Group #19098563 — subgroups

Subgroups — #19098563

Order 5056.

162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 55 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×#11929625	C₂	1	1	yes	maximal, characteristic
2	C₂×#11929607	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579085	C₂	1	1	yes	maximal, characteristic, complemented
5	#14579083	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579081	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#11929625	—	2	2	no	—
9	#11929625	C₄	1	4	yes	complemented
10	C₂×D₃₁₆	—	2	1	no	—
11	C₂×D₃₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₇₉	—	2	1	no	—
13	C₂×C₄×D₇₉	—	2	1	no	—
14	C₂×C₄×D₇₉	C₂²	1	1	yes	characteristic
15	#11929607	—	2	2	no	—
16	C₂×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
18	Dic₇₉⋊C₄	—	2	1	no	—
19	C₂×Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×D₇₉	—	2	1	no	—
23	C₂²×D₇₉	D₄	1	1	yes	characteristic
24	Q₈×C₇₉	—	2	1	no	—
25	Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
26	C₂×C₄×C₇₉	—	2	1	no	—
27	C₂×C₄×C₇₉	—	2	1	no	—
28	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
29	C₂×Dic₇₉	—	2	1	no	—
30	C₂×Dic₇₉	D₄	1	1	yes	characteristic
31	D₃₁₆	—	2	4	no	—
32	D₃₁₆	—	2	1	no	—
33	D₃₁₆	C₂×C₄	1	2	yes	complemented
34	C₄×D₇₉	—	2	4	no	—
35	C₄×D₇₉	—	4	2	no	—
36	C₄×D₇₉	C₂×C₄	1	2	yes	—
37	C₄×D₇₉	D₄	1	2	yes	—
38	C₈×C₇₉	—	2	1	no	—
39	C₇₉⋊C₈	—	2	1	no	—
40	C₂²×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₂×D₇₉	—	2	1	no	—
42	C₂×D₇₉	—	2	1	no	—
43	C₂×D₇₉	—	2	2	no	—
44	C₂×D₇₉	—	4	1	no	—
45	C₂×D₇₉	—	4	1	no	—
46	C₂×D₇₉	C₂²⋊C₄	1	2	yes	—
47	C₄×C₇₉	—	2	2	no	—
48	C₄×C₇₉	—	4	1	no	—
49	C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
50	C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
51	Dic₇₉	—	4	1	no	—
52	Dic₇₉	C₂²⋊C₄	1	2	yes	—
53	C₂×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₂×C₇₉	#137	1	1	yes	characteristic
56	D₇₉	—	2	2	no	—
57	D₇₉	—	4	2	no	—
58	C₇₉	#417	1	1	yes	characteristic, complemented, Sylow
59	#417	—	79	1	no	maximal, Sylow
60	C₂×#41	—	79	1	no	—
61	C₂×M₁₆	—	79	1	no	—
62	C₂×C₄⋊C₄	—	79	1	no	—
63	#103	—	79	1	no	—
64	#103	D₇₉	1	1	yes	characteristic, complemented
65	#102	—	79	1	no	—
66	#102	—	79	1	no	—
67	#41	—	79	4	no	—
68	#41	—	158	2	no	—
69	C₂×Q₈	C₂×D₇₉	1	1	yes	characteristic
70	C₂×D₄	—	79	1	no	—
71	C₂×D₄	—	158	1	no	—
72	C₂²×C₄	—	79	1	no	—
73	C₂²×C₄	—	158	1	no	—
74	C₂²×C₄	—	158	1	no	—
75	M₁₆	—	158	2	no	—
76	C₂×C₈	—	79	1	no	—
77	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
78	C₄⋊C₄	—	79	1	no	—
79	C₄⋊C₄	—	158	1	no	—
80	C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
81	C₂³	—	79	1	no	—
82	C₂³	—	158	1	no	—
83	Q₈	—	2	1	no	—
84	Q₈	C₄×D₇₉	1	2	yes	complemented
85	D₄	—	79	2	no	—
86	D₄	—	158	4	no	—
87	D₄	—	158	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	316	2	no	—
91	C₂×C₄	—	79	1	no	—
92	C₂×C₄	—	79	2	no	—
93	C₂×C₄	—	79	2	no	—
94	C₂×C₄	—	158	4	no	—
95	C₂×C₄	—	158	1	no	—
96	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
97	C₈	—	2	1	no	—
98	C₈	—	158	1	no	—
99	C₂²	—	316	1	no	—
100	C₂²	—	316	1	no	—
101	C₂²	—	79	2	no	—
102	C₂²	—	158	2	no	—
103	C₂²	—	158	1	no	—
104	C₂²	—	158	1	no	—
105	C₂²	D₄×D₇₉	1	1	yes	characteristic
106	C₄	—	2	2	no	—
107	C₄	—	4	1	no	—
108	C₄	—	316	1	no	—
109	C₄	—	79	2	no	—
110	C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
111	C₄	D₄×D₇₉	1	1	yes	characteristic
112	C₂	—	316	2	no	—
113	C₂	—	158	2	no	—
114	C₂	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
115	C₂	#14579188	1	1	yes	characteristic
116	C₂	#14579193	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11929625

C₂

yes

maximal, characteristic

C₂×#11929607

C₂

yes

maximal, characteristic, complemented

C₄⋊C₄×D₇₉

C₂

yes

maximal, characteristic, complemented

#14579085

C₂

yes

maximal, characteristic, complemented

#14579083

C₂

yes

maximal, characteristic, complemented

#14579081

C₂

yes

maximal, characteristic, complemented

#103×C₇₉

C₂

yes

maximal, characteristic, complemented

#11929625

—

#11929625

C₄

yes

complemented

C₂×D₃₁₆

—

C₂×D₃₁₆

C₂²

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₂²

yes

characteristic

#11929607

—

C₂×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Dic₇₉

C₂²

yes

characteristic

Dic₇₉⋊C₄

—

C₂×Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

D₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

C₂×C₄

yes

complemented

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

D₄

yes

characteristic

D₃₁₆

—

D₃₁₆

—

D₃₁₆

C₂×C₄

yes

complemented

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

C₂×C₄

yes

—

C₄×D₇₉

D₄

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

C₂²⋊C₄

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²×C₄

yes

characteristic

C₄×C₇₉

C₂×D₄

yes

characteristic

Dic₇₉

—

Dic₇₉

C₂²⋊C₄

yes

—

C₂×C₇₉

C₂×C₂²⋊C₄

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

D₇₉

—

C₇₉

#417

yes

characteristic, complemented, Sylow

#417

—

maximal, Sylow

C₂×#41

—

C₂×M₁₆

—

C₂×C₄⋊C₄

—

#103

—

#103

D₇₉

yes

characteristic, complemented

—

—

—

—

158

—

C₂×Q₈

C₂×D₇₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

158

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

C₂×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

C₂×D₇₉

yes

characteristic

C₂³

—

C₂³

—

158

—

Q₈

—

Q₈

C₄×D₇₉

yes

complemented

D₄

—

D₄

—

158

—

D₄

—

158

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂²×D₇₉

yes

characteristic

C₈

—

C₈

—

158

—

C₂²

—

316

—

100

C₂²

—

316

—

101

C₂²

—

102

C₂²

—

158

—

103

C₂²

—

158

—

104

C₂²

—

158

—

105

C₂²

D₄×D₇₉

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

316

—

109

C₄

—

110

C₄

C₂×C₄×D₇₉

yes

characteristic

111

C₄

D₄×D₇₉

yes

characteristic

112

C₂

—

316

—

113

C₂

—

158

—

114

C₂

C₂²⋊C₄×D₇₉

yes

characteristic

115

C₂

#14579188

yes

characteristic

116

C₂

#14579193

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₇₉
commutator	C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇₉
Fitting	#103×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₄
hypercenter	#103	D₇₉
hypocenter	C₇₉	#417
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

subgroup

G/H

center

C₂²

D₄×D₇₉

commutator

C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×D₇₉

Fitting

#103×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

N	H ≅ G/N	type
2. C₂×#11929607	C₂	semidirect
3. C₄⋊C₄×D₇₉	C₂	semidirect
4. #14579085	C₂	semidirect
5. #14579083	C₂	semidirect
6. #14579081	C₂	semidirect
7. #103×C₇₉	C₂	semidirect
9. #11929625	C₄	semidirect
25. Q₈×C₇₉	C₂×C₄	semidirect
33. D₃₁₆	C₂×C₄	semidirect
58. C₇₉	#417	semidirect
64. #103	D₇₉	semidirect
84. Q₈	C₄×D₇₉	semidirect

H ≅ G/N

type

2. C₂×#11929607

C₂

semidirect

3. C₄⋊C₄×D₇₉

C₂

semidirect

4. #14579085

C₂

semidirect

5. #14579083

C₂

semidirect

6. #14579081

C₂

semidirect

7. #103×C₇₉

C₂

semidirect

9. #11929625

C₄

semidirect

25. Q₈×C₇₉

C₂×C₄

semidirect

33. D₃₁₆

C₂×C₄

semidirect

58. C₇₉

#417

semidirect

64. #103

D₇₉

semidirect

84. Q₈

C₄×D₇₉

semidirect

Subgroups — #19098563

Conjugacy classes of subgroups

Complements