Group #22627002 — subgroups

Subgroups — #22627002

Order 9344.

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

normal subgroups only

This group has 160 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	C₂×#14556686	C₂	1	2	yes	maximal
2	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
3	#14556686	—	2	2	no	—
4	#14556686	—	2	2	no	—
5	C₂×#11924040	C₄	1	4	yes	complemented
6	C₂×#11924036	C₂²	1	1	yes	characteristic
7	C₂×C₄×#64408	C₄	1	1	yes	characteristic
8	C₈×#64408	—	2	2	no	—
9	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
10	#11924040	—	2	4	no	—
11	C₂²×#64408	C₈	1	2	yes	—
12	#11924036	D₄	1	1	yes	characteristic
13	#11924036	D₄	1	2	yes	—
14	#11924036	Q₈	1	1	yes	characteristic
15	C₂×#10596833	C₂×C₄	1	2	yes	—
16	C₄×#64408	—	2	1	no	—
17	C₄×#64408	—	2	1	no	—
18	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	C₈	1	1	yes	characteristic
20	C₈×D₇₃	—	2	1	no	—
21	C₈×D₇₃	—	2	1	no	—
22	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
23	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
24	C₂×#64408	—	2	2	no	—
25	C₂×#64408	—	2	2	no	—
26	C₂×#64408	C₁₆	1	4	yes	complemented
27	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
29	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
31	C₄×D₇₃	M₁₆	1	1	yes	characteristic
32	C₄×D₇₃	M₁₆	1	1	yes	characteristic
33	#10596833	C₂²⋊C₄	1	2	yes	—
34	#10596833	C₄⋊C₄	1	2	yes	—
35	C₈×C₇₃	—	2	1	no	—
36	#10596831	—	2	1	no	—
37	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
38	C₂×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
40	C₂×D₇₃	C₂×C₁₆	1	2	yes	—
41	C₂×D₇₃	M₃₂	1	2	yes	—
42	#64408	—	2	4	no	—
43	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
45	Dic₇₃	#95	1	1	yes	characteristic
46	Dic₇₃	#97	1	1	yes	characteristic
47	C₂×C₇₃	#336	1	1	yes	characteristic
48	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
49	C₂×C₇₃	#346	1	1	yes	characteristic
50	D₇₃	C₂²⋊C₁₆	1	2	yes	—
51	D₇₃	C₄⋊C₁₆	1	2	yes	—
52	#1374	—	73	1	no	maximal, Sylow
53	C₇₃	#1374	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₁₆	—	73	2	no	—
55	C₂×C₄×C₈	—	73	1	no	—
56	C₂²×C₈	—	73	1	no	—
57	C₂²×C₈	—	73	1	no	—
58	C₂×C₄²	—	73	1	no	—
59	C₂×C₁₆	—	73	4	no	—
60	C₂×C₁₆	—	146	2	no	—
61	C₂×C₁₆	—	146	2	no	—
62	C₄×C₈	—	146	2	no	—
63	C₂²×C₄	—	73	1	no	—
64	C₂²×C₄	—	73	2	no	—
65	C₂×C₈	—	73	2	no	—
66	C₂×C₈	—	73	2	no	—
67	C₂×C₈	—	73	1	no	—
68	C₂×C₈	—	73	1	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	—	146	1	no	—
71	C₂×C₈	—	146	1	no	—
72	C₂×C₈	#10596842	1	1	yes	characteristic
73	C₄²	—	146	1	no	—
74	C₄²	—	146	1	no	—
75	C₁₆	—	146	4	no	—
76	C₂³	—	73	1	no	—
77	C₂×C₄	—	73	1	no	—
78	C₂×C₄	—	73	1	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	—	73	1	no	—
82	C₂×C₄	—	73	4	no	—
83	C₂×C₄	—	146	2	no	—
84	C₂×C₄	—	146	2	no	—
85	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	73	2	no	—
88	C₈	—	73	2	no	—
89	C₈	—	146	1	no	—
90	C₂²	—	73	1	no	—
91	C₂²	—	73	1	no	—
92	C₂²	—	73	2	no	—
93	C₂²	—	73	2	no	—
94	C₂²	C₄×#10596842	1	1	yes	characteristic
95	C₄	—	73	1	no	—
96	C₄	—	73	1	no	—
97	C₄	—	146	4	no	—
98	C₄	C₂²⋊#10596842	1	1	yes	characteristic
99	C₄	C₄⋊#10596842	1	1	yes	characteristic
100	C₂	—	73	2	no	—
101	C₂	—	73	2	no	—
102	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
103	C₂	#64408⋊C₁₆	1	1	yes	characteristic
104	C₂	#17989682	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556686

C₂

yes

maximal

C₂×C₈×#64408

C₂

yes

maximal, characteristic

#14556686

—

#14556686

—

C₂×#11924040

C₄

yes

complemented

C₂×#11924036

C₂²

yes

characteristic

C₂×C₄×#64408

C₄

yes

characteristic

C₈×#64408

—

C₂×C₈×D₇₃

C₄

yes

characteristic

#11924040

—

C₂²×#64408

C₈

yes

—

#11924036

D₄

yes

characteristic

#11924036

D₄

yes

—

#11924036

Q₈

yes

characteristic

C₂×#10596833

C₂×C₄

yes

—

C₄×#64408

—

C₄×#64408

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₂×C₈×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

—

—

C₁₆

yes

complemented

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

#10596833

C₂²⋊C₄

yes

—

#10596833

C₄⋊C₄

yes

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

C₂×C₁₆

yes

—

C₂×D₇₃

M₃₂

yes

—

#64408

—

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

C₄×C₁₆

yes

characteristic

C₂×C₇₃

#346

yes

characteristic

D₇₃

C₂²⋊C₁₆

yes

—

D₇₃

C₄⋊C₁₆

yes

—

#1374

—

maximal, Sylow

C₇₃

#1374

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

#10596842

yes

characteristic

C₄²

—

146

—

C₄²

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₄×#10596842

yes

characteristic

C₄

—

C₄

—

C₄

—

146

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

103

C₂

#64408⋊C₁₆

yes

characteristic

104

C₂

#17989682

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10596842
commutator	C₂×C₇₃	C₄×C₁₆
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂²×C₇₃	C₄×C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1374
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂×#10596842

commutator

C₂×C₇₃

C₄×C₁₆

Fitting

C₂×C₈×C₇₃

C₈

socle

C₂²×C₇₃

C₄×C₈

C₂×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂×C₈

N	H ≅ G/N	type
5. C₂×#11924040	C₄	semidirect
26. C₂×#64408	C₁₆	semidirect
53. C₇₃	#1374	semidirect

H ≅ G/N

type

5. C₂×#11924040

C₄

semidirect

26. C₂×#64408

C₁₆

semidirect

53. C₇₃

#1374

semidirect

Subgroups — #22627002

Conjugacy classes of subgroups

Complements