Group #22626321 — subgroups

Subgroups — #22626321

Order 9344.

144 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 66 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	#17989645	C₂	1	2	yes	maximal, complemented
2	#17989509	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989485	C₂	1	2	yes	maximal, complemented
4	#17989476	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988704	C₂	1	1	yes	maximal, characteristic
6	#14556665	—	2	2	no	—
7	#14556665	C₂²	1	2	yes	—
8	C₂×#11924031	—	2	2	no	—
9	C₂×#11924031	C₂²	1	1	yes	characteristic
10	C₂×#11924031	C₂²	1	1	yes	characteristic
11	#14556598	C₂²	1	2	yes	—
12	#14556527	C₄	1	1	yes	characteristic
13	#14556518	C₄	1	2	yes	—
14	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
15	#135×C₇₃	C₄	1	1	yes	characteristic
16	#11924031	—	2	2	no	—
17	#11924031	—	2	1	no	—
18	#11924031	D₄	1	2	yes	—
19	#11924012	—	2	2	no	—
20	#11924012	C₂×C₄	1	2	yes	—
21	C₂×#10596831	—	2	2	no	—
22	C₂×#10596831	C₂³	1	1	yes	characteristic
23	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	#41×C₇₃	C₂×C₄	1	2	yes	—
25	Q₁₆×C₇₃	C₈	1	1	yes	characteristic
26	SD₁₆×C₇₃	C₈	1	2	yes	—
27	D₈×C₇₃	C₈	1	1	yes	characteristic
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	Q₈×C₇₃	C₂×C₈	1	2	yes	—
30	D₄×C₇₃	—	2	2	no	—
31	D₄×C₇₃	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₇₃	—	2	1	no	—
35	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
37	#10596831	—	2	2	no	—
38	#10596831	C₂×D₄	1	1	yes	characteristic
39	#10596831	#41	1	1	yes	characteristic
40	C₂²×C₇₃	—	2	2	no	—
41	C₂²×C₇₃	#131	1	1	yes	characteristic
42	C₄×C₇₃	—	2	2	no	—
43	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
44	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
45	Dic₇₃	—	4	1	no	—
46	C₂×C₇₃	—	2	1	no	—
47	C₂×C₇₃	—	4	2	no	—
48	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
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	#64408	1	1	yes	characteristic
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	C₂×#64408	1	2	yes	—
67	Q₁₆	#10596833	1	1	yes	characteristic
68	SD₁₆	#10596833	1	2	yes	—
69	D₈	#10596833	1	1	yes	characteristic
70	M₁₆	—	73	2	no	—
71	M₁₆	—	146	2	no	—
72	C₂×C₈	—	73	1	no	—
73	C₂×C₈	—	146	2	no	—
74	C₂×C₈	C₂×#64408	1	1	yes	characteristic
75	C₄²	—	73	1	no	—
76	C₁₆	—	73	2	no	—
77	C₁₆	—	146	1	no	—
78	C₁₆	—	146	2	no	—
79	Q₈	C₂×#10596833	1	2	yes	—
80	D₄	—	2	2	no	—
81	D₄	C₂×#10596833	1	2	yes	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	146	1	no	—
84	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
85	C₈	—	73	1	no	—
86	C₈	—	73	1	no	—
87	C₈	—	146	2	no	—
88	C₈	C₂×#10596833	1	1	yes	characteristic
89	C₈	C₂×#10596833	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#14556678	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	292	1	no	—
94	C₄	D₄×#64408	1	1	yes	characteristic
95	C₄	C₂²×#10596833	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	4	2	no	—
98	C₂	D₄×#10596833	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989645

C₂

yes

maximal, complemented

#17989509

C₂

yes

maximal, characteristic, complemented

#17989485

C₂

yes

maximal, complemented

#17989476

C₂

yes

maximal, characteristic, complemented

#17988704

C₂

yes

maximal, characteristic

#14556665

—

#14556665

C₂²

yes

—

C₂×#11924031

—

C₂×#11924031

C₂²

yes

characteristic

C₂×#11924031

C₂²

yes

characteristic

#14556598

C₂²

yes

—

#14556527

C₄

yes

characteristic

#14556518

C₄

yes

—

C₈×Dic₇₃

C₂²

yes

characteristic

#135×C₇₃

C₄

yes

—

—

D₄

yes

—

#11924012

—

#11924012

C₂×C₄

yes

—

C₂×#10596831

—

C₂×#10596831

C₂³

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

#41×C₇₃

C₂×C₄

yes

—

Q₁₆×C₇₃

C₈

yes

characteristic

SD₁₆×C₇₃

C₈

yes

—

D₈×C₇₃

C₈

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

Q₈×C₇₃

C₂×C₈

yes

—

D₄×C₇₃

—

D₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₈×C₇₃

C₂×C₈

yes

characteristic

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

—

#10596831

C₂×D₄

yes

yes

C₂²×C₇₃

—

C₂²×C₇₃

#131

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₈×D₄

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

—

—

yes

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#108

—

#104

—

C₄×C₈

—

#41

C₂×#64408

yes

—

Q₁₆

#10596833

yes

characteristic

SD₁₆

#10596833

yes

—

D₈

#10596833

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

—

146

—

C₁₆

—

146

—

Q₈

C₂×#10596833

yes

—

D₄

—

D₄

C₂×#10596833

yes

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

C₈

—

146

—

C₈

yes

C₈

yes

C₂²

—

C₂²

#14556678

yes

characteristic

C₄

—

C₄

—

292

—

C₄

yes

C₄

yes

C₂

—

C₂

—

C₂

D₄×#10596833

yes

characteristic

	subgroup	G/H
center	C₄	D₄×#64408
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	#135×C₇₃	C₄
socle	C₂×C₇₃	C₈×D₄
hypercenter	#135	#64408
hypocenter	C₇₃	#2171
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

subgroup

G/H

center

C₄

D₄×#64408

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×#64408

Fitting

#135×C₇₃

C₄

socle

C₂×C₇₃

C₈×D₄

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

N	H ≅ G/N	type
1. #17989645	C₂	semidirect
2. #17989509	C₂	semidirect
3. #17989485	C₂	semidirect
4. #17989476	C₂	semidirect
50. C₇₃	#2171	semidirect

H ≅ G/N

type

1. #17989645

C₂

semidirect

2. #17989509

C₂

semidirect

3. #17989485

C₂

semidirect

4. #17989476

C₂

semidirect

50. C₇₃

#2171

semidirect

Subgroups — #22626321

Conjugacy classes of subgroups

Complements