Group #17949238 — subgroups

Subgroups — #17949238

Order 4352.

110 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 48 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	C₄⋊#10587467	C₂	1	1	yes	maximal, characteristic
2	#14543891	C₂	1	1	yes	maximal, characteristic
3	#14530689	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587467	—	2	1	no	—
5	C₂×#10587467	—	2	1	no	—
6	C₈×Dic₃₄	C₄	1	1	yes	characteristic
7	#11762627	—	2	1	no	—
8	#11762584	—	2	1	no	—
9	C₄×#63214	C₂²	1	1	yes	characteristic
10	C₁₇×C₄⋊C₁₆	C₄	1	1	yes	characteristic
11	C₄×Dic₃₄	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₁₇	—	2	1	no	—
13	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
14	#10587485	—	2	1	no	—
15	C₈×Dic₁₇	—	2	1	no	—
16	C₂×#63214	D₄	1	1	yes	characteristic
17	C₂×#63214	D₄	1	1	yes	characteristic
18	C₄⋊#3622	C₈	1	1	yes	characteristic
19	#10587467	—	2	2	no	—
20	#10587467	—	4	1	no	—
21	C₂×Dic₃₄	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₇	M₁₆	1	1	yes	characteristic
24	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
25	C₄⋊Dic₁₇	C₁₆	1	1	yes	characteristic
26	#63225	—	2	1	no	—
27	C₄×Dic₁₇	—	2	1	no	—
28	C₂×#3622	—	2	1	no	—
29	C₁₆×C₁₇	—	4	1	no	—
30	#63214	—	2	1	no	—
31	#63214	SD₁₆	1	1	yes	characteristic
32	#63214	Q₁₆	1	1	yes	characteristic
33	#7393	—	17	1	no	maximal, Sylow
34	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
35	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
36	C₂×C₄×C₁₇	M₃₂	1	1	yes	characteristic
37	C₂×Dic₁₇	—	2	1	no	—
38	C₂×Dic₁₇	—	2	1	no	—
39	Dic₃₄	—	4	1	no	—
40	C₈×C₁₇	—	2	1	no	—
41	C₈×C₁₇	#103	1	1	yes	characteristic
42	C₈×C₁₇	#104	1	1	yes	characteristic
43	#3622	—	4	1	no	—
44	#2183	—	17	1	no	—
45	C₄⋊C₃₂	—	17	1	no	—
46	#1397	—	17	1	no	—
47	C₂²×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
48	C₄×C₁₇	—	2	1	no	—
49	C₄×C₁₇	—	2	1	no	—
50	C₄×C₁₇	Q₈⋊C₈	1	1	yes	characteristic
51	C₄×C₁₇	#350	1	1	yes	characteristic
52	Dic₁₇	—	4	1	no	—
53	Dic₁₇	—	4	1	no	—
54	C₈×Q₈	—	17	1	no	—
55	C₂×C₃₂	—	34	1	no	—
56	C₂×C₃₂	—	34	1	no	—
57	C₄⋊C₁₆	—	34	1	no	—
58	C₄⋊C₁₆	#595	1	1	yes	characteristic
59	#346	—	34	1	no	—
60	C₄×C₁₆	—	17	1	no	—
61	C₂×C₁₇	Q₈⋊C₁₆	1	1	yes	characteristic
62	C₂×C₁₇	#1400	1	1	yes	characteristic
63	C₂×C₁₇	#1401	1	1	yes	characteristic
64	C₄×Q₈	—	17	1	no	—
65	C₂×C₁₆	—	2	1	no	—
66	C₂×C₁₆	—	17	1	no	—
67	C₂×C₁₆	—	17	1	no	—
68	C₄⋊C₈	—	17	1	no	—
69	C₄⋊C₈	—	34	1	no	—
70	C₄×C₈	—	34	1	no	—
71	C₄×C₈	C₂×#595	1	1	yes	characteristic
72	C₃₂	—	34	2	no	—
73	C₃₂	—	68	1	no	—
74	C₁₇	#7393	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₈	—	17	1	no	—
76	C₂×C₈	—	34	1	no	—
77	C₂×C₈	#63243	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
79	C₄⋊C₄	—	17	1	no	—
80	C₄⋊C₄	—	34	1	no	—
81	C₄²	—	34	1	no	—
82	C₄²	#63242	1	1	yes	characteristic
83	C₁₆	—	4	1	no	—
84	C₁₆	—	17	1	no	—
85	C₁₆	—	17	1	no	—
86	C₁₆	—	34	1	no	—
87	Q₈	—	68	1	no	—
88	C₂×C₄	—	34	1	no	—
89	C₂×C₄	—	34	1	no	—
90	C₂×C₄	#10587529	1	1	yes	characteristic
91	C₂×C₄	#10587530	1	1	yes	characteristic
92	C₂×C₄	#10587543	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	68	1	no	—
95	C₈	#10587548	1	1	yes	characteristic
96	C₈	#10587549	1	1	yes	characteristic
97	C₂²	#11763704	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	68	1	no	—
101	C₄	—	68	1	no	—
102	C₄	#11763659	1	1	yes	characteristic
103	C₄	#11763708	1	1	yes	characteristic
104	C₂	#14543751	1	1	yes	characteristic
105	C₂	#14543900	1	1	yes	characteristic
106	C₂	#14543902	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#10587467

C₂

yes

maximal, characteristic

#14543891

C₂

yes

maximal, characteristic

#14530689

C₂

yes

maximal, characteristic

C₂×#10587467

—

C₂×#10587467

—

C₈×Dic₃₄

C₄

yes

—

—

C₂²

yes

characteristic

C₁₇×C₄⋊C₁₆

C₄

yes

characteristic

C₄×Dic₃₄

C₈

yes

characteristic

C₂×C₁₆×C₁₇

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

#10587485

—

C₈×Dic₁₇

—

C₂×#63214

D₄

yes

characteristic

C₂×#63214

D₄

yes

characteristic

C₄⋊#3622

C₈

yes

characteristic

#10587467

—

#10587467

—

C₂×Dic₃₄

C₁₆

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

M₁₆

yes

characteristic

C₄²×C₁₇

C₂×C₈

yes

characteristic

C₄⋊Dic₁₇

C₁₆

yes

characteristic

#63225

—

C₄×Dic₁₇

—

C₂×#3622

—

C₁₆×C₁₇

—

#63214

—

#63214

SD₁₆

yes

characteristic

#63214

Q₁₆

yes

characteristic

#7393

—

maximal, Sylow

C₂×C₄×C₁₇

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

M₃₂

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

Dic₃₄

—

C₈×C₁₇

—

C₈×C₁₇

yes

C₈×C₁₇

yes

—

—

C₄⋊C₃₂

—

#1397

—

C₂²×C₁₇

C₂²⋊C₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

Q₈⋊C₈

yes

characteristic

C₄×C₁₇

#350

yes

characteristic

Dic₁₇

—

Dic₁₇

—

C₈×Q₈

—

C₂×C₃₂

—

C₂×C₃₂

—

C₄⋊C₁₆

—

C₄⋊C₁₆

#595

yes

characteristic

#346

—

C₄×C₁₆

—

C₂×C₁₇

Q₈⋊C₁₆

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

C₂×#595

yes

characteristic

C₃₂

—

C₃₂

—

C₁₇

#7393

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

#63243

yes

characteristic

C₂×C₈

C₂²⋊#595

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

#63242

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

#11763659

yes

characteristic

103

C₄

#11763708

yes

characteristic

104

C₂

#14543751

yes

characteristic

105

C₂

#14543900

yes

characteristic

106

C₂

#14543902

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×#595
Fitting	C₁₇×C₄⋊C₁₆	C₄
socle, prime radical	C₂²×C₁₇	C₂²⋊C₁₆
cosocle	C₄×#63214	C₂²
hypercenter	C₄⋊C₁₆	#595
hypocenter	C₁₇	#7393
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂×C₈

C₂²⋊#595

commutator

C₂×C₄×C₁₇

C₂×C₁₆

Frattini

C₄×C₈

C₂×#595

Fitting

C₁₇×C₄⋊C₁₆

C₄

socle, prime radical

C₂²×C₁₇

C₂²⋊C₁₆

C₂²

C₄⋊C₁₆

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
74. C₁₇	#7393	semidirect

H ≅ G/N

type

74. C₁₇

#7393

semidirect

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

subgroup	index
C₄⋊#10587467	2
#14543891	2
#14530689	2
#7393	17

subgroup

index

Subgroups — #17949238

Conjugacy classes of subgroups

Complements

Maximal subgroups