Group #47982077 — subgroups

Subgroups — #47982077

Order 35456.

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	#31800132	C₂	1	2	yes	maximal
2	C₄×Dic₁₁₀₈	C₂	1	1	yes	maximal, characteristic
3	#31799753	C₂	1	1	yes	maximal, characteristic
4	#31799734	C₂	1	2	yes	maximal
5	#322×C₂₇₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₀₈	C₄	1	1	yes	characteristic
7	C₄×Dic₅₅₄	C₂²	1	2	yes	—
8	#22579814	C₄	1	1	yes	characteristic
9	C₄⋊#14555660	C₂²	1	2	yes	—
10	#22579809	—	2	2	no	—
11	#22579805	C₄	1	2	yes	—
12	#22579790	—	2	2	no	—
13	C₄×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
16	C₂×Dic₅₅₄	C₂×C₄	1	2	yes	—
17	Dic₁₁₀₈	—	2	2	no	—
18	C₂×#14555660	—	2	2	no	—
19	C₄⋊Dic₂₇₇	C₂×C₄	1	2	yes	—
20	#17984542	—	2	2	no	—
21	C₄×Dic₂₇₇	—	2	2	no	—
22	C₂×C₈×C₂₇₇	—	2	1	no	—
23	C₂×C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₂₇₇	D₄	1	2	yes	—
26	C₄²×C₂₇₇	C₂³	1	1	yes	characteristic
27	Dic₅₅₄	—	2	2	no	—
28	Dic₅₅₄	—	2	2	no	—
29	C₂×Dic₂₇₇	—	2	2	no	—
30	C₂×Dic₂₇₇	—	2	2	no	—
31	#14555660	—	4	2	no	—
32	C₂×C₄×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₇₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₇₇	#41	1	1	yes	characteristic
35	C₈×C₂₇₇	—	2	1	no	—
36	C₈×C₂₇₇	—	2	2	no	—
37	C₈×C₂₇₇	—	4	1	no	—
38	C₈×C₂₇₇	M₁₆	1	2	yes	—
39	C₂²×C₂₇₇	C₄×D₄	1	1	yes	characteristic
40	C₄×C₂₇₇	—	2	1	no	—
41	C₄×C₂₇₇	C₂×M₁₆	1	1	yes	characteristic
42	C₄×C₂₇₇	#131	1	1	yes	characteristic
43	C₄×C₂₇₇	#137	1	2	yes	—
44	Dic₂₇₇	—	4	2	no	—
45	Dic₂₇₇	—	4	2	no	—
46	C₂×C₂₇₇	#436	1	1	yes	characteristic
47	C₂×C₂₇₇	#441	1	1	yes	characteristic
48	C₂×C₂₇₇	#444	1	1	yes	characteristic
49	C₂₇₇	#1593	1	1	yes	characteristic, complemented, Sylow
50	#1593	—	277	1	no	maximal, Sylow
51	#446	—	277	2	no	—
52	C₄×Q₁₆	—	277	1	no	—
53	#334	—	277	1	no	—
54	Q₈⋊C₈	—	277	2	no	—
55	#322	D₂₇₇	1	1	yes	characteristic
56	C₂×Q₁₆	—	277	1	no	—
57	C₄×Q₈	—	277	2	no	—
58	#107	—	277	1	no	—
59	C₄⋊C₈	—	277	2	no	—
60	C₄⋊C₈	—	554	2	no	—
61	#103	—	277	2	no	—
62	#97	—	554	2	no	—
63	C₄×C₈	C₂×D₂₇₇	1	1	yes	characteristic
64	C₄×C₈	C₂×D₂₇₇	1	1	yes	characteristic
65	C₄×C₈	C₂×D₂₇₇	1	1	yes	characteristic
66	C₂×Q₈	—	277	2	no	—
67	Q₁₆	—	554	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	554	2	no	—
70	C₂×C₈	C₄×D₂₇₇	1	1	yes	characteristic
71	C₂×C₈	C₄×D₂₇₇	1	1	yes	characteristic
72	C₂×C₈	D₁₁₀₈	1	2	yes	—
73	C₄⋊C₄	—	277	2	no	—
74	C₄⋊C₄	—	554	2	no	—
75	C₄²	—	554	2	no	—
76	C₄²	C₂²×D₂₇₇	1	1	yes	characteristic
77	Q₈	—	554	2	no	—
78	Q₈	—	554	2	no	—
79	C₂×C₄	—	554	2	no	—
80	C₂×C₄	—	554	2	no	—
81	C₂×C₄	C₂×C₄×D₂₇₇	1	1	yes	characteristic
82	C₂×C₄	C₂×D₁₁₀₈	1	1	yes	characteristic
83	C₂×C₄	#17984563	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	1108	2	no	—
88	C₈	#17984546	1	2	yes	—
89	C₂²	C₄×D₁₁₀₈	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	1108	2	no	—
92	C₄	—	1108	2	no	—
93	C₄	C₂×#17984546	1	1	yes	characteristic
94	C₄	#22579886	1	1	yes	characteristic
95	C₄	#22579913	1	2	yes	—
96	C₂	#31800081	1	1	yes	characteristic
97	C₂	#31800110	1	1	yes	characteristic
98	C₂	#31800125	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31800132

C₂

yes

maximal

C₄×Dic₁₁₀₈

C₂

yes

maximal, characteristic

#31799753

C₂

yes

maximal, characteristic

#31799734

C₂

yes

maximal

#322×C₂₇₇

C₂

yes

maximal, characteristic

C₂×Dic₁₁₀₈

C₄

yes

characteristic

C₄×Dic₅₅₄

C₂²

yes

—

#22579814

C₄

yes

characteristic

C₄⋊#14555660

C₂²

yes

—

#22579809

—

#22579805

C₄

yes

—

#22579790

—

C₄×C₈×C₂₇₇

C₂²

yes

characteristic

C₄×C₈×C₂₇₇

C₂²

yes

characteristic

C₄×C₈×C₂₇₇

C₂²

yes

characteristic

C₂×Dic₅₅₄

C₂×C₄

yes

—

Dic₁₁₀₈

—

C₂×#14555660

—

C₄⋊Dic₂₇₇

C₂×C₄

yes

—

#17984542

—

C₄×Dic₂₇₇

—

C₂×C₈×C₂₇₇

—

C₂×C₈×C₂₇₇

C₂×C₄

yes

characteristic

C₂×C₈×C₂₇₇

C₂×C₄

yes

characteristic

C₂×C₈×C₂₇₇

D₄

yes

—

C₄²×C₂₇₇

C₂³

yes

characteristic

Dic₅₅₄

—

Dic₅₅₄

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

#14555660

—

C₂×C₄×C₂₇₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₇₇

C₂×D₄

yes

characteristic

C₂×C₄×C₂₇₇

#41

yes

characteristic

C₈×C₂₇₇

—

C₈×C₂₇₇

—

C₈×C₂₇₇

—

C₈×C₂₇₇

M₁₆

yes

—

C₂²×C₂₇₇

C₄×D₄

yes

characteristic

C₄×C₂₇₇

—

C₄×C₂₇₇

C₂×M₁₆

yes

C₄×C₂₇₇

yes

C₄×C₂₇₇

yes

—

Dic₂₇₇

—

Dic₂₇₇

—

C₂×C₂₇₇

yes

C₂×C₂₇₇

yes

C₂×C₂₇₇

yes

C₂₇₇

yes

characteristic, complemented, Sylow

#1593

—

277

maximal, Sylow

#446

—

277

—

C₄×Q₁₆

—

277

—

#334

—

277

—

Q₈⋊C₈

—

277

—

#322

D₂₇₇

yes

characteristic

C₂×Q₁₆

—

277

—

C₄×Q₈

—

277

—

#107

—

277

—

C₄⋊C₈

—

277

—

C₄⋊C₈

—

554

—

#103

—

277

—

#97

—

554

—

C₄×C₈

C₂×D₂₇₇

yes

characteristic

C₄×C₈

C₂×D₂₇₇

yes

characteristic

C₄×C₈

C₂×D₂₇₇

yes

characteristic

C₂×Q₈

—

277

—

Q₁₆

—

554

—

C₂×C₈

—

C₂×C₈

—

554

—

C₂×C₈

C₄×D₂₇₇

yes

characteristic

C₂×C₈

C₄×D₂₇₇

yes

characteristic

C₂×C₈

D₁₁₀₈

yes

—

C₄⋊C₄

—

277

—

C₄⋊C₄

—

554

—

C₄²

—

554

—

C₄²

C₂²×D₂₇₇

yes

characteristic

Q₈

—

554

—

Q₈

—

554

—

C₂×C₄

—

554

—

C₂×C₄

—

554

—

C₂×C₄

C₂×C₄×D₂₇₇

yes

characteristic

C₂×C₄

C₂×D₁₁₀₈

yes

characteristic

C₂×C₄

#17984563

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

1108

—

C₈

#17984546

yes

—

C₂²

C₄×D₁₁₀₈

yes

characteristic

C₄

—

C₄

—

1108

—

C₄

—

1108

—

C₄

yes

C₄

yes

C₄

yes

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁₀₈
commutator	C₂×C₄×C₂₇₇	C₂²×C₄
Frattini	C₄²	C₂²×D₂₇₇
Fitting	#322×C₂₇₇	C₂
socle, prime radical	C₂²×C₂₇₇	C₄×D₄
cosocle	C₄²×C₂₇₇	C₂³
hypercenter	#322	D₂₇₇
hypocenter	C₂₇₇	#1593
LCS	G ▷ C₂×C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₁₁₀₈

commutator

C₂×C₄×C₂₇₇

C₂²×C₄

Frattini

C₄²

C₂²×D₂₇₇

Fitting

#322×C₂₇₇

C₂

socle, prime radical

C₂²×C₂₇₇

C₄×D₄

cosocle

C₄²×C₂₇₇

C₂³

D₂₇₇

C₂₇₇

G ▷ C₂×C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
49. C₂₇₇	#1593	semidirect

H ≅ G/N

type

49. C₂₇₇

#1593

semidirect

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

subgroup	index
#31800132	2
C₄×Dic₁₁₀₈	2
#31799753	2
#31799734	2
#322×C₂₇₇	2
#1593	277

subgroup

index

C₄×Dic₁₁₀₈

#322×C₂₇₇

277

Subgroups — #47982077

Conjugacy classes of subgroups

Complements

Maximal subgroups