Group #22601449 — subgroups

Subgroups — C₂²×#14556072 #22601449

Order 9088.

400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₂²×Dic₂₈₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556072	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₈×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₄₂	—	2	1	no	—
6	C₂×Dic₂₈₄	—	2	3	no	—
7	C₂×Dic₂₈₄	C₂²	1	6	yes	complemented
8	#14556072	C₂²	1	16	yes	direct product factor
9	C₂×C₇₁⋊C₁₆	C₂²	1	6	yes	complemented
10	C₂²×D₄×C₇₁	—	2	1	no	—
11	C₂×D₈×C₇₁	—	2	3	no	—
12	C₂×D₈×C₇₁	C₂²	1	6	yes	—
13	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₄₂	—	2	6	no	—
15	C₂×Dic₁₄₂	—	4	3	no	—
16	C₂²×Dic₇₁	—	4	1	no	—
17	Dic₂₈₄	—	2	6	no	—
18	Dic₂₈₄	C₂³	1	4	yes	complemented
19	C₇₁⋊C₁₆	C₂³	1	4	yes	complemented
20	C₂⁴×C₇₁	—	4	1	no	—
21	C₂×D₄×C₇₁	—	2	6	no	—
22	C₂×D₄×C₇₁	—	4	3	no	—
23	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
24	D₈×C₇₁	—	2	6	no	—
25	D₈×C₇₁	C₂³	1	4	yes	—
26	C₂×C₈×C₇₁	D₄	1	3	yes	—
27	C₂×C₈×C₇₁	C₂³	1	3	yes	—
28	C₂³×C₇₁	—	4	6	no	—
29	C₂³×C₇₁	—	8	4	no	—
30	C₂³×C₇₁	D₈	1	1	yes	characteristic
31	D₄×C₇₁	—	2	4	no	—
32	D₄×C₇₁	—	4	6	no	—
33	C₂×C₄×C₇₁	D₈	1	3	yes	—
34	C₂×C₄×C₇₁	C₂×D₄	1	3	yes	—
35	C₂×Dic₇₁	—	4	6	no	—
36	Dic₁₄₂	—	2	4	no	—
37	Dic₁₄₂	—	4	6	no	—
38	C₈×C₇₁	C₂×D₄	1	3	yes	—
39	C₈×C₇₁	C₂⁴	1	1	yes	characteristic
40	C₂²×C₇₁	—	4	4	no	—
41	C₂²×C₇₁	—	8	12	no	—
42	C₂²×C₇₁	SD₃₂	1	4	yes	complemented
43	C₂²×C₇₁	C₂×D₈	1	3	yes	—
44	C₄×C₇₁	C₂×D₈	1	3	yes	—
45	C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
46	Dic₇₁	—	4	4	no	—
47	C₂×C₇₁	—	8	4	no	—
48	C₂×C₇₁	C₂×SD₃₂	1	6	yes	complemented
49	C₂×C₇₁	C₂²×D₈	1	1	yes	characteristic
50	C₂²×SD₃₂	—	71	1	no	maximal, Sylow
51	C₇₁	C₂²×SD₃₂	1	1	yes	characteristic, complemented, Sylow
52	C₂²×Q₁₆	—	71	1	no	—
53	C₂²×D₈	D₇₁	1	1	yes	characteristic
54	C₂×SD₃₂	—	71	12	no	—
55	C₂²×C₁₆	—	71	1	no	—
56	C₂²×Q₈	—	142	1	no	—
57	C₂²×D₄	—	2	1	no	—
58	C₂×Q₁₆	—	71	6	no	—
59	C₂×Q₁₆	—	142	3	no	—
60	C₂×D₈	—	2	3	no	—
61	C₂×D₈	C₂×D₇₁	1	6	yes	—
62	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
63	SD₃₂	—	71	16	no	—
64	C₂×C₁₆	—	71	6	no	—
65	C₂⁴	—	4	1	no	—
66	C₂×Q₈	—	284	3	no	—
67	C₂×Q₈	—	142	6	no	—
68	C₂×D₄	—	2	6	no	—
69	C₂×D₄	—	4	3	no	—
70	C₂²×C₄	—	284	1	no	—
71	C₂²×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
72	Q₁₆	—	71	4	no	—
73	Q₁₆	—	142	6	no	—
74	D₈	—	2	6	no	—
75	D₈	C₂²×D₇₁	1	4	yes	—
76	C₂×C₈	C₂²⋊D₇₁	1	3	yes	—
77	C₂×C₈	C₂²×D₇₁	1	3	yes	—
78	C₁₆	—	71	4	no	—
79	C₂³	—	4	6	no	—
80	C₂³	—	8	4	no	—
81	C₂³	#11765850	1	1	yes	characteristic
82	Q₈	—	284	6	no	—
83	Q₈	—	142	4	no	—
84	D₄	—	2	4	no	—
85	D₄	—	4	6	no	—
86	C₂×C₄	—	284	6	no	—
87	C₂×C₄	#11765850	1	3	yes	—
88	C₂×C₄	C₂×C₂²⋊D₇₁	1	3	yes	—
89	C₈	C₂×C₂²⋊D₇₁	1	3	yes	—
90	C₈	C₂³×D₇₁	1	1	yes	characteristic
91	C₂²	—	4	4	no	—
92	C₂²	—	8	12	no	—
93	C₂²	#14556072	1	4	yes	direct product factor
94	C₂²	C₂×#11765850	1	3	yes	—
95	C₄	—	284	4	no	—
96	C₄	C₂×#11765850	1	3	yes	—
97	C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
98	C₂	—	8	4	no	—
99	C₂	C₂×#14556072	1	6	yes	direct product factor
100	C₂	C₂²×#11765850	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₂₈₄

C₂

yes

maximal, characteristic, complemented

C₂×#14556072

C₂

yes

maximal, direct product factor

C₂²×C₇₁⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₇₁

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₂

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

C₂²

yes

complemented

#14556072

C₂²

yes

direct product factor

C₂×C₇₁⋊C₁₆

C₂²

yes

complemented

C₂²×D₄×C₇₁

—

C₂×D₈×C₇₁

—

C₂×D₈×C₇₁

C₂²

yes

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

Dic₂₈₄

—

Dic₂₈₄

C₂³

yes

complemented

C₇₁⋊C₁₆

C₂³

yes

complemented

C₂⁴×C₇₁

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

C₂²×C₄×C₇₁

D₄

yes

characteristic

D₈×C₇₁

—

D₈×C₇₁

C₂³

yes

—

C₂×C₈×C₇₁

D₄

yes

—

C₂×C₈×C₇₁

C₂³

yes

—

C₂³×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

D₈

yes

characteristic

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

D₈

yes

—

C₂×C₄×C₇₁

C₂×D₄

yes

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

C₂×D₄

yes

—

C₈×C₇₁

C₂⁴

yes

characteristic

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

SD₃₂

yes

complemented

C₂²×C₇₁

C₂×D₈

yes

—

C₄×C₇₁

C₂×D₈

yes

—

C₄×C₇₁

C₂²×D₄

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

C₂×SD₃₂

yes

complemented

C₂×C₇₁

C₂²×D₈

yes

characteristic

C₂²×SD₃₂

—

maximal, Sylow

C₇₁

C₂²×SD₃₂

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂²×D₈

D₇₁

yes

characteristic

C₂×SD₃₂

—

C₂²×C₁₆

—

C₂²×Q₈

—

142

—

C₂²×D₄

—

C₂×Q₁₆

—

C₂×Q₁₆

—

142

—

C₂×D₈

—

C₂×D₈

C₂×D₇₁

yes

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

SD₃₂

—

C₂×C₁₆

—

C₂⁴

—

C₂×Q₈

—

284

—

C₂×Q₈

—

142

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

284

—

C₂²×C₄

C₂²⋊D₇₁

yes

characteristic

Q₁₆

—

Q₁₆

—

142

—

D₈

—

D₈

C₂²×D₇₁

yes

—

C₂×C₈

C₂²⋊D₇₁

yes

—

C₂×C₈

C₂²×D₇₁

yes

—

C₁₆

—

C₂³

—

C₂³

—

C₂³

#11765850

yes

characteristic

Q₈

—

284

—

Q₈

—

142

—

D₄

—

D₄

—

C₂×C₄

—

284

—

C₂×C₄

#11765850

yes

—

C₂×C₄

C₂×C₂²⋊D₇₁

yes

—

C₈

C₂×C₂²⋊D₇₁

yes

—

C₈

C₂³×D₇₁

yes

characteristic

C₂²

—

C₂²

—

C₂²

#14556072

yes

direct product factor

C₂²

C₂×#11765850

yes

—

C₄

—

284

—

C₄

C₂×#11765850

yes

—

C₄

C₂²×C₂²⋊D₇₁

yes

characteristic

C₂

—

C₂

C₂×#14556072

yes

direct product factor

100

C₂

C₂²×#11765850

yes

characteristic

	subgroup	G/H
center	C₂³	#11765850
commutator	C₈×C₇₁	C₂⁴
Frattini	C₈	C₂³×D₇₁
Fitting	C₂²×D₈×C₇₁	C₂
socle	C₂³×C₇₁	D₈
hypercenter	C₂²×D₈	D₇₁
hypocenter	C₇₁	C₂²×SD₃₂
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₈

subgroup

G/H

center

C₂³

#11765850

commutator

C₈×C₇₁

C₂⁴

Frattini

C₈

C₂³×D₇₁

Fitting

C₂²×D₈×C₇₁

C₂

socle

C₂³×C₇₁

D₈

hypercenter

C₂²×D₈

D₇₁

hypocenter

C₇₁

C₂²×SD₃₂

LCS

G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₈

N	H ≅ G/N	type
1. C₂²×Dic₂₈₄	C₂	semidirect
2. C₂×#14556072	C₂	direct (N × H)
3. C₂²×C₇₁⋊C₁₆	C₂	semidirect
7. C₂×Dic₂₈₄	C₂²	semidirect
8. #14556072	C₂²	direct (N × H)
9. C₂×C₇₁⋊C₁₆	C₂²	semidirect
18. Dic₂₈₄	C₂³	semidirect
19. C₇₁⋊C₁₆	C₂³	semidirect
42. C₂²×C₇₁	SD₃₂	semidirect
48. C₂×C₇₁	C₂×SD₃₂	semidirect
51. C₇₁	C₂²×SD₃₂	semidirect
93. C₂²	#14556072	direct (N × H)
99. C₂	C₂×#14556072	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₂₈₄

C₂

semidirect

2. C₂×#14556072

C₂

direct (N × H)

3. C₂²×C₇₁⋊C₁₆

C₂

semidirect

7. C₂×Dic₂₈₄

C₂²

semidirect

8. #14556072

C₂²

direct (N × H)

9. C₂×C₇₁⋊C₁₆

C₂²

semidirect

18. Dic₂₈₄

C₂³

semidirect

19. C₇₁⋊C₁₆

C₂³

semidirect

42. C₂²×C₇₁

SD₃₂

semidirect

48. C₂×C₇₁

C₂×SD₃₂

semidirect

51. C₇₁

C₂²×SD₃₂

semidirect

93. C₂²

#14556072

direct (N × H)

99. C₂

C₂×#14556072

direct (N × H)

Subgroups — C₂²×#14556072 #22601449

Conjugacy classes of subgroups

Complements

Subgroups — C22×#14556072 #22601449

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14556072 #22601449