Group #22608017 — subgroups

Subgroups — #22608017

Order 9344.

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

normal subgroups only

This group has 132 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	C₂×#14556531	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556531	C₂	1	1	yes	maximal, characteristic
3	#405×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556531	—	2	1	no	—
5	#14556531	—	2	1	no	—
6	#14556531	—	2	1	no	—
7	#14556531	C₄	1	2	yes	complemented
8	C₂×#11924003	—	2	1	no	—
9	C₂×#11924003	C₄	1	2	yes	complemented
10	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
11	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	#117×C₇₃	C₄	1	1	yes	characteristic
13	#97×C₇₃	—	2	1	no	—
14	C₄×C₈×C₇₃	—	2	1	no	—
15	#11924003	—	2	2	no	—
16	#11924003	—	2	2	no	—
17	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
18	M₁₆×C₇₃	—	2	1	no	—
19	M₁₆×C₇₃	C₈	1	2	yes	—
20	C₂×C₈×C₇₃	—	2	1	no	—
21	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	Q₈	1	1	yes	characteristic
27	C₄⋊C₄×C₇₃	—	2	1	no	—
28	C₂²⋊C₄×C₇₃	C₈	1	2	yes	—
29	C₄²×C₇₃	—	2	1	no	—
30	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
38	C₈×C₇₃	—	2	2	no	—
39	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₇₃	—	4	1	no	—
44	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
45	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
46	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₇₃	—	4	2	no	—
48	C₄×C₇₃	#95	1	1	yes	characteristic
49	C₄×C₇₃	#97	1	1	yes	characteristic
50	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₇₃	—	2	1	no	—
53	C₂×C₇₃	—	2	1	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	#336	1	1	yes	characteristic
56	#1378	—	73	1	no	maximal, Sylow
57	C₇₃	#1378	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₃₂	—	73	1	no	—
59	C₂×M₃₂	—	73	1	no	—
60	#405	D₇₃	1	1	yes	characteristic
61	C₂×M₁₆	Dic₇₃	1	1	yes	characteristic
62	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
63	#117	Dic₇₃	1	1	yes	characteristic
64	M₃₂	—	73	2	no	—
65	M₃₂	—	146	1	no	—
66	M₃₂	—	146	1	no	—
67	M₃₂	—	146	1	no	—
68	C₂×C₁₆	—	73	2	no	—
69	C₂×C₁₆	—	146	1	no	—
70	#97	—	2	1	no	—
71	C₄×C₈	—	2	1	no	—
72	C₂²×C₄	C₂×Dic₇₃	1	1	yes	characteristic
73	M₁₆	—	2	1	no	—
74	M₁₆	#10596831	1	2	yes	—
75	C₂×C₈	—	2	1	no	—
76	C₂×C₈	Dic₁₄₆	1	1	yes	characteristic
77	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
78	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
79	C₂×C₈	D₂₉₂	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
82	C₄⋊C₄	—	2	1	no	—
83	C₂²⋊C₄	#10596831	1	2	yes	—
84	C₄²	—	2	1	no	—
85	C₁₆	—	146	2	no	—
86	C₁₆	—	146	2	no	—
87	C₂³	C₂×#10596831	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	C₄×Dic₇₃	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
91	C₂×C₄	C₄⋊Dic₇₃	1	1	yes	characteristic
92	C₂×C₄	C₂×#10596831	1	1	yes	characteristic
93	C₂×C₄	#11924012	1	1	yes	characteristic
94	C₂×C₄	#11924012	1	1	yes	characteristic
95	C₈	—	2	2	no	—
96	C₈	#11924005	1	1	yes	characteristic
97	C₈	#11924005	1	1	yes	characteristic
98	C₈	#11924007	1	1	yes	characteristic
99	C₈	#11924007	1	1	yes	characteristic
100	C₂²	—	4	1	no	—
101	C₂²	C₄×#10596831	1	1	yes	characteristic
102	C₂²	C₂²⋊#10596831	1	1	yes	characteristic
103	C₂²	C₄⋊#10596831	1	1	yes	characteristic
104	C₄	—	4	2	no	—
105	C₄	#14556498	1	1	yes	characteristic
106	C₄	#14556502	1	1	yes	characteristic
107	C₄	C₂²⋊#10596831	1	1	yes	characteristic
108	C₄	C₄⋊#10596831	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#17988342	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556531

C₂

yes

maximal, characteristic

C₂×#14556531

C₂

yes

maximal, characteristic

#405×C₇₃

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

complemented

C₂×#11924003

—

C₂×#11924003

C₄

yes

complemented

C₂×M₁₆×C₇₃

C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#117×C₇₃

C₄

yes

characteristic

#97×C₇₃

—

C₄×C₈×C₇₃

—

#11924003

—

#11924003

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

C₈

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

Q₈

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

C₈

yes

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

—

#405

D₇₃

yes

characteristic

C₂×M₁₆

Dic₇₃

yes

characteristic

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

Dic₇₃

yes

characteristic

M₃₂

—

M₃₂

—

146

—

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#97

—

C₄×C₈

—

C₂²×C₄

C₂×Dic₇₃

yes

characteristic

M₁₆

—

M₁₆

#10596831

yes

—

C₂×C₈

—

C₂×C₈

Dic₁₄₆

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

#10596831

yes

—

C₄²

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

C₂×#10596831

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄×Dic₇₃

yes

characteristic

C₂×C₄

C₂²⋊Dic₇₃

yes

characteristic

C₂×C₄

C₄⋊Dic₇₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

yes

C₈

yes

C₈

yes

C₈

yes

100

C₂²

—

101

C₂²

C₄×#10596831

yes

characteristic

102

C₂²

C₂²⋊#10596831

yes

characteristic

103

C₂²

C₄⋊#10596831

yes

characteristic

104

C₄

—

105

C₄

#14556498

yes

characteristic

106

C₄

#14556502

yes

characteristic

107

C₄

C₂²⋊#10596831

yes

characteristic

108

C₄

C₄⋊#10596831

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

112

C₂

#17988342

yes

characteristic

	subgroup	G/H
center	C₈	#11924005
commutator	C₂²×C₇₃	C₄×C₈
Frattini	C₂²×C₈	C₂×D₇₃
Fitting	#405×C₇₃	C₂
socle	C₂×C₇₃	#336
hypercenter	#405	D₇₃
hypocenter	C₇₃	#1378
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

subgroup

G/H

center

C₈

#11924005

commutator

C₂²×C₇₃

C₄×C₈

Frattini

C₂²×C₈

C₂×D₇₃

Fitting

#405×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

N	H ≅ G/N	type
7. #14556531	C₄	semidirect
9. C₂×#11924003	C₄	semidirect
57. C₇₃	#1378	semidirect

H ≅ G/N

type

7. #14556531

C₄

semidirect

9. C₂×#11924003

C₄

semidirect

57. C₇₃

#1378

semidirect

Subgroups — #22608017

Conjugacy classes of subgroups

Complements