Group #22610049 — subgroups

Subgroups — #22610049

Order 9344.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14556520	C₂	1	2	yes	maximal
2	#17988433	C₂	1	1	yes	maximal, characteristic
3	#17988342	C₂	1	1	yes	maximal, characteristic
4	#17988341	C₂	1	2	yes	maximal
5	#336×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596831	C₂²	1	2	yes	—
7	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
9	#14556520	—	2	4	no	—
10	#14556498	C₄	1	2	yes	—
11	#14556498	C₄	1	2	yes	—
12	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
17	C₂×#10596831	—	2	2	no	—
18	C₂×#10596831	—	2	2	no	—
19	C₂×#10596831	—	2	2	no	—
20	C₄×Dic₇₃	—	2	2	no	—
21	C₄×Dic₇₃	D₄	1	2	yes	—
22	C₄×Dic₇₃	Q₈	1	2	yes	—
23	C₂²×C₄×C₇₃	C₂×C₄	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	—	2	2	no	—
28	C₄²×C₇₃	—	2	2	no	—
29	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	2	2	no	—
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₇₃	#41	1	2	yes	—
36	C₂×C₄×C₇₃	#41	1	2	yes	—
37	C₂×Dic₇₃	—	2	2	no	—
38	C₂×Dic₇₃	—	2	2	no	—
39	C₂×Dic₇₃	—	2	1	no	—
40	C₂×Dic₇₃	—	2	1	no	—
41	C₂×Dic₇₃	—	2	2	no	—
42	C₂×Dic₇₃	—	2	2	no	—
43	C₂×Dic₇₃	C₄⋊C₄	1	4	yes	—
44	C₈×C₇₃	—	4	2	no	—
45	#10596831	—	4	2	no	—
46	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₇₃	#117	1	1	yes	characteristic
48	C₂²×C₇₃	#117	1	1	yes	characteristic
49	C₂²×C₇₃	#131	1	2	yes	—
50	C₂²×C₇₃	#131	1	2	yes	—
51	C₄×C₇₃	—	4	2	no	—
52	C₄×C₇₃	#124	1	2	yes	—
53	C₄×C₇₃	#125	1	2	yes	—
54	Dic₇₃	—	2	4	no	—
55	Dic₇₃	—	4	1	no	—
56	Dic₇₃	—	4	1	no	—
57	C₂×C₇₃	#382	1	1	yes	characteristic
58	C₂×C₇₃	#424	1	2	yes	—
59	C₂×C₇₃	#433	1	2	yes	—
60	C₂×C₇₃	#433	1	1	yes	characteristic
61	C₂×C₇₃	#433	1	1	yes	characteristic
62	#1832	—	73	1	no	maximal, Sylow
63	C₇₃	#1832	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₄⋊C₈	—	73	2	no	—
65	#376	—	73	1	no	—
66	#336	—	73	2	no	—
67	#336	—	73	1	no	—
68	#336	D₇₃	1	1	yes	characteristic
69	C₂²×C₈	—	73	2	no	—
70	C₂²×C₈	C₂×D₇₃	1	2	yes	—
71	C₂×C₄²	—	73	1	no	—
72	C₂×C₄²	—	73	1	no	—
73	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
74	C₄⋊C₈	—	146	4	no	—
75	#95	—	73	2	no	—
76	#95	—	73	2	no	—
77	C₂²×C₄	—	73	2	no	—
78	C₂²×C₄	—	73	1	no	—
79	C₂²×C₄	—	73	1	no	—
80	C₂²×C₄	C₄×D₇₃	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	—	2	2	no	—
85	C₂×C₈	—	146	2	no	—
86	C₂×C₈	—	146	2	no	—
87	C₂×C₈	—	146	2	no	—
88	C₄²	—	2	2	no	—
89	C₄²	—	73	2	no	—
90	C₄²	—	73	2	no	—
91	C₄²	—	146	2	no	—
92	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	73	4	no	—
97	C₂×C₄	—	146	1	no	—
98	C₂×C₄	—	146	1	no	—
99	C₂×C₄	—	146	2	no	—
100	C₂×C₄	—	146	2	no	—
101	C₂×C₄	—	146	2	no	—
102	C₂×C₄	—	146	2	no	—
103	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
104	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
105	C₂×C₄	#11924027	1	2	yes	—
106	C₂×C₄	#11924028	1	2	yes	—
107	C₈	—	4	2	no	—
108	C₈	—	292	2	no	—
109	C₂²	C₄⋊C₄×D₇₃	1	1	yes	characteristic
110	C₂²	#14556547	1	1	yes	characteristic
111	C₂²	#14556548	1	1	yes	characteristic
112	C₂²	#14556597	1	2	yes	—
113	C₂²	#14556599	1	2	yes	—
114	C₄	—	4	2	no	—
115	C₄	—	292	1	no	—
116	C₄	—	292	1	no	—
117	C₄	—	146	4	no	—
118	C₄	#14556577	1	2	yes	—
119	C₄	#14556581	1	2	yes	—
120	C₂	#17988451	1	1	yes	characteristic
121	C₂	#17988612	1	2	yes	—
122	C₂	#17988645	1	2	yes	—
123	C₂	#17988646	1	1	yes	characteristic
124	C₂	#17988649	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556520

C₂

yes

maximal

#17988433

C₂

yes

maximal, characteristic

#17988342

C₂

yes

maximal, characteristic

#17988341

C₂

yes

maximal

#336×C₇₃

C₂

yes

maximal, characteristic

C₂²×#10596831

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556520

—

#14556498

C₄

yes

—

#14556498

C₄

yes

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

Q₈

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₂²×C₇₃

#131

yes

—

C₄×C₇₃

—

C₄×C₇₃

#124

yes

—

C₄×C₇₃

#125

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#382

yes

characteristic

C₂×C₇₃

#424

yes

—

C₂×C₇₃

#433

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

—

—

—

D₇₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

146

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₂³

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

100

C₂×C₄

—

146

—

101

C₂×C₄

—

146

—

102

C₂×C₄

—

146

—

103

C₂×C₄

D₄×D₇₃

yes

characteristic

104

C₂×C₄

Q₈×D₇₃

yes

characteristic

105

C₂×C₄

#11924027

yes

—

106

C₂×C₄

#11924028

yes

—

107

C₈

—

108

C₈

—

292

—

109

C₂²

C₄⋊C₄×D₇₃

yes

characteristic

110

C₂²

#14556547

yes

characteristic

111

C₂²

#14556548

yes

characteristic

112

C₂²

#14556597

yes

—

113

C₂²

#14556599

yes

—

114

C₄

—

115

C₄

—

292

—

116

C₄

—

292

—

117

C₄

—

146

—

118

C₄

#14556577

yes

—

119

C₄

#14556581

yes

—

120

C₂

#17988451

yes

characteristic

121

C₂

#17988612

yes

—

122

C₂

#17988645

yes

—

123

C₂

#17988646

yes

characteristic

124

C₂

#17988649

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₃
commutator, socle	C₂³×C₇₃	C₂²×C₄
Fitting	#336×C₇₃	C₂
hypercenter	#336	D₇₃
hypocenter	C₇₃	#1832
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₇₃

commutator, socle

C₂³×C₇₃

C₂²×C₄

Fitting

#336×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
63. C₇₃	#1832	semidirect

H ≅ G/N

type

63. C₇₃

#1832

semidirect

Subgroups — #22610049

Conjugacy classes of subgroups

Complements