Group #22626273 — subgroups

Subgroups — #22626273

Order 9344.

152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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	#17989643	C₂	1	2	yes	maximal
2	#17989510	C₂	1	2	yes	maximal, complemented
3	#17989509	C₂	1	2	yes	maximal, complemented
4	#17988544	C₂	1	1	yes	maximal, characteristic
5	#14556666	—	2	2	no	—
6	#14556665	C₂²	1	4	yes	—
7	#14556664	—	2	2	no	—
8	C₂×#11924011	C₄	1	1	yes	characteristic
9	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
10	#14556548	C₄	1	1	yes	characteristic
11	#14556501	C₄	1	1	yes	characteristic
12	C₄×#10596831	C₂²	1	1	yes	characteristic
13	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	#97×C₇₃	C₄	1	1	yes	characteristic
15	#11924031	—	2	4	no	—
16	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
17	#11924011	C₈	1	4	yes	—
18	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	C₂³	1	1	yes	characteristic
20	C₈×D₇₃	D₄	1	2	yes	—
21	C₈×D₇₃	Q₈	1	2	yes	—
22	#11924007	—	2	1	no	—
23	#11924005	—	2	1	no	—
24	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₇₃	—	2	1	no	—
32	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
33	C₄×D₇₃	C₄⋊C₄	1	2	yes	—
34	C₄×D₇₃	C₂×C₈	1	2	yes	—
35	C₈×C₇₃	C₄⋊C₄	1	2	yes	—
36	C₈×C₇₃	C₂×C₈	1	2	yes	—
37	#10596831	C₂×C₈	1	2	yes	—
38	#10596831	C₂×D₄	1	1	yes	characteristic
39	#10596831	C₂×Q₈	1	1	yes	characteristic
40	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
41	C₂×D₇₃	—	4	1	no	—
42	C₂×D₇₃	C₄⋊C₈	1	2	yes	—
43	C₄×C₇₃	—	4	1	no	—
44	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
46	Dic₇₃	—	4	1	no	—
47	Dic₇₃	C₄⋊C₈	1	2	yes	—
48	C₂×C₇₃	—	2	1	no	—
49	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
50	D₇₃	—	2	2	no	—
51	#2153	—	73	1	no	maximal, Sylow
52	C₇₃	#2153	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₃₂	—	73	2	no	—
54	#405	—	73	1	no	—
55	#364	—	73	2	no	—
56	#364	—	73	2	no	—
57	C₂×M₁₆	—	73	1	no	—
58	C₂²×C₈	—	73	1	no	—
59	#117	—	73	1	no	—
60	M₃₂	—	73	4	no	—
61	M₃₂	—	146	2	no	—
62	C₂×C₁₆	—	146	2	no	—
63	#97	—	73	1	no	—
64	#97	#64408	1	1	yes	characteristic
65	C₄×C₈	—	73	1	no	—
66	C₄×C₈	—	73	1	no	—
67	C₂²×C₄	—	73	1	no	—
68	M₁₆	—	73	4	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	—	73	1	no	—
71	C₂×C₈	—	73	2	no	—
72	C₂×C₈	—	73	2	no	—
73	C₂×C₈	C₂×#64408	1	1	yes	characteristic
74	C₂×C₈	C₂×#64408	1	1	yes	characteristic
75	C₄⋊C₄	—	146	1	no	—
76	C₂²⋊C₄	—	146	1	no	—
77	C₄²	—	73	1	no	—
78	C₄²	C₂×#64408	1	1	yes	characteristic
79	C₁₆	—	146	4	no	—
80	C₂³	—	73	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	73	1	no	—
83	C₂×C₄	—	73	2	no	—
84	C₂×C₄	—	73	2	no	—
85	C₂×C₄	—	146	1	no	—
86	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
87	C₈	—	73	2	no	—
88	C₈	—	73	1	no	—
89	C₈	—	73	1	no	—
90	C₈	C₄⋊#64408	1	2	yes	—
91	C₈	#11924036	1	2	yes	—
92	C₂²	—	292	1	no	—
93	C₂²	—	73	2	no	—
94	C₂²	D₇₃⋊M₁₆	1	1	yes	characteristic
95	C₄	—	4	1	no	—
96	C₄	—	292	1	no	—
97	C₄	—	73	2	no	—
98	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
99	C₄	C₂×#11924036	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	146	2	no	—
102	C₂	#17989588	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989643

C₂

yes

maximal

#17989510

C₂

yes

maximal, complemented

#17989509

C₂

yes

maximal, complemented

#17988544

C₂

yes

maximal, characteristic

#14556666

—

#14556665

C₂²

yes

—

#14556664

—

C₂×#11924011

C₄

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556548

C₄

yes

characteristic

#14556501

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

#97×C₇₃

C₄

yes

characteristic

#11924031

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

#11924011

C₈

yes

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

D₄

yes

—

C₈×D₇₃

Q₈

yes

—

#11924007

—

#11924005

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

—

C₄×D₇₃

C₂×C₈

yes

—

C₈×C₇₃

C₄⋊C₄

yes

—

C₈×C₇₃

C₂×C₈

yes

—

#10596831

C₂×C₈

yes

—

#10596831

C₂×D₄

yes

characteristic

#10596831

C₂×Q₈

yes

characteristic

C₂²×C₇₃

C₂×M₁₆

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄⋊C₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄⋊C₈

yes

—

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄⋊C₈

yes

characteristic

D₇₃

—

#2153

—

maximal, Sylow

C₇₃

#2153

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

#405

—

#364

—

#364

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

C₄⋊#64408

yes

—

C₈

#11924036

yes

—

C₂²

—

292

—

C₂²

—

C₂²

D₇₃⋊M₁₆

yes

characteristic

C₄

—

C₄

—

292

—

C₄

—

C₄

C₂×C₄⋊#64408

yes

characteristic

C₄

C₂×#11924036

yes

characteristic

100

C₂

—

101

C₂

—

146

—

102

C₂

#17989588

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₄⋊#64408
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	#97×C₇₃	C₄
socle	C₂×C₇₃	C₂×C₄⋊C₈
hypercenter	#97	#64408
hypocenter	C₇₃	#2153
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

subgroup

G/H

center

C₄

C₂×C₄⋊#64408

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×#64408

Fitting

#97×C₇₃

C₄

socle

C₂×C₇₃

C₂×C₄⋊C₈

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

N	H ≅ G/N	type
2. #17989510	C₂	semidirect
3. #17989509	C₂	semidirect
52. C₇₃	#2153	semidirect

H ≅ G/N

type

2. #17989510

C₂

semidirect

3. #17989509

C₂

semidirect

52. C₇₃

#2153

semidirect

Subgroups — #22626273

Conjugacy classes of subgroups

Complements