2	2	no	—
16	#11929608	—	4	1	no	—
17	C₂×C₇₉⋊C₈	—	4	1	no	—
18	C₇₉⋊C₁₆	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
20	M₁₆×C₇₉	—	2	2	no	—
21	M₁₆×C₇₉	—	4	1	no	—
22	C₂×C₈×C₇₉	—	4	1	no	—
23	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
27	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
28	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
29	C₂³×C₇₉	Q₁₆	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₉	Q₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
36	C₈×C₇₉	—	4	2	no	—
37	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
38	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
41	C₇₉⋊C₈	—	4	2	no	—
42	C₂²×C₇₉	—	2	2	no	—
43	C₂²×C₇₉	#107	1	1	yes	characteristic
44	C₂²×C₇₉	#107	1	1	yes	characteristic
45	C₂²×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₇₉	#107	1	1	yes	characteristic
47	C₄×C₇₉	#107	1	1	yes	characteristic
48	C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
50	C₂×C₇₉	—	2	1	no	—
51	C₂×C₇₉	—	2	1	no	—
52	C₂×C₇₉	#368	1	2	yes	complemented
53	C₂×C₇₉	C₂×#107	1	1	yes	characteristic
54	C₂×#368	—	79	1	no	maximal, Sylow
55	C₇₉	C₂×#368	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₁₆	—	79	1	no	—
57	C₂×#108	—	79	1	no	—
58	C₂×#108	D₇₉	1	1	yes	characteristic
59	#368	—	79	4	no	—
60	C₂×M₁₆	—	2	1	no	—
61	C₂×M₁₆	—	158	1	no	—
62	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
63	C₂×C₁₆	—	79	2	no	—
64	C₂×C₁₆	—	79	2	no	—
65	C₂×C₁₆	—	79	2	no	—
66	#108	—	2	1	no	—
67	#108	—	79	2	no	—
68	#108	—	158	1	no	—
69	#108	C₂×D₇₉	1	2	yes	—
70	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	4	1	no	—
73	M₁₆	—	316	1	no	—
74	M₁₆	—	158	2	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	—	316	1	no	—
77	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
78	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
79	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
80	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
83	C₁₆	—	79	4	no	—
84	C₂³	#11929614	1	1	yes	characteristic
85	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
86	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
87	C₂×C₄	#11929609	1	1	yes	characteristic
88	C₂×C₄	#11929609	1	1	yes	characteristic
89	C₂×C₄	#11929614	1	1	yes	characteristic
90	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	316	2	no	—
93	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
94	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
95	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
96	C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
97	C₂²	—	2	2	no	—
98	C₂²	#14579094	1	1	yes	characteristic
99	C₂²	#14579094	1	1	yes	characteristic
100	C₂²	C₂×#11929614	1	1	yes	characteristic
101	C₄	#14579094	1	1	yes	characteristic
102	C₄	#14579094	1	1	yes	characteristic
103	C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
104	C₄	C₂×#11929609	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	2	1	no	—
107	C₂	#19098392	1	2	yes	direct product factor
108	C₂	C₂×#14579094	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₇₉⋊C₁₆

C₂

yes

maximal, characteristic

C₂×#14579097

C₂

yes

maximal, characteristic

#19098392

C₂

yes

maximal, direct product factor

C₂×#108×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

—

C₂×C₇₉⋊C₁₆

C₄

yes

—

C₂×C₇₉⋊C₁₆

C₄

yes

—

C₂×C₇₉⋊C₁₆

C₂²

yes

—

#14579097

—

#14579097

C₂²

yes

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#108×C₇₉

—

#108×C₇₉

C₂²

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₇₉⋊C₁₆

C₂×C₄

yes

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

Q₁₆

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

Q₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

C₄⋊C₄

yes

characteristic

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

C₂×Q₈

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

C₂×Q₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×#108

—

C₂×#108

D₇₉

yes

characteristic

#368

—

C₂×M₁₆

—

C₂×M₁₆

—

158

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#108

—

#108

—

158

—

#108

C₂×D₇₉

yes

—

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

316

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

316

—

C₂×C₈

Dic₁₅₈

yes

characteristic

C₂×C₈

Dic₁₅₈

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₁₆

—

C₂³

#11929614

yes

characteristic

C₂×C₄

Dic₇₉⋊C₄

yes

characteristic

C₂×C₄

Dic₇₉⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

C₈

—

C₈

—

316

—

C₈

Dic₇₉⋊C₄

yes

characteristic

C₈

Dic₇₉⋊C₄

yes

characteristic

C₈

C₂×C₄×D₇₉

yes

characteristic

C₈

C₂×Dic₁₅₈

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

100

C₂²

C₂×#11929614

yes

characteristic

101

C₄

#14579094

yes

characteristic

102

C₄

#14579094

yes

characteristic

103

C₄

C₂×Dic₇₉⋊C₄

yes

characteristic

104

C₄

C₂×#11929609

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

#19098392

yes

direct product factor

108

C₂

C₂×#14579094

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#11929609
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₂×#108×C₇₉	C₂
socle	C₂²×C₇₉	#107
prime radical	C₂³×C₇₉	Q₁₆
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₂×#108	D₇₉
hypocenter	C₇₉	C₂×#368
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

#11929609

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₂×#108×C₇₉

C₂

socle

C₂²×C₇₉

#107

prime radical

C₂³×C₇₉

Q₁₆

cosocle

C₂×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
3. #19098392	C₂	direct (N × H)
52. C₂×C₇₉	#368	semidirect
55. C₇₉	C₂×#368	semidirect
107. C₂	#19098392	direct (N × H)

H ≅ G/N

type

3. #19098392

C₂

direct (N × H)

52. C₂×C₇₉

#368

semidirect

55. C₇₉

C₂×#368

semidirect

107. C₂

#19098392

direct (N × H)

Subgroups — C₂×#19098392 #23765191

Conjugacy classes of subgroups

Complements

Subgroups — C2×#19098392 #23765191

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19098392 #23765191