Group #22626934 — subgroups

Subgroups — #22626934

Order 9344.

168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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	#17989700	C₂	1	2	yes	maximal
2	#17989523	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10596842	—	2	2	no	—
4	C₂²⋊#10596842	—	2	2	no	—
5	C₄×#10596842	C₄	1	4	yes	complemented
6	C₂×C₄×#64408	C₄	1	1	yes	characteristic
7	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
8	(C₂×#64408)⋊C₄	—	2	2	no	—
9	C₄²×D₇₃	C₄	1	1	yes	characteristic
10	C₂×#10596842	—	2	4	no	—
11	C₂²×#64408	—	2	1	no	—
12	C₂²×#64408	D₄	1	2	yes	—
13	C₄×#64408	—	2	1	no	—
14	C₄×#64408	C₈	1	2	yes	complemented
15	C₄×#64408	C₂×C₄	1	2	yes	—
16	C₄×#64408	D₄	1	1	yes	characteristic
17	C₄×#64408	Q₈	1	1	yes	characteristic
18	C₂×C₄×D₇₃	—	2	1	no	—
19	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₇₃	—	2	1	no	—
21	C₄×Dic₇₃	C₈	1	1	yes	characteristic, complemented
22	C₄²×C₇₃	C₈	1	1	yes	characteristic, complemented
23	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×#64408	—	2	2	no	—
25	C₂×#64408	—	4	2	no	—
26	C₂×#64408	—	4	2	no	—
27	C₂×#64408	C₂²⋊C₄	1	2	yes	—
28	C₂×#64408	C₄⋊C₄	1	2	yes	—
29	#10596842	—	4	4	no	—
30	C₂×C₄×C₇₃	—	2	1	no	—
31	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×Dic₇₃	—	2	1	no	—
33	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
34	C₄×D₇₃	—	4	2	no	—
35	C₄×D₇₃	C₄²	1	1	yes	characteristic
36	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
38	C₄×D₇₃	M₁₆	1	1	yes	characteristic
39	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
40	C₂×D₇₃	—	2	2	no	—
41	C₂×D₇₃	#95	1	1	yes	characteristic
42	C₂×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
43	#64408	—	2	2	no	—
44	#64408	—	2	2	no	—
45	#64408	—	4	2	no	—
46	C₄×C₇₃	—	4	1	no	—
47	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
48	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
49	Dic₇₃	—	4	1	no	—
50	Dic₇₃	#97	1	1	yes	characteristic
51	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₇₃	—	2	1	no	—
53	C₂×C₇₃	#336	1	1	yes	characteristic
54	D₇₃	—	2	1	no	—
55	D₇₃	H(3,ℤ/4)	1	2	yes	—
56	#1274	—	73	1	no	maximal, Sylow
57	C₇₃	#1274	1	1	yes	characteristic, complemented, Sylow
58	#431	—	73	2	no	—
59	#376	—	73	1	no	—
60	C₂×C₄²	—	73	1	no	—
61	C₂×C₄²	—	73	1	no	—
62	C₂×C₄²	—	73	1	no	—
63	C₄⋊C₈	—	146	2	no	—
64	C₂²⋊C₈	—	146	2	no	—
65	C₄×C₈	—	73	4	no	—
66	#95	—	146	2	no	—
67	C₂²×C₄	—	73	2	no	—
68	C₂²×C₄	—	73	1	no	—
69	C₂²×C₄	—	146	1	no	—
70	C₂²×C₄	—	146	1	no	—
71	C₂×C₈	—	146	4	no	—
72	C₄²	—	73	2	no	—
73	C₄²	—	73	1	no	—
74	C₄²	—	73	1	no	—
75	C₄²	—	73	2	no	—
76	C₄²	—	73	1	no	—
77	C₄²	—	146	1	no	—
78	C₄²	—	146	1	no	—
79	C₄²	#10596842	1	1	yes	characteristic, complemented
80	C₂³	—	73	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	292	2	no	—
83	C₂×C₄	—	292	2	no	—
84	C₂×C₄	—	292	2	no	—
85	C₂×C₄	—	73	1	no	—
86	C₂×C₄	—	73	1	no	—
87	C₂×C₄	—	73	1	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	73	2	no	—
91	C₂×C₄	—	73	2	no	—
92	C₂×C₄	—	146	2	no	—
93	C₂×C₄	—	146	1	no	—
94	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
95	C₈	—	292	4	no	—
96	C₂²	—	73	1	no	—
97	C₂²	—	73	1	no	—
98	C₂²	—	146	2	no	—
99	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
100	C₄	—	4	1	no	—
101	C₄	—	292	1	no	—
102	C₄	—	292	2	no	—
103	C₄	—	73	1	no	—
104	C₄	—	73	1	no	—
105	C₄	—	146	2	no	—
106	C₄	—	146	2	no	—
107	C₄	C₄×#10596842	1	1	yes	characteristic
108	C₄	C₄⋊#10596842	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	73	2	no	—
111	C₂	—	146	1	no	—
112	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989700

C₂

yes

maximal

#17989523

C₂

yes

maximal, characteristic

C₄⋊#10596842

—

C₂²⋊#10596842

—

C₄×#10596842

C₄

yes

complemented

C₂×C₄×#64408

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

(C₂×#64408)⋊C₄

—

C₄²×D₇₃

C₄

yes

characteristic

C₂×#10596842

—

C₂²×#64408

—

C₂²×#64408

D₄

yes

—

C₄×#64408

—

C₄×#64408

C₈

yes

complemented

C₄×#64408

C₂×C₄

yes

—

C₄×#64408

D₄

yes

characteristic

C₄×#64408

Q₈

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

C₈

yes

characteristic, complemented

C₄²×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₂²⋊C₄

yes

—

—

—

C₂²⋊C₄

yes

—

C₂×#64408

C₄⋊C₄

yes

—

#10596842

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#95

yes

characteristic

C₂×D₇₃

C₂²⋊C₈

yes

—

—

—

C₄×C₇₃

—

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

#97

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

#336

yes

characteristic

D₇₃

—

D₇₃

H(3,ℤ/4)

yes

—

#1274

—

maximal, Sylow

C₇₃

#1274

yes

characteristic, complemented, Sylow

#431

—

#376

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

146

—

C₄×C₈

—

#95

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₄²

—

146

—

C₄²

#10596842

yes

characteristic, complemented

C₂³

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

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

—

292

—

C₂²

—

C₂²

—

C₂²

—

146

—

C₂²

C₂²⋊#10596842

yes

characteristic

100

C₄

—

101

C₄

—

292

—

102

C₄

—

292

—

103

C₄

—

104

C₄

—

105

C₄

—

146

—

106

C₄

—

146

—

107

C₄

C₄×#10596842

yes

characteristic

108

C₄

C₄⋊#10596842

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

146

—

112

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	C₄×#10596842
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₄²×C₇₃	C₈
socle	C₂×C₇₃	#336
hypercenter	C₄²	#10596842
hypocenter	C₇₃	#1274
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₄²

subgroup

G/H

center

C₄

C₄×#10596842

commutator

C₄×C₇₃

C₄×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

C₄²×C₇₃

C₈

C₂×C₇₃

C₄²

C₇₃

G ▷ C₄×C₇₃ ▷ C₇₃

C₁ ◁ C₄ ◁ C₄²

N	H ≅ G/N	type
5. C₄×#10596842	C₄	semidirect
14. C₄×#64408	C₈	semidirect
21. C₄×Dic₇₃	C₈	semidirect
22. C₄²×C₇₃	C₈	semidirect
57. C₇₃	#1274	semidirect
79. C₄²	#10596842	semidirect

H ≅ G/N

type

5. C₄×#10596842

C₄

semidirect

14. C₄×#64408

C₈

semidirect

21. C₄×Dic₇₃

C₈

semidirect

22. C₄²×C₇₃

C₈

semidirect

57. C₇₃

#1274

semidirect

79. C₄²

#10596842

semidirect

Subgroups — #22626934

Conjugacy classes of subgroups

Complements