Group #22608513 — subgroups

Subgroups — #330×D₇₃ #22608513

Order 9344.

232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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	#125×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#97×D₇₃	C₂	1	2	yes	maximal
3	#17988329	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988328	C₂	1	2	yes	maximal, complemented
5	#330×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₃	—	2	2	no	—
7	#14556583	C₂²	1	1	yes	characteristic
8	#14556582	C₄	1	2	yes	—
9	#14556581	—	2	2	no	—
10	C₄⋊C₄×D₇₃	—	2	2	no	—
11	C₄⋊C₄×D₇₃	C₄	1	2	yes	—
12	C₄²×D₇₃	C₂²	1	1	yes	characteristic
13	#14556502	C₂²	1	2	yes	—
14	#14556501	—	2	2	no	—
15	#125×C₇₃	C₂²	1	1	yes	characteristic
16	#97×C₇₃	C₂²	1	2	yes	—
17	C₂×C₄×D₇₃	—	2	2	no	—
18	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₇₃	D₄	1	2	yes	—
20	C₂×#10596831	—	2	2	no	—
21	C₈×D₇₃	—	2	8	no	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
24	#11924007	—	2	2	no	—
25	#11924007	—	2	2	no	—
26	#11924007	—	2	2	no	—
27	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₇₃	D₄	1	2	yes	—
29	C₂×C₈×C₇₃	—	2	2	no	—
30	C₄⋊C₄×C₇₃	—	2	2	no	—
31	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
32	C₄²×C₇₃	C₂³	1	1	yes	characteristic
33	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	—	2	2	no	—
35	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
37	C₂×Dic₇₃	—	2	2	no	—
38	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₄×D₇₃	—	2	2	no	—
41	C₄×D₇₃	—	2	4	no	—
42	C₄×D₇₃	—	4	4	no	—
43	C₈×C₇₃	—	2	4	no	—
44	#10596831	—	2	4	no	—
45	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×D₇₃	#101	1	2	yes	—
47	C₂×D₇₃	#104	1	4	yes	—
48	C₄×C₇₃	—	2	1	no	—
49	C₄×C₇₃	—	2	2	no	—
50	C₄×C₇₃	—	4	2	no	—
51	Dic₇₃	—	2	1	no	—
52	Dic₇₃	—	2	2	no	—
53	Dic₇₃	—	4	2	no	—
54	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
55	C₂×C₇₃	C₂×#104	1	2	yes	—
56	D₇₃	#330	1	4	yes	direct product factor
57	C₂×#330	—	73	1	no	maximal, Sylow
58	C₇₃	C₂×#330	1	1	yes	characteristic, complemented, Sylow
59	C₂×#125	—	73	1	no	—
60	C₂×#97	—	73	2	no	—
61	#330	—	73	1	no	—
62	#330	—	73	2	no	—
63	#330	D₇₃	1	1	yes	characteristic, direct product factor
64	C₂²×C₈	—	146	2	no	—
65	#125	—	73	2	no	—
66	#125	—	73	1	no	—
67	#125	—	146	2	no	—
68	#125	C₂×D₇₃	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	73	2	no	—
70	C₂×C₄⋊C₄	—	146	2	no	—
71	C₂×C₄²	—	73	1	no	—
72	#97	—	73	2	no	—
73	#97	—	146	2	no	—
74	#97	C₂×D₇₃	1	2	yes	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	—	73	2	no	—
77	C₂²×C₄	—	146	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	146	8	no	—
80	C₂×C₈	—	146	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	73	2	no	—
83	C₄⋊C₄	—	146	2	no	—
84	C₄⋊C₄	—	146	2	no	—
85	C₄⋊C₄	—	146	2	no	—
86	C₄⋊C₄	—	146	2	no	—
87	C₄⋊C₄	C₄×D₇₃	1	2	yes	—
88	C₄²	—	73	1	no	—
89	C₄²	—	73	2	no	—
90	C₄²	C₂²×D₇₃	1	1	yes	characteristic
91	C₂³	—	73	1	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	292	4	no	—
94	C₂×C₄	—	73	1	no	—
95	C₂×C₄	—	73	2	no	—
96	C₂×C₄	—	146	4	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	—	146	2	no	—
99	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
100	C₂×C₄	D₄×D₇₃	1	2	yes	—
101	C₈	—	2	4	no	—
102	C₈	—	146	4	no	—
103	C₂²	—	73	2	no	—
104	C₂²	—	73	4	no	—
105	C₂²	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	2	no	—
108	C₄	—	4	2	no	—
109	C₄	—	292	2	no	—
110	C₄	—	146	1	no	—
111	C₄	—	146	2	no	—
112	C₂	—	73	4	no	—
113	C₂	#101×D₇₃	1	1	yes	characteristic
114	C₂	#104×D₇₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#125×D₇₃

C₂

yes

maximal, characteristic

#97×D₇₃

C₂

yes

maximal

#17988329

C₂

yes

maximal, characteristic, complemented

#17988328

C₂

yes

maximal, complemented

#330×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₃

—

#14556583

C₂²

yes

characteristic

#14556582

C₄

yes

—

#14556581

—

C₄⋊C₄×D₇₃

—

C₄⋊C₄×D₇₃

C₄

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#14556502

C₂²

yes

—

#14556501

—

#125×C₇₃

C₂²

yes

characteristic

#97×C₇₃

C₂²

yes

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

—

C₂×#10596831

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

#11924007

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₃

#101

yes

—

C₂×D₇₃

#104

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

C₂×#101

yes

characteristic

C₂×C₇₃

C₂×#104

yes

—

D₇₃

#330

yes

direct product factor

C₂×#330

—

maximal, Sylow

C₇₃

C₂×#330

yes

characteristic, complemented, Sylow

C₂×#125

—

C₂×#97

—

#330

—

#330

—

#330

D₇₃

yes

characteristic, direct product factor

C₂²×C₈

—

146

—

#125

—

#125

—

#125

—

146

—

#125

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

#97

—

#97

—

146

—

#97

C₂×D₇₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₄×D₇₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

100

C₂×C₄

D₄×D₇₃

yes

—

101

C₈

—

102

C₈

—

146

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₂²⋊C₄×D₇₃

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

292

—

110

C₄

—

146

—

111

C₄

—

146

—

112

C₂

—

113

C₂

#101×D₇₃

yes

characteristic

114

C₂

#104×D₇₃

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#330×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#330	D₇₃
hypocenter	C₇₃	C₂×#330
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#330×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #17988329	C₂	semidirect
4. #17988328	C₂	semidirect
5. #330×C₇₃	C₂	semidirect
56. D₇₃	#330	direct (N × H)
58. C₇₃	C₂×#330	semidirect
63. #330	D₇₃	direct (N × H)

H ≅ G/N

type

3. #17988329

C₂

semidirect

4. #17988328

C₂

semidirect

5. #330×C₇₃

C₂

semidirect

56. D₇₃

#330

direct (N × H)

58. C₇₃

C₂×#330

semidirect

63. #330

D₇₃

direct (N × H)

Subgroups — #330×D₇₃ #22608513

Conjugacy classes of subgroups

Complements

Subgroups — #330×D73 #22608513

Conjugacy classes of subgroups

Complements

Subgroups — #330×D₇₃ #22608513