Group #33000697 — subgroups

Subgroups — #33000697

Order 18688.

310 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 95 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	#22612184	C₂	1	1	yes	maximal, characteristic
2	#22612183	C₂	1	2	yes	maximal
3	#22609547	C₂	1	2	yes	maximal
4	C₁₆×#10596831	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2247	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₈₄	—	2	2	no	—
7	C₂×#14556537	—	2	4	no	—
8	#17988990	—	2	4	no	—
9	#17988967	C₂²	1	2	yes	—
10	C₄×#11924003	C₂²	1	1	yes	characteristic
11	C₈×#10596831	C₂²	1	1	yes	characteristic
12	C₂×Q₃₂×C₇₃	—	2	2	no	—
13	#494×C₇₃	C₂²	1	2	yes	—
14	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₂₉₂	—	2	2	no	—
16	C₂×Dic₂₉₂	—	2	2	no	—
17	#14556591	—	2	2	no	—
18	Dic₅₈₄	—	4	4	no	—
19	#14556537	—	4	8	no	—
20	C₂×#11924003	D₄	1	2	yes	—
21	#14556524	—	4	8	no	—
22	C₄×#10596831	D₄	1	2	yes	—
23	C₂×Q₁₆×C₇₃	—	2	2	no	—
24	C₂×Q₁₆×C₇₃	—	2	2	no	—
25	C₄⋊Q₈×C₇₃	—	2	2	no	—
26	Q₃₂×C₇₃	—	4	4	no	—
27	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
28	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
29	C₂×Dic₁₄₆	—	4	2	no	—
30	Dic₂₉₂	—	4	4	no	—
31	Dic₂₉₂	—	4	4	no	—
32	C₂×#10596831	D₈	1	4	yes	—
33	C₄⋊Dic₇₃	—	4	4	no	—
34	#11924003	D₈	1	4	yes	—
35	C₂×Q₈×C₇₃	—	4	2	no	—
36	Q₁₆×C₇₃	—	4	4	no	—
37	Q₁₆×C₇₃	—	4	4	no	—
38	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₄⋊C₄×C₇₃	—	4	4	no	—
41	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
42	C₁₆×C₇₃	D₈	1	4	yes	—
43	Q₈×C₇₃	—	8	2	no	—
44	Q₈×C₇₃	—	8	2	no	—
45	C₂×C₄×C₇₃	—	8	2	no	—
46	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
47	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
48	C₂×Dic₇₃	—	8	2	no	—
49	Dic₁₄₆	—	8	2	no	—
50	Dic₁₄₆	—	8	2	no	—
51	C₈×C₇₃	C₂×D₈	1	2	yes	—
52	C₈×C₇₃	C₂×D₈	1	2	yes	—
53	#10596831	Q₃₂	1	8	yes	complemented
54	C₂²×C₇₃	#493	1	1	yes	characteristic
55	C₄×C₇₃	—	16	2	no	—
56	C₄×C₇₃	#493	1	1	yes	characteristic
57	C₄×C₇₃	#493	1	1	yes	characteristic
58	C₄×C₇₃	C₂×Q₃₂	1	4	yes	—
59	Dic₇₃	—	16	2	no	—
60	#12516	—	73	1	no	maximal, Sylow
61	C₂×C₇₃	#1712	1	1	yes	characteristic
62	C₂×C₇₃	#2247	1	2	yes	—
63	#2247	—	73	2	no	—
64	#2247	—	73	1	no	—
65	#2247	D₇₃	1	1	yes	characteristic
66	#1713	—	73	2	no	—
67	C₈×C₁₆	—	73	1	no	—
68	C₇₃	#12516	1	1	yes	characteristic, complemented, Sylow
69	C₂×Q₃₂	—	2	2	no	—
70	C₂×Q₃₂	—	146	4	no	—
71	C₂×Q₃₂	—	146	2	no	—
72	#500	—	146	4	no	—
73	#494	—	73	2	no	—
74	#494	C₂×D₇₃	1	2	yes	—
75	C₄×C₁₆	—	73	1	no	—
76	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
77	C₈²	—	73	1	no	—
78	C₂×Q₁₆	—	2	2	no	—
79	C₂×Q₁₆	—	2	2	no	—
80	C₂×Q₁₆	—	146	2	no	—
81	C₂×Q₁₆	—	146	2	no	—
82	C₄⋊Q₈	—	2	2	no	—
83	C₄⋊Q₈	—	146	2	no	—
84	Q₃₂	—	4	4	no	—
85	Q₃₂	—	292	8	no	—
86	Q₃₂	—	292	4	no	—
87	C₂×C₁₆	—	73	2	no	—
88	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
89	#107	—	292	8	no	—
90	C₄×C₈	—	73	2	no	—
91	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
92	C₂×Q₈	—	4	2	no	—
93	C₂×Q₈	—	292	2	no	—
94	Q₁₆	—	4	4	no	—
95	Q₁₆	—	4	4	no	—
96	Q₁₆	—	292	4	no	—
97	Q₁₆	—	292	4	no	—
98	C₂×C₈	—	73	4	no	—
99	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
100	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
101	C₄⋊C₄	—	4	4	no	—
102	C₄⋊C₄	—	292	4	no	—
103	C₄²	D₄×D₇₃	1	1	yes	characteristic
104	C₁₆	—	73	4	no	—
105	C₁₆	#11924013	1	4	yes	—
106	Q₈	—	8	2	no	—
107	Q₈	—	8	2	no	—
108	Q₈	—	584	2	no	—
109	Q₈	—	584	2	no	—
110	C₂×C₄	—	8	2	no	—
111	C₂×C₄	—	584	2	no	—
112	C₂×C₄	#14556587	1	1	yes	characteristic
113	C₂×C₄	D₈×D₇₃	1	2	yes	—
114	C₈	—	73	8	no	—
115	C₈	D₈×D₇₃	1	2	yes	—
116	C₈	C₂×#11924013	1	2	yes	—
117	C₂²	#17988962	1	1	yes	characteristic
118	C₄	—	16	2	no	—
119	C₄	—	1168	2	no	—
120	C₄	#17988962	1	1	yes	characteristic
121	C₄	#17988963	1	1	yes	characteristic
122	C₄	Q₃₂×D₇₃	1	4	yes	—
123	C₂	#22609545	1	1	yes	characteristic
124	C₂	#22612182	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22612184

C₂

yes

maximal, characteristic

#22612183

C₂

yes

maximal

#22609547

C₂

yes

maximal

C₁₆×#10596831

C₂

yes

maximal, characteristic

C₇₃×#2247

C₂

yes

maximal, characteristic

C₂×Dic₅₈₄

—

C₂×#14556537

—

#17988990

—

#17988967

C₂²

yes

—

C₄×#11924003

C₂²

yes

characteristic

C₈×#10596831

C₂²

yes

characteristic

C₂×Q₃₂×C₇₃

—

#494×C₇₃

C₂²

yes

—

C₄×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

#14556591

—

Dic₅₈₄

—

#14556537

—

C₂×#11924003

D₄

yes

—

#14556524

—

C₄×#10596831

D₄

yes

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₄⋊Q₈×C₇₃

—

Q₃₂×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

C₂³

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

C₂×#10596831

D₈

yes

—

C₄⋊Dic₇₃

—

#11924003

D₈

yes

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₁₆×C₇₃

D₈

yes

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#127

yes

characteristic

C₂×C₄×C₇₃

C₂×D₈

yes

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×D₈

yes

—

C₈×C₇₃

C₂×D₈

yes

—

#10596831

Q₃₂

yes

complemented

C₂²×C₇₃

#493

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

C₂×Q₃₂

yes

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

#2247

—

#2247

—

#2247

D₇₃

yes

characteristic

#1713

—

C₈×C₁₆

—

C₇₃

#12516

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×Q₃₂

—

146

—

C₂×Q₃₂

—

146

—

#500

—

146

—

#494

—

#494

C₂×D₇₃

yes

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₇₃

yes

characteristic

C₈²

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

—

146

—

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

Q₃₂

—

Q₃₂

—

292

—

Q₃₂

—

292

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₇₃

yes

—

#107

—

292

—

C₄×C₈

—

C₄×C₈

C₂²×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

292

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

292

—

Q₁₆

—

292

—

C₂×C₈

—

C₂×C₈

D₄×D₇₃

yes

characteristic

100

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

292

—

103

C₄²

D₄×D₇₃

yes

characteristic

104

C₁₆

—

105

C₁₆

#11924013

yes

—

106

Q₈

—

107

Q₈

—

108

Q₈

—

584

—

109

Q₈

—

584

—

110

C₂×C₄

—

111

C₂×C₄

—

584

—

112

C₂×C₄

#14556587

yes

characteristic

113

C₂×C₄

D₈×D₇₃

yes

—

114

C₈

—

115

C₈

D₈×D₇₃

yes

—

116

C₈

C₂×#11924013

yes

—

117

C₂²

#17988962

yes

characteristic

118

C₄

—

119

C₄

—

1168

—

120

C₄

#17988962

yes

characteristic

121

C₄

#17988963

yes

characteristic

122

C₄

Q₃₂×D₇₃

yes

—

123

C₂

#22609545

yes

characteristic

124

C₂

#22612182

yes

—

	subgroup	G/H
center	C₂²	#17988962
commutator, cosocle	C₄×C₈×C₇₃	C₂³
Frattini	C₄×C₈	C₂²×D₇₃
Fitting	C₇₃×#2247	C₂
socle, prime radical	C₂²×C₇₃	#493
hypercenter	#2247	D₇₃
hypocenter	C₇₃	#12516
LCS	G ▷ C₄×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2247

subgroup

G/H

center

C₂²

#17988962

commutator, cosocle

C₄×C₈×C₇₃

C₂³

Frattini

C₄×C₈

C₂²×D₇₃

Fitting

C₇₃×#2247

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2247

N	H ≅ G/N	type
53. #10596831	Q₃₂	semidirect
68. C₇₃	#12516	semidirect

H ≅ G/N

type

53. #10596831

Q₃₂

semidirect

68. C₇₃

#12516

semidirect

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

subgroup	index
#22612184	2
#22612183	2
#22609547	2
C₁₆×#10596831	2
C₇₃×#2247	2
#12516	73

subgroup

index

#22612184

#22612183

#22609547

C₁₆×#10596831

C₇₃×#2247

#12516

Subgroups — #33000697

Conjugacy classes of subgroups

Complements

Maximal subgroups