Group #22610751 — subgroups

Subgroups — #22610751

Order 9344.

308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14556591	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556516	C₂	1	4	yes	maximal
3	#17988453	C₂	1	1	yes	maximal, characteristic
4	C₂×#97×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
6	#14556591	—	2	2	no	—
7	#14556591	C₄	1	4	yes	complemented
8	C₂×C₄⋊Dic₇₃	—	2	2	no	—
9	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
10	#14556516	—	2	8	no	—
11	#14556498	—	2	2	no	—
12	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
14	#97×C₇₃	—	2	2	no	—
15	C₂×Dic₁₄₆	—	2	4	no	—
16	C₂×Dic₁₄₆	—	2	4	no	—
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×Dic₁₄₆	C₂×C₄	1	4	yes	—
19	C₂²×Dic₇₃	—	2	2	no	—
20	C₂²×Dic₇₃	—	2	2	no	—
21	C₄⋊Dic₇₃	—	2	8	no	—
22	C₄⋊Dic₇₃	—	2	4	no	—
23	C₂²×C₄×C₇₃	D₄	1	2	yes	—
24	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₇₃	—	2	2	no	—
26	C₂×C₈×C₇₃	—	2	2	no	—
27	C₂×C₈×C₇₃	D₄	1	4	yes	—
28	C₄²×C₇₃	C₂×C₄	1	2	yes	—
29	C₄²×C₇₃	D₄	1	2	yes	—
30	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	4	no	—
32	C₂×C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₇₃	#41	1	2	yes	—
37	C₂×Dic₇₃	—	2	4	no	—
38	C₂×Dic₇₃	—	4	2	no	—
39	C₂×Dic₇₃	—	4	2	no	—
40	C₂×Dic₇₃	—	4	2	no	—
41	C₂×Dic₇₃	—	4	4	no	—
42	Dic₁₄₆	—	2	8	no	—
43	Dic₁₄₆	—	4	4	no	—
44	C₈×C₇₃	—	2	4	no	—
45	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₇₃	#124	1	1	yes	characteristic
47	C₂²×C₇₃	#127	1	1	yes	characteristic
48	C₂²×C₇₃	#137	1	4	yes	—
49	C₄×C₇₃	—	2	4	no	—
50	C₄×C₇₃	C₄×D₄	1	2	yes	—
51	C₄×C₇₃	#121	1	2	yes	—
52	Dic₇₃	—	4	4	no	—
53	Dic₇₃	—	8	2	no	—
54	C₂×C₇₃	#390	1	1	yes	characteristic
55	C₂×C₇₃	#419	1	2	yes	—
56	C₂×C₇₃	#491	1	2	yes	—
57	C₂×C₇₃	#497	1	2	yes	—
58	#1960	—	73	1	no	maximal, Sylow
59	C₇₃	#1960	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₄⋊Q₈	—	73	1	no	—
61	C₂×#103	—	73	4	no	—
62	C₂×#97	D₇₃	1	1	yes	characteristic
63	#382	—	73	1	no	—
64	C₂²×Q₈	—	73	2	no	—
65	C₂²×C₈	C₂×D₇₃	1	2	yes	—
66	C₄⋊Q₈	—	73	4	no	—
67	C₄⋊Q₈	—	146	2	no	—
68	C₂×C₄⋊C₄	—	73	2	no	—
69	C₂×C₄⋊C₄	—	146	2	no	—
70	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
71	#103	—	146	8	no	—
72	#97	—	2	2	no	—
73	#95	—	146	2	no	—
74	C₂×Q₈	—	73	4	no	—
75	C₂×Q₈	—	146	4	no	—
76	C₂×Q₈	—	146	4	no	—
77	C₂×Q₈	—	146	2	no	—
78	C₂²×C₄	—	146	2	no	—
79	C₂²×C₄	—	146	2	no	—
80	C₂²×C₄	D₂₉₂	1	2	yes	—
81	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	D₂₉₂	1	4	yes	—
85	C₄⋊C₄	—	146	4	no	—
86	C₄⋊C₄	—	146	8	no	—
87	C₄²	C₄×D₇₃	1	2	yes	—
88	C₄²	C₂²⋊D₇₃	1	2	yes	—
89	C₂³	C₂×D₂₉₂	1	1	yes	characteristic
90	Q₈	—	292	4	no	—
91	Q₈	—	146	8	no	—
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	—	292	2	no	—
94	C₂×C₄	—	292	2	no	—
95	C₂×C₄	—	292	2	no	—
96	C₂×C₄	—	292	4	no	—
97	C₂×C₄	—	146	4	no	—
98	C₂×C₄	#11924005	1	4	yes	—
99	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
100	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
101	C₂×C₄	C₂×D₂₉₂	1	2	yes	—
102	C₂×C₄	#11924028	1	2	yes	—
103	C₈	—	2	4	no	—
104	C₂²	C₂×#11924005	1	1	yes	characteristic
105	C₂²	#14556579	1	1	yes	characteristic
106	C₂²	#14556588	1	1	yes	characteristic
107	C₂²	#14556624	1	4	yes	—
108	C₄	—	2	4	no	—
109	C₄	—	292	4	no	—
110	C₄	—	584	2	no	—
111	C₄	C₄×D₂₉₂	1	2	yes	—
112	C₄	#14556565	1	2	yes	—
113	C₂	#17988489	1	1	yes	characteristic
114	C₂	#17988597	1	2	yes	—
115	C₂	#17988956	1	2	yes	—
116	C₂	#17988981	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556591

C₂

yes

maximal, characteristic

C₂×#14556516

C₂

yes

maximal

#17988453

C₂

yes

maximal, characteristic

C₂×#97×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

#14556591

—

#14556591

C₄

yes

complemented

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

#14556516

—

#14556498

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#97×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

D₄

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

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×D₄

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

—

C₄×C₇₃

#121

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#390

yes

characteristic

C₂×C₇₃

#419

yes

—

C₂×C₇₃

#491

yes

—

C₂×C₇₃

#497

yes

—

#1960

—

maximal, Sylow

C₇₃

#1960

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×#97

D₇₃

yes

characteristic

#382

—

C₂²×Q₈

—

C₂²×C₈

C₂×D₇₃

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#103

—

146

—

#97

—

#95

—

146

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

D₂₉₂

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₂₉₂

yes

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

C₄×D₇₃

yes

—

C₄²

C₂²⋊D₇₃

yes

—

C₂³

C₂×D₂₉₂

yes

characteristic

Q₈

—

292

—

Q₈

—

146

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

#11924005

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

100

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

101

C₂×C₄

C₂×D₂₉₂

yes

—

102

C₂×C₄

#11924028

yes

—

103

C₈

—

104

C₂²

C₂×#11924005

yes

characteristic

105

C₂²

#14556579

yes

characteristic

106

C₂²

#14556588

yes

characteristic

107

C₂²

#14556624

yes

—

108

C₄

—

109

C₄

—

292

—

110

C₄

—

584

—

111

C₄

C₄×D₂₉₂

yes

—

112

C₄

#14556565

yes

—

113

C₂

#17988489

yes

characteristic

114

C₂

#17988597

yes

—

115

C₂

#17988956

yes

—

116

C₂

#17988981

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#97×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	C₂×#97	D₇₃
hypocenter	C₇₃	#1960
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₂₉₂

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#97×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

hypercenter

C₂×#97

D₇₃

hypocenter

C₇₃

#1960

LCS

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
7. #14556591	C₄	semidirect
59. C₇₃	#1960	semidirect

H ≅ G/N

type

7. #14556591

C₄

semidirect

59. C₇₃

#1960

semidirect

Subgroups — #22610751

Conjugacy classes of subgroups

Complements