Group #22624753 — subgroups

Subgroups — #22624753

Order 9344.

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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×C₄×#10596833	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10596833	C₄	1	4	yes	—
4	C₄×#10596833	—	2	2	no	—
5	C₄×#10596833	—	2	2	no	—
6	C₂²×#10596831	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
8	C₈×Dic₇₃	—	2	2	no	—
9	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
10	C₂×#10596833	—	2	4	no	—
11	C₂×#10596833	—	2	4	no	—
12	C₂×#10596833	C₈	1	8	yes	complemented
13	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
14	C₂×#10596831	—	2	1	no	—
15	C₂×#10596831	—	2	1	no	—
16	C₂×#10596831	C₈	1	2	yes	complemented
17	C₄×Dic₇₃	D₄	1	1	yes	characteristic
18	C₄×Dic₇₃	D₄	1	2	yes	—
19	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
20	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	—	2	1	no	—
22	C₂×C₈×C₇₃	—	2	1	no	—
23	C₂×C₈×C₇₃	C₈	1	2	yes	complemented
24	C₂³×C₇₃	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
31	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
32	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
33	C₂×Dic₇₃	C₂×C₈	1	4	yes	—
34	C₂×Dic₇₃	M₁₆	1	4	yes	—
35	#10596833	—	2	8	no	—
36	C₈×C₇₃	—	2	2	no	—
37	#10596831	—	2	2	no	—
38	C₂²×C₇₃	#95	1	1	yes	characteristic
39	C₂²×C₇₃	C₄×C₈	1	2	yes	—
40	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
41	C₂²×C₇₃	#97	1	2	yes	—
42	C₂²×C₇₃	#97	1	1	yes	characteristic
43	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
45	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
46	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
47	Dic₇₃	C₂²⋊C₈	1	4	yes	—
48	Dic₇₃	C₄⋊C₈	1	4	yes	—
49	C₂×C₇₃	C₈²	1	1	yes	characteristic
50	C₂×C₇₃	#322	1	1	yes	characteristic
51	C₂×C₇₃	#322	1	2	yes	—
52	C₂×C₇₃	#336	1	2	yes	—
53	C₂×C₇₃	#336	1	1	yes	characteristic
54	#1273	—	73	1	no	maximal, Sylow
55	C₇₃	#1273	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄×C₈	—	73	2	no	—
57	C₂×C₄×C₈	—	73	1	no	—
58	C₂²×C₈	—	73	4	no	—
59	C₂²×C₈	—	73	1	no	—
60	C₂²×C₈	#64408	1	1	yes	characteristic
61	C₂×C₄²	—	73	1	no	—
62	C₄×C₈	—	146	2	no	—
63	C₄×C₈	—	146	2	no	—
64	C₄×C₈	—	146	2	no	—
65	C₂²×C₄	—	73	2	no	—
66	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	73	8	no	—
70	C₂×C₈	—	73	2	no	—
71	C₂×C₈	—	146	4	no	—
72	C₂×C₈	—	146	4	no	—
73	C₂×C₈	—	146	1	no	—
74	C₂×C₈	—	146	1	no	—
75	C₂×C₈	#10596833	1	2	yes	complemented
76	C₄²	—	73	2	no	—
77	C₄²	—	73	1	no	—
78	C₄²	—	73	1	no	—
79	C₂³	C₄×#64408	1	1	yes	characteristic
80	C₂×C₄	—	73	2	no	—
81	C₂×C₄	—	73	2	no	—
82	C₂×C₄	—	73	4	no	—
83	C₂×C₄	—	73	4	no	—
84	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
85	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
86	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
87	C₂×C₄	#11924036	1	1	yes	characteristic
88	C₂×C₄	#11924037	1	1	yes	characteristic
89	C₂×C₄	#11924038	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	146	8	no	—
92	C₈	—	146	2	no	—
93	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
94	C₂²	C₈×#64408	1	2	yes	—
95	C₂²	C₄×#10596833	1	1	yes	characteristic
96	C₂²	#14556645	1	2	yes	—
97	C₂²	#14556646	1	1	yes	characteristic
98	C₄	—	73	4	no	—
99	C₄	—	73	4	no	—
100	C₄	C₂²⋊#10596833	1	1	yes	characteristic
101	C₄	#14556648	1	1	yes	characteristic
102	C₄	C₄⋊#10596833	1	1	yes	characteristic
103	C₄	#14556658	1	1	yes	characteristic
104	C₂	C₈×#10596833	1	1	yes	characteristic
105	C₂	#17989428	1	1	yes	characteristic
106	C₂	#17989429	1	2	yes	—
107	C₂	#17989452	1	2	yes	—
108	C₂	#17989453	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×#10596833

C₂

yes

maximal

C₂×C₈×Dic₇₃

C₂

yes

maximal, characteristic

C₂²×#10596833

C₄

yes

—

C₄×#10596833

—

C₄×#10596833

—

C₂²×#10596831

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

—

C₂²×C₈×C₇₃

C₄

yes

—

—

C₈

yes

complemented

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

C₈

yes

complemented

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

Q₈

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₈

yes

complemented

C₂³×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

M₁₆

yes

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#95

yes

characteristic

C₂²×C₇₃

C₄×C₈

yes

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂²×C₇₃

#97

yes

—

C₂²×C₇₃

#97

yes

characteristic

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

C₂²⋊C₈

yes

—

Dic₇₃

C₄⋊C₈

yes

—

C₂×C₇₃

C₈²

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#336

yes

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

#64408

yes

characteristic

C₂×C₄²

—

C₄×C₈

—

146

—

C₄×C₈

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

#10596833

yes

complemented

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

146

—

C₈

—

146

—

C₂²

(C₂×#64408)⋊C₄

yes

characteristic

C₂²

C₈×#64408

yes

—

C₂²

C₄×#10596833

yes

characteristic

C₂²

#14556645

yes

—

C₂²

#14556646

yes

characteristic

C₄

—

C₄

—

100

C₄

C₂²⋊#10596833

yes

characteristic

101

C₄

#14556648

yes

characteristic

102

C₄

C₄⋊#10596833

yes

characteristic

103

C₄

#14556658

yes

characteristic

104

C₂

C₈×#10596833

yes

characteristic

105

C₂

#17989428

yes

characteristic

106

C₂

#17989429

yes

—

107

C₂

#17989452

yes

—

108

C₂

#17989453

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×#64408
commutator	C₂×C₇₃	C₈²
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂³×C₇₃	C₄²
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	#1273
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂×#64408

commutator

C₂×C₇₃

C₈²

Fitting

C₂²×C₈×C₇₃

C₄

socle

C₂³×C₇₃

C₄²

C₂²×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
12. C₂×#10596833	C₈	semidirect
16. C₂×#10596831	C₈	semidirect
23. C₂×C₈×C₇₃	C₈	semidirect
55. C₇₃	#1273	semidirect
75. C₂×C₈	#10596833	semidirect

H ≅ G/N

type

12. C₂×#10596833

C₈

semidirect

16. C₂×#10596831

C₈

semidirect

23. C₂×C₈×C₇₃

C₈

semidirect

55. C₇₃

#1273

semidirect

75. C₂×C₈

#10596833

semidirect

Subgroups — #22624753

Conjugacy classes of subgroups

Complements