Group #22625431 — subgroups

Subgroups — D₇₃⋊#333 #22625431

Order 9344.

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

normal subgroups only

This group has 256 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	#17989588	C₂	1	2	yes	maximal
2	#17989447	C₂	1	4	yes	maximal, complemented
3	C₄⋊Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924036	—	2	2	no	—
5	#14556658	C₂²	1	4	yes	—
6	C₄⋊#10596833	—	2	2	no	—
7	C₂×Q₈×D₇₃	C₄	1	2	yes	—
8	#14556591	C₄	1	1	yes	characteristic
9	#14556590	—	2	2	no	—
10	#14556589	C₂²	1	2	yes	—
11	C₄⋊C₄×D₇₃	—	2	2	no	—
12	C₄²×D₇₃	C₂²	1	1	yes	characteristic
13	C₄⋊Q₈×C₇₃	C₄	1	1	yes	characteristic
14	#11924036	—	4	4	no	—
15	C₂×#10596833	—	2	4	no	—
16	C₂×Dic₁₄₆	—	2	2	no	—
17	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
18	Q₈×D₇₃	—	4	4	no	—
19	C₂×C₄×D₇₃	—	2	2	no	—
20	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×D₇₃	D₄	1	2	yes	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	#11924007	—	2	4	no	—
24	C₄×Dic₇₃	D₄	1	2	yes	—
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₂×Q₈×C₇₃	C₂×C₄	1	2	yes	—
27	C₄⋊C₄×C₇₃	—	2	2	no	—
28	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	Q₈×C₇₃	—	4	2	no	—
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₇₃	—	2	2	no	—
35	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
37	C₄×D₇₃	—	2	2	no	—
38	C₄×D₇₃	—	4	4	no	—
39	C₄×D₇₃	SD₁₆	1	4	yes	—
40	C₄×D₇₃	Q₁₆	1	4	yes	—
41	Dic₁₄₆	—	4	4	no	—
42	Dic₁₄₆	—	4	2	no	—
43	#10596833	—	4	4	no	—
44	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×D₇₃	#100	1	2	yes	—
46	C₂×D₇₃	#103	1	4	yes	—
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	—	4	2	no	—
49	C₄×C₇₃	#103	1	4	yes	—
50	Dic₇₃	—	2	1	no	—
51	Dic₇₃	—	4	2	no	—
52	Dic₇₃	C₂×SD₁₆	1	2	yes	—
53	Dic₇₃	C₂×Q₁₆	1	2	yes	—
54	C₂×C₇₃	C₂×#100	1	1	yes	characteristic
55	C₂×C₇₃	C₂×#103	1	2	yes	—
56	D₇₃	#333	1	4	yes	complemented
57	C₂×#333	—	73	1	no	maximal, Sylow
58	C₇₃	C₂×#333	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₄⋊Q₈	—	73	1	no	—
60	C₂×C₄⋊C₈	—	73	2	no	—
61	#333	—	73	4	no	—
62	C₂²×Q₈	—	73	2	no	—
63	C₂²×C₈	—	146	2	no	—
64	C₄⋊Q₈	—	73	2	no	—
65	C₄⋊Q₈	—	73	1	no	—
66	C₄⋊Q₈	—	146	2	no	—
67	C₄⋊Q₈	#64408	1	1	yes	characteristic
68	C₂×C₄⋊C₄	—	146	2	no	—
69	C₂×C₄²	—	73	1	no	—
70	C₄⋊C₈	—	73	4	no	—
71	C₄⋊C₈	—	146	2	no	—
72	C₂×Q₈	—	292	4	no	—
73	C₂×Q₈	—	73	2	no	—
74	C₂×Q₈	—	146	2	no	—
75	C₂×Q₈	C₂×#64408	1	2	yes	—
76	C₂²×C₄	—	73	2	no	—
77	C₂²×C₄	—	73	1	no	—
78	C₂²×C₄	—	146	2	no	—
79	C₂×C₈	—	292	4	no	—
80	C₂×C₈	—	146	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	146	4	no	—
83	C₄⋊C₄	—	146	2	no	—
84	C₄²	—	73	2	no	—
85	C₄²	—	73	1	no	—
86	C₄²	C₂×#64408	1	1	yes	characteristic
87	C₂³	—	73	1	no	—
88	Q₈	—	4	2	no	—
89	Q₈	—	292	2	no	—
90	Q₈	—	292	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	292	4	no	—
93	C₂×C₄	—	73	2	no	—
94	C₂×C₄	—	73	4	no	—
95	C₂×C₄	—	73	4	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	—	146	2	no	—
99	C₂×C₄	C₂²⋊#64408	1	2	yes	—
100	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
101	C₈	—	292	4	no	—
102	C₂²	—	73	2	no	—
103	C₂²	—	73	4	no	—
104	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	4	2	no	—
107	C₄	—	292	2	no	—
108	C₄	—	73	2	no	—
109	C₄	—	73	2	no	—
110	C₄	—	146	1	no	—
111	C₄	#14556654	1	4	yes	—
112	C₂	—	73	4	no	—
113	C₂	D₇₃⋊#100	1	1	yes	characteristic
114	C₂	C₂×#14556654	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989588

C₂

yes

maximal

#17989447

C₂

yes

maximal, complemented

C₄⋊Q₈×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924036

—

#14556658

C₂²

yes

—

C₄⋊#10596833

—

C₂×Q₈×D₇₃

C₄

yes

—

#14556591

C₄

yes

characteristic

#14556590

—

#14556589

C₂²

yes

—

C₄⋊C₄×D₇₃

—

C₄²×D₇₃

C₂²

yes

characteristic

C₄⋊Q₈×C₇₃

C₄

yes

characteristic

#11924036

—

C₂×#10596833

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

Q₈×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

#11924007

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×Q₈×C₇₃

C₂×C₄

yes

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

SD₁₆

yes

—

C₄×D₇₃

Q₁₆

yes

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₃

#100

yes

—

C₂×D₇₃

#103

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#103

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

C₂×SD₁₆

yes

—

Dic₇₃

C₂×Q₁₆

yes

—

C₂×C₇₃

C₂×#100

yes

characteristic

C₂×C₇₃

C₂×#103

yes

—

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

C₂×C₄⋊C₈

—

#333

—

C₂²×Q₈

—

C₂²×C₈

—

146

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

#64408

yes

characteristic

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂×Q₈

—

292

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂×#64408

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

292

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

—

100

C₂×C₄

C₂²×#64408

yes

characteristic

101

C₈

—

292

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×C₂²⋊#64408

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

292

—

108

C₄

—

109

C₄

—

110

C₄

—

146

—

111

C₄

#14556654

yes

—

112

C₂

—

113

C₂

D₇₃⋊#100

yes

characteristic

114

C₂

C₂×#14556654

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄⋊Q₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	C₄⋊Q₈	#64408
hypocenter	C₇₃	C₂×#333
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄⋊Q₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₄⋊Q₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

N	H ≅ G/N	type
2. #17989447	C₂	semidirect
56. D₇₃	#333	semidirect
58. C₇₃	C₂×#333	semidirect

H ≅ G/N

type

2. #17989447

C₂

semidirect

56. D₇₃

#333

semidirect

58. C₇₃

C₂×#333

semidirect

Subgroups — D₇₃⋊#333 #22625431

Conjugacy classes of subgroups

Complements

Subgroups — D73⋊#333 #22625431

Conjugacy classes of subgroups

Complements

Subgroups — D₇₃⋊#333 #22625431