Group #22610899 — subgroups

Subgroups — #22610899

Order 9344.

260 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 105 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×#14556583	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556502	C₂	1	1	yes	maximal, characteristic
3	#17988349	C₂	1	4	yes	maximal
4	#384×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10596831	C₂²	1	2	yes	—
6	#14556583	—	2	2	no	—
7	#14556583	C₄	1	4	yes	complemented
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	C₂×#11924007	—	2	2	no	—
10	#14556502	—	2	2	no	—
11	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
12	C₂×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×Dic₇₃	—	2	2	no	—
15	C₂×#10596831	—	2	2	no	—
16	C₂×#10596831	—	2	2	no	—
17	C₂×#10596831	Q₈	1	4	yes	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	C₂×C₄	1	4	yes	—
20	#11924007	—	2	8	no	—
21	C₂²×C₄×C₇₃	—	2	2	no	—
22	C₂²×C₄×C₇₃	D₄	1	2	yes	—
23	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₇₃	—	2	4	no	—
25	C₄⋊C₄×C₇₃	—	4	4	no	—
26	C₄²×C₇₃	C₂×C₄	1	2	yes	—
27	C₄²×C₇₃	D₄	1	2	yes	—
28	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	2	2	no	—
30	C₂×C₄×C₇₃	—	2	2	no	—
31	C₂×C₄×C₇₃	—	4	2	no	—
32	C₂×C₄×C₇₃	—	4	4	no	—
33	C₂×C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
34	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
37	C₂×C₄×C₇₃	#41	1	2	yes	—
38	C₂×Dic₇₃	—	2	4	no	—
39	C₂×Dic₇₃	—	4	2	no	—
40	C₂×Dic₇₃	—	4	2	no	—
41	#10596831	—	2	4	no	—
42	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₇₃	#124	1	1	yes	characteristic
44	C₂²×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
45	C₂²×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
46	C₂²×C₇₃	#137	1	2	yes	—
47	C₄×C₇₃	—	2	4	no	—
48	C₄×C₇₃	—	8	2	no	—
49	C₄×C₇₃	C₄×Q₈	1	2	yes	—
50	C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
51	Dic₇₃	—	4	4	no	—
52	C₂×C₇₃	#391	1	1	yes	characteristic
53	C₂×C₇₃	#417	1	2	yes	—
54	C₂×C₇₃	#490	1	1	yes	characteristic
55	C₂×C₇₃	#491	1	1	yes	characteristic
56	C₂×C₇₃	#501	1	2	yes	—
57	#1992	—	73	1	no	maximal, Sylow
58	C₇₃	#1992	1	1	yes	characteristic, complemented, Sylow
59	C₂×#125	—	73	1	no	—
60	C₂×#97	—	73	1	no	—
61	#384	D₇₃	1	1	yes	characteristic
62	#340	—	73	4	no	—
63	C₂²×C₈	—	73	2	no	—
64	#125	—	73	4	no	—
65	#125	—	146	2	no	—
66	C₂×C₄⋊C₄	—	2	2	no	—
67	C₂×C₄⋊C₄	—	73	2	no	—
68	C₂×C₄⋊C₄	—	146	2	no	—
69	C₂×C₄⋊C₄	C₂×D₇₃	1	2	yes	—
70	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
71	#97	—	146	2	no	—
72	C₂²×C₄	—	2	2	no	—
73	C₂²×C₄	—	146	2	no	—
74	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
75	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
76	C₂×C₈	—	73	4	no	—
77	C₂×C₈	—	146	2	no	—
78	C₂×C₈	—	146	2	no	—
79	C₄⋊C₄	—	2	4	no	—
80	C₄⋊C₄	—	4	4	no	—
81	C₄⋊C₄	—	73	4	no	—
82	C₄⋊C₄	—	146	8	no	—
83	C₄⋊C₄	—	146	2	no	—
84	C₄²	C₄×D₇₃	1	2	yes	—
85	C₄²	D₂₉₂	1	2	yes	—
86	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	4	no	—
91	C₂×C₄	—	292	2	no	—
92	C₂×C₄	—	292	2	no	—
93	C₂×C₄	—	146	4	no	—
94	C₂×C₄	#11924005	1	4	yes	—
95	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
96	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
97	C₂×C₄	Q₈×D₇₃	1	2	yes	—
98	C₂×C₄	#11924027	1	2	yes	—
99	C₈	—	146	4	no	—
100	C₂²	C₂×#11924005	1	1	yes	characteristic
101	C₂²	#14556578	1	1	yes	characteristic
102	C₂²	#14556589	1	1	yes	characteristic
103	C₂²	#14556617	1	2	yes	—
104	C₂²	#14556622	1	2	yes	—
105	C₄	—	2	4	no	—
106	C₄	—	8	2	no	—
107	C₄	—	292	4	no	—
108	C₄	#14556556	1	2	yes	—
109	C₄	#14556571	1	2	yes	—
110	C₂	#17988492	1	1	yes	characteristic
111	C₂	#17988586	1	2	yes	—
112	C₂	#17988951	1	1	yes	characteristic
113	C₂	#17988955	1	1	yes	characteristic
114	C₂	#17988993	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556583

C₂

yes

maximal, characteristic

C₂×#14556502

C₂

yes

maximal, characteristic

#17988349

C₂

yes

maximal

#384×C₇₃

C₂

yes

maximal, characteristic

C₂²×#10596831

C₂²

yes

—

#14556583

—

#14556583

C₄

yes

complemented

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

—

#14556502

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

Q₈

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

D₄

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

#124

yes

characteristic

C₂²×C₇₃

C₄⋊Q₈

yes

characteristic

C₂²×C₇₃

AGL(1,ℤ/8)

yes

—

C₂²×C₇₃

#137

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×Q₈

yes

—

C₄×C₇₃

C₂²⋊Q₈

yes

—

Dic₇₃

—

C₂×C₇₃

#391

yes

characteristic

C₂×C₇₃

#417

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

#1992

—

maximal, Sylow

C₇₃

#1992

yes

characteristic, complemented, Sylow

C₂×#125

—

C₂×#97

—

#384

D₇₃

yes

characteristic

#340

—

C₂²×C₈

—

#125

—

#125

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#97

—

146

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

C₄×D₇₃

yes

—

C₄²

D₂₉₂

yes

—

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

#11924005

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

Q₈×D₇₃

yes

—

C₂×C₄

#11924027

yes

—

C₈

—

146

—

100

C₂²

C₂×#11924005

yes

characteristic

101

C₂²

#14556578

yes

characteristic

102

C₂²

#14556589

yes

characteristic

103

C₂²

#14556617

yes

—

104

C₂²

#14556622

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

292

—

108

C₄

#14556556

yes

—

109

C₄

#14556571

yes

—

110

C₂

#17988492

yes

characteristic

111

C₂

#17988586

yes

—

112

C₂

#17988951

yes

characteristic

113

C₂

#17988955

yes

characteristic

114

C₂

#17988993

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#384×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#384	D₇₃
hypocenter	C₇₃	#1992
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#384×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
7. #14556583	C₄	semidirect
58. C₇₃	#1992	semidirect

H ≅ G/N

type

7. #14556583

C₄

semidirect

58. C₇₃

#1992

semidirect

Subgroups — #22610899

Conjugacy classes of subgroups

Complements