Group #37591179 — subgroups

Subgroups — C₂×#334×C₁₉₃ #37591179

Order 24704.

200 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 152 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	C₂×C₄⋊C₈×C₁₉₃	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₁₉₃	C₂	1	1	yes	maximal, characteristic
3	#334×C₁₉₃	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₉₃	—	2	2	no	—
5	C₂²×C₈×C₁₉₃	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₁₉₃	C₄	1	1	yes	characteristic
7	C₂×C₄²×C₁₉₃	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₁₉₃	—	2	2	no	—
9	C₄⋊C₈×C₁₉₃	C₂²	1	4	yes	—
10	C₄×C₈×C₁₉₃	C₄	1	2	yes	—
11	C₄×C₈×C₁₉₃	C₂²	1	2	yes	—
12	C₂²×C₄×C₁₉₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄×C₁₉₃	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₉₃	Q₈	1	1	yes	characteristic
15	C₂×C₈×C₁₉₃	—	2	2	no	—
16	C₂×C₈×C₁₉₃	—	2	4	no	—
17	C₂×C₈×C₁₉₃	—	4	4	no	—
18	C₂×C₈×C₁₉₃	C₈	1	4	yes	complemented
19	C₂×C₈×C₁₉₃	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₁₉₃	C₂×C₄	1	2	yes	—
21	C₄²×C₁₉₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₉₃	D₄	1	1	yes	characteristic
23	C₄²×C₁₉₃	Q₈	1	1	yes	characteristic
24	C₄²×C₁₉₃	C₂³	1	1	yes	characteristic
25	C₂³×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₉₃	—	2	2	no	—
27	C₂×C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉₃	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₁₉₃	M₁₆	1	2	yes	—
32	C₂×C₄×C₁₉₃	SD₁₆	1	4	yes	—
33	C₂×C₄×C₁₉₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉₃	C₂×Q₈	1	1	yes	characteristic
36	C₈×C₁₉₃	—	2	2	no	—
37	C₈×C₁₉₃	—	4	4	no	—
38	C₈×C₁₉₃	C₂×C₈	1	4	yes	complemented
39	C₂²×C₁₉₃	C₄⋊C₈	1	2	yes	—
40	C₂²×C₁₉₃	#106	1	2	yes	—
41	C₂²×C₁₉₃	#108	1	2	yes	—
42	C₂²×C₁₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₁₉₃	—	2	1	no	—
44	C₄×C₁₉₃	—	2	1	no	—
45	C₄×C₁₉₃	C₄⋊C₈	1	2	yes	—
46	C₄×C₁₉₃	#106	1	2	yes	—
47	C₄×C₁₉₃	C₂²×C₈	1	1	yes	characteristic
48	C₄×C₁₉₃	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₁₉₃	C₂×SD₁₆	1	2	yes	—
50	C₂×C₁₉₃	#334	1	4	yes	direct product factor
51	C₂×C₁₉₃	C₂×C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₁₉₃	C₂×#106	1	1	yes	characteristic
53	C₂×C₁₉₃	C₂×#108	1	1	yes	characteristic
54	C₁₉₃	C₂×#334	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×#334	C₁₉₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₄⋊C₈	C₂×C₁₉₃	1	2	yes	—
57	C₂×C₄×C₈	C₂×C₁₉₃	1	1	yes	characteristic
58	#334	C₂×C₁₉₃	1	4	yes	direct product factor
59	C₂²×C₈	—	2	2	no	—
60	C₂²×C₈	C₄×C₁₉₃	1	1	yes	characteristic
61	C₂²×C₈	C₄×C₁₉₃	1	1	yes	characteristic
62	C₂×C₄²	C₂²×C₁₉₃	1	1	yes	characteristic
63	C₄⋊C₈	—	2	2	no	—
64	C₄⋊C₈	C₂²×C₁₉₃	1	4	yes	—
65	C₄×C₈	C₄×C₁₉₃	1	2	yes	—
66	C₄×C₈	C₂²×C₁₉₃	1	2	yes	—
67	C₂²×C₄	C₂×C₄×C₁₉₃	1	1	yes	characteristic
68	C₂²×C₄	D₄×C₁₉₃	1	1	yes	characteristic
69	C₂²×C₄	Q₈×C₁₉₃	1	1	yes	characteristic
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	—	2	4	no	—
72	C₂×C₈	—	4	4	no	—
73	C₂×C₈	C₈×C₁₉₃	1	4	yes	complemented
74	C₂×C₈	C₂×C₄×C₁₉₃	1	2	yes	—
75	C₂×C₈	C₂×C₄×C₁₉₃	1	2	yes	—
76	C₄²	C₂×C₄×C₁₉₃	1	1	yes	characteristic
77	C₄²	D₄×C₁₉₃	1	1	yes	characteristic
78	C₄²	Q₈×C₁₉₃	1	1	yes	characteristic
79	C₄²	C₂³×C₁₉₃	1	1	yes	characteristic
80	C₂³	C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
83	C₂×C₄	C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
84	C₂×C₄	C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
85	C₂×C₄	C₂×C₈×C₁₉₃	1	2	yes	—
86	C₂×C₄	M₁₆×C₁₉₃	1	2	yes	—
87	C₂×C₄	SD₁₆×C₁₉₃	1	4	yes	—
88	C₂×C₄	C₂²×C₄×C₁₉₃	1	1	yes	characteristic
89	C₂×C₄	C₂×D₄×C₁₉₃	1	1	yes	characteristic
90	C₂×C₄	C₂×Q₈×C₁₉₃	1	1	yes	characteristic
91	C₈	—	2	2	no	—
92	C₈	—	4	4	no	—
93	C₈	C₂×C₈×C₁₉₃	1	4	yes	complemented
94	C₂²	C₄⋊C₈×C₁₉₃	1	2	yes	—
95	C₂²	#106×C₁₉₃	1	2	yes	—
96	C₂²	#108×C₁₉₃	1	2	yes	—
97	C₂²	C₂×C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	C₄⋊C₈×C₁₉₃	1	2	yes	—
101	C₄	#106×C₁₉₃	1	2	yes	—
102	C₄	C₂²×C₈×C₁₉₃	1	1	yes	characteristic
103	C₄	C₂×M₁₆×C₁₉₃	1	1	yes	characteristic
104	C₄	C₂×SD₁₆×C₁₉₃	1	2	yes	—
105	C₂	#334×C₁₉₃	1	4	yes	direct product factor
106	C₂	C₂×C₄⋊C₈×C₁₉₃	1	1	yes	characteristic
107	C₂	C₂×#106×C₁₉₃	1	1	yes	characteristic
108	C₂	C₂×#108×C₁₉₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊C₈×C₁₉₃

C₂

yes

maximal

C₂×C₄×C₈×C₁₉₃

C₂

yes

maximal, characteristic

#334×C₁₉₃

C₂

yes

maximal, direct product factor

C₂²×C₈×C₁₉₃

—

C₂²×C₈×C₁₉₃

C₄

yes

characteristic

C₂²×C₈×C₁₉₃

C₄

yes

characteristic

C₂×C₄²×C₁₉₃

C₂²

yes

characteristic

C₄⋊C₈×C₁₉₃

—

C₄⋊C₈×C₁₉₃

C₂²

yes

—

C₄×C₈×C₁₉₃

C₄

yes

—

C₄×C₈×C₁₉₃

C₂²

yes

—

C₂²×C₄×C₁₉₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉₃

D₄

yes

characteristic

C₂²×C₄×C₁₉₃

Q₈

yes

characteristic

C₂×C₈×C₁₉₃

—

C₂×C₈×C₁₉₃

—

C₂×C₈×C₁₉₃

—

C₂×C₈×C₁₉₃

C₈

yes

complemented

C₂×C₈×C₁₉₃

C₂×C₄

yes

—

C₂×C₈×C₁₉₃

C₂×C₄

yes

—

C₄²×C₁₉₃

C₂×C₄

yes

characteristic

C₄²×C₁₉₃

D₄

yes

characteristic

C₄²×C₁₉₃

Q₈

yes

characteristic

C₄²×C₁₉₃

C₂³

yes

characteristic

C₂³×C₁₉₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉₃

—

C₂×C₄×C₁₉₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉₃

C₂×C₈

yes

—

C₂×C₄×C₁₉₃

M₁₆

yes

—

C₂×C₄×C₁₉₃

SD₁₆

yes

—

C₂×C₄×C₁₉₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₃

C₂×Q₈

yes

characteristic

C₈×C₁₉₃

—

C₈×C₁₉₃

—

C₈×C₁₉₃

C₂×C₈

yes

complemented

C₂²×C₁₉₃

C₄⋊C₈

yes

—

C₂²×C₁₉₃

#106

yes

—

C₂²×C₁₉₃

#108

yes

—

C₂²×C₁₉₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉₃

—

C₄×C₁₉₃

—

C₄×C₁₉₃

C₄⋊C₈

yes

—

C₄×C₁₉₃

#106

yes

—

C₄×C₁₉₃

C₂²×C₈

yes

characteristic

C₄×C₁₉₃

C₂×M₁₆

yes

characteristic

C₄×C₁₉₃

C₂×SD₁₆

yes

—

C₂×C₁₉₃

#334

yes

direct product factor

C₂×C₁₉₃

C₂×C₄⋊C₈

yes

C₂×C₁₉₃

yes

C₂×C₁₉₃

yes

C₁₉₃

yes

characteristic, direct product factor, Sylow

C₂×#334

C₁₉₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₄⋊C₈

C₂×C₁₉₃

yes

—

C₂×C₄×C₈

C₂×C₁₉₃

yes

characteristic

#334

C₂×C₁₉₃

yes

direct product factor

C₂²×C₈

—

C₂²×C₈

C₄×C₁₉₃

yes

characteristic

C₂²×C₈

C₄×C₁₉₃

yes

characteristic

C₂×C₄²

C₂²×C₁₉₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

C₂²×C₁₉₃

yes

—

C₄×C₈

C₄×C₁₉₃

yes

—

C₄×C₈

C₂²×C₁₉₃

yes

—

C₂²×C₄

C₂×C₄×C₁₉₃

yes

characteristic

C₂²×C₄

D₄×C₁₉₃

yes

characteristic

C₂²×C₄

Q₈×C₁₉₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×C₁₉₃

yes

complemented

C₂×C₈

C₂×C₄×C₁₉₃

yes

—

C₂×C₈

C₂×C₄×C₁₉₃

yes

—

C₄²

C₂×C₄×C₁₉₃

yes

characteristic

C₄²

D₄×C₁₉₃

yes

characteristic

C₄²

Q₈×C₁₉₃

yes

characteristic

C₄²

C₂³×C₁₉₃

yes

characteristic

C₂³

C₄⋊C₄×C₁₉₃

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄⋊C₄×C₁₉₃

yes

characteristic

C₂×C₄

C₄⋊C₄×C₁₉₃

yes

characteristic

C₂×C₄

C₄⋊C₄×C₁₉₃

yes

characteristic

C₂×C₄

C₂×C₈×C₁₉₃

yes

—

C₂×C₄

M₁₆×C₁₉₃

yes

—

C₂×C₄

SD₁₆×C₁₉₃

yes

—

C₂×C₄

C₂²×C₄×C₁₉₃

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉₃

yes

characteristic

C₂×C₄

C₂×Q₈×C₁₉₃

yes

characteristic

C₈

—

C₈

—

C₈

C₂×C₈×C₁₉₃

yes

complemented

C₂²

C₄⋊C₈×C₁₉₃

yes

—

C₂²

#106×C₁₉₃

yes

—

C₂²

#108×C₁₉₃

yes

—

C₂²

C₂×C₄⋊C₄×C₁₉₃

yes

characteristic

C₄

—

C₄

—

100

C₄

C₄⋊C₈×C₁₉₃

yes

—

101

C₄

#106×C₁₉₃

yes

—

102

C₄

C₂²×C₈×C₁₉₃

yes

characteristic

103

C₄

C₂×M₁₆×C₁₉₃

yes

characteristic

104

C₄

C₂×SD₁₆×C₁₉₃

yes

—

105

C₂

#334×C₁₉₃

yes

direct product factor

106

C₂

C₂×C₄⋊C₈×C₁₉₃

yes

characteristic

107

C₂

C₂×#106×C₁₉₃

yes

characteristic

108

C₂

C₂×#108×C₁₉₃

yes

characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉₃	D₄
commutator	C₄	C₂²×C₈×C₁₉₃
Frattini, cosocle	C₄²	C₂³×C₁₉₃
socle, prime radical	C₂³×C₁₉₃	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉₃ ◁ C₂×C₄²×C₁₉₃ ◁ G

subgroup

G/H

center

C₂²×C₄×C₁₉₃

D₄

commutator

C₄

C₂²×C₈×C₁₉₃

Frattini, cosocle

C₄²

C₂³×C₁₉₃

socle, prime radical

C₂³×C₁₉₃

C₄⋊C₄

LCS

G ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₄×C₁₉₃ ◁ C₂×C₄²×C₁₉₃ ◁ G

N	H ≅ G/N	type
3. #334×C₁₉₃	C₂	direct (N × H)
18. C₂×C₈×C₁₉₃	C₈	semidirect
38. C₈×C₁₉₃	C₂×C₈	semidirect
50. C₂×C₁₉₃	#334	direct (N × H)
54. C₁₉₃	C₂×#334	direct (N × H)
55. C₂×#334	C₁₉₃	direct (N × H)
58. #334	C₂×C₁₉₃	direct (N × H)
73. C₂×C₈	C₈×C₁₉₃	semidirect
93. C₈	C₂×C₈×C₁₉₃	semidirect
105. C₂	#334×C₁₉₃	direct (N × H)

H ≅ G/N

type

3. #334×C₁₉₃

C₂

direct (N × H)

18. C₂×C₈×C₁₉₃

C₈

semidirect

38. C₈×C₁₉₃

C₂×C₈

semidirect

50. C₂×C₁₉₃

#334

direct (N × H)

54. C₁₉₃

C₂×#334

direct (N × H)

55. C₂×#334

C₁₉₃

direct (N × H)

58. #334

C₂×C₁₉₃

direct (N × H)

73. C₂×C₈

C₈×C₁₉₃

semidirect

93. C₈

C₂×C₈×C₁₉₃

semidirect

105. C₂

#334×C₁₉₃

direct (N × H)

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

subgroup	index
C₂×C₄⋊C₈×C₁₉₃	2
C₂×C₄×C₈×C₁₉₃	2
#334×C₁₉₃	2
C₂×#334	193

subgroup

index

C₂×C₄⋊C₈×C₁₉₃

C₂×C₄×C₈×C₁₉₃

#334×C₁₉₃

C₂×#334

193

Subgroups — C₂×#334×C₁₉₃ #37591179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#334×C193 #37591179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#334×C₁₉₃ #37591179