Group #22627073 — subgroups

Subgroups — #22627073

Order 9344.

260 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 91 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	—	2	4	no	—
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	4	no	—
12	C₂×#10596842	—	2	8	no	—
13	C₂²×#64408	C₂×C₄	1	1	yes	characteristic
14	C₂²×#64408	C₂×C₄	1	2	yes	—
15	C₂²×#64408	C₂³	1	1	yes	characteristic
16	C₄×#64408	—	2	4	no	—
17	C₄×#64408	—	2	4	no	—
18	C₄×#64408	—	2	2	no	—
19	C₄×#64408	D₄	1	2	yes	—
20	C₄×#64408	Q₈	1	2	yes	—
21	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₇₃	C₈	1	1	yes	characteristic, complemented
24	C₄×Dic₇₃	C₈	1	2	yes	complemented
25	C₄²×C₇₃	C₈	1	1	yes	characteristic, complemented
26	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×#64408	—	2	2	no	—
28	C₂×#64408	—	2	2	no	—
29	C₂×#64408	—	2	2	no	—
30	C₂×#64408	C₄⋊C₄	1	2	yes	—
31	C₂×#64408	M₁₆	1	4	yes	—
32	C₂×#64408	C₂×D₄	1	1	yes	characteristic
33	C₂×#64408	C₂×Q₈	1	1	yes	characteristic
34	C₂×#64408	#41	1	4	yes	—
35	#10596842	—	4	4	no	—
36	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
39	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
40	C₄×D₇₃	—	2	2	no	—
41	C₄×D₇₃	—	2	2	no	—
42	C₄×D₇₃	C₄⋊C₄	1	2	yes	—
43	C₄×D₇₃	M₁₆	1	2	yes	—
44	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
45	C₂×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×D₇₃	#117	1	2	yes	—
47	C₂×D₇₃	C₂×M₁₆	1	2	yes	—
48	C₂×D₇₃	C₂×M₁₆	1	1	yes	characteristic
49	#64408	—	2	2	no	—
50	#64408	—	2	4	no	—
51	#64408	#124	1	2	yes	—
52	#64408	#125	1	2	yes	—
53	C₄×C₇₃	—	2	2	no	—
54	C₄×C₇₃	C₄⋊C₈	1	2	yes	—
55	Dic₇₃	—	2	2	no	—
56	Dic₇₃	C₄⋊C₈	1	2	yes	—
57	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
58	C₂×C₇₃	#431	1	2	yes	—
59	D₇₃	#382	1	1	yes	characteristic
60	D₇₃	#423	1	1	yes	characteristic
61	D₇₃	#432	1	2	yes	—
62	#1831	—	73	1	no	maximal, Sylow
63	C₇₃	#1831	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₄⋊C₈	—	73	2	no	—
65	C₄³	—	73	1	no	—
66	#336	—	73	4	no	—
67	C₂²×C₈	—	73	4	no	—
68	C₂×C₄²	—	73	1	no	—
69	C₂×C₄²	—	73	1	no	—
70	C₂×C₄²	—	73	2	no	—
71	C₂×C₄²	—	73	1	no	—
72	C₂×C₄²	—	73	2	no	—
73	C₄⋊C₈	—	146	4	no	—
74	C₂²×C₄	—	73	1	no	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	—	73	1	no	—
77	C₂²×C₄	—	73	2	no	—
78	C₂²×C₄	—	73	2	no	—
79	C₂×C₈	—	146	4	no	—
80	C₂×C₈	—	146	8	no	—
81	C₄²	—	73	2	no	—
82	C₄²	—	73	2	no	—
83	C₄²	—	73	2	no	—
84	C₄²	—	73	1	no	—
85	C₄²	—	146	4	no	—
86	C₄²	—	146	2	no	—
87	C₄²	—	146	4	no	—
88	C₄²	#10596842	1	1	yes	characteristic, complemented
89	C₂³	—	73	1	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	4	no	—
93	C₂×C₄	—	73	1	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	73	2	no	—
96	C₂×C₄	—	73	2	no	—
97	C₂×C₄	—	73	4	no	—
98	C₂×C₄	—	73	2	no	—
99	C₂×C₄	—	146	2	no	—
100	C₂×C₄	—	146	2	no	—
101	C₂×C₄	—	146	2	no	—
102	C₂×C₄	—	146	2	no	—
103	C₂×C₄	—	146	2	no	—
104	C₂×C₄	C₂×#10596842	1	2	yes	—
105	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
106	C₈	—	292	4	no	—
107	C₂²	—	73	1	no	—
108	C₂²	—	73	1	no	—
109	C₂²	—	73	2	no	—
110	C₂²	—	73	2	no	—
111	C₂²	C₂²×#10596842	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	73	2	no	—
114	C₄	—	73	2	no	—
115	C₄	—	73	2	no	—
116	C₄	—	146	2	no	—
117	C₄	—	146	4	no	—
118	C₄	—	146	2	no	—
119	C₄	C₄⋊#10596842	1	2	yes	—
120	C₂	—	73	1	no	—
121	C₂	—	73	1	no	—
122	C₂	—	73	2	no	—
123	C₂	C₂×C₄⋊#10596842	1	1	yes	characteristic
124	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

—

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

—

C₂²×#64408

C₂×C₄

yes

characteristic

C₂²×#64408

C₂×C₄

yes

—

C₂²×#64408

C₂³

yes

—

—

—

D₄

yes

—

C₄×#64408

Q₈

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₈

yes

characteristic, complemented

C₄×Dic₇₃

C₈

yes

complemented

C₄²×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₂²×C₄

yes

—

—

—

C₄⋊C₄

yes

—

C₂×#64408

M₁₆

yes

—

C₂×#64408

C₂×D₄

yes

characteristic

C₂×#64408

C₂×Q₈

yes

characteristic

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

C₄⋊C₄

yes

—

C₄×D₇₃

M₁₆

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

#117

yes

—

C₂×D₇₃

C₂×M₁₆

yes

—

C₂×D₇₃

C₂×M₁₆

yes

—

—

yes

—

#64408

#125

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

yes

D₇₃

yes

D₇₃

yes

—

#1831

—

maximal, Sylow

C₇₃

#1831

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

C₄³

—

#336

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

146

—

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

—

100

C₂×C₄

—

146

—

101

C₂×C₄

—

146

—

102

C₂×C₄

—

146

—

103

C₂×C₄

—

146

—

104

C₂×C₄

C₂×#10596842

yes

—

105

C₂×C₄

C₂×#10596842

yes

characteristic

106

C₈

—

292

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂²×#10596842

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

146

—

117

C₄

—

146

—

118

C₄

—

146

—

119

C₄

C₄⋊#10596842

yes

—

120

C₂

—

121

C₂

—

122

C₂

—

123

C₂

C₂×C₄⋊#10596842

yes

characteristic

124

C₂

#17989700

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10596842
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	C₄²×C₇₃	C₈
hypercenter	C₄²	#10596842
hypocenter	C₇₃	#1831
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄²

subgroup

G/H

center, Frattini

C₂²

C₂²×#10596842

commutator, socle

C₂²×C₇₃

C₂²×C₈

Fitting

C₄²×C₇₃

C₈

C₄²

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂² ◁ C₄²

N	H ≅ G/N	type
23. C₄×Dic₇₃	C₈	semidirect
24. C₄×Dic₇₃	C₈	semidirect
25. C₄²×C₇₃	C₈	semidirect
63. C₇₃	#1831	semidirect
88. C₄²	#10596842	semidirect

H ≅ G/N

type

23. C₄×Dic₇₃

C₈

semidirect

24. C₄×Dic₇₃

C₈

semidirect

25. C₄²×C₇₃

C₈

semidirect

63. C₇₃

#1831

semidirect

88. C₄²

#10596842

semidirect

Subgroups — #22627073

Conjugacy classes of subgroups

Complements