Group #22625652 — subgroups

Subgroups — #22625652

Order 9344.

200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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	#17989550	C₂	1	2	yes	maximal
2	#17989456	C₂	1	1	yes	maximal, characteristic
3	#17989455	C₂	1	1	yes	maximal, characteristic
4	#17989454	C₂	1	2	yes	maximal
5	#17988541	C₂	1	1	yes	maximal, characteristic
6	D₇₃⋊M₁₆	C₂²	1	2	yes	—
7	#14556670	C₂²	1	2	yes	—
8	#14556645	C₄	1	4	yes	complemented
9	C₈×#64408	C₄	1	4	yes	complemented
10	C₂×#11924011	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
12	#14556548	C₂²	1	1	yes	characteristic
13	#14556502	C₄	1	1	yes	characteristic, complemented
14	#14556501	C₄	1	1	yes	characteristic, complemented
15	C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
16	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
17	#11924038	—	2	2	no	—
18	#11924037	—	2	2	no	—
19	#11924036	C₂×C₄	1	4	yes	—
20	C₄⋊#64408	—	2	2	no	—
21	C₂²⋊#64408	—	2	2	no	—
22	C₄×#64408	C₂×C₄	1	4	yes	—
23	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
24	#11924011	—	2	2	no	—
25	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
26	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
27	C₈×D₇₃	C₂×C₄	1	2	yes	—
28	C₈×D₇₃	C₂×C₄	1	2	yes	—
29	#11924007	—	2	1	no	—
30	#11924005	—	2	1	no	—
31	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₇₃	#41	1	1	yes	characteristic
36	C₂×#64408	—	2	4	no	—
37	C₂×C₄×C₇₃	—	2	1	no	—
38	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₇₃	—	2	1	no	—
40	C₂×Dic₇₃	#41	1	1	yes	characteristic
41	C₄×D₇₃	C₂²×C₄	1	2	yes	—
42	C₄×D₇₃	#41	1	2	yes	—
43	#10596833	—	2	4	no	—
44	C₈×C₇₃	—	2	1	no	—
45	C₈×C₇₃	C₄²	1	1	yes	characteristic
46	C₈×C₇₃	C₄²	1	1	yes	characteristic
47	#10596831	—	2	1	no	—
48	#10596831	C₄²	1	2	yes	—
49	C₂²×C₇₃	#117	1	1	yes	characteristic
50	C₂×D₇₃	—	4	1	no	—
51	C₂×D₇₃	#117	1	2	yes	—
52	#64408	—	4	4	no	—
53	C₄×C₇₃	—	4	1	no	—
54	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
55	C₄×C₇₃	#117	1	1	yes	characteristic
56	Dic₇₃	—	4	1	no	—
57	Dic₇₃	#117	1	2	yes	—
58	C₂×C₇₃	—	2	1	no	—
59	C₂×C₇₃	#376	1	1	yes	characteristic
60	D₇₃	—	2	2	no	—
61	#1747	—	73	1	no	maximal, Sylow
62	C₇₃	#1747	1	1	yes	characteristic, complemented, Sylow
63	#405	—	73	2	no	—
64	#405	—	73	1	no	—
65	#338	—	73	1	no	—
66	H(3,ℤ/4)	—	73	2	no	—
67	H(3,ℤ/4)	—	73	1	no	—
68	C₂×M₁₆	—	73	2	no	—
69	C₂×M₁₆	—	73	1	no	—
70	C₂²×C₈	—	73	1	no	—
71	#117	—	73	2	no	—
72	#117	—	73	1	no	—
73	#97	—	73	4	no	—
74	#97	—	73	1	no	—
75	#97	—	73	1	no	—
76	C₄×C₈	—	73	4	no	—
77	C₄×C₈	—	73	1	no	—
78	C₄×C₈	#64408	1	1	yes	characteristic, complemented
79	C₂²×C₄	—	73	1	no	—
80	M₁₆	—	146	2	no	—
81	M₁₆	—	146	2	no	—
82	M₁₆	—	146	2	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	2	no	—
85	C₂×C₈	—	73	2	no	—
86	C₂×C₈	—	73	4	no	—
87	C₂×C₈	—	73	1	no	—
88	C₂×C₈	C₂×#64408	1	1	yes	characteristic
89	C₂×C₈	C₂×#64408	1	1	yes	characteristic
90	C₄⋊C₄	—	146	1	no	—
91	C₄⋊C₄	—	146	2	no	—
92	C₂²⋊C₄	—	146	1	no	—
93	C₂²⋊C₄	—	146	2	no	—
94	C₄²	—	73	4	no	—
95	C₄²	—	73	1	no	—
96	C₄²	C₂×#64408	1	1	yes	characteristic
97	C₂³	—	73	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	2	no	—
101	C₂×C₄	—	73	2	no	—
102	C₂×C₄	—	146	4	no	—
103	C₂×C₄	—	146	1	no	—
104	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	73	2	no	—
107	C₈	—	146	4	no	—
108	C₈	—	146	1	no	—
109	C₈	C₄×#64408	1	1	yes	characteristic
110	C₈	C₄×#64408	1	1	yes	characteristic
111	C₂²	—	292	1	no	—
112	C₂²	—	73	2	no	—
113	C₂²	#14556670	1	1	yes	characteristic
114	C₄	—	4	1	no	—
115	C₄	—	292	1	no	—
116	C₄	—	292	4	no	—
117	C₄	—	73	2	no	—
118	C₄	C₂×C₄×#64408	1	1	yes	characteristic
119	C₄	#14556670	1	1	yes	characteristic
120	C₂	—	2	1	no	—
121	C₂	—	146	2	no	—
122	C₂	#17989523	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989550

C₂

yes

maximal

#17989456

C₂

yes

maximal, characteristic

#17989455

C₂

yes

maximal, characteristic

#17989454

C₂

yes

maximal

#17988541

C₂

yes

maximal, characteristic

D₇₃⋊M₁₆

C₂²

yes

—

#14556670

C₂²

yes

—

#14556645

C₄

yes

complemented

C₈×#64408

C₄

yes

complemented

C₂×#11924011

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556548

C₂²

yes

characteristic

#14556502

C₄

yes

characteristic, complemented

#14556501

C₄

yes

characteristic, complemented

C₈×Dic₇₃

C₄

yes

characteristic, complemented

C₄×C₈×C₇₃

C₄

yes

characteristic, complemented

#11924038

—

#11924037

—

#11924036

C₂×C₄

yes

—

C₄⋊#64408

—

C₂²⋊#64408

—

C₄×#64408

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

#11924011

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

#11924007

—

#11924005

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

C₂²×D₇₃

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

#41

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

—

C₄×D₇₃

#41

yes

—

#10596833

—

C₈×C₇₃

—

C₈×C₇₃

C₄²

yes

characteristic

C₈×C₇₃

C₄²

yes

characteristic

#10596831

—

#10596831

C₄²

yes

—

C₂²×C₇₃

#117

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#117

yes

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

#117

yes

characteristic

Dic₇₃

—

Dic₇₃

#117

yes

—

C₂×C₇₃

—

C₂×C₇₃

#376

yes

characteristic

D₇₃

—

#1747

—

maximal, Sylow

C₇₃

#1747

yes

characteristic, complemented, Sylow

—

—

—

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic, complemented

C₂²×C₄

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

146

—

103

C₂×C₄

—

146

—

104

C₂×C₄

C₂²×#64408

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

146

—

108

C₈

—

146

—

109

C₈

C₄×#64408

yes

characteristic

110

C₈

C₄×#64408

yes

characteristic

111

C₂²

—

292

—

112

C₂²

—

113

C₂²

#14556670

yes

characteristic

114

C₄

—

115

C₄

—

292

—

116

C₄

—

292

—

117

C₄

—

118

C₄

C₂×C₄×#64408

yes

characteristic

119

C₄

#14556670

yes

characteristic

120

C₂

—

121

C₂

—

146

—

122

C₂

#17989523

yes

characteristic

	subgroup	G/H
center	C₈	C₄×#64408
commutator	C₄×C₇₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂×C₇₃	#376
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1747
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₄×C₈

subgroup

G/H

center

C₈

C₄×#64408

commutator

C₄×C₇₃

C₂×C₄²

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

C₂×C₇₃

C₄×C₈

C₇₃

G ▷ C₄×C₇₃ ▷ C₇₃

C₁ ◁ C₈ ◁ C₄×C₈

N	H ≅ G/N	type
8. #14556645	C₄	semidirect
9. C₈×#64408	C₄	semidirect
13. #14556502	C₄	semidirect
14. #14556501	C₄	semidirect
15. C₈×Dic₇₃	C₄	semidirect
16. C₄×C₈×C₇₃	C₄	semidirect
62. C₇₃	#1747	semidirect
78. C₄×C₈	#64408	semidirect

H ≅ G/N

type

8. #14556645

C₄

semidirect

9. C₈×#64408

C₄

semidirect

13. #14556502

C₄

semidirect

14. #14556501

C₄

semidirect

15. C₈×Dic₇₃

C₄

semidirect

16. C₄×C₈×C₇₃

C₄

semidirect

62. C₇₃

#1747

semidirect

78. C₄×C₈

#64408

semidirect

Subgroups — #22625652

Conjugacy classes of subgroups

Complements