Group #22627152 — subgroups

Subgroups — #22627152

Order 9344.

144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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	#17989709	C₂	1	2	yes	maximal, complemented
2	#17989691	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989688	C₂	1	2	yes	maximal, complemented
4	#17989682	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989631	C₂	1	1	yes	maximal, characteristic
6	#14556688	—	2	2	no	—
7	#14556688	C₂²	1	2	yes	—
8	#14556686	—	2	2	no	—
9	#14556686	C₂²	1	1	yes	characteristic
10	#14556686	C₂²	1	1	yes	characteristic
11	#14556679	C₂²	1	2	yes	—
12	#14556662	C₄	1	1	yes	characteristic
13	#14556656	C₄	1	2	yes	—
14	C₈×#64408	C₂²	1	1	yes	characteristic
15	#14556614	C₄	1	1	yes	characteristic
16	#11924040	—	2	2	no	—
17	#11924040	—	2	1	no	—
18	#11924040	D₄	1	2	yes	—
19	#11924038	—	2	2	no	—
20	#11924038	C₂×C₄	1	2	yes	—
21	#11924036	—	2	2	no	—
22	#11924036	C₂³	1	1	yes	characteristic
23	C₄×#64408	C₂×C₄	1	1	yes	characteristic
24	#11924029	C₂×C₄	1	2	yes	—
25	#11924015	C₈	1	2	yes	—
26	D₅₈₄	C₈	1	1	yes	characteristic
27	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
28	Q₁₆×C₇₃	C₈	1	1	yes	characteristic
29	C₂×#64408	—	2	1	no	—
30	Q₈×C₇₃	C₂×C₈	1	2	yes	—
31	D₂₉₂	—	2	2	no	—
32	D₂₉₂	C₂×C₈	1	2	yes	—
33	C₄×D₇₃	—	2	2	no	—
34	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
35	#10596833	—	2	2	no	—
36	#10596833	C₂×D₄	1	1	yes	characteristic
37	#10596833	#41	1	1	yes	characteristic
38	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
39	#10596831	C₂×C₈	1	1	yes	characteristic
40	C₂×D₇₃	—	2	2	no	—
41	C₂×D₇₃	#131	1	1	yes	characteristic
42	#64408	—	4	1	no	—
43	C₄×C₇₃	—	2	2	no	—
44	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
45	Dic₇₃	C₄×D₄	1	1	yes	characteristic
46	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
47	D₇₃	—	2	1	no	—
48	D₇₃	—	4	2	no	—
49	#2171	—	73	1	no	maximal, Sylow
50	C₇₃	#2171	1	1	yes	characteristic, complemented, Sylow
51	#504	—	73	2	no	—
52	#443	—	73	1	no	—
53	#364	—	73	1	no	—
54	#350	—	73	2	no	—
55	#346	—	73	1	no	—
56	#135	—	73	1	no	—
57	#131	—	73	2	no	—
58	M₃₂	—	73	2	no	—
59	M₃₂	—	146	2	no	—
60	C₂×C₁₆	—	73	1	no	—
61	C₂×C₁₆	—	73	1	no	—
62	C₂×C₁₆	—	146	2	no	—
63	#108	—	73	1	no	—
64	#104	—	73	2	no	—
65	C₄×C₈	—	73	1	no	—
66	#41	—	73	2	no	—
67	Q₁₆	#10596842	1	1	yes	characteristic
68	SD₁₆	—	73	2	no	—
69	D₈	—	73	1	no	—
70	M₁₆	—	73	2	no	—
71	M₁₆	—	146	2	no	—
72	C₂×C₈	—	73	1	no	—
73	C₂×C₈	—	73	1	no	—
74	C₂×C₈	—	146	2	no	—
75	C₄²	—	73	1	no	—
76	C₁₆	—	73	2	no	—
77	C₁₆	—	146	1	no	—
78	C₁₆	—	146	2	no	—
79	Q₈	C₂×#10596842	1	2	yes	—
80	D₄	—	73	2	no	—
81	D₄	—	146	2	no	—
82	C₂×C₄	—	73	1	no	—
83	C₂×C₄	—	146	2	no	—
84	C₂×C₄	—	146	1	no	—
85	C₈	—	73	1	no	—
86	C₈	—	73	1	no	—
87	C₈	—	73	1	no	—
88	C₈	—	146	2	no	—
89	C₈	C₂×#10596842	1	1	yes	characteristic
90	C₂²	—	73	1	no	—
91	C₂²	—	146	2	no	—
92	C₄	—	2	2	no	—
93	C₄	—	292	1	no	—
94	C₄	—	73	1	no	—
95	C₄	C₂²×#10596842	1	1	yes	characteristic
96	C₂	—	292	2	no	—
97	C₂	—	146	1	no	—
98	C₂	D₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989709

C₂

yes

maximal, complemented

#17989691

C₂

yes

maximal, characteristic, complemented

#17989688

C₂

yes

maximal, complemented

#17989682

C₂

yes

maximal, characteristic, complemented

#17989631

C₂

yes

maximal, characteristic

#14556688

—

#14556688

C₂²

yes

—

#14556686

—

#14556686

C₂²

yes

characteristic

#14556686

C₂²

yes

characteristic

#14556679

C₂²

yes

—

#14556662

C₄

yes

characteristic

#14556656

C₄

yes

—

C₈×#64408

C₂²

yes

characteristic

#14556614

C₄

yes

—

—

D₄

yes

—

#11924038

—

#11924038

C₂×C₄

yes

—

#11924036

—

#11924036

C₂³

yes

characteristic

C₄×#64408

C₂×C₄

yes

characteristic

#11924029

C₂×C₄

yes

—

#11924015

C₈

yes

—

D₅₈₄

C₈

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

Q₁₆×C₇₃

C₈

yes

characteristic

C₂×#64408

—

Q₈×C₇₃

C₂×C₈

yes

—

D₂₉₂

—

D₂₉₂

C₂×C₈

yes

—

C₄×D₇₃

—

C₄×D₇₃

C₂²×C₄

yes

characteristic

#10596833

—

#10596833

C₂×D₄

yes

yes

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#131

yes

characteristic

#64408

—

C₄×C₇₃

—

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₄×D₄

yes

characteristic

C₂×C₇₃

C₈×D₄

yes

characteristic

D₇₃

—

D₇₃

—

#2171

—

maximal, Sylow

C₇₃

#2171

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#108

—

#104

—

C₄×C₈

—

#41

—

Q₁₆

#10596842

yes

characteristic

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄²

—

C₁₆

—

C₁₆

—

146

—

C₁₆

—

146

—

Q₈

C₂×#10596842

yes

—

D₄

—

D₄

—

146

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₈

—

C₈

—

C₈

—

C₈

—

146

—

C₈

C₂×#10596842

yes

characteristic

C₂²

—

C₂²

—

146

—

C₄

—

C₄

—

292

—

C₄

—

C₄

C₂²×#10596842

yes

characteristic

C₂

—

292

—

C₂

—

146

—

C₂

D₄×#10596842

yes

characteristic

	subgroup	G/H
center	C₂	D₄×#10596842
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₄	C₂²×#10596842
Fitting	Q₁₆×C₇₃	C₈
socle	C₂×C₇₃	C₈×D₄
hypercenter	Q₁₆	#10596842
hypocenter	C₇₃	#2171
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

subgroup

G/H

center

C₂

D₄×#10596842

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₄

C₂²×#10596842

Fitting

Q₁₆×C₇₃

C₈

socle

C₂×C₇₃

C₈×D₄

Q₁₆

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

N	H ≅ G/N	type
1. #17989709	C₂	semidirect
2. #17989691	C₂	semidirect
3. #17989688	C₂	semidirect
4. #17989682	C₂	semidirect
50. C₇₃	#2171	semidirect

H ≅ G/N

type

1. #17989709

C₂

semidirect

2. #17989691

C₂

semidirect

3. #17989688

C₂

semidirect

4. #17989682

C₂

semidirect

50. C₇₃

#2171

semidirect

Subgroups — #22627152

Conjugacy classes of subgroups

Complements