Group #23768773 — subgroups

Subgroups — #23768773

Order 10112.

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

normal subgroups only

This group has 484 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×C₄×Dic₁₅₈	C₂	1	2	yes	maximal
2	#19098493	C₂	1	4	yes	maximal
3	#19098468	C₂	1	4	yes	maximal
4	#19098462	C₂	1	4	yes	maximal
5	#384×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₅₈	C₂²	1	2	yes	—
7	C₄×Dic₁₅₈	—	2	8	no	—
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₇₉	C₂²	1	4	yes	—
10	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
12	C₇₉⋊#95	C₂²	1	8	yes	—
13	C₇₉⋊#95	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₇₉	C₂²	1	4	yes	—
15	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
16	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₅₈	—	2	4	no	—
18	C₂×Dic₁₅₈	—	2	4	no	—
19	C₂×Dic₁₅₈	Q₈	1	8	yes	complemented
20	C₂²×Dic₇₉	C₂³	1	4	yes	—
21	C₂²×Dic₇₉	C₂³	1	4	yes	—
22	C₄⋊Dic₇₉	—	2	4	no	—
23	C₄⋊Dic₇₉	—	4	4	no	—
24	Dic₇₉⋊C₄	—	2	8	no	—
25	C₄×Dic₇₉	—	2	8	no	—
26	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
27	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
29	C₄⋊C₄×C₇₉	—	2	8	no	—
30	C₄⋊C₄×C₇₉	—	4	2	no	—
31	C₄²×C₇₉	D₄	1	4	yes	—
32	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
33	C₂×C₄×C₇₉	—	2	1	no	—
34	C₂×C₄×C₇₉	—	2	1	no	—
35	C₂×C₄×C₇₉	—	2	8	no	—
36	C₂×C₄×C₇₉	—	2	4	no	—
37	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
38	C₂×C₄×C₇₉	C₂×D₄	1	4	yes	—
39	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
40	C₂×C₄×C₇₉	#41	1	4	yes	—
41	C₂×Dic₇₉	—	2	4	no	—
42	C₂×Dic₇₉	—	2	4	no	—
43	C₂×Dic₇₉	—	2	4	no	—
44	C₂×Dic₇₉	—	2	4	no	—
45	C₂×Dic₇₉	—	2	4	no	—
46	C₂×Dic₇₉	C₂×Q₈	1	8	yes	—
47	Dic₁₅₈	—	2	16	no	—
48	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
49	C₂²×C₇₉	C₂²×Q₈	1	2	yes	—
50	C₂²×C₇₉	C₂×#41	1	2	yes	—
51	C₂²×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
52	C₂²×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
53	C₄×C₇₉	—	2	2	no	—
54	C₄×C₇₉	—	4	4	no	—
55	C₄×C₇₉	C₂²⋊Q₈	1	8	yes	—
56	Dic₇₉	—	2	8	no	—
57	Dic₇₉	—	4	4	no	—
58	C₂×C₇₉	C₂×C₂²⋊Q₈	1	2	yes	—
59	C₂×C₇₉	#537	1	1	yes	characteristic
60	C₂×C₇₉	#557	1	2	yes	—
61	C₂×C₇₉	Q₈²	1	1	yes	characteristic
62	C₂×C₇₉	#559	1	1	yes	characteristic
63	#2582	—	79	1	no	maximal, Sylow
64	C₇₉	#2582	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄×Q₈	—	79	2	no	—
66	#398	—	79	4	no	—
67	#391	—	79	4	no	—
68	#389	—	79	4	no	—
69	#384	D₇₉	1	1	yes	characteristic
70	C₂²×Q₈	—	79	2	no	—
71	C₄×Q₈	—	158	8	no	—
72	C₂×C₄⋊C₄	—	79	4	no	—
73	C₂×C₄⋊C₄	—	79	2	no	—
74	C₂×C₄⋊C₄	—	79	4	no	—
75	C₂×C₄⋊C₄	C₂×D₇₉	1	4	yes	—
76	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
77	C₂×C₄²	—	79	4	no	—
78	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
79	#95	—	79	8	no	—
80	#95	—	79	4	no	—
81	C₂×Q₈	—	79	8	no	—
82	C₂×Q₈	—	158	4	no	—
83	C₂×Q₈	—	158	4	no	—
84	C₂²×C₄	—	79	4	no	—
85	C₂²×C₄	—	79	4	no	—
86	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
87	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
88	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
89	C₄⋊C₄	—	2	8	no	—
90	C₄⋊C₄	—	4	2	no	—
91	C₄⋊C₄	—	316	4	no	—
92	C₄⋊C₄	—	158	8	no	—
93	C₄⋊C₄	—	158	4	no	—
94	C₄²	—	158	8	no	—
95	C₄²	D₃₁₆	1	4	yes	—
96	C₂³	C₂³×D₇₉	1	1	yes	characteristic
97	Q₈	—	158	16	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	8	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	79	8	no	—
103	C₂×C₄	—	158	4	no	—
104	C₂×C₄	—	158	4	no	—
105	C₂×C₄	—	158	4	no	—
106	C₂×C₄	—	158	4	no	—
107	C₂×C₄	—	158	4	no	—
108	C₂×C₄	C₂×D₃₁₆	1	2	yes	—
109	C₂×C₄	C₂×D₃₁₆	1	4	yes	—
110	C₂×C₄	Q₈×D₇₉	1	4	yes	—
111	C₂×C₄	#11929623	1	4	yes	—
112	C₂²	C₂²×D₃₁₆	1	1	yes	characteristic
113	C₂²	C₂×Q₈×D₇₉	1	2	yes	—
114	C₂²	C₂×#11929623	1	2	yes	—
115	C₂²	#14579206	1	1	yes	characteristic
116	C₂²	#14579209	1	1	yes	characteristic
117	C₄	—	2	2	no	—
118	C₄	—	4	4	no	—
119	C₄	—	316	4	no	—
120	C₄	—	158	8	no	—
121	C₄	#14579141	1	8	yes	—
122	C₂	C₂×#14579141	1	2	yes	—
123	C₂	#19099144	1	1	yes	characteristic
124	C₂	#19099288	1	2	yes	—
125	C₂	#19099293	1	1	yes	characteristic
126	C₂	#19099299	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₁₅₈

C₂

yes

maximal

#19098493

C₂

yes

maximal

#19098468

C₂

yes

maximal

#19098462

C₂

yes

maximal

#384×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

Q₈

yes

complemented

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×Q₈

yes

—

Dic₁₅₈

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂²×C₇₉

C₂²×Q₈

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₇₉

2₋¹⁺⁴

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

C₂×C₂²⋊Q₈

yes

—

C₂×C₇₉

#537

yes

characteristic

C₂×C₇₉

#557

yes

—

C₂×C₇₉

Q₈²

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×C₄×Q₈

—

—

—

—

D₇₉

yes

characteristic

C₂²×Q₈

—

C₄×Q₈

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#95

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

D₃₁₆

yes

—

C₂³

C₂³×D₇₉

yes

characteristic

Q₈

—

158

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

158

—

104

C₂×C₄

—

158

—

105

C₂×C₄

—

158

—

106

C₂×C₄

—

158

—

107

C₂×C₄

—

158

—

108

C₂×C₄

C₂×D₃₁₆

yes

—

109

C₂×C₄

C₂×D₃₁₆

yes

—

110

C₂×C₄

Q₈×D₇₉

yes

—

111

C₂×C₄

#11929623

yes

—

112

C₂²

C₂²×D₃₁₆

yes

characteristic

113

C₂²

C₂×Q₈×D₇₉

yes

—

114

C₂²

C₂×#11929623

yes

—

115

C₂²

#14579206

yes

characteristic

116

C₂²

#14579209

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

316

—

120

C₄

—

158

—

121

C₄

#14579141

yes

—

122

C₂

C₂×#14579141

yes

—

123

C₂

#19099144

yes

characteristic

124

C₂

#19099288

yes

—

125

C₂

#19099293

yes

characteristic

126

C₂

#19099299

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#384×C₇₉	C₂
hypercenter	#384	D₇₉
hypocenter	C₇₉	#2582
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#384×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
19. C₂×Dic₁₅₈	Q₈	semidirect
64. C₇₉	#2582	semidirect

H ≅ G/N

type

19. C₂×Dic₁₅₈

Q₈

semidirect

64. C₇₉

#2582

semidirect

Subgroups — #23768773

Conjugacy classes of subgroups

Complements