Group #22625150 — subgroups

Subgroups — #22625150

Order 9344.

190 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 84 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	#17989604	C₂	1	2	yes	maximal
2	#17989429	C₂	1	2	yes	maximal, complemented
3	#17989428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#10596833	C₂	1	1	yes	maximal, characteristic, complemented
5	M₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556658	C₄	1	4	yes	—
7	C₂²⋊#10596833	C₄	1	4	yes	—
8	C₄×#10596833	C₂²	1	2	yes	—
9	C₄×#10596833	C₂²	1	2	yes	—
10	C₂×#11924012	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
12	#14556501	C₄	1	1	yes	characteristic
13	#14556501	C₄	1	1	yes	characteristic
14	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
15	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
17	C₂×#10596833	C₂×C₄	1	4	yes	—
18	C₂×#10596833	C₂×C₄	1	4	yes	—
19	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
20	#11924012	—	2	2	no	—
21	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
27	M₁₆×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₇₃	C₄²	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	1	no	—
32	C₂×C₄×C₇₃	—	2	1	no	—
33	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	—	2	4	no	—
36	C₂×Dic₇₃	C₄²	1	2	yes	—
37	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
38	#10596833	—	2	4	no	—
39	#10596833	—	2	4	no	—
40	C₈×C₇₃	—	2	1	no	—
41	C₈×C₇₃	M₁₆	1	2	yes	—
42	#10596831	—	2	1	no	—
43	#10596831	M₁₆	1	2	yes	—
44	C₂²×C₇₃	—	2	1	no	—
45	C₂²×C₇₃	—	2	2	no	—
46	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
50	Dic₇₃	—	2	2	no	—
51	Dic₇₃	#131	1	4	yes	—
52	C₂×C₇₃	—	4	1	no	—
53	C₂×C₇₃	C₄×M₁₆	1	1	yes	characteristic
54	C₂×C₇₃	#405	1	2	yes	—
55	#1453	—	73	1	no	maximal, Sylow
56	C₇₃	#1453	1	1	yes	characteristic, complemented, Sylow
57	#431	—	73	2	no	—
58	C₄×M₁₆	—	73	1	no	—
59	#322	—	73	1	no	—
60	#322	—	73	2	no	—
61	C₈²	—	73	1	no	—
62	C₂×M₁₆	—	73	1	no	—
63	C₂×M₁₆	#64408	1	1	yes	characteristic
64	C₂×C₄²	—	73	1	no	—
65	C₄⋊C₈	—	73	4	no	—
66	C₂²⋊C₈	—	73	4	no	—
67	#97	—	73	1	no	—
68	#97	—	73	1	no	—
69	C₄×C₈	—	73	2	no	—
70	C₄×C₈	—	73	2	no	—
71	C₄×C₈	—	73	1	no	—
72	C₄×C₈	—	73	1	no	—
73	C₂²×C₄	—	73	2	no	—
74	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
75	M₁₆	—	2	2	no	—
76	M₁₆	—	146	2	no	—
77	C₂×C₈	—	73	1	no	—
78	C₂×C₈	—	73	4	no	—
79	C₂×C₈	—	73	4	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	C₂×#64408	1	1	yes	characteristic
82	C₂×C₈	C₂×#64408	1	1	yes	characteristic
83	C₄²	—	73	2	no	—
84	C₄²	—	73	1	no	—
85	C₄²	—	73	1	no	—
86	C₂³	C₄×#64408	1	1	yes	characteristic
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	73	2	no	—
90	C₂×C₄	—	73	2	no	—
91	C₂×C₄	—	146	4	no	—
92	C₂×C₄	C₄×#64408	1	1	yes	characteristic
93	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	73	2	no	—
96	C₈	—	146	4	no	—
97	C₈	—	146	4	no	—
98	C₈	—	146	1	no	—
99	C₈	#11924037	1	2	yes	—
100	C₂²	—	2	1	no	—
101	C₂²	—	2	2	no	—
102	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	73	4	no	—
105	C₄	—	146	2	no	—
106	C₄	C₂×#11924037	1	1	yes	characteristic
107	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
108	C₂	—	4	1	no	—
109	C₂	C₄×#11924037	1	1	yes	characteristic
110	C₂	#17989553	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989604

C₂

yes

maximal

#17989429

C₂

yes

maximal, complemented

#17989428

C₂

yes

maximal, characteristic, complemented

C₈×#10596833

C₂

yes

maximal, characteristic, complemented

M₁₆×Dic₇₃

C₂

yes

maximal, characteristic

#14556658

C₄

yes

—

C₂²⋊#10596833

C₄

yes

—

C₄×#10596833

C₂²

yes

—

C₄×#10596833

C₂²

yes

—

C₂×#11924012

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556501

C₄

yes

characteristic

#14556501

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

—

#11924012

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄²

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

#10596833

—

#10596833

—

C₈×C₇₃

—

C₈×C₇₃

M₁₆

yes

—

#10596831

—

#10596831

M₁₆

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

#131

yes

—

C₂×C₇₃

—

C₂×C₇₃

C₄×M₁₆

yes

characteristic

C₂×C₇₃

#405

yes

—

#1453

—

maximal, Sylow

C₇₃

#1453

yes

characteristic, complemented, Sylow

#431

—

C₄×M₁₆

—

#322

—

#322

—

C₈²

—

C₂×M₁₆

—

C₂×M₁₆

#64408

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₄×#64408

yes

characteristic

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

C₈

—

146

—

C₈

—

146

—

C₈

—

146

—

C₈

#11924037

yes

—

100

C₂²

—

101

C₂²

—

102

C₂²

C₂×C₄×#64408

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

146

—

106

C₄

C₂×#11924037

yes

characteristic

107

C₄

D₇₃⋊M₁₆

yes

characteristic

108

C₂

—

109

C₂

C₄×#11924037

yes

characteristic

110

C₂

#17989553

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂×C₄²
Fitting	C₂×M₁₆×C₇₃	C₄
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	#1453
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator, socle

C₂²×C₇₃

C₂×C₄²

Fitting

C₂×M₁₆×C₇₃

C₄

C₂×M₁₆

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
2. #17989429	C₂	semidirect
3. #17989428	C₂	semidirect
4. C₈×#10596833	C₂	semidirect
56. C₇₃	#1453	semidirect

H ≅ G/N

type

2. #17989429

C₂

semidirect

3. #17989428

C₂

semidirect

4. C₈×#10596833

C₂

semidirect

56. C₇₃

#1453

semidirect

Subgroups — #22625150

Conjugacy classes of subgroups

Complements