Group #22626933 — subgroups

Subgroups — (C₂×#10596842)⋊C₈ #22626933

Order 9344.

212 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 85 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×#10596842	C₂	1	2	yes	maximal
2	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10596842	C₄	1	4	yes	—
4	C₄×#10596842	—	2	2	no	—
5	C₄×#10596842	—	2	2	no	—
6	C₂×#11924036	C₄	1	1	yes	characteristic
7	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
8	C₈×#64408	—	2	2	no	—
9	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
10	C₂×#10596842	—	2	4	no	—
11	C₂×#10596842	—	2	4	no	—
12	C₂×#10596842	C₈	1	8	yes	complemented
13	C₂²×#64408	C₂×C₄	1	2	yes	—
14	#11924036	—	2	1	no	—
15	#11924036	—	2	1	no	—
16	C₂×#10596833	C₈	1	2	yes	complemented
17	C₄×#64408	D₄	1	2	yes	—
18	C₄×#64408	D₄	1	1	yes	characteristic
19	C₄×#64408	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×#10596831	C₈	1	1	yes	characteristic, complemented
22	C₈×D₇₃	—	2	1	no	—
23	C₈×D₇₃	—	2	1	no	—
24	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic, complemented
25	C₂²×D₇₃	C₄²	1	1	yes	characteristic
26	C₂×#64408	C₂²⋊C₄	1	2	yes	—
27	C₂×#64408	C₄⋊C₄	1	2	yes	—
28	C₂×#64408	C₂×C₈	1	4	yes	—
29	C₂×#64408	M₁₆	1	4	yes	—
30	#10596842	—	2	8	no	—
31	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
33	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₄×D₇₃	M₁₆	1	1	yes	characteristic
36	C₄×D₇₃	M₁₆	1	1	yes	characteristic
37	#10596833	—	2	2	no	—
38	C₈×C₇₃	—	2	1	no	—
39	#10596831	—	2	1	no	—
40	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
41	C₂×D₇₃	#95	1	1	yes	characteristic
42	C₂×D₇₃	C₄×C₈	1	2	yes	—
43	C₂×D₇₃	#97	1	1	yes	characteristic
44	C₂×D₇₃	#97	1	2	yes	—
45	#64408	C₂²⋊C₈	1	4	yes	—
46	#64408	C₄⋊C₈	1	4	yes	—
47	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
48	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
49	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
50	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
51	C₂×C₇₃	C₈²	1	1	yes	characteristic
52	C₂×C₇₃	#322	1	1	yes	characteristic
53	C₂×C₇₃	#336	1	1	yes	characteristic
54	D₇₃	#322	1	2	yes	—
55	D₇₃	#336	1	2	yes	—
56	#1273	—	73	1	no	maximal, Sylow
57	C₇₃	#1273	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₄×C₈	—	73	2	no	—
59	C₂×C₄×C₈	—	73	1	no	—
60	C₂²×C₈	—	73	1	no	—
61	C₂²×C₈	—	73	4	no	—
62	C₂²×C₈	—	73	1	no	—
63	C₂×C₄²	—	73	1	no	—
64	C₄×C₈	—	146	2	no	—
65	C₄×C₈	—	146	2	no	—
66	C₄×C₈	—	146	2	no	—
67	C₂²×C₄	—	73	2	no	—
68	C₂²×C₄	—	73	1	no	—
69	C₂×C₈	—	73	2	no	—
70	C₂×C₈	—	73	8	no	—
71	C₂×C₈	—	73	1	no	—
72	C₂×C₈	—	146	1	no	—
73	C₂×C₈	—	146	1	no	—
74	C₂×C₈	—	146	1	no	—
75	C₂×C₈	—	146	1	no	—
76	C₂×C₈	—	146	4	no	—
77	C₂×C₈	—	146	4	no	—
78	C₂×C₈	#10596842	1	1	yes	characteristic, complemented
79	C₄²	—	73	1	no	—
80	C₄²	—	73	2	no	—
81	C₄²	—	73	1	no	—
82	C₂³	—	73	1	no	—
83	C₂×C₄	—	73	2	no	—
84	C₂×C₄	—	73	2	no	—
85	C₂×C₄	—	73	4	no	—
86	C₂×C₄	—	73	4	no	—
87	C₂×C₄	—	73	1	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	146	2	no	—
95	C₈	—	146	8	no	—
96	C₈	—	146	1	no	—
97	C₂²	—	73	2	no	—
98	C₂²	—	73	2	no	—
99	C₂²	—	73	1	no	—
100	C₂²	—	73	1	no	—
101	C₂²	C₄×#10596842	1	1	yes	characteristic
102	C₄	—	73	4	no	—
103	C₄	—	73	4	no	—
104	C₄	—	73	1	no	—
105	C₄	—	73	1	no	—
106	C₄	C₂²⋊#10596842	1	1	yes	characteristic
107	C₄	C₄⋊#10596842	1	1	yes	characteristic
108	C₂	—	73	2	no	—
109	C₂	—	73	2	no	—
110	C₂	C₈×#10596842	1	1	yes	characteristic
111	C₂	#17989671	1	1	yes	characteristic
112	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×#10596842

C₂

yes

maximal

C₂×C₈×#64408

C₂

yes

maximal, characteristic

C₂²×#10596842

C₄

yes

—

C₄×#10596842

—

C₄×#10596842

—

C₂×#11924036

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

C₈×#64408

—

C₂×C₈×D₇₃

C₄

yes

—

—

C₈

yes

complemented

C₂²×#64408

C₂×C₄

yes

—

#11924036

—

#11924036

—

C₂×#10596833

C₈

yes

complemented

C₄×#64408

D₄

yes

—

C₄×#64408

D₄

yes

characteristic

C₄×#64408

Q₈

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic, complemented

C₈×D₇₃

—

C₈×D₇₃

—

C₂×C₈×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₄²

yes

characteristic

C₂×#64408

C₂²⋊C₄

yes

—

C₂×#64408

C₄⋊C₄

yes

—

C₂×#64408

C₂×C₈

yes

—

C₂×#64408

M₁₆

yes

—

#10596842

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

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

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

#95

yes

characteristic

C₂×D₇₃

C₄×C₈

yes

—

C₂×D₇₃

#97

yes

characteristic

C₂×D₇₃

#97

yes

—

#64408

C₂²⋊C₈

yes

—

#64408

C₄⋊C₈

yes

—

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

C₂²⋊C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

C₈²

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

yes

—

D₇₃

#336

yes

—

#1273

—

maximal, Sylow

C₇₃

#1273

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄×C₈

—

146

—

C₄×C₈

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

#10596842

yes

characteristic, complemented

C₄²

—

C₄²

—

C₄²

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

C₈

—

146

—

C₈

—

146

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

C₄×#10596842

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

C₂²⋊#10596842

yes

characteristic

107

C₄

C₄⋊#10596842

yes

characteristic

108

C₂

—

109

C₂

—

110

C₂

C₈×#10596842

yes

characteristic

111

C₂

#17989671

yes

characteristic

112

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10596842
commutator	C₂×C₇₃	C₈²
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂²×C₇₃	C₄×C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1273
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂×#10596842

commutator

C₂×C₇₃

C₈²

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
12. C₂×#10596842	C₈	semidirect
16. C₂×#10596833	C₈	semidirect
21. C₂×#10596831	C₈	semidirect
24. C₂×C₈×C₇₃	C₈	semidirect
57. C₇₃	#1273	semidirect
78. C₂×C₈	#10596842	semidirect

H ≅ G/N

type

12. C₂×#10596842

C₈

semidirect

16. C₂×#10596833

C₈

semidirect

21. C₂×#10596831

C₈

semidirect

24. C₂×C₈×C₇₃

C₈

semidirect

57. C₇₃

#1273

semidirect

78. C₂×C₈

#10596842

semidirect

Subgroups — (C₂×#10596842)⋊C₈ #22626933

Conjugacy classes of subgroups

Complements

Subgroups — (C2×#10596842)⋊C8 #22626933

Conjugacy classes of subgroups

Complements

Subgroups — (C₂×#10596842)⋊C₈ #22626933