Group #32990480 — subgroups

Subgroups — #32990480

Order 18688.

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

normal subgroups only

This group has 406 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	#22610100	C₂	1	3	yes	maximal
2	#22607812	C₂	1	3	yes	maximal
3	C₇₃×#2844	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556524	—	2	3	no	—
5	C₂×#14556522	—	2	3	no	—
6	C₂×#14556502	C₂²	1	3	yes	—
7	#17988457	C₂²	1	1	yes	characteristic
8	#400×C₇₃	—	2	3	no	—
9	#395×C₇₃	—	2	3	no	—
10	#382×C₇₃	C₂²	1	3	yes	—
11	C₂²×#10596831	—	2	3	no	—
12	C₂×C₄⋊Dic₇₃	—	2	3	no	—
13	#14556524	—	4	6	no	—
14	#14556522	—	4	6	no	—
15	#14556502	—	2	3	no	—
16	#14556502	Q₈	1	6	yes	complemented
17	C₂²×Q₈×C₇₃	—	2	1	no	—
18	C₂×C₄⋊C₄×C₇₃	—	2	3	no	—
19	C₂×C₄⋊C₄×C₇₃	D₄	1	3	yes	—
20	C₂×C₄⋊C₄×C₇₃	D₄	1	3	yes	—
21	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
22	#95×C₇₃	—	2	3	no	—
23	#95×C₇₃	—	2	1	no	—
24	#95×C₇₃	—	2	6	no	—
25	C₂²×Dic₇₃	—	4	1	no	—
26	C₂×#10596831	—	2	6	no	—
27	C₂×#10596831	—	2	6	no	—
28	C₂×#10596831	—	2	6	no	—
29	C₄⋊Dic₇₃	—	4	3	no	—
30	C₄⋊Dic₇₃	—	4	3	no	—
31	C₂×Q₈×C₇₃	—	8	3	no	—
32	C₂²×C₄×C₇₃	—	2	3	no	—
33	C₂²×C₄×C₇₃	—	2	3	no	—
34	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
35	C₄⋊C₄×C₇₃	—	4	3	no	—
36	C₄⋊C₄×C₇₃	—	4	3	no	—
37	C₄⋊C₄×C₇₃	—	8	3	no	—
38	C₄²×C₇₃	C₂×Q₈	1	3	yes	—
39	C₄²×C₇₃	#41	1	1	yes	characteristic
40	C₂³×C₇₃	#120	1	1	yes	characteristic
41	Q₈×C₇₃	—	8	4	no	—
42	C₂×C₄×C₇₃	—	2	3	no	—
43	C₂×C₄×C₇₃	—	2	3	no	—
44	C₂×C₄×C₇₃	—	4	3	no	—
45	C₂×C₄×C₇₃	—	4	3	no	—
46	C₂×C₄×C₇₃	—	4	6	no	—
47	C₂×C₄×C₇₃	—	4	6	no	—
48	C₂×C₄×C₇₃	C₂²⋊Q₈	1	3	yes	—
49	C₂×C₄×C₇₃	C₄⋊Q₈	1	3	yes	—
50	C₂×Dic₇₃	—	8	3	no	—
51	#10596831	—	2	12	no	—
52	C₂²×C₇₃	#395	1	1	yes	characteristic
53	C₂²×C₇₃	#453	1	3	yes	—
54	C₂²×C₇₃	#456	1	3	yes	—
55	C₄×C₇₃	—	2	3	no	—
56	C₄×C₇₃	—	2	3	no	—
57	C₄×C₇₃	—	8	3	no	—
58	C₄×C₇₃	—	8	3	no	—
59	Dic₇₃	—	16	1	no	—
60	#10583	—	73	1	no	maximal, Sylow
61	C₂×C₇₃	#1655	1	1	yes	characteristic
62	C₂×C₇₃	#1660	1	3	yes	—
63	C₂×C₇₃	#2060	1	3	yes	—
64	#2844	D₇₃	1	1	yes	characteristic
65	#1847	—	73	3	no	—
66	#1295	—	73	3	no	—
67	C₇₃	#10583	1	1	yes	characteristic, complemented, Sylow
68	C₂×#107	—	146	3	no	—
69	C₂×#106	—	146	3	no	—
70	C₂×#97	—	73	3	no	—
71	#400	—	2	3	no	—
72	#395	—	2	3	no	—
73	#384	—	73	1	no	—
74	#382	C₂×D₇₃	1	3	yes	—
75	C₂²×Q₈	—	2	1	no	—
76	C₂²×C₈	—	146	3	no	—
77	C₂×C₄⋊C₄	—	2	3	no	—
78	C₂×C₄⋊C₄	—	146	3	no	—
79	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	3	yes	—
80	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	3	yes	—
81	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
82	#107	—	292	6	no	—
83	#106	—	292	6	no	—
84	#97	—	73	6	no	—
85	#97	—	146	3	no	—
86	#95	—	2	3	no	—
87	#95	—	2	1	no	—
88	#95	—	2	6	no	—
89	C₂×Q₈	—	8	3	no	—
90	C₂²×C₄	—	2	3	no	—
91	C₂²×C₄	—	2	3	no	—
92	C₂²×C₄	—	292	1	no	—
93	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
94	C₂×C₈	—	146	6	no	—
95	C₂×C₈	—	146	6	no	—
96	C₂×C₈	—	146	6	no	—
97	C₄⋊C₄	—	4	3	no	—
98	C₄⋊C₄	—	4	3	no	—
99	C₄⋊C₄	—	8	3	no	—
100	C₄⋊C₄	—	292	3	no	—
101	C₄⋊C₄	—	292	3	no	—
102	C₄²	Q₈×D₇₃	1	3	yes	—
103	C₄²	#11924029	1	1	yes	characteristic
104	C₂³	#14556560	1	1	yes	characteristic
105	Q₈	—	8	4	no	—
106	C₂×C₄	—	2	3	no	—
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	4	3	no	—
109	C₂×C₄	—	4	3	no	—
110	C₂×C₄	—	4	6	no	—
111	C₂×C₄	—	4	6	no	—
112	C₂×C₄	—	584	3	no	—
113	C₂×C₄	#14556567	1	3	yes	—
114	C₂×C₄	#14556589	1	3	yes	—
115	C₈	—	146	12	no	—
116	C₂²	#17988506	1	1	yes	characteristic
117	C₂²	#17988755	1	3	yes	—
118	C₂²	#17988770	1	3	yes	—
119	C₄	—	2	3	no	—
120	C₄	—	2	3	no	—
121	C₄	—	8	3	no	—
122	C₄	—	8	3	no	—
123	C₄	—	1168	1	no	—
124	C₂	#22609220	1	1	yes	characteristic
125	C₂	#22609242	1	3	yes	—
126	C₂	#22611273	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22610100

C₂

yes

maximal

#22607812

C₂

yes

maximal

C₇₃×#2844

C₂

yes

maximal, characteristic

C₂×#14556524

—

C₂×#14556522

—

C₂×#14556502

C₂²

yes

—

#17988457

C₂²

yes

characteristic

#400×C₇₃

—

#395×C₇₃

—

#382×C₇₃

C₂²

yes

—

C₂²×#10596831

—

C₂×C₄⋊Dic₇₃

—

—

—

—

Q₈

yes

complemented

C₂²×Q₈×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#95×C₇₃

—

#95×C₇₃

—

#95×C₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×Q₈

yes

—

C₄²×C₇₃

yes

C₂³×C₇₃

yes

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₃

C₄⋊Q₈

yes

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

#395

yes

characteristic

C₂²×C₇₃

#453

yes

—

C₂²×C₇₃

#456

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#2060

yes

—

#2844

D₇₃

yes

characteristic

#1847

—

#1295

—

C₇₃

#10583

yes

characteristic, complemented, Sylow

C₂×#107

—

146

—

C₂×#106

—

146

—

C₂×#97

—

—

—

—

C₂×D₇₃

yes

—

C₂²×Q₈

—

C₂²×C₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

#107

—

292

—

#106

—

292

—

#97

—

#97

—

146

—

#95

—

#95

—

#95

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

292

—

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

292

—

101

C₄⋊C₄

—

292

—

102

C₄²

Q₈×D₇₃

yes

—

103

C₄²

#11924029

yes

characteristic

104

C₂³

#14556560

yes

characteristic

105

Q₈

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

584

—

113

C₂×C₄

#14556567

yes

—

114

C₂×C₄

#14556589

yes

—

115

C₈

—

146

—

116

C₂²

#17988506

yes

characteristic

117

C₂²

#17988755

yes

—

118

C₂²

#17988770

yes

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

1168

—

124

C₂

#22609220

yes

characteristic

125

C₂

#22609242

yes

—

126

C₂

#22611273

yes

—

	subgroup	G/H
center	C₂³	#14556560
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#2844	C₂
socle, prime radical	C₂³×C₇₃	#120
hypercenter	#2844	D₇₃
hypocenter	C₇₃	#10583
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2844

subgroup

G/H

center

C₂³

#14556560

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#2844

C₂

C₂³×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2844

N	H ≅ G/N	type
16. #14556502	Q₈	semidirect
67. C₇₃	#10583	semidirect

H ≅ G/N

type

16. #14556502

Q₈

semidirect

67. C₇₃

#10583

semidirect

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

subgroup	index
#22610100	2
#22607812	2
C₇₃×#2844	2
#10583	73

subgroup

index

#22610100

#22607812

C₇₃×#2844

#10583

Subgroups — #32990480

Conjugacy classes of subgroups

Complements

Maximal subgroups