Group #22625430 — subgroups

Subgroups — C₂×#17989447 #22625430

Order 9344.

256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14556658	C₂	1	2	yes	maximal
2	#17989447	C₂	1	4	yes	maximal, direct product factor
3	C₂×#14556589	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10596833	—	2	2	no	—
5	#14556658	—	2	2	no	—
6	#14556658	C₂²	1	4	yes	—
7	C₂²×Dic₁₄₆	C₄	1	1	yes	characteristic
8	#14556589	—	2	2	no	—
9	#14556589	C₄	1	2	yes	—
10	#14556589	C₂²	1	2	yes	—
11	C₂×#11924007	—	2	2	no	—
12	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
13	C₂²×Q₈×C₇₃	C₄	1	1	yes	characteristic
14	C₂×#10596833	—	2	4	no	—
15	C₂×#10596833	—	4	4	no	—
16	C₂×Dic₁₄₆	—	2	1	no	—
17	C₂×Dic₁₄₆	—	4	2	no	—
18	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
19	C₂²×Dic₇₃	—	2	1	no	—
20	C₂²×Dic₇₃	D₄	1	2	yes	—
21	#11924007	—	2	4	no	—
22	#11924007	—	2	4	no	—
23	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₇₃	D₄	1	2	yes	—
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₂×Q₈×C₇₃	—	2	1	no	—
27	C₂×Q₈×C₇₃	—	4	2	no	—
28	C₂×Q₈×C₇₃	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₇₃	—	2	1	no	—
30	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	Q₈×C₇₃	—	4	2	no	—
33	Q₈×C₇₃	—	4	2	no	—
34	C₂×C₄×C₇₃	—	2	2	no	—
35	C₂×C₄×C₇₃	—	2	2	no	—
36	C₂×C₄×C₇₃	—	4	2	no	—
37	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₇₃	—	2	2	no	—
40	C₂×Dic₇₃	—	4	2	no	—
41	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
42	C₂×Dic₇₃	SD₁₆	1	4	yes	—
43	C₂×Dic₇₃	Q₁₆	1	4	yes	—
44	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
45	Dic₁₄₆	—	4	2	no	—
46	Dic₁₄₆	—	4	2	no	—
47	#10596833	—	4	4	no	—
48	C₂²×C₇₃	#100	1	2	yes	—
49	C₂²×C₇₃	#103	1	4	yes	—
50	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	C₄×C₇₃	—	2	1	no	—
52	C₄×C₇₃	—	2	1	no	—
53	C₄×C₇₃	—	4	2	no	—
54	Dic₇₃	—	4	2	no	—
55	Dic₇₃	#103	1	4	yes	—
56	Dic₇₃	C₂×SD₁₆	1	2	yes	—
57	Dic₇₃	C₂×Q₁₆	1	2	yes	—
58	C₂×C₇₃	#333	1	4	yes	complemented
59	C₂×C₇₃	C₂×#100	1	1	yes	characteristic
60	C₂×C₇₃	C₂×#103	1	2	yes	—
61	C₂×#333	—	73	1	no	maximal, Sylow
62	C₇₃	C₂×#333	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₄⋊Q₈	—	73	1	no	—
64	C₂×C₄⋊C₈	—	73	2	no	—
65	#333	—	73	4	no	—
66	C₂²×Q₈	—	73	1	no	—
67	C₂²×Q₈	#64408	1	1	yes	characteristic
68	C₂²×C₈	—	146	2	no	—
69	C₄⋊Q₈	—	73	2	no	—
70	C₄⋊Q₈	—	73	2	no	—
71	C₄⋊Q₈	—	146	2	no	—
72	C₂×C₄⋊C₄	—	146	2	no	—
73	C₂×C₄²	—	73	1	no	—
74	C₄⋊C₈	—	73	4	no	—
75	C₄⋊C₈	—	146	2	no	—
76	C₂×Q₈	—	2	1	no	—
77	C₂×Q₈	—	4	2	no	—
78	C₂×Q₈	—	292	2	no	—
79	C₂×Q₈	—	73	2	no	—
80	C₂×Q₈	—	146	1	no	—
81	C₂×Q₈	C₂×#64408	1	2	yes	—
82	C₂²×C₄	—	2	1	no	—
83	C₂²×C₄	—	73	2	no	—
84	C₂²×C₄	—	146	1	no	—
85	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
86	C₂×C₈	—	292	4	no	—
87	C₂×C₈	—	146	4	no	—
88	C₄⋊C₄	—	146	4	no	—
89	C₄⋊C₄	—	146	4	no	—
90	C₄²	—	73	2	no	—
91	C₄²	—	73	1	no	—
92	C₄²	—	73	1	no	—
93	C₂³	C₂²⋊#64408	1	1	yes	characteristic
94	Q₈	—	4	2	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	292	2	no	—
97	Q₈	—	292	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	292	2	no	—
102	C₂×C₄	—	73	4	no	—
103	C₂×C₄	—	73	4	no	—
104	C₂×C₄	—	73	2	no	—
105	C₂×C₄	—	73	2	no	—
106	C₂×C₄	—	146	2	no	—
107	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
108	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
109	C₈	—	292	4	no	—
110	C₂²	#14556651	1	2	yes	—
111	C₂²	#14556654	1	4	yes	—
112	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	4	2	no	—
116	C₄	—	292	2	no	—
117	C₄	—	73	2	no	—
118	C₄	—	73	4	no	—
119	C₄	—	73	2	no	—
120	C₂	#17989447	1	4	yes	direct product factor
121	C₂	C₂×#14556651	1	1	yes	characteristic
122	C₂	C₂×#14556654	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556658

C₂

yes

maximal

#17989447

C₂

yes

maximal, direct product factor

C₂×#14556589

C₂

yes

maximal, characteristic

C₂²×#10596833

—

#14556658

—

#14556658

C₂²

yes

—

C₂²×Dic₁₄₆

C₄

yes

characteristic

#14556589

—

#14556589

C₄

yes

—

#14556589

C₂²

yes

—

C₂×#11924007

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₂²×Q₈×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×#10596833

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

—

#11924007

—

#11924007

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

SD₁₆

yes

—

C₂×Dic₇₃

Q₁₆

yes

—

C₂×Dic₇₃

C₂×D₄

yes

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

#100

yes

—

C₂²×C₇₃

#103

yes

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

#103

yes

—

Dic₇₃

C₂×SD₁₆

yes

—

Dic₇₃

C₂×Q₁₆

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×#333

—

maximal, Sylow

C₇₃

C₂×#333

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

C₂×C₄⋊C₈

—

#333

—

C₂²×Q₈

—

C₂²×Q₈

#64408

yes

characteristic

C₂²×C₈

—

146

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

292

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂×#64408

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

292

—

C₂×C₈

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²⋊#64408

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

292

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

146

—

107

C₂×C₄

C₂²⋊#64408

yes

characteristic

108

C₂×C₄

C₂²×#64408

yes

characteristic

109

C₈

—

292

—

110

C₂²

#14556651

yes

—

111

C₂²

#14556654

yes

—

112

C₂²

C₂×C₂²⋊#64408

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

292

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₂

#17989447

yes

direct product factor

121

C₂

C₂×#14556651

yes

characteristic

122

C₂

C₂×#14556654

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂²×Q₈×C₇₃	C₄
socle	C₂³×C₇₃	C₂²⋊C₄
hypercenter	C₂²×Q₈	#64408
hypocenter	C₇₃	C₂×#333
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

subgroup

G/H

center

C₂³

C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₂²×Q₈×C₇₃

C₄

socle

C₂³×C₇₃

C₂²⋊C₄

C₂²×Q₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

N	H ≅ G/N	type
2. #17989447	C₂	direct (N × H)
58. C₂×C₇₃	#333	semidirect
62. C₇₃	C₂×#333	semidirect
120. C₂	#17989447	direct (N × H)

H ≅ G/N

type

2. #17989447

C₂

direct (N × H)

58. C₂×C₇₃

#333

semidirect

62. C₇₃

C₂×#333

semidirect

120. C₂

#17989447

direct (N × H)

Subgroups — C₂×#17989447 #22625430

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17989447 #22625430

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989447 #22625430