Group #22626281 — subgroups

Subgroups — C₂×#17989514 #22626281

Order 9344.

168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 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×#14556660	C₂	1	2	yes	maximal
2	#17989514	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#64408	—	2	2	no	—
5	#14556660	—	2	2	no	—
6	#14556660	C₂²	1	4	yes	—
7	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
8	C₂×#11924003	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₇₃	C₄	1	2	yes	complemented
10	C₁₆×D₇₃	C₂²	1	2	yes	—
11	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
12	C₂²×#64408	—	4	2	no	—
13	C₄⋊#64408	—	2	4	no	—
14	C₄⋊#64408	—	4	2	no	—
15	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
16	C₂×#10596831	Q₈	1	1	yes	characteristic
17	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
18	C₈×D₇₃	D₄	1	1	yes	characteristic
19	C₈×D₇₃	Q₈	1	1	yes	characteristic
20	C₈×D₇₃	C₂³	1	1	yes	characteristic
21	#11924003	C₂×C₄	1	2	yes	complemented
22	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
24	C₂²×D₇₃	D₈	1	1	yes	characteristic
25	C₂×#64408	—	4	4	no	—
26	C₂×#64408	—	8	4	no	—
27	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×Dic₇₃	Q₁₆	1	1	yes	characteristic
29	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
30	C₄×D₇₃	D₈	1	1	yes	characteristic
31	C₄×D₇₃	Q₁₆	1	1	yes	characteristic
32	C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
33	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
34	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	#10596831	C₄⋊C₄	1	1	yes	characteristic
36	#10596831	C₂×Q₈	1	1	yes	characteristic
37	C₂²×C₇₃	#107	1	1	yes	characteristic
38	C₂×D₇₃	#107	1	1	yes	characteristic
39	C₂×D₇₃	SD₃₂	1	4	yes	—
40	C₂×D₇₃	C₂×D₈	1	1	yes	characteristic
41	#64408	—	8	4	no	—
42	C₄×C₇₃	#107	1	1	yes	characteristic
43	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	Dic₇₃	#107	1	1	yes	characteristic
45	Dic₇₃	C₂×Q₁₆	1	1	yes	characteristic
46	C₂×C₇₃	#367	1	2	yes	complemented
47	C₂×C₇₃	C₂×#107	1	1	yes	characteristic
48	D₇₃	#367	1	2	yes	complemented
49	D₇₃	C₂×SD₃₂	1	2	yes	—
50	C₂×#367	—	73	1	no	maximal, Sylow
51	C₇₃	C₂×#367	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₁₆	—	73	1	no	—
53	C₂×#107	—	73	2	no	—
54	#367	—	73	4	no	—
55	C₂²×C₈	—	73	1	no	—
56	C₂×C₄⋊C₄	—	146	2	no	—
57	C₂×C₁₆	—	73	1	no	—
58	C₂×C₁₆	—	73	2	no	—
59	C₂×C₁₆	—	73	2	no	—
60	C₂×C₁₆	#64408	1	1	yes	characteristic, complemented
61	#107	—	73	4	no	—
62	#107	—	146	2	no	—
63	C₂²×C₄	—	292	2	no	—
64	C₂²×C₄	—	73	1	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	—	73	1	no	—
68	C₂×C₈	—	73	1	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	C₂×#64408	1	1	yes	characteristic
71	C₄⋊C₄	—	292	2	no	—
72	C₄⋊C₄	—	146	4	no	—
73	C₁₆	—	73	2	no	—
74	C₁₆	C₂×#64408	1	2	yes	complemented
75	C₂³	—	73	1	no	—
76	C₂×C₄	—	292	4	no	—
77	C₂×C₄	—	584	4	no	—
78	C₂×C₄	—	73	1	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	—	73	1	no	—
82	C₂×C₄	—	73	1	no	—
83	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
84	C₈	—	73	1	no	—
85	C₈	—	73	1	no	—
86	C₈	C₄⋊#64408	1	1	yes	characteristic
87	C₈	C₂²×#64408	1	1	yes	characteristic
88	C₂²	—	73	4	no	—
89	C₂²	—	73	1	no	—
90	C₂²	—	73	1	no	—
91	C₂²	#14556660	1	1	yes	characteristic
92	C₄	—	584	4	no	—
93	C₄	—	73	1	no	—
94	C₄	—	73	1	no	—
95	C₄	#14556660	1	1	yes	characteristic
96	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
97	C₂	—	73	2	no	—
98	C₂	—	73	2	no	—
99	C₂	#17989514	1	2	yes	direct product factor
100	C₂	C₂×#14556660	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556660

C₂

yes

maximal

#17989514

C₂

yes

maximal, direct product factor

C₂×C₁₆×D₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#64408

—

#14556660

—

#14556660

C₂²

yes

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₂×#11924003

C₄

yes

characteristic, complemented

C₁₆×D₇₃

C₄

yes

complemented

C₁₆×D₇₃

C₂²

yes

—

C₂×C₁₆×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

C₄⋊#64408

—

C₄⋊#64408

—

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×#10596831

Q₈

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

C₈×D₇₃

C₂³

yes

characteristic

#11924003

C₂×C₄

yes

complemented

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

C₂×C₄

yes

complemented

C₂²×D₇₃

D₈

yes

characteristic

C₂×#64408

—

C₂×#64408

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

Q₁₆

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

D₈

yes

characteristic

C₄×D₇₃

Q₁₆

yes

characteristic

C₄×D₇₃

C₂×D₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₂²×C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

#10596831

C₂×Q₈

yes

C₂²×C₇₃

yes

C₂×D₇₃

yes

C₂×D₇₃

SD₃₂

yes

—

C₂×D₇₃

C₂×D₈

yes

characteristic

#64408

—

C₄×C₇₃

#107

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

Dic₇₃

#107

yes

characteristic

Dic₇₃

C₂×Q₁₆

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

yes

D₇₃

C₂×SD₃₂

yes

—

C₂×#367

—

maximal, Sylow

C₇₃

C₂×#367

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×#107

—

#367

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

#64408

yes

characteristic, complemented

#107

—

#107

—

146

—

C₂²×C₄

—

292

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₁₆

—

C₁₆

C₂×#64408

yes

complemented

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊#64408

yes

characteristic

C₈

—

C₈

—

C₈

C₄⋊#64408

yes

characteristic

C₈

C₂²×#64408

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

#14556660

yes

characteristic

C₄

—

584

—

C₄

—

C₄

—

C₄

#14556660

yes

characteristic

C₄

C₂×C₄⋊#64408

yes

characteristic

C₂

—

C₂

—

C₂

#17989514

yes

direct product factor

100

C₂

C₂×#14556660

yes

characteristic

	subgroup	G/H
center	C₂²	#14556660
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₈	C₂²×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#107
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	C₂×#367
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

subgroup

G/H

center

C₂²

#14556660

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₈

C₂²×#64408

Fitting

C₂×C₁₆×C₇₃

C₄

C₂²×C₇₃

C₂×C₁₆

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
2. #17989514	C₂	direct (N × H)
8. C₂×#11924003	C₄	semidirect
9. C₁₆×D₇₃	C₄	semidirect
11. C₂×C₁₆×C₇₃	C₄	semidirect
21. #11924003	C₂×C₄	semidirect
23. C₁₆×C₇₃	C₂×C₄	semidirect
46. C₂×C₇₃	#367	semidirect
48. D₇₃	#367	semidirect
51. C₇₃	C₂×#367	semidirect
60. C₂×C₁₆	#64408	semidirect
74. C₁₆	C₂×#64408	semidirect
99. C₂	#17989514	direct (N × H)

H ≅ G/N

type

2. #17989514

C₂

direct (N × H)

8. C₂×#11924003

C₄

semidirect

9. C₁₆×D₇₃

C₄

semidirect

11. C₂×C₁₆×C₇₃

C₄

semidirect

21. #11924003

C₂×C₄

semidirect

23. C₁₆×C₇₃

C₂×C₄

semidirect

46. C₂×C₇₃

#367

semidirect

48. D₇₃

#367

semidirect

51. C₇₃

C₂×#367

semidirect

60. C₂×C₁₆

#64408

semidirect

74. C₁₆

C₂×#64408

semidirect

99. C₂

#17989514

direct (N × H)

Subgroups — C₂×#17989514 #22626281

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17989514 #22626281

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989514 #22626281