Group #22627148 — subgroups

Subgroups — #22627148

Order 9344.

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

normal subgroups only

This group has 146 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	#17989708	C₂	1	2	yes	maximal, complemented
2	#17989692	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989687	C₂	1	2	yes	maximal, complemented
4	#64408⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989629	C₂	1	1	yes	maximal, characteristic
6	#14556688	C₂²	1	2	yes	—
7	#14556687	—	2	2	no	—
8	#14556686	C₂²	1	1	yes	characteristic
9	#14556686	C₂²	1	1	yes	characteristic
10	C₂×#11924040	—	2	2	no	—
11	#14556678	C₂²	1	2	yes	—
12	#14556662	C₄	1	1	yes	characteristic
13	#14556655	C₄	1	2	yes	—
14	C₈×#64408	C₂²	1	1	yes	characteristic
15	#14556610	C₄	1	1	yes	characteristic
16	#11924040	—	2	2	no	—
17	#11924040	—	2	1	no	—
18	#11924040	D₄	1	1	yes	characteristic
19	#11924040	D₄	1	1	yes	characteristic
20	#11924038	C₂×C₄	1	2	yes	—
21	#11924037	—	2	2	no	—
22	#11924036	C₂³	1	1	yes	characteristic
23	C₂×#10596833	—	2	2	no	—
24	C₄×#64408	C₂×C₄	1	1	yes	characteristic
25	#11924027	C₂×C₄	1	2	yes	—
26	Dic₂₉₂	C₈	1	1	yes	characteristic
27	#11924016	C₈	1	2	yes	—
28	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
29	D₈×C₇₃	C₈	1	1	yes	characteristic
30	C₂×#64408	—	2	1	no	—
31	D₄×C₇₃	C₂×C₈	1	2	yes	—
32	C₂²⋊D₇₃	—	2	2	no	—
33	C₂×Dic₇₃	—	2	2	no	—
34	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
35	Dic₁₄₆	C₂×C₈	1	2	yes	—
36	#10596833	—	2	2	no	—
37	#10596833	C₂×D₄	1	1	yes	characteristic
38	#10596833	#41	1	1	yes	characteristic
39	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
40	#10596831	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₇₃	—	2	2	no	—
42	C₂×D₇₃	#131	1	1	yes	characteristic
43	#64408	—	2	2	no	—
44	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
45	Dic₇₃	—	2	2	no	—
46	Dic₇₃	C₄×D₄	1	1	yes	characteristic
47	C₂×C₇₃	—	4	2	no	—
48	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
49	D₇₃	—	2	1	no	—
50	#2170	—	73	1	no	maximal, Sylow
51	C₇₃	#2170	1	1	yes	characteristic, complemented, Sylow
52	#504	—	73	2	no	—
53	#443	—	73	1	no	—
54	#364	—	73	1	no	—
55	#350	—	73	2	no	—
56	C₄×C₁₆	—	73	1	no	—
57	#135	—	73	1	no	—
58	#131	—	73	2	no	—
59	M₃₂	—	73	2	no	—
60	M₃₂	—	146	2	no	—
61	C₂×C₁₆	—	73	1	no	—
62	C₂×C₁₆	—	73	1	no	—
63	C₂×C₁₆	—	146	2	no	—
64	#108	—	73	1	no	—
65	#104	—	73	2	no	—
66	C₄×C₈	—	73	1	no	—
67	#41	—	73	2	no	—
68	Q₁₆	—	73	1	no	—
69	SD₁₆	—	73	2	no	—
70	D₈	#10596842	1	1	yes	characteristic
71	M₁₆	—	73	2	no	—
72	M₁₆	—	146	2	no	—
73	C₂×C₈	—	73	1	no	—
74	C₂×C₈	—	73	1	no	—
75	C₂×C₈	—	146	2	no	—
76	C₄²	—	73	1	no	—
77	C₁₆	—	73	1	no	—
78	C₁₆	—	73	1	no	—
79	C₁₆	—	146	1	no	—
80	C₁₆	—	146	2	no	—
81	Q₈	—	73	2	no	—
82	D₄	—	146	2	no	—
83	D₄	C₂×#10596842	1	2	yes	—
84	C₂×C₄	—	73	1	no	—
85	C₂×C₄	—	146	2	no	—
86	C₂×C₄	—	146	1	no	—
87	C₈	—	73	1	no	—
88	C₈	—	73	1	no	—
89	C₈	—	73	1	no	—
90	C₈	—	146	2	no	—
91	C₈	C₂×#10596842	1	1	yes	characteristic
92	C₂²	—	2	2	no	—
93	C₂²	—	73	1	no	—
94	C₄	—	73	1	no	—
95	C₄	—	146	2	no	—
96	C₄	—	146	2	no	—
97	C₄	C₂²×#10596842	1	1	yes	characteristic
98	C₂	—	4	2	no	—
99	C₂	—	146	1	no	—
100	C₂	D₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989708

C₂

yes

maximal, complemented

#17989692

C₂

yes

maximal, characteristic, complemented

#17989687

C₂

yes

maximal, complemented

#64408⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#17989629

C₂

yes

maximal, characteristic

#14556688

C₂²

yes

—

#14556687

—

#14556686

C₂²

yes

characteristic

#14556686

C₂²

yes

characteristic

C₂×#11924040

—

#14556678

C₂²

yes

—

#14556662

C₄

yes

characteristic

#14556655

C₄

yes

—

C₈×#64408

C₂²

yes

characteristic

#14556610

C₄

yes

—

—

D₄

yes

characteristic

#11924040

D₄

yes

characteristic

#11924038

C₂×C₄

yes

—

#11924037

—

#11924036

C₂³

yes

characteristic

C₂×#10596833

—

C₄×#64408

C₂×C₄

yes

characteristic

#11924027

C₂×C₄

yes

—

Dic₂₉₂

C₈

yes

characteristic

#11924016

C₈

yes

—

C₈×D₇₃

C₂×C₄

yes

characteristic

D₈×C₇₃

C₈

yes

characteristic

C₂×#64408

—

D₄×C₇₃

C₂×C₈

yes

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₄×D₇₃

C₂²×C₄

yes

characteristic

Dic₁₄₆

C₂×C₈

yes

—

#10596833

—

#10596833

C₂×D₄

yes

yes

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

C₂²×C₇₃

—

C₂×D₇₃

#131

yes

characteristic

#64408

—

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄×D₄

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₈×D₄

yes

characteristic

D₇₃

—

#2170

—

maximal, Sylow

C₇₃

#2170

yes

characteristic, complemented, Sylow

—

—

—

—

C₄×C₁₆

—

#135

—

#131

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#108

—

#104

—

C₄×C₈

—

#41

—

Q₁₆

—

SD₁₆

—

D₈

#10596842

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

146

—

C₁₆

—

146

—

Q₈

—

D₄

—

146

—

D₄

C₂×#10596842

yes

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₈

—

C₈

—

C₈

—

C₈

—

146

—

C₈

C₂×#10596842

yes

characteristic

C₂²

—

C₂²

—

C₄

—

C₄

—

146

—

C₄

—

146

—

C₄

C₂²×#10596842

yes

characteristic

C₂

—

C₂

—

146

—

100

C₂

D₄×#10596842

yes

characteristic

	subgroup	G/H
center	C₂	D₄×#10596842
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₄	C₂²×#10596842
Fitting	D₈×C₇₃	C₈
socle	C₂×C₇₃	C₈×D₄
hypercenter	D₈	#10596842
hypocenter	C₇₃	#2170
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

subgroup

G/H

center

C₂

D₄×#10596842

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₄

C₂²×#10596842

Fitting

D₈×C₇₃

C₈

socle

C₂×C₇₃

C₈×D₄

D₈

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ D₈

N	H ≅ G/N	type
1. #17989708	C₂	semidirect
2. #17989692	C₂	semidirect
3. #17989687	C₂	semidirect
4. #64408⋊C₁₆	C₂	semidirect
51. C₇₃	#2170	semidirect

H ≅ G/N

type

1. #17989708

C₂

semidirect

2. #17989692

C₂

semidirect

3. #17989687

C₂

semidirect

4. #64408⋊C₁₆

C₂

semidirect

51. C₇₃

#2170

semidirect

Subgroups — #22627148

Conjugacy classes of subgroups

Complements