Group #22627085 — subgroups

Subgroups — C₂×#64408⋊C₁₆ #22627085

Order 9344.

216 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 119 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	#64408⋊C₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
4	#14556686	C₄	1	4	yes	complemented
5	#14556686	C₂²	1	4	yes	—
6	C₂×#11924040	C₄	1	4	yes	complemented
7	C₂×#11924036	C₂²	1	1	yes	characteristic
8	C₂×C₄×#64408	C₄	1	1	yes	characteristic
9	C₈×#64408	C₄	1	2	yes	—
10	C₈×#64408	C₂²	1	2	yes	—
11	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
12	#11924040	C₂×C₄	1	8	yes	complemented
13	C₂²×#64408	C₈	1	2	yes	—
14	#11924036	C₂×C₄	1	1	yes	characteristic
15	#11924036	C₂×C₄	1	2	yes	—
16	#11924036	C₂³	1	1	yes	characteristic
17	C₂×#10596833	C₂×C₄	1	2	yes	—
18	C₄×#64408	C₈	1	2	yes	—
19	C₄×#64408	C₂×C₄	1	2	yes	—
20	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×#10596831	C₈	1	1	yes	characteristic
22	C₈×D₇₃	C₈	1	2	yes	—
23	C₈×D₇₃	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
25	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂×#64408	C₁₆	1	8	yes	complemented
27	C₂×#64408	C₂×C₈	1	4	yes	—
28	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
29	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
30	C₄×D₇₃	C₄²	1	1	yes	characteristic
31	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
32	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
33	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
34	#10596833	C₄²	1	2	yes	—
35	#10596833	C₂²×C₄	1	2	yes	—
36	C₈×C₇₃	C₂×C₈	1	2	yes	—
37	#10596831	C₂×C₈	1	2	yes	—
38	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
39	C₂×D₇₃	C₄×C₈	1	1	yes	characteristic
40	C₂×D₇₃	C₂×C₁₆	1	4	yes	—
41	C₂×D₇₃	C₂²×C₈	1	1	yes	characteristic
42	#64408	C₂×C₁₆	1	8	yes	complemented
43	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
44	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
45	Dic₇₃	C₄×C₈	1	1	yes	characteristic
46	Dic₇₃	C₂×C₄²	1	1	yes	characteristic
47	C₂×C₇₃	C₄×C₁₆	1	2	yes	complemented
48	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
49	D₇₃	C₄×C₁₆	1	2	yes	complemented
50	D₇₃	C₂²×C₁₆	1	2	yes	—
51	C₂×C₄×C₁₆	—	73	1	no	maximal, Sylow
52	C₇₃	C₂×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₁₆	—	73	2	no	—
54	C₂×C₄×C₈	—	73	1	no	—
55	C₄×C₁₆	—	73	4	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	—	73	4	no	—
61	C₂×C₁₆	—	73	4	no	—
62	C₄×C₈	—	73	2	no	—
63	C₄×C₈	—	73	2	no	—
64	C₂²×C₄	—	73	2	no	—
65	C₂²×C₄	—	73	1	no	—
66	C₂×C₈	—	73	2	no	—
67	C₂×C₈	—	73	1	no	—
68	C₂×C₈	—	73	2	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	—	73	1	no	—
71	C₂×C₈	—	73	2	no	—
72	C₂×C₈	—	73	2	no	—
73	C₂×C₈	#10596842	1	1	yes	characteristic
74	C₄²	—	73	2	no	—
75	C₄²	—	73	2	no	—
76	C₁₆	—	73	8	no	—
77	C₂³	—	73	1	no	—
78	C₂×C₄	—	73	4	no	—
79	C₂×C₄	—	73	8	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	—	73	1	no	—
82	C₂×C₄	—	73	1	no	—
83	C₂×C₄	—	73	1	no	—
84	C₂×C₄	—	73	1	no	—
85	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
86	C₈	—	73	2	no	—
87	C₈	—	73	2	no	—
88	C₈	—	73	2	no	—
89	C₈	C₂×#10596842	1	2	yes	—
90	C₂²	—	73	4	no	—
91	C₂²	—	73	1	no	—
92	C₂²	—	73	1	no	—
93	C₂²	C₄×#10596842	1	1	yes	characteristic
94	C₄	—	73	8	no	—
95	C₄	—	73	1	no	—
96	C₄	—	73	1	no	—
97	C₄	C₄×#10596842	1	1	yes	characteristic
98	C₄	C₂²×#10596842	1	1	yes	characteristic
99	C₂	—	73	2	no	—
100	C₂	—	73	2	no	—
101	C₂	#64408⋊C₁₆	1	2	yes	direct product factor
102	C₂	C₂×C₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556686

C₂

yes

maximal

#64408⋊C₁₆

C₂

yes

maximal, direct product factor

C₂×C₈×#64408

C₂

yes

maximal, characteristic

#14556686

C₄

yes

complemented

#14556686

C₂²

yes

—

C₂×#11924040

C₄

yes

complemented

C₂×#11924036

C₂²

yes

characteristic

C₂×C₄×#64408

C₄

yes

characteristic

C₈×#64408

C₄

yes

—

C₈×#64408

C₂²

yes

—

C₂×C₈×D₇₃

C₄

yes

characteristic

#11924040

C₂×C₄

yes

complemented

C₂²×#64408

C₈

yes

—

#11924036

C₂×C₄

yes

characteristic

#11924036

C₂×C₄

yes

—

#11924036

C₂³

yes

characteristic

C₂×#10596833

C₂×C₄

yes

—

C₄×#64408

C₈

yes

—

C₄×#64408

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic

C₈×D₇₃

C₈

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×#64408

C₁₆

yes

complemented

C₂×#64408

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

#10596833

C₄²

yes

—

#10596833

C₂²×C₄

yes

—

C₈×C₇₃

C₂×C₈

yes

—

#10596831

C₂×C₈

yes

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

C₂×C₁₆

yes

—

C₂×D₇₃

C₂²×C₈

yes

characteristic

#64408

C₂×C₁₆

yes

complemented

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₄×C₈

yes

characteristic

Dic₇₃

C₂×C₄²

yes

characteristic

C₂×C₇₃

C₄×C₁₆

yes

complemented

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

D₇₃

C₄×C₁₆

yes

complemented

D₇₃

C₂²×C₁₆

yes

—

C₂×C₄×C₁₆

—

maximal, Sylow

C₇₃

C₂×C₄×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10596842

yes

characteristic

C₄²

—

C₄²

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

C₂×#10596842

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₄×#10596842

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

#64408⋊C₁₆

yes

direct product factor

102

C₂

C₂×C₄×#10596842

yes

characteristic

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

subgroup

G/H

center, hypercenter

C₂×C₈

#10596842

commutator, hypocenter

C₇₃

C₂×C₄×C₁₆

Frattini

C₄

C₂²×#10596842

Fitting

C₂×C₈×C₇₃

C₈

socle

C₂²×C₇₃

C₄×C₈

LCS

G ▷ C₇₃

UCS

C₁ ◁ C₂×C₈

N	H ≅ G/N	type
2. #64408⋊C₁₆	C₂	direct (N × H)
4. #14556686	C₄	semidirect
6. C₂×#11924040	C₄	semidirect
12. #11924040	C₂×C₄	semidirect
26. C₂×#64408	C₁₆	semidirect
42. #64408	C₂×C₁₆	semidirect
47. C₂×C₇₃	C₄×C₁₆	semidirect
49. D₇₃	C₄×C₁₆	semidirect
52. C₇₃	C₂×C₄×C₁₆	semidirect
101. C₂	#64408⋊C₁₆	direct (N × H)

H ≅ G/N

type

2. #64408⋊C₁₆

C₂

direct (N × H)

4. #14556686

C₄

semidirect

6. C₂×#11924040

C₄

semidirect

12. #11924040

C₂×C₄

semidirect

26. C₂×#64408

C₁₆

semidirect

42. #64408

C₂×C₁₆

semidirect

47. C₂×C₇₃

C₄×C₁₆

semidirect

49. D₇₃

C₄×C₁₆

semidirect

52. C₇₃

C₂×C₄×C₁₆

semidirect

101. C₂

#64408⋊C₁₆

direct (N × H)

Subgroups — C₂×#64408⋊C₁₆ #22627085

Conjugacy classes of subgroups

Complements

Subgroups — C2×#64408⋊C16 #22627085

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#64408⋊C₁₆ #22627085