Group #22627065 — subgroups

Subgroups — #22627065

Order 9344.

296 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 119 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×C₄×#10596842	C₂	1	2	yes	maximal
2	(C₂×#10596842)⋊C₄	C₂	1	4	yes	maximal
3	C₄²×#64408	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10596842	C₂²	1	4	yes	—
5	C₄×#10596842	C₄	1	8	yes	complemented
6	C₂×C₄×#64408	C₄	1	2	yes	—
7	C₂×C₄×#64408	C₄	1	1	yes	characteristic
8	C₂×C₄×#64408	C₂²	1	2	yes	—
9	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
10	C₄²×D₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596842	—	2	8	no	—
12	C₂×#10596842	C₂×C₄	1	8	yes	—
13	C₂²×#64408	C₂×C₄	1	2	yes	—
14	C₂²×#64408	C₂×C₄	1	1	yes	characteristic
15	C₂²×#64408	C₂³	1	1	yes	characteristic
16	C₄×#64408	—	2	4	no	—
17	C₄×#64408	—	2	4	no	—
18	C₄×#64408	C₈	1	4	yes	complemented
19	C₄×#64408	C₂×C₄	1	4	yes	—
20	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	C₈	1	2	yes	complemented
23	C₄×Dic₇₃	C₈	1	1	yes	characteristic, complemented
24	C₄²×C₇₃	C₈	1	1	yes	characteristic, complemented
25	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×#64408	—	2	2	no	—
27	C₂×#64408	—	2	2	no	—
28	C₂×#64408	C₄²	1	2	yes	—
29	C₂×#64408	C₂×C₈	1	4	yes	—
30	C₂×#64408	M₁₆	1	4	yes	—
31	C₂×#64408	C₂²×C₄	1	2	yes	—
32	C₂×#64408	#41	1	4	yes	—
33	#10596842	—	2	8	no	—
34	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
35	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
37	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
38	C₄×D₇₃	—	2	2	no	—
39	C₄×D₇₃	—	2	2	no	—
40	C₄×D₇₃	C₄²	1	2	yes	—
41	C₄×D₇₃	C₂×C₈	1	2	yes	—
42	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
43	C₂×D₇₃	C₂×C₄²	1	1	yes	characteristic
44	C₂×D₇₃	#117	1	2	yes	—
45	C₂×D₇₃	C₂²×C₈	1	1	yes	characteristic
46	C₂×D₇₃	C₂×M₁₆	1	2	yes	—
47	#64408	—	2	4	no	—
48	#64408	#97	1	4	yes	—
49	#64408	#117	1	4	yes	—
50	C₄×C₇₃	—	2	2	no	—
51	C₄×C₇₃	C₄×C₈	1	2	yes	—
52	Dic₇₃	—	2	2	no	—
53	Dic₇₃	C₄×C₈	1	2	yes	—
54	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
55	C₂×C₇₃	#431	1	2	yes	—
56	D₇₃	#376	1	1	yes	characteristic
57	D₇₃	C₂×#97	1	1	yes	characteristic
58	D₇₃	#431	1	2	yes	—
59	#1744	—	73	1	no	maximal, Sylow
60	C₇₃	#1744	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₄×C₈	—	73	2	no	—
62	C₄³	—	73	1	no	—
63	#336	—	73	4	no	—
64	C₂²×C₈	—	73	4	no	—
65	C₂×C₄²	—	73	1	no	—
66	C₂×C₄²	—	73	1	no	—
67	C₂×C₄²	—	73	1	no	—
68	C₂×C₄²	—	73	2	no	—
69	C₂×C₄²	—	73	2	no	—
70	C₄×C₈	—	73	8	no	—
71	C₂²×C₄	—	73	1	no	—
72	C₂²×C₄	—	73	1	no	—
73	C₂²×C₄	—	73	1	no	—
74	C₂²×C₄	—	73	2	no	—
75	C₂²×C₄	—	73	2	no	—
76	C₂×C₈	—	73	8	no	—
77	C₂×C₈	—	146	8	no	—
78	C₄²	—	73	4	no	—
79	C₄²	—	73	4	no	—
80	C₄²	—	73	2	no	—
81	C₄²	—	73	1	no	—
82	C₄²	—	146	4	no	—
83	C₄²	—	146	4	no	—
84	C₄²	#10596842	1	1	yes	characteristic, complemented
85	C₂³	—	73	1	no	—
86	C₂×C₄	—	73	2	no	—
87	C₂×C₄	—	73	2	no	—
88	C₂×C₄	—	73	4	no	—
89	C₂×C₄	—	73	4	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	73	2	no	—
92	C₂×C₄	—	73	2	no	—
93	C₂×C₄	—	73	4	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	146	2	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	—	146	2	no	—
99	C₂×C₄	C₂×#10596842	1	2	yes	—
100	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
101	C₈	—	146	8	no	—
102	C₂²	—	73	1	no	—
103	C₂²	—	73	1	no	—
104	C₂²	—	73	2	no	—
105	C₂²	—	73	2	no	—
106	C₂²	C₂²×#10596842	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	—	73	4	no	—
109	C₄	—	73	4	no	—
110	C₄	—	73	2	no	—
111	C₄	—	146	4	no	—
112	C₄	—	146	2	no	—
113	C₄	C₄×#10596842	1	2	yes	—
114	C₂	—	73	1	no	—
115	C₂	—	73	1	no	—
116	C₂	—	73	2	no	—
117	C₂	C₂×C₄×#10596842	1	1	yes	characteristic
118	C₂	#17989700	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×#10596842

C₂

yes

maximal

(C₂×#10596842)⋊C₄

C₂

yes

maximal

C₄²×#64408

C₂

yes

maximal, characteristic

C₂²×#10596842

C₂²

yes

—

C₄×#10596842

C₄

yes

complemented

C₂×C₄×#64408

C₄

yes

—

C₂×C₄×#64408

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

—

C₂×C₄×#64408

C₂²

yes

characteristic

C₄²×D₇₃

C₄

yes

characteristic

C₂×#10596842

—

C₂×#10596842

C₂×C₄

yes

—

C₂²×#64408

C₂×C₄

yes

—

C₂²×#64408

C₂×C₄

yes

characteristic

C₂²×#64408

C₂³

yes

—

—

C₈

yes

complemented

C₄×#64408

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₈

yes

complemented

C₄×Dic₇₃

C₈

yes

characteristic, complemented

C₄²×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₂²×C₄

yes

—

—

C₄²

yes

—

C₂×#64408

C₂×C₈

yes

—

C₂×#64408

M₁₆

yes

—

C₂×#64408

C₂²×C₄

yes

—

C₂×#64408

#41

yes

—

#10596842

—

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

C₄²

yes

—

C₄×D₇₃

C₂×C₈

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

C₂×C₄²

yes

characteristic

C₂×D₇₃

#117

yes

—

C₂×D₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

C₂×M₁₆

yes

—

#64408

—

#64408

#97

yes

—

#64408

#117

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₄×C₈

yes

—

Dic₇₃

—

Dic₇₃

C₄×C₈

yes

—

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

C₂×C₇₃

#431

yes

—

D₇₃

#376

yes

characteristic

D₇₃

C₂×#97

yes

characteristic

D₇₃

#431

yes

—

#1744

—

maximal, Sylow

C₇₃

#1744

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₄³

—

#336

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₄²

—

146

—

C₄²

#10596842

yes

characteristic, complemented

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596842

yes

—

100

C₂×C₄

C₂×#10596842

yes

characteristic

101

C₈

—

146

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂²×#10596842

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

146

—

112

C₄

—

146

—

113

C₄

C₄×#10596842

yes

—

114

C₂

—

115

C₂

—

116

C₂

—

117

C₂

C₂×C₄×#10596842

yes

characteristic

118

C₂

#17989700

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#10596842
commutator	C₂×C₇₃	C₂×C₄×C₈
Frattini	C₂²	C₂²×#10596842
Fitting	C₄²×C₇₃	C₈
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	C₄²	#10596842
hypocenter	C₇₃	#1744
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

subgroup

G/H

center

C₂×C₄

C₂×#10596842

commutator

C₂×C₇₃

C₂×C₄×C₈

Frattini

C₂²

C₂²×#10596842

Fitting

C₄²×C₇₃

C₈

socle

C₂²×C₇₃

C₂²×C₈

C₄²

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₄²

N	H ≅ G/N	type
5. C₄×#10596842	C₄	semidirect
18. C₄×#64408	C₈	semidirect
22. C₄×Dic₇₃	C₈	semidirect
23. C₄×Dic₇₃	C₈	semidirect
24. C₄²×C₇₃	C₈	semidirect
60. C₇₃	#1744	semidirect
84. C₄²	#10596842	semidirect

H ≅ G/N

type

5. C₄×#10596842

C₄

semidirect

18. C₄×#64408

C₈

semidirect

22. C₄×Dic₇₃

C₈

semidirect

23. C₄×Dic₇₃

C₈

semidirect

24. C₄²×C₇₃

C₈

semidirect

60. C₇₃

#1744

semidirect

84. C₄²

#10596842

semidirect

Subgroups — #22627065

Conjugacy classes of subgroups

Complements