Group #22611752 — subgroups

Subgroups — C₁₆×D₂₉₂ #22611752

Order 9344.

174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 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×C₁₆×D₇₃	C₂	1	2	yes	maximal, complemented
2	C₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11924003	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988366	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₃	C₂²	1	2	yes	—
7	C₄×D₂₉₂	C₄	1	1	yes	characteristic
8	C₂×#11924003	C₂²	1	2	yes	—
9	C₁₆×D₇₃	—	2	4	no	—
10	C₄⋊#10596831	C₄	1	1	yes	characteristic
11	#14556503	C₄	1	2	yes	—
12	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×D₂₉₂	C₈	1	1	yes	characteristic
16	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
17	C₂×#10596831	C₂×C₄	1	2	yes	—
18	C₈×D₇₃	—	2	2	no	—
19	C₈×D₇₃	—	2	2	no	—
20	C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
21	#11924005	C₈	1	2	yes	—
22	#11924003	—	2	2	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
25	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₁₆×C₇₃	—	2	1	no	—
27	C₁₆×C₇₃	D₄	1	2	yes	complemented
28	C₂²×D₇₃	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
33	D₂₉₂	C₁₆	1	4	yes	direct product factor
34	C₄×D₇₃	—	2	2	no	—
35	C₄×D₇₃	—	2	2	no	—
36	C₈×C₇₃	—	2	1	no	—
37	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₈×C₇₃	#41	1	1	yes	characteristic
39	#10596831	—	2	2	no	—
40	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
41	C₂×D₇₃	—	2	2	no	—
42	C₂×D₇₃	—	2	2	no	—
43	C₂×D₇₃	C₂×C₁₆	1	4	yes	complemented
44	C₄×C₇₃	—	2	1	no	—
45	C₄×C₇₃	C₂×C₁₆	1	2	yes	complemented
46	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
47	C₄×C₇₃	#131	1	1	yes	characteristic
48	Dic₇₃	—	2	2	no	—
49	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
50	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
51	C₂×C₇₃	#504	1	1	yes	characteristic
52	D₇₃	—	2	4	no	—
53	D₄×C₁₆	—	73	1	no	maximal, Sylow
54	C₇₃	D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₁₆	—	73	2	no	—
56	C₈×D₄	—	73	1	no	—
57	C₄⋊C₁₆	—	73	1	no	—
58	C₂²⋊C₁₆	—	73	2	no	—
59	C₄×C₁₆	D₇₃	1	1	yes	characteristic, complemented
60	C₂²×C₈	—	73	2	no	—
61	C₄×D₄	—	73	1	no	—
62	C₂×C₁₆	—	73	2	no	—
63	C₂×C₁₆	—	146	4	no	—
64	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
66	C₄⋊C₈	—	73	1	no	—
67	C₂²⋊C₈	—	73	2	no	—
68	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
69	C₂×D₄	—	73	1	no	—
70	C₂²×C₄	—	73	2	no	—
71	C₂×C₈	—	73	2	no	—
72	C₂×C₈	—	146	2	no	—
73	C₂×C₈	—	146	2	no	—
74	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
76	C₄⋊C₄	—	73	1	no	—
77	C₂²⋊C₄	—	73	2	no	—
78	C₄²	C₄×D₇₃	1	1	yes	characteristic
79	C₁₆	—	2	1	no	—
80	C₁₆	—	146	2	no	—
81	C₁₆	D₂₉₂	1	2	yes	direct product factor
82	C₂³	—	73	2	no	—
83	D₄	—	73	4	no	—
84	C₂×C₄	—	73	2	no	—
85	C₂×C₄	—	146	2	no	—
86	C₂×C₄	—	146	2	no	—
87	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
88	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
89	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
90	C₈	—	2	1	no	—
91	C₈	—	146	2	no	—
92	C₈	C₂×D₂₉₂	1	1	yes	characteristic
93	C₈	#11924028	1	1	yes	characteristic
94	C₂²	—	73	4	no	—
95	C₂²	—	146	2	no	—
96	C₂²	—	146	2	no	—
97	C₂²	C₂×C₈×D₇₃	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	146	2	no	—
100	C₄	C₁₆×D₇₃	1	2	yes	complemented
101	C₄	C₄×D₂₉₂	1	1	yes	characteristic
102	C₄	#14556597	1	1	yes	characteristic
103	C₂	—	146	4	no	—
104	C₂	C₈×D₂₉₂	1	1	yes	characteristic
105	C₂	C₂×C₁₆×D₇₃	1	1	yes	characteristic
106	C₂	#17989003	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₇₃

C₂

yes

maximal, complemented

C₈×D₂₉₂

C₂

yes

maximal, characteristic

C₄⋊#11924003

C₂

yes

maximal, characteristic, complemented

#17988366

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₃

C₂²

yes

—

C₄×D₂₉₂

C₄

yes

characteristic

C₂×#11924003

C₂²

yes

—

C₁₆×D₇₃

—

C₄⋊#10596831

C₄

yes

characteristic

#14556503

C₄

yes

—

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×D₂₉₂

C₈

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

—

C₈×D₇₃

—

C₄⋊Dic₇₃

C₈

yes

characteristic

#11924005

C₈

yes

—

#11924003

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

D₄

yes

complemented

C₂²×D₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

—

D₂₉₂

C₁₆

yes

direct product factor

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂×C₁₆

yes

complemented

C₄×C₇₃

—

C₄×C₇₃

C₂×C₁₆

yes

complemented

C₄×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

#131

yes

characteristic

Dic₇₃

—

C₂×C₇₃

C₈×D₄

yes

characteristic

C₂×C₇₃

C₂²×C₁₆

yes

characteristic

C₂×C₇₃

#504

yes

characteristic

D₇₃

—

D₄×C₁₆

—

maximal, Sylow

C₇₃

D₄×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₈×D₄

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

D₇₃

yes

characteristic, complemented

C₂²×C₈

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₄×D₇₃

yes

characteristic

C₁₆

—

C₁₆

—

146

—

C₁₆

D₂₉₂

yes

direct product factor

C₂³

—

D₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₈×D₇₃

yes

characteristic

C₂×C₄

C₈×D₇₃

yes

characteristic

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₈

—

C₈

—

146

—

C₈

C₂×D₂₉₂

yes

characteristic

C₈

#11924028

yes

characteristic

C₂²

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

C₂×C₈×D₇₃

yes

characteristic

C₄

—

C₄

—

146

—

100

C₄

C₁₆×D₇₃

yes

complemented

101

C₄

C₄×D₂₉₂

yes

characteristic

102

C₄

#14556597

yes

characteristic

103

C₂

—

146

—

104

C₂

C₈×D₂₉₂

yes

characteristic

105

C₂

C₂×C₁₆×D₇₃

yes

characteristic

106

C₂

#17989003

yes

characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₇₃
commutator	C₂×C₇₃	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₄×C₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	C₄×C₁₆	D₇₃
hypocenter	C₇₃	D₄×C₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₁₆

C₂×D₇₃

commutator

C₂×C₇₃

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₄×C₁₆×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×C₈

hypercenter

C₄×C₁₆

D₇₃

hypocenter

C₇₃

D₄×C₁₆

LCS

G ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. C₂×C₁₆×D₇₃	C₂	semidirect
3. C₄⋊#11924003	C₂	semidirect
4. #17988366	C₂	semidirect
5. C₄×C₁₆×C₇₃	C₂	semidirect
27. C₁₆×C₇₃	D₄	semidirect
33. D₂₉₂	C₁₆	direct (N × H)
43. C₂×D₇₃	C₂×C₁₆	semidirect
45. C₄×C₇₃	C₂×C₁₆	semidirect
54. C₇₃	D₄×C₁₆	semidirect
59. C₄×C₁₆	D₇₃	semidirect
81. C₁₆	D₂₉₂	direct (N × H)
100. C₄	C₁₆×D₇₃	semidirect

H ≅ G/N

type

1. C₂×C₁₆×D₇₃

C₂

semidirect

3. C₄⋊#11924003

C₂

semidirect

4. #17988366

C₂

semidirect

5. C₄×C₁₆×C₇₃

C₂

semidirect

27. C₁₆×C₇₃

D₄

semidirect

33. D₂₉₂

C₁₆

direct (N × H)

43. C₂×D₇₃

C₂×C₁₆

semidirect

45. C₄×C₇₃

C₂×C₁₆

semidirect

54. C₇₃

D₄×C₁₆

semidirect

59. C₄×C₁₆

D₇₃

semidirect

81. C₁₆

D₂₉₂

direct (N × H)

100. C₄

C₁₆×D₇₃

semidirect

Subgroups — C₁₆×D₂₉₂ #22611752

Conjugacy classes of subgroups

Complements

Subgroups — C16×D292 #22611752

Conjugacy classes of subgroups

Complements

Subgroups — C₁₆×D₂₉₂ #22611752