Group #47983286 — subgroups

Subgroups — #47983286

Order 35456.

216 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂×C₄⋊#14555660	C₂	1	1	yes	maximal, characteristic
2	#31799848	C₂	1	1	yes	maximal, characteristic
3	#31799756	C₂	1	4	yes	maximal
4	C₂×C₄⋊C₈×C₂₇₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14555660	C₂²	1	2	yes	—
6	C₂×C₄×Dic₂₇₇	C₂²	1	2	yes	—
7	C₄⋊#14555660	—	2	2	no	—
8	#22579787	C₄	1	2	yes	—
9	#22579787	C₄	1	2	yes	—
10	C₂²×C₈×C₂₇₇	C₂²	1	2	yes	—
11	C₂×C₄²×C₂₇₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₂₇₇	—	2	2	no	—
13	C₂²×Dic₂₇₇	C₂×C₄	1	4	yes	—
14	C₂×#14555660	—	2	2	no	—
15	C₂×#14555660	—	2	4	no	—
16	C₄×Dic₂₇₇	—	2	2	no	—
17	C₄×Dic₂₇₇	—	2	2	no	—
18	C₂²×C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₂₇₇	—	2	2	no	—
22	C₂×C₈×C₂₇₇	—	2	4	no	—
23	C₄²×C₂₇₇	D₄	1	2	yes	—
24	C₄²×C₂₇₇	Q₈	1	2	yes	—
25	C₂×Dic₂₇₇	—	2	4	no	—
26	C₂×Dic₂₇₇	—	2	4	no	—
27	C₂×Dic₂₇₇	—	2	4	no	—
28	#14555660	—	4	2	no	—
29	C₂³×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₇₇	—	2	2	no	—
31	C₂×C₄×C₂₇₇	—	2	2	no	—
32	C₂×C₄×C₂₇₇	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₂₇₇	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₂₇₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₂₇₇	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₂₇₇	#41	1	2	yes	—
37	C₂×C₄×C₂₇₇	#41	1	2	yes	—
38	C₈×C₂₇₇	—	4	2	no	—
39	C₂²×C₂₇₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₂₇₇	#117	1	2	yes	—
41	C₂²×C₂₇₇	#131	1	2	yes	—
42	C₂²×C₂₇₇	#131	1	2	yes	—
43	C₄×C₂₇₇	—	2	2	no	—
44	C₄×C₂₇₇	—	2	2	no	—
45	C₄×C₂₇₇	#124	1	1	yes	characteristic
46	C₄×C₂₇₇	#124	1	1	yes	characteristic
47	C₄×C₂₇₇	#125	1	2	yes	—
48	Dic₂₇₇	—	4	4	no	—
49	C₂×C₂₇₇	#382	1	1	yes	characteristic
50	C₂×C₂₇₇	#424	1	1	yes	characteristic
51	C₂×C₂₇₇	#424	1	1	yes	characteristic
52	C₂×C₂₇₇	#433	1	4	yes	—
53	C₂₇₇	#1832	1	1	yes	characteristic, complemented, Sylow
54	#1832	—	277	1	no	maximal, Sylow
55	C₂×C₄⋊C₈	—	277	1	no	—
56	C₂×C₄⋊C₈	D₂₇₇	1	1	yes	characteristic
57	#376	—	277	1	no	—
58	#336	—	277	4	no	—
59	C₂²×C₈	—	277	2	no	—
60	C₂²×C₈	C₂×D₂₇₇	1	2	yes	—
61	C₂×C₄²	—	277	2	no	—
62	C₂×C₄²	C₂×D₂₇₇	1	1	yes	characteristic
63	C₄⋊C₈	—	2	2	no	—
64	C₄⋊C₈	—	554	2	no	—
65	#95	—	277	2	no	—
66	#95	—	277	2	no	—
67	C₂²×C₄	—	277	4	no	—
68	C₂²×C₄	C₄×D₂₇₇	1	1	yes	characteristic
69	C₂²×C₄	C₄×D₂₇₇	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₂₇₇	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	4	no	—
73	C₂×C₈	—	554	2	no	—
74	C₂×C₈	—	554	4	no	—
75	C₄²	—	554	2	no	—
76	C₄²	—	554	2	no	—
77	C₄²	C₂²⋊D₂₇₇	1	2	yes	—
78	C₄²	Dic₅₅₄	1	2	yes	—
79	C₂³	C₂×C₄×D₂₇₇	1	1	yes	characteristic
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	554	4	no	—
83	C₂×C₄	—	554	4	no	—
84	C₂×C₄	—	554	4	no	—
85	C₂×C₄	#17984542	1	2	yes	—
86	C₂×C₄	#17984542	1	2	yes	—
87	C₂×C₄	C₂×C₂²⋊D₂₇₇	1	1	yes	characteristic
88	C₂×C₄	C₂×Dic₅₅₄	1	1	yes	characteristic
89	C₂×C₄	#17984562	1	2	yes	—
90	C₂×C₄	#17984564	1	2	yes	—
91	C₈	—	4	2	no	—
92	C₈	—	1108	2	no	—
93	C₂²	C₂×#17984542	1	1	yes	characteristic
94	C₂²	#22579838	1	2	yes	—
95	C₂²	#22579886	1	2	yes	—
96	C₂²	#22579888	1	2	yes	—
97	C₄	—	2	2	no	—
98	C₄	—	2	2	no	—
99	C₄	—	1108	4	no	—
100	C₄	#22579867	1	1	yes	characteristic
101	C₄	#22579869	1	1	yes	characteristic
102	C₄	#22579871	1	2	yes	—
103	C₂	#31799867	1	1	yes	characteristic
104	C₂	#31800028	1	1	yes	characteristic
105	C₂	#31800030	1	1	yes	characteristic
106	C₂	#31800062	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#14555660

C₂

yes

maximal, characteristic

#31799848

C₂

yes

maximal, characteristic

#31799756

C₂

yes

maximal

C₂×C₄⋊C₈×C₂₇₇

C₂

yes

maximal, characteristic

C₂²×#14555660

C₂²

yes

—

C₂×C₄×Dic₂₇₇

C₂²

yes

—

C₄⋊#14555660

—

#22579787

C₄

yes

—

#22579787

C₄

yes

—

C₂²×C₈×C₂₇₇

C₂²

yes

—

C₂×C₄²×C₂₇₇

C₂²

yes

characteristic

C₄⋊C₈×C₂₇₇

—

C₂²×Dic₂₇₇

C₂×C₄

yes

—

C₂×#14555660

—

C₂×#14555660

—

C₄×Dic₂₇₇

—

C₄×Dic₂₇₇

—

C₂²×C₄×C₂₇₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₇₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₇₇

C₂³

yes

characteristic

C₂×C₈×C₂₇₇

—

C₂×C₈×C₂₇₇

—

C₄²×C₂₇₇

D₄

yes

—

C₄²×C₂₇₇

Q₈

yes

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

C₂×Dic₂₇₇

—

#14555660

—

C₂³×C₂₇₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₇₇

—

C₂×C₄×C₂₇₇

—

C₂×C₄×C₂₇₇

C₄⋊C₄

yes

—

C₂×C₄×C₂₇₇

C₄⋊C₄

yes

—

C₂×C₄×C₂₇₇

C₂×D₄

yes

characteristic

C₂×C₄×C₂₇₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₇₇

#41

yes

—

C₂×C₄×C₂₇₇

#41

yes

—

C₈×C₂₇₇

—

C₂²×C₂₇₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₇₇

#117

yes

—

C₂²×C₂₇₇

#131

yes

—

C₂²×C₂₇₇

#131

yes

—

C₄×C₂₇₇

—

C₄×C₂₇₇

—

C₄×C₂₇₇

yes

C₄×C₂₇₇

yes

C₄×C₂₇₇

yes

—

Dic₂₇₇

—

C₂×C₂₇₇

yes

C₂×C₂₇₇

yes

C₂×C₂₇₇

yes

C₂×C₂₇₇

yes

—

C₂₇₇

#1832

yes

characteristic, complemented, Sylow

#1832

—

277

maximal, Sylow

C₂×C₄⋊C₈

—

277

—

C₂×C₄⋊C₈

D₂₇₇

yes

characteristic

#376

—

277

—

#336

—

277

—

C₂²×C₈

—

277

—

C₂²×C₈

C₂×D₂₇₇

yes

—

C₂×C₄²

—

277

—

C₂×C₄²

C₂×D₂₇₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

554

—

#95

—

277

—

#95

—

277

—

C₂²×C₄

—

277

—

C₂²×C₄

C₄×D₂₇₇

yes

characteristic

C₂²×C₄

C₄×D₂₇₇

yes

characteristic

C₂²×C₄

C₂²×D₂₇₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

554

—

C₂×C₈

—

554

—

C₄²

—

554

—

C₄²

—

554

—

C₄²

C₂²⋊D₂₇₇

yes

—

C₄²

Dic₅₅₄

yes

—

C₂³

C₂×C₄×D₂₇₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

554

—

C₂×C₄

—

554

—

C₂×C₄

—

554

—

C₂×C₄

#17984542

yes

—

C₂×C₄

#17984542

yes

—

C₂×C₄

C₂×C₂²⋊D₂₇₇

yes

characteristic

C₂×C₄

C₂×Dic₅₅₄

yes

characteristic

C₂×C₄

#17984562

yes

—

C₂×C₄

#17984564

yes

—

C₈

—

C₈

—

1108

—

C₂²

C₂×#17984542

yes

characteristic

C₂²

#22579838

yes

—

C₂²

#22579886

yes

—

C₂²

#22579888

yes

—

C₄

—

C₄

—

C₄

—

1108

—

100

C₄

#22579867

yes

characteristic

101

C₄

#22579869

yes

characteristic

102

C₄

#22579871

yes

—

103

C₂

#31799867

yes

characteristic

104

C₂

#31800028

yes

characteristic

105

C₂

#31800030

yes

characteristic

106

C₂

#31800062

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₇₇
commutator, socle, prime radical	C₂³×C₂₇₇	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₂₇₇	C₂
cosocle	C₂²×C₄×C₂₇₇	C₂³
hypercenter	C₂×C₄⋊C₈	D₂₇₇
hypocenter	C₂₇₇	#1832
LCS	G ▷ C₂³×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₇₇

commutator, socle, prime radical

C₂³×C₂₇₇

C₂²×C₄

Fitting

C₂×C₄⋊C₈×C₂₇₇

C₂

cosocle

C₂²×C₄×C₂₇₇

C₂³

hypercenter

C₂×C₄⋊C₈

D₂₇₇

C₂₇₇

G ▷ C₂³×C₂₇₇ ▷ C₂₇₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
53. C₂₇₇	#1832	semidirect

H ≅ G/N

type

53. C₂₇₇

#1832

semidirect

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

subgroup	index
C₂×C₄⋊#14555660	2
#31799848	2
#31799756	2
C₂×C₄⋊C₈×C₂₇₇	2
#1832	277

subgroup

index

C₂×C₄⋊C₈×C₂₇₇

277

Subgroups — #47983286

Conjugacy classes of subgroups

Complements

Maximal subgroups