Group #22609298 — subgroups

Subgroups — #22609298

Order 9344.

156 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 57 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	#17988869	C₂	1	2	yes	maximal
2	C₈×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic
3	#17988340	C₂	1	1	yes	maximal, characteristic
4	#17988333	C₂	1	2	yes	maximal
5	#494×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
7	#14556522	—	2	2	no	—
8	C₄⋊#10596831	C₂²	1	2	yes	—
9	C₄⋊#10596831	C₂²	1	1	yes	characteristic
10	#14556520	—	2	1	no	—
11	#14556514	—	2	2	no	—
12	C₈×Dic₇₃	—	2	1	no	—
13	C₂×Q₁₆×C₇₃	—	2	1	no	—
14	C₂×Q₁₆×C₇₃	—	2	1	no	—
15	C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
18	C₂×#10596831	—	2	1	no	—
19	C₂×#10596831	—	2	2	no	—
20	C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
21	#11924007	—	2	1	no	—
22	C₄×Dic₇₃	—	2	1	no	—
23	C₂×Q₈×C₇₃	—	2	2	no	—
24	Q₁₆×C₇₃	—	4	2	no	—
25	Q₁₆×C₇₃	—	4	2	no	—
26	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
27	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
28	C₄⋊C₄×C₇₃	—	2	2	no	—
29	C₄⋊C₄×C₇₃	—	2	2	no	—
30	C₄²×C₇₃	C₂³	1	1	yes	characteristic
31	Q₈×C₇₃	—	4	2	no	—
32	Q₈×C₇₃	—	4	2	no	—
33	C₂×C₄×C₇₃	—	4	2	no	—
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
37	C₂×Dic₇₃	—	2	1	no	—
38	C₂×Dic₇₃	—	2	1	no	—
39	Dic₁₄₆	—	2	1	no	—
40	Dic₁₄₆	Q₁₆	1	2	yes	complemented
41	C₈×C₇₃	—	2	1	no	—
42	C₈×C₇₃	SD₁₆	1	2	yes	—
43	#10596831	—	4	2	no	—
44	#10596831	—	4	1	no	—
45	C₂²×C₇₃	#121	1	1	yes	characteristic
46	C₄×C₇₃	—	2	1	no	—
47	C₄×C₇₃	—	8	2	no	—
48	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
49	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
50	C₄×C₇₃	#135	1	1	yes	characteristic
51	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
52	Dic₇₃	—	2	2	no	—
53	Dic₇₃	—	4	1	no	—
54	C₂×C₇₃	#460	1	1	yes	characteristic
55	C₂×C₇₃	#467	1	1	yes	characteristic
56	C₂×C₇₃	#473	1	1	yes	characteristic
57	#1670	—	73	1	no	maximal, Sylow
58	C₇₃	#1670	1	1	yes	characteristic, complemented, Sylow
59	#494	D₇₃	1	1	yes	characteristic
60	#475	—	73	2	no	—
61	C₈×Q₈	—	73	1	no	—
62	#335	—	73	1	no	—
63	#332	—	73	2	no	—
64	C₂×Q₁₆	—	2	1	no	—
65	C₂×Q₁₆	—	2	1	no	—
66	C₄⋊Q₈	C₂×D₇₃	1	2	yes	—
67	C₄×Q₈	—	73	1	no	—
68	#106	—	146	2	no	—
69	C₄⋊C₈	—	73	1	no	—
70	C₄⋊C₈	—	73	2	no	—
71	C₄⋊C₈	—	146	1	no	—
72	#103	—	146	2	no	—
73	C₄×C₈	—	146	1	no	—
74	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
75	C₂×Q₈	—	2	2	no	—
76	C₂×Q₈	—	73	1	no	—
77	Q₁₆	—	4	2	no	—
78	Q₁₆	—	4	2	no	—
79	C₂×C₈	—	146	2	no	—
80	C₂×C₈	—	146	1	no	—
81	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
83	C₄⋊C₄	—	2	2	no	—
84	C₄⋊C₄	—	2	2	no	—
85	C₄⋊C₄	—	73	1	no	—
86	C₄⋊C₄	—	146	1	no	—
87	C₄²	—	146	1	no	—
88	C₄²	C₂²×D₇₃	1	1	yes	characteristic
89	Q₈	—	4	2	no	—
90	Q₈	—	4	2	no	—
91	Q₈	—	73	2	no	—
92	Q₈	—	146	1	no	—
93	C₂×C₄	—	4	2	no	—
94	C₂×C₄	—	146	1	no	—
95	C₂×C₄	—	146	1	no	—
96	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
97	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
98	C₂×C₄	#11924027	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	292	2	no	—
101	C₈	—	292	1	no	—
102	C₈	#11924016	1	2	yes	—
103	C₂²	#14556562	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	8	2	no	—
106	C₄	—	292	1	no	—
107	C₄	—	146	2	no	—
108	C₄	C₂×#11924016	1	1	yes	characteristic
109	C₄	Q₁₆×D₇₃	1	1	yes	characteristic
110	C₄	#14556614	1	1	yes	characteristic
111	C₄	#14556617	1	1	yes	characteristic
112	C₂	#17988784	1	1	yes	characteristic
113	C₂	#17988825	1	1	yes	characteristic
114	C₂	#17988859	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988869

C₂

yes

maximal

C₈×Dic₁₄₆

C₂

yes

maximal, characteristic

#17988340

C₂

yes

maximal, characteristic

#17988333

C₂

yes

maximal

#494×C₇₃

C₂

yes

maximal, characteristic

C₄×Dic₁₄₆

C₂²

yes

characteristic

#14556522

—

C₄⋊#10596831

C₂²

yes

—

C₄⋊#10596831

C₂²

yes

characteristic

#14556520

—

#14556514

—

C₈×Dic₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₄⋊Q₈×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

D₄

yes

characteristic

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

D₄

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

Q₁₆

yes

complemented

C₈×C₇₃

—

C₈×C₇₃

SD₁₆

yes

—

#10596831

—

#10596831

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₄×C₇₃

C₂×Q₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#494

D₇₃

yes

characteristic

#475

—

C₈×Q₈

—

#335

—

#332

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

C₂×D₇₃

yes

—

C₄×Q₈

—

#106

—

146

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

#103

—

146

—

C₄×C₈

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄²

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

146

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₂×C₄

#11924027

yes

characteristic

C₈

—

100

C₈

—

292

—

101

C₈

—

292

—

102

C₈

#11924016

yes

—

103

C₂²

#14556562

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

292

—

107

C₄

—

146

—

108

C₄

C₂×#11924016

yes

characteristic

109

C₄

Q₁₆×D₇₃

yes

characteristic

110

C₄

#14556614

yes

characteristic

111

C₄

#14556617

yes

characteristic

112

C₂

#17988784

yes

characteristic

113

C₂

#17988825

yes

characteristic

114

C₂

#17988859

yes

characteristic

	subgroup	G/H
center	C₂²	#14556562
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#494×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#494	D₇₃
hypocenter	C₇₃	#1670
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#14556562

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#494×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
40. Dic₁₄₆	Q₁₆	semidirect
58. C₇₃	#1670	semidirect

H ≅ G/N

type

40. Dic₁₄₆

Q₁₆

semidirect

58. C₇₃

#1670

semidirect

Subgroups — #22609298

Conjugacy classes of subgroups

Complements