Group #22608016 — subgroups

Subgroups — #22608016

Order 9344.

132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₂×#14556531	C₂	1	1	yes	maximal, characteristic
2	#17988542	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924012	C₄	1	1	yes	characteristic
5	#14556550	C₄	1	1	yes	characteristic
6	#14556531	—	2	1	no	—
7	#14556531	C₄	1	2	yes	complemented
8	C₂×#11924003	—	2	1	no	—
9	#14556501	—	2	1	no	—
10	C₈×Dic₇₃	—	2	1	no	—
11	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	M₃₂×C₇₃	—	2	1	no	—
13	M₃₂×C₇₃	—	2	1	no	—
14	C₂×C₁₆×C₇₃	C₄	1	2	yes	complemented
15	#11924012	—	2	1	no	—
16	#11924012	C₈	1	2	yes	—
17	C₂×#10596831	—	2	1	no	—
18	C₄⋊Dic₇₃	—	2	1	no	—
19	C₂²⋊Dic₇₃	C₈	1	2	yes	—
20	C₄×Dic₇₃	—	2	1	no	—
21	#11924003	—	2	2	no	—
22	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
27	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	Q₈	1	1	yes	characteristic
29	C₁₆×C₇₃	—	2	2	no	—
30	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
36	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
37	C₂×Dic₇₃	—	2	2	no	—
38	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
42	#10596831	—	2	2	no	—
43	C₂²×C₇₃	—	4	1	no	—
44	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
45	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
46	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₇₃	#95	1	1	yes	characteristic
48	C₄×C₇₃	#97	1	1	yes	characteristic
49	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
50	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
51	Dic₇₃	—	4	2	no	—
52	C₂×C₇₃	—	2	1	no	—
53	C₂×C₇₃	—	2	1	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	#336	1	1	yes	characteristic
56	#1378	—	73	1	no	maximal, Sylow
57	C₇₃	#1378	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₃₂	—	73	1	no	—
59	C₂×M₃₂	D₇₃	1	1	yes	characteristic
60	#405	—	73	1	no	—
61	C₂×M₁₆	—	73	1	no	—
62	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
63	#117	—	73	1	no	—
64	M₃₂	—	2	1	no	—
65	M₃₂	—	2	1	no	—
66	M₃₂	—	73	2	no	—
67	M₃₂	—	146	1	no	—
68	C₂×C₁₆	—	146	1	no	—
69	C₂×C₁₆	Dic₇₃	1	2	yes	complemented
70	#97	—	146	1	no	—
71	C₄×C₈	—	146	1	no	—
72	C₂²×C₄	C₄×D₇₃	1	1	yes	characteristic
73	M₁₆	—	73	2	no	—
74	M₁₆	—	146	1	no	—
75	C₂×C₈	—	146	1	no	—
76	C₂×C₈	Dic₁₄₆	1	1	yes	characteristic
77	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
78	C₂×C₈	D₂₉₂	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₇₃	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
82	C₄⋊C₄	—	146	1	no	—
83	C₂²⋊C₄	—	73	2	no	—
84	C₄²	—	146	1	no	—
85	C₁₆	—	2	2	no	—
86	C₁₆	—	146	2	no	—
87	C₂³	C₈×D₇₃	1	1	yes	characteristic
88	C₂×C₄	—	146	2	no	—
89	C₂×C₄	C₄×Dic₇₃	1	1	yes	characteristic
90	C₂×C₄	#11924005	1	1	yes	characteristic
91	C₂×C₄	#11924007	1	1	yes	characteristic
92	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
93	C₂×C₄	#11924011	1	1	yes	characteristic
94	C₂×C₄	#11924011	1	1	yes	characteristic
95	C₈	—	146	2	no	—
96	C₈	#11924005	1	1	yes	characteristic
97	C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
98	C₈	#11924007	1	1	yes	characteristic
99	C₈	C₄⋊Dic₇₃	1	1	yes	characteristic
100	C₂²	—	4	1	no	—
101	C₂²	C₈×Dic₇₃	1	1	yes	characteristic
102	C₂²	#14556503	1	1	yes	characteristic
103	C₂²	#14556520	1	1	yes	characteristic
104	C₄	—	292	2	no	—
105	C₄	#14556498	1	1	yes	characteristic
106	C₄	#14556501	1	1	yes	characteristic
107	C₄	#14556503	1	1	yes	characteristic
108	C₄	#14556520	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#17988341	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556531

C₂

yes

maximal, characteristic

#17988542

C₂

yes

maximal, characteristic

C₂×M₃₂×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₄

yes

characteristic

#14556550

C₄

yes

characteristic

#14556531

—

#14556531

C₄

yes

complemented

C₂×#11924003

—

#14556501

—

C₈×Dic₇₃

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

C₄

yes

complemented

#11924012

—

#11924012

C₈

yes

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

C₈

yes

—

C₄×Dic₇₃

—

#11924003

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

Q₈

yes

characteristic

C₁₆×C₇₃

—

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×Dic₇₃

—

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂²×C₇₃

C₄⋊C₈

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

D₇₃

yes

characteristic

#405

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

C₂×C₁₆

Dic₇₃

yes

complemented

#97

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

C₄×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

146

—

C₂×C₈

Dic₁₄₆

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂×Dic₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

C₄²

—

146

—

C₁₆

—

C₁₆

—

146

—

C₂³

C₈×D₇₃

yes

characteristic

C₂×C₄

—

146

—

C₂×C₄

C₄×Dic₇₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₈×D₇₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

146

—

C₈

#11924005

yes

characteristic

C₈

C₂²⋊Dic₇₃

yes

characteristic

C₈

#11924007

yes

characteristic

C₈

C₄⋊Dic₇₃

yes

characteristic

100

C₂²

—

101

C₂²

C₈×Dic₇₃

yes

characteristic

102

C₂²

#14556503

yes

characteristic

103

C₂²

#14556520

yes

characteristic

104

C₄

—

292

—

105

C₄

#14556498

yes

characteristic

106

C₄

#14556501

yes

characteristic

107

C₄

#14556503

yes

characteristic

108

C₄

#14556520

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

112

C₂

#17988341

yes

characteristic

	subgroup	G/H
center	C₈	C₂²⋊Dic₇₃
commutator	C₂²×C₇₃	C₄×C₈
Frattini	C₂²×C₈	C₂×D₇₃
Fitting	C₂×M₃₂×C₇₃	C₂
socle	C₂×C₇₃	#336
hypercenter	C₂×M₃₂	D₇₃
hypocenter	C₇₃	#1378
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₈

C₂²⋊Dic₇₃

commutator

C₂²×C₇₃

C₄×C₈

Frattini

C₂²×C₈

C₂×D₇₃

Fitting

C₂×M₃₂×C₇₃

C₂

socle

C₂×C₇₃

#336

hypercenter

C₂×M₃₂

D₇₃

hypocenter

C₇₃

#1378

LCS

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
7. #14556531	C₄	semidirect
14. C₂×C₁₆×C₇₃	C₄	semidirect
57. C₇₃	#1378	semidirect
69. C₂×C₁₆	Dic₇₃	semidirect

H ≅ G/N

type

7. #14556531

C₄

semidirect

14. C₂×C₁₆×C₇₃

C₄

semidirect

57. C₇₃

#1378

semidirect

69. C₂×C₁₆

Dic₇₃

semidirect

Subgroups — #22608016

Conjugacy classes of subgroups

Complements