Group #22611507 — subgroups

Subgroups — #22611507

Order 9344.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#17988636	C₂	1	1	yes	maximal, characteristic
2	#17988610	C₂	1	1	yes	maximal, characteristic
3	#17988357	C₂	1	2	yes	maximal
4	#17988346	C₂	1	2	yes	maximal
5	H(3,ℤ/4)×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	1	yes	characteristic
7	C₂×#11924012	C₂²	1	2	yes	—
8	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
9	#14556527	—	2	2	no	—
10	#14556520	—	2	2	no	—
11	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
12	#117×C₇₃	C₂²	1	2	yes	—
13	C₂²×Dic₇₃	—	2	1	no	—
14	#11924012	—	2	2	no	—
15	#11924012	—	2	2	no	—
16	#11924012	—	2	2	no	—
17	C₂×#10596831	—	2	1	no	—
18	C₂×#10596831	—	2	2	no	—
19	C₄×Dic₇₃	—	2	1	no	—
20	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
21	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
22	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
23	M₁₆×C₇₃	—	2	2	no	—
24	C₂×C₈×C₇₃	D₄	1	2	yes	—
25	C₄⋊C₄×C₇₃	—	2	2	no	—
26	C₂²⋊C₄×C₇₃	—	2	2	no	—
27	C₄²×C₇₃	—	2	2	no	—
28	C₂³×C₇₃	#41	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	4	2	no	—
30	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₇₃	#41	1	2	yes	—
33	C₂×C₄×C₇₃	#41	1	2	yes	—
34	C₂×Dic₇₃	—	2	1	no	—
35	C₂×Dic₇₃	—	2	1	no	—
36	C₂×Dic₇₃	—	4	2	no	—
37	C₈×C₇₃	—	2	2	no	—
38	#10596831	—	4	1	no	—
39	#10596831	—	4	2	no	—
40	C₂²×C₇₃	—	4	1	no	—
41	C₂²×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
42	C₂²×C₇₃	#126	1	2	yes	—
43	C₄×C₇₃	—	8	2	no	—
44	C₄×C₇₃	#123	1	1	yes	characteristic
45	C₄×C₇₃	#124	1	1	yes	characteristic
46	C₄×C₇₃	#125	1	2	yes	—
47	Dic₇₃	—	2	2	no	—
48	Dic₇₃	—	4	1	no	—
49	C₂×C₇₃	—	2	1	no	—
50	C₂×C₇₃	—	2	2	no	—
51	C₂×C₇₃	#400	1	1	yes	characteristic
52	#2102	—	73	1	no	maximal, Sylow
53	C₇₃	#2102	1	1	yes	characteristic, complemented, Sylow
54	#430	—	73	1	no	—
55	#423	—	73	1	no	—
56	#344	—	73	2	no	—
57	#339	—	73	2	no	—
58	H(3,ℤ/4)	D₇₃	1	1	yes	characteristic
59	C₂×M₁₆	—	73	2	no	—
60	C₂×M₁₆	—	73	1	no	—
61	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
62	#117	C₂×D₇₃	1	2	yes	—
63	C₂×C₄²	—	73	1	no	—
64	#108	—	146	2	no	—
65	C₄⋊C₈	—	146	2	no	—
66	C₂²×C₄	—	146	1	no	—
67	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	146	2	no	—
70	M₁₆	—	146	2	no	—
71	M₁₆	—	146	2	no	—
72	C₂×C₈	—	146	1	no	—
73	C₂×C₈	—	146	2	no	—
74	C₂×C₈	D₂₉₂	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₂²⋊C₄	—	2	2	no	—
77	C₄²	—	2	2	no	—
78	C₄²	—	73	1	no	—
79	C₄²	—	73	1	no	—
80	C₄²	—	146	1	no	—
81	C₂³	#11924027	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	292	2	no	—
84	C₂×C₄	—	146	1	no	—
85	C₂×C₄	—	146	1	no	—
86	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
87	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
88	C₂×C₄	#11924027	1	2	yes	—
89	C₂×C₄	#11924028	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	292	1	no	—
92	C₈	—	292	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#14556571	1	1	yes	characteristic
95	C₂²	#14556584	1	2	yes	—
96	C₄	—	8	2	no	—
97	C₄	—	292	1	no	—
98	C₄	—	146	2	no	—
99	C₄	#14556575	1	1	yes	characteristic
100	C₄	#14556579	1	1	yes	characteristic
101	C₄	#14556581	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#17988527	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988636

C₂

yes

maximal, characteristic

#17988610

C₂

yes

maximal, characteristic

#17988357

C₂

yes

maximal

#17988346

C₂

yes

maximal

H(3,ℤ/4)×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

characteristic

C₂×#11924012

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556527

—

#14556520

—

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

#117×C₇₃

C₂²

yes

—

C₂²×Dic₇₃

—

—

—

—

—

—

C₄×Dic₇₃

—

C₄×Dic₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

#41

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₃

#126

yes

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

characteristic

#117

C₂×D₇₃

yes

—

C₂×C₄²

—

#108

—

146

—

C₄⋊C₈

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

D₂₉₂

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₂³

#11924027

yes

characteristic

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

Q₈×D₇₃

yes

characteristic

C₂×C₄

#11924027

yes

—

C₂×C₄

#11924028

yes

—

C₈

—

C₈

—

292

—

C₈

—

292

—

C₂²

—

C₂²

#14556571

yes

characteristic

C₂²

#14556584

yes

—

C₄

—

C₄

—

292

—

C₄

—

146

—

C₄

#14556575

yes

characteristic

100

C₄

#14556579

yes

characteristic

101

C₄

#14556581

yes

—

102

C₂

—

103

C₂

—

104

C₂

#17988527

yes

characteristic

	subgroup	G/H
center	C₄	#14556579
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	H(3,ℤ/4)×C₇₃	C₂
socle	C₂×C₇₃	#400
hypercenter	H(3,ℤ/4)	D₇₃
hypocenter	C₇₃	#2102
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#14556579

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

H(3,ℤ/4)×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
53. C₇₃	#2102	semidirect

H ≅ G/N

type

53. C₇₃

#2102

semidirect

Subgroups — #22611507

Conjugacy classes of subgroups

Complements