Group #22625852 — subgroups

Subgroups — #22625852

Order 9344.

248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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	#17989533	C₂	1	2	yes	maximal
2	#17989461	C₂	1	4	yes	maximal
3	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#64408	—	2	2	no	—
5	C₂×C₄⋊#64408	—	2	2	no	—
6	C₂×C₄⋊#64408	C₂²	1	4	yes	—
7	C₂×C₈×D₇₃	C₂²	1	2	yes	—
8	C₄²×D₇₃	C₂²	1	1	yes	characteristic
9	C₄×#10596831	C₄	1	1	yes	characteristic, complemented
10	C₈×Dic₇₃	C₄	1	2	yes	complemented
11	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
12	C₂²×#64408	—	2	4	no	—
13	C₄⋊#64408	—	2	8	no	—
14	C₄⋊#64408	—	4	4	no	—
15	C₄⋊#64408	—	4	4	no	—
16	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
17	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
18	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
19	C₂×#10596831	C₂×C₄	1	2	yes	—
20	C₈×D₇₃	—	2	4	no	—
21	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
23	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
25	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₇₃	C₂×D₄	1	1	yes	characteristic
27	C₂×#64408	—	4	4	no	—
28	C₂×#64408	—	4	4	no	—
29	C₂×#64408	—	4	4	no	—
30	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
36	C₄×D₇₃	D₈	1	2	yes	—
37	C₄×D₇₃	SD₁₆	1	4	yes	—
38	C₄×D₇₃	Q₁₆	1	2	yes	—
39	C₄×D₇₃	#41	1	4	yes	—
40	C₈×C₇₃	—	2	2	no	—
41	#10596831	—	2	2	no	—
42	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂×D₇₃	#124	1	2	yes	—
44	C₂×D₇₃	C₂×D₈	1	1	yes	characteristic
45	C₂×D₇₃	C₂×SD₁₆	1	2	yes	—
46	C₂×D₇₃	C₂×Q₁₆	1	1	yes	characteristic
47	#64408	—	8	4	no	—
48	C₄×C₇₃	#106	1	2	yes	—
49	C₄×C₇₃	#107	1	2	yes	—
50	C₄×C₇₃	#117	1	2	yes	—
51	Dic₇₃	#106	1	2	yes	—
52	Dic₇₃	#107	1	2	yes	—
53	Dic₇₃	#125	1	2	yes	—
54	C₂×C₇₃	#382	1	1	yes	characteristic
55	C₂×C₇₃	C₂×#106	1	1	yes	characteristic
56	C₂×C₇₃	C₂×#107	1	1	yes	characteristic
57	D₇₃	#486	1	2	yes	—
58	D₇₃	#487	1	2	yes	—
59	#1834	—	73	1	no	maximal, Sylow
60	C₇₃	#1834	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₄×C₈	—	73	1	no	—
62	#384	—	73	2	no	—
63	#340	—	73	4	no	—
64	C₂²×C₈	—	73	2	no	—
65	C₂×C₄⋊C₄	—	73	4	no	—
66	C₂×C₄⋊C₄	—	146	2	no	—
67	C₂×C₄⋊C₄	—	146	2	no	—
68	C₂×C₄²	—	73	1	no	—
69	C₄×C₈	—	73	2	no	—
70	C₄×C₈	—	73	1	no	—
71	C₄×C₈	#64408	1	1	yes	characteristic, complemented
72	C₂²×C₄	—	73	1	no	—
73	C₂²×C₄	—	73	1	no	—
74	C₂²×C₄	—	73	1	no	—
75	C₂²×C₄	—	146	4	no	—
76	C₂×C₈	—	73	2	no	—
77	C₂×C₈	—	146	4	no	—
78	C₂×C₈	C₂×#64408	1	2	yes	—
79	C₄⋊C₄	—	292	4	no	—
80	C₄⋊C₄	—	292	4	no	—
81	C₄⋊C₄	—	146	8	no	—
82	C₄²	—	73	1	no	—
83	C₄²	—	73	1	no	—
84	C₄²	—	73	1	no	—
85	C₄²	C₂×#64408	1	1	yes	characteristic
86	C₂³	—	73	1	no	—
87	C₂×C₄	—	292	4	no	—
88	C₂×C₄	—	292	4	no	—
89	C₂×C₄	—	292	4	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	73	4	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	73	2	no	—
96	C₂×C₄	—	73	4	no	—
97	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
98	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
99	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
100	C₈	—	2	2	no	—
101	C₈	—	146	2	no	—
102	C₂²	—	73	2	no	—
103	C₂²	—	73	2	no	—
104	C₂²	—	73	1	no	—
105	C₂²	—	73	1	no	—
106	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
107	C₄	—	584	4	no	—
108	C₄	—	73	2	no	—
109	C₄	—	73	2	no	—
110	C₄	—	73	2	no	—
111	C₄	#14556659	1	2	yes	—
112	C₄	#14556660	1	2	yes	—
113	C₄	#14556670	1	2	yes	—
114	C₂	—	73	2	no	—
115	C₂	—	73	2	no	—
116	C₂	#17989531	1	1	yes	characteristic
117	C₂	C₂×#14556659	1	1	yes	characteristic
118	C₂	C₂×#14556660	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989533

C₂

yes

maximal

#17989461

C₂

yes

maximal

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#64408

—

C₂×C₄⋊#64408

—

C₂×C₄⋊#64408

C₂²

yes

—

C₂×C₈×D₇₃

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

C₄×#10596831

C₄

yes

characteristic, complemented

C₈×Dic₇₃

C₄

yes

complemented

C₄×C₈×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

C₄⋊#64408

—

C₄⋊#64408

—

C₄⋊#64408

—

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂×D₄

yes

—

—

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

C₄×D₇₃

D₈

yes

—

C₄×D₇₃

SD₁₆

yes

—

C₄×D₇₃

Q₁₆

yes

—

C₄×D₇₃

#41

yes

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

#124

yes

—

C₂×D₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

C₂×SD₁₆

yes

—

C₂×D₇₃

C₂×Q₁₆

yes

characteristic

#64408

—

C₄×C₇₃

#106

yes

—

C₄×C₇₃

#107

yes

—

C₄×C₇₃

#117

yes

—

Dic₇₃

#106

yes

—

Dic₇₃

#107

yes

—

Dic₇₃

#125

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

yes

—

D₇₃

#487

yes

—

#1834

—

maximal, Sylow

C₇₃

#1834

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

#384

—

#340

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic, complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×#64408

yes

characteristic

100

C₈

—

101

C₈

—

146

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂×C₄⋊#64408

yes

characteristic

107

C₄

—

584

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#14556659

yes

—

112

C₄

#14556660

yes

—

113

C₄

#14556670

yes

—

114

C₂

—

115

C₂

—

116

C₂

#17989531

yes

characteristic

117

C₂

C₂×#14556659

yes

characteristic

118

C₂

C₂×#14556660

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1834
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₄×C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
9. C₄×#10596831	C₄	semidirect
10. C₈×Dic₇₃	C₄	semidirect
11. C₄×C₈×C₇₃	C₄	semidirect
60. C₇₃	#1834	semidirect
71. C₄×C₈	#64408	semidirect

H ≅ G/N

type

9. C₄×#10596831

C₄

semidirect

10. C₈×Dic₇₃

C₄

semidirect

11. C₄×C₈×C₇₃

C₄

semidirect

60. C₇₃

#1834

semidirect

71. C₄×C₈

#64408

semidirect

Subgroups — #22625852

Conjugacy classes of subgroups

Complements