Group #22611693 — subgroups

Subgroups — C₂×#17988407 #22611693

Order 9344.

168 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 93 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	C₂×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	#17988407	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10596831	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
7	#14556531	—	2	1	no	—
8	#14556531	C₂²	1	2	yes	—
9	C₂×#11924003	—	2	1	no	—
10	C₈×Dic₇₃	C₄	1	2	yes	—
11	C₈×Dic₇₃	C₂²	1	2	yes	—
12	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	M₃₂×C₇₃	—	2	1	no	—
14	M₃₂×C₇₃	C₂²	1	2	yes	—
15	C₂×C₁₆×C₇₃	—	2	1	no	—
16	C₂²×Dic₇₃	—	2	1	no	—
17	C₂×#10596831	C₈	1	2	yes	—
18	C₂×#10596831	C₈	1	2	yes	—
19	C₂×#10596831	C₂×C₄	1	2	yes	—
20	C₄×Dic₇₃	—	2	1	no	—
21	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
22	#11924003	—	2	2	no	—
23	C₂²×C₄×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	Q₈	1	1	yes	characteristic
28	C₂×C₈×C₇₃	Q₈	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
30	C₁₆×C₇₃	—	2	2	no	—
31	C₂³×C₇₃	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₄⋊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	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₇₃	—	2	4	no	—
39	C₂×Dic₇₃	—	2	2	no	—
40	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
43	C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
44	#10596831	C₂×C₈	1	4	yes	—
45	C₂²×C₇₃	—	2	2	no	—
46	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
47	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
48	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
50	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
51	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
53	Dic₇₃	—	2	4	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	—	2	1	no	—
56	C₂×C₇₃	#364	1	2	yes	complemented
57	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
58	C₂×#364	—	73	1	no	maximal, Sylow
59	C₇₃	C₂×#364	1	1	yes	characteristic, complemented, Sylow
60	C₂×M₃₂	—	73	1	no	—
61	C₂×M₃₂	D₇₃	1	1	yes	characteristic
62	C₂×C₄×C₈	—	73	1	no	—
63	#364	—	73	4	no	—
64	C₂²×C₈	—	73	1	no	—
65	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
66	C₂×C₄²	—	73	1	no	—
67	M₃₂	—	2	1	no	—
68	M₃₂	—	73	2	no	—
69	M₃₂	—	146	1	no	—
70	M₃₂	C₂×D₇₃	1	2	yes	—
71	C₂×C₁₆	—	2	1	no	—
72	C₂×C₁₆	—	146	1	no	—
73	C₄×C₈	—	73	2	no	—
74	C₄×C₈	—	73	2	no	—
75	C₂²×C₄	—	146	1	no	—
76	C₂²×C₄	C₄×D₇₃	1	1	yes	characteristic
77	C₂×C₈	—	73	2	no	—
78	C₂×C₈	—	73	2	no	—
79	C₂×C₈	—	73	2	no	—
80	C₂×C₈	Dic₁₄₆	1	1	yes	characteristic
81	C₂×C₈	Dic₁₄₆	1	1	yes	characteristic
82	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
84	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
85	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
86	C₄²	—	73	2	no	—
87	C₄²	—	146	1	no	—
88	C₁₆	—	2	2	no	—
89	C₁₆	—	146	2	no	—
90	C₂³	#11924011	1	1	yes	characteristic
91	C₂×C₄	—	146	4	no	—
92	C₂×C₄	—	146	2	no	—
93	C₂×C₄	#11924007	1	1	yes	characteristic
94	C₂×C₄	#11924007	1	1	yes	characteristic
95	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
96	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
97	C₂×C₄	#11924011	1	1	yes	characteristic
98	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
99	C₈	—	73	4	no	—
100	C₈	#11924007	1	1	yes	characteristic
101	C₈	#11924007	1	1	yes	characteristic
102	C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
103	C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
104	C₂²	—	2	2	no	—
105	C₂²	#14556520	1	1	yes	characteristic
106	C₂²	#14556520	1	1	yes	characteristic
107	C₂²	C₂×#11924011	1	1	yes	characteristic
108	C₄	—	146	4	no	—
109	C₄	#14556520	1	1	yes	characteristic
110	C₄	#14556520	1	1	yes	characteristic
111	C₄	C₂×#11924007	1	1	yes	characteristic
112	C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#17988407	1	2	yes	direct product factor
116	C₂	C₂×#14556520	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556531

C₂

yes

maximal, characteristic

C₂×C₈×Dic₇₃

C₂

yes

maximal, characteristic

#17988407

C₂

yes

maximal, direct product factor

C₂×M₃₂×C₇₃

C₂

yes

maximal, characteristic

C₂²×#10596831

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₄

yes

characteristic

#14556531

—

#14556531

C₂²

yes

—

C₂×#11924003

—

C₈×Dic₇₃

C₄

yes

—

C₈×Dic₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

C₂²

yes

—

C₂×C₁₆×C₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

C₈

yes

—

C₂×#10596831

C₈

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

—

#11924003

—

C₂²×C₄×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

Q₈

yes

characteristic

C₂×C₈×C₇₃

Q₈

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₁₆×C₇₃

—

C₂³×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₂×D₄

yes

characteristic

C₈×C₇₃

C₂×Q₈

yes

characteristic

#10596831

C₂×C₈

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₂²×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#364

yes

complemented

C₂×C₇₃

C₂×C₄⋊C₈

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

D₇₃

yes

characteristic

C₂×C₄×C₈

—

#364

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

146

—

M₃₂

C₂×D₇₃

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

146

—

C₂²×C₄

C₄×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₄₆

yes

characteristic

C₂×C₈

Dic₁₄₆

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄²

—

C₄²

—

146

—

C₁₆

—

C₁₆

—

146

—

C₂³

#11924011

yes

characteristic

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₈×D₇₃

yes

characteristic

C₂×C₄

C₈×D₇₃

yes

characteristic

C₂×C₄

#11924011

yes

characteristic

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₈

—

100

C₈

#11924007

yes

characteristic

101

C₈

#11924007

yes

characteristic

102

C₈

C₂×C₂²⋊D₇₃

yes

characteristic

103

C₈

C₂×Dic₁₄₆

yes

characteristic

104

C₂²

—

105

C₂²

#14556520

yes

characteristic

106

C₂²

#14556520

yes

characteristic

107

C₂²

C₂×#11924011

yes

characteristic

108

C₄

—

146

—

109

C₄

#14556520

yes

characteristic

110

C₄

#14556520

yes

characteristic

111

C₄

C₂×#11924007

yes

characteristic

112

C₄

C₂×C₈×D₇₃

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#17988407

yes

direct product factor

116

C₂

C₂×#14556520

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₇₃
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂×M₃₂×C₇₃	C₂
socle	C₂²×C₇₃	C₄⋊C₈
hypercenter	C₂×M₃₂	D₇₃
hypocenter	C₇₃	C₂×#364
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₈

C₂²⋊D₇₃

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂×M₃₂×C₇₃

C₂

socle

C₂²×C₇₃

C₄⋊C₈

hypercenter

C₂×M₃₂

D₇₃

hypocenter

C₇₃

C₂×#364

LCS

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #17988407	C₂	direct (N × H)
56. C₂×C₇₃	#364	semidirect
59. C₇₃	C₂×#364	semidirect
115. C₂	#17988407	direct (N × H)

H ≅ G/N

type

3. #17988407

C₂

direct (N × H)

56. C₂×C₇₃

#364

semidirect

59. C₇₃

C₂×#364

semidirect

115. C₂

#17988407

direct (N × H)

Subgroups — C₂×#17988407 #22611693

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17988407 #22611693

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17988407 #22611693