Group #22611725 — subgroups

Subgroups — #22611725

Order 9344.

140 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 81 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	#17988416	C₂	1	4	yes	maximal, complemented
4	C₂×#108×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924012	—	2	1	no	—
6	#14556531	C₄	1	2	yes	—
7	#14556531	C₄	1	2	yes	—
8	C₂×#11924003	C₂²	1	2	yes	—
9	#14556527	—	2	1	no	—
10	#14556527	C₂²	1	2	yes	—
11	C₂×M₁₆×C₇₃	—	2	1	no	—
12	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	#108×C₇₃	—	2	1	no	—
14	#108×C₇₃	C₂²	1	2	yes	—
15	#11924012	—	2	2	no	—
16	#11924012	—	4	1	no	—
17	C₂×#10596831	—	4	1	no	—
18	#11924003	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
20	M₁₆×C₇₃	—	2	2	no	—
21	M₁₆×C₇₃	—	4	1	no	—
22	C₂×C₈×C₇₃	—	4	1	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	Q₈	1	1	yes	characteristic
27	C₂×C₈×C₇₃	Q₈	1	1	yes	characteristic
28	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
29	C₂³×C₇₃	Q₁₆	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
33	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₃	Q₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₈×C₇₃	—	4	2	no	—
37	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
41	#10596831	—	4	2	no	—
42	C₂²×C₇₃	—	4	1	no	—
43	C₂²×C₇₃	#107	1	1	yes	characteristic
44	C₂²×C₇₃	#107	1	1	yes	characteristic
45	C₂²×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₇₃	#107	1	1	yes	characteristic
47	C₄×C₇₃	#107	1	1	yes	characteristic
48	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₇₃	C₂×D₈	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	C₂×#107	1	1	yes	characteristic
54	#2161	—	73	1	no	maximal, Sylow
55	C₇₃	#2161	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₃₂	—	73	1	no	—
57	C₂×#108	—	73	1	no	—
58	C₂×#108	D₇₃	1	1	yes	characteristic
59	#368	—	73	4	no	—
60	C₂×M₁₆	—	2	1	no	—
61	C₂×M₁₆	—	146	1	no	—
62	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
63	M₃₂	—	73	2	no	—
64	M₃₂	—	73	2	no	—
65	C₂×C₁₆	—	73	2	no	—
66	#108	—	2	1	no	—
67	#108	—	73	2	no	—
68	#108	—	146	1	no	—
69	#108	C₂×D₇₃	1	2	yes	—
70	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	4	1	no	—
73	M₁₆	—	292	1	no	—
74	M₁₆	—	146	2	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	—	292	1	no	—
77	C₂×C₈	Dic₁₄₆	1	1	yes	characteristic
78	C₂×C₈	Dic₁₄₆	1	1	yes	characteristic
79	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
80	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
83	C₁₆	—	73	4	no	—
84	C₂³	#11924018	1	1	yes	characteristic
85	C₂×C₄	#11924007	1	1	yes	characteristic
86	C₂×C₄	#11924007	1	1	yes	characteristic
87	C₂×C₄	#11924013	1	1	yes	characteristic
88	C₂×C₄	#11924013	1	1	yes	characteristic
89	C₂×C₄	#11924018	1	1	yes	characteristic
90	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	292	2	no	—
93	C₈	#11924007	1	1	yes	characteristic
94	C₈	#11924007	1	1	yes	characteristic
95	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
96	C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
97	C₂²	—	4	1	no	—
98	C₂²	#14556524	1	1	yes	characteristic
99	C₂²	#14556524	1	1	yes	characteristic
100	C₂²	C₂×#11924018	1	1	yes	characteristic
101	C₄	#14556524	1	1	yes	characteristic
102	C₄	#14556524	1	1	yes	characteristic
103	C₄	C₂×#11924007	1	1	yes	characteristic
104	C₄	C₂×#11924013	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	2	1	no	—
107	C₂	—	2	1	no	—
108	C₂	C₂×#14556524	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556531

C₂

yes

maximal, characteristic

C₂×#14556527

C₂

yes

maximal, characteristic

#17988416

C₂

yes

maximal, complemented

C₂×#108×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

—

#14556531

C₄

yes

—

#14556531

C₄

yes

—

C₂×#11924003

C₂²

yes

—

#14556527

—

#14556527

C₂²

yes

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#108×C₇₃

—

#108×C₇₃

C₂²

yes

—

—

—

—

C₂×C₄

yes

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

Q₈

yes

characteristic

C₂×C₈×C₇₃

Q₈

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

Q₁₆

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

Q₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₂²×C₄

yes

characteristic

C₈×C₇₃

C₂×Q₈

yes

characteristic

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

C₂×Q₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

C₂×#108

D₇₃

yes

characteristic

#368

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

—

#108

—

146

—

#108

C₂×D₇₃

yes

—

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

292

—

C₂×C₈

Dic₁₄₆

yes

characteristic

C₂×C₈

Dic₁₄₆

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₁₆

—

C₂³

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₈

—

C₈

—

292

—

C₈

yes

C₈

yes

C₈

C₂×C₄×D₇₃

yes

characteristic

C₈

C₂×Dic₁₄₆

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

100

C₂²

C₂×#11924018

yes

characteristic

101

C₄

#14556524

yes

characteristic

102

C₄

#14556524

yes

characteristic

103

C₄

C₂×#11924007

yes

characteristic

104

C₄

C₂×#11924013

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

108

C₂

C₂×#14556524

yes

characteristic

	subgroup	G/H
center	C₄	C₂×#11924013
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂×#108×C₇₃	C₂
socle	C₂×C₇₃	C₂×#107
hypercenter	C₂×#108	D₇₃
hypocenter	C₇₃	#2161
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₄

C₂×#11924013

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂×#108×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
3. #17988416	C₂	semidirect
55. C₇₃	#2161	semidirect

H ≅ G/N

type

3. #17988416

C₂

semidirect

55. C₇₃

#2161

semidirect

Subgroups — #22611725

Conjugacy classes of subgroups

Complements