Group #32973443 — subgroups

Subgroups — #32973443

Order 18688.

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

normal subgroups only

This group has 124 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	#22608065	C₂	1	1	yes	maximal, characteristic
2	#22608005	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556497	—	2	1	no	—
5	#17988340	—	2	1	no	—
6	C₂×Q₃₂×C₇₃	C₄	1	1	yes	characteristic
7	C₄×Q₁₆×C₇₃	—	2	1	no	—
8	#366×C₇₃	C₄	1	1	yes	characteristic
9	#358×C₇₃	—	2	1	no	—
10	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₄⋊#10596831	—	4	1	no	—
12	#14556497	—	2	2	no	—
13	C₂×Q₁₆×C₇₃	—	2	1	no	—
14	C₄×Q₈×C₇₃	—	4	1	no	—
15	Q₃₂×C₇₃	—	2	1	no	—
16	Q₃₂×C₇₃	C₈	1	2	yes	complemented
17	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
19	#107×C₇₃	—	2	1	no	—
20	#103×C₇₃	—	4	1	no	—
21	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
22	C₂×#10596831	—	8	1	no	—
23	C₂×Q₈×C₇₃	—	4	1	no	—
24	Q₁₆×C₇₃	—	2	2	no	—
25	Q₁₆×C₇₃	—	4	1	no	—
26	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₃	SD₁₆	1	1	yes	characteristic
28	C₄⋊C₄×C₇₃	—	4	1	no	—
29	C₄⋊C₄×C₇₃	—	8	1	no	—
30	C₄²×C₇₃	—	8	1	no	—
31	C₄²×C₇₃	D₈	1	1	yes	characteristic
32	C₁₆×C₇₃	—	2	1	no	—
33	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
34	C₁₆×C₇₃	M₁₆	1	1	yes	characteristic
35	Q₈×C₇₃	—	4	2	no	—
36	Q₈×C₇₃	—	8	1	no	—
37	C₂×C₄×C₇₃	—	8	1	no	—
38	C₂×C₄×C₇₃	—	8	1	no	—
39	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
40	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
41	C₂×C₄×C₇₃	SD₃₂	1	1	yes	characteristic
42	C₈×C₇₃	—	2	1	no	—
43	C₈×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₈×C₇₃	#104	1	1	yes	characteristic
45	#10596831	—	16	1	no	—
46	C₂²×C₇₃	#357	1	1	yes	characteristic
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	—	2	1	no	—
49	C₄×C₇₃	—	8	2	no	—
50	C₄×C₇₃	—	16	1	no	—
51	C₄×C₇₃	D₄⋊C₈	1	1	yes	characteristic
52	C₄×C₇₃	#359	1	1	yes	characteristic
53	#7386	—	73	1	no	maximal, Sylow
54	C₂×C₇₃	#1331	1	1	yes	characteristic
55	C₂×C₇₃	#1418	1	1	yes	characteristic
56	C₂×C₇₃	#1420	1	1	yes	characteristic
57	C₄×Q₃₂	D₇₃	1	1	yes	characteristic
58	#1397	—	73	1	no	—
59	#1372	—	73	1	no	—
60	C₇₃	#7386	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₃₂	Dic₇₃	1	1	yes	characteristic
62	C₄×Q₁₆	—	2	1	no	—
63	C₂×C₃₂	—	146	1	no	—
64	#366	Dic₇₃	1	1	yes	characteristic
65	#358	—	2	1	no	—
66	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
67	#335	—	146	1	no	—
68	C₂×Q₁₆	—	2	1	no	—
69	C₄×Q₈	—	4	1	no	—
70	Q₃₂	—	2	1	no	—
71	Q₃₂	#10596831	1	2	yes	complemented
72	C₂×C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
73	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
74	#107	—	2	1	no	—
75	C₄⋊C₈	—	292	1	no	—
76	#103	—	4	1	no	—
77	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
78	C₃₂	—	146	2	no	—
79	C₂×Q₈	—	4	1	no	—
80	Q₁₆	—	2	2	no	—
81	Q₁₆	—	4	1	no	—
82	C₂×C₈	—	584	1	no	—
83	C₂×C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
84	C₂×C₈	#11924016	1	1	yes	characteristic
85	C₄⋊C₄	—	4	1	no	—
86	C₄⋊C₄	—	8	1	no	—
87	C₄²	—	8	1	no	—
88	C₄²	#11924013	1	1	yes	characteristic
89	C₁₆	—	2	1	no	—
90	C₁₆	C₂×#10596831	1	1	yes	characteristic
91	C₁₆	#11924012	1	1	yes	characteristic
92	Q₈	—	4	2	no	—
93	Q₈	—	8	1	no	—
94	C₂×C₄	—	8	1	no	—
95	C₂×C₄	—	8	1	no	—
96	C₂×C₄	#14556512	1	1	yes	characteristic
97	C₂×C₄	#14556532	1	1	yes	characteristic
98	C₂×C₄	#14556535	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	1168	1	no	—
101	C₈	C₂²⋊#10596831	1	1	yes	characteristic
102	C₈	#14556518	1	1	yes	characteristic
103	C₂²	#17988388	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	8	2	no	—
107	C₄	—	16	1	no	—
108	C₄	D₄⋊#10596831	1	1	yes	characteristic
109	C₄	#17988394	1	1	yes	characteristic
110	C₂	#22607892	1	1	yes	characteristic
111	C₂	#22608118	1	1	yes	characteristic
112	C₂	#22608124	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22608065

C₂

yes

maximal, characteristic

#22608005

C₂

yes

maximal, characteristic

C₄×Q₃₂×C₇₃

C₂

yes

maximal, characteristic

C₂×#14556497

—

#17988340

—

C₂×Q₃₂×C₇₃

C₄

yes

characteristic

C₄×Q₁₆×C₇₃

—

#366×C₇₃

C₄

yes

characteristic

#358×C₇₃

—

C₄×C₁₆×C₇₃

C₂²

yes

characteristic

C₄⋊#10596831

—

#14556497

—

C₂×Q₁₆×C₇₃

—

C₄×Q₈×C₇₃

—

Q₃₂×C₇₃

—

Q₃₂×C₇₃

C₈

yes

complemented

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

#107×C₇₃

—

#103×C₇₃

—

C₄×C₈×C₇₃

D₄

yes

characteristic

C₂×#10596831

—

C₂×Q₈×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

—

C₄²×C₇₃

D₈

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

C₂×C₈

yes

characteristic

C₁₆×C₇₃

M₁₆

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×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

C₂²⋊C₈

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

#357

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

D₄⋊C₈

yes

C₄×C₇₃

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₄×Q₃₂

D₇₃

yes

characteristic

#1397

—

#1372

—

C₇₃

#7386

yes

characteristic, complemented, Sylow

C₂×Q₃₂

Dic₇₃

yes

characteristic

C₄×Q₁₆

—

C₂×C₃₂

—

146

—

#366

Dic₇₃

yes

characteristic

#358

—

C₄×C₁₆

C₂×D₇₃

yes

characteristic

#335

—

146

—

C₂×Q₁₆

—

C₄×Q₈

—

Q₃₂

—

Q₃₂

#10596831

yes

complemented

C₂×C₁₆

C₂×Dic₇₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

#107

—

C₄⋊C₈

—

292

—

#103

—

C₄×C₈

C₂²⋊D₇₃

yes

characteristic

C₃₂

—

146

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

584

—

C₂×C₈

C₂²⋊Dic₇₃

yes

characteristic

C₂×C₈

#11924016

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

#11924013

yes

characteristic

C₁₆

—

C₁₆

yes

C₁₆

yes

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

100

C₈

—

1168

—

101

C₈

C₂²⋊#10596831

yes

characteristic

102

C₈

#14556518

yes

characteristic

103

C₂²

#17988388

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

D₄⋊#10596831

yes

characteristic

109

C₄

#17988394

yes

characteristic

110

C₂

#22607892

yes

characteristic

111

C₂

#22608118

yes

characteristic

112

C₂

#22608124

yes

characteristic

	subgroup	G/H
center	C₂²	#17988388
commutator	C₁₆×C₇₃	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₇₃
Fitting	C₄×Q₃₂×C₇₃	C₂
socle, prime radical	C₂²×C₇₃	#357
cosocle	C₄×C₁₆×C₇₃	C₂²
hypercenter	C₄×Q₃₂	D₇₃
hypocenter	C₇₃	#7386
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×Q₃₂

subgroup

G/H

center

C₂²

#17988388

commutator

C₁₆×C₇₃

C₂×C₈

Frattini

C₄×C₁₆

C₂×D₇₃

Fitting

C₄×Q₃₂×C₇₃

C₂

socle, prime radical

C₂²×C₇₃

#357

cosocle

C₄×C₁₆×C₇₃

C₂²

hypercenter

C₄×Q₃₂

D₇₃

hypocenter

C₇₃

#7386

LCS

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×Q₃₂

N	H ≅ G/N	type
16. Q₃₂×C₇₃	C₈	semidirect
60. C₇₃	#7386	semidirect
71. Q₃₂	#10596831	semidirect

H ≅ G/N

type

16. Q₃₂×C₇₃

C₈

semidirect

60. C₇₃

#7386

semidirect

71. Q₃₂

#10596831

semidirect

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

subgroup	index
#22608065	2
#22608005	2
C₄×Q₃₂×C₇₃	2
#7386	73

subgroup

index

#22608065

#22608005

C₄×Q₃₂×C₇₃

#7386

Subgroups — #32973443

Conjugacy classes of subgroups

Complements

Maximal subgroups