Group #33006471 — subgroups

Subgroups — #33006471

Order 18688.

206 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 123 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	C₂²×#14556497	C₂	1	1	yes	maximal, characteristic
2	#22611527	C₂	1	1	yes	maximal, characteristic
3	#22608126	C₂	1	4	yes	maximal, complemented
4	C₂×M₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556531	C₄	1	1	yes	characteristic
6	#17988542	C₄	1	1	yes	characteristic
7	C₂×#14556497	—	2	2	no	—
8	C₂×#14556497	C₂²	1	2	yes	—
9	#17988362	C₄	1	2	yes	—
10	C₁₆×Dic₇₃	C₂²	1	2	yes	—
11	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
12	M₆₄×C₇₃	—	2	2	no	—
13	C₂×C₃₂×C₇₃	C₂²	1	2	yes	—
14	C₂×#11924012	C₈	1	1	yes	characteristic
15	#14556550	C₈	1	1	yes	characteristic
16	#14556531	—	2	2	no	—
17	C₂×#11924003	C₂×C₄	1	2	yes	—
18	#14556501	C₈	1	2	yes	—
19	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
20	#14556497	—	2	2	no	—
21	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
24	C₂×C₁₆×C₇₃	Q₈	1	2	yes	—
25	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
26	C₃₂×C₇₃	—	2	2	no	—
27	#11924012	—	2	2	no	—
28	C₂×#10596831	C₂×C₈	1	2	yes	—
29	C₄⋊Dic₇₃	C₁₆	1	2	yes	—
30	C₂²⋊Dic₇₃	C₁₆	1	2	yes	—
31	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
32	#11924003	—	2	2	no	—
33	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₇₃	M₁₆	1	2	yes	—
37	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₁₆×C₇₃	C₄⋊C₄	1	2	yes	—
39	C₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₁₆×C₇₃	C₂×Q₈	1	1	yes	characteristic
41	C₂³×C₇₃	C₂×C₁₆	1	1	yes	characteristic
42	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
43	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
44	C₂×C₄×C₇₃	M₃₂	1	2	yes	—
45	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
46	C₂×Dic₇₃	C₂×C₁₆	1	4	yes	—
47	C₈×C₇₃	C₄⋊C₈	1	2	yes	—
48	C₈×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₈×C₇₃	C₂×M₁₆	1	1	yes	characteristic
50	#10596831	—	2	2	no	—
51	C₂²×C₇₃	—	2	2	no	—
52	C₂²×C₇₃	C₄⋊C₁₆	1	2	yes	—
53	C₂²×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
54	C₄×C₇₃	C₄⋊C₁₆	1	2	yes	—
55	C₄×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
56	C₄×C₇₃	C₂×M₃₂	1	1	yes	characteristic
57	Dic₇₃	—	2	4	no	—
58	#13628	—	73	1	no	maximal, Sylow
59	C₂×C₇₃	—	2	2	no	—
60	C₂×C₇₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
61	C₂×C₇₃	#2258	1	2	yes	—
62	C₂×M₆₄	D₇₃	1	1	yes	characteristic
63	C₂²×C₃₂	—	73	1	no	—
64	#2108	—	73	1	no	—
65	C₄⋊C₃₂	—	73	4	no	—
66	C₇₃	#13628	1	1	yes	characteristic, complemented, Sylow
67	C₂×M₃₂	—	73	1	no	—
68	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
69	#405	—	73	1	no	—
70	M₆₄	—	2	2	no	—
71	C₂×C₃₂	—	73	2	no	—
72	C₂×C₃₂	—	146	2	no	—
73	C₂×C₃₂	C₂×D₇₃	1	2	yes	—
74	#346	—	73	2	no	—
75	C₄×C₁₆	—	73	2	no	—
76	C₂×M₁₆	—	73	1	no	—
77	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
78	#117	—	73	1	no	—
79	M₃₂	—	146	2	no	—
80	C₂×C₁₆	—	73	2	no	—
81	C₂×C₁₆	Dic₁₄₆	1	2	yes	—
82	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
83	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
84	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
85	#97	—	73	2	no	—
86	C₄×C₈	—	73	2	no	—
87	C₃₂	—	2	2	no	—
88	C₃₂	—	146	2	no	—
89	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
90	M₁₆	—	146	2	no	—
91	C₂×C₈	—	73	2	no	—
92	C₂×C₈	#11924007	1	2	yes	—
93	C₂×C₈	C₈×D₇₃	1	1	yes	characteristic
94	C₂×C₈	#11924011	1	2	yes	—
95	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
96	C₄⋊C₄	—	73	2	no	—
97	C₂²⋊C₄	—	73	2	no	—
98	C₄²	—	73	2	no	—
99	C₁₆	—	146	2	no	—
100	C₁₆	#11924007	1	2	yes	—
101	C₁₆	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
102	C₁₆	C₂×Dic₁₄₆	1	1	yes	characteristic
103	C₂³	C₁₆×D₇₃	1	1	yes	characteristic
104	C₂×C₄	—	73	4	no	—
105	C₂×C₄	#14556520	1	2	yes	—
106	C₂×C₄	C₁₆×D₇₃	1	1	yes	characteristic
107	C₂×C₄	#14556530	1	2	yes	—
108	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
109	C₈	—	146	2	no	—
110	C₈	#14556520	1	2	yes	—
111	C₈	C₂×#11924007	1	1	yes	characteristic
112	C₈	C₂×#11924011	1	1	yes	characteristic
113	C₂²	—	2	2	no	—
114	C₂²	#17988405	1	2	yes	—
115	C₂²	C₂×C₁₆×D₇₃	1	1	yes	characteristic
116	C₄	—	146	4	no	—
117	C₄	#17988405	1	2	yes	—
118	C₄	C₂×#14556520	1	1	yes	characteristic
119	C₄	C₂×#14556530	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₂×#17988405	1	1	yes	characteristic
122	C₂	#22612226	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14556497

C₂

yes

maximal, characteristic

#22611527

C₂

yes

maximal, characteristic

#22608126

C₂

yes

maximal, complemented

C₂×M₆₄×C₇₃

C₂

yes

maximal, characteristic

C₂×#14556531

C₄

yes

characteristic

#17988542

C₄

yes

characteristic

C₂×#14556497

—

C₂×#14556497

C₂²

yes

—

#17988362

C₄

yes

—

C₁₆×Dic₇₃

C₂²

yes

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

M₆₄×C₇₃

—

C₂×C₃₂×C₇₃

C₂²

yes

—

C₂×#11924012

C₈

yes

characteristic

#14556550

C₈

yes

characteristic

#14556531

—

C₂×#11924003

C₂×C₄

yes

—

#14556501

C₈

yes

—

C₈×Dic₇₃

C₂×C₄

yes

—

#14556497

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

Q₈

yes

—

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

C₃₂×C₇₃

—

#11924012

—

C₂×#10596831

C₂×C₈

yes

—

C₄⋊Dic₇₃

C₁₆

yes

—

C₂²⋊Dic₇₃

C₁₆

yes

—

C₄×Dic₇₃

C₂×C₈

yes

—

#11924003

—

C₂²×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

C₂×C₈

yes

characteristic

C₂×C₈×C₇₃

M₁₆

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₁₆×C₇₃

C₄⋊C₄

yes

—

C₁₆×C₇₃

C₂×D₄

yes

characteristic

C₁₆×C₇₃

C₂×Q₈

yes

characteristic

C₂³×C₇₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₈

yes

—

C₂×C₄×C₇₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₃

M₃₂

yes

—

C₂×C₄×C₇₃

C₂²×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₁₆

yes

—

C₈×C₇₃

C₄⋊C₈

yes

—

C₈×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₂×M₁₆

yes

characteristic

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄⋊C₁₆

yes

—

C₂²×C₇₃

C₂²×C₁₆

yes

characteristic

C₄×C₇₃

C₄⋊C₁₆

yes

—

C₄×C₇₃

C₂×C₄⋊C₈

yes

characteristic

C₄×C₇₃

C₂×M₃₂

yes

characteristic

Dic₇₃

—

#13628

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₇₃

#2258

yes

—

C₂×M₆₄

D₇₃

yes

characteristic

C₂²×C₃₂

—

#2108

—

C₄⋊C₃₂

—

C₇₃

#13628

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

#405

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

—

146

—

C₂×C₃₂

C₂×D₇₃

yes

—

#346

—

C₄×C₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₄×D₇₃

yes

characteristic

#117

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

Dic₁₄₆

yes

—

C₂×C₁₆

C₄×D₇₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₃

yes

—

C₂×C₁₆

C₂²×D₇₃

yes

characteristic

#97

—

C₄×C₈

—

C₃₂

—

C₃₂

—

146

—

C₂²×C₄

C₈×D₇₃

yes

characteristic

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

#11924007

yes

—

C₂×C₈

C₈×D₇₃

yes

characteristic

C₂×C₈

#11924011

yes

—

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

146

—

100

C₁₆

#11924007

yes

—

101

C₁₆

C₂×C₂²⋊D₇₃

yes

characteristic

102

C₁₆

C₂×Dic₁₄₆

yes

characteristic

103

C₂³

C₁₆×D₇₃

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

#14556520

yes

—

106

C₂×C₄

C₁₆×D₇₃

yes

characteristic

107

C₂×C₄

#14556530

yes

—

108

C₂×C₄

C₂×C₈×D₇₃

yes

characteristic

109

C₈

—

146

—

110

C₈

#14556520

yes

—

111

C₈

C₂×#11924007

yes

characteristic

112

C₈

C₂×#11924011

yes

characteristic

113

C₂²

—

114

C₂²

#17988405

yes

—

115

C₂²

C₂×C₁₆×D₇₃

yes

characteristic

116

C₄

—

146

—

117

C₄

#17988405

yes

—

118

C₄

C₂×#14556520

yes

characteristic

119

C₄

C₂×#14556530

yes

characteristic

120

C₂

—

121

C₂

C₂×#17988405

yes

characteristic

122

C₂

#22612226

yes

—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₇₃
commutator, socle	C₂²×C₇₃	C₂²×C₁₆
Fitting	C₂×M₆₄×C₇₃	C₂
prime radical	C₂³×C₇₃	C₂×C₁₆
cosocle	C₂×C₁₆×C₇₃	C₂³
hypercenter	C₂×M₆₄	D₇₃
hypocenter	C₇₃	#13628
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×M₆₄

subgroup

G/H

center, Frattini

C₂×C₁₆

C₂²×D₇₃

commutator, socle

C₂²×C₇₃

C₂²×C₁₆

Fitting

C₂×M₆₄×C₇₃

C₂

prime radical

C₂³×C₇₃

C₂×C₁₆

cosocle

C₂×C₁₆×C₇₃

C₂³

hypercenter

C₂×M₆₄

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₁₆ ◁ C₂×M₆₄

N	H ≅ G/N	type
3. #22608126	C₂	semidirect
66. C₇₃	#13628	semidirect

H ≅ G/N

type

3. #22608126

C₂

semidirect

66. C₇₃

#13628

semidirect

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

subgroup	index
C₂²×#14556497	2
#22611527	2
#22608126	2
C₂×M₆₄×C₇₃	2
#13628	73

subgroup

index

C₂×M₆₄×C₇₃

Subgroups — #33006471

Conjugacy classes of subgroups

Complements

Maximal subgroups