Group #44450720 — subgroups

Subgroups — #44450720

Order 29824.

148 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 65 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	#28416565	C₂	1	2	yes	maximal
2	C₄×Dic₉₃₂	C₂	1	1	yes	maximal, characteristic
3	#28416186	C₂	1	1	yes	maximal, characteristic
4	#28416167	C₂	1	2	yes	maximal
5	#322×C₂₃₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₃₂	C₄	1	1	yes	characteristic
7	C₄×Dic₄₆₆	C₂²	1	2	yes	—
8	#21418469	C₄	1	1	yes	characteristic
9	C₄⋊#14272338	C₂²	1	2	yes	—
10	#21418464	—	2	2	no	—
11	#21418460	C₄	1	2	yes	—
12	#21418445	—	2	2	no	—
13	C₄×C₈×C₂₃₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₃₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₂₃₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₆₆	C₂×C₄	1	2	yes	—
17	Dic₉₃₂	—	2	2	no	—
18	C₂×#14272338	—	2	2	no	—
19	C₄⋊Dic₂₃₃	C₂×C₄	1	2	yes	—
20	#16836573	—	2	2	no	—
21	C₄×Dic₂₃₃	—	2	2	no	—
22	C₂×C₈×C₂₃₃	—	2	1	no	—
23	C₂×C₈×C₂₃₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₂₃₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₂₃₃	D₄	1	2	yes	—
26	C₄²×C₂₃₃	C₂³	1	1	yes	characteristic
27	Dic₄₆₆	—	2	2	no	—
28	Dic₄₆₆	—	2	2	no	—
29	C₂×Dic₂₃₃	—	2	2	no	—
30	C₂×Dic₂₃₃	—	2	2	no	—
31	#14272338	—	4	2	no	—
32	C₂×C₄×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₃₃	#41	1	1	yes	characteristic
35	C₈×C₂₃₃	—	2	1	no	—
36	C₈×C₂₃₃	—	2	2	no	—
37	C₈×C₂₃₃	—	4	1	no	—
38	C₈×C₂₃₃	M₁₆	1	2	yes	—
39	C₂²×C₂₃₃	C₄×D₄	1	1	yes	characteristic
40	C₄×C₂₃₃	—	2	1	no	—
41	C₄×C₂₃₃	C₂×M₁₆	1	1	yes	characteristic
42	C₄×C₂₃₃	#131	1	1	yes	characteristic
43	C₄×C₂₃₃	#137	1	2	yes	—
44	Dic₂₃₃	—	4	2	no	—
45	Dic₂₃₃	—	4	2	no	—
46	C₂×C₂₃₃	#436	1	1	yes	characteristic
47	C₂×C₂₃₃	#441	1	1	yes	characteristic
48	C₂×C₂₃₃	#444	1	1	yes	characteristic
49	C₂₃₃	#1593	1	1	yes	characteristic, complemented, Sylow
50	#1593	—	233	1	no	maximal, Sylow
51	#446	—	233	2	no	—
52	C₄×Q₁₆	—	233	1	no	—
53	#334	—	233	1	no	—
54	Q₈⋊C₈	—	233	2	no	—
55	#322	D₂₃₃	1	1	yes	characteristic
56	C₂×Q₁₆	—	233	1	no	—
57	C₄×Q₈	—	233	2	no	—
58	#107	—	233	1	no	—
59	C₄⋊C₈	—	466	2	no	—
60	C₄⋊C₈	—	233	2	no	—
61	#103	—	233	2	no	—
62	#97	—	466	2	no	—
63	C₄×C₈	C₂×D₂₃₃	1	1	yes	characteristic
64	C₄×C₈	C₂×D₂₃₃	1	1	yes	characteristic
65	C₄×C₈	C₂×D₂₃₃	1	1	yes	characteristic
66	C₂×Q₈	—	233	2	no	—
67	Q₁₆	—	466	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	466	2	no	—
70	C₂×C₈	C₄×D₂₃₃	1	1	yes	characteristic
71	C₂×C₈	C₄×D₂₃₃	1	1	yes	characteristic
72	C₂×C₈	D₉₃₂	1	2	yes	—
73	C₄⋊C₄	—	466	2	no	—
74	C₄⋊C₄	—	233	2	no	—
75	C₄²	—	466	2	no	—
76	C₄²	C₂²×D₂₃₃	1	1	yes	characteristic
77	Q₈	—	466	2	no	—
78	Q₈	—	466	2	no	—
79	C₂×C₄	—	466	2	no	—
80	C₂×C₄	—	466	2	no	—
81	C₂×C₄	C₂×C₄×D₂₃₃	1	1	yes	characteristic
82	C₂×C₄	C₂×D₉₃₂	1	1	yes	characteristic
83	C₂×C₄	#16836594	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	932	2	no	—
88	C₈	#16836577	1	2	yes	—
89	C₂²	C₄×D₉₃₂	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	932	2	no	—
92	C₄	—	932	2	no	—
93	C₄	C₂×#16836577	1	1	yes	characteristic
94	C₄	#21418541	1	1	yes	characteristic
95	C₄	#21418568	1	2	yes	—
96	C₂	#28416514	1	1	yes	characteristic
97	C₂	#28416543	1	1	yes	characteristic
98	C₂	#28416558	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#28416565

C₂

yes

maximal

C₄×Dic₉₃₂

C₂

yes

maximal, characteristic

#28416186

C₂

yes

maximal, characteristic

#28416167

C₂

yes

maximal

#322×C₂₃₃

C₂

yes

maximal, characteristic

C₂×Dic₉₃₂

C₄

yes

characteristic

C₄×Dic₄₆₆

C₂²

yes

—

#21418469

C₄

yes

characteristic

C₄⋊#14272338

C₂²

yes

—

#21418464

—

#21418460

C₄

yes

—

#21418445

—

C₄×C₈×C₂₃₃

C₂²

yes

characteristic

C₄×C₈×C₂₃₃

C₂²

yes

characteristic

C₄×C₈×C₂₃₃

C₂²

yes

characteristic

C₂×Dic₄₆₆

C₂×C₄

yes

—

Dic₉₃₂

—

C₂×#14272338

—

C₄⋊Dic₂₃₃

C₂×C₄

yes

—

#16836573

—

C₄×Dic₂₃₃

—

C₂×C₈×C₂₃₃

—

C₂×C₈×C₂₃₃

C₂×C₄

yes

characteristic

C₂×C₈×C₂₃₃

C₂×C₄

yes

characteristic

C₂×C₈×C₂₃₃

D₄

yes

—

C₄²×C₂₃₃

C₂³

yes

characteristic

Dic₄₆₆

—

Dic₄₆₆

—

C₂×Dic₂₃₃

—

C₂×Dic₂₃₃

—

#14272338

—

C₂×C₄×C₂₃₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₃₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₃₃

#41

yes

characteristic

C₈×C₂₃₃

—

C₈×C₂₃₃

—

C₈×C₂₃₃

—

C₈×C₂₃₃

M₁₆

yes

—

C₂²×C₂₃₃

C₄×D₄

yes

characteristic

C₄×C₂₃₃

—

C₄×C₂₃₃

C₂×M₁₆

yes

C₄×C₂₃₃

yes

C₄×C₂₃₃

yes

—

Dic₂₃₃

—

Dic₂₃₃

—

C₂×C₂₃₃

yes

C₂×C₂₃₃

yes

C₂×C₂₃₃

yes

C₂₃₃

yes

characteristic, complemented, Sylow

#1593

—

233

maximal, Sylow

#446

—

233

—

C₄×Q₁₆

—

233

—

#334

—

233

—

Q₈⋊C₈

—

233

—

#322

D₂₃₃

yes

characteristic

C₂×Q₁₆

—

233

—

C₄×Q₈

—

233

—

#107

—

233

—

C₄⋊C₈

—

466

—

C₄⋊C₈

—

233

—

#103

—

233

—

#97

—

466

—

C₄×C₈

C₂×D₂₃₃

yes

characteristic

C₄×C₈

C₂×D₂₃₃

yes

characteristic

C₄×C₈

C₂×D₂₃₃

yes

characteristic

C₂×Q₈

—

233

—

Q₁₆

—

466

—

C₂×C₈

—

C₂×C₈

—

466

—

C₂×C₈

C₄×D₂₃₃

yes

characteristic

C₂×C₈

C₄×D₂₃₃

yes

characteristic

C₂×C₈

D₉₃₂

yes

—

C₄⋊C₄

—

466

—

C₄⋊C₄

—

233

—

C₄²

—

466

—

C₄²

C₂²×D₂₃₃

yes

characteristic

Q₈

—

466

—

Q₈

—

466

—

C₂×C₄

—

466

—

C₂×C₄

—

466

—

C₂×C₄

C₂×C₄×D₂₃₃

yes

characteristic

C₂×C₄

C₂×D₉₃₂

yes

characteristic

C₂×C₄

#16836594

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

932

—

C₈

#16836577

yes

—

C₂²

C₄×D₉₃₂

yes

characteristic

C₄

—

C₄

—

932

—

C₄

—

932

—

C₄

yes

C₄

yes

C₄

yes

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₉₃₂
commutator	C₂×C₄×C₂₃₃	C₂²×C₄
Frattini	C₄²	C₂²×D₂₃₃
Fitting	#322×C₂₃₃	C₂
socle, prime radical	C₂²×C₂₃₃	C₄×D₄
cosocle	C₄²×C₂₃₃	C₂³
hypercenter	#322	D₂₃₃
hypocenter	C₂₃₃	#1593
LCS	G ▷ C₂×C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₉₃₂

commutator

C₂×C₄×C₂₃₃

C₂²×C₄

Frattini

C₄²

C₂²×D₂₃₃

Fitting

#322×C₂₃₃

C₂

socle, prime radical

C₂²×C₂₃₃

C₄×D₄

cosocle

C₄²×C₂₃₃

C₂³

D₂₃₃

C₂₃₃

G ▷ C₂×C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
49. C₂₃₃	#1593	semidirect

H ≅ G/N

type

49. C₂₃₃

#1593

semidirect

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

subgroup	index
#28416565	2
C₄×Dic₉₃₂	2
#28416186	2
#28416167	2
#322×C₂₃₃	2
#1593	233

subgroup

index

C₄×Dic₉₃₂

#322×C₂₃₃

233

Subgroups — #44450720

Conjugacy classes of subgroups

Complements

Maximal subgroups