Group #32990493 — subgroups

Subgroups — #32990493

Order 18688.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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	#22610064	C₂	1	3	yes	maximal
2	#22607812	C₂	1	3	yes	maximal
3	C₇₃×#2845	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556502	C₂²	1	3	yes	—
5	#17988457	C₂²	1	1	yes	characteristic
6	#17988349	—	2	6	no	—
7	#398×C₇₃	—	2	6	no	—
8	#382×C₇₃	C₂²	1	3	yes	—
9	C₂²×#10596831	—	2	3	no	—
10	C₂×C₄⋊Dic₇₃	—	2	3	no	—
11	#14556502	—	2	3	no	—
12	#14556502	Q₈	1	6	yes	—
13	C₂×C₄⋊C₄×C₇₃	—	2	6	no	—
14	C₂×C₄⋊C₄×C₇₃	D₄	1	6	yes	—
15	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
16	#95×C₇₃	—	2	2	no	—
17	#95×C₇₃	—	2	6	no	—
18	C₂²×Dic₇₃	—	4	1	no	—
19	C₂×#10596831	—	2	6	no	—
20	C₂×#10596831	—	4	3	no	—
21	C₂×#10596831	—	4	3	no	—
22	C₄⋊Dic₇₃	—	4	6	no	—
23	C₂²×C₄×C₇₃	—	2	6	no	—
24	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
25	C₄⋊C₄×C₇₃	—	4	6	no	—
26	C₄⋊C₄×C₇₃	—	8	6	no	—
27	C₄²×C₇₃	C₂×Q₈	1	3	yes	—
28	C₄²×C₇₃	#41	1	1	yes	characteristic
29	C₂³×C₇₃	#120	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	2	3	no	—
31	C₂×C₄×C₇₃	—	2	3	no	—
32	C₂×C₄×C₇₃	—	4	6	no	—
33	C₂×C₄×C₇₃	—	4	6	no	—
34	C₂×C₄×C₇₃	—	4	6	no	—
35	C₂×C₄×C₇₃	C₂²⋊Q₈	1	3	yes	—
36	C₂×C₄×C₇₃	C₄⋊Q₈	1	3	yes	—
37	C₂×Dic₇₃	—	8	3	no	—
38	#10596831	—	4	6	no	—
39	C₂²×C₇₃	#395	1	1	yes	characteristic
40	C₂²×C₇₃	#454	1	3	yes	—
41	C₂²×C₇₃	#455	1	3	yes	—
42	C₄×C₇₃	—	2	3	no	—
43	C₄×C₇₃	—	2	3	no	—
44	C₄×C₇₃	—	8	6	no	—
45	Dic₇₃	—	16	1	no	—
46	#10586	—	73	1	no	maximal, Sylow
47	C₂×C₇₃	#1658	1	1	yes	characteristic
48	C₂×C₇₃	#1662	1	3	yes	—
49	C₂×C₇₃	#2061	1	3	yes	—
50	#2845	D₇₃	1	1	yes	characteristic
51	#1836	—	73	3	no	—
52	#1295	—	73	3	no	—
53	C₇₃	#10586	1	1	yes	characteristic, complemented, Sylow
54	C₂×#97	—	73	3	no	—
55	#398	—	2	6	no	—
56	#384	—	73	1	no	—
57	#382	C₂×D₇₃	1	3	yes	—
58	#340	—	146	6	no	—
59	C₂²×C₈	—	146	3	no	—
60	C₂×C₄⋊C₄	—	2	6	no	—
61	C₂×C₄⋊C₄	—	146	3	no	—
62	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	6	yes	—
63	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
64	#97	—	73	6	no	—
65	#97	—	146	3	no	—
66	#95	—	2	2	no	—
67	#95	—	2	6	no	—
68	C₂²×C₄	—	2	6	no	—
69	C₂²×C₄	—	292	1	no	—
70	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
71	C₂×C₈	—	292	3	no	—
72	C₂×C₈	—	292	3	no	—
73	C₂×C₈	—	146	6	no	—
74	C₄⋊C₄	—	4	6	no	—
75	C₄⋊C₄	—	8	6	no	—
76	C₄⋊C₄	—	292	6	no	—
77	C₄²	Q₈×D₇₃	1	3	yes	—
78	C₄²	#11924029	1	1	yes	characteristic
79	C₂³	#14556560	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	584	3	no	—
86	C₂×C₄	#14556567	1	3	yes	—
87	C₂×C₄	#14556589	1	3	yes	—
88	C₈	—	292	6	no	—
89	C₂²	#17988506	1	1	yes	characteristic
90	C₂²	#17988760	1	3	yes	—
91	C₂²	#17988765	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	1168	1	no	—
96	C₂	#22609233	1	1	yes	characteristic
97	C₂	#22609254	1	3	yes	—
98	C₂	#22611278	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22610064

C₂

yes

maximal

#22607812

C₂

yes

maximal

C₇₃×#2845

C₂

yes

maximal, characteristic

C₂×#14556502

C₂²

yes

—

#17988457

C₂²

yes

characteristic

#17988349

—

#398×C₇₃

—

#382×C₇₃

C₂²

yes

—

C₂²×#10596831

—

C₂×C₄⋊Dic₇₃

—

#14556502

—

#14556502

Q₈

yes

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#95×C₇₃

—

#95×C₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×Q₈

yes

—

C₄²×C₇₃

yes

C₂³×C₇₃

yes

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₃

C₄⋊Q₈

yes

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

#395

yes

characteristic

C₂²×C₇₃

#454

yes

—

C₂²×C₇₃

#455

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#2061

yes

—

#2845

D₇₃

yes

characteristic

#1836

—

#1295

—

C₇₃

#10586

yes

characteristic, complemented, Sylow

C₂×#97

—

#398

—

#384

—

#382

C₂×D₇₃

yes

—

#340

—

146

—

C₂²×C₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

#97

—

#97

—

146

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

292

—

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄²

Q₈×D₇₃

yes

—

C₄²

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

584

—

C₂×C₄

#14556567

yes

—

C₂×C₄

#14556589

yes

—

C₈

—

292

—

C₂²

#17988506

yes

characteristic

C₂²

#17988760

yes

—

C₂²

#17988765

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

1168

—

C₂

#22609233

yes

characteristic

C₂

#22609254

yes

—

C₂

#22611278

yes

—

	subgroup	G/H
center	C₂³	#14556560
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#2845	C₂
socle, prime radical	C₂³×C₇₃	#120
hypercenter	#2845	D₇₃
hypocenter	C₇₃	#10586
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#14556560

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#2845

C₂

C₂³×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
53. C₇₃	#10586	semidirect

H ≅ G/N

type

53. C₇₃

#10586

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22610064	2
#22607812	2
C₇₃×#2845	2
#10586	73

subgroup

index

#22610064

#22607812

C₇₃×#2845

#10586

Subgroups — #32990493

Conjugacy classes of subgroups

Complements

Maximal subgroups