Group #22625471 — subgroups

Subgroups — #22625471

Order 9344.

210 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 60 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	#17989592	C₂	1	2	yes	maximal
2	#17989446	C₂	1	4	yes	maximal, complemented
3	#17989143	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924038	—	2	2	no	—
5	#14556658	—	2	2	no	—
6	#14556658	C₂²	1	4	yes	—
7	#14556590	C₂²	1	2	yes	—
8	#14556583	C₄	1	1	yes	characteristic
9	#14556569	—	2	2	no	—
10	#14556556	—	2	2	no	—
11	#14556549	C₄	1	2	yes	—
12	C₄²×D₇₃	C₂²	1	1	yes	characteristic
13	#125×C₇₃	C₄	1	1	yes	characteristic
14	#11924038	—	4	4	no	—
15	C₂×#10596833	—	2	4	no	—
16	C₂×Dic₁₄₆	—	2	2	no	—
17	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₇₃	D₄	1	2	yes	—
19	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
20	#11924007	—	2	2	no	—
21	#11924007	—	2	2	no	—
22	#11924005	—	2	2	no	—
23	C₄×Dic₇₃	—	2	2	no	—
24	C₄×Dic₇₃	D₄	1	2	yes	—
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
28	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	2	2	no	—
31	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₇₃	—	2	2	no	—
34	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
36	C₄×D₇₃	—	2	2	no	—
37	C₄×D₇₃	—	2	2	no	—
38	C₄×D₇₃	—	2	2	no	—
39	Dic₁₄₆	—	4	2	no	—
40	Dic₁₄₆	—	4	2	no	—
41	#10596833	—	4	4	no	—
42	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	C₂×D₇₃	—	2	1	no	—
44	C₂×D₇₃	—	2	2	no	—
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	—	2	2	no	—
47	C₄×C₇₃	—	4	2	no	—
48	Dic₇₃	—	4	2	no	—
49	Dic₇₃	#101	1	2	yes	—
50	Dic₇₃	AGL(1,ℤ/8)	1	2	yes	—
51	Dic₇₃	#137	1	2	yes	—
52	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
53	C₂×C₇₃	#417	1	2	yes	—
54	D₇₃	—	4	1	no	—
55	#1561	—	73	1	no	maximal, Sylow
56	C₇₃	#1561	1	1	yes	characteristic, complemented, Sylow
57	#533	—	73	1	no	—
58	#423	—	73	2	no	—
59	#332	—	73	4	no	—
60	C₂×M₁₆	—	146	2	no	—
61	C₄⋊Q₈	—	73	2	no	—
62	#125	—	73	1	no	—
63	#125	#64408	1	1	yes	characteristic
64	C₂²⋊Q₈	—	146	2	no	—
65	C₄×Q₈	—	146	2	no	—
66	#117	—	73	2	no	—
67	C₂×C₄²	—	73	1	no	—
68	C₄⋊C₈	—	73	4	no	—
69	C₄⋊C₈	—	146	2	no	—
70	C₂×Q₈	—	146	2	no	—
71	C₂²×C₄	—	73	2	no	—
72	C₂²×C₄	—	73	1	no	—
73	M₁₆	—	292	4	no	—
74	C₂×C₈	—	146	4	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	73	2	no	—
77	C₄⋊C₄	—	146	2	no	—
78	C₄⋊C₄	—	146	2	no	—
79	C₄⋊C₄	C₂×#64408	1	2	yes	—
80	C₂²⋊C₄	—	146	2	no	—
81	C₄²	—	73	2	no	—
82	C₄²	—	73	1	no	—
83	C₄²	—	146	2	no	—
84	C₄²	C₂×#64408	1	1	yes	characteristic
85	C₂³	—	73	1	no	—
86	Q₈	—	292	2	no	—
87	Q₈	—	292	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	73	2	no	—
91	C₂×C₄	—	146	2	no	—
92	C₂×C₄	—	146	2	no	—
93	C₂×C₄	—	146	2	no	—
94	C₂×C₄	—	146	2	no	—
95	C₂×C₄	C₂²⋊#64408	1	2	yes	—
96	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
97	C₈	—	292	4	no	—
98	C₂²	—	146	1	no	—
99	C₂²	—	146	2	no	—
100	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	2	2	no	—
103	C₄	—	4	2	no	—
104	C₄	—	292	2	no	—
105	C₄	—	73	2	no	—
106	C₄	—	73	2	no	—
107	C₄	—	73	2	no	—
108	C₂	—	292	1	no	—
109	C₂	D₇₃⋊#101	1	1	yes	characteristic
110	C₂	#17989578	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989592

C₂

yes

maximal

#17989446

C₂

yes

maximal, complemented

#17989143

C₂

yes

maximal, characteristic

C₂×#11924038

—

#14556658

—

#14556658

C₂²

yes

—

#14556590

C₂²

yes

—

#14556583

C₄

yes

—

—

C₄

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#125×C₇₃

C₄

yes

characteristic

#11924038

—

C₂×#10596833

—

C₂×Dic₁₄₆

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

#11924005

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

#101

yes

—

Dic₇₃

AGL(1,ℤ/8)

yes

—

Dic₇₃

#137

yes

—

C₂×C₇₃

C₂×#101

yes

characteristic

C₂×C₇₃

#417

yes

—

D₇₃

—

#1561

—

maximal, Sylow

C₇₃

#1561

yes

characteristic, complemented, Sylow

#533

—

#423

—

#332

—

C₂×M₁₆

—

146

—

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

146

—

C₄×Q₈

—

146

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

292

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₂×#64408

yes

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

292

—

C₂²

—

146

—

C₂²

—

146

—

100

C₂²

C₂×C₂²⋊#64408

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

292

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₂

—

292

—

109

C₂

D₇₃⋊#101

yes

characteristic

110

C₂

#17989578

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#125×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#125	#64408
hypocenter	C₇₃	#1561
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#125×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #125

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

H ≅ G/N

type

2. #17989446

C₂

semidirect

56. C₇₃

#1561

semidirect

Subgroups — #22625471

Conjugacy classes of subgroups

Complements