Group #37591180 — subgroups

Subgroups — C₂×#335×C₁₉₃ #37591180

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	#335×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	D₈	1	2	yes	—
33	C₂×C₄×C₁₉₃	Q₁₆	1	2	yes	—
34	C₂×C₄×C₁₉₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉₃	C₂×Q₈	1	1	yes	characteristic
37	C₈×C₁₉₃	—	2	2	no	—
38	C₈×C₁₉₃	—	4	4	no	—
39	C₈×C₁₉₃	C₂×C₈	1	4	yes	complemented
40	C₂²×C₁₉₃	C₄⋊C₈	1	2	yes	—
41	C₂²×C₁₉₃	#107	1	2	yes	—
42	C₂²×C₁₉₃	#108	1	2	yes	—
43	C₂²×C₁₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₄×C₁₉₃	—	2	1	no	—
45	C₄×C₁₉₃	—	2	1	no	—
46	C₄×C₁₉₃	C₄⋊C₈	1	2	yes	—
47	C₄×C₁₉₃	#107	1	2	yes	—
48	C₄×C₁₉₃	C₂²×C₈	1	1	yes	characteristic
49	C₄×C₁₉₃	C₂×M₁₆	1	1	yes	characteristic
50	C₄×C₁₉₃	C₂×D₈	1	1	yes	characteristic
51	C₄×C₁₉₃	C₂×Q₁₆	1	1	yes	characteristic
52	C₂×C₁₉₃	#335	1	4	yes	direct product factor
53	C₂×C₁₉₃	C₂×C₄⋊C₈	1	1	yes	characteristic
54	C₂×C₁₉₃	C₂×#107	1	1	yes	characteristic
55	C₂×C₁₉₃	C₂×#108	1	1	yes	characteristic
56	C₁₉₃	C₂×#335	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×#335	C₁₉₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂×C₄⋊C₈	C₂×C₁₉₃	1	2	yes	—
59	C₂×C₄×C₈	C₂×C₁₉₃	1	1	yes	characteristic
60	#335	C₂×C₁₉₃	1	4	yes	direct product factor
61	C₂²×C₈	—	2	2	no	—
62	C₂²×C₈	C₄×C₁₉₃	1	1	yes	characteristic
63	C₂²×C₈	C₄×C₁₉₃	1	1	yes	characteristic
64	C₂×C₄²	C₂²×C₁₉₃	1	1	yes	characteristic
65	C₄⋊C₈	—	2	2	no	—
66	C₄⋊C₈	C₂²×C₁₉₃	1	4	yes	—
67	C₄×C₈	C₄×C₁₉₃	1	2	yes	—
68	C₄×C₈	C₂²×C₁₉₃	1	2	yes	—
69	C₂²×C₄	C₂×C₄×C₁₉₃	1	1	yes	characteristic
70	C₂²×C₄	D₄×C₁₉₃	1	1	yes	characteristic
71	C₂²×C₄	Q₈×C₁₉₃	1	1	yes	characteristic
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	4	no	—
74	C₂×C₈	—	4	4	no	—
75	C₂×C₈	C₈×C₁₉₃	1	4	yes	complemented
76	C₂×C₈	C₂×C₄×C₁₉₃	1	2	yes	—
77	C₂×C₈	C₂×C₄×C₁₉₃	1	2	yes	—
78	C₄²	C₂×C₄×C₁₉₃	1	1	yes	characteristic
79	C₄²	D₄×C₁₉₃	1	1	yes	characteristic
80	C₄²	Q₈×C₁₉₃	1	1	yes	characteristic
81	C₄²	C₂³×C₁₉₃	1	1	yes	characteristic
82	C₂³	C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
85	C₂×C₄	C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
86	C₂×C₄	C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
87	C₂×C₄	C₂×C₈×C₁₉₃	1	2	yes	—
88	C₂×C₄	M₁₆×C₁₉₃	1	2	yes	—
89	C₂×C₄	D₈×C₁₉₃	1	2	yes	—
90	C₂×C₄	Q₁₆×C₁₉₃	1	2	yes	—
91	C₂×C₄	C₂²×C₄×C₁₉₃	1	1	yes	characteristic
92	C₂×C₄	C₂×D₄×C₁₉₃	1	1	yes	characteristic
93	C₂×C₄	C₂×Q₈×C₁₉₃	1	1	yes	characteristic
94	C₈	—	2	2	no	—
95	C₈	—	4	4	no	—
96	C₈	C₂×C₈×C₁₉₃	1	4	yes	complemented
97	C₂²	C₄⋊C₈×C₁₉₃	1	2	yes	—
98	C₂²	#107×C₁₉₃	1	2	yes	—
99	C₂²	#108×C₁₉₃	1	2	yes	—
100	C₂²	C₂×C₄⋊C₄×C₁₉₃	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	2	1	no	—
103	C₄	C₄⋊C₈×C₁₉₃	1	2	yes	—
104	C₄	#107×C₁₉₃	1	2	yes	—
105	C₄	C₂²×C₈×C₁₉₃	1	1	yes	characteristic
106	C₄	C₂×M₁₆×C₁₉₃	1	1	yes	characteristic
107	C₄	C₂×D₈×C₁₉₃	1	1	yes	characteristic
108	C₄	C₂×Q₁₆×C₁₉₃	1	1	yes	characteristic
109	C₂	#335×C₁₉₃	1	4	yes	direct product factor
110	C₂	C₂×C₄⋊C₈×C₁₉₃	1	1	yes	characteristic
111	C₂	C₂×#107×C₁₉₃	1	1	yes	characteristic
112	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

#335×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

D₈

yes

—

C₂×C₄×C₁₉₃

Q₁₆

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

#107

yes

—

C₂²×C₁₉₃

#108

yes

—

C₂²×C₁₉₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉₃

—

C₄×C₁₉₃

—

C₄×C₁₉₃

C₄⋊C₈

yes

—

C₄×C₁₉₃

#107

yes

—

C₄×C₁₉₃

C₂²×C₈

yes

characteristic

C₄×C₁₉₃

C₂×M₁₆

yes

characteristic

C₄×C₁₉₃

C₂×D₈

yes

characteristic

C₄×C₁₉₃

C₂×Q₁₆

yes

characteristic

C₂×C₁₉₃

#335

yes

direct product factor

C₂×C₁₉₃

C₂×C₄⋊C₈

yes

C₂×C₁₉₃

yes

C₂×C₁₉₃

yes

C₁₉₃

yes

characteristic, direct product factor, Sylow

C₂×#335

C₁₉₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₄⋊C₈

C₂×C₁₉₃

yes

—

C₂×C₄×C₈

C₂×C₁₉₃

yes

characteristic

#335

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

D₈×C₁₉₃

yes

—

C₂×C₄

Q₁₆×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

#107×C₁₉₃

yes

—

C₂²

#108×C₁₉₃

yes

—

100

C₂²

C₂×C₄⋊C₄×C₁₉₃

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

C₄⋊C₈×C₁₉₃

yes

—

104

C₄

#107×C₁₉₃

yes

—

105

C₄

C₂²×C₈×C₁₉₃

yes

characteristic

106

C₄

C₂×M₁₆×C₁₉₃

yes

characteristic

107

C₄

C₂×D₈×C₁₉₃

yes

characteristic

108

C₄

C₂×Q₁₆×C₁₉₃

yes

characteristic

109

C₂

#335×C₁₉₃

yes

direct product factor

110

C₂

C₂×C₄⋊C₈×C₁₉₃

yes

characteristic

111

C₂

C₂×#107×C₁₉₃

yes

characteristic

112

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. #335×C₁₉₃	C₂	direct (N × H)
18. C₂×C₈×C₁₉₃	C₈	semidirect
39. C₈×C₁₉₃	C₂×C₈	semidirect
52. C₂×C₁₉₃	#335	direct (N × H)
56. C₁₉₃	C₂×#335	direct (N × H)
57. C₂×#335	C₁₉₃	direct (N × H)
60. #335	C₂×C₁₉₃	direct (N × H)
75. C₂×C₈	C₈×C₁₉₃	semidirect
96. C₈	C₂×C₈×C₁₉₃	semidirect
109. C₂	#335×C₁₉₃	direct (N × H)

H ≅ G/N

type

3. #335×C₁₉₃

C₂

direct (N × H)

18. C₂×C₈×C₁₉₃

C₈

semidirect

39. C₈×C₁₉₃

C₂×C₈

semidirect

52. C₂×C₁₉₃

#335

direct (N × H)

56. C₁₉₃

C₂×#335

direct (N × H)

57. C₂×#335

C₁₉₃

direct (N × H)

60. #335

C₂×C₁₉₃

direct (N × H)

75. C₂×C₈

C₈×C₁₉₃

semidirect

96. C₈

C₂×C₈×C₁₉₃

semidirect

109. C₂

#335×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
#335×C₁₉₃	2
C₂×#335	193

subgroup

index

C₂×C₄⋊C₈×C₁₉₃

C₂×C₄×C₈×C₁₉₃

#335×C₁₉₃

C₂×#335

193

Subgroups — C₂×#335×C₁₉₃ #37591180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#335×C193 #37591180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#335×C₁₉₃ #37591180