Group #22610774 — subgroups

Subgroups — #22610774

Order 9344.

292 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14556509	C₂	1	4	yes	maximal
3	C₄×#11924012	C₂	1	1	yes	maximal, characteristic
4	#423×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
6	C₂×#11924012	C₂²	1	2	yes	—
7	#14556591	—	2	1	no	—
8	#14556591	—	2	1	no	—
9	#14556591	—	2	2	no	—
10	C₂×C₄⋊Dic₇₃	C₄	1	4	yes	—
11	#14556509	—	2	8	no	—
12	#14556502	—	2	1	no	—
13	C₄×#10596831	—	2	1	no	—
14	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₇₃	—	2	2	no	—
17	C₂×Dic₁₄₆	—	2	4	no	—
18	C₂×Dic₁₄₆	—	2	2	no	—
19	C₂×Dic₁₄₆	—	2	2	no	—
20	C₂×Dic₁₄₆	—	2	4	no	—
21	C₂²×Dic₇₃	C₂×C₄	1	4	yes	—
22	#11924012	—	2	2	no	—
23	#11924012	D₄	1	4	yes	—
24	C₂×#10596831	—	2	2	no	—
25	C₄⋊Dic₇₃	—	2	4	no	—
26	C₄⋊Dic₇₃	—	2	4	no	—
27	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
29	M₁₆×C₇₃	—	2	4	no	—
30	C₂×C₈×C₇₃	—	2	2	no	—
31	C₄²×C₇₃	D₄	1	1	yes	characteristic
32	C₄²×C₇₃	D₄	1	1	yes	characteristic
33	C₄²×C₇₃	D₄	1	2	yes	—
34	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	—	2	4	no	—
36	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₇₃	#41	1	2	yes	—
42	C₂×Dic₇₃	—	2	4	no	—
43	C₂×Dic₇₃	—	2	8	no	—
44	Dic₁₄₆	—	4	4	no	—
45	Dic₁₄₆	—	4	2	no	—
46	Dic₁₄₆	—	4	2	no	—
47	C₈×C₇₃	—	4	2	no	—
48	#10596831	—	2	4	no	—
49	C₂²×C₇₃	—	2	2	no	—
50	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₇₃	C₄×D₄	1	2	yes	—
52	C₄×C₇₃	—	2	2	no	—
53	C₄×C₇₃	#101	1	4	yes	complemented
54	C₄×C₇₃	#121	1	2	yes	—
55	C₄×C₇₃	#124	1	1	yes	characteristic
56	C₄×C₇₃	#127	1	1	yes	characteristic
57	Dic₇₃	—	4	4	no	—
58	C₂×C₇₃	—	2	2	no	—
59	C₂×C₇₃	#390	1	1	yes	characteristic
60	C₂×C₇₃	C₂×#101	1	2	yes	—
61	#1966	—	73	1	no	maximal, Sylow
62	C₇₃	#1966	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₄⋊Q₈	—	73	1	no	—
64	#423	D₇₃	1	1	yes	characteristic
65	C₂×#101	—	73	4	no	—
66	C₄×M₁₆	—	73	1	no	—
67	C₂²×Q₈	—	73	2	no	—
68	C₂×M₁₆	—	73	2	no	—
69	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
70	C₄⋊Q₈	—	146	1	no	—
71	C₄⋊Q₈	—	146	1	no	—
72	C₄⋊Q₈	—	146	2	no	—
73	C₂×C₄⋊C₄	—	73	4	no	—
74	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
75	C₄⋊C₈	—	2	2	no	—
76	#101	—	146	8	no	—
77	#97	—	146	1	no	—
78	C₄×C₈	—	146	1	no	—
79	C₂×Q₈	—	146	4	no	—
80	C₂×Q₈	—	146	2	no	—
81	C₂×Q₈	—	146	2	no	—
82	C₂×Q₈	—	146	4	no	—
83	C₂²×C₄	—	73	4	no	—
84	C₂²×C₄	C₄×D₇₃	1	2	yes	—
85	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
86	M₁₆	—	2	4	no	—
87	M₁₆	—	73	4	no	—
88	M₁₆	—	146	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	146	2	no	—
91	C₄⋊C₄	—	146	4	no	—
92	C₄⋊C₄	—	146	4	no	—
93	C₄²	D₂₉₂	1	1	yes	characteristic
94	C₄²	D₂₉₂	1	1	yes	characteristic
95	C₄²	C₂²⋊D₇₃	1	2	yes	—
96	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
97	Q₈	—	292	4	no	—
98	Q₈	—	292	2	no	—
99	Q₈	—	292	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	146	4	no	—
102	C₂×C₄	—	146	8	no	—
103	C₂×C₄	#11924005	1	2	yes	—
104	C₂×C₄	#11924005	1	2	yes	—
105	C₂×C₄	D₄×D₇₃	1	2	yes	—
106	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
107	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
108	C₂×C₄	#11924029	1	2	yes	—
109	C₈	—	4	2	no	—
110	C₈	—	146	4	no	—
111	C₂²	—	2	2	no	—
112	C₂²	C₂×#11924005	1	1	yes	characteristic
113	C₂²	#14556553	1	2	yes	—
114	C₄	—	2	2	no	—
115	C₄	—	292	4	no	—
116	C₄	#14556509	1	4	yes	complemented
117	C₄	#14556566	1	2	yes	—
118	C₄	#14556580	1	1	yes	characteristic
119	C₄	#14556587	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	#17988488	1	1	yes	characteristic
122	C₂	C₂×#14556509	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556591

C₂

yes

maximal, characteristic

C₂×#14556509

C₂

yes

maximal

C₄×#11924012

C₂

yes

maximal, characteristic

#423×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

C₂×#11924012

C₂²

yes

—

#14556591

—

#14556591

—

#14556591

—

C₂×C₄⋊Dic₇₃

C₄

yes

—

#14556509

—

#14556502

—

C₄×#10596831

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂×C₄

yes

—

#11924012

—

#11924012

D₄

yes

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

D₄

yes

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

C₄×D₄

yes

—

C₄×C₇₃

—

C₄×C₇₃

#101

yes

complemented

C₄×C₇₃

#121

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#390

yes

characteristic

C₂×C₇₃

C₂×#101

yes

—

#1966

—

maximal, Sylow

C₇₃

#1966

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

#423

D₇₃

yes

characteristic

C₂×#101

—

C₄×M₁₆

—

C₂²×Q₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

#101

—

146

—

#97

—

146

—

C₄×C₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

D₂₉₂

yes

characteristic

C₄²

D₂₉₂

yes

characteristic

C₄²

C₂²⋊D₇₃

yes

—

C₂³

C₂×C₄×D₇₃

yes

characteristic

Q₈

—

292

—

Q₈

—

292

—

Q₈

—

292

—

100

C₂×C₄

—

101

C₂×C₄

—

146

—

102

C₂×C₄

—

146

—

103

C₂×C₄

#11924005

yes

—

104

C₂×C₄

#11924005

yes

—

105

C₂×C₄

D₄×D₇₃

yes

—

106

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

107

C₂×C₄

C₂×D₂₉₂

yes

characteristic

108

C₂×C₄

#11924029

yes

—

109

C₈

—

110

C₈

—

146

—

111

C₂²

—

112

C₂²

C₂×#11924005

yes

characteristic

113

C₂²

#14556553

yes

—

114

C₄

—

115

C₄

—

292

—

116

C₄

#14556509

yes

complemented

117

C₄

#14556566

yes

—

118

C₄

#14556580

yes

characteristic

119

C₄

#14556587

yes

characteristic

120

C₂

—

121

C₂

#17988488

yes

characteristic

122

C₂

C₂×#14556509

yes

—

	subgroup	G/H
center	C₂²	C₂×#11924005
commutator	C₂³×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#423×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#423	D₇₃
hypocenter	C₇₃	#1966
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂×#11924005

commutator

C₂³×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#423×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
53. C₄×C₇₃	#101	semidirect
62. C₇₃	#1966	semidirect
116. C₄	#14556509	semidirect

H ≅ G/N

type

53. C₄×C₇₃

#101

semidirect

62. C₇₃

#1966

semidirect

116. C₄

#14556509

semidirect

Subgroups — #22610774

Conjugacy classes of subgroups

Complements