Group #22627001 — subgroups

Subgroups — #22627001

Order 9344.

160 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 75 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	C₂²×#11924040	C₂	1	2	yes	maximal
2	C₂×C₄×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924040	—	2	2	no	—
4	C₂×#11924040	—	2	2	no	—
5	C₂×#11924040	C₄	1	4	yes	complemented
6	C₂²×#10596833	C₄	1	1	yes	characteristic
7	C₂²×#10596833	C₂²	1	1	yes	characteristic
8	C₄×#10596833	—	2	2	no	—
9	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
10	#11924040	—	2	4	no	—
11	C₂×#10596833	—	2	1	no	—
12	C₂×#10596833	—	2	1	no	—
13	C₂×#10596833	C₈	1	2	yes	—
14	C₂×#10596833	C₂×C₄	1	2	yes	—
15	C₂×#10596833	D₄	1	1	yes	characteristic
16	C₂×#10596833	D₄	1	2	yes	—
17	C₂×#10596833	Q₈	1	1	yes	characteristic
18	C₂²×Dic₇₃	C₈	1	1	yes	characteristic
19	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₇₃	—	2	1	no	—
21	C₄×Dic₇₃	—	2	1	no	—
22	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
23	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₇₃	—	2	1	no	—
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	C₁₆	1	2	yes	complemented
27	C₂×Dic₇₃	—	2	1	no	—
28	C₂×Dic₇₃	—	2	1	no	—
29	C₂×Dic₇₃	C₁₆	1	2	yes	complemented
30	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
31	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
34	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
35	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
36	#10596833	—	2	2	no	—
37	#10596833	C₂²⋊C₄	1	2	yes	—
38	#10596833	C₄⋊C₄	1	2	yes	—
39	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
40	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
41	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
42	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
43	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
44	C₂²×C₇₃	M₃₂	1	1	yes	characteristic
45	C₂²×C₇₃	M₃₂	1	1	yes	characteristic
46	C₄×C₇₃	—	2	2	no	—
47	Dic₇₃	—	2	2	no	—
48	Dic₇₃	#95	1	1	yes	characteristic
49	Dic₇₃	#97	1	1	yes	characteristic
50	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
51	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₇₃	#336	1	1	yes	characteristic
53	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
54	C₂×C₇₃	#346	1	1	yes	characteristic
55	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
56	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
57	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
58	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
59	#1374	—	73	1	no	maximal, Sylow
60	C₇₃	#1374	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₁₆	—	73	2	no	—
62	C₂×C₄×C₈	—	73	1	no	—
63	C₂²×C₈	—	73	1	no	—
64	C₂²×C₈	—	73	1	no	—
65	C₂×C₄²	—	73	1	no	—
66	C₂×C₁₆	—	73	4	no	—
67	C₂×C₁₆	—	146	2	no	—
68	C₂×C₁₆	—	146	2	no	—
69	C₄×C₈	—	146	2	no	—
70	C₂²×C₄	—	73	1	no	—
71	C₂²×C₄	—	73	1	no	—
72	C₂²×C₄	#10596842	1	1	yes	characteristic
73	C₂×C₈	—	73	2	no	—
74	C₂×C₈	—	73	2	no	—
75	C₂×C₈	—	73	1	no	—
76	C₂×C₈	—	73	1	no	—
77	C₂×C₈	—	73	2	no	—
78	C₂×C₈	—	146	1	no	—
79	C₂×C₈	—	146	1	no	—
80	C₄²	—	146	1	no	—
81	C₄²	—	146	1	no	—
82	C₁₆	—	146	4	no	—
83	C₂³	C₂×#10596842	1	1	yes	characteristic
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	73	1	no	—
87	C₂×C₄	—	73	1	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	2	no	—
93	C₂×C₄	—	146	1	no	—
94	C₂×C₄	—	146	1	no	—
95	C₂×C₄	#11924040	1	2	yes	complemented
96	C₈	—	73	2	no	—
97	C₈	—	73	2	no	—
98	C₈	—	146	2	no	—
99	C₂²	C₄×#10596842	1	1	yes	characteristic
100	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
101	C₂²	C₄⋊#10596842	1	1	yes	characteristic
102	C₂²	C₂×#11924040	1	1	yes	characteristic
103	C₂²	#14556686	1	1	yes	characteristic
104	C₂²	#14556687	1	1	yes	characteristic
105	C₂²	#14556688	1	1	yes	characteristic
106	C₄	—	2	2	no	—
107	C₄	—	73	1	no	—
108	C₄	—	73	1	no	—
109	C₄	—	73	1	no	—
110	C₄	—	73	1	no	—
111	C₄	—	146	2	no	—
112	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
113	C₂	C₄×#11924040	1	1	yes	characteristic
114	C₂	#17989681	1	1	yes	characteristic
115	C₂	C₂²⋊#11924040	1	1	yes	characteristic
116	C₂	#17989684	1	1	yes	characteristic
117	C₂	C₄⋊#11924040	1	1	yes	characteristic
118	C₂	#17989690	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924040

C₂

yes

maximal

C₂×C₄×#10596833

C₂

yes

maximal, characteristic

C₂×#11924040

—

C₂×#11924040

—

C₂×#11924040

C₄

yes

complemented

C₂²×#10596833

C₄

yes

characteristic

C₂²×#10596833

C₂²

yes

characteristic

C₄×#10596833

—

C₂×C₄×Dic₇₃

C₄

yes

—

—

—

C₈

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

D₄

yes

characteristic

C₂×#10596833

D₄

yes

—

C₂×#10596833

Q₈

yes

characteristic

C₂²×Dic₇₃

C₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₈

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₁₆

yes

complemented

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₁₆

yes

complemented

C₂×Dic₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

characteristic

#10596833

—

#10596833

C₂²⋊C₄

yes

—

#10596833

C₄⋊C₄

yes

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₂²×C₇₃

C₂×C₁₆

yes

characteristic

C₂²×C₇₃

C₂×C₁₆

yes

characteristic

C₂²×C₇₃

M₃₂

yes

characteristic

C₂²×C₇₃

M₃₂

yes

characteristic

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

Dic₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

#336

yes

characteristic

C₂×C₇₃

C₄×C₁₆

yes

characteristic

C₂×C₇₃

#346

yes

characteristic

C₂×C₇₃

C₂²⋊C₁₆

yes

characteristic

C₂×C₇₃

C₂²⋊C₁₆

yes

characteristic

C₂×C₇₃

C₄⋊C₁₆

yes

characteristic

C₂×C₇₃

C₄⋊C₁₆

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#10596842

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

146

—

C₄²

—

146

—

C₁₆

—

146

—

C₂³

C₂×#10596842

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

#11924040

yes

complemented

C₈

—

C₈

—

C₈

—

146

—

C₂²

C₄×#10596842

yes

characteristic

100

C₂²

C₂²⋊#10596842

yes

characteristic

101

C₂²

C₄⋊#10596842

yes

characteristic

102

C₂²

C₂×#11924040

yes

characteristic

103

C₂²

#14556686

yes

characteristic

104

C₂²

#14556687

yes

characteristic

105

C₂²

#14556688

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

146

—

112

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

113

C₂

C₄×#11924040

yes

characteristic

114

C₂

#17989681

yes

characteristic

115

C₂

C₂²⋊#11924040

yes

characteristic

116

C₂

#17989684

yes

characteristic

117

C₂

C₄⋊#11924040

yes

characteristic

118

C₂

#17989690

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂×#10596842
commutator	C₂×C₇₃	C₄×C₁₆
Fitting	C₂²×C₄×C₇₃	C₈
socle	C₂³×C₇₃	C₂×C₈
hypercenter	C₂²×C₄	#10596842
hypocenter	C₇₃	#1374
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

subgroup

G/H

center, Frattini

C₂³

C₂×#10596842

commutator

C₂×C₇₃

C₄×C₁₆

Fitting

C₂²×C₄×C₇₃

C₈

socle

C₂³×C₇₃

C₂×C₈

C₂²×C₄

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ C₂²×C₄

N	H ≅ G/N	type
5. C₂×#11924040	C₄	semidirect
26. C₂×C₄×C₇₃	C₁₆	semidirect
29. C₂×Dic₇₃	C₁₆	semidirect
60. C₇₃	#1374	semidirect
95. C₂×C₄	#11924040	semidirect

H ≅ G/N

type

5. C₂×#11924040

C₄

semidirect

26. C₂×C₄×C₇₃

C₁₆

semidirect

29. C₂×Dic₇₃

C₁₆

semidirect

60. C₇₃

#1374

semidirect

95. C₂×C₄

#11924040

semidirect

Subgroups — #22627001

Conjugacy classes of subgroups

Complements