Group #22608047 — subgroups

Subgroups — #22608047

Order 9344.

128 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14556527	C₂	1	1	yes	maximal, characteristic
3	#427×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924012	—	2	1	no	—
5	#14556531	—	2	1	no	—
6	#14556531	C₄	1	2	yes	complemented
7	C₂×#11924003	—	2	1	no	—
8	#14556527	—	2	1	no	—
9	#14556527	C₄	1	2	yes	complemented
10	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	#117×C₇₃	—	2	1	no	—
12	#107×C₇₃	—	2	1	no	—
13	#106×C₇₃	C₄	1	2	yes	—
14	#11924012	—	2	2	no	—
15	#11924012	—	4	1	no	—
16	C₂×#10596831	—	4	1	no	—
17	#11924003	—	2	2	no	—
18	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
23	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	Q₈	1	1	yes	characteristic
25	C₄⋊C₄×C₇₃	—	2	2	no	—
26	C₂²⋊C₄×C₇₃	—	4	1	no	—
27	C₄²×C₇₃	—	4	1	no	—
28	C₂³×C₇₃	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	4	2	no	—
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	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₃	Q₁₆	1	1	yes	characteristic
36	C₈×C₇₃	C₄²	1	1	yes	characteristic
37	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
40	#10596831	—	4	2	no	—
41	C₂²×C₇₃	—	4	1	no	—
42	C₂²×C₇₃	#102	1	1	yes	characteristic
43	C₂²×C₇₃	#103	1	1	yes	characteristic
44	C₂²×C₇₃	#106	1	1	yes	characteristic
45	C₄×C₇₃	—	8	2	no	—
46	C₄×C₇₃	#95	1	1	yes	characteristic
47	C₄×C₇₃	#102	1	1	yes	characteristic
48	C₄×C₇₃	#103	1	1	yes	characteristic
49	C₄×C₇₃	#107	1	1	yes	characteristic
50	C₂×C₇₃	—	2	1	no	—
51	C₂×C₇₃	—	2	1	no	—
52	C₂×C₇₃	—	2	1	no	—
53	C₂×C₇₃	#340	1	1	yes	characteristic
54	#1389	—	73	1	no	maximal, Sylow
55	C₇₃	#1389	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₃₂	—	73	1	no	—
57	C₂×#108	—	73	1	no	—
58	#427	D₇₃	1	1	yes	characteristic
59	C₂×M₁₆	—	146	1	no	—
60	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
61	#117	—	2	1	no	—
62	M₃₂	—	73	2	no	—
63	M₃₂	—	146	1	no	—
64	C₂×C₁₆	—	146	1	no	—
65	#108	—	73	2	no	—
66	#108	—	146	1	no	—
67	#107	—	2	1	no	—
68	#106	Dic₇₃	1	2	yes	—
69	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
70	M₁₆	—	292	1	no	—
71	M₁₆	—	146	2	no	—
72	C₂×C₈	—	292	1	no	—
73	C₂×C₈	Dic₁₄₆	1	1	yes	characteristic
74	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
75	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
76	C₂×C₈	D₂₉₂	1	1	yes	characteristic
77	C₂×C₈	C₂×Dic₇₃	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
79	C₄⋊C₄	—	2	2	no	—
80	C₂²⋊C₄	—	4	1	no	—
81	C₄²	—	4	1	no	—
82	C₁₆	—	146	2	no	—
83	C₂³	#11924016	1	1	yes	characteristic
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	#11924005	1	1	yes	characteristic
86	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
87	C₂×C₄	#11924007	1	1	yes	characteristic
88	C₂×C₄	#11924013	1	1	yes	characteristic
89	C₂×C₄	#11924015	1	1	yes	characteristic
90	C₂×C₄	#11924018	1	1	yes	characteristic
91	C₈	—	292	2	no	—
92	C₈	C₄×Dic₇₃	1	1	yes	characteristic
93	C₈	#11924005	1	1	yes	characteristic
94	C₈	#11924007	1	1	yes	characteristic
95	C₈	C₄⋊Dic₇₃	1	1	yes	characteristic
96	C₂²	—	4	1	no	—
97	C₂²	#14556512	1	1	yes	characteristic
98	C₂²	#14556514	1	1	yes	characteristic
99	C₂²	#14556522	1	1	yes	characteristic
100	C₄	—	8	2	no	—
101	C₄	#14556498	1	1	yes	characteristic
102	C₄	#14556511	1	1	yes	characteristic
103	C₄	#14556515	1	1	yes	characteristic
104	C₄	#14556524	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	2	1	no	—
107	C₂	—	2	1	no	—
108	C₂	#17988349	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556531

C₂

yes

maximal, characteristic

C₂×#14556527

C₂

yes

maximal, characteristic

#427×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

—

#14556531

—

#14556531

C₄

yes

—

—

C₄

yes

complemented

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#117×C₇₃

—

#107×C₇₃

—

#106×C₇₃

C₄

yes

—

—

—

—

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

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

Q₈

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

Q₁₆

yes

characteristic

C₈×C₇₃

C₄²

yes

characteristic

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

#427

D₇₃

yes

characteristic

C₂×M₁₆

—

146

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

#108

—

#108

—

146

—

#107

—

#106

Dic₇₃

yes

—

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

Dic₁₄₆

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂×Dic₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

146

—

C₂³

#11924016

yes

characteristic

C₂×C₄

—

C₂×C₄

#11924005

yes

characteristic

C₂×C₄

C₂²⋊Dic₇₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

292

—

C₈

C₄×Dic₇₃

yes

C₈

yes

C₈

yes

C₈

C₄⋊Dic₇₃

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

100

C₄

—

101

C₄

#14556498

yes

characteristic

102

C₄

#14556511

yes

characteristic

103

C₄

#14556515

yes

characteristic

104

C₄

#14556524

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

108

C₂

#17988349

yes

characteristic

	subgroup	G/H
center	C₄	#14556511
commutator	C₈×C₇₃	C₄²
Frattini	C₂²×C₈	C₂×D₇₃
Fitting	#427×C₇₃	C₂
socle	C₂×C₇₃	#340
hypercenter	#427	D₇₃
hypocenter	C₇₃	#1389
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

subgroup

G/H

center

C₄

#14556511

commutator

C₈×C₇₃

C₄²

Frattini

C₂²×C₈

C₂×D₇₃

Fitting

#427×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

N	H ≅ G/N	type
6. #14556531	C₄	semidirect
9. #14556527	C₄	semidirect
55. C₇₃	#1389	semidirect

H ≅ G/N

type

6. #14556531

C₄

semidirect

9. #14556527

C₄

semidirect

55. C₇₃

#1389

semidirect

Subgroups — #22608047

Conjugacy classes of subgroups

Complements