Group #32975340 — subgroups

Subgroups — #32975340

Order 18688.

574 conjugacy classes of subgroups; only the 387 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 387 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	#22609677	C₂	1	2	yes	maximal
2	C₂×#17988308	C₂	1	2	yes	maximal
3	C₂×C₈×#10596831	C₂	1	2	yes	maximal
4	C₄²×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#10596831	C₂²	1	4	yes	—
6	#17988342	C₄	1	8	yes	—
7	#17988308	C₄	1	8	yes	complemented
8	C₈×#10596831	C₄	1	8	yes	complemented
9	C₂×C₄×C₈×C₇₃	C₄	1	4	yes	—
10	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	C₄³×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×#10596831	C₂×C₄	1	8	yes	—
14	C₄×#10596831	C₂×C₄	1	8	yes	—
15	C₄×#10596831	C₂×C₄	1	8	yes	—
16	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₇₃	C₂×C₄	1	4	yes	—
19	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
21	C₄×C₈×C₇₃	C₈	1	16	yes	complemented
22	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	—
23	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	—
24	C₂×#10596831	—	2	16	no	—
25	C₂×#10596831	C₄²	1	16	yes	—
26	C₂²×C₄×C₇₃	C₄²	1	4	yes	—
27	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
28	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₄²	1	4	yes	—
30	C₂×C₈×C₇₃	C₄²	1	4	yes	—
31	C₂×C₈×C₇₃	C₂×C₈	1	8	yes	—
32	C₂×C₈×C₇₃	C₂×C₈	1	8	yes	—
33	C₄²×C₇₃	—	2	8	no	—
34	C₄²×C₇₃	C₂×C₈	1	8	yes	—
35	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
36	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
37	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
38	C₂×C₄×C₇₃	—	2	8	no	—
39	C₂×C₄×C₇₃	C₄×C₈	1	8	yes	—
40	C₂×C₄×C₇₃	C₂×C₄²	1	4	yes	—
41	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
43	C₂×C₄×C₇₃	C₂²×C₈	1	4	yes	—
44	C₂×C₄×C₇₃	#131	1	8	yes	—
45	C₈×C₇₃	C₄×C₈	1	8	yes	—
46	C₈×C₇₃	C₄×C₈	1	8	yes	—
47	#10596831	—	2	16	no	—
48	C₂²×C₇₃	C₄³	1	1	yes	characteristic
49	C₂²×C₇₃	C₂×C₄×C₈	1	2	yes	—
50	C₂²×C₇₃	#405	1	4	yes	—
51	C₄×C₇₃	—	2	8	no	—
52	C₄×C₇₃	C₂×C₄×C₈	1	2	yes	—
53	C₄×C₇₃	C₂×C₄×C₈	1	2	yes	—
54	C₄×C₇₃	#405	1	8	yes	—
55	#7841	—	73	1	no	maximal, Sylow
56	C₂×C₇₃	#1450	1	4	yes	—
57	C₂×C₇₃	C₄²×C₈	1	1	yes	characteristic
58	C₂×C₇₃	#1726	1	2	yes	—
59	#1744	—	73	2	no	—
60	C₄²×C₈	D₇₃	1	1	yes	characteristic
61	C₂×#322	—	73	2	no	—
62	C₂×C₈²	—	73	2	no	—
63	C₇₃	#7841	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₄×C₈	—	73	4	no	—
65	C₂×C₄×C₈	Dic₇₃	1	4	yes	—
66	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
67	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
68	C₄³	C₂×D₇₃	1	1	yes	characteristic
69	#336	—	73	8	no	—
70	#322	—	73	8	no	—
71	C₈²	—	73	8	no	—
72	C₂²×C₈	—	73	8	no	—
73	C₂²×C₈	C₂×Dic₇₃	1	2	yes	—
74	C₂²×C₈	C₂×Dic₇₃	1	2	yes	—
75	C₂×C₄²	C₄×D₇₃	1	4	yes	—
76	C₂×C₄²	C₂×Dic₇₃	1	2	yes	—
77	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
78	C₄×C₈	—	73	8	no	—
79	C₄×C₈	—	73	8	no	—
80	C₄×C₈	#10596831	1	16	yes	complemented
81	C₄×C₈	C₄×D₇₃	1	4	yes	—
82	C₄×C₈	C₄×D₇₃	1	4	yes	—
83	C₂²×C₄	C₄×Dic₇₃	1	4	yes	—
84	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
85	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
86	C₂×C₈	—	73	16	no	—
87	C₂×C₈	—	146	16	no	—
88	C₂×C₈	C₄×Dic₇₃	1	4	yes	—
89	C₂×C₈	C₄×Dic₇₃	1	4	yes	—
90	C₂×C₈	C₂×#10596831	1	8	yes	—
91	C₂×C₈	C₂×#10596831	1	8	yes	—
92	C₄²	—	2	8	no	—
93	C₄²	C₂×#10596831	1	8	yes	—
94	C₄²	C₂×C₄×D₇₃	1	2	yes	—
95	C₄²	C₂×C₄×D₇₃	1	2	yes	—
96	C₂³	C₂×C₄×Dic₇₃	1	1	yes	characteristic
97	C₂×C₄	—	2	8	no	—
98	C₂×C₄	C₄×#10596831	1	8	yes	—
99	C₂×C₄	C₄²×D₇₃	1	4	yes	—
100	C₂×C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
102	C₂×C₄	C₂²×#10596831	1	4	yes	—
103	C₂×C₄	#14556597	1	8	yes	—
104	C₈	—	146	16	no	—
105	C₈	C₄×#10596831	1	8	yes	—
106	C₈	C₄×#10596831	1	8	yes	—
107	C₂²	C₄²×Dic₇₃	1	1	yes	characteristic
108	C₂²	C₂×C₄×#10596831	1	2	yes	—
109	C₂²	#17988542	1	4	yes	—
110	C₄	—	2	8	no	—
111	C₄	C₂×C₄×#10596831	1	2	yes	—
112	C₄	C₂×C₄×#10596831	1	2	yes	—
113	C₄	#17988541	1	8	yes	—
114	C₂	#22608214	1	4	yes	—
115	C₂	C₄²×#10596831	1	1	yes	characteristic
116	C₂	#22609617	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22609677

C₂

yes

maximal

C₂×#17988308

C₂

yes

maximal

C₂×C₈×#10596831

C₂

yes

maximal

C₄²×C₈×C₇₃

C₂

yes

maximal, characteristic

C₂×C₄×#10596831

C₂²

yes

—

#17988342

C₄

yes

—

#17988308

C₄

yes

complemented

C₈×#10596831

C₄

yes

complemented

C₂×C₄×C₈×C₇₃

C₄

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

C₄³×C₇₃

C₂²

yes

characteristic

C₂²×#10596831

C₂×C₄

yes

—

C₄×#10596831

C₂×C₄

yes

—

C₄×#10596831

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄×C₈×C₇₃

C₈

yes

complemented

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₂×#10596831

—

C₂×#10596831

C₄²

yes

—

C₂²×C₄×C₇₃

C₄²

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₄²

yes

—

C₂×C₈×C₇₃

C₄²

yes

—

C₂×C₈×C₇₃

C₂×C₈

yes

—

C₂×C₈×C₇₃

C₂×C₈

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×C₈

yes

—

C₄²×C₇₃

C₂²×C₄

yes

—

C₄²×C₇₃

C₂²×C₄

yes

—

C₂³×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₄²

yes

—

C₂×C₄×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₈

yes

—

C₂×C₄×C₇₃

#131

yes

—

C₈×C₇₃

C₄×C₈

yes

—

C₈×C₇₃

C₄×C₈

yes

—

#10596831

—

C₂²×C₇₃

C₄³

yes

characteristic

C₂²×C₇₃

C₂×C₄×C₈

yes

—

C₂²×C₇₃

#405

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄×C₈

yes

—

C₄×C₇₃

C₂×C₄×C₈

yes

—

C₄×C₇₃

#405

yes

—

#7841

—

maximal, Sylow

C₂×C₇₃

#1450

yes

—

C₂×C₇₃

C₄²×C₈

yes

characteristic

C₂×C₇₃

#1726

yes

—

#1744

—

C₄²×C₈

D₇₃

yes

characteristic

C₂×#322

—

C₂×C₈²

—

C₇₃

#7841

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

Dic₇₃

yes

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

C₄³

C₂×D₇₃

yes

characteristic

#336

—

#322

—

C₈²

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₇₃

yes

—

C₂²×C₈

C₂×Dic₇₃

yes

—

C₂×C₄²

C₄×D₇₃

yes

—

C₂×C₄²

C₂×Dic₇₃

yes

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#10596831

yes

complemented

C₄×C₈

C₄×D₇₃

yes

—

C₄×C₈

C₄×D₇₃

yes

—

C₂²×C₄

C₄×Dic₇₃

yes

—

C₂²×C₄

C₂×C₄×D₇₃

yes

—

C₂²×C₄

C₂²×Dic₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₄×Dic₇₃

yes

—

C₂×C₈

C₄×Dic₇₃

yes

—

C₂×C₈

C₂×#10596831

yes

—

C₂×C₈

C₂×#10596831

yes

—

C₄²

—

C₄²

C₂×#10596831

yes

—

C₄²

C₂×C₄×D₇₃

yes

—

C₄²

C₂×C₄×D₇₃

yes

—

C₂³

C₂×C₄×Dic₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄×#10596831

yes

—

C₂×C₄

C₄²×D₇₃

yes

—

100

C₂×C₄

C₂×C₄×Dic₇₃

yes

characteristic

101

C₂×C₄

C₂×C₄×Dic₇₃

yes

characteristic

102

C₂×C₄

C₂²×#10596831

yes

—

103

C₂×C₄

#14556597

yes

—

104

C₈

—

146

—

105

C₈

C₄×#10596831

yes

—

106

C₈

C₄×#10596831

yes

—

107

C₂²

C₄²×Dic₇₃

yes

characteristic

108

C₂²

C₂×C₄×#10596831

yes

—

109

C₂²

#17988542

yes

—

110

C₄

—

111

C₄

C₂×C₄×#10596831

yes

—

112

C₄

C₂×C₄×#10596831

yes

—

113

C₄

#17988541

yes

—

114

C₂

#22608214

yes

—

115

C₂

C₄²×#10596831

yes

characteristic

116

C₂

#22609617

yes

—

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₇₃
commutator	C₂×C₇₃	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₄²×C₈×C₇₃	C₂
socle, prime radical	C₂³×C₇₃	C₂×C₄²
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	C₄²×C₈	D₇₃
hypocenter	C₇₃	#7841
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₄²×C₈

subgroup

G/H

center

C₂×C₄×C₈

C₂×D₇₃

commutator

C₂×C₇₃

C₄²×C₈

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₄²×C₈×C₇₃

C₂

socle, prime radical

C₂³×C₇₃

C₂×C₄²

cosocle

C₂×C₄²×C₇₃

C₂³

hypercenter

C₄²×C₈

D₇₃

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄×C₈ ◁ C₄²×C₈

N	H ≅ G/N	type
7. #17988308	C₄	semidirect
8. C₈×#10596831	C₄	semidirect
21. C₄×C₈×C₇₃	C₈	semidirect
63. C₇₃	#7841	semidirect
80. C₄×C₈	#10596831	semidirect

H ≅ G/N

type

7. #17988308

C₄

semidirect

8. C₈×#10596831

C₄

semidirect

21. C₄×C₈×C₇₃

C₈

semidirect

63. C₇₃

#7841

semidirect

80. C₄×C₈

#10596831

semidirect

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

subgroup	index
#22609677	2
C₂×#17988308	2
C₂×C₈×#10596831	2
C₄²×C₈×C₇₃	2
#7841	73

subgroup

index

C₄²×C₈×C₇₃

Subgroups — #32975340

Conjugacy classes of subgroups

Complements

Maximal subgroups