Group #33002334 — subgroups

Subgroups — #33002334

Order 18688.

322 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 171 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×C₄⋊#11924003	C₂	1	2	yes	maximal
2	#22608009	C₂	1	4	yes	maximal
3	C₇₃×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11924003	C₂²	1	4	yes	—
5	C₄⋊#11924003	—	2	4	no	—
6	C₂×#97×C₇₃	C₄	1	2	yes	—
7	C₂×#97×C₇₃	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
10	#376×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#11924003	—	2	4	no	—
12	C₂×#11924003	—	2	8	no	—
13	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
15	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
18	#97×C₇₃	—	2	4	no	—
19	#97×C₇₃	—	2	2	no	—
20	C₄×C₈×C₇₃	—	2	4	no	—
21	C₄×C₈×C₇₃	D₄	1	2	yes	—
22	C₄×C₈×C₇₃	Q₈	1	2	yes	—
23	#95×C₇₃	C₈	1	4	yes	—
24	#11924003	—	4	4	no	—
25	C₂²×C₄×C₇₃	C₂×C₈	1	4	yes	—
26	C₂²×C₄×C₇₃	C₂×C₈	1	2	yes	—
27	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	—	2	2	no	—
30	C₂×C₈×C₇₃	—	2	2	no	—
31	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₇₃	M₁₆	1	4	yes	—
33	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈×C₇₃	#41	1	4	yes	—
36	C₄²×C₇₃	—	2	2	no	—
37	C₄²×C₇₃	—	2	2	no	—
38	C₄²×C₇₃	C₄⋊C₄	1	2	yes	—
39	C₄²×C₇₃	M₁₆	1	2	yes	—
40	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
41	C₂×C₄×C₇₃	—	2	4	no	—
42	C₂×C₄×C₇₃	—	2	4	no	—
43	C₂×C₄×C₇₃	—	2	8	no	—
44	C₂×C₄×C₇₃	C₄⋊C₈	1	4	yes	—
45	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	#117	1	2	yes	—
47	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
48	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
49	C₈×C₇₃	—	2	2	no	—
50	C₈×C₇₃	—	2	4	no	—
51	C₈×C₇₃	#124	1	2	yes	—
52	C₈×C₇₃	#125	1	2	yes	—
53	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
54	C₂²×C₇₃	#431	1	2	yes	—
55	C₂²×C₇₃	#504	1	4	yes	—
56	C₄×C₇₃	—	2	4	no	—
57	C₄×C₇₃	—	4	4	no	—
58	C₄×C₇₃	#382	1	1	yes	characteristic
59	C₄×C₇₃	#423	1	1	yes	characteristic
60	C₄×C₇₃	#432	1	2	yes	—
61	#12880	—	73	1	no	maximal, Sylow
62	C₂×C₇₃	#1831	1	1	yes	characteristic
63	C₂×C₇₃	#2151	1	2	yes	—
64	C₂×C₇₃	#2164	1	4	yes	—
65	C₂×C₄⋊C₁₆	—	73	2	no	—
66	#1726	D₇₃	1	1	yes	characteristic
67	#1374	—	73	4	no	—
68	C₇₃	#12880	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₁₆	—	73	4	no	—
70	C₂×#97	Dic₇₃	1	2	yes	—
71	C₂×#97	Dic₇₃	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂×D₇₃	1	2	yes	—
73	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
74	#376	Dic₇₃	1	1	yes	characteristic
75	C₄⋊C₁₆	—	146	4	no	—
76	C₂²×C₈	C₂×Dic₇₃	1	1	yes	characteristic
77	C₂²×C₈	C₂×Dic₇₃	1	2	yes	—
78	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
79	C₂×C₄²	C₂×Dic₇₃	1	2	yes	—
80	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
81	C₂×C₁₆	—	146	4	no	—
82	C₂×C₁₆	—	146	8	no	—
83	#97	—	2	4	no	—
84	#97	—	2	2	no	—
85	C₄×C₈	—	2	4	no	—
86	C₄×C₈	Dic₁₄₆	1	2	yes	—
87	C₄×C₈	D₂₉₂	1	2	yes	—
88	#95	#10596831	1	4	yes	—
89	C₂²×C₄	C₂×#10596831	1	4	yes	—
90	C₂²×C₄	C₂×#10596831	1	2	yes	—
91	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	C₄⋊Dic₇₃	1	2	yes	—
96	C₂×C₈	#11924012	1	4	yes	—
97	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
98	C₂×C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
99	C₂×C₈	#11924028	1	4	yes	—
100	C₄²	—	2	2	no	—
101	C₄²	—	2	2	no	—
102	C₄²	C₄⋊Dic₇₃	1	2	yes	—
103	C₄²	#11924012	1	2	yes	—
104	C₁₆	—	292	4	no	—
105	C₂³	C₂²×#10596831	1	1	yes	characteristic
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	—	2	8	no	—
109	C₂×C₄	C₄⋊#10596831	1	4	yes	—
110	C₂×C₄	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
111	C₂×C₄	#14556550	1	2	yes	—
112	C₂×C₄	C₂×#11924012	1	2	yes	—
113	C₂×C₄	C₂×#11924012	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	2	4	no	—
116	C₈	#14556579	1	2	yes	—
117	C₈	#14556583	1	2	yes	—
118	C₂²	C₂×C₄⋊#10596831	1	1	yes	characteristic
119	C₂²	#17988640	1	2	yes	—
120	C₂²	#17989004	1	4	yes	—
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	#17988453	1	1	yes	characteristic
124	C₄	#17988611	1	1	yes	characteristic
125	C₄	#17988644	1	2	yes	—
126	C₂	#22610048	1	1	yes	characteristic
127	C₂	#22611690	1	2	yes	—
128	C₂	#22611738	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#11924003

C₂

yes

maximal

#22608009

C₂

yes

maximal

C₇₃×#1726

C₂

yes

maximal, characteristic

C₂²×#11924003

C₂²

yes

—

C₄⋊#11924003

—

C₂×#97×C₇₃

C₄

yes

—

C₂×#97×C₇₃

C₄

yes

characteristic

C₂×C₄×C₈×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#376×C₇₃

C₄

yes

characteristic

C₂×#11924003

—

C₂×#11924003

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

#97×C₇₃

—

#97×C₇₃

—

C₄×C₈×C₇₃

—

C₄×C₈×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

Q₈

yes

—

#95×C₇₃

C₈

yes

—

#11924003

—

C₂²×C₄×C₇₃

C₂×C₈

yes

—

C₂²×C₄×C₇₃

C₂×C₈

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

M₁₆

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₄⋊C₄

yes

—

C₄²×C₇₃

M₁₆

yes

—

C₂³×C₇₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₈

yes

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

#117

yes

—

C₂×C₄×C₇₃

C₂×M₁₆

yes

—

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

#124

yes

—

C₈×C₇₃

#125

yes

—

C₂²×C₇₃

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₇₃

#431

yes

—

C₂²×C₇₃

#504

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#2164

yes

—

C₂×C₄⋊C₁₆

—

#1726

D₇₃

yes

characteristic

#1374

—

C₇₃

#12880

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×#97

Dic₇₃

yes

—

C₂×#97

Dic₇₃

yes

characteristic

C₂×C₄×C₈

C₂×D₇₃

yes

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

#376

Dic₇₃

yes

characteristic

C₄⋊C₁₆

—

146

—

C₂²×C₈

C₂×Dic₇₃

yes

characteristic

C₂²×C₈

C₂×Dic₇₃

yes

—

C₂²×C₈

C₂²×D₇₃

yes

characteristic

C₂×C₄²

C₂×Dic₇₃

yes

—

C₂×C₄²

C₂×Dic₇₃

yes

characteristic

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₁₄₆

yes

—

C₄×C₈

D₂₉₂

yes

—

#95

#10596831

yes

—

C₂²×C₄

C₂×#10596831

yes

—

C₂²×C₄

C₂×#10596831

yes

—

C₂²×C₄

C₂²×Dic₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₇₃

yes

—

C₂×C₈

#11924012

yes

—

C₂×C₈

C₂×D₂₉₂

yes

characteristic

C₂×C₈

C₂×Dic₁₄₆

yes

characteristic

C₂×C₈

#11924028

yes

—

100

C₄²

—

101

C₄²

—

102

C₄²

C₄⋊Dic₇₃

yes

—

103

C₄²

#11924012

yes

—

104

C₁₆

—

292

—

105

C₂³

C₂²×#10596831

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄⋊#10596831

yes

—

110

C₂×C₄

C₂×C₄⋊Dic₇₃

yes

characteristic

111

C₂×C₄

#14556550

yes

—

112

C₂×C₄

C₂×#11924012

yes

—

113

C₂×C₄

C₂×#11924012

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

#14556579

yes

—

117

C₈

#14556583

yes

—

118

C₂²

C₂×C₄⋊#10596831

yes

characteristic

119

C₂²

#17988640

yes

—

120

C₂²

#17989004

yes

—

121

C₄

—

122

C₄

—

123

C₄

#17988453

yes

characteristic

124

C₄

#17988611

yes

characteristic

125

C₄

#17988644

yes

—

126

C₂

#22610048

yes

characteristic

127

C₂

#22611690

yes

—

128

C₂

#22611738

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₇₃
commutator, socle, prime radical	C₂³×C₇₃	C₂²×C₈
Fitting	C₇₃×#1726	C₂
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#1726	D₇₃
hypocenter	C₇₃	#12880
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₇₃

commutator, socle, prime radical

C₂³×C₇₃

C₂²×C₈

Fitting

C₇₃×#1726

C₂

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₈ ◁ #1726

N	H ≅ G/N	type
68. C₇₃	#12880	semidirect

H ≅ G/N

type

68. C₇₃

#12880

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄⋊#11924003	2
#22608009	2
C₇₃×#1726	2
#12880	73

subgroup

index

C₂×C₄⋊#11924003

#22608009

C₇₃×#1726

#12880

Subgroups — #33002334

Conjugacy classes of subgroups

Complements

Maximal subgroups