Group #22624787 — subgroups

Subgroups — #22624787

Order 9344.

126 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 42 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	#17989610	C₂	1	1	yes	maximal, characteristic
2	#17989606	C₂	1	1	yes	maximal, characteristic
3	#17988642	C₂	1	1	yes	maximal, characteristic
4	#14556658	—	2	1	no	—
5	C₄⋊#10596833	—	2	1	no	—
6	#14556648	—	2	1	no	—
7	#14556648	C₄	1	2	yes	—
8	#14556646	—	2	1	no	—
9	C₄×#10596833	C₄	1	2	yes	—
10	C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	#14556520	—	2	1	no	—
12	#14556503	—	2	1	no	—
13	#14556502	C₄	1	1	yes	characteristic
14	#97×C₇₃	C₄	1	1	yes	characteristic
15	C₂×#10596833	—	2	2	no	—
16	C₂×#10596833	—	2	2	no	—
17	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
19	C₂×C₄×D₇₃	Q₈	1	1	yes	characteristic
20	C₂×#10596831	—	2	1	no	—
21	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	D₄	1	1	yes	characteristic
23	C₄×Dic₇₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	—	2	1	no	—
25	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
33	C₄×D₇₃	—	2	2	no	—
34	C₄×D₇₃	—	4	1	no	—
35	C₄×D₇₃	—	4	1	no	—
36	#10596833	—	4	2	no	—
37	#10596833	—	4	2	no	—
38	C₈×C₇₃	—	4	1	no	—
39	#10596831	—	4	1	no	—
40	C₂²×C₇₃	#95	1	1	yes	characteristic
41	C₂×D₇₃	—	2	1	no	—
42	C₂×D₇₃	—	2	1	no	—
43	C₂×D₇₃	—	2	1	no	—
44	C₄×C₇₃	—	2	1	no	—
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	—	2	1	no	—
47	Dic₇₃	—	2	1	no	—
48	Dic₇₃	—	2	1	no	—
49	Dic₇₃	#108	1	2	yes	—
50	C₂×C₇₃	H(3,ℤ/4)	1	1	yes	characteristic
51	C₂×C₇₃	#341	1	1	yes	characteristic
52	C₂×C₇₃	#344	1	1	yes	characteristic
53	D₇₃	—	4	1	no	—
54	#1287	—	73	1	no	maximal, Sylow
55	C₇₃	#1287	1	1	yes	characteristic, complemented, Sylow
56	#432	—	73	1	no	—
57	#432	—	73	1	no	—
58	#431	—	73	1	no	—
59	C₂×C₄²	—	73	1	no	—
60	C₄⋊C₈	—	146	1	no	—
61	C₄⋊C₈	—	146	1	no	—
62	C₄⋊C₈	—	146	1	no	—
63	C₂²⋊C₈	—	73	2	no	—
64	C₂²⋊C₈	—	146	1	no	—
65	C₂²⋊C₈	—	146	1	no	—
66	#97	—	73	1	no	—
67	#97	—	146	1	no	—
68	#97	#64408	1	1	yes	characteristic
69	C₄×C₈	—	73	2	no	—
70	C₂²×C₄	—	73	1	no	—
71	C₂²×C₄	—	73	1	no	—
72	C₂²×C₄	—	73	1	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	146	2	no	—
75	C₂×C₈	—	146	2	no	—
76	C₂×C₈	—	146	1	no	—
77	C₄²	—	73	1	no	—
78	C₄²	—	73	1	no	—
79	C₄²	—	73	1	no	—
80	C₄²	C₂×#64408	1	1	yes	characteristic
81	C₂³	—	73	1	no	—
82	C₂×C₄	—	292	1	no	—
83	C₂×C₄	—	292	1	no	—
84	C₂×C₄	—	73	1	no	—
85	C₂×C₄	—	73	1	no	—
86	C₂×C₄	—	73	1	no	—
87	C₂×C₄	—	146	2	no	—
88	C₂×C₄	C₄×#64408	1	1	yes	characteristic
89	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
90	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
91	C₈	—	4	1	no	—
92	C₈	—	292	1	no	—
93	C₈	—	292	2	no	—
94	C₈	—	292	2	no	—
95	C₂²	—	146	1	no	—
96	C₂²	—	146	1	no	—
97	C₂²	—	146	1	no	—
98	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	2	1	no	—
101	C₄	—	2	1	no	—
102	C₄	—	73	2	no	—
103	C₄	—	146	1	no	—
104	C₄	—	146	1	no	—
105	C₂	—	292	1	no	—
106	C₂	#17989454	1	1	yes	characteristic
107	C₂	#17989462	1	1	yes	characteristic
108	C₂	#17989470	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989610

C₂

yes

maximal, characteristic

#17989606

C₂

yes

maximal, characteristic

#17988642

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

—

#14556646

—

C₄×#10596833

C₄

yes

—

C₄²×D₇₃

C₂²

yes

—

—

C₄

yes

characteristic

#97×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×#10596833

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

Q₈

yes

characteristic

C₂×#10596831

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

#10596833

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#95

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#108

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1287

—

maximal, Sylow

C₇₃

#1287

yes

characteristic, complemented, Sylow

#432

—

#432

—

#431

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

C₂²⋊C₈

—

146

—

C₂²⋊C₈

—

146

—

#97

—

#97

—

146

—

#97

#64408

yes

characteristic

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

292

—

C₈

—

292

—

C₈

—

292

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

(C₂×#64408)⋊C₄

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

146

—

104

C₄

—

146

—

105

C₂

—

292

—

106

C₂

#17989454

yes

characteristic

107

C₂

#17989462

yes

characteristic

108

C₂

#17989470

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#64408)⋊C₄
commutator	C₂×C₄×C₇₃	C₄²
Frattini	C₄²	C₂×#64408
Fitting	#97×C₇₃	C₄
socle	C₂²×C₇₃	#95
hypercenter	#97	#64408
hypocenter	C₇₃	#1287
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

(C₂×#64408)⋊C₄

commutator

C₂×C₄×C₇₃

C₄²

Frattini

C₄²

C₂×#64408

Fitting

#97×C₇₃

C₄

C₂²×C₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
55. C₇₃	#1287	semidirect

H ≅ G/N

type

55. C₇₃

#1287

semidirect

Subgroups — #22624787

Conjugacy classes of subgroups

Complements