Group #22626932 — subgroups

Subgroups — #22626932

Order 9344.

166 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 41 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×#10596842)⋊C₄	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	C₄	1	1	yes	characteristic
5	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
6	(C₂×#64408)⋊C₄	—	2	2	no	—
7	C₂×Q₈×D₇₃	C₄	1	1	yes	characteristic
8	C₂×#10596842	—	2	4	no	—
9	C₂×#10596842	—	4	2	no	—
10	C₂×#10596842	—	4	2	no	—
11	C₂²×#64408	—	2	1	no	—
12	C₂²×#64408	D₄	1	2	yes	—
13	C₄⋊#64408	—	4	1	no	—
14	C₄×#64408	—	4	1	no	—
15	C₂×Dic₁₄₆	—	2	1	no	—
16	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic, complemented
17	Q₈×D₇₃	—	4	1	no	—
18	Q₈×D₇₃	—	4	1	no	—
19	C₂×C₄×D₇₃	—	2	1	no	—
20	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×Q₈×C₇₃	C₈	1	1	yes	characteristic, complemented
22	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×#64408	—	2	2	no	—
24	C₂×#64408	—	2	2	no	—
25	C₂×#64408	—	4	1	no	—
26	C₂×#64408	—	4	2	no	—
27	C₂×#64408	SD₁₆	1	2	yes	—
28	C₂×#64408	Q₁₆	1	2	yes	—
29	#10596842	—	4	4	no	—
30	Q₈×C₇₃	—	4	1	no	—
31	C₂×C₄×C₇₃	—	2	1	no	—
32	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
33	C₂×Dic₇₃	—	2	1	no	—
34	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
35	C₄×D₇₃	—	2	1	no	—
36	C₄×D₇₃	—	2	1	no	—
37	C₄×D₇₃	—	4	1	no	—
38	C₄×D₇₃	—	4	1	no	—
39	Dic₁₄₆	—	4	2	no	—
40	Dic₁₄₆	—	4	1	no	—
41	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₂×D₇₃	#99	1	1	yes	characteristic
43	C₂×D₇₃	#100	1	1	yes	characteristic
44	C₂×D₇₃	#103	1	2	yes	—
45	C₂×D₇₃	#104	1	2	yes	—
46	#64408	—	2	2	no	—
47	#64408	—	2	2	no	—
48	#64408	—	8	1	no	—
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	—	4	1	no	—
51	Dic₇₃	—	2	1	no	—
52	Dic₇₃	—	4	1	no	—
53	C₂×C₇₃	#323	1	1	yes	characteristic
54	C₂×C₇₃	Q₈⋊C₈	1	2	yes	—
55	D₇₃	#328	1	2	yes	—
56	D₇₃	#329	1	1	yes	characteristic
57	D₇₃	#333	1	1	yes	characteristic
58	#1272	—	73	1	no	maximal, Sylow
59	C₇₃	#1272	1	1	yes	characteristic, complemented, Sylow
60	#391	—	73	1	no	—
61	#336	—	73	2	no	—
62	C₂²×Q₈	—	73	1	no	—
63	C₂²×C₈	—	146	2	no	—
64	C₂×C₄⋊C₄	—	73	1	no	—
65	C₂×C₄²	—	73	1	no	—
66	#95	—	146	2	no	—
67	C₂×Q₈	—	292	1	no	—
68	C₂×Q₈	—	292	1	no	—
69	C₂×Q₈	—	73	1	no	—
70	C₂×Q₈	—	146	1	no	—
71	C₂×Q₈	#10596842	1	1	yes	characteristic, complemented
72	C₂²×C₄	—	73	2	no	—
73	C₂²×C₄	—	73	1	no	—
74	C₂²×C₄	—	146	1	no	—
75	C₂²×C₄	—	146	1	no	—
76	C₂×C₈	—	292	2	no	—
77	C₂×C₈	—	292	2	no	—
78	C₂×C₈	—	146	4	no	—
79	C₄⋊C₄	—	292	1	no	—
80	C₄²	—	292	1	no	—
81	C₂³	—	73	1	no	—
82	Q₈	—	4	1	no	—
83	Q₈	—	292	1	no	—
84	Q₈	—	292	2	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	292	1	no	—
87	C₂×C₄	—	292	1	no	—
88	C₂×C₄	—	292	1	no	—
89	C₂×C₄	—	292	2	no	—
90	C₂×C₄	—	73	2	no	—
91	C₂×C₄	—	73	2	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	146	1	no	—
94	C₂×C₄	—	146	1	no	—
95	C₂×C₄	—	146	1	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
99	C₈	—	292	4	no	—
100	C₂²	—	73	1	no	—
101	C₂²	—	73	1	no	—
102	C₂²	—	73	2	no	—
103	C₂²	—	73	2	no	—
104	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	4	1	no	—
107	C₄	—	292	1	no	—
108	C₄	—	584	1	no	—
109	C₄	—	146	2	no	—
110	C₄	—	146	2	no	—
111	C₄	—	146	1	no	—
112	C₂	—	73	1	no	—
113	C₂	—	73	2	no	—
114	C₂	—	73	1	no	—
115	C₂	#17989672	1	1	yes	characteristic
116	C₂	Q₈⋊#10596842	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

(C₂×#10596842)⋊C₄

C₂

yes

maximal

(C₂×#64408)⋊Q₈

C₂

yes

maximal, characteristic

C₂²×#10596842

—

C₂×C₄⋊#64408

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

(C₂×#64408)⋊C₄

—

C₂×Q₈×D₇₃

C₄

yes

—

—

—

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

—

—

—

—

SD₁₆

yes

—

C₂×#64408

Q₁₆

yes

—

#10596842

—

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

C₂×D₇₃

yes

C₂×D₇₃

yes

C₂×D₇₃

yes

—

C₂×D₇₃

#104

yes

—

#64408

—

#64408

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#323

yes

characteristic

C₂×C₇₃

Q₈⋊C₈

yes

—

D₇₃

#328

yes

—

D₇₃

yes

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#391

—

#336

—

C₂²×Q₈

—

C₂²×C₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

#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

—

C₂×C₈

—

292

—

C₂×C₈

—

146

—

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

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

292

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂²⋊#10596842

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

292

—

108

C₄

—

584

—

109

C₄

—

146

—

110

C₄

—

146

—

111

C₄

—

146

—

112

C₂

—

113

C₂

—

114

C₂

—

115

C₂

#17989672

yes

characteristic

116

C₂

Q₈⋊#10596842

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊#10596842
commutator	C₂×C₄×C₇₃	C₂×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₂×Q₈×C₇₃	C₈
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₂×Q₈	#10596842
hypocenter	C₇₃	#1272
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

subgroup

G/H

center

C₂²

C₂²⋊#10596842

commutator

C₂×C₄×C₇₃

C₂×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

C₂×Q₈×C₇₃

C₈

socle

C₂²×C₇₃

C₂²⋊C₈

C₂×Q₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

N	H ≅ G/N	type
16. C₂×Dic₁₄₆	C₈	semidirect
21. C₂×Q₈×C₇₃	C₈	semidirect
59. C₇₃	#1272	semidirect
71. C₂×Q₈	#10596842	semidirect

H ≅ G/N

type

16. C₂×Dic₁₄₆

C₈

semidirect

21. C₂×Q₈×C₇₃

C₈

semidirect

59. C₇₃

#1272

semidirect

71. C₂×Q₈

#10596842

semidirect

Subgroups — #22626932

Conjugacy classes of subgroups

Complements