Group #22589925 — subgroups

Subgroups — C₄×C₁₆×D₇₁ #22589925

Order 9088.

216 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 137 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×C₁₆×D₇₁	C₂	1	2	yes	maximal
2	C₄×C₈×D₇₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×Dic₇₁	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₁	C₄	1	1	yes	characteristic
7	C₂×C₈×D₇₁	C₂²	1	1	yes	characteristic
8	C₄²×D₇₁	C₄	1	1	yes	characteristic
9	C₂×C₇₁⋊C₁₆	C₂²	1	2	yes	—
10	C₁₆×D₇₁	C₄	1	8	yes	direct product factor
11	C₄×C₇₁⋊C₈	C₄	1	1	yes	characteristic
12	C₈×Dic₇₁	C₄	1	1	yes	characteristic
13	C₈×Dic₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₁	C₂²	1	2	yes	—
15	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₇₁	C₈	1	2	yes	—
17	C₂×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
20	C₈×D₇₁	C₈	1	4	yes	—
21	C₈×D₇₁	C₂×C₄	1	4	yes	—
22	C₄×Dic₇₁	C₈	1	2	yes	—
23	C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
24	C₇₁⋊C₁₆	C₂×C₄	1	4	yes	complemented
25	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
27	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₇₁	C₂×C₄	1	4	yes	complemented
29	C₂²×D₇₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₁	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₇₁	C₂×C₈	1	1	yes	characteristic
33	C₂×Dic₇₁	C₂×C₈	1	2	yes	—
34	C₄×D₇₁	C₁₆	1	8	yes	direct product factor
35	C₄×D₇₁	C₄²	1	2	yes	—
36	C₄×D₇₁	C₂×C₈	1	2	yes	—
37	C₈×C₇₁	C₂×C₈	1	2	yes	—
38	C₈×C₇₁	C₂²×C₄	1	2	yes	—
39	C₇₁⋊C₈	C₄²	1	2	yes	—
40	C₇₁⋊C₈	C₂×C₈	1	2	yes	—
41	C₂²×C₇₁	C₂²×C₈	1	1	yes	characteristic
42	C₂×D₇₁	C₄×C₈	1	2	yes	—
43	C₂×D₇₁	C₂×C₁₆	1	4	yes	—
44	C₄×C₇₁	C₂×C₁₆	1	4	yes	complemented
45	C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
46	C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
47	Dic₇₁	C₄×C₈	1	2	yes	—
48	Dic₇₁	C₂×C₁₆	1	4	yes	complemented
49	C₂×C₇₁	C₂×C₄×C₈	1	1	yes	characteristic
50	C₂×C₇₁	C₂²×C₁₆	1	2	yes	—
51	D₇₁	C₄×C₁₆	1	4	yes	direct product factor
52	C₂×C₄×C₁₆	—	71	1	no	maximal, Sylow
53	C₇₁	C₂×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₁₆	—	71	2	no	—
55	C₂×C₄×C₈	—	71	1	no	—
56	C₄×C₁₆	—	71	2	no	—
57	C₄×C₁₆	—	71	1	no	—
58	C₄×C₁₆	D₇₁	1	1	yes	characteristic, direct product factor
59	C₂²×C₈	—	71	1	no	—
60	C₂²×C₈	—	71	1	no	—
61	C₂×C₄²	—	71	1	no	—
62	C₂×C₁₆	—	71	2	no	—
63	C₂×C₁₆	—	71	8	no	—
64	C₂×C₁₆	C₂×D₇₁	1	2	yes	—
65	C₄×C₈	—	71	1	no	—
66	C₄×C₈	—	71	1	no	—
67	C₄×C₈	—	71	1	no	—
68	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
69	C₂²×C₄	—	71	2	no	—
70	C₂²×C₄	—	71	1	no	—
71	C₂×C₈	—	71	1	no	—
72	C₂×C₈	—	71	1	no	—
73	C₂×C₈	—	71	4	no	—
74	C₂×C₈	—	71	4	no	—
75	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
77	C₄²	—	71	2	no	—
78	C₄²	—	71	1	no	—
79	C₄²	C₄×D₇₁	1	1	yes	characteristic
80	C₁₆	—	71	4	no	—
81	C₁₆	C₄×D₇₁	1	4	yes	direct product factor
82	C₂³	—	71	1	no	—
83	C₂×C₄	—	71	2	no	—
84	C₂×C₄	—	71	1	no	—
85	C₂×C₄	—	71	8	no	—
86	C₂×C₄	—	71	2	no	—
87	C₂×C₄	—	71	2	no	—
88	C₂×C₄	C₈×D₇₁	1	2	yes	—
89	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
90	C₈	—	71	2	no	—
91	C₈	—	71	2	no	—
92	C₈	C₈×D₇₁	1	2	yes	—
93	C₈	C₂×C₄×D₇₁	1	2	yes	—
94	C₂²	—	71	4	no	—
95	C₂²	—	71	2	no	—
96	C₂²	C₂×C₈×D₇₁	1	1	yes	characteristic
97	C₄	—	71	4	no	—
98	C₄	—	71	2	no	—
99	C₄	C₁₆×D₇₁	1	4	yes	direct product factor
100	C₄	C₄²×D₇₁	1	1	yes	characteristic
101	C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
102	C₂	—	71	4	no	—
103	C₂	C₄×C₈×D₇₁	1	1	yes	characteristic
104	C₂	C₂×C₁₆×D₇₁	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₇₁

C₂

yes

maximal

C₄×C₈×D₇₁

C₂

yes

maximal, characteristic

C₄×C₇₁⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₇₁

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₁

C₄

yes

characteristic

C₂×C₈×D₇₁

C₂²

yes

characteristic

C₄²×D₇₁

C₄

yes

characteristic

C₂×C₇₁⋊C₁₆

C₂²

yes

—

C₁₆×D₇₁

C₄

yes

direct product factor

C₄×C₇₁⋊C₈

C₄

yes

characteristic

C₈×Dic₇₁

C₄

yes

characteristic

C₈×Dic₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×C₄×D₇₁

C₈

yes

—

C₂×C₄×D₇₁

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₈×D₇₁

C₈

yes

—

C₈×D₇₁

C₂×C₄

yes

—

C₄×Dic₇₁

C₈

yes

—

C₄×Dic₇₁

C₂×C₄

yes

characteristic

C₇₁⋊C₁₆

C₂×C₄

yes

complemented

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

C₂×C₄

yes

characteristic

C₁₆×C₇₁

C₂×C₄

yes

complemented

C₂²×D₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₈

yes

—

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×Dic₇₁

C₂×C₈

yes

characteristic

C₂×Dic₇₁

C₂×C₈

yes

—

C₄×D₇₁

C₁₆

yes

direct product factor

C₄×D₇₁

C₄²

yes

—

C₄×D₇₁

C₂×C₈

yes

—

C₈×C₇₁

C₂×C₈

yes

—

C₈×C₇₁

C₂²×C₄

yes

—

C₇₁⋊C₈

C₄²

yes

—

C₇₁⋊C₈

C₂×C₈

yes

—

C₂²×C₇₁

C₂²×C₈

yes

characteristic

C₂×D₇₁

C₄×C₈

yes

—

C₂×D₇₁

C₂×C₁₆

yes

—

C₄×C₇₁

C₂×C₁₆

yes

complemented

C₄×C₇₁

C₂×C₄²

yes

characteristic

C₄×C₇₁

C₂²×C₈

yes

characteristic

Dic₇₁

C₄×C₈

yes

—

Dic₇₁

C₂×C₁₆

yes

complemented

C₂×C₇₁

C₂×C₄×C₈

yes

characteristic

C₂×C₇₁

C₂²×C₁₆

yes

—

D₇₁

C₄×C₁₆

yes

direct product factor

C₂×C₄×C₁₆

—

maximal, Sylow

C₇₁

C₂×C₄×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

D₇₁

yes

characteristic, direct product factor

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄²

—

C₄²

—

C₄²

C₄×D₇₁

yes

characteristic

C₁₆

—

C₁₆

C₄×D₇₁

yes

direct product factor

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₇₁

yes

—

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₇₁

yes

—

C₈

C₂×C₄×D₇₁

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₇₁

yes

characteristic

C₄

—

C₄

—

C₄

C₁₆×D₇₁

yes

direct product factor

100

C₄

C₄²×D₇₁

yes

characteristic

101

C₄

C₂×C₈×D₇₁

yes

characteristic

102

C₂

—

103

C₂

C₄×C₈×D₇₁

yes

characteristic

104

C₂

C₂×C₁₆×D₇₁

yes

—

	subgroup	G/H
center, hypercenter	C₄×C₁₆	D₇₁
commutator, hypocenter	C₇₁	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂²×C₈
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₄×C₁₆

subgroup

G/H

center, hypercenter

C₄×C₁₆

D₇₁

commutator, hypocenter

C₇₁

C₂×C₄×C₁₆

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₄×C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂²×C₈

LCS

G ▷ C₇₁

UCS

C₁ ◁ C₄×C₁₆

N	H ≅ G/N	type
3. C₄×C₇₁⋊C₁₆	C₂	semidirect
4. C₁₆×Dic₇₁	C₂	semidirect
5. C₄×C₁₆×C₇₁	C₂	semidirect
10. C₁₆×D₇₁	C₄	direct (N × H)
24. C₇₁⋊C₁₆	C₂×C₄	semidirect
28. C₁₆×C₇₁	C₂×C₄	semidirect
34. C₄×D₇₁	C₁₆	direct (N × H)
44. C₄×C₇₁	C₂×C₁₆	semidirect
48. Dic₇₁	C₂×C₁₆	semidirect
51. D₇₁	C₄×C₁₆	direct (N × H)
53. C₇₁	C₂×C₄×C₁₆	semidirect
58. C₄×C₁₆	D₇₁	direct (N × H)
81. C₁₆	C₄×D₇₁	direct (N × H)
99. C₄	C₁₆×D₇₁	direct (N × H)

H ≅ G/N

type

3. C₄×C₇₁⋊C₁₆

C₂

semidirect

4. C₁₆×Dic₇₁

C₂

semidirect

5. C₄×C₁₆×C₇₁

C₂

semidirect

10. C₁₆×D₇₁

C₄

direct (N × H)

24. C₇₁⋊C₁₆

C₂×C₄

semidirect

28. C₁₆×C₇₁

C₂×C₄

semidirect

34. C₄×D₇₁

C₁₆

direct (N × H)

44. C₄×C₇₁

C₂×C₁₆

semidirect

48. Dic₇₁

C₂×C₁₆

semidirect

51. D₇₁

C₄×C₁₆

direct (N × H)

53. C₇₁

C₂×C₄×C₁₆

semidirect

58. C₄×C₁₆

D₇₁

direct (N × H)

81. C₁₆

C₄×D₇₁

direct (N × H)

99. C₄

C₁₆×D₇₁

direct (N × H)

Subgroups — C₄×C₁₆×D₇₁ #22589925

Conjugacy classes of subgroups

Complements

Subgroups — C4×C16×D71 #22589925

Conjugacy classes of subgroups

Complements

Subgroups — C₄×C₁₆×D₇₁ #22589925