Group #22612048 — subgroups

Subgroups — #22612048

Order 9344.

148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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	#17989003	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988854	C₂	1	2	yes	maximal, complemented
3	#17988417	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988400	C₂	1	2	yes	maximal, complemented
5	C₂×D₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556617	—	2	2	no	—
7	#14556597	C₂²	1	1	yes	characteristic
8	#14556531	C₂²	1	1	yes	characteristic
9	#14556530	—	2	1	no	—
10	C₁₆×D₇₃	—	2	1	no	—
11	#14556527	C₂²	1	2	yes	—
12	#14556508	—	2	2	no	—
13	C₂×D₈×C₇₃	C₂²	1	2	yes	—
14	D₁₆×C₇₃	—	2	1	no	—
15	D₁₆×C₇₃	—	2	1	no	—
16	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	#11924028	D₄	1	1	yes	characteristic
18	#11924016	—	4	2	no	—
19	#11924013	—	4	2	no	—
20	#11924012	—	2	2	no	—
21	#11924012	D₄	1	1	yes	characteristic
22	#11924011	—	2	1	no	—
23	C₈×D₇₃	—	2	1	no	—
24	#11924003	—	2	1	no	—
25	C₂×D₄×C₇₃	—	2	2	no	—
26	D₈×C₇₃	—	2	2	no	—
27	D₈×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
29	C₁₆×C₇₃	D₄	1	1	yes	characteristic
30	C₁₆×C₇₃	D₄	1	1	yes	characteristic
31	C₂³×C₇₃	—	4	2	no	—
32	D₄×C₇₃	—	4	2	no	—
33	D₄×C₇₃	—	4	2	no	—
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂²⋊D₇₃	—	2	1	no	—
36	D₂₉₂	D₈	1	1	yes	characteristic
37	C₄×D₇₃	—	2	1	no	—
38	Dic₁₄₆	D₈	1	1	yes	characteristic
39	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₈×C₇₃	#41	1	1	yes	characteristic
41	#10596831	—	2	1	no	—
42	#10596831	—	4	2	no	—
43	C₂²×C₇₃	—	8	2	no	—
44	C₂²×C₇₃	—	16	2	no	—
45	C₂²×C₇₃	#135	1	1	yes	characteristic
46	C₂×D₇₃	—	2	1	no	—
47	C₄×C₇₃	#121	1	1	yes	characteristic
48	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
49	Dic₇₃	—	2	1	no	—
50	C₂×C₇₃	—	2	1	no	—
51	C₂×C₇₃	—	16	2	no	—
52	C₂×C₇₃	#466	1	1	yes	characteristic
53	D₇₃	—	4	1	no	—
54	#2221	—	73	1	no	maximal, Sylow
55	C₇₃	#2221	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₁₆	D₇₃	1	1	yes	characteristic, complemented
57	#504	—	73	1	no	—
58	#472	—	73	2	no	—
59	#368	—	73	1	no	—
60	#361	—	73	2	no	—
61	AGL(1,ℤ/8)	—	146	2	no	—
62	C₂×D₈	C₂×D₇₃	1	2	yes	—
63	#131	—	73	1	no	—
64	D₁₆	—	2	1	no	—
65	D₁₆	—	2	1	no	—
66	M₃₂	—	73	1	no	—
67	M₃₂	—	146	1	no	—
68	C₂×C₁₆	—	146	1	no	—
69	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
70	#108	—	73	2	no	—
71	#100	—	146	2	no	—
72	#41	—	73	1	no	—
73	C₂×D₄	—	2	2	no	—
74	SD₁₆	—	292	2	no	—
75	D₈	—	2	2	no	—
76	D₈	—	2	2	no	—
77	D₈	—	292	2	no	—
78	M₁₆	—	73	1	no	—
79	M₁₆	—	146	2	no	—
80	M₁₆	—	146	1	no	—
81	C₂×C₈	—	146	1	no	—
82	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
83	C₁₆	—	146	1	no	—
84	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
85	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
86	C₂³	—	4	2	no	—
87	Q₈	—	73	1	no	—
88	D₄	—	4	2	no	—
89	D₄	—	4	2	no	—
90	D₄	—	73	1	no	—
91	D₄	—	146	1	no	—
92	C₂×C₄	—	146	1	no	—
93	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
94	C₈	—	292	2	no	—
95	C₈	—	146	1	no	—
96	C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
97	C₈	#11924027	1	1	yes	characteristic
98	C₂²	—	8	2	no	—
99	C₂²	—	16	2	no	—
100	C₂²	—	146	1	no	—
101	C₂²	#14556610	1	1	yes	characteristic
102	C₄	—	146	1	no	—
103	C₄	#14556562	1	1	yes	characteristic
104	C₄	D₈×D₇₃	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	16	2	no	—
107	C₂	—	292	1	no	—
108	C₂	#17988820	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989003

C₂

yes

maximal, characteristic, complemented

#17988854

C₂

yes

maximal, complemented

#17988417

C₂

yes

maximal, characteristic, complemented

#17988400

C₂

yes

maximal, complemented

C₂×D₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556617

—

#14556597

C₂²

yes

characteristic

#14556531

C₂²

yes

characteristic

#14556530

—

C₁₆×D₇₃

—

#14556527

C₂²

yes

—

#14556508

—

C₂×D₈×C₇₃

C₂²

yes

—

D₁₆×C₇₃

—

D₁₆×C₇₃

—

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

#11924028

D₄

yes

—

—

—

D₄

yes

characteristic

#11924011

—

C₈×D₇₃

—

#11924003

—

C₂×D₄×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₁₆×C₇₃

D₄

yes

characteristic

C₁₆×C₇₃

D₄

yes

characteristic

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²⋊D₇₃

—

D₂₉₂

D₈

yes

characteristic

C₄×D₇₃

—

Dic₁₄₆

D₈

yes

characteristic

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#135

yes

characteristic

C₂×D₇₃

—

C₄×C₇₃

#121

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#466

yes

characteristic

D₇₃

—

#2221

—

maximal, Sylow

C₇₃

#2221

yes

characteristic, complemented, Sylow

C₂×D₁₆

D₇₃

yes

characteristic, complemented

—

—

—

—

—

146

—

C₂×D₈

C₂×D₇₃

yes

—

#131

—

D₁₆

—

D₁₆

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#108

—

#100

—

146

—

#41

—

C₂×D₄

—

SD₁₆

—

292

—

D₈

—

D₈

—

D₈

—

292

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₁₆

—

146

—

C₁₆

C₂²⋊D₇₃

yes

characteristic

C₁₆

C₂²⋊D₇₃

yes

characteristic

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₈

—

292

—

C₈

—

146

—

C₈

C₂×C₂²⋊D₇₃

yes

characteristic

C₈

#11924027

yes

characteristic

C₂²

—

C₂²

—

100

C₂²

—

146

—

101

C₂²

#14556610

yes

characteristic

102

C₄

—

146

—

103

C₄

#14556562

yes

characteristic

104

C₄

D₈×D₇₃

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

292

—

108

C₂

#17988820

yes

characteristic

	subgroup	G/H
center	C₂	#17988820
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂×D₁₆×C₇₃	C₂
socle	C₂×C₇₃	#466
hypercenter	C₂×D₁₆	D₇₃
hypocenter	C₇₃	#2221
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂

#17988820

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂×D₁₆×C₇₃

C₂

socle

C₂×C₇₃

#466

hypercenter

C₂×D₁₆

D₇₃

hypocenter

C₇₃

#2221

LCS

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. #17989003	C₂	semidirect
2. #17988854	C₂	semidirect
3. #17988417	C₂	semidirect
4. #17988400	C₂	semidirect
5. C₂×D₁₆×C₇₃	C₂	semidirect
55. C₇₃	#2221	semidirect
56. C₂×D₁₆	D₇₃	semidirect

H ≅ G/N

type

1. #17989003

C₂

semidirect

2. #17988854

C₂

semidirect

3. #17988417

C₂

semidirect

4. #17988400

C₂

semidirect

5. C₂×D₁₆×C₇₃

C₂

semidirect

55. C₇₃

#2221

semidirect

56. C₂×D₁₆

D₇₃

semidirect

Subgroups — #22612048

Conjugacy classes of subgroups

Complements