Group #22624425 — subgroups

Subgroups — #22624425

Order 9344.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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	C₇₃⋊#564	C₂	1	3	yes	maximal, complemented
2	#17989314	C₂	1	12	yes	maximal, complemented
3	#17989196	C₂	1	12	yes	maximal
4	#17989143	C₂	1	3	yes	maximal
5	#564×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556590	C₂²	1	6	yes	—
7	#14556590	C₂²	1	12	yes	—
8	#14556586	C₂²	1	12	yes	—
9	#14556585	C₂²	1	4	yes	—
10	#14556583	C₂²	1	3	yes	—
11	#14556582	C₂²	1	12	yes	—
12	#14556581	C₂²	1	12	yes	—
13	#14556581	C₂²	1	12	yes	—
14	#14556581	C₂²	1	12	yes	—
15	#14556569	C₂²	1	12	yes	—
16	C₄×Dic₁₄₆	C₂²	1	12	yes	—
17	#14556556	C₂²	1	12	yes	—
18	#14556556	C₂²	1	12	yes	—
19	#14556549	C₂²	1	6	yes	—
20	C₄²×D₇₃	C₂²	1	1	yes	characteristic
21	#125×C₇₃	C₂²	1	3	yes	—
22	#125×C₇₃	C₂²	1	12	yes	—
23	C₂×Dic₁₄₆	C₂³	1	12	yes	—
24	C₂×C₄×D₇₃	C₂³	1	3	yes	—
25	C₄⋊Dic₇₃	C₂³	1	6	yes	—
26	C₄⋊Dic₇₃	C₂³	1	12	yes	—
27	#11924007	C₂³	1	12	yes	—
28	#11924007	C₂³	1	12	yes	—
29	#11924007	C₂³	1	12	yes	—
30	#11924007	C₂³	1	12	yes	—
31	#11924005	C₂³	1	12	yes	—
32	C₄×Dic₇₃	C₂³	1	3	yes	—
33	C₄×Dic₇₃	C₂³	1	12	yes	—
34	C₄×Dic₇₃	C₂³	1	12	yes	—
35	C₄⋊C₄×C₇₃	C₂³	1	6	yes	—
36	C₄⋊C₄×C₇₃	C₂³	1	12	yes	—
37	C₄⋊C₄×C₇₃	C₂³	1	12	yes	—
38	C₄²×C₇₃	C₂³	1	1	yes	characteristic
39	C₄²×C₇₃	C₂³	1	4	yes	—
40	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
41	C₂×C₄×C₇₃	C₂⁴	1	12	yes	—
42	C₂×C₄×C₇₃	C₂⁴	1	3	yes	—
43	C₂×Dic₇₃	C₂⁴	1	12	yes	—
44	C₂×Dic₇₃	C₂⁴	1	3	yes	—
45	C₄×D₇₃	—	2	6	no	—
46	Dic₁₄₆	—	2	24	no	—
47	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
48	C₂×D₇₃	—	2	3	no	—
49	C₄×C₇₃	—	2	12	no	—
50	C₄×C₇₃	—	2	3	no	—
51	Dic₇₃	—	2	12	no	—
52	Dic₇₃	2₋¹⁺⁴	1	6	yes	—
53	C₂×C₇₃	C₂×2₋¹⁺⁴	1	3	yes	—
54	D₇₃	—	4	1	no	—
55	#3556	—	73	1	no	maximal, Sylow
56	C₇₃	#3556	1	1	yes	characteristic, complemented, Sylow
57	#564	—	73	3	no	—
58	#564	D₇₃	1	1	yes	characteristic, complemented
59	#557	—	73	12	no	—
60	#541	—	73	12	no	—
61	#533	—	73	3	no	—
62	C₄⋊Q₈	—	73	6	no	—
63	C₄⋊Q₈	—	73	12	no	—
64	#126	—	73	12	no	—
65	#126	—	73	4	no	—
66	#125	—	73	12	no	—
67	#125	—	73	12	no	—
68	#125	—	73	12	no	—
69	#125	—	73	12	no	—
70	#125	—	73	3	no	—
71	#125	C₂×D₇₃	1	3	yes	—
72	#125	C₂×D₇₃	1	12	yes	—
73	C₂²⋊Q₈	—	73	12	no	—
74	C₄×Q₈	—	73	12	no	—
75	C₄×Q₈	—	73	12	no	—
76	C₄×Q₈	—	73	12	no	—
77	#117	—	73	6	no	—
78	C₂×C₄²	—	73	1	no	—
79	C₂×Q₈	—	73	12	no	—
80	C₂²×C₄	—	73	3	no	—
81	C₄⋊C₄	—	73	12	no	—
82	C₄⋊C₄	—	73	12	no	—
83	C₄⋊C₄	—	73	12	no	—
84	C₄⋊C₄	—	73	12	no	—
85	C₄⋊C₄	—	73	6	no	—
86	C₄⋊C₄	—	73	12	no	—
87	C₄⋊C₄	C₂²×D₇₃	1	6	yes	—
88	C₄⋊C₄	C₂²×D₇₃	1	12	yes	—
89	C₄⋊C₄	C₂²×D₇₃	1	12	yes	—
90	C₂²⋊C₄	—	73	12	no	—
91	C₄²	—	73	3	no	—
92	C₄²	—	73	12	no	—
93	C₄²	—	73	12	no	—
94	C₄²	C₂²×D₇₃	1	1	yes	characteristic
95	C₄²	C₂²×D₇₃	1	4	yes	—
96	C₂³	—	73	1	no	—
97	Q₈	—	146	24	no	—
98	C₂×C₄	—	73	3	no	—
99	C₂×C₄	—	73	12	no	—
100	C₂×C₄	—	146	6	no	—
101	C₂×C₄	C₂³×D₇₃	1	12	yes	—
102	C₂×C₄	C₂³×D₇₃	1	3	yes	—
103	C₂²	—	146	3	no	—
104	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
105	C₄	—	2	3	no	—
106	C₄	—	2	12	no	—
107	C₄	—	73	6	no	—
108	C₄	—	146	12	no	—
109	C₂	—	292	1	no	—
110	C₂	2₋¹⁺⁴×D₇₃	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃⋊#564

C₂

yes

maximal, complemented

#17989314

C₂

yes

maximal, complemented

#17989196

C₂

yes

maximal

#17989143

C₂

yes

maximal

#564×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556590

C₂²

yes

—

#14556590

C₂²

yes

—

#14556586

C₂²

yes

—

#14556585

C₂²

yes

—

#14556583

C₂²

yes

—

#14556582

C₂²

yes

—

#14556581

C₂²

yes

—

#14556581

C₂²

yes

—

#14556581

C₂²

yes

—

#14556569

C₂²

yes

—

C₄×Dic₁₄₆

C₂²

yes

—

#14556556

C₂²

yes

—

#14556556

C₂²

yes

—

#14556549

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#125×C₇₃

C₂²

yes

—

#125×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

C₂³

yes

—

C₂×C₄×D₇₃

C₂³

yes

—

C₄⋊Dic₇₃

C₂³

yes

—

C₄⋊Dic₇₃

C₂³

yes

—

#11924007

C₂³

yes

—

#11924007

C₂³

yes

—

#11924007

C₂³

yes

—

#11924007

C₂³

yes

—

#11924005

C₂³

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

C₂³

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

C₂³

yes

—

C₂²×D₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₇₃

C₂⁴

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

—

C₂×Dic₇₃

C₂⁴

yes

—

C₂×Dic₇₃

C₂⁴

yes

—

C₄×D₇₃

—

Dic₁₄₆

—

C₂²×C₇₃

C₂⁵

yes

characteristic

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

2₋¹⁺⁴

yes

—

C₂×C₇₃

C₂×2₋¹⁺⁴

yes

—

D₇₃

—

#3556

—

maximal, Sylow

C₇₃

#3556

yes

characteristic, complemented, Sylow

#564

—

#564

D₇₃

yes

characteristic, complemented

#557

—

#541

—

#533

—

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

—

—

C₂×D₇₃

yes

—

#125

C₂×D₇₃

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

C₂²×D₇₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₃

yes

characteristic

C₄²

C₂²×D₇₃

yes

—

C₂³

—

Q₈

—

146

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

146

—

101

C₂×C₄

C₂³×D₇₃

yes

—

102

C₂×C₄

C₂³×D₇₃

yes

—

103

C₂²

—

146

—

104

C₂²

C₂⁴×D₇₃

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

146

—

109

C₂

—

292

—

110

C₂

2₋¹⁺⁴×D₇₃

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#564×C₇₃	C₂
hypercenter	#564	D₇₃
hypocenter	C₇₃	#3556
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #564

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₇₃

commutator, socle

C₂²×C₇₃

C₂⁵

Fitting

#564×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. C₇₃⋊#564	C₂	semidirect
2. #17989314	C₂	semidirect
5. #564×C₇₃	C₂	semidirect
56. C₇₃	#3556	semidirect
58. #564	D₇₃	semidirect

H ≅ G/N

type

1. C₇₃⋊#564

C₂

semidirect

2. #17989314

C₂

semidirect

5. #564×C₇₃

C₂

semidirect

56. C₇₃

#3556

semidirect

58. #564

D₇₃

semidirect

Subgroups — #22624425

Conjugacy classes of subgroups

Complements