Group #22609072 — subgroups

Subgroups — #22609072

Order 9344.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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	#17989317	C₂	1	1	yes	maximal, characteristic
2	#17988966	C₂	1	1	yes	maximal, characteristic
3	#17988883	C₂	1	2	yes	maximal
4	#17988317	C₂	1	2	yes	maximal
5	#333×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924018	—	2	2	no	—
7	#14556591	C₂²	1	1	yes	characteristic
8	#14556590	—	2	2	no	—
9	#14556589	—	2	2	no	—
10	C₄×Dic₁₄₆	C₂²	1	2	yes	—
11	#14556556	—	2	2	no	—
12	#14556525	—	2	2	no	—
13	#14556516	—	2	2	no	—
14	C₄×#10596831	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
17	C₂×Dic₁₄₆	—	2	1	no	—
18	C₂×Dic₁₄₆	—	2	2	no	—
19	C₂×Dic₁₄₆	D₄	1	2	yes	—
20	#11924018	—	4	4	no	—
21	C₂×#10596831	—	2	1	no	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	C₄⋊Dic₇₃	D₄	1	2	yes	—
24	#11924007	—	2	4	no	—
25	#11924007	—	2	2	no	—
26	C₄×Dic₇₃	—	2	2	no	—
27	C₄×Dic₇₃	—	2	2	no	—
28	C₂×Q₈×C₇₃	D₄	1	2	yes	—
29	C₂×C₈×C₇₃	—	2	2	no	—
30	C₄⋊C₄×C₇₃	—	2	2	no	—
31	C₄²×C₇₃	C₂³	1	1	yes	characteristic
32	Q₈×C₇₃	—	4	2	no	—
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₇₃	—	2	2	no	—
37	C₂×Dic₇₃	—	2	2	no	—
38	C₂×Dic₇₃	—	4	1	no	—
39	Dic₁₄₆	—	2	2	no	—
40	Dic₁₄₆	—	4	2	no	—
41	Dic₁₄₆	—	8	2	no	—
42	Dic₁₄₆	Q₁₆	1	4	yes	complemented
43	C₈×C₇₃	—	4	2	no	—
44	#10596831	—	2	2	no	—
45	C₂²×C₇₃	#120	1	1	yes	characteristic
46	C₄×C₇₃	—	2	1	no	—
47	C₄×C₇₃	—	4	2	no	—
48	C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
49	C₄×C₇₃	#137	1	2	yes	—
50	Dic₇₃	—	2	4	no	—
51	Dic₇₃	—	4	2	no	—
52	Dic₇₃	—	8	1	no	—
53	C₂×C₇₃	#451	1	2	yes	—
54	C₂×C₇₃	#453	1	1	yes	characteristic
55	#1633	—	73	1	no	maximal, Sylow
56	C₇₃	#1633	1	1	yes	characteristic, complemented, Sylow
57	Q₈²	—	73	1	no	—
58	#494	—	73	1	no	—
59	#477	—	73	2	no	—
60	#333	D₇₃	1	1	yes	characteristic
61	Q₈⋊C₈	—	73	2	no	—
62	C₂×Q₁₆	—	146	2	no	—
63	C₄⋊Q₈	—	73	1	no	—
64	C₄⋊Q₈	—	146	2	no	—
65	C₄⋊Q₈	—	146	2	no	—
66	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
67	C₄×Q₈	—	73	2	no	—
68	C₄×Q₈	—	146	2	no	—
69	#107	—	146	2	no	—
70	C₄⋊C₈	C₂×D₇₃	1	2	yes	—
71	#103	—	146	2	no	—
72	C₄×C₈	—	73	1	no	—
73	C₂×Q₈	—	73	2	no	—
74	C₂×Q₈	—	146	2	no	—
75	C₂×Q₈	—	146	1	no	—
76	C₂×Q₈	D₂₉₂	1	2	yes	—
77	Q₁₆	—	292	4	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	146	1	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	73	2	no	—
82	C₄⋊C₄	—	146	4	no	—
83	C₄⋊C₄	—	146	2	no	—
84	C₄⋊C₄	—	146	2	no	—
85	C₄²	—	146	2	no	—
86	C₄²	—	146	2	no	—
87	C₄²	C₂²×D₇₃	1	1	yes	characteristic
88	Q₈	—	4	2	no	—
89	Q₈	—	292	2	no	—
90	Q₈	—	584	2	no	—
91	Q₈	—	73	4	no	—
92	Q₈	—	146	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	292	1	no	—
95	C₂×C₄	—	146	2	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	D₄×D₇₃	1	2	yes	—
98	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
99	C₈	—	4	2	no	—
100	C₈	—	146	2	no	—
101	C₂²	#14556561	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	4	2	no	—
104	C₄	—	292	2	no	—
105	C₄	—	584	1	no	—
106	C₄	—	146	4	no	—
107	C₄	Q₁₆×D₇₃	1	2	yes	—
108	C₄	#14556620	1	2	yes	—
109	C₂	#17988744	1	2	yes	—
110	C₂	#17988757	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989317

C₂

yes

maximal, characteristic

#17988966

C₂

yes

maximal, characteristic

#17988883

C₂

yes

maximal

#17988317

C₂

yes

maximal

#333×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924018

—

#14556591

C₂²

yes

characteristic

#14556590

—

#14556589

—

C₄×Dic₁₄₆

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

#11924018

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

—

#11924007

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

Q₁₆

yes

complemented

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#120

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×Q₁₆

yes

—

C₄×C₇₃

#137

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#451

yes

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

Q₈²

—

#494

—

#477

—

#333

D₇₃

yes

characteristic

Q₈⋊C₈

—

C₂×Q₁₆

—

146

—

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

146

—

#107

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

—

#103

—

146

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

D₂₉₂

yes

—

Q₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

146

—

C₄²

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

Q₈

—

Q₈

—

292

—

Q₈

—

584

—

Q₈

—

Q₈

—

146

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

—

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₈

—

100

C₈

—

146

—

101

C₂²

#14556561

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

292

—

105

C₄

—

584

—

106

C₄

—

146

—

107

C₄

Q₁₆×D₇₃

yes

—

108

C₄

#14556620

yes

—

109

C₂

#17988744

yes

—

110

C₂

#17988757

yes

characteristic

	subgroup	G/H
center	C₂²	#14556561
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#333×C₇₃	C₂
socle	C₂²×C₇₃	#120
hypercenter	#333	D₇₃
hypocenter	C₇₃	#1633
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#14556561

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#333×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
42. Dic₁₄₆	Q₁₆	semidirect
56. C₇₃	#1633	semidirect

H ≅ G/N

type

42. Dic₁₄₆

Q₁₆

semidirect

56. C₇₃

#1633

semidirect

Subgroups — #22609072

Conjugacy classes of subgroups

Complements