Group #32995039 — subgroups

Subgroups — #32995039

Order 18688.

228 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 123 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	#22611734	C₂	1	2	yes	maximal
2	#22607852	C₂	1	4	yes	maximal, complemented
3	C₇₃×#1450	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#11924003	C₄	1	4	yes	—
5	C₂²⋊#11924003	C₄	1	4	yes	—
6	#17988363	C₂²	1	4	yes	—
7	#431×C₇₃	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
9	#322×C₇₃	C₂²	1	2	yes	—
10	C₈²×C₇₃	C₄	1	2	yes	—
11	C₂×#11924003	C₂×C₄	1	8	yes	—
12	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₄⋊C₈×C₇₃	—	2	2	no	—
15	C₂²⋊C₈×C₇₃	—	2	2	no	—
16	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	—
18	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
20	#11924003	—	2	8	no	—
21	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
22	C₂²×C₄×C₇₃	M₁₆	1	2	yes	—
23	C₂×C₈×C₇₃	—	2	4	no	—
24	C₂×C₈×C₇₃	—	2	4	no	—
25	C₂×C₈×C₇₃	C₄²	1	2	yes	—
26	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
27	C₄²×C₇₃	C₄²	1	1	yes	characteristic
28	C₄²×C₇₃	M₁₆	1	2	yes	—
29	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂³×C₇₃	#97	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	—	4	2	no	—
33	C₂×C₄×C₇₃	#97	1	2	yes	—
34	C₂×C₄×C₇₃	#97	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
37	C₈×C₇₃	—	2	2	no	—
38	C₈×C₇₃	—	4	4	no	—
39	C₈×C₇₃	#131	1	4	yes	—
40	C₂²×C₇₃	—	2	2	no	—
41	C₂²×C₇₃	—	2	1	no	—
42	C₂²×C₇₃	C₂×#97	1	1	yes	characteristic
43	C₄×C₇₃	—	2	2	no	—
44	C₄×C₇₃	—	2	2	no	—
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	#405	1	2	yes	—
47	#11416	—	73	1	no	maximal, Sylow
48	C₂×C₇₃	—	4	1	no	—
49	C₂×C₇₃	#1452	1	1	yes	characteristic
50	C₂×C₇₃	#2110	1	2	yes	—
51	#2163	—	73	2	no	—
52	#1450	D₇₃	1	1	yes	characteristic
53	#1313	—	73	4	no	—
54	C₇₃	#11416	1	1	yes	characteristic, complemented, Sylow
55	#431	Dic₇₃	1	2	yes	—
56	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
57	C₄⋊C₁₆	—	73	4	no	—
58	C₂²⋊C₁₆	—	73	4	no	—
59	#346	—	73	4	no	—
60	#322	C₂×D₇₃	1	2	yes	—
61	C₈²	Dic₇₃	1	2	yes	—
62	C₂²×C₈	C₄×D₇₃	1	2	yes	—
63	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
64	C₂×C₁₆	—	73	8	no	—
65	C₄⋊C₈	—	2	2	no	—
66	C₂²⋊C₈	—	2	2	no	—
67	C₄×C₈	C₄×D₇₃	1	2	yes	—
68	C₄×C₈	C₂×Dic₇₃	1	4	yes	—
69	C₄×C₈	C₂×Dic₇₃	1	1	yes	characteristic
70	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
71	C₂²×C₄	C₄×Dic₇₃	1	1	yes	characteristic
72	C₂²×C₄	#11924012	1	2	yes	—
73	C₂×C₈	—	2	4	no	—
74	C₂×C₈	—	2	4	no	—
75	C₂×C₈	C₄×Dic₇₃	1	2	yes	—
76	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
77	C₄²	C₄×Dic₇₃	1	1	yes	characteristic
78	C₄²	#11924012	1	2	yes	—
79	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
80	C₁₆	—	146	8	no	—
81	C₂³	#14556502	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	#14556502	1	2	yes	—
85	C₂×C₄	#14556502	1	1	yes	characteristic
86	C₂×C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
87	C₂×C₄	C₂×#11924012	1	2	yes	—
88	C₈	—	2	2	no	—
89	C₈	—	4	4	no	—
90	C₈	#14556597	1	4	yes	—
91	C₂²	—	2	2	no	—
92	C₂²	—	2	1	no	—
93	C₂²	C₂×#14556502	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	2	2	no	—
96	C₄	—	2	1	no	—
97	C₄	#17988542	1	2	yes	—
98	C₂	—	4	1	no	—
99	C₂	#22608223	1	1	yes	characteristic
100	C₂	#22611536	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22611734

C₂

yes

maximal

#22607852

C₂

yes

maximal, complemented

C₇₃×#1450

C₂

yes

maximal, characteristic

C₄⋊#11924003

C₄

yes

—

C₂²⋊#11924003

C₄

yes

—

#17988363

C₂²

yes

—

#431×C₇₃

C₄

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#322×C₇₃

C₂²

yes

—

C₈²×C₇₃

C₄

yes

—

C₂×#11924003

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

C₂³

yes

characteristic

#11924003

—

C₂²×C₄×C₇₃

C₄²

yes

characteristic

C₂²×C₄×C₇₃

M₁₆

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₄²

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

—

C₄²×C₇₃

C₄²

yes

characteristic

C₄²×C₇₃

M₁₆

yes

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₂³×C₇₃

#97

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#97

yes

—

C₂×C₄×C₇₃

#97

yes

characteristic

C₂×C₄×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

#131

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×#97

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#405

yes

—

#11416

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

#1452

yes

characteristic

C₂×C₇₃

#2110

yes

—

#2163

—

#1450

D₇₃

yes

characteristic

#1313

—

C₇₃

#11416

yes

characteristic, complemented, Sylow

#431

Dic₇₃

yes

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#322

C₂×D₇₃

yes

—

C₈²

Dic₇₃

yes

—

C₂²×C₈

C₄×D₇₃

yes

—

C₂×C₄²

C₂×Dic₇₃

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₄×D₇₃

yes

—

C₄×C₈

C₂×Dic₇₃

yes

—

C₄×C₈

C₂×Dic₇₃

yes

characteristic

C₄×C₈

C₂²×D₇₃

yes

characteristic

C₂²×C₄

C₄×Dic₇₃

yes

characteristic

C₂²×C₄

#11924012

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×Dic₇₃

yes

—

C₂×C₈

C₂×C₄×D₇₃

yes

—

C₄²

C₄×Dic₇₃

yes

characteristic

C₄²

#11924012

yes

—

C₄²

C₂²×Dic₇₃

yes

characteristic

C₁₆

—

146

—

C₂³

#14556502

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#14556502

yes

—

C₂×C₄

#14556502

yes

characteristic

C₂×C₄

C₂×C₄×Dic₇₃

yes

characteristic

C₂×C₄

C₂×#11924012

yes

—

C₈

—

C₈

—

C₈

#14556597

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#14556502

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#17988542

yes

—

C₂

—

C₂

#22608223

yes

characteristic

100

C₂

#22611536

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₇₃
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₄×C₈	C₂²×D₇₃
Fitting	C₇₃×#1450	C₂
socle	C₂²×C₇₃	C₂×#97
prime radical	C₂³×C₇₃	#97
cosocle	C₄×C₈×C₇₃	C₂³
hypercenter	#1450	D₇₃
hypocenter	C₇₃	#11416
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #1450

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₇₃

commutator

C₂×C₄×C₇₃

C₂×C₄²

Frattini

C₄×C₈

C₂²×D₇₃

Fitting

C₇₃×#1450

C₂

socle

C₂²×C₇₃

C₂×#97

prime radical

C₂³×C₇₃

#97

cosocle

C₄×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #1450

N	H ≅ G/N	type
2. #22607852	C₂	semidirect
54. C₇₃	#11416	semidirect

H ≅ G/N

type

2. #22607852

C₂

semidirect

54. C₇₃

#11416

semidirect

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

subgroup	index
#22611734	2
#22607852	2
C₇₃×#1450	2
#11416	73

subgroup

index

#22611734

#22607852

C₇₃×#1450

#11416

Subgroups — #32995039

Conjugacy classes of subgroups

Complements

Maximal subgroups