Group #23773898 — subgroups

Subgroups — C₂×#19098960 #23773898

Order 10112.

424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14579160	C₂	1	2	yes	maximal
2	#19098960	C₂	1	8	yes	maximal, direct product factor
3	C₂×#14579093	C₂	1	1	yes	maximal, characteristic
4	C₂×#14579092	C₂	1	2	yes	maximal
5	C₂×C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#106×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₁₅₈	—	2	2	no	—
8	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
9	#14579160	—	2	4	no	—
10	#14579160	C₂²	1	8	yes	—
11	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
12	C₂×Dic₇₉⋊C₄	—	2	2	no	—
13	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
14	#14579093	C₂²	1	4	yes	—
15	#14579092	C₂²	1	8	yes	—
16	C₈×Dic₇₉	C₂²	1	4	yes	—
17	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
19	#106×C₇₉	C₂²	1	4	yes	—
20	C₂×Dic₁₅₈	—	2	8	no	—
21	C₂×Dic₁₅₈	—	4	8	no	—
22	C₂²×Dic₇₉	—	2	2	no	—
23	C₂²×Dic₇₉	D₄	1	2	yes	—
24	C₂×C₇₉⋊C₈	Q₈	1	4	yes	complemented
25	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
26	C₄⋊Dic₇₉	—	2	2	no	—
27	C₄⋊Dic₇₉	C₂³	1	4	yes	—
28	Dic₇₉⋊C₄	—	2	8	no	—
29	C₄×Dic₇₉	D₄	1	2	yes	—
30	C₄×Dic₇₉	C₂³	1	2	yes	—
31	C₂²×C₄×C₇₉	—	2	2	no	—
32	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
33	C₂×C₈×C₇₉	Q₈	1	4	yes	complemented
34	C₂×C₈×C₇₉	C₂³	1	2	yes	—
35	C₄⋊C₄×C₇₉	—	2	2	no	—
36	C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
37	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₉	—	2	4	no	—
39	C₂×C₄×C₇₉	—	4	4	no	—
40	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
42	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
43	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
44	C₂×Dic₇₉	—	2	4	no	—
45	C₂×Dic₇₉	—	4	4	no	—
46	C₂×Dic₇₉	SD₁₆	1	8	yes	—
47	C₂×Dic₇₉	C₂×D₄	1	4	yes	—
48	Dic₁₅₈	—	4	16	no	—
49	C₈×C₇₉	C₂×Q₈	1	4	yes	complemented
50	C₇₉⋊C₈	C₂×Q₈	1	4	yes	complemented
51	C₂²×C₇₉	C₄⋊Q₈	1	2	yes	—
52	C₂²×C₇₉	C₂×SD₁₆	1	4	yes	—
53	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
54	C₄×C₇₉	—	4	4	no	—
55	C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
56	C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
57	C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
58	Dic₇₉	—	4	4	no	—
59	Dic₇₉	C₂×SD₁₆	1	8	yes	—
60	C₂×C₇₉	#498	1	4	yes	complemented
61	C₂×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
62	C₂×C₇₉	C₂²×SD₁₆	1	2	yes	—
63	C₂×#498	—	79	1	no	maximal, Sylow
64	C₇₉	C₂×#498	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄⋊Q₈	—	79	2	no	—
66	#498	—	79	8	no	—
67	C₂×#106	—	79	1	no	—
68	C₂×#106	—	79	2	no	—
69	C₂×#106	D₇₉	1	1	yes	characteristic
70	C₂×C₄×C₈	—	79	1	no	—
71	C₂²×Q₈	—	158	2	no	—
72	C₂²×C₈	—	79	1	no	—
73	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
74	C₄⋊Q₈	—	79	8	no	—
75	C₄⋊Q₈	—	158	4	no	—
76	C₂×C₄⋊C₄	—	79	2	no	—
77	C₂×C₄⋊C₄	—	158	2	no	—
78	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
79	C₂×C₄²	—	79	1	no	—
80	#106	—	79	4	no	—
81	#106	—	79	8	no	—
82	#106	C₂×D₇₉	1	4	yes	—
83	C₄×C₈	—	79	4	no	—
84	C₂×Q₈	—	316	8	no	—
85	C₂×Q₈	—	158	8	no	—
86	C₂²×C₄	—	2	2	no	—
87	C₂²×C₄	—	79	2	no	—
88	C₂²×C₄	—	158	2	no	—
89	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
90	C₂×C₈	—	79	4	no	—
91	C₂×C₈	—	79	2	no	—
92	C₂×C₈	Dic₁₅₈	1	4	yes	complemented
93	C₂×C₈	C₂²×D₇₉	1	2	yes	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	79	4	no	—
96	C₄⋊C₄	—	158	8	no	—
97	C₄⋊C₄	—	158	2	no	—
98	C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
99	C₄²	—	79	2	no	—
100	C₄²	—	79	2	no	—
101	C₂³	D₄×D₇₉	1	1	yes	characteristic
102	Q₈	—	316	16	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	4	4	no	—
105	C₂×C₄	—	316	4	no	—
106	C₂×C₄	—	79	8	no	—
107	C₂×C₄	—	79	4	no	—
108	C₂×C₄	—	158	4	no	—
109	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
110	C₂×C₄	Q₈×D₇₉	1	2	yes	—
111	C₂×C₄	C₂×Dic₁₅₈	1	2	yes	—
112	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
113	C₈	—	79	4	no	—
114	C₈	C₂×Dic₁₅₈	1	4	yes	complemented
115	C₂²	#14579160	1	2	yes	—
116	C₂²	SD₁₆×D₇₉	1	4	yes	—
117	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
118	C₄	—	4	4	no	—
119	C₄	—	316	4	no	—
120	C₄	—	79	8	no	—
121	C₄	#14579160	1	2	yes	—
122	C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
123	C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
124	C₂	#19098960	1	4	yes	direct product factor
125	C₂	C₂×#14579160	1	1	yes	characteristic
126	C₂	C₂×SD₁₆×D₇₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579160

C₂

yes

maximal

#19098960

C₂

yes

maximal, direct product factor

C₂×#14579093

C₂

yes

maximal, characteristic

C₂×#14579092

C₂

yes

maximal

C₂×C₈×Dic₇₉

C₂

yes

maximal, characteristic

C₂×#106×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

—

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

#14579160

—

#14579160

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

#14579093

C₂²

yes

—

#14579092

C₂²

yes

—

C₈×Dic₇₉

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

#106×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

D₄

yes

—

C₂×C₇₉⋊C₈

Q₈

yes

complemented

C₂×C₇₉⋊C₈

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

D₄

yes

—

C₄×Dic₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

complemented

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

SD₁₆

yes

—

C₂×Dic₇₉

C₂×D₄

yes

—

Dic₁₅₈

—

C₈×C₇₉

C₂×Q₈

yes

complemented

C₇₉⋊C₈

C₂×Q₈

yes

complemented

C₂²×C₇₉

C₄⋊Q₈

yes

—

C₂²×C₇₉

C₂×SD₁₆

yes

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₄⋊Q₈

yes

—

C₄×C₇₉

C₂²×Q₈

yes

characteristic

C₄×C₇₉

C₂²×Q₈

yes

characteristic

Dic₇₉

—

Dic₇₉

C₂×SD₁₆

yes

—

C₂×C₇₉

#498

yes

complemented

C₂×C₇₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₇₉

C₂²×SD₁₆

yes

—

C₂×#498

—

maximal, Sylow

C₇₉

C₂×#498

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

—

—

—

D₇₉

yes

characteristic

C₂×C₄×C₈

—

C₂²×Q₈

—

158

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

#106

—

#106

—

#106

C₂×D₇₉

yes

—

C₄×C₈

—

C₂×Q₈

—

316

—

C₂×Q₈

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₅₈

yes

complemented

C₂×C₈

C₂²×D₇₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

C₂²×D₇₉

yes

—

C₄²

—

100

C₄²

—

101

C₂³

D₄×D₇₉

yes

characteristic

102

Q₈

—

316

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

316

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

158

—

109

C₂×C₄

D₄×D₇₉

yes

characteristic

110

C₂×C₄

Q₈×D₇₉

yes

—

111

C₂×C₄

C₂×Dic₁₅₈

yes

—

112

C₂×C₄

C₂³×D₇₉

yes

characteristic

113

C₈

—

114

C₈

C₂×Dic₁₅₈

yes

complemented

115

C₂²

#14579160

yes

—

116

C₂²

SD₁₆×D₇₉

yes

—

117

C₂²

C₂×D₄×D₇₉

yes

characteristic

118

C₄

—

119

C₄

—

316

—

120

C₄

—

121

C₄

#14579160

yes

—

122

C₄

C₂×Q₈×D₇₉

yes

characteristic

123

C₄

C₂²×Dic₁₅₈

yes

characteristic

124

C₂

#19098960

yes

direct product factor

125

C₂

C₂×#14579160

yes

characteristic

126

C₂

C₂×SD₁₆×D₇₉

yes

—

	subgroup	G/H
center	C₂³	D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	C₂×#106×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
hypercenter	C₂×#106	D₇₉
hypocenter	C₇₉	C₂×#498
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

C₂×#106×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
2. #19098960	C₂	direct (N × H)
24. C₂×C₇₉⋊C₈	Q₈	semidirect
33. C₂×C₈×C₇₉	Q₈	semidirect
49. C₈×C₇₉	C₂×Q₈	semidirect
50. C₇₉⋊C₈	C₂×Q₈	semidirect
60. C₂×C₇₉	#498	semidirect
64. C₇₉	C₂×#498	semidirect
92. C₂×C₈	Dic₁₅₈	semidirect
114. C₈	C₂×Dic₁₅₈	semidirect
124. C₂	#19098960	direct (N × H)

H ≅ G/N

type

2. #19098960

C₂

direct (N × H)

24. C₂×C₇₉⋊C₈

Q₈

semidirect

33. C₂×C₈×C₇₉

Q₈

semidirect

49. C₈×C₇₉

C₂×Q₈

semidirect

50. C₇₉⋊C₈

C₂×Q₈

semidirect

60. C₂×C₇₉

#498

semidirect

64. C₇₉

C₂×#498

semidirect

92. C₂×C₈

Dic₁₅₈

semidirect

114. C₈

C₂×Dic₁₅₈

semidirect

124. C₂

#19098960

direct (N × H)

Subgroups — C₂×#19098960 #23773898

Conjugacy classes of subgroups

Complements

Subgroups — C2×#19098960 #23773898

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19098960 #23773898