Group #22611774 — subgroups

Subgroups — #22611774

Order 9344.

144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 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	#17989003	C₂	1	2	yes	maximal, complemented
2	#17988705	C₂	1	1	yes	maximal, characteristic
3	#17988408	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988370	C₂	1	2	yes	maximal, complemented
5	#346×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556613	C₄	1	1	yes	characteristic
7	#14556597	C₂²	1	2	yes	—
8	#14556531	C₂²	1	2	yes	—
9	#14556530	—	2	2	no	—
10	C₁₆×D₇₃	—	2	2	no	—
11	#14556527	C₄	1	1	yes	characteristic
12	#14556519	C₄	1	2	yes	—
13	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	#11924028	C₂×C₄	1	2	yes	—
17	Dic₂₉₂	C₈	1	1	yes	characteristic
18	#11924017	C₈	1	2	yes	—
19	D₅₈₄	C₈	1	1	yes	characteristic
20	#11924012	C₂×C₄	1	2	yes	—
21	#11924011	—	2	2	no	—
22	C₈×D₇₃	—	2	2	no	—
23	#11924003	—	2	2	no	—
24	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
26	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₇₃	—	2	1	no	—
28	C₁₆×C₇₃	D₄	1	2	yes	—
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂²⋊D₇₃	—	2	2	no	—
32	D₂₉₂	C₂×C₈	1	2	yes	—
33	C₄×D₇₃	—	2	2	no	—
34	Dic₁₄₆	C₂×C₈	1	2	yes	—
35	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
37	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₈×C₇₃	#41	1	1	yes	characteristic
39	#10596831	—	2	2	no	—
40	C₂²×C₇₃	#131	1	1	yes	characteristic
41	C₂×D₇₃	—	2	2	no	—
42	C₄×C₇₃	—	4	1	no	—
43	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
44	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
45	Dic₇₃	—	2	2	no	—
46	C₂×C₇₃	—	2	1	no	—
47	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
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	D₇₃	1	1	yes	characteristic, complemented
56	#135	—	73	1	no	—
57	#131	—	73	2	no	—
58	M₃₂	—	73	2	no	—
59	M₃₂	—	146	2	no	—
60	C₂×C₁₆	—	146	2	no	—
61	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
62	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
63	#108	—	73	1	no	—
64	#104	—	73	2	no	—
65	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
66	#41	—	73	2	no	—
67	Q₁₆	—	73	1	no	—
68	SD₁₆	—	73	2	no	—
69	D₈	—	73	1	no	—
70	M₁₆	—	73	2	no	—
71	M₁₆	—	146	2	no	—
72	C₂×C₈	—	146	2	no	—
73	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
75	C₄²	C₄×D₇₃	1	1	yes	characteristic
76	C₁₆	—	2	1	no	—
77	C₁₆	—	146	2	no	—
78	C₁₆	D₂₉₂	1	2	yes	—
79	Q₈	—	73	2	no	—
80	D₄	—	73	2	no	—
81	D₄	—	146	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	146	2	no	—
84	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
85	C₈	—	146	2	no	—
86	C₈	C₈×D₇₃	1	1	yes	characteristic
87	C₈	C₈×D₇₃	1	1	yes	characteristic
88	C₈	C₂×D₂₉₂	1	1	yes	characteristic
89	C₈	#11924028	1	1	yes	characteristic
90	C₂²	—	146	2	no	—
91	C₂²	#14556597	1	1	yes	characteristic
92	C₄	—	4	1	no	—
93	C₄	—	146	2	no	—
94	C₄	C₄×D₂₉₂	1	1	yes	characteristic
95	C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	292	2	no	—
98	C₂	C₈×D₂₉₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989003

C₂

yes

maximal, complemented

#17988705

C₂

yes

maximal, characteristic

#17988408

C₂

yes

maximal, characteristic, complemented

#17988370

C₂

yes

maximal, complemented

#346×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556613

C₄

yes

characteristic

#14556597

C₂²

yes

—

#14556531

C₂²

yes

—

#14556530

—

C₁₆×D₇₃

—

#14556527

C₄

yes

characteristic

#14556519

C₄

yes

—

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

#11924028

C₂×C₄

yes

—

Dic₂₉₂

C₈

yes

characteristic

#11924017

C₈

yes

—

D₅₈₄

C₈

yes

characteristic

#11924012

C₂×C₄

yes

—

#11924011

—

C₈×D₇₃

—

#11924003

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

D₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²⋊D₇₃

—

D₂₉₂

C₂×C₈

yes

—

C₄×D₇₃

—

Dic₁₄₆

C₂×C₈

yes

—

C₈×C₇₃

C₂×C₈

yes

characteristic

C₈×C₇₃

C₂×C₈

yes

characteristic

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

#131

yes

characteristic

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₈×D₄

yes

characteristic

D₇₃

—

#2171

—

maximal, Sylow

C₇₃

#2171

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic, complemented

#135

—

#131

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#108

—

#104

—

C₄×C₈

C₂×D₇₃

yes

characteristic

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄²

C₄×D₇₃

yes

characteristic

C₁₆

—

C₁₆

—

146

—

C₁₆

D₂₉₂

yes

—

Q₈

—

D₄

—

D₄

—

146

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₈

—

146

—

C₈

C₈×D₇₃

yes

characteristic

C₈

C₈×D₇₃

yes

characteristic

C₈

C₂×D₂₉₂

yes

characteristic

C₈

#11924028

yes

characteristic

C₂²

—

146

—

C₂²

#14556597

yes

characteristic

C₄

—

C₄

—

146

—

C₄

C₄×D₂₉₂

yes

characteristic

C₄

C₂×C₈×D₇₃

yes

characteristic

C₂

—

C₂

—

292

—

C₂

C₈×D₂₉₂

yes

characteristic

	subgroup	G/H
center	C₈	C₂×D₂₉₂
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#346×C₇₃	C₂
socle	C₂×C₇₃	C₈×D₄
hypercenter	#346	D₇₃
hypocenter	C₇₃	#2171
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #346

subgroup

G/H

center

C₈

C₂×D₂₉₂

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#346×C₇₃

C₂

socle

C₂×C₇₃

C₈×D₄

D₇₃

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #346

N	H ≅ G/N	type
1. #17989003	C₂	semidirect
3. #17988408	C₂	semidirect
4. #17988370	C₂	semidirect
5. #346×C₇₃	C₂	semidirect
50. C₇₃	#2171	semidirect
55. #346	D₇₃	semidirect

H ≅ G/N

type

1. #17989003

C₂

semidirect

3. #17988408

C₂

semidirect

4. #17988370

C₂

semidirect

5. #346×C₇₃

C₂

semidirect

50. C₇₃

#2171

semidirect

55. #346

D₇₃

semidirect

Subgroups — #22611774

Conjugacy classes of subgroups

Complements