Group #32973442 — subgroups

Subgroups — #32973442

Order 18688.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic
2	#22608065	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#1372	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₅₈₄	C₄	1	1	yes	characteristic
5	C₄×Dic₂₉₂	—	2	1	no	—
6	C₂×#14556497	—	2	1	no	—
7	#17988413	C₄	1	1	yes	characteristic
8	#17988392	—	2	1	no	—
9	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	#335×C₇₃	—	2	1	no	—
11	C₂×Dic₂₉₂	—	2	1	no	—
12	C₄×Dic₁₄₆	—	4	1	no	—
13	Dic₅₈₄	—	2	1	no	—
14	Dic₅₈₄	C₈	1	2	yes	complemented
15	#14556525	—	2	1	no	—
16	#14556516	—	4	1	no	—
17	#14556497	—	2	2	no	—
18	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
20	C₄⋊C₈×C₇₃	—	4	1	no	—
21	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
22	C₂×Dic₁₄₆	—	4	1	no	—
23	Dic₂₉₂	—	2	2	no	—
24	Dic₂₉₂	—	4	1	no	—
25	C₄⋊Dic₇₃	—	4	1	no	—
26	#11924007	—	8	1	no	—
27	C₄×Dic₇₃	—	8	1	no	—
28	C₂×C₈×C₇₃	—	8	1	no	—
29	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	SD₁₆	1	1	yes	characteristic
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	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
36	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₃	SD₃₂	1	1	yes	characteristic
38	C₂×Dic₇₃	—	8	1	no	—
39	C₂×Dic₇₃	—	8	1	no	—
40	Dic₁₄₆	—	4	2	no	—
41	Dic₁₄₆	—	8	1	no	—
42	C₈×C₇₃	—	2	1	no	—
43	C₈×C₇₃	—	16	1	no	—
44	C₈×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
45	C₈×C₇₃	#104	1	1	yes	characteristic
46	C₂²×C₇₃	#357	1	1	yes	characteristic
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	—	2	1	no	—
49	C₄×C₇₃	D₄⋊C₈	1	1	yes	characteristic
50	C₄×C₇₃	#359	1	1	yes	characteristic
51	Dic₇₃	—	8	2	no	—
52	Dic₇₃	—	16	1	no	—
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	—	73	1	no	—
58	#1397	—	73	1	no	—
59	#1372	D₇₃	1	1	yes	characteristic
60	C₇₃	#7386	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₃₂	—	73	1	no	—
62	C₄×Q₁₆	—	146	1	no	—
63	C₂×C₃₂	—	146	1	no	—
64	#366	—	73	1	no	—
65	#358	—	146	1	no	—
66	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
67	#335	—	2	1	no	—
68	C₂×Q₁₆	—	146	1	no	—
69	C₄×Q₈	—	292	1	no	—
70	Q₃₂	—	73	2	no	—
71	Q₃₂	—	146	1	no	—
72	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
73	C₂×C₁₆	D₂₉₂	1	1	yes	characteristic
74	#107	—	146	1	no	—
75	C₄⋊C₈	—	4	1	no	—
76	#103	—	292	1	no	—
77	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
78	C₃₂	—	146	2	no	—
79	C₂×Q₈	—	292	1	no	—
80	Q₁₆	—	292	1	no	—
81	Q₁₆	—	146	2	no	—
82	C₂×C₈	—	8	1	no	—
83	C₂×C₈	#11924005	1	1	yes	characteristic
84	C₂×C₈	#11924015	1	1	yes	characteristic
85	C₄⋊C₄	—	292	1	no	—
86	C₄⋊C₄	—	584	1	no	—
87	C₄²	—	584	1	no	—
88	C₄²	#11924013	1	1	yes	characteristic
89	C₁₆	—	2	1	no	—
90	C₁₆	C₈×D₇₃	1	1	yes	characteristic
91	C₁₆	#11924011	1	1	yes	characteristic
92	Q₈	—	292	2	no	—
93	Q₈	—	584	1	no	—
94	C₂×C₄	—	584	1	no	—
95	C₂×C₄	—	584	1	no	—
96	C₂×C₄	#14556511	1	1	yes	characteristic
97	C₂×C₄	#14556532	1	1	yes	characteristic
98	C₂×C₄	#14556534	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	16	1	no	—
101	C₈	#14556503	1	1	yes	characteristic
102	C₈	#14556517	1	1	yes	characteristic
103	C₂²	#17988387	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	584	2	no	—
107	C₄	—	1168	1	no	—
108	C₄	#17988314	1	1	yes	characteristic
109	C₄	#17988393	1	1	yes	characteristic
110	C₂	#22607891	1	1	yes	characteristic
111	C₂	#22608117	1	1	yes	characteristic
112	C₂	#22608123	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×Dic₅₈₄

C₂

yes

maximal, characteristic

#22608065

C₂

yes

maximal, characteristic

C₇₃×#1372

C₂

yes

maximal, characteristic

C₂×Dic₅₈₄

C₄

yes

characteristic

C₄×Dic₂₉₂

—

C₂×#14556497

—

#17988413

C₄

yes

characteristic

#17988392

—

C₄×C₁₆×C₇₃

C₂²

yes

characteristic

#335×C₇₃

—

C₂×Dic₂₉₂

—

C₄×Dic₁₄₆

—

Dic₅₈₄

—

Dic₅₈₄

C₈

yes

—

—

—

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄×C₈×C₇₃

D₄

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

#11924007

—

C₄×Dic₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

SD₁₆

yes

characteristic

C₄²×C₇₃

D₈

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

C₂×C₈

yes

characteristic

C₁₆×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

#102

yes

characteristic

C₂×C₄×C₇₃

D₁₆

yes

characteristic

C₂×C₄×C₇₃

SD₃₂

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

C₂²⋊C₈

yes

C₈×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

D₄⋊C₈

yes

characteristic

C₄×C₇₃

#359

yes

characteristic

Dic₇₃

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₄×Q₃₂

—

#1397

—

#1372

D₇₃

yes

characteristic

C₇₃

#7386

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₄×Q₁₆

—

146

—

C₂×C₃₂

—

146

—

#366

—

#358

—

146

—

C₄×C₁₆

C₂×D₇₃

yes

characteristic

#335

—

C₂×Q₁₆

—

146

—

C₄×Q₈

—

292

—

Q₃₂

—

Q₃₂

—

146

—

C₂×C₁₆

C₄×D₇₃

yes

characteristic

C₂×C₁₆

D₂₉₂

yes

characteristic

#107

—

146

—

C₄⋊C₈

—

#103

—

292

—

C₄×C₈

C₂²⋊D₇₃

yes

characteristic

C₃₂

—

146

—

C₂×Q₈

—

292

—

Q₁₆

—

292

—

Q₁₆

—

146

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

292

—

C₄⋊C₄

—

584

—

C₄²

—

584

—

C₄²

#11924013

yes

characteristic

C₁₆

—

C₁₆

C₈×D₇₃

yes

characteristic

C₁₆

#11924011

yes

characteristic

Q₈

—

292

—

Q₈

—

584

—

C₂×C₄

—

584

—

C₂×C₄

—

584

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

100

C₈

—

101

C₈

#14556503

yes

characteristic

102

C₈

#14556517

yes

characteristic

103

C₂²

#17988387

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

584

—

107

C₄

—

1168

—

108

C₄

#17988314

yes

characteristic

109

C₄

#17988393

yes

characteristic

110

C₂

#22607891

yes

characteristic

111

C₂

#22608117

yes

characteristic

112

C₂

#22608123

yes

characteristic

	subgroup	G/H
center	C₂²	#17988387
commutator	C₁₆×C₇₃	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₇₃
Fitting	C₇₃×#1372	C₂
socle, prime radical	C₂²×C₇₃	#357
cosocle	C₄×C₁₆×C₇₃	C₂²
hypercenter	#1372	D₇₃
hypocenter	C₇₃	#7386
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1372

subgroup

G/H

center

C₂²

#17988387

commutator

C₁₆×C₇₃

C₂×C₈

Frattini

C₄×C₁₆

C₂×D₇₃

Fitting

C₇₃×#1372

C₂

socle, prime radical

C₂²×C₇₃

#357

cosocle

C₄×C₁₆×C₇₃

C₂²

D₇₃

C₇₃

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1372

N	H ≅ G/N	type
14. Dic₅₈₄	C₈	semidirect
60. C₇₃	#7386	semidirect

H ≅ G/N

type

14. Dic₅₈₄

C₈

semidirect

60. C₇₃

#7386

semidirect

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

subgroup	index
C₄×Dic₅₈₄	2
#22608065	2
C₇₃×#1372	2
#7386	73

subgroup

index

C₄×Dic₅₈₄

#22608065

C₇₃×#1372

#7386

Subgroups — #32973442

Conjugacy classes of subgroups

Complements

Maximal subgroups