Group #22624917 — subgroups

Subgroups — #22624917

Order 9344.

126 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 32 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	#17989482	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989461	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988820	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#64408	—	2	1	no	—
5	C₂×#11924031	—	2	1	no	—
6	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
7	#14556562	—	2	1	no	—
8	#14556525	C₄	1	1	yes	characteristic, complemented
9	#14556512	—	2	1	no	—
10	C₂×D₈×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₂²×#64408	—	4	1	no	—
12	C₄⋊#64408	—	2	2	no	—
13	C₄⋊#64408	—	4	1	no	—
14	#11924031	—	4	1	no	—
15	C₂×C₂²⋊D₇₃	—	4	1	no	—
16	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
17	C₂×#10596831	D₄	1	1	yes	characteristic
18	C₈×D₇₃	—	4	1	no	—
19	C₄⋊Dic₇₃	—	2	1	no	—
20	C₂²⋊Dic₇₃	—	4	1	no	—
21	C₂×D₄×C₇₃	—	2	1	no	—
22	D₈×C₇₃	—	4	1	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₇₃	—	4	1	no	—
25	C₂²×D₇₃	D₈	1	1	yes	characteristic
26	C₂×#64408	—	4	2	no	—
27	C₂×#64408	—	8	1	no	—
28	C₂×#64408	—	8	1	no	—
29	D₄×C₇₃	—	4	1	no	—
30	D₄×C₇₃	—	4	1	no	—
31	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²⋊D₇₃	—	8	1	no	—
33	C₂²⋊D₇₃	—	8	1	no	—
34	C₂×Dic₇₃	—	4	1	no	—
35	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
36	C₄×D₇₃	—	2	1	no	—
37	C₄×D₇₃	—	2	1	no	—
38	C₈×C₇₃	—	2	1	no	—
39	#10596831	—	2	1	no	—
40	C₂²×C₇₃	—	8	1	no	—
41	C₂²×C₇₃	—	8	1	no	—
42	C₂²×C₇₃	—	8	1	no	—
43	C₂²×C₇₃	#102	1	1	yes	characteristic
44	C₂×D₇₃	—	2	1	no	—
45	C₂×D₇₃	—	2	1	no	—
46	C₂×D₇₃	D₁₆	1	1	yes	characteristic
47	C₂×D₇₃	SD₃₂	1	1	yes	characteristic
48	#64408	—	8	2	no	—
49	C₄×C₇₃	#99	1	1	yes	characteristic
50	C₄×C₇₃	#104	1	1	yes	characteristic
51	Dic₇₃	—	2	1	no	—
52	Dic₇₃	—	8	1	no	—
53	C₂×C₇₃	—	16	1	no	—
54	C₂×C₇₃	#327	1	1	yes	characteristic
55	C₂×C₇₃	#357	1	1	yes	characteristic
56	C₂×C₇₃	#360	1	1	yes	characteristic
57	D₇₃	—	2	1	no	—
58	D₇₃	—	2	1	no	—
59	#1347	—	73	1	no	maximal, Sylow
60	C₇₃	#1347	1	1	yes	characteristic, complemented, Sylow
61	#466	—	73	1	no	—
62	C₂²⋊C₁₆	—	73	1	no	—
63	#340	—	73	1	no	—
64	C₂×D₈	#64408	1	1	yes	characteristic, complemented
65	C₂²×C₈	—	73	1	no	—
66	#121	—	146	1	no	—
67	C₂×C₄⋊C₄	—	146	1	no	—
68	C₂×C₁₆	—	146	1	no	—
69	#107	—	73	1	no	—
70	#102	—	146	1	no	—
71	C₂×D₄	—	2	1	no	—
72	C₂×D₄	—	292	1	no	—
73	C₂²×C₄	—	292	1	no	—
74	C₂²×C₄	—	73	1	no	—
75	D₈	—	4	1	no	—
76	C₂×C₈	—	292	1	no	—
77	C₂×C₈	—	73	1	no	—
78	C₂×C₈	C₂×#64408	1	1	yes	characteristic
79	C₄⋊C₄	—	292	1	no	—
80	C₄⋊C₄	—	146	2	no	—
81	C₄⋊C₄	—	146	1	no	—
82	C₂²⋊C₄	—	292	1	no	—
83	C₁₆	—	292	1	no	—
84	C₂³	—	4	1	no	—
85	C₂³	—	73	1	no	—
86	D₄	—	4	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	584	1	no	—
89	D₄	—	584	1	no	—
90	C₂×C₄	—	292	2	no	—
91	C₂×C₄	—	292	1	no	—
92	C₂×C₄	—	584	1	no	—
93	C₂×C₄	—	584	1	no	—
94	C₂×C₄	—	73	1	no	—
95	C₂×C₄	—	146	1	no	—
96	C₂×C₄	—	146	1	no	—
97	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
98	C₈	—	2	1	no	—
99	C₈	—	146	1	no	—
100	C₂²	—	8	1	no	—
101	C₂²	—	8	1	no	—
102	C₂²	—	8	1	no	—
103	C₂²	—	73	1	no	—
104	C₂²	—	73	1	no	—
105	C₂²	—	146	1	no	—
106	C₂²	—	146	1	no	—
107	C₂²	#14556653	1	1	yes	characteristic
108	C₄	—	584	2	no	—
109	C₄	—	584	1	no	—
110	C₄	—	146	1	no	—
111	C₄	#14556649	1	1	yes	characteristic
112	C₄	#14556655	1	1	yes	characteristic
113	C₂	—	16	1	no	—
114	C₂	—	146	1	no	—
115	C₂	—	146	1	no	—
116	C₂	#17989438	1	1	yes	characteristic
117	C₂	#17989499	1	1	yes	characteristic
118	C₂	#17989503	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989482

C₂

yes

maximal, characteristic, complemented

#17989461

C₂

yes

maximal, characteristic, complemented

#17988820

C₂

yes

maximal, characteristic

C₂×C₄⋊#64408

—

C₂×#11924031

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556562

—

#14556525

C₄

yes

characteristic, complemented

#14556512

—

C₂×D₈×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

C₄⋊#64408

—

C₄⋊#64408

—

#11924031

—

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₈×D₇₃

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂×D₄×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

—

C₂²×D₇₃

D₈

yes

—

—

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#102

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

D₁₆

yes

characteristic

C₂×D₇₃

SD₃₂

yes

characteristic

#64408

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

D₇₃

—

#1347

—

maximal, Sylow

C₇₃

#1347

yes

characteristic, complemented, Sylow

#466

—

C₂²⋊C₁₆

—

#340

—

C₂×D₈

#64408

yes

characteristic, complemented

C₂²×C₈

—

#121

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₁₆

—

146

—

#107

—

#102

—

146

—

C₂×D₄

—

C₂×D₄

—

292

—

C₂²×C₄

—

292

—

C₂²×C₄

—

D₈

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

292

—

C₁₆

—

292

—

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

584

—

D₄

—

584

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

584

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

C₈

—

146

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

146

—

106

C₂²

—

146

—

107

C₂²

#14556653

yes

characteristic

108

C₄

—

584

—

109

C₄

—

584

—

110

C₄

—

146

—

111

C₄

#14556649

yes

characteristic

112

C₄

#14556655

yes

characteristic

113

C₂

—

114

C₂

—

146

—

115

C₂

—

146

—

116

C₂

#17989438

yes

characteristic

117

C₂

#17989499

yes

characteristic

118

C₂

#17989503

yes

characteristic

	subgroup	G/H
center	C₂²	#14556653
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×D₈×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	C₂×D₈	#64408
hypocenter	C₇₃	#1347
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂²

#14556653

commutator

C₂×C₈×C₇₃

C₂×C₄

Frattini

C₂×C₈

C₂×#64408

Fitting

C₂×D₈×C₇₃

C₄

C₂²×C₇₃

C₂×D₈

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #17989482	C₂	semidirect
2. #17989461	C₂	semidirect
8. #14556525	C₄	semidirect
10. C₂×D₈×C₇₃	C₄	semidirect
60. C₇₃	#1347	semidirect
64. C₂×D₈	#64408	semidirect

H ≅ G/N

type

1. #17989482

C₂

semidirect

2. #17989461

C₂

semidirect

8. #14556525

C₄

semidirect

10. C₂×D₈×C₇₃

C₄

semidirect

60. C₇₃

#1347

semidirect

64. C₂×D₈

#64408

semidirect

Subgroups — #22624917

Conjugacy classes of subgroups

Complements