Group #22611438 — subgroups

Subgroups — #22611438

Order 9344.

176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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	#17988629	C₂	1	2	yes	maximal
2	C₂×#14556525	C₂	1	1	yes	maximal, characteristic
3	#17988613	C₂	1	1	yes	maximal, characteristic
4	#17988355	C₂	1	2	yes	maximal
5	#341×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	1	yes	characteristic
7	#14556550	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	#14556525	—	2	2	no	—
10	#14556525	—	2	2	no	—
11	#14556523	—	2	2	no	—
12	#14556520	—	2	2	no	—
13	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₃	—	2	2	no	—
16	#11924012	—	2	2	no	—
17	C₂×#10596831	—	2	1	no	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	—	2	2	no	—
20	C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
21	C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
22	C₂²⋊Dic₇₃	—	2	1	no	—
23	C₄×Dic₇₃	—	2	1	no	—
24	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
25	M₁₆×C₇₃	—	2	2	no	—
26	M₁₆×C₇₃	Q₈	1	4	yes	—
27	C₂×C₈×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	D₄	1	2	yes	—
30	C₂³×C₇₃	#41	1	1	yes	characteristic
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	—	2	1	no	—
36	C₂×Dic₇₃	—	2	1	no	—
37	C₂×Dic₇₃	—	4	2	no	—
38	C₂×Dic₇₃	—	8	2	no	—
39	C₈×C₇₃	—	2	4	no	—
40	C₈×C₇₃	—	2	2	no	—
41	#10596831	—	4	1	no	—
42	C₂²×C₇₃	—	2	1	no	—
43	C₂²×C₇₃	—	2	1	no	—
44	C₂²×C₇₃	#121	1	1	yes	characteristic
45	C₂²×C₇₃	#125	1	2	yes	—
46	C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₇₃	#123	1	1	yes	characteristic
48	C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
49	Dic₇₃	—	4	1	no	—
50	Dic₇₃	—	4	1	no	—
51	Dic₇₃	—	8	2	no	—
52	C₂×C₇₃	—	2	2	no	—
53	C₂×C₇₃	#398	1	1	yes	characteristic
54	C₂×C₇₃	#472	1	1	yes	characteristic
55	C₂×C₇₃	#473	1	1	yes	characteristic
56	#2089	—	73	1	no	maximal, Sylow
57	C₇₃	#2089	1	1	yes	characteristic, complemented, Sylow
58	#428	—	73	2	no	—
59	C₂×#107	—	73	1	no	—
60	#424	—	73	1	no	—
61	#343	—	73	2	no	—
62	#341	D₇₃	1	1	yes	characteristic
63	C₂×M₁₆	—	73	1	no	—
64	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
65	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
66	#117	—	73	1	no	—
67	C₂×C₄⋊C₄	—	73	2	no	—
68	#107	—	146	2	no	—
69	#107	—	146	2	no	—
70	#106	—	146	2	no	—
71	C₄⋊C₈	—	146	2	no	—
72	C₂²×C₄	—	146	2	no	—
73	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	146	2	no	—
76	M₁₆	Dic₁₄₆	1	4	yes	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	146	1	no	—
80	C₂×C₈	D₂₉₂	1	2	yes	—
81	C₄⋊C₄	—	73	1	no	—
82	C₄⋊C₄	—	73	1	no	—
83	C₄⋊C₄	—	146	2	no	—
84	C₄⋊C₄	—	146	2	no	—
85	C₂²⋊C₄	—	146	1	no	—
86	C₄²	—	146	1	no	—
87	C₂³	#11924029	1	1	yes	characteristic
88	C₂×C₄	—	292	2	no	—
89	C₂×C₄	—	584	2	no	—
90	C₂×C₄	—	146	1	no	—
91	C₂×C₄	—	146	1	no	—
92	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
93	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
94	C₂×C₄	C₂×Dic₁₄₆	1	2	yes	—
95	C₂×C₄	#11924027	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	2	2	no	—
98	C₈	—	292	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#14556566	1	1	yes	characteristic
102	C₂²	#14556582	1	2	yes	—
103	C₄	—	292	1	no	—
104	C₄	—	292	1	no	—
105	C₄	—	584	2	no	—
106	C₄	#14556568	1	2	yes	—
107	C₄	#14556575	1	1	yes	characteristic
108	C₄	#14556591	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#17988519	1	1	yes	characteristic
111	C₂	#17988858	1	1	yes	characteristic
112	C₂	#17988863	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988629

C₂

yes

maximal

C₂×#14556525

C₂

yes

maximal, characteristic

#17988613

C₂

yes

maximal, characteristic

#17988355

C₂

yes

maximal

#341×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

characteristic

#14556550

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₂²

yes

—

—

—

—

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂²×Dic₇₃

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

characteristic

C₄⋊Dic₇₃

D₄

yes

characteristic

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

Q₈

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₂³×C₇₃

#41

yes

characteristic

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

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

characteristic

C₂²×C₇₃

#125

yes

—

C₄×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

#123

yes

characteristic

C₄×C₇₃

C₄⋊Q₈

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#107

—

146

—

#107

—

146

—

#106

—

146

—

C₄⋊C₈

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

146

—

M₁₆

Dic₁₄₆

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

D₂₉₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

146

—

C₂³

#11924029

yes

characteristic

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

C₂×Dic₁₄₆

yes

—

C₂×C₄

#11924027

yes

—

C₈

—

C₈

—

C₈

—

292

—

C₂²

—

100

C₂²

—

101

C₂²

#14556566

yes

characteristic

102

C₂²

#14556582

yes

—

103

C₄

—

292

—

104

C₄

—

292

—

105

C₄

—

584

—

106

C₄

#14556568

yes

—

107

C₄

#14556575

yes

characteristic

108

C₄

#14556591

yes

characteristic

109

C₂

—

110

C₂

#17988519

yes

characteristic

111

C₂

#17988858

yes

characteristic

112

C₂

#17988863

yes

characteristic

	subgroup	G/H
center	C₂²	#14556566
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#341×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#341	D₇₃
hypocenter	C₇₃	#2089
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#14556566

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#341×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
57. C₇₃	#2089	semidirect

H ≅ G/N

type

57. C₇₃

#2089

semidirect

Subgroups — #22611438

Conjugacy classes of subgroups

Complements