Group #22626959 — subgroups

Subgroups — #22626959

Order 9344.

134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 27 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	#17989673	C₂	1	2	yes	maximal
2	(C₂×#64408)⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#10596842	—	2	2	no	—
4	C₂×C₄⋊#64408	C₂²	1	1	yes	characteristic
5	C₂×C₄×#64408	C₄	1	1	yes	characteristic
6	(C₂×#64408)⋊C₄	—	2	2	no	—
7	C₂×Q₈×D₇₃	C₄	1	1	yes	characteristic
8	C₂×#10596842	—	4	2	no	—
9	C₂²×#64408	—	2	1	no	—
10	C₂²×#64408	D₄	1	2	yes	—
11	C₄⋊#64408	—	4	1	no	—
12	C₄×#64408	—	4	1	no	—
13	C₂×Dic₁₄₆	—	2	1	no	—
14	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic, complemented
15	Q₈×D₇₃	—	4	1	no	—
16	Q₈×D₇₃	—	4	1	no	—
17	C₂×C₄×D₇₃	—	2	1	no	—
18	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×Q₈×C₇₃	C₈	1	1	yes	characteristic, complemented
20	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×#64408	—	2	2	no	—
22	C₂×#64408	—	2	2	no	—
23	C₂×#64408	—	4	1	no	—
24	C₂×#64408	—	4	1	no	—
25	C₂×#64408	—	4	2	no	—
26	#10596842	—	8	2	no	—
27	Q₈×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	—	2	1	no	—
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×Dic₇₃	—	2	1	no	—
31	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
32	C₄×D₇₃	—	2	1	no	—
33	C₄×D₇₃	—	2	1	no	—
34	C₄×D₇₃	—	4	1	no	—
35	C₄×D₇₃	—	4	1	no	—
36	Dic₁₄₆	—	4	2	no	—
37	Dic₁₄₆	—	4	1	no	—
38	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₂×D₇₃	—	2	1	no	—
40	C₂×D₇₃	—	2	1	no	—
41	C₂×D₇₃	#99	1	1	yes	characteristic
42	C₂×D₇₃	#100	1	1	yes	characteristic
43	#64408	—	4	2	no	—
44	#64408	—	4	2	no	—
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	—	4	1	no	—
47	Dic₇₃	—	2	1	no	—
48	Dic₇₃	—	4	1	no	—
49	C₂×C₇₃	—	2	1	no	—
50	C₂×C₇₃	#323	1	1	yes	characteristic
51	D₇₃	—	2	1	no	—
52	D₇₃	#354	1	1	yes	characteristic
53	D₇₃	#356	1	1	yes	characteristic
54	#1319	—	73	1	no	maximal, Sylow
55	C₇₃	#1319	1	1	yes	characteristic, complemented, Sylow
56	#391	—	73	1	no	—
57	#324	—	73	2	no	—
58	C₂²×Q₈	—	73	1	no	—
59	C₂×C₄⋊C₄	—	73	1	no	—
60	C₂×C₄²	—	73	1	no	—
61	C₂²⋊C₈	—	146	2	no	—
62	#95	—	146	2	no	—
63	C₂×Q₈	—	292	1	no	—
64	C₂×Q₈	—	292	1	no	—
65	C₂×Q₈	—	73	1	no	—
66	C₂×Q₈	—	146	1	no	—
67	C₂×Q₈	#10596842	1	1	yes	characteristic, complemented
68	C₂²×C₄	—	73	2	no	—
69	C₂²×C₄	—	73	1	no	—
70	C₂²×C₄	—	146	1	no	—
71	C₂²×C₄	—	146	1	no	—
72	C₂×C₈	—	292	2	no	—
73	C₄⋊C₄	—	292	1	no	—
74	C₄²	—	292	1	no	—
75	C₂³	—	73	1	no	—
76	Q₈	—	4	1	no	—
77	Q₈	—	292	1	no	—
78	Q₈	—	292	2	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	292	1	no	—
81	C₂×C₄	—	292	1	no	—
82	C₂×C₄	—	292	1	no	—
83	C₂×C₄	—	292	1	no	—
84	C₂×C₄	—	292	2	no	—
85	C₂×C₄	—	73	1	no	—
86	C₂×C₄	—	146	1	no	—
87	C₂×C₄	—	146	1	no	—
88	C₂×C₄	—	146	2	no	—
89	C₂×C₄	—	146	2	no	—
90	C₂×C₄	—	146	1	no	—
91	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
92	C₈	—	584	2	no	—
93	C₂²	—	73	1	no	—
94	C₂²	—	73	1	no	—
95	C₂²	—	146	1	no	—
96	C₂²	—	146	1	no	—
97	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	4	1	no	—
100	C₄	—	292	2	no	—
101	C₄	—	292	2	no	—
102	C₄	—	292	1	no	—
103	C₄	—	146	1	no	—
104	C₂	—	2	1	no	—
105	C₂	—	73	1	no	—
106	C₂	—	73	1	no	—
107	C₂	—	146	1	no	—
108	C₂	#17989672	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989673

C₂

yes

maximal

(C₂×#64408)⋊Q₈

C₂

yes

maximal, characteristic

C₂²⋊#10596842

—

C₂×C₄⋊#64408

C₂²

yes

characteristic

C₂×C₄×#64408

C₄

yes

characteristic

(C₂×#64408)⋊C₄

—

C₂×Q₈×D₇₃

C₄

yes

characteristic

C₂×#10596842

—

C₂²×#64408

—

C₂²×#64408

D₄

yes

—

C₄⋊#64408

—

C₄×#64408

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₈

yes

characteristic, complemented

Q₈×D₇₃

—

Q₈×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×Q₈×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₂²⋊C₄

yes

—

—

—

—

—

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

yes

C₂×D₇₃

yes

—

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#323

yes

characteristic

D₇₃

—

D₇₃

yes

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#391

—

#324

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

146

—

#95

—

146

—

C₂×Q₈

—

292

—

C₂×Q₈

—

292

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

#10596842

yes

characteristic, complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂×C₈

—

292

—

C₄⋊C₄

—

292

—

C₄²

—

292

—

C₂³

—

Q₈

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

584

—

C₂²

—

C₂²

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

C₂²⋊#10596842

yes

characteristic

C₄

—

C₄

—

100

C₄

—

292

—

101

C₄

—

292

—

102

C₄

—

292

—

103

C₄

—

146

—

104

C₂

—

105

C₂

—

106

C₂

—

107

C₂

—

146

—

108

C₂

#17989672

yes

characteristic

	subgroup	G/H
center	C₂	#17989672
commutator	C₂×C₄×C₇₃	C₂×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₂×Q₈×C₇₃	C₈
socle	C₂×C₇₃	#323
hypercenter	C₂×Q₈	#10596842
hypocenter	C₇₃	#1319
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

subgroup

G/H

center

C₂

#17989672

commutator

C₂×C₄×C₇₃

C₂×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

C₂×Q₈×C₇₃

C₈

C₂×C₇₃

C₂×Q₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

N	H ≅ G/N	type
14. C₂×Dic₁₄₆	C₈	semidirect
19. C₂×Q₈×C₇₃	C₈	semidirect
55. C₇₃	#1319	semidirect
67. C₂×Q₈	#10596842	semidirect

H ≅ G/N

type

14. C₂×Dic₁₄₆

C₈

semidirect

19. C₂×Q₈×C₇₃

C₈

semidirect

55. C₇₃

#1319

semidirect

67. C₂×Q₈

#10596842

semidirect

Subgroups — #22626959

Conjugacy classes of subgroups

Complements