Group #22624968 — subgroups

Subgroups — #22624968

Order 9344.

160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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×#14556664	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924036	C₄	1	1	yes	characteristic
5	C₂×C₄×#64408	C₄	1	1	yes	characteristic
6	#14556664	—	2	1	no	—
7	#14556664	—	2	1	no	—
8	C₂×#11924031	C₄	1	2	yes	complemented
9	C₈×#64408	—	2	1	no	—
10	C₈×#64408	—	2	1	no	—
11	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
12	C₂×#11924003	C₄	1	1	yes	characteristic, complemented
13	C₁₆×D₇₃	—	2	1	no	—
14	C₁₆×D₇₃	—	2	1	no	—
15	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
16	C₂²×#64408	C₈	1	2	yes	—
17	#11924036	—	2	1	no	—
18	#11924036	—	2	1	no	—
19	C₂×#10596833	C₈	1	2	yes	—
20	C₄×#64408	—	2	1	no	—
21	C₄×#64408	—	2	1	no	—
22	#11924031	—	2	2	no	—
23	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
25	C₈×D₇₃	D₄	1	1	yes	characteristic
26	C₈×D₇₃	D₄	1	1	yes	characteristic
27	C₈×D₇₃	D₄	1	1	yes	characteristic
28	C₈×D₇₃	Q₈	1	1	yes	characteristic
29	#11924003	—	2	1	no	—
30	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₁₆×C₇₃	—	2	1	no	—
32	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
33	C₂×#64408	—	2	2	no	—
34	C₂×#64408	—	2	2	no	—
35	C₂×#64408	C₁₆	1	4	yes	complemented
36	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
37	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
38	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₇₃	M₁₆	1	1	yes	characteristic
41	C₄×D₇₃	M₁₆	1	1	yes	characteristic
42	#10596833	—	2	2	no	—
43	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
45	#10596831	C₂²⋊C₄	1	1	yes	characteristic
46	#10596831	C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
48	C₂×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
49	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
50	C₂×D₇₃	C₂×C₁₆	1	2	yes	—
51	C₂×D₇₃	M₃₂	1	2	yes	—
52	#64408	—	2	4	no	—
53	C₄×C₇₃	#95	1	1	yes	characteristic
54	C₄×C₇₃	#97	1	1	yes	characteristic
55	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
56	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₇₃	#336	1	1	yes	characteristic
58	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
59	C₂×C₇₃	#346	1	1	yes	characteristic
60	D₇₃	C₂²⋊C₁₆	1	2	yes	—
61	D₇₃	C₄⋊C₁₆	1	2	yes	—
62	#1374	—	73	1	no	maximal, Sylow
63	C₇₃	#1374	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₁₆	—	73	1	no	—
65	C₂²×C₁₆	—	73	1	no	—
66	C₂×C₄×C₈	—	73	1	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂×C₄²	—	73	1	no	—
70	C₂×C₁₆	—	73	2	no	—
71	C₂×C₁₆	—	73	1	no	—
72	C₂×C₁₆	—	146	1	no	—
73	C₂×C₁₆	—	146	1	no	—
74	C₂×C₁₆	—	146	1	no	—
75	C₂×C₁₆	—	146	1	no	—
76	C₂×C₁₆	#64408	1	1	yes	characteristic, complemented
77	C₄×C₈	—	146	1	no	—
78	C₄×C₈	—	146	1	no	—
79	C₂²×C₄	—	73	1	no	—
80	C₂²×C₄	—	73	2	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	73	2	no	—
87	C₂×C₈	—	146	1	no	—
88	C₂×C₈	—	146	1	no	—
89	C₂×C₈	C₂×#64408	1	1	yes	characteristic
90	C₄²	—	146	1	no	—
91	C₄²	—	146	1	no	—
92	C₁₆	—	2	1	no	—
93	C₁₆	—	146	2	no	—
94	C₁₆	—	146	1	no	—
95	C₂³	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	4	no	—
102	C₂×C₄	—	146	2	no	—
103	C₂×C₄	—	146	2	no	—
104	C₂×C₄	C₄×#64408	1	1	yes	characteristic
105	C₈	—	73	1	no	—
106	C₈	—	73	1	no	—
107	C₈	—	146	2	no	—
108	C₈	C₂²⋊#64408	1	1	yes	characteristic
109	C₈	C₄⋊#64408	1	1	yes	characteristic
110	C₂²	—	73	1	no	—
111	C₂²	—	73	1	no	—
112	C₂²	—	73	2	no	—
113	C₂²	—	73	2	no	—
114	C₂²	C₈×#64408	1	1	yes	characteristic
115	C₄	—	73	1	no	—
116	C₄	—	73	1	no	—
117	C₄	—	146	4	no	—
118	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
119	C₄	#14556645	1	1	yes	characteristic
120	C₂	—	73	2	no	—
121	C₂	—	73	2	no	—
122	C₂	#17989452	1	1	yes	characteristic
123	C₂	C₁₆×#64408	1	1	yes	characteristic
124	C₂	#17989474	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556664

C₂

yes

maximal, characteristic

C₂×C₈×#64408

C₂

yes

maximal, characteristic

C₂×C₁₆×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924036

C₄

yes

characteristic

C₂×C₄×#64408

C₄

yes

—

—

C₄

yes

complemented

C₈×#64408

—

C₈×#64408

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₂×#11924003

C₄

yes

characteristic, complemented

C₁₆×D₇₃

—

C₁₆×D₇₃

—

C₂×C₁₆×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

C₈

yes

—

#11924036

—

#11924036

—

C₂×#10596833

C₈

yes

—

C₄×#64408

—

C₄×#64408

—

#11924031

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

#11924003

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

—

C₂²×D₇₃

C₂×C₈

yes

—

—

C₁₆

yes

complemented

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

#10596833

—

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

#10596831

C₂²⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

C₂×C₁₆

yes

—

C₂×D₇₃

M₃₂

yes

—

#64408

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

#336

yes

characteristic

C₂×C₇₃

C₄×C₁₆

yes

characteristic

C₂×C₇₃

#346

yes

characteristic

D₇₃

C₂²⋊C₁₆

yes

—

D₇₃

C₄⋊C₁₆

yes

—

#1374

—

maximal, Sylow

C₇₃

#1374

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₂×C₁₆

#64408

yes

characteristic, complemented

C₄×C₈

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄²

—

146

—

C₄²

—

146

—

C₁₆

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

146

—

103

C₂×C₄

—

146

—

104

C₂×C₄

C₄×#64408

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

146

—

108

C₈

C₂²⋊#64408

yes

characteristic

109

C₈

C₄⋊#64408

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₈×#64408

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

146

—

118

C₄

(C₂×#64408)⋊C₄

yes

characteristic

119

C₄

#14556645

yes

characteristic

120

C₂

—

121

C₂

—

122

C₂

#17989452

yes

characteristic

123

C₂

C₁₆×#64408

yes

characteristic

124

C₂

#17989474

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#64408
commutator	C₂×C₇₃	C₄×C₁₆
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₄×C₈
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	#1374
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂×#64408

commutator

C₂×C₇₃

C₄×C₁₆

Fitting

C₂×C₁₆×C₇₃

C₄

socle

C₂²×C₇₃

C₄×C₈

C₂×C₁₆

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
8. C₂×#11924031	C₄	semidirect
12. C₂×#11924003	C₄	semidirect
15. C₂×C₁₆×C₇₃	C₄	semidirect
35. C₂×#64408	C₁₆	semidirect
63. C₇₃	#1374	semidirect
76. C₂×C₁₆	#64408	semidirect

H ≅ G/N

type

8. C₂×#11924031

C₄

semidirect

12. C₂×#11924003

C₄

semidirect

15. C₂×C₁₆×C₇₃

C₄

semidirect

35. C₂×#64408

C₁₆

semidirect

63. C₇₃

#1374

semidirect

76. C₂×C₁₆

#64408

semidirect

Subgroups — #22624968

Conjugacy classes of subgroups

Complements