Group #22611441 — subgroups

Subgroups — #22611441

Order 9344.

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

normal subgroups only

This group has 176 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	#17988630	C₂	1	2	yes	maximal
2	C₂×#14556523	C₂	1	1	yes	maximal, characteristic
3	#17988355	C₂	1	2	yes	maximal
4	#17988352	C₂	1	1	yes	maximal, characteristic
5	#424×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
8	#14556524	—	2	2	no	—
9	#14556523	—	2	2	no	—
10	#14556522	—	2	2	no	—
11	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	#117×C₇₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₃	—	2	2	no	—
15	C₂²×Dic₇₃	—	2	2	no	—
16	#11924012	—	2	2	no	—
17	#11924012	Q₈	1	4	yes	—
18	C₂×#10596831	—	2	2	no	—
19	C₄⋊Dic₇₃	—	2	2	no	—
20	C₄⋊Dic₇₃	—	2	2	no	—
21	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
22	M₁₆×C₇₃	—	2	2	no	—
23	C₂×C₈×C₇₃	—	2	2	no	—
24	C₂×C₈×C₇₃	—	2	1	no	—
25	C₂×C₈×C₇₃	D₄	1	2	yes	—
26	C₄⋊C₄×C₇₃	D₄	1	2	yes	—
27	C₂²⋊C₄×C₇₃	—	2	1	no	—
28	C₄²×C₇₃	—	2	1	no	—
29	C₂³×C₇₃	#41	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	2	2	no	—
31	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₇₃	#41	1	2	yes	—
35	C₂×Dic₇₃	—	4	2	no	—
36	C₂×Dic₇₃	—	8	2	no	—
37	C₈×C₇₃	—	2	2	no	—
38	C₈×C₇₃	—	4	1	no	—
39	#10596831	—	2	4	no	—
40	C₂²×C₇₃	—	2	2	no	—
41	C₂²×C₇₃	#121	1	1	yes	characteristic
42	C₂²×C₇₃	#125	1	2	yes	—
43	C₄×C₇₃	—	4	2	no	—
44	C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
45	C₄×C₇₃	#123	1	1	yes	characteristic
46	C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
47	Dic₇₃	—	8	2	no	—
48	C₂×C₇₃	—	2	2	no	—
49	C₂×C₇₃	#398	1	1	yes	characteristic
50	C₂×C₇₃	#471	1	2	yes	—
51	#2090	—	73	1	no	maximal, Sylow
52	C₇₃	#2090	1	1	yes	characteristic, complemented, Sylow
53	#428	—	73	2	no	—
54	C₂×#106	—	73	1	no	—
55	#424	D₇₃	1	1	yes	characteristic
56	#343	—	73	2	no	—
57	#341	—	73	1	no	—
58	C₂×M₁₆	—	73	2	no	—
59	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
60	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
61	#117	C₂×D₇₃	1	1	yes	characteristic
62	C₂×C₄⋊C₄	—	73	2	no	—
63	#107	—	146	2	no	—
64	#106	—	146	2	no	—
65	#106	—	146	2	no	—
66	C₄⋊C₈	—	2	2	no	—
67	C₂²×C₄	—	146	2	no	—
68	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	73	4	no	—
71	M₁₆	—	146	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	146	2	no	—
75	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
76	C₄⋊C₄	—	146	2	no	—
77	C₄⋊C₄	—	146	2	no	—
78	C₄⋊C₄	D₂₉₂	1	2	yes	—
79	C₂²⋊C₄	—	2	1	no	—
80	C₄²	—	2	1	no	—
81	C₂³	#11924028	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	292	2	no	—
84	C₂×C₄	—	584	2	no	—
85	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
86	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
87	C₂×C₄	Q₈×D₇₃	1	2	yes	—
88	C₂×C₄	#11924027	1	2	yes	—
89	C₈	—	2	2	no	—
90	C₈	—	4	1	no	—
91	C₈	—	146	4	no	—
92	C₂²	—	2	2	no	—
93	C₂²	#14556565	1	1	yes	characteristic
94	C₂²	#14556581	1	2	yes	—
95	C₄	—	4	2	no	—
96	C₄	—	584	2	no	—
97	C₄	#14556571	1	2	yes	—
98	C₄	#14556572	1	1	yes	characteristic
99	C₄	#14556589	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	#17988517	1	1	yes	characteristic
102	C₂	#17988850	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988630

C₂

yes

maximal

C₂×#14556523

C₂

yes

maximal, characteristic

#17988355

C₂

yes

maximal

#17988352

C₂

yes

maximal, characteristic

#424×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

#14556524

—

#14556523

—

#14556522

—

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#117×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²×Dic₇₃

—

#11924012

—

#11924012

Q₈

yes

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

D₄

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

#41

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

characteristic

C₂²×C₇₃

#125

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

#123

yes

characteristic

C₄×C₇₃

C₄⋊Q₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#398

yes

characteristic

C₂×C₇₃

#471

yes

—

#2090

—

maximal, Sylow

C₇₃

#2090

yes

characteristic, complemented, Sylow

#428

—

C₂×#106

—

#424

D₇₃

yes

characteristic

#343

—

#341

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

characteristic

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

146

—

#106

—

146

—

#106

—

146

—

C₄⋊C₈

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

D₂₉₂

yes

—

C₂²⋊C₄

—

C₄²

—

C₂³

#11924028

yes

characteristic

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

Q₈×D₇₃

yes

—

C₂×C₄

#11924027

yes

—

C₈

—

C₈

—

C₈

—

146

—

C₂²

—

C₂²

#14556565

yes

characteristic

C₂²

#14556581

yes

—

C₄

—

C₄

—

584

—

C₄

#14556571

yes

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#17988517

yes

characteristic

102

C₂

#17988850

yes

—

	subgroup	G/H
center	C₂²	#14556565
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#424×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#424	D₇₃
hypocenter	C₇₃	#2090
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#14556565

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#424×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
52. C₇₃	#2090	semidirect

H ≅ G/N

type

52. C₇₃

#2090

semidirect

Subgroups — #22611441

Conjugacy classes of subgroups

Complements