Group #19098708 — subgroups

Subgroups — #19098708

Order 5056.

162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 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×#11929611	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11929609	C₂	1	1	yes	maximal, characteristic, complemented
3	#14579135	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579085	C₂	1	1	yes	maximal, characteristic, complemented
5	#14579082	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#41×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊D₇₉	—	2	1	no	—
10	#11929611	—	2	2	no	—
11	#11929609	—	2	2	no	—
12	C₂×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
15	(C₂×D₇₉)⋊C₄	—	2	1	no	—
16	#41×C₇₉	—	2	2	no	—
17	#41×C₇₉	—	2	2	no	—
18	C₂×Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₇₉	—	2	1	no	—
20	C₂×D₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₇₉	—	2	1	no	—
22	C₂²×C₄×C₇₉	C₂²	1	1	yes	characteristic
23	C₂³×C₇₉	—	2	1	no	—
24	C₂³×C₇₉	D₄	1	1	yes	characteristic
25	C₂²×D₇₉	—	2	1	no	—
26	Q₈×C₇₉	—	2	1	no	—
27	Q₈×C₇₉	D₄	1	2	yes	complemented
28	D₄×C₇₉	—	2	4	no	—
29	D₄×C₇₉	—	2	1	no	—
30	D₄×C₇₉	D₄	1	2	yes	complemented
31	C₂×C₄×C₇₉	—	2	4	no	—
32	C₂×C₄×C₇₉	—	2	1	no	—
33	C₂×C₄×C₇₉	—	2	1	no	—
34	C₂×C₄×C₇₉	—	2	1	no	—
35	C₂×C₄×C₇₉	D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
37	C₂²⋊D₇₉	—	4	2	no	—
38	C₂×Dic₇₉	—	2	1	no	—
39	D₃₁₆	—	2	1	no	—
40	D₃₁₆	—	2	1	no	—
41	C₇₉⋊C₈	—	2	1	no	—
42	C₇₉⋊C₈	—	2	1	no	—
43	C₂²×C₇₉	—	2	1	no	—
44	C₂²×C₇₉	—	2	2	no	—
45	C₂²×C₇₉	—	2	1	no	—
46	C₂²×C₇₉	—	2	1	no	—
47	C₂²×C₇₉	—	4	1	no	—
48	C₂²×C₇₉	—	4	1	no	—
49	C₂²×C₇₉	C₂×D₄	1	1	yes	characteristic
50	C₂×D₇₉	—	4	1	no	—
51	C₂×D₇₉	—	4	1	no	—
52	C₂×D₇₉	—	4	1	no	—
53	C₄×C₇₉	—	2	1	no	—
54	C₄×C₇₉	—	2	2	no	—
55	C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
56	C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
57	Dic₇₉	—	4	1	no	—
58	C₂×C₇₉	—	4	1	no	—
59	C₂×C₇₉	—	4	2	no	—
60	C₂×C₇₉	#120	1	1	yes	characteristic
61	C₂×C₇₉	#135	1	1	yes	characteristic
62	C₂×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
63	D₇₉	—	8	1	no	—
64	C₇₉	#449	1	1	yes	characteristic, complemented, Sylow
65	#449	—	79	1	no	maximal, Sylow
66	C₂×#41	D₇₉	1	1	yes	characteristic, complemented
67	C₂×SD₁₆	—	79	1	no	—
68	C₂×D₈	—	79	1	no	—
69	#121	—	79	1	no	—
70	#103	—	79	1	no	—
71	#102	—	79	1	no	—
72	C₂²⋊C₈	—	79	1	no	—
73	#41	—	2	2	no	—
74	#41	—	2	2	no	—
75	C₂×Q₈	C₂×D₇₉	1	1	yes	characteristic
76	C₂×D₄	—	2	1	no	—
77	C₂×D₄	—	79	1	no	—
78	C₂×D₄	—	158	1	no	—
79	C₂×D₄	C₂×D₇₉	1	1	yes	characteristic
80	C₂²×C₄	—	2	1	no	—
81	C₂²×C₄	C₂×D₇₉	1	1	yes	characteristic
82	SD₁₆	—	158	2	no	—
83	D₈	—	158	2	no	—
84	C₂×C₈	—	79	1	no	—
85	C₂×C₈	—	79	1	no	—
86	C₄⋊C₄	—	79	1	no	—
87	C₂²⋊C₄	—	158	1	no	—
88	C₂³	—	2	1	no	—
89	C₂³	—	158	1	no	—
90	C₂³	C₂²⋊D₇₉	1	1	yes	characteristic
91	Q₈	—	2	1	no	—
92	Q₈	C₂²⋊D₇₉	1	2	yes	complemented
93	D₄	—	2	4	no	—
94	D₄	—	2	1	no	—
95	D₄	—	316	2	no	—
96	D₄	—	158	1	no	—
97	D₄	—	158	1	no	—
98	D₄	C₂²⋊D₇₉	1	2	yes	complemented
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	158	1	no	—
104	C₂×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
105	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
106	C₈	—	158	1	no	—
107	C₈	—	158	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	—	2	2	no	—
110	C₂²	—	2	1	no	—
111	C₂²	—	2	1	no	—
112	C₂²	—	4	1	no	—
113	C₂²	—	4	1	no	—
114	C₂²	—	316	1	no	—
115	C₂²	—	316	1	no	—
116	C₂²	—	316	1	no	—
117	C₂²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	2	2	no	—
120	C₄	—	316	1	no	—
121	C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
122	C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
123	C₂	—	4	1	no	—
124	C₂	—	4	2	no	—
125	C₂	—	632	1	no	—
126	C₂	#14579130	1	1	yes	characteristic
127	C₂	#14579181	1	1	yes	characteristic
128	C₂	#14579186	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11929611

C₂

yes

maximal, characteristic, complemented

C₂×#11929609

C₂

yes

maximal, characteristic, complemented

#14579135

C₂

yes

maximal, characteristic, complemented

#14579085

C₂

yes

maximal, characteristic, complemented

#14579082

C₂

yes

maximal, characteristic, complemented

C₂²⋊(C₇₉⋊C₈)

C₂

yes

maximal, characteristic, complemented

C₂×#41×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×D₃₁₆

C₂²

yes

characteristic

C₂×C₂²⋊D₇₉

—

#11929611

—

#11929609

—

C₂×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Dic₇₉

C₂²

yes

characteristic

(C₂×D₇₉)⋊C₄

—

#41×C₇₉

—

#41×C₇₉

—

C₂×Q₈×C₇₉

C₂²

yes

characteristic

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

C₂²

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²

yes

characteristic

C₂³×C₇₉

—

C₂³×C₇₉

D₄

yes

characteristic

C₂²×D₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

D₄

yes

complemented

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

D₄

yes

complemented

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

D₄

yes

characteristic

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×D₄

yes

characteristic

C₄×C₇₉

C₂×D₄

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

C₇₉

#449

yes

characteristic, complemented, Sylow

#449

—

maximal, Sylow

C₂×#41

D₇₉

yes

characteristic, complemented

C₂×SD₁₆

—

C₂×D₈

—

#121

—

#103

—

#102

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

C₂×D₇₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

158

—

C₂×D₄

C₂×D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂×D₇₉

yes

characteristic

SD₁₆

—

158

—

D₈

—

158

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

158

—

C₂³

—

C₂³

—

158

—

C₂³

C₂²⋊D₇₉

yes

characteristic

Q₈

—

Q₈

C₂²⋊D₇₉

yes

complemented

D₄

—

D₄

—

D₄

—

316

—

D₄

—

158

—

D₄

—

158

—

D₄

C₂²⋊D₇₉

yes

complemented

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

158

—

104

C₂×C₄

C₂²⋊D₇₉

yes

characteristic

105

C₂×C₄

C₂²×D₇₉

yes

characteristic

106

C₈

—

158

—

107

C₈

—

158

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

316

—

115

C₂²

—

316

—

116

C₂²

—

316

—

117

C₂²

C₂×C₂²⋊D₇₉

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

316

—

121

C₄

C₂×C₂²⋊D₇₉

yes

characteristic

122

C₄

C₂×C₂²⋊D₇₉

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

—

632

—

126

C₂

#14579130

yes

characteristic

127

C₂

#14579181

yes

characteristic

128

C₂

#14579186

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₇₉
Fitting	C₂×#41×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₄
hypercenter	C₂×#41	D₇₉
hypocenter	C₇₉	#449
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#41

subgroup

G/H

center

C₂²

C₂×C₂²⋊D₇₉

commutator

C₂×C₄×C₇₉

C₂³

Frattini

C₂×C₄

C₂²×D₇₉

Fitting

C₂×#41×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₄

hypercenter

C₂×#41

D₇₉

hypocenter

C₇₉

#449

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#41

N	H ≅ G/N	type
1. C₂×#11929611	C₂	semidirect
2. C₂×#11929609	C₂	semidirect
3. #14579135	C₂	semidirect
4. #14579085	C₂	semidirect
5. #14579082	C₂	semidirect
6. C₂²⋊(C₇₉⋊C₈)	C₂	semidirect
7. C₂×#41×C₇₉	C₂	semidirect
27. Q₈×C₇₉	D₄	semidirect
30. D₄×C₇₉	D₄	semidirect
64. C₇₉	#449	semidirect
66. C₂×#41	D₇₉	semidirect
92. Q₈	C₂²⋊D₇₉	semidirect
98. D₄	C₂²⋊D₇₉	semidirect

H ≅ G/N

type

1. C₂×#11929611

C₂

semidirect

2. C₂×#11929609

C₂

semidirect

3. #14579135

C₂

semidirect

4. #14579085

C₂

semidirect

5. #14579082

C₂

semidirect

6. C₂²⋊(C₇₉⋊C₈)

C₂

semidirect

7. C₂×#41×C₇₉

C₂

semidirect

27. Q₈×C₇₉

D₄

semidirect

30. D₄×C₇₉

D₄

semidirect

64. C₇₉

#449

semidirect

66. C₂×#41

D₇₉

semidirect

92. Q₈

C₂²⋊D₇₉

semidirect

98. D₄

C₂²⋊D₇₉

semidirect

Subgroups — #19098708

Conjugacy classes of subgroups

Complements