Group #33086237 — subgroups

Subgroups — #33086237

Order 18688.

830 conjugacy classes of subgroups; only the 331 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 331 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	#22610076	C₂	1	8	yes	maximal, complemented
2	#22609625	C₂	1	6	yes	maximal
3	C₂×#376×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11924012	C₂²	1	4	yes	—
5	#17988342	C₂²	1	24	yes	—
6	C₂²×C₄²×C₇₃	C₂²	1	3	yes	—
7	#376×C₇₃	C₄	1	4	yes	—
8	#376×C₇₃	C₂²	1	4	yes	—
9	C₂×#95×C₇₃	C₄	1	4	yes	—
10	C₂×#11924012	—	2	24	no	—
11	C₂²×#10596831	C₂³	1	8	yes	—
12	C₂³×C₄×C₇₃	C₂×C₄	1	6	yes	—
13	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
14	C₂×C₄²×C₇₃	—	2	12	no	—
15	C₂×C₄²×C₇₃	C₂×C₄	1	6	yes	—
16	C₂×C₄²×C₇₃	C₂³	1	6	yes	—
17	#95×C₇₃	C₂×C₄	1	16	yes	—
18	#11924012	—	4	16	no	—
19	C₂×#10596831	—	2	24	no	—
20	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	—	2	12	no	—
22	C₂²×C₄×C₇₃	—	4	12	no	—
23	C₂²×C₄×C₇₃	C₂²×C₄	1	12	yes	—
24	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₇₃	#41	1	12	yes	—
26	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
27	C₄²×C₇₃	—	2	12	no	—
28	C₄²×C₇₃	—	2	12	no	—
29	C₂³×C₇₃	—	2	4	no	—
30	C₂³×C₇₃	#117	1	6	yes	—
31	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	—	2	12	no	—
33	C₂×C₄×C₇₃	—	2	24	no	—
34	C₂×C₄×C₇₃	—	4	24	no	—
35	C₂×C₄×C₇₃	#117	1	6	yes	—
36	C₂×C₄×C₇₃	#126	1	16	yes	—
37	C₂×C₄×C₇₃	C₂×#41	1	6	yes	—
38	#10596831	—	4	8	no	—
39	C₂²×C₇₃	—	2	12	no	—
40	C₂²×C₇₃	#383	1	4	yes	—
41	C₂²×C₇₃	C₂×#117	1	3	yes	—
42	C₂²×C₇₃	#568	1	4	yes	—
43	C₄×C₇₃	—	4	12	no	—
44	C₄×C₇₃	#383	1	4	yes	—
45	C₄×C₇₃	C₂×#126	1	4	yes	—
46	#20773	—	73	1	no	maximal, Sylow
47	C₂×C₇₃	—	2	4	no	—
48	C₂×C₇₃	C₂×#383	1	1	yes	characteristic
49	C₂×C₇₃	#2921	1	6	yes	—
50	C₂×#376	D₇₃	1	1	yes	characteristic
51	#1840	—	73	8	no	—
52	#1728	—	73	6	no	—
53	C₇₃	#20773	1	1	yes	characteristic, complemented, Sylow
54	C₂²×M₁₆	—	73	4	no	—
55	C₂²×C₄²	C₂×D₇₃	1	3	yes	—
56	#376	Dic₇₃	1	4	yes	—
57	#376	C₂×D₇₃	1	4	yes	—
58	C₂×#95	Dic₇₃	1	4	yes	—
59	#336	—	73	24	no	—
60	C₂³×C₄	C₂×Dic₇₃	1	6	yes	—
61	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
62	C₂×M₁₆	—	146	24	no	—
63	C₂²×C₈	—	73	8	no	—
64	C₂×C₄²	—	2	12	no	—
65	C₂×C₄²	C₂×Dic₇₃	1	6	yes	—
66	C₂×C₄²	C₂²×D₇₃	1	6	yes	—
67	#95	C₂×Dic₇₃	1	16	yes	—
68	C₂⁴	C₂²×Dic₇₃	1	1	yes	characteristic
69	C₂²×C₄	—	2	12	no	—
70	C₂²×C₄	—	4	12	no	—
71	C₂²×C₄	C₂²×Dic₇₃	1	12	yes	—
72	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
73	C₂²×C₄	#11924028	1	12	yes	—
74	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
75	M₁₆	—	292	16	no	—
76	C₂×C₈	—	146	24	no	—
77	C₄²	—	2	12	no	—
78	C₄²	—	2	12	no	—
79	C₂³	—	2	4	no	—
80	C₂³	#14556550	1	6	yes	—
81	C₂³	C₂³×Dic₇₃	1	1	yes	characteristic
82	C₂×C₄	—	2	12	no	—
83	C₂×C₄	—	2	24	no	—
84	C₂×C₄	—	4	24	no	—
85	C₂×C₄	#14556550	1	6	yes	—
86	C₂×C₄	#14556585	1	16	yes	—
87	C₂×C₄	C₂×#11924028	1	6	yes	—
88	C₈	—	292	8	no	—
89	C₂²	—	2	12	no	—
90	C₂²	#17988455	1	4	yes	—
91	C₂²	C₂×#14556550	1	3	yes	—
92	C₂²	#17989354	1	4	yes	—
93	C₄	—	4	12	no	—
94	C₄	#17988455	1	4	yes	—
95	C₄	C₂×#14556585	1	4	yes	—
96	C₂	—	2	4	no	—
97	C₂	C₂×#17988455	1	1	yes	characteristic
98	C₂	#22618569	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22610076

C₂

yes

maximal, complemented

#22609625

C₂

yes

maximal

C₂×#376×C₇₃

C₂

yes

maximal, characteristic

C₂²×#11924012

C₂²

yes

—

#17988342

C₂²

yes

—

C₂²×C₄²×C₇₃

C₂²

yes

—

#376×C₇₃

C₄

yes

—

#376×C₇₃

C₂²

yes

—

C₂×#95×C₇₃

C₄

yes

—

C₂×#11924012

—

C₂²×#10596831

C₂³

yes

—

C₂³×C₄×C₇₃

C₂×C₄

yes

—

C₂³×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

—

#95×C₇₃

C₂×C₄

yes

—

#11924012

—

C₂×#10596831

—

C₂⁴×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

—

C₂²×C₄×C₇₃

C₂⁴

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#117

yes

—

C₂³×C₇₃

C₂³×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#117

yes

—

C₂×C₄×C₇₃

#126

yes

—

C₂×C₄×C₇₃

C₂×#41

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#383

yes

—

C₂²×C₇₃

C₂×#117

yes

—

C₂²×C₇₃

#568

yes

—

C₄×C₇₃

—

C₄×C₇₃

#383

yes

—

C₄×C₇₃

C₂×#126

yes

—

#20773

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

C₂×#383

yes

characteristic

C₂×C₇₃

#2921

yes

—

C₂×#376

D₇₃

yes

characteristic

#1840

—

#1728

—

C₇₃

#20773

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂²×C₄²

C₂×D₇₃

yes

—

#376

Dic₇₃

yes

—

#376

C₂×D₇₃

yes

—

C₂×#95

Dic₇₃

yes

—

#336

—

C₂³×C₄

C₂×Dic₇₃

yes

—

C₂³×C₄

C₂²×D₇₃

yes

characteristic

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₇₃

yes

—

C₂×C₄²

C₂²×D₇₃

yes

—

#95

C₂×Dic₇₃

yes

—

C₂⁴

C₂²×Dic₇₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×Dic₇₃

yes

—

C₂²×C₄

C₂²×Dic₇₃

yes

characteristic

C₂²×C₄

#11924028

yes

—

C₂²×C₄

C₂³×D₇₃

yes

characteristic

M₁₆

—

292

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₂³

—

C₂³

#14556550

yes

—

C₂³

C₂³×Dic₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#14556550

yes

—

C₂×C₄

#14556585

yes

—

C₂×C₄

C₂×#11924028

yes

—

C₈

—

292

—

C₂²

—

C₂²

#17988455

yes

—

C₂²

C₂×#14556550

yes

—

C₂²

#17989354

yes

—

C₄

—

C₄

#17988455

yes

—

C₄

C₂×#14556585

yes

—

C₂

—

C₂

C₂×#17988455

yes

characteristic

C₂

#22618569

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting	C₂×#376×C₇₃	C₂
prime radical	C₂⁴×C₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂×#376	D₇₃
hypocenter	C₇₃	#20773
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂³×C₄

Fitting

C₂×#376×C₇₃

C₂

prime radical

C₂⁴×C₇₃

C₂²×C₄

cosocle

C₂²×C₄×C₇₃

C₂⁴

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ C₂×#376

N	H ≅ G/N	type
1. #22610076	C₂	semidirect
53. C₇₃	#20773	semidirect

H ≅ G/N

type

1. #22610076

C₂

semidirect

53. C₇₃

#20773

semidirect

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

subgroup	index
#22610076	2
#22609625	2
C₂×#376×C₇₃	2
#20773	73

subgroup

index

#22610076

#22609625

C₂×#376×C₇₃

#20773

Subgroups — #33086237

Conjugacy classes of subgroups

Complements

Maximal subgroups