Group #32973620 — subgroups

Subgroups — #32973620

Order 18688.

132 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 55 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	C₄⋊#14556497	C₂	1	1	yes	maximal, characteristic
2	#22608003	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2247	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556497	—	2	1	no	—
5	#17988340	—	2	1	no	—
6	C₂×Q₃₂×C₇₃	—	2	1	no	—
7	C₂×Q₃₂×C₇₃	C₄	1	2	yes	—
8	#494×C₇₃	—	2	1	no	—
9	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	C₄⋊#10596831	—	4	1	no	—
11	#14556497	—	4	1	no	—
12	C₂×Q₁₆×C₇₃	—	2	2	no	—
13	C₂×Q₁₆×C₇₃	—	4	1	no	—
14	C₄⋊Q₈×C₇₃	—	4	1	no	—
15	Q₃₂×C₇₃	—	4	2	no	—
16	Q₃₂×C₇₃	—	4	1	no	—
17	Q₃₂×C₇₃	—	4	1	no	—
18	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
20	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
21	C₂×#10596831	—	8	1	no	—
22	C₂×Q₈×C₇₃	—	4	2	no	—
23	Q₁₆×C₇₃	—	4	2	no	—
24	Q₁₆×C₇₃	—	4	2	no	—
25	Q₁₆×C₇₃	—	8	2	no	—
26	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₃	SD₁₆	1	1	yes	characteristic
28	C₄⋊C₄×C₇₃	—	8	1	no	—
29	C₄⋊C₄×C₇₃	—	8	1	no	—
30	C₄²×C₇₃	D₈	1	1	yes	characteristic
31	C₁₆×C₇₃	—	2	1	no	—
32	C₁₆×C₇₃	D₈	1	1	yes	characteristic
33	C₁₆×C₇₃	SD₁₆	1	1	yes	characteristic
34	Q₈×C₇₃	—	8	2	no	—
35	Q₈×C₇₃	—	8	2	no	—
36	C₂×C₄×C₇₃	—	8	2	no	—
37	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
38	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
39	C₂×C₄×C₇₃	SD₃₂	1	1	yes	characteristic
40	C₈×C₇₃	—	2	1	no	—
41	C₈×C₇₃	#100	1	1	yes	characteristic
42	C₈×C₇₃	#102	1	1	yes	characteristic
43	#10596831	—	16	1	no	—
44	C₂²×C₇₃	#357	1	1	yes	characteristic
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	—	16	2	no	—
47	C₄×C₇₃	#331	1	1	yes	characteristic
48	C₄×C₇₃	#361	1	1	yes	characteristic
49	C₄×C₇₃	SD₆₄	1	1	yes	characteristic
50	C₄×C₇₃	Q₆₄	1	1	yes	characteristic
51	#7445	—	73	1	no	maximal, Sylow
52	C₂×C₇₃	#1361	1	1	yes	characteristic
53	C₂×C₇₃	#1416	1	1	yes	characteristic
54	C₂×C₇₃	#1420	1	1	yes	characteristic
55	#2247	D₇₃	1	1	yes	characteristic
56	C₄⋊C₃₂	—	73	1	no	—
57	#1371	—	73	1	no	—
58	C₇₃	#7445	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₃₂	—	2	1	no	—
60	C₂×Q₃₂	Dic₇₃	1	2	yes	—
61	#494	—	2	1	no	—
62	C₂×C₃₂	—	146	1	no	—
63	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
64	#335	—	146	1	no	—
65	C₂×Q₁₆	—	2	2	no	—
66	C₂×Q₁₆	—	4	1	no	—
67	C₄⋊Q₈	—	4	1	no	—
68	Q₃₂	—	4	2	no	—
69	Q₃₂	—	4	1	no	—
70	Q₃₂	—	4	1	no	—
71	C₂×C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
72	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
73	C₄⋊C₈	—	292	1	no	—
74	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
75	C₃₂	—	292	1	no	—
76	C₂×Q₈	—	4	2	no	—
77	Q₁₆	—	4	2	no	—
78	Q₁₆	—	4	2	no	—
79	Q₁₆	—	8	2	no	—
80	C₂×C₈	—	584	1	no	—
81	C₂×C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
82	C₂×C₈	#11924016	1	1	yes	characteristic
83	C₄⋊C₄	—	8	1	no	—
84	C₄⋊C₄	—	8	1	no	—
85	C₄²	#11924013	1	1	yes	characteristic
86	C₁₆	—	2	1	no	—
87	C₁₆	#11924013	1	1	yes	characteristic
88	C₁₆	#11924016	1	1	yes	characteristic
89	Q₈	—	8	2	no	—
90	Q₈	—	8	2	no	—
91	C₂×C₄	—	8	2	no	—
92	C₂×C₄	#14556512	1	1	yes	characteristic
93	C₂×C₄	#14556532	1	1	yes	characteristic
94	C₂×C₄	#14556535	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	—	1168	1	no	—
97	C₈	#14556508	1	1	yes	characteristic
98	C₈	#14556512	1	1	yes	characteristic
99	C₂²	#17988388	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	16	2	no	—
102	C₄	#17988331	1	1	yes	characteristic
103	C₄	#17988400	1	1	yes	characteristic
104	C₄	#17988424	1	1	yes	characteristic
105	C₄	#17988427	1	1	yes	characteristic
106	C₂	#22607977	1	1	yes	characteristic
107	C₂	#22608112	1	1	yes	characteristic
108	C₂	#22608124	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#14556497

C₂

yes

maximal, characteristic

#22608003

C₂

yes

maximal, characteristic

C₇₃×#2247

C₂

yes

maximal, characteristic

C₂×#14556497

—

#17988340

—

C₂×Q₃₂×C₇₃

—

C₂×Q₃₂×C₇₃

C₄

yes

—

#494×C₇₃

—

C₄×C₁₆×C₇₃

C₂²

yes

characteristic

C₄⋊#10596831

—

#14556497

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₄⋊Q₈×C₇₃

—

Q₃₂×C₇₃

—

Q₃₂×C₇₃

—

Q₃₂×C₇₃

—

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

characteristic

C₂×#10596831

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

SD₁₆

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

D₈

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

D₈

yes

characteristic

C₁₆×C₇₃

SD₁₆

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#102

yes

characteristic

C₂×C₄×C₇₃

D₁₆

yes

characteristic

C₂×C₄×C₇₃

SD₃₂

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

#357

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

SD₆₄

yes

characteristic

C₄×C₇₃

Q₆₄

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

yes

characteristic

C₄⋊C₃₂

—

#1371

—

C₇₃

#7445

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×Q₃₂

Dic₇₃

yes

—

#494

—

C₂×C₃₂

—

146

—

C₄×C₁₆

C₂×D₇₃

yes

characteristic

#335

—

146

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

C₂×Dic₇₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₈

—

292

—

C₄×C₈

C₂²⋊D₇₃

yes

characteristic

C₃₂

—

292

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

584

—

C₂×C₈

C₂²⋊Dic₇₃

yes

characteristic

C₂×C₈

#11924016

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

#11924013

yes

characteristic

C₁₆

—

C₁₆

yes

C₁₆

yes

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

1168

—

C₈

yes

C₈

yes

C₂²

yes

100

C₄

—

101

C₄

—

102

C₄

#17988331

yes

characteristic

103

C₄

#17988400

yes

characteristic

104

C₄

#17988424

yes

characteristic

105

C₄

#17988427

yes

characteristic

106

C₂

#22607977

yes

characteristic

107

C₂

#22608112

yes

characteristic

108

C₂

#22608124

yes

characteristic

	subgroup	G/H
center	C₂²	#17988388
commutator	C₂×C₁₆×C₇₃	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₇₃
Fitting	C₇₃×#2247	C₂
socle, prime radical	C₂²×C₇₃	#357
cosocle	C₄×C₁₆×C₇₃	C₂²
hypercenter	#2247	D₇₃
hypocenter	C₇₃	#7445
LCS	G ▷ C₂×C₁₆×C₇₃ ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

subgroup

G/H

center

C₂²

#17988388

commutator

C₂×C₁₆×C₇₃

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₇₃

Fitting

C₇₃×#2247

C₂

socle, prime radical

C₂²×C₇₃

#357

cosocle

C₄×C₁₆×C₇₃

C₂²

D₇₃

C₇₃

G ▷ C₂×C₁₆×C₇₃ ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

N	H ≅ G/N	type
58. C₇₃	#7445	semidirect

H ≅ G/N

type

58. C₇₃

#7445

semidirect

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

subgroup	index
C₄⋊#14556497	2
#22608003	2
C₇₃×#2247	2
#7445	73

subgroup

index

C₄⋊#14556497

#22608003

C₇₃×#2247

#7445

Subgroups — #32973620

Conjugacy classes of subgroups

Complements

Maximal subgroups