Group #22624079 — subgroups

Subgroups — #22624079

Order 9344.

930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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	#17989341	C₂	1	10	yes	maximal, complemented
2	#17989335	C₂	1	5	yes	maximal, complemented
3	#17989143	C₂	1	5	yes	maximal, complemented
4	#17989122	C₂	1	10	yes	maximal, complemented
5	#564×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556590	C₂²	1	10	yes	—
7	#14556586	C₂²	1	20	yes	—
8	#14556583	C₂²	1	5	yes	—
9	#14556579	C₂²	1	10	yes	—
10	#14556576	C₂²	1	20	yes	—
11	#14556571	C₂²	1	10	yes	—
12	#14556569	C₂²	1	20	yes	—
13	#14556566	C₂²	1	10	yes	—
14	#14556556	C₂²	1	10	yes	—
15	#14556553	C₂²	1	10	yes	—
16	#14556549	C₂²	1	10	yes	—
17	C₄²×D₇₃	C₂²	1	5	yes	—
18	#125×C₇₃	C₂²	1	10	yes	—
19	#125×C₇₃	C₂²	1	5	yes	—
20	C₂×Dic₁₄₆	C₂³	1	10	yes	—
21	C₂×D₂₉₂	C₂³	1	10	yes	—
22	C₂×C₄×D₇₃	C₂³	1	5	yes	—
23	C₂×C₄×D₇₃	C₂³	1	10	yes	—
24	C₄⋊Dic₇₃	C₂³	1	10	yes	—
25	#11924007	C₂³	1	20	yes	—
26	#11924005	C₂³	1	20	yes	—
27	#11924005	C₂³	1	20	yes	—
28	C₄×Dic₇₃	C₂³	1	10	yes	—
29	C₄×Dic₇₃	C₂³	1	5	yes	—
30	C₄⋊C₄×C₇₃	C₂³	1	10	yes	—
31	C₄⋊C₄×C₇₃	C₂³	1	10	yes	—
32	C₄⋊C₄×C₇₃	C₂³	1	10	yes	—
33	C₄²×C₇₃	C₂³	1	5	yes	—
34	C₂²×D₇₃	C₂⁴	1	5	yes	—
35	C₂×C₄×C₇₃	C₂⁴	1	5	yes	—
36	C₂×C₄×C₇₃	C₂⁴	1	10	yes	—
37	C₂×Dic₇₃	C₂⁴	1	10	yes	—
38	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
39	D₂₉₂	—	4	10	no	—
40	C₄×D₇₃	—	2	10	no	—
41	C₄×D₇₃	—	4	10	no	—
42	Dic₁₄₆	—	4	10	no	—
43	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
44	C₂×D₇₃	—	2	5	no	—
45	C₂×D₇₃	—	2	10	no	—
46	C₄×C₇₃	—	2	5	no	—
47	C₄×C₇₃	—	2	10	no	—
48	Dic₇₃	—	2	10	no	—
49	Dic₇₃	2₋¹⁺⁴	1	2	yes	—
50	C₂×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
51	C₂×C₇₃	#585	1	2	yes	—
52	D₇₃	—	4	5	no	—
53	#3531	—	73	1	no	maximal, Sylow
54	C₇₃	#3531	1	1	yes	characteristic, complemented, Sylow
55	#564	D₇₃	1	1	yes	characteristic, complemented
56	#563	—	73	10	no	—
57	#562	—	73	5	no	—
58	#533	—	73	5	no	—
59	#529	—	73	10	no	—
60	C₄⋊Q₈	—	73	10	no	—
61	#126	—	73	20	no	—
62	#125	—	73	5	no	—
63	#125	C₂×D₇₃	1	10	yes	—
64	#125	C₂×D₇₃	1	5	yes	—
65	#124	—	73	10	no	—
66	#123	—	73	20	no	—
67	C₂²⋊Q₈	—	73	10	no	—
68	C₂²⋊Q₈	—	73	20	no	—
69	#121	—	73	10	no	—
70	C₄×Q₈	—	73	10	no	—
71	C₄×D₄	—	73	10	no	—
72	#117	—	73	10	no	—
73	C₂×C₄²	—	73	5	no	—
74	C₂×Q₈	—	73	10	no	—
75	C₂×D₄	—	73	10	no	—
76	C₂²×C₄	—	73	10	no	—
77	C₂²×C₄	—	73	5	no	—
78	C₄⋊C₄	—	73	20	no	—
79	C₄⋊C₄	—	73	10	no	—
80	C₄⋊C₄	C₂²×D₇₃	1	10	yes	—
81	C₄⋊C₄	C₂²×D₇₃	1	10	yes	—
82	C₄⋊C₄	C₂²×D₇₃	1	10	yes	—
83	C₂²⋊C₄	—	73	20	no	—
84	C₂²⋊C₄	—	73	20	no	—
85	C₄²	—	73	10	no	—
86	C₄²	—	73	5	no	—
87	C₄²	C₂²×D₇₃	1	5	yes	—
88	C₂³	—	73	5	no	—
89	Q₈	—	292	10	no	—
90	D₄	—	292	10	no	—
91	C₂×C₄	—	292	10	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	73	10	no	—
94	C₂×C₄	—	146	10	no	—
95	C₂×C₄	C₂³×D₇₃	1	5	yes	—
96	C₂×C₄	C₂³×D₇₃	1	10	yes	—
97	C₂²	—	146	5	no	—
98	C₂²	—	146	10	no	—
99	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
100	C₄	—	2	5	no	—
101	C₄	—	2	10	no	—
102	C₄	—	73	2	no	—
103	C₄	—	146	10	no	—
104	C₂	—	292	5	no	—
105	C₂	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
106	C₂	#17989424	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989341

C₂

yes

maximal, complemented

#17989335

C₂

yes

maximal, complemented

#17989143

C₂

yes

maximal, complemented

#17989122

C₂

yes

maximal, complemented

#564×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556590

C₂²

yes

—

#14556586

C₂²

yes

—

#14556583

C₂²

yes

—

#14556579

C₂²

yes

—

#14556576

C₂²

yes

—

#14556571

C₂²

yes

—

#14556569

C₂²

yes

—

#14556566

C₂²

yes

—

#14556556

C₂²

yes

—

#14556553

C₂²

yes

—

#14556549

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

—

#125×C₇₃

C₂²

yes

—

#125×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

C₂³

yes

—

C₂×D₂₉₂

C₂³

yes

—

C₂×C₄×D₇₃

C₂³

yes

—

C₂×C₄×D₇₃

C₂³

yes

—

C₄⋊Dic₇₃

C₂³

yes

—

#11924007

C₂³

yes

—

#11924005

C₂³

yes

—

#11924005

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

—

C₂²×D₇₃

C₂⁴

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

—

C₂×Dic₇₃

C₂⁴

yes

—

C₂×Dic₇₃

C₂⁴

yes

characteristic

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₂²×C₇₃

C₂⁵

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

2₋¹⁺⁴

yes

—

C₂×C₇₃

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₇₃

#585

yes

—

D₇₃

—

#3531

—

maximal, Sylow

C₇₃

#3531

yes

characteristic, complemented, Sylow

#564

D₇₃

yes

characteristic, complemented

—

—

—

—

C₄⋊Q₈

—

#126

—

#125

—

#125

C₂×D₇₃

yes

—

#125

C₂×D₇₃

yes

—

#124

—

#123

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

C₂²×D₇₃

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₃

yes

—

C₂³

—

Q₈

—

292

—

D₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂³×D₇₃

yes

—

C₂×C₄

C₂³×D₇₃

yes

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

C₂⁴×D₇₃

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

146

—

104

C₂

—

292

—

105

C₂

2₋¹⁺⁴×D₇₃

yes

characteristic

106

C₂

#17989424

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#564×C₇₃	C₂
hypercenter	#564	D₇₃
hypocenter	C₇₃	#3531
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. #17989341	C₂	semidirect
2. #17989335	C₂	semidirect
3. #17989143	C₂	semidirect
4. #17989122	C₂	semidirect
5. #564×C₇₃	C₂	semidirect
54. C₇₃	#3531	semidirect
55. #564	D₇₃	semidirect

H ≅ G/N

type

1. #17989341

C₂

semidirect

2. #17989335

C₂

semidirect

3. #17989143

C₂

semidirect

4. #17989122

C₂

semidirect

5. #564×C₇₃

C₂

semidirect

54. C₇₃

#3531

semidirect

55. #564

D₇₃

semidirect

Subgroups — #22624079

Conjugacy classes of subgroups

Complements