Group #22625564 — subgroups

Subgroups — #22625564

Order 9344.

180 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 58 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	#17989622	C₂	1	2	yes	maximal, complemented
2	#17989450	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄⋊#10596833	C₂	1	2	yes	maximal, complemented
4	C₈×#10596833	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924037	—	2	2	no	—
7	C₄⋊#10596833	C₂²	1	2	yes	—
8	C₂²⋊#10596833	—	2	2	no	—
9	C₄×#10596833	C₂²	1	1	yes	characteristic
10	C₄×#10596833	C₂²	1	1	yes	characteristic
11	D₄×Dic₇₃	C₂²	1	2	yes	—
12	#14556525	C₄	1	1	yes	characteristic
13	#14556512	C₄	1	2	yes	—
14	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
15	C₂×D₈×C₇₃	C₄	1	1	yes	characteristic
16	#11924037	—	4	4	no	—
17	C₂×#10596833	—	2	1	no	—
18	C₂×#10596833	—	2	2	no	—
19	C₂×#10596833	D₄	1	1	yes	characteristic
20	C₂×#10596833	D₄	1	1	yes	characteristic
21	C₂²×Dic₇₃	—	2	2	no	—
22	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
23	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
24	C₂²⋊Dic₇₃	—	2	2	no	—
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₂×D₄×C₇₃	C₂×C₄	1	2	yes	—
27	D₈×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₇₃	—	2	2	no	—
30	D₄×C₇₃	—	2	2	no	—
31	D₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₇₃	—	2	2	no	—
34	C₂×Dic₇₃	—	4	2	no	—
35	C₂×Dic₇₃	—	4	2	no	—
36	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₇₃	#41	1	1	yes	characteristic
38	#10596833	—	2	2	no	—
39	#10596833	—	2	1	no	—
40	#10596833	—	4	2	no	—
41	#10596833	D₈	1	2	yes	complemented
42	C₈×C₇₃	M₁₆	1	2	yes	complemented
43	#10596831	—	2	1	no	—
44	C₂²×C₇₃	—	4	2	no	—
45	C₂²×C₇₃	—	4	2	no	—
46	C₂²×C₇₃	—	4	2	no	—
47	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
48	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₇₃	#131	1	1	yes	characteristic
50	Dic₇₃	—	2	1	no	—
51	Dic₇₃	—	4	2	no	—
52	Dic₇₃	C₂×D₈	1	1	yes	characteristic
53	Dic₇₃	#135	1	1	yes	characteristic
54	C₂×C₇₃	—	8	2	no	—
55	C₂×C₇₃	#436	1	1	yes	characteristic
56	C₂×C₇₃	C₄×D₈	1	1	yes	characteristic
57	C₂×C₇₃	#443	1	1	yes	characteristic
58	#1589	—	73	1	no	maximal, Sylow
59	C₇₃	#1589	1	1	yes	characteristic, complemented, Sylow
60	C₄×D₈	—	73	1	no	—
61	#436	—	73	2	no	—
62	#335	—	73	1	no	—
63	D₄⋊C₈	—	73	2	no	—
64	C₈²	—	73	1	no	—
65	C₂×D₈	#64408	1	1	yes	characteristic
66	C₂×M₁₆	—	146	2	no	—
67	C₄×D₄	—	73	2	no	—
68	#107	—	73	1	no	—
69	C₄⋊C₈	—	73	2	no	—
70	#102	—	73	2	no	—
71	C₂²⋊C₈	—	146	2	no	—
72	C₄×C₈	—	73	1	no	—
73	C₄×C₈	—	73	1	no	—
74	C₄×C₈	—	73	1	no	—
75	C₂×D₄	C₂×#64408	1	2	yes	—
76	C₂²×C₄	—	146	2	no	—
77	D₈	—	2	2	no	—
78	M₁₆	—	292	4	no	—
79	C₂×C₈	—	73	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	146	2	no	—
83	C₂×C₈	—	146	1	no	—
84	C₂×C₈	C₂×#64408	1	1	yes	characteristic
85	C₄⋊C₄	—	73	2	no	—
86	C₂²⋊C₄	—	146	2	no	—
87	C₄²	—	73	1	no	—
88	C₂³	—	2	2	no	—
89	D₄	—	2	2	no	—
90	D₄	—	2	2	no	—
91	C₂×C₄	—	292	2	no	—
92	C₂×C₄	—	292	2	no	—
93	C₂×C₄	—	73	1	no	—
94	C₂×C₄	—	73	1	no	—
95	C₂×C₄	—	146	2	no	—
96	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
97	C₈	—	292	2	no	—
98	C₈	—	73	2	no	—
99	C₈	—	146	1	no	—
100	C₈	—	146	2	no	—
101	C₈	—	146	1	no	—
102	C₈	#11924037	1	2	yes	complemented
103	C₂²	—	4	2	no	—
104	C₂²	—	4	2	no	—
105	C₂²	—	4	2	no	—
106	C₂²	D₄×#64408	1	1	yes	characteristic
107	C₄	—	292	2	no	—
108	C₄	—	73	1	no	—
109	C₄	—	73	1	no	—
110	C₄	—	146	1	no	—
111	C₄	C₂×#11924037	1	1	yes	characteristic
112	C₄	#14556678	1	1	yes	characteristic
113	C₂	—	8	2	no	—
114	C₂	#17989622	1	1	yes	characteristic
115	C₂	D₈×#64408	1	1	yes	characteristic
116	C₂	#17989629	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989622

C₂

yes

maximal, complemented

#17989450

C₂

yes

maximal, characteristic, complemented

D₄⋊#10596833

C₂

yes

maximal, complemented

C₈×#10596833

C₂

yes

maximal, characteristic, complemented

D₈×Dic₇₃

C₂

yes

maximal, characteristic

C₂×#11924037

—

C₄⋊#10596833

C₂²

yes

—

C₂²⋊#10596833

—

C₄×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

D₄×Dic₇₃

C₂²

yes

—

#14556525

C₄

yes

characteristic

#14556512

C₄

yes

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×D₈×C₇₃

C₄

yes

—

—

—

D₄

yes

characteristic

C₂×#10596833

D₄

yes

characteristic

C₂²×Dic₇₃

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₄⋊Dic₇₃

C₂×C₄

yes

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×D₄×C₇₃

C₂×C₄

yes

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

C₂×Dic₇₃

yes

—

—

—

D₈

yes

complemented

C₈×C₇₃

M₁₆

yes

complemented

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

#131

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

C₂×D₈

yes

characteristic

Dic₇₃

#135

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

#436

yes

characteristic

C₂×C₇₃

C₄×D₈

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₄×D₈

—

#436

—

#335

—

D₄⋊C₈

—

C₈²

—

C₂×D₈

#64408

yes

characteristic

C₂×M₁₆

—

146

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×D₄

C₂×#64408

yes

—

C₂²×C₄

—

146

—

D₈

—

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

146

—

C₄²

—

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

292

—

C₈

—

C₈

—

146

—

100

C₈

—

146

—

101

C₈

—

146

—

102

C₈

#11924037

yes

complemented

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

D₄×#64408

yes

characteristic

107

C₄

—

292

—

108

C₄

—

109

C₄

—

110

C₄

—

146

—

111

C₄

C₂×#11924037

yes

characteristic

112

C₄

#14556678

yes

characteristic

113

C₂

—

114

C₂

#17989622

yes

characteristic

115

C₂

D₈×#64408

yes

characteristic

116

C₂

#17989629

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂×D₈×C₇₃	C₄
socle	C₂²×C₇₃	C₄×D₄
hypercenter	C₂×D₈	#64408
hypocenter	C₇₃	#1589
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

subgroup

G/H

center

C₂²

D₄×#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₂×D₈×C₇₃

C₄

socle

C₂²×C₇₃

C₄×D₄

C₂×D₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

N	H ≅ G/N	type
1. #17989622	C₂	semidirect
2. #17989450	C₂	semidirect
3. D₄⋊#10596833	C₂	semidirect
4. C₈×#10596833	C₂	semidirect
41. #10596833	D₈	semidirect
42. C₈×C₇₃	M₁₆	semidirect
59. C₇₃	#1589	semidirect
102. C₈	#11924037	semidirect

H ≅ G/N

type

1. #17989622

C₂

semidirect

2. #17989450

C₂

semidirect

3. D₄⋊#10596833

C₂

semidirect

4. C₈×#10596833

C₂

semidirect

41. #10596833

D₈

semidirect

42. C₈×C₇₃

M₁₆

semidirect

59. C₇₃

#1589

semidirect

102. C₈

#11924037

semidirect

Subgroups — #22625564

Conjugacy classes of subgroups

Complements