Group #22625470 — subgroups

Subgroups — #22625470

Order 9344.

210 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 62 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	#17989590	C₂	1	2	yes	maximal
2	#17989446	C₂	1	4	yes	maximal, complemented
3	#17989140	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924037	—	2	2	no	—
5	#14556658	C₂²	1	4	yes	—
6	C₄⋊#10596833	—	2	2	no	—
7	#14556590	C₂²	1	2	yes	—
8	#14556582	C₄	1	2	yes	—
9	#14556568	—	2	2	no	—
10	C₄×Dic₁₄₆	—	2	2	no	—
11	#14556550	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
13	#117×C₇₃	C₄	1	1	yes	characteristic
14	#11924037	—	4	4	no	—
15	C₂×#10596833	—	2	4	no	—
16	C₂×Dic₁₄₆	—	2	2	no	—
17	C₂²×Dic₇₃	D₄	1	2	yes	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
20	#11924007	—	2	2	no	—
21	#11924007	—	2	2	no	—
22	C₂²⋊Dic₇₃	—	2	1	no	—
23	C₄×Dic₇₃	—	2	1	no	—
24	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₇₃	D₄	1	2	yes	—
26	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
29	C₂²⋊C₄×C₇₃	—	2	1	no	—
30	C₄²×C₇₃	—	2	1	no	—
31	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₇₃	—	2	2	no	—
37	C₂×Dic₇₃	—	2	2	no	—
38	C₂×Dic₇₃	—	2	2	no	—
39	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
40	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
41	Dic₁₄₆	—	4	2	no	—
42	Dic₁₄₆	—	4	2	no	—
43	#10596833	—	4	4	no	—
44	C₂²×C₇₃	—	2	1	no	—
45	C₂²×C₇₃	—	2	2	no	—
46	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	—	4	2	no	—
49	C₄×C₇₃	#101	1	2	yes	—
50	Dic₇₃	—	2	2	no	—
51	Dic₇₃	—	4	2	no	—
52	Dic₇₃	AGL(1,ℤ/8)	1	2	yes	—
53	Dic₇₃	#137	1	2	yes	—
54	C₂×C₇₃	—	4	1	no	—
55	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
56	C₂×C₇₃	#417	1	2	yes	—
57	#1561	—	73	1	no	maximal, Sylow
58	C₇₃	#1561	1	1	yes	characteristic, complemented, Sylow
59	#533	—	73	1	no	—
60	#423	—	73	2	no	—
61	#332	—	73	4	no	—
62	C₂×M₁₆	—	146	2	no	—
63	C₄⋊Q₈	—	73	2	no	—
64	#125	—	73	2	no	—
65	C₂²⋊Q₈	—	146	2	no	—
66	C₄×Q₈	—	146	2	no	—
67	#117	—	73	1	no	—
68	#117	#64408	1	1	yes	characteristic
69	C₂×C₄²	—	73	1	no	—
70	C₄⋊C₈	—	73	4	no	—
71	C₄⋊C₈	—	146	2	no	—
72	C₂×Q₈	—	146	2	no	—
73	C₂²×C₄	—	73	2	no	—
74	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
75	M₁₆	—	292	4	no	—
76	C₂×C₈	—	146	4	no	—
77	C₄⋊C₄	—	73	2	no	—
78	C₄⋊C₄	—	146	2	no	—
79	C₄⋊C₄	—	146	2	no	—
80	C₄⋊C₄	—	146	2	no	—
81	C₄⋊C₄	C₂×#64408	1	2	yes	—
82	C₂²⋊C₄	—	2	1	no	—
83	C₂²⋊C₄	—	146	1	no	—
84	C₄²	—	2	1	no	—
85	C₄²	—	73	2	no	—
86	C₄²	—	73	1	no	—
87	C₄²	—	73	1	no	—
88	C₄²	—	146	1	no	—
89	C₂³	C₂²⋊#64408	1	1	yes	characteristic
90	Q₈	—	292	2	no	—
91	Q₈	—	292	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	73	2	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	—	146	2	no	—
99	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
100	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
101	C₈	—	292	4	no	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	2	no	—
104	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	4	2	no	—
107	C₄	—	292	2	no	—
108	C₄	—	73	2	no	—
109	C₄	—	73	2	no	—
110	C₄	—	146	2	no	—
111	C₄	#14556652	1	2	yes	—
112	C₂	—	4	1	no	—
113	C₂	C₂×#14556652	1	1	yes	characteristic
114	C₂	#17989578	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989590

C₂

yes

maximal

#17989446

C₂

yes

maximal, complemented

#17989140

C₂

yes

maximal, characteristic

C₂×#11924037

—

#14556658

C₂²

yes

—

C₄⋊#10596833

—

#14556590

C₂²

yes

—

#14556582

C₄

yes

—

#14556568

—

C₄×Dic₁₄₆

—

#14556550

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#117×C₇₃

C₄

yes

characteristic

#11924037

—

C₂×#10596833

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#101

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

AGL(1,ℤ/8)

yes

—

Dic₇₃

#137

yes

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#101

yes

characteristic

C₂×C₇₃

#417

yes

—

#1561

—

maximal, Sylow

C₇₃

#1561

yes

characteristic, complemented, Sylow

#533

—

#423

—

#332

—

C₂×M₁₆

—

146

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

146

—

C₄×Q₈

—

146

—

—

yes

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

292

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₂×#64408

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₂³

C₂²⋊#64408

yes

characteristic

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

100

C₂×C₄

C₂²×#64408

yes

characteristic

101

C₈

—

292

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×C₂²⋊#64408

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

292

—

108

C₄

—

109

C₄

—

110

C₄

—

146

—

111

C₄

#14556652

yes

—

112

C₂

—

113

C₂

C₂×#14556652

yes

characteristic

114

C₂

#17989578

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#117×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#117	#64408
hypocenter	C₇₃	#1561
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#117×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

N	H ≅ G/N	type
2. #17989446	C₂	semidirect
58. C₇₃	#1561	semidirect

H ≅ G/N

type

2. #17989446

C₂

semidirect

58. C₇₃

#1561

semidirect

Subgroups — #22625470

Conjugacy classes of subgroups

Complements