Group #16776996 — subgroups

Subgroups — #16776996

Order 3328.

152 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 42 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	#13129859	C₂	1	2	yes	maximal, complemented
2	#13114443	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#494	C₄	1	1	yes	characteristic
4	#11718749	—	2	2	no	—
5	#11718356	C₄	1	1	yes	characteristic
6	C₄⋊#6092	—	2	2	no	—
7	C₈×#1055	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×Q₁₆	—	4	1	no	—
9	C₁₃×C₄⋊Q₈	—	2	1	no	—
10	C₂×D₁₀₄	—	4	1	no	—
11	#88128	—	2	1	no	—
12	C₂×#6092	—	4	2	no	—
13	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	#88049	—	4	2	no	—
15	#88049	—	4	2	no	—
16	C₄×#1055	D₄	1	2	yes	—
17	#7092	—	13	1	no	maximal, Sylow
18	C₂×Q₈×C₁₃	—	4	1	no	—
19	C₂×D₅₂	—	4	1	no	—
20	C₂×D₅₂	—	4	2	no	—
21	C₁₃×Q₁₆	—	8	2	no	—
22	C₂×C₈×C₁₃	—	2	1	no	—
23	C₁₃×C₄⋊C₄	—	4	2	no	—
24	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×#1055	D₈	1	2	yes	—
26	C₂×#1055	SD₁₆	1	2	yes	—
27	D₁₀₄	—	8	2	no	—
28	#6092	—	8	2	no	—
29	#1709	—	13	1	no	—
30	#1367	—	13	2	no	—
31	C₂²×D₁₃	—	8	1	no	—
32	Q₈×C₁₃	—	8	2	no	—
33	C₂×C₄×C₁₃	—	8	1	no	—
34	C₂×C₄×C₁₃	#100	1	1	yes	characteristic
35	C₂×C₄×C₁₃	#102	1	2	yes	—
36	D₅₂	—	8	2	no	—
37	D₅₂	—	8	2	no	—
38	D₅₂	—	8	2	no	—
39	C₈×C₁₃	—	2	2	no	—
40	#1055	—	2	2	no	—
41	#1055	—	2	2	no	—
42	#494	#261	1	1	yes	characteristic
43	#493	—	13	1	no	—
44	#486	—	26	2	no	—
45	C₄⋊C₁₆	—	26	2	no	—
46	C₈²	—	13	1	no	—
47	C₂²×C₁₃	#331	1	1	yes	characteristic
48	C₂×D₁₃	—	16	1	no	—
49	C₂×D₁₃	—	16	2	no	—
50	C₄×C₁₃	—	2	1	no	—
51	C₄×C₁₃	—	16	1	no	—
52	C₄×C₁₃	#359	1	2	yes	—
53	C₄×C₁₃	#360	1	2	yes	—
54	C₂×Q₁₆	—	4	1	no	—
55	C₂×D₈	—	52	1	no	—
56	C₄⋊Q₈	—	2	1	no	—
57	#127	—	26	1	no	—
58	C₂×C₁₆	—	52	2	no	—
59	#102	—	52	2	no	—
60	#102	—	52	2	no	—
61	C₄×C₈	—	13	2	no	—
62	C₄×C₈	C₂×#261	1	1	yes	characteristic
63	C₂×C₁₃	#1357	1	1	yes	characteristic
64	C₂×C₁₃	#1360	1	2	yes	—
65	D₁₃	—	32	1	no	—
66	C₂×Q₈	—	4	1	no	—
67	C₂×D₄	—	52	2	no	—
68	C₂×D₄	—	52	1	no	—
69	Q₁₆	—	8	2	no	—
70	D₈	—	104	2	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	13	2	no	—
73	C₂×C₈	—	13	2	no	—
74	C₄⋊C₄	—	4	2	no	—
75	C₄²	C₂²⋊#261	1	1	yes	characteristic
76	C₁₆	—	104	2	no	—
77	C₁₃	#7092	1	1	yes	characteristic, complemented, Sylow
78	C₂³	—	104	1	no	—
79	Q₈	—	8	2	no	—
80	D₄	—	104	2	no	—
81	D₄	—	104	2	no	—
82	D₄	—	104	2	no	—
83	C₂×C₄	—	8	1	no	—
84	C₂×C₄	#88115	1	2	yes	—
85	C₂×C₄	#88121	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	26	2	no	—
88	C₈	—	26	2	no	—
89	C₂²	—	208	1	no	—
90	C₂²	—	208	2	no	—
91	C₂²	#11718297	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	16	1	no	—
94	C₄	#11718279	1	2	yes	—
95	C₄	#11718281	1	2	yes	—
96	C₂	—	416	1	no	—
97	C₂	#13129844	1	1	yes	characteristic
98	C₂	#13129849	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13129859

C₂

yes

maximal, complemented

#13114443

C₂

yes

maximal, characteristic

C₁₃×#494

C₄

yes

characteristic

#11718749

—

#11718356

C₄

yes

characteristic

C₄⋊#6092

—

C₈×#1055

C₂²

yes

characteristic

C₂×C₁₃×Q₁₆

—

C₁₃×C₄⋊Q₈

—

C₂×D₁₀₄

—

#88128

—

C₂×#6092

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

—

D₄

yes

—

#7092

—

maximal, Sylow

C₂×Q₈×C₁₃

—

C₂×D₅₂

—

C₂×D₅₂

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×#1055

D₈

yes

—

C₂×#1055

SD₁₆

yes

—

D₁₀₄

—

#6092

—

#1709

—

#1367

—

C₂²×D₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#100

yes

characteristic

C₂×C₄×C₁₃

#102

yes

—

D₅₂

—

D₅₂

—

D₅₂

—

C₈×C₁₃

—

—

—

yes

—

—

C₄⋊C₁₆

—

C₈²

—

C₂²×C₁₃

#331

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#359

yes

—

C₄×C₁₃

#360

yes

—

C₂×Q₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

—

#102

—

#102

—

C₄×C₈

—

C₄×C₈

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

D₁₃

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

D₈

—

104

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

C₂²⋊#261

yes

characteristic

C₁₆

—

104

—

C₁₃

#7092

yes

characteristic, complemented, Sylow

C₂³

—

104

—

Q₈

—

D₄

—

104

—

D₄

—

104

—

D₄

—

104

—

C₂×C₄

—

C₂×C₄

#88115

yes

—

C₂×C₄

#88121

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

208

—

C₂²

—

208

—

C₂²

#11718297

yes

characteristic

C₄

—

C₄

—

C₄

#11718279

yes

—

C₄

#11718281

yes

—

C₂

—

416

—

C₂

#13129844

yes

characteristic

C₂

#13129849

yes

—

	subgroup	G/H
center	C₂²	#11718297
commutator	C₄×C₈×C₁₃	C₂×C₄
Frattini	C₄×C₈	C₂×#261
Fitting	C₁₃×#494	C₄
socle	C₂²×C₁₃	#331
prime radical	#11718356	C₄
cosocle	C₈×#1055	C₂²
hypercenter	#494	#261
hypocenter	C₁₃	#7092
LCS	G ▷ C₄×C₈×C₁₃ ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂²

#11718297

commutator

C₄×C₈×C₁₃

C₂×C₄

Frattini

C₄×C₈

C₂×#261

Fitting

C₁₃×#494

C₄

C₂²×C₁₃

C₄

C₂²

C₁₃

G ▷ C₄×C₈×C₁₃ ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
1. #13129859	C₂	semidirect
77. C₁₃	#7092	semidirect

H ≅ G/N

type

1. #13129859

C₂

semidirect

77. C₁₃

#7092

semidirect

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

subgroup	index
#13129859	2
#13114443	2
#7092	13

subgroup

index

#13129859

#13114443

#7092

Subgroups — #16776996

Conjugacy classes of subgroups

Complements

Maximal subgroups