Group #22626587 — subgroups

Subgroups — C₂²×#14556661 #22626587

Order 9344.

480 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 218 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×#11924038	C₂	1	2	yes	maximal
2	C₂×#14556661	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924038	—	2	6	no	—
5	C₂×#11924038	C₂²	1	12	yes	—
6	C₂²×#10596833	—	2	2	no	—
7	#14556661	C₂²	1	16	yes	direct product factor
8	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
9	C₂²×#10596831	C₄	1	1	yes	characteristic
10	C₂×C₈×D₇₃	C₄	1	6	yes	—
11	C₂×C₈×D₇₃	C₂²	1	6	yes	—
12	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
13	#11924038	—	2	12	no	—
14	#11924038	C₂³	1	8	yes	—
15	C₂×#10596833	—	2	12	no	—
16	C₂³×D₇₃	Q₈	1	1	yes	characteristic
17	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
18	C₂×C₄×D₇₃	C₂×C₄	1	3	yes	—
19	C₂×C₄×D₇₃	D₄	1	3	yes	—
20	C₂×C₄×D₇₃	Q₈	1	3	yes	—
21	C₂×C₄×D₇₃	C₂³	1	3	yes	—
22	C₂×#10596831	C₂×C₄	1	6	yes	—
23	C₈×D₇₃	C₂×C₄	1	12	yes	—
24	C₈×D₇₃	C₂³	1	4	yes	—
25	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	C₂×C₄	1	6	yes	—
27	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×D₇₃	—	2	4	no	—
29	C₂²×D₇₃	C₄⋊C₄	1	3	yes	—
30	C₂²×D₇₃	C₂×Q₈	1	3	yes	—
31	C₂×C₄×C₇₃	C₄⋊C₄	1	3	yes	—
32	C₂×C₄×C₇₃	C₂²×C₄	1	3	yes	—
33	C₂×Dic₇₃	C₄⋊C₄	1	3	yes	—
34	C₂×Dic₇₃	C₂×D₄	1	3	yes	—
35	C₄×D₇₃	C₄⋊C₄	1	6	yes	—
36	C₄×D₇₃	C₂²×C₄	1	3	yes	—
37	C₄×D₇₃	C₂×D₄	1	3	yes	—
38	C₄×D₇₃	C₂×Q₈	1	3	yes	—
39	C₄×D₇₃	C₂⁴	1	1	yes	characteristic
40	#10596833	—	2	8	no	—
41	C₈×C₇₃	C₂²×C₄	1	4	yes	—
42	#10596831	C₂²×C₄	1	4	yes	—
43	C₂²×C₇₃	#108	1	4	yes	complemented
44	C₂²×C₇₃	C₂×C₄⋊C₄	1	3	yes	—
45	C₂×D₇₃	—	2	6	no	—
46	C₂×D₇₃	—	2	6	no	—
47	C₂×D₇₃	C₂×C₄⋊C₄	1	3	yes	—
48	C₂×D₇₃	C₂²×Q₈	1	1	yes	characteristic
49	C₄×C₇₃	C₂×C₄⋊C₄	1	3	yes	—
50	C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
51	Dic₇₃	C₂×C₄⋊C₄	1	3	yes	—
52	Dic₇₃	C₂²×D₄	1	1	yes	characteristic
53	C₂×C₇₃	C₂×#108	1	6	yes	complemented
54	C₂×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
55	D₇₃	—	2	3	no	—
56	D₇₃	—	2	1	no	—
57	C₂²×#108	—	73	1	no	maximal, Sylow
58	C₇₃	C₂²×#108	1	1	yes	characteristic, complemented, Sylow
59	C₂²×M₁₆	—	73	2	no	—
60	C₂³×C₈	—	73	1	no	—
61	C₂×#108	—	73	12	no	—
62	C₂³×C₄	—	73	1	no	—
63	C₂×M₁₆	—	73	12	no	—
64	C₂×M₁₆	—	146	6	no	—
65	C₂²×C₈	—	73	1	no	—
66	C₂²×C₈	—	73	6	no	—
67	C₂²×C₈	—	73	6	no	—
68	C₂²×C₈	—	146	2	no	—
69	C₂²×C₈	#64408	1	1	yes	characteristic
70	#108	—	73	16	no	—
71	C₂⁴	—	73	1	no	—
72	C₂²×C₄	—	73	1	no	—
73	C₂²×C₄	—	73	3	no	—
74	C₂²×C₄	—	73	3	no	—
75	C₂²×C₄	—	73	3	no	—
76	C₂²×C₄	—	73	3	no	—
77	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
78	M₁₆	—	73	8	no	—
79	M₁₆	—	146	12	no	—
80	C₂×C₈	—	73	6	no	—
81	C₂×C₈	—	73	12	no	—
82	C₂×C₈	—	73	4	no	—
83	C₂×C₈	—	146	12	no	—
84	C₂×C₈	C₂×#64408	1	6	yes	—
85	C₂³	—	73	3	no	—
86	C₂³	—	73	3	no	—
87	C₂³	—	146	4	no	—
88	C₂³	C₄⋊#64408	1	1	yes	characteristic
89	C₂×C₄	—	73	3	no	—
90	C₂×C₄	—	73	3	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	3	no	—
93	C₂×C₄	—	73	3	no	—
94	C₂×C₄	—	73	6	no	—
95	C₂×C₄	—	73	3	no	—
96	C₂×C₄	C₄⋊#64408	1	3	yes	—
97	C₂×C₄	C₂²×#64408	1	3	yes	—
98	C₈	—	73	4	no	—
99	C₈	—	146	8	no	—
100	C₈	C₂²×#64408	1	4	yes	—
101	C₂²	—	73	3	no	—
102	C₂²	—	73	1	no	—
103	C₂²	—	146	6	no	—
104	C₂²	—	146	6	no	—
105	C₂²	#14556661	1	4	yes	direct product factor
106	C₂²	C₂×C₄⋊#64408	1	3	yes	—
107	C₄	—	73	1	no	—
108	C₄	—	73	3	no	—
109	C₄	C₂×C₄⋊#64408	1	3	yes	—
110	C₄	C₂³×#64408	1	1	yes	characteristic
111	C₂	—	146	3	no	—
112	C₂	—	146	1	no	—
113	C₂	C₂×#14556661	1	6	yes	direct product factor
114	C₂	C₂²×C₄⋊#64408	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924038

C₂

yes

maximal

C₂×#14556661

C₂

yes

maximal, direct product factor

C₂²×C₈×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924038

—

C₂×#11924038

C₂²

yes

—

C₂²×#10596833

—

#14556661

C₂²

yes

direct product factor

C₂²×C₄×D₇₃

C₂²

yes

characteristic

C₂²×#10596831

C₄

yes

characteristic

C₂×C₈×D₇₃

C₄

yes

—

C₂×C₈×D₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₄

yes

characteristic

#11924038

—

#11924038

C₂³

yes

—

C₂×#10596833

—

C₂³×D₇₃

Q₈

yes

characteristic

C₂²×Dic₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

D₄

yes

—

C₂×C₄×D₇₃

Q₈

yes

—

C₂×C₄×D₇₃

C₂³

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

C₄⋊C₄

yes

—

C₂²×D₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

—

C₄×D₇₃

C₄⋊C₄

yes

—

C₄×D₇₃

C₂²×C₄

yes

—

C₄×D₇₃

C₂×D₄

yes

—

C₄×D₇₃

C₂×Q₈

yes

—

C₄×D₇₃

C₂⁴

yes

characteristic

#10596833

—

C₈×C₇₃

C₂²×C₄

yes

—

#10596831

C₂²×C₄

yes

—

C₂²×C₇₃

#108

yes

complemented

C₂²×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂×C₄⋊C₄

yes

—

C₂×D₇₃

C₂²×Q₈

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₄×C₇₃

C₂³×C₄

yes

characteristic

Dic₇₃

C₂×C₄⋊C₄

yes

—

Dic₇₃

C₂²×D₄

yes

characteristic

C₂×C₇₃

C₂×#108

yes

complemented

C₂×C₇₃

C₂²×C₄⋊C₄

yes

characteristic

D₇₃

—

D₇₃

—

C₂²×#108

—

maximal, Sylow

C₇₃

C₂²×#108

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂³×C₈

—

C₂×#108

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

146

—

C₂²×C₈

#64408

yes

characteristic

#108

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₂³

—

C₂³

—

C₂³

—

146

—

C₂³

C₄⋊#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊#64408

yes

—

C₂×C₄

C₂²×#64408

yes

—

C₈

—

C₈

—

146

—

100

C₈

C₂²×#64408

yes

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

146

—

104

C₂²

—

146

—

105

C₂²

#14556661

yes

direct product factor

106

C₂²

C₂×C₄⋊#64408

yes

—

107

C₄

—

108

C₄

—

109

C₄

C₂×C₄⋊#64408

yes

—

110

C₄

C₂³×#64408

yes

characteristic

111

C₂

—

146

—

112

C₂

—

146

—

113

C₂

C₂×#14556661

yes

direct product factor

114

C₂

C₂²×C₄⋊#64408

yes

characteristic

	subgroup	G/H
center	C₂³	C₄⋊#64408
commutator	C₄×C₇₃	C₂³×C₄
Frattini	C₄	C₂³×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂³×C₇₃	C₄⋊C₄
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	C₂²×#108
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂³

C₄⋊#64408

commutator

C₄×C₇₃

C₂³×C₄

Frattini

C₄

C₂³×#64408

Fitting

C₂²×C₈×C₇₃

C₄

socle

C₂³×C₇₃

C₄⋊C₄

hypercenter

C₂²×C₈

#64408

hypocenter

C₇₃

C₂²×#108

LCS

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. C₂×#14556661	C₂	direct (N × H)
7. #14556661	C₂²	direct (N × H)
43. C₂²×C₇₃	#108	semidirect
53. C₂×C₇₃	C₂×#108	semidirect
58. C₇₃	C₂²×#108	semidirect
105. C₂²	#14556661	direct (N × H)
113. C₂	C₂×#14556661	direct (N × H)

H ≅ G/N

type

2. C₂×#14556661

C₂

direct (N × H)

7. #14556661

C₂²

direct (N × H)

43. C₂²×C₇₃

#108

semidirect

53. C₂×C₇₃

C₂×#108

semidirect

58. C₇₃

C₂²×#108

semidirect

105. C₂²

#14556661

direct (N × H)

113. C₂

C₂×#14556661

direct (N × H)

Subgroups — C₂²×#14556661 #22626587

Conjugacy classes of subgroups

Complements

Subgroups — C22×#14556661 #22626587

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14556661 #22626587