Group #32973465 — subgroups

Subgroups — #32973465

Order 18688.

110 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 53 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	#22611839	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#14556497	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#1397	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₁₄₆	C₄	1	1	yes	characteristic
5	C₂×#14556497	—	2	1	no	—
6	C₄⋊#11924003	C₄	1	1	yes	characteristic
7	#17988405	—	2	1	no	—
8	#17988362	—	2	1	no	—
9	C₂×C₃₂×C₇₃	—	2	1	no	—
10	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₄×Dic₁₄₆	C₈	1	1	yes	characteristic
12	C₂×#11924003	—	2	1	no	—
13	C₄⋊#10596831	C₈	1	1	yes	characteristic
14	#14556520	—	2	1	no	—
15	C₈×Dic₇₃	—	2	1	no	—
16	#14556497	—	4	1	no	—
17	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
18	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
19	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
20	C₃₂×C₇₃	—	2	2	no	—
21	C₂×Dic₁₄₆	C₁₆	1	1	yes	characteristic
22	C₂×#10596831	—	2	1	no	—
23	C₄⋊Dic₇₃	C₁₆	1	1	yes	characteristic
24	#11924007	—	2	1	no	—
25	C₄×Dic₇₃	—	2	1	no	—
26	#11924003	—	4	1	no	—
27	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	M₁₆	1	1	yes	characteristic
29	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₁₆×C₇₃	—	2	1	no	—
31	C₁₆×C₇₃	SD₁₆	1	1	yes	characteristic
32	C₁₆×C₇₃	Q₁₆	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₃	M₃₂	1	1	yes	characteristic
36	C₂×Dic₇₃	—	2	1	no	—
37	C₂×Dic₇₃	—	2	1	no	—
38	Dic₁₄₆	—	4	1	no	—
39	C₈×C₇₃	—	2	1	no	—
40	C₈×C₇₃	#103	1	1	yes	characteristic
41	C₈×C₇₃	#104	1	1	yes	characteristic
42	#10596831	—	4	1	no	—
43	C₂²×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
44	C₄×C₇₃	—	2	1	no	—
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	Q₈⋊C₈	1	1	yes	characteristic
47	C₄×C₇₃	#350	1	1	yes	characteristic
48	Dic₇₃	—	4	1	no	—
49	Dic₇₃	—	4	1	no	—
50	#7393	—	73	1	no	maximal, Sylow
51	C₂×C₇₃	Q₈⋊C₁₆	1	1	yes	characteristic
52	C₂×C₇₃	#1400	1	1	yes	characteristic
53	C₂×C₇₃	#1401	1	1	yes	characteristic
54	#2183	—	73	1	no	—
55	C₄⋊C₃₂	—	73	1	no	—
56	#1397	D₇₃	1	1	yes	characteristic
57	C₇₃	#7393	1	1	yes	characteristic, complemented, Sylow
58	C₈×Q₈	—	73	1	no	—
59	C₂×C₃₂	—	2	1	no	—
60	C₂×C₃₂	—	146	1	no	—
61	C₄⋊C₁₆	—	73	1	no	—
62	C₄⋊C₁₆	—	146	1	no	—
63	#346	—	146	1	no	—
64	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
65	C₄×Q₈	—	73	1	no	—
66	C₂×C₁₆	—	146	1	no	—
67	C₂×C₁₆	D₂₉₂	1	1	yes	characteristic
68	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
69	C₄⋊C₈	—	73	1	no	—
70	C₄⋊C₈	—	146	1	no	—
71	C₄×C₈	—	146	1	no	—
72	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
73	C₃₂	—	2	2	no	—
74	C₃₂	—	292	1	no	—
75	C₂×Q₈	—	73	1	no	—
76	C₂×C₈	—	146	1	no	—
77	C₂×C₈	#11924005	1	1	yes	characteristic
78	C₂×C₈	#11924011	1	1	yes	characteristic
79	C₄⋊C₄	—	73	1	no	—
80	C₄⋊C₄	—	146	1	no	—
81	C₄²	—	146	1	no	—
82	C₄²	C₈×D₇₃	1	1	yes	characteristic
83	C₁₆	—	2	1	no	—
84	C₁₆	—	292	1	no	—
85	C₁₆	#11924017	1	1	yes	characteristic
86	C₁₆	Dic₂₉₂	1	1	yes	characteristic
87	Q₈	—	292	1	no	—
88	C₂×C₄	—	146	1	no	—
89	C₂×C₄	—	146	1	no	—
90	C₂×C₄	#14556503	1	1	yes	characteristic
91	C₂×C₄	C₁₆×D₇₃	1	1	yes	characteristic
92	C₂×C₄	#14556530	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	292	1	no	—
95	C₈	#14556516	1	1	yes	characteristic
96	C₈	#14556519	1	1	yes	characteristic
97	C₂²	#17988366	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	292	1	no	—
101	C₄	—	292	1	no	—
102	C₄	#17988319	1	1	yes	characteristic
103	C₄	#17988370	1	1	yes	characteristic
104	C₂	#22607911	1	1	yes	characteristic
105	C₂	#22608070	1	1	yes	characteristic
106	C₂	#22608074	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22611839

C₂

yes

maximal, characteristic

C₄⋊#14556497

C₂

yes

maximal, characteristic

C₇₃×#1397

C₂

yes

maximal, characteristic

C₈×Dic₁₄₆

C₄

yes

characteristic

C₂×#14556497

—

C₄⋊#11924003

C₄

yes

characteristic

#17988405

—

#17988362

—

C₂×C₃₂×C₇₃

—

C₄×C₁₆×C₇₃

C₂²

yes

characteristic

C₄×Dic₁₄₆

C₈

yes

characteristic

C₂×#11924003

—

C₄⋊#10596831

C₈

yes

characteristic

#14556520

—

C₈×Dic₇₃

—

#14556497

—

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₃₂×C₇₃

—

C₂×Dic₁₄₆

C₁₆

yes

characteristic

C₂×#10596831

—

C₄⋊Dic₇₃

C₁₆

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

#11924003

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

M₁₆

yes

characteristic

C₄²×C₇₃

C₂×C₈

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

SD₁₆

yes

characteristic

C₁₆×C₇₃

Q₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₃

M₃₂

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

C₂²⋊C₁₆

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

Q₈⋊C₈

yes

characteristic

C₄×C₇₃

#350

yes

characteristic

Dic₇₃

—

Dic₇₃

—

#7393

—

maximal, Sylow

C₂×C₇₃

Q₈⋊C₁₆

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₄⋊C₃₂

—

#1397

D₇₃

yes

characteristic

C₇₃

#7393

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₂×C₃₂

—

C₂×C₃₂

—

146

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

146

—

#346

—

146

—

C₄×C₁₆

C₂×D₇₃

yes

characteristic

C₄×Q₈

—

C₂×C₁₆

—

146

—

C₂×C₁₆

D₂₉₂

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄×C₈

—

146

—

C₄×C₈

C₄×D₇₃

yes

characteristic

C₃₂

—

C₃₂

—

292

—

C₂×Q₈

—

C₂×C₈

—

146

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄²

—

146

—

C₄²

C₈×D₇₃

yes

characteristic

C₁₆

—

C₁₆

—

292

—

C₁₆

#11924017

yes

characteristic

C₁₆

Dic₂₉₂

yes

characteristic

Q₈

—

292

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

#14556503

yes

characteristic

C₂×C₄

C₁₆×D₇₃

yes

characteristic

C₂×C₄

#14556530

yes

characteristic

C₈

—

C₈

—

292

—

C₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

100

C₄

—

292

—

101

C₄

—

292

—

102

C₄

#17988319

yes

characteristic

103

C₄

#17988370

yes

characteristic

104

C₂

#22607911

yes

characteristic

105

C₂

#22608070

yes

characteristic

106

C₂

#22608074

yes

characteristic

	subgroup	G/H
center	C₂×C₈	#11924005
commutator	C₂×C₄×C₇₃	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₇₃
Fitting	C₇₃×#1397	C₂
socle, prime radical	C₂²×C₇₃	C₂²⋊C₁₆
cosocle	C₄×C₁₆×C₇₃	C₂²
hypercenter	#1397	D₇₃
hypocenter	C₇₃	#7393
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ #1397

subgroup

G/H

center

C₂×C₈

#11924005

commutator

C₂×C₄×C₇₃

C₂×C₁₆

Frattini

C₄×C₁₆

C₂×D₇₃

Fitting

C₇₃×#1397

C₂

socle, prime radical

C₂²×C₇₃

C₂²⋊C₁₆

cosocle

C₄×C₁₆×C₇₃

C₂²

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ #1397

N	H ≅ G/N	type
57. C₇₃	#7393	semidirect

H ≅ G/N

type

57. C₇₃

#7393

semidirect

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

subgroup	index
#22611839	2
C₄⋊#14556497	2
C₇₃×#1397	2
#7393	73

subgroup

index

#22611839

C₄⋊#14556497

C₇₃×#1397

#7393

Subgroups — #32973465

Conjugacy classes of subgroups

Complements

Maximal subgroups