Group #22611812 — subgroups

Subgroups — #22611812

Order 9344.

146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 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	#17988704	C₂	1	2	yes	maximal, complemented
2	#17988417	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988394	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#508×C₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556598	—	2	2	no	—
7	C₂×#11924003	C₂²	1	1	yes	characteristic
8	#14556527	C₂²	1	2	yes	—
9	#14556518	—	2	2	no	—
10	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
11	#135×C₇₃	C₂²	1	2	yes	—
12	Q₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
13	SD₃₂×C₇₃	C₄	1	2	yes	complemented
14	D₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
16	#11924012	—	2	2	no	—
17	#11924012	—	4	2	no	—
18	C₂×#10596831	—	4	2	no	—
19	C₂×#10596831	D₄	1	1	yes	characteristic
20	C₄×Dic₇₃	D₄	1	1	yes	characteristic
21	#11924003	—	2	1	no	—
22	#41×C₇₃	—	2	2	no	—
23	Q₁₆×C₇₃	C₂×C₄	1	2	yes	—
24	SD₁₆×C₇₃	—	2	2	no	—
25	D₈×C₇₃	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
27	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
29	Q₈×C₇₃	—	2	2	no	—
30	D₄×C₇₃	—	2	2	no	—
31	D₄×C₇₃	—	4	2	no	—
32	C₂×C₄×C₇₃	—	4	2	no	—
33	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₇₃	—	2	1	no	—
35	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₇₃	#41	1	1	yes	characteristic
37	#10596831	—	4	2	no	—
38	#10596831	D₈	1	1	yes	characteristic
39	#10596831	D₈	1	1	yes	characteristic
40	C₂²×C₇₃	—	4	2	no	—
41	C₂²×C₇₃	#135	1	1	yes	characteristic
42	C₄×C₇₃	—	4	2	no	—
43	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
44	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
45	Dic₇₃	—	2	2	no	—
46	C₂×C₇₃	—	2	1	no	—
47	C₂×C₇₃	—	8	2	no	—
48	C₂×C₇₃	C₄×D₈	1	1	yes	characteristic
49	#2178	—	73	1	no	maximal, Sylow
50	C₇₃	#2178	1	1	yes	characteristic, complemented, Sylow
51	#508	D₇₃	1	1	yes	characteristic
52	#443	—	73	2	no	—
53	#368	—	73	1	no	—
54	#359	—	73	2	no	—
55	C₄×C₁₆	—	73	1	no	—
56	#135	C₂×D₇₃	1	2	yes	—
57	#131	—	146	2	no	—
58	Q₃₂	Dic₇₃	1	1	yes	characteristic, complemented
59	SD₃₂	Dic₇₃	1	2	yes	complemented
60	D₁₆	Dic₇₃	1	1	yes	characteristic, complemented
61	C₂×C₁₆	—	73	1	no	—
62	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
63	#108	—	73	2	no	—
64	#104	—	146	2	no	—
65	C₄×C₈	—	73	1	no	—
66	#41	—	2	2	no	—
67	Q₁₆	C₂×Dic₇₃	1	2	yes	—
68	SD₁₆	—	2	2	no	—
69	D₈	C₂×Dic₇₃	1	2	yes	—
70	M₁₆	—	292	2	no	—
71	M₁₆	—	146	2	no	—
72	C₂×C₈	—	292	2	no	—
73	C₂×C₈	—	73	1	no	—
74	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
75	C₄²	—	73	1	no	—
76	C₁₆	—	146	1	no	—
77	C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
78	C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
79	Q₈	—	2	2	no	—
80	D₄	—	2	2	no	—
81	D₄	—	4	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	146	1	no	—
84	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
85	C₈	—	292	2	no	—
86	C₈	—	73	1	no	—
87	C₈	—	73	1	no	—
88	C₈	C₂²×Dic₇₃	1	1	yes	characteristic
89	C₈	#11924027	1	1	yes	characteristic
90	C₂²	—	4	2	no	—
91	C₂²	#14556610	1	1	yes	characteristic
92	C₄	—	4	2	no	—
93	C₄	—	146	2	no	—
94	C₄	D₄×Dic₇₃	1	1	yes	characteristic
95	C₄	D₈×D₇₃	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	8	2	no	—
98	C₂	D₈×Dic₇₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988704

C₂

yes

maximal, complemented

#17988417

C₂

yes

maximal, characteristic, complemented

#17988394

C₂

yes

maximal, complemented

C₁₆×Dic₇₃

C₂

yes

maximal, characteristic, complemented

#508×C₇₃

C₂

yes

maximal, characteristic

#14556598

—

C₂×#11924003

C₂²

yes

characteristic

#14556527

C₂²

yes

—

#14556518

—

C₈×Dic₇₃

C₂²

yes

characteristic

#135×C₇₃

C₂²

yes

—

Q₃₂×C₇₃

C₄

yes

characteristic, complemented

SD₃₂×C₇₃

C₄

yes

complemented

D₁₆×C₇₃

C₄

yes

characteristic, complemented

C₂×C₁₆×C₇₃

C₂²

yes

—

—

—

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

#11924003

—

#41×C₇₃

—

Q₁₆×C₇₃

C₂×C₄

yes

—

SD₁₆×C₇₃

—

D₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

C₂×C₄

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₈×C₇₃

C₂²×C₄

yes

C₈×C₇₃

yes

—

D₈

yes

characteristic

#10596831

D₈

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

#135

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₄×D₈

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#508

D₇₃

yes

—

—

—

C₄×C₁₆

—

#135

C₂×D₇₃

yes

—

#131

—

146

—

Q₃₂

Dic₇₃

yes

characteristic, complemented

SD₃₂

Dic₇₃

yes

complemented

D₁₆

Dic₇₃

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#108

—

#104

—

146

—

C₄×C₈

—

#41

—

Q₁₆

C₂×Dic₇₃

yes

—

SD₁₆

—

D₈

C₂×Dic₇₃

yes

—

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄²

—

C₁₆

—

146

—

C₁₆

C₂×Dic₇₃

yes

characteristic

C₁₆

C₂×Dic₇₃

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₈

—

292

—

C₈

—

C₈

—

C₈

C₂²×Dic₇₃

yes

characteristic

C₈

#11924027

yes

characteristic

C₂²

—

C₂²

#14556610

yes

characteristic

C₄

—

C₄

—

146

—

C₄

D₄×Dic₇₃

yes

characteristic

C₄

D₈×D₇₃

yes

characteristic

C₂

—

C₂

—

C₂

D₈×Dic₇₃

yes

characteristic

	subgroup	G/H
center	C₄	D₈×D₇₃
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#508×C₇₃	C₂
socle	C₂×C₇₃	C₄×D₈
hypercenter	#508	D₇₃
hypocenter	C₇₃	#2178
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

subgroup

G/H

center

C₄

D₈×D₇₃

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#508×C₇₃

C₂

socle

C₂×C₇₃

C₄×D₈

D₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

N	H ≅ G/N	type
1. #17988704	C₂	semidirect
2. #17988417	C₂	semidirect
3. #17988394	C₂	semidirect
4. C₁₆×Dic₇₃	C₂	semidirect
12. Q₃₂×C₇₃	C₄	semidirect
13. SD₃₂×C₇₃	C₄	semidirect
14. D₁₆×C₇₃	C₄	semidirect
50. C₇₃	#2178	semidirect
58. Q₃₂	Dic₇₃	semidirect
59. SD₃₂	Dic₇₃	semidirect
60. D₁₆	Dic₇₃	semidirect

H ≅ G/N

type

1. #17988704

C₂

semidirect

2. #17988417

C₂

semidirect

3. #17988394

C₂

semidirect

4. C₁₆×Dic₇₃

C₂

semidirect

12. Q₃₂×C₇₃

C₄

semidirect

13. SD₃₂×C₇₃

C₄

semidirect

14. D₁₆×C₇₃

C₄

semidirect

50. C₇₃

#2178

semidirect

58. Q₃₂

Dic₇₃

semidirect

59. SD₃₂

Dic₇₃

semidirect

60. D₁₆

Dic₇₃

semidirect

Subgroups — #22611812

Conjugacy classes of subgroups

Complements