Group #22627061 — subgroups

Subgroups — #22627061

Order 9344.

160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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	Q₈×#10596842	C₂	1	2	yes	maximal
2	#17989676	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊#10596842	C₂	1	2	yes	maximal
4	#17989671	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×#64408	C₂	1	1	yes	maximal, characteristic
6	C₄⋊#10596842	—	2	2	no	—
7	C₄⋊#10596842	C₂²	1	2	yes	—
8	C₄×#10596842	—	2	2	no	—
9	C₄×#10596842	C₂²	1	1	yes	characteristic
10	C₄×#10596842	C₂²	1	1	yes	characteristic
11	Q₈×#64408	C₂²	1	2	yes	—
12	#14556660	C₄	1	1	yes	characteristic
13	#14556654	C₄	1	2	yes	—
14	C₈×#64408	C₂²	1	1	yes	characteristic
15	Q₁₆×D₇₃	C₄	1	1	yes	characteristic
16	C₂×#10596842	—	2	2	no	—
17	C₂×#10596842	—	2	1	no	—
18	C₂×#10596842	D₄	1	2	yes	—
19	#11924036	C₂×C₄	1	1	yes	characteristic
20	C₄⋊#64408	—	2	2	no	—
21	C₄⋊#64408	C₂×C₄	1	2	yes	—
22	C₄×#64408	—	2	2	no	—
23	C₄×#64408	C₂³	1	1	yes	characteristic
24	Q₈×D₇₃	C₂×C₄	1	2	yes	—
25	Dic₂₉₂	C₈	1	1	yes	characteristic, complemented
26	#11924018	C₈	1	2	yes	complemented
27	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
28	Q₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
29	C₂×#64408	—	2	2	no	—
30	C₂×#64408	C₂×D₄	1	1	yes	characteristic
31	C₂×#64408	#41	1	1	yes	characteristic
32	#10596842	—	2	2	no	—
33	#10596842	—	4	1	no	—
34	#10596842	—	4	2	no	—
35	Q₈×C₇₃	C₂×C₈	1	2	yes	—
36	C₄×D₇₃	—	2	2	no	—
37	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
38	Dic₁₄₆	—	2	2	no	—
39	Dic₁₄₆	C₂×C₈	1	2	yes	—
40	#10596833	—	2	1	no	—
41	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
42	#10596831	C₂×C₈	1	1	yes	characteristic
43	C₂×D₇₃	C₄×D₄	1	1	yes	characteristic
44	#64408	—	2	1	no	—
45	#64408	—	4	2	no	—
46	#64408	#137	1	2	yes	—
47	C₄×C₇₃	—	2	2	no	—
48	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
49	Dic₇₃	—	2	2	no	—
50	Dic₇₃	#131	1	1	yes	characteristic
51	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
52	D₇₃	#441	1	1	yes	characteristic
53	D₇₃	#444	1	1	yes	characteristic
54	#1579	—	73	1	no	maximal, Sylow
55	C₇₃	#1579	1	1	yes	characteristic, complemented, Sylow
56	C₈×Q₈	—	73	2	no	—
57	C₄×Q₁₆	—	73	1	no	—
58	#334	—	73	1	no	—
59	Q₈⋊C₈	—	73	2	no	—
60	#322	—	73	1	no	—
61	C₂×Q₁₆	—	73	1	no	—
62	C₄×Q₈	—	73	2	no	—
63	#107	—	73	1	no	—
64	C₄⋊C₈	—	73	2	no	—
65	C₄⋊C₈	—	146	2	no	—
66	#103	—	73	2	no	—
67	C₄×C₈	—	73	1	no	—
68	C₄×C₈	—	73	1	no	—
69	C₄×C₈	—	73	1	no	—
70	C₄×C₈	—	146	2	no	—
71	C₂×Q₈	—	73	2	no	—
72	Q₁₆	—	73	2	no	—
73	Q₁₆	—	73	1	no	—
74	Q₁₆	#10596842	1	1	yes	characteristic, complemented
75	C₂×C₈	—	73	1	no	—
76	C₂×C₈	—	73	1	no	—
77	C₂×C₈	—	73	2	no	—
78	C₂×C₈	—	146	1	no	—
79	C₂×C₈	—	146	2	no	—
80	C₄⋊C₄	—	73	2	no	—
81	C₄⋊C₄	—	146	2	no	—
82	C₄²	—	73	1	no	—
83	C₄²	—	146	2	no	—
84	Q₈	—	73	2	no	—
85	Q₈	—	146	2	no	—
86	Q₈	C₂×#10596842	1	2	yes	—
87	C₂×C₄	—	73	1	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	146	2	no	—
91	C₂×C₄	—	146	2	no	—
92	C₈	—	292	2	no	—
93	C₈	—	292	1	no	—
94	C₈	—	73	1	no	—
95	C₈	—	146	1	no	—
96	C₈	—	146	2	no	—
97	C₈	C₂×#10596842	1	1	yes	characteristic
98	C₂²	—	73	1	no	—
99	C₄	—	2	2	no	—
100	C₄	—	292	2	no	—
101	C₄	—	73	2	no	—
102	C₄	—	73	1	no	—
103	C₄	—	146	1	no	—
104	C₄	—	146	2	no	—
105	C₄	C₂²×#10596842	1	1	yes	characteristic
106	C₂	—	73	1	no	—
107	C₂	—	73	1	no	—
108	C₂	D₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×#10596842

C₂

yes

maximal

#17989676

C₂

yes

maximal, characteristic

Q₈⋊#10596842

C₂

yes

maximal

#17989671

C₂

yes

maximal, characteristic

Q₁₆×#64408

C₂

yes

maximal, characteristic

C₄⋊#10596842

—

C₄⋊#10596842

C₂²

yes

—

C₄×#10596842

—

C₄×#10596842

C₂²

yes

characteristic

C₄×#10596842

C₂²

yes

characteristic

Q₈×#64408

C₂²

yes

—

#14556660

C₄

yes

characteristic

#14556654

C₄

yes

—

C₈×#64408

C₂²

yes

characteristic

Q₁₆×D₇₃

C₄

yes

—

—

D₄

yes

—

#11924036

C₂×C₄

yes

characteristic

C₄⋊#64408

—

C₄⋊#64408

C₂×C₄

yes

—

C₄×#64408

—

C₄×#64408

C₂³

yes

characteristic

Q₈×D₇₃

C₂×C₄

yes

—

Dic₂₉₂

C₈

yes

characteristic, complemented

#11924018

C₈

yes

complemented

C₈×D₇₃

C₂×C₄

yes

characteristic

Q₁₆×C₇₃

C₈

yes

characteristic, complemented

C₂×#64408

—

C₂×#64408

C₂×D₄

yes

yes

—

—

—

Q₈×C₇₃

C₂×C₈

yes

—

C₄×D₇₃

—

C₄×D₇₃

C₂²×C₄

yes

characteristic

Dic₁₄₆

—

Dic₁₄₆

C₂×C₈

yes

—

#10596833

—

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

C₂×D₇₃

C₄×D₄

yes

—

—

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

#131

yes

characteristic

C₂×C₇₃

C₈×D₄

yes

D₇₃

yes

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

—

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

#103

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

146

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

#10596842

yes

characteristic, complemented

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

—

146

—

Q₈

—

Q₈

—

146

—

Q₈

C₂×#10596842

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₈

—

292

—

C₈

—

292

—

C₈

—

C₈

—

146

—

C₈

—

146

—

C₈

C₂×#10596842

yes

characteristic

C₂²

—

C₄

—

100

C₄

—

292

—

101

C₄

—

102

C₄

—

103

C₄

—

146

—

104

C₄

—

146

—

105

C₄

C₂²×#10596842

yes

characteristic

106

C₂

—

107

C₂

—

108

C₂

D₄×#10596842

yes

characteristic

	subgroup	G/H
center	C₂	D₄×#10596842
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₄	C₂²×#10596842
Fitting	Q₁₆×C₇₃	C₈
socle	C₂×C₇₃	C₈×D₄
hypercenter	Q₁₆	#10596842
hypocenter	C₇₃	#1579
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

subgroup

G/H

center

C₂

D₄×#10596842

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₄

C₂²×#10596842

Fitting

Q₁₆×C₇₃

C₈

socle

C₂×C₇₃

C₈×D₄

Q₁₆

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

N	H ≅ G/N	type
25. Dic₂₉₂	C₈	semidirect
26. #11924018	C₈	semidirect
28. Q₁₆×C₇₃	C₈	semidirect
55. C₇₃	#1579	semidirect
74. Q₁₆	#10596842	semidirect

H ≅ G/N

type

25. Dic₂₉₂

C₈

semidirect

26. #11924018

C₈

semidirect

28. Q₁₆×C₇₃

C₈

semidirect

55. C₇₃

#1579

semidirect

74. Q₁₆

#10596842

semidirect

Subgroups — #22627061

Conjugacy classes of subgroups

Complements