Group #22611652 — subgroups

Subgroups — #22611652

Order 9344.

220 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic
2	#17988625	C₂	1	1	yes	maximal, characteristic
3	#17988392	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₄₆	—	2	1	no	—
6	C₂×Dic₂₉₂	—	2	1	no	—
7	C₂×Dic₂₉₂	—	2	2	no	—
8	C₂×Dic₂₉₂	C₄	1	4	yes	complemented
9	C₂×Dic₂₉₂	C₂²	1	2	yes	—
10	#14556550	—	2	1	no	—
11	#14556525	C₂²	1	2	yes	—
12	#14556523	—	2	1	no	—
13	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	M₃₂×C₇₃	—	2	2	no	—
15	C₂×C₁₆×C₇₃	C₂²	1	2	yes	—
16	C₂×Dic₁₄₆	—	2	4	no	—
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×Dic₁₄₆	—	4	1	no	—
19	C₂×Dic₁₄₆	—	4	2	no	—
20	C₂²×Dic₇₃	—	4	1	no	—
21	Dic₂₉₂	—	2	4	no	—
22	Dic₂₉₂	—	2	2	no	—
23	Dic₂₉₂	C₂×C₄	1	4	yes	—
24	C₄⋊Dic₇₃	—	2	2	no	—
25	C₂²⋊Dic₇₃	—	4	1	no	—
26	C₄×Dic₇₃	—	4	1	no	—
27	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	D₄	1	2	yes	—
31	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
32	C₁₆×C₇₃	—	2	2	no	—
33	C₂³×C₇₃	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
36	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₃	—	4	4	no	—
39	C₂×Dic₇₃	—	4	2	no	—
40	C₂×Dic₇₃	—	4	2	no	—
41	Dic₁₄₆	—	2	4	no	—
42	Dic₁₄₆	—	4	4	no	—
43	Dic₁₄₆	—	4	2	no	—
44	C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
45	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₇₃	—	2	2	no	—
48	C₂²×C₇₃	#102	1	2	yes	—
49	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
50	C₄×C₇₃	#102	1	2	yes	—
51	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
53	Dic₇₃	—	4	4	no	—
54	Dic₇₃	—	8	2	no	—
55	C₂×C₇₃	—	2	2	no	—
56	C₂×C₇₃	C₂×#102	1	1	yes	characteristic
57	C₂×C₇₃	#510	1	2	yes	—
58	#2141	—	73	1	no	maximal, Sylow
59	C₇₃	#2141	1	1	yes	characteristic, complemented, Sylow
60	C₂²×Q₁₆	—	73	1	no	—
61	C₂×M₃₂	D₇₃	1	1	yes	characteristic
62	#427	—	73	1	no	—
63	#358	—	73	4	no	—
64	C₂²×Q₈	—	146	1	no	—
65	C₂×Q₁₆	—	73	4	no	—
66	C₂×Q₁₆	—	73	2	no	—
67	C₂×Q₁₆	—	146	1	no	—
68	C₂×Q₁₆	—	146	2	no	—
69	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
70	#117	—	146	1	no	—
71	M₃₂	—	2	2	no	—
72	C₂×C₁₆	C₂×D₇₃	1	2	yes	—
73	#107	—	73	2	no	—
74	#106	—	146	1	no	—
75	C₂×Q₈	—	292	1	no	—
76	C₂×Q₈	—	292	2	no	—
77	C₂×Q₈	—	146	4	no	—
78	C₂×Q₈	—	146	2	no	—
79	C₂²×C₄	—	292	1	no	—
80	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
81	Q₁₆	—	73	4	no	—
82	Q₁₆	—	146	4	no	—
83	Q₁₆	—	146	2	no	—
84	C₂×C₈	C₄×D₇₃	1	2	yes	—
85	C₂×C₈	D₂₉₂	1	1	yes	characteristic
86	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
87	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
88	C₄⋊C₄	—	146	2	no	—
89	C₂²⋊C₄	—	292	1	no	—
90	C₄²	—	292	1	no	—
91	C₁₆	—	2	2	no	—
92	C₂³	D₅₈₄	1	1	yes	characteristic
93	Q₈	—	292	4	no	—
94	Q₈	—	292	2	no	—
95	Q₈	—	146	4	no	—
96	C₂×C₄	—	292	4	no	—
97	C₂×C₄	—	292	2	no	—
98	C₂×C₄	—	292	2	no	—
99	C₂×C₄	#11924005	1	2	yes	—
100	C₂×C₄	D₅₈₄	1	1	yes	characteristic
101	C₂×C₄	#11924017	1	2	yes	—
102	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
103	C₈	#11924005	1	2	yes	—
104	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
105	C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
106	C₂²	—	2	2	no	—
107	C₂²	#14556513	1	2	yes	—
108	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
109	C₄	—	292	4	no	—
110	C₄	—	584	2	no	—
111	C₄	#14556513	1	2	yes	—
112	C₄	C₂×#11924005	1	1	yes	characteristic
113	C₄	C₂×#11924017	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	C₂×#14556513	1	1	yes	characteristic
116	C₂	#17989030	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₂₉₂

C₂

yes

maximal, characteristic

#17988625

C₂

yes

maximal, characteristic

#17988392

C₂

yes

maximal, complemented

C₂×M₃₂×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₄

yes

complemented

C₂×Dic₂₉₂

C₂²

yes

—

#14556550

—

#14556525

C₂²

yes

—

#14556523

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

C₂×C₄

yes

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₁₆×C₇₃

—

C₂³×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂²⋊C₄

yes

—

C₈×C₇₃

C₂²×C₄

yes

characteristic

C₈×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

#102

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

#102

yes

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#102

yes

characteristic

C₂×C₇₃

#510

yes

—

#2141

—

maximal, Sylow

C₇₃

#2141

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂×M₃₂

D₇₃

yes

characteristic

#427

—

#358

—

C₂²×Q₈

—

146

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

—

146

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

—

146

—

M₃₂

—

C₂×C₁₆

C₂×D₇₃

yes

—

#107

—

#106

—

146

—

C₂×Q₈

—

292

—

C₂×Q₈

—

292

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

292

—

C₂²×C₄

D₂₉₂

yes

characteristic

Q₁₆

—

Q₁₆

—

146

—

Q₁₆

—

146

—

C₂×C₈

C₄×D₇₃

yes

—

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

292

—

C₄²

—

292

—

C₁₆

—

C₂³

D₅₈₄

yes

characteristic

Q₈

—

292

—

Q₈

—

292

—

Q₈

—

146

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

#11924005

yes

—

100

C₂×C₄

D₅₈₄

yes

characteristic

101

C₂×C₄

#11924017

yes

—

102

C₂×C₄

C₂×D₂₉₂

yes

characteristic

103

C₈

#11924005

yes

—

104

C₈

C₂×C₄×D₇₃

yes

characteristic

105

C₈

C₂×C₂²⋊D₇₃

yes

characteristic

106

C₂²

—

107

C₂²

#14556513

yes

—

108

C₂²

C₂×D₅₈₄

yes

characteristic

109

C₄

—

292

—

110

C₄

—

584

—

111

C₄

#14556513

yes

—

112

C₄

C₂×#11924005

yes

characteristic

113

C₄

C₂×#11924017

yes

characteristic

114

C₂

—

115

C₂

C₂×#14556513

yes

characteristic

116

C₂

#17989030

yes

—

	subgroup	G/H
center	C₂²	C₂×D₅₈₄
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂×M₃₂×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₂×M₃₂	D₇₃
hypocenter	C₇₃	#2141
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

C₂×D₅₈₄

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂×M₃₂×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

hypercenter

C₂×M₃₂

D₇₃

hypocenter

C₇₃

#2141

LCS

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #17988392	C₂	semidirect
8. C₂×Dic₂₉₂	C₄	semidirect
59. C₇₃	#2141	semidirect

H ≅ G/N

type

3. #17988392

C₂

semidirect

8. C₂×Dic₂₉₂

C₄

semidirect

59. C₇₃

#2141

semidirect

Subgroups — #22611652

Conjugacy classes of subgroups

Complements