Group #22607759 — subgroups

Subgroups — #22607759

Order 9344.

168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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	#17988640	C₂	1	1	yes	maximal, characteristic
2	#17988433	C₂	1	1	yes	maximal, characteristic
3	#431×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Dic₇₃	C₄	1	2	yes	—
5	C₄⋊#10596831	—	2	1	no	—
6	C₂²⋊#10596831	—	2	1	no	—
7	C₄×#10596831	C₄	1	2	yes	complemented
8	#14556498	—	2	1	no	—
9	#14556498	—	2	1	no	—
10	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₇₃	—	2	1	no	—
12	C₂²⋊C₈×C₇₃	—	2	1	no	—
13	C₄×C₈×C₇₃	C₄	1	2	yes	complemented
14	C₂²×Dic₇₃	—	2	2	no	—
15	C₂×#10596831	—	2	2	no	—
16	C₄×Dic₇₃	—	2	2	no	—
17	C₄×Dic₇₃	C₈	1	4	yes	complemented
18	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	—	2	2	no	—
22	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₇₃	D₄	1	1	yes	characteristic
25	C₄²×C₇₃	Q₈	1	1	yes	characteristic
26	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	—	4	1	no	—
29	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₇₃	M₁₆	1	2	yes	—
37	C₂×Dic₇₃	—	2	4	no	—
38	C₂×Dic₇₃	—	4	2	no	—
39	C₂×Dic₇₃	—	4	2	no	—
40	C₈×C₇₃	—	4	2	no	—
41	#10596831	—	4	2	no	—
42	C₂²×C₇₃	—	2	1	no	—
43	C₂²×C₇₃	—	2	1	no	—
44	C₂²×C₇₃	#95	1	1	yes	characteristic
45	C₂²×C₇₃	C₂²⋊C₈	1	2	yes	—
46	C₄×C₇₃	—	2	1	no	—
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	—	2	1	no	—
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
51	C₄×C₇₃	#97	1	1	yes	characteristic
52	C₄×C₇₃	C₄⋊C₈	1	2	yes	—
53	Dic₇₃	—	4	4	no	—
54	C₂×C₇₃	—	2	2	no	—
55	C₂×C₇₃	#336	1	1	yes	characteristic
56	C₂×C₇₃	H(3,ℤ/4)	1	1	yes	characteristic
57	C₂×C₇₃	H(3,ℤ/4)	1	1	yes	characteristic
58	#1274	—	73	1	no	maximal, Sylow
59	C₇₃	#1274	1	1	yes	characteristic, complemented, Sylow
60	#431	—	73	1	no	—
61	#431	D₇₃	1	1	yes	characteristic
62	#376	—	73	1	no	—
63	C₂×C₄²	—	73	2	no	—
64	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
65	C₄⋊C₈	—	2	1	no	—
66	C₄⋊C₈	—	146	1	no	—
67	C₂²⋊C₈	—	2	1	no	—
68	C₂²⋊C₈	—	146	1	no	—
69	C₄×C₈	—	73	2	no	—
70	C₄×C₈	Dic₇₃	1	2	yes	complemented
71	#95	—	146	1	no	—
72	#95	—	146	1	no	—
73	C₂²×C₄	—	146	2	no	—
74	C₂²×C₄	C₄×D₇₃	1	1	yes	characteristic
75	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
76	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	146	2	no	—
79	C₄²	—	73	4	no	—
80	C₄²	—	146	2	no	—
81	C₄²	Dic₁₄₆	1	1	yes	characteristic
82	C₄²	C₄×D₇₃	1	1	yes	characteristic
83	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
84	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
85	C₂³	#11924005	1	1	yes	characteristic
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	292	2	no	—
89	C₂×C₄	—	292	2	no	—
90	C₂×C₄	—	146	4	no	—
91	C₂×C₄	C₄×Dic₇₃	1	1	yes	characteristic
92	C₂×C₄	#11924005	1	1	yes	characteristic
93	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
94	C₂×C₄	#11924007	1	1	yes	characteristic
95	C₂×C₄	#11924007	1	1	yes	characteristic
96	C₂×C₄	C₄⋊Dic₇₃	1	1	yes	characteristic
97	C₂×C₄	C₈×D₇₃	1	2	yes	—
98	C₂×C₄	#11924011	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	292	2	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	2	1	no	—
103	C₂²	#14556498	1	1	yes	characteristic
104	C₂²	#14556503	1	2	yes	—
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	292	4	no	—
110	C₄	C₈×Dic₇₃	1	1	yes	characteristic
111	C₄	#14556501	1	1	yes	characteristic
112	C₄	#14556520	1	2	yes	—
113	C₂	—	2	2	no	—
114	C₂	#17988341	1	1	yes	characteristic
115	C₂	#17988343	1	1	yes	characteristic
116	C₂	#17988344	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988640

C₂

yes

maximal, characteristic

#17988433

C₂

yes

maximal, characteristic

#431×C₇₃

C₂

yes

maximal, characteristic

C₂×C₄×Dic₇₃

C₄

yes

—

C₄⋊#10596831

—

C₂²⋊#10596831

—

C₄×#10596831

C₄

yes

complemented

#14556498

—

#14556498

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₄

yes

complemented

C₂²×Dic₇₃

—

C₂×#10596831

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₈

yes

complemented

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

Q₈

yes

characteristic

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

M₁₆

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#95

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

#97

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#431

—

#431

D₇₃

yes

characteristic

#376

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

C₂²⋊C₈

—

146

—

C₄×C₈

—

C₄×C₈

Dic₇₃

yes

complemented

#95

—

146

—

#95

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₄×D₇₃

yes

characteristic

C₂²×C₄

D₂₉₂

yes

characteristic

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

146

—

C₄²

Dic₁₄₆

yes

characteristic

C₄²

C₄×D₇₃

yes

characteristic

C₄²

C₂×Dic₇₃

yes

characteristic

C₄²

C₂²⋊D₇₃

yes

characteristic

C₂³

#11924005

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

C₄×Dic₇₃

yes

characteristic

C₂×C₄

#11924005

yes

characteristic

C₂×C₄

C₂²⋊Dic₇₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₄⋊Dic₇₃

yes

characteristic

C₂×C₄

C₈×D₇₃

yes

—

C₂×C₄

#11924011

yes

—

C₈

—

100

C₈

—

292

—

101

C₂²

—

102

C₂²

—

103

C₂²

#14556498

yes

characteristic

104

C₂²

#14556503

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

292

—

110

C₄

C₈×Dic₇₃

yes

characteristic

111

C₄

#14556501

yes

characteristic

112

C₄

#14556520

yes

—

113

C₂

—

114

C₂

#17988341

yes

characteristic

115

C₂

#17988343

yes

characteristic

116

C₂

#17988344

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄×Dic₇₃
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₂×C₄²	C₂×D₇₃
Fitting	#431×C₇₃	C₂
socle	C₂²×C₇₃	#95
hypercenter	#431	D₇₃
hypocenter	C₇₃	#1274
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #431

subgroup

G/H

center

C₂×C₄

C₄×Dic₇₃

commutator

C₄×C₇₃

C₄×C₈

Frattini

C₂×C₄²

C₂×D₇₃

Fitting

#431×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #431

N	H ≅ G/N	type
7. C₄×#10596831	C₄	semidirect
13. C₄×C₈×C₇₃	C₄	semidirect
17. C₄×Dic₇₃	C₈	semidirect
59. C₇₃	#1274	semidirect
70. C₄×C₈	Dic₇₃	semidirect

H ≅ G/N

type

7. C₄×#10596831

C₄

semidirect

13. C₄×C₈×C₇₃

C₄

semidirect

17. C₄×Dic₇₃

C₈

semidirect

59. C₇₃

#1274

semidirect

70. C₄×C₈

Dic₇₃

semidirect

Subgroups — #22607759

Conjugacy classes of subgroups

Complements