Group #17981412 — subgroups

Subgroups — #17981412

Order 4352.

152 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 29 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	#14545824	C₂	1	2	yes	maximal
2	#14544725	C₂	1	1	yes	maximal, characteristic
3	#11763908	—	2	2	no	—
4	C₂×#10587536	—	2	2	no	—
5	#11763813	C₄	1	1	yes	characteristic
6	#11763813	C₂²	1	1	yes	characteristic
7	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
8	C₂×#63243	—	2	1	no	—
9	C₂×#63243	D₄	1	2	yes	—
10	#10587670	—	4	2	no	—
11	C₂×C₈×D₁₇	—	2	1	no	—
12	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
13	C₄⋊#3624	—	4	1	no	—
14	C₄⋊#3624	—	4	1	no	—
15	#10587536	—	4	4	no	—
16	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
17	C₈×Dic₁₇	—	2	1	no	—
18	C₄×#3622	C₈	1	1	yes	characteristic
19	C₂×C₄×D₁₇	—	2	1	no	—
20	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×#3624	—	2	2	no	—
22	C₂×#3624	—	4	1	no	—
23	#63243	—	4	2	no	—
24	#63243	—	4	2	no	—
25	#63241	—	8	2	no	—
26	C₂×C₈×C₁₇	—	2	1	no	—
27	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
28	C₄×Dic₁₇	—	2	1	no	—
29	C₄×Dic₁₇	M₁₆	1	1	yes	characteristic
30	C₂×#3622	—	2	1	no	—
31	C₈×D₁₇	—	2	2	no	—
32	C₈×D₁₇	—	2	2	no	—
33	#7373	—	17	1	no	maximal, Sylow
34	C₂²×D₁₇	#101	1	1	yes	characteristic
35	C₂×C₄×C₁₇	—	2	1	no	—
36	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×Dic₁₇	—	2	1	no	—
38	C₂×Dic₁₇	#99	1	1	yes	characteristic
39	C₄×D₁₇	—	2	1	no	—
40	C₄×D₁₇	—	2	1	no	—
41	C₄×D₁₇	—	4	2	no	—
42	#3624	—	4	2	no	—
43	#3624	—	8	1	no	—
44	C₈×C₁₇	—	2	2	no	—
45	#3622	—	2	2	no	—
46	#1848	—	17	1	no	—
47	#1327	—	17	2	no	—
48	C₂²×C₁₇	#324	1	1	yes	characteristic
49	C₂×D₁₇	—	2	1	no	—
50	C₂×D₁₇	—	4	1	no	—
51	C₄×C₁₇	—	2	2	no	—
52	C₄×C₁₇	—	2	1	no	—
53	Dic₁₇	—	4	1	no	—
54	Dic₁₇	#353	1	1	yes	characteristic
55	Dic₁₇	#356	1	1	yes	characteristic
56	C₂×#108	—	34	2	no	—
57	#423	—	17	1	no	—
58	#423	—	17	1	no	—
59	C₂×C₄×C₈	—	17	1	no	—
60	#349	—	34	2	no	—
61	C₂×C₁₇	—	2	1	no	—
62	C₂×C₁₇	#1325	1	1	yes	characteristic
63	D₁₇	—	4	1	no	—
64	C₂×M₁₆	—	17	2	no	—
65	C₂×M₁₆	—	34	1	no	—
66	C₂²×C₈	—	34	1	no	—
67	C₂×C₄²	—	17	1	no	—
68	M₃₂	—	68	2	no	—
69	#108	—	68	4	no	—
70	C₄⋊C₈	—	68	1	no	—
71	C₄⋊C₈	—	68	1	no	—
72	C₄×C₈	—	17	1	no	—
73	C₄×C₈	—	34	1	no	—
74	C₄×C₈	#3633	1	1	yes	characteristic
75	C₁₇	#7373	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₄	—	17	1	no	—
77	C₂²×C₄	—	34	1	no	—
78	M₁₆	—	68	2	no	—
79	M₁₆	—	68	2	no	—
80	C₂×C₈	—	2	1	no	—
81	C₂×C₈	—	34	2	no	—
82	C₂×C₈	—	34	2	no	—
83	C₂×C₈	—	34	1	no	—
84	C₂×C₈	—	34	2	no	—
85	C₂×C₈	—	68	1	no	—
86	C₄²	—	17	1	no	—
87	C₄²	—	34	1	no	—
88	C₄²	C₂×#3633	1	1	yes	characteristic
89	C₁₆	—	136	2	no	—
90	C₂³	—	17	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	17	1	no	—
93	C₂×C₄	—	34	1	no	—
94	C₂×C₄	—	34	1	no	—
95	C₂×C₄	—	34	1	no	—
96	C₂×C₄	—	68	2	no	—
97	C₂×C₄	C₂²⋊#3633	1	1	yes	characteristic
98	C₈	—	2	2	no	—
99	C₈	—	34	2	no	—
100	C₈	—	68	2	no	—
101	C₈	—	136	1	no	—
102	C₂²	—	34	1	no	—
103	C₂²	—	68	1	no	—
104	C₂²	#11763895	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	2	1	no	—
107	C₄	—	17	1	no	—
108	C₄	—	17	1	no	—
109	C₄	—	68	1	no	—
110	C₂	—	2	1	no	—
111	C₂	—	68	1	no	—
112	C₂	#14545821	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545824

C₂

yes

maximal

#14544725

C₂

yes

maximal, characteristic

#11763908

—

C₂×#10587536

—

#11763813

C₄

yes

characteristic

#11763813

C₂²

yes

characteristic

C₄×C₈×D₁₇

C₄

yes

characteristic

C₂×#63243

—

C₂×#63243

D₄

yes

—

#10587670

—

C₂×C₈×D₁₇

—

C₄²×D₁₇

C₂×C₄

yes

—

—

—

C₄×C₈×C₁₇

C₈

yes

characteristic

C₈×Dic₁₇

—

C₄×#3622

C₈

yes

characteristic

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₂²⋊C₄

yes

—

—

—

—

—

C₂×C₈×C₁₇

—

C₄²×C₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

M₁₆

yes

characteristic

C₂×#3622

—

C₈×D₁₇

—

C₈×D₁₇

—

—

C₂²×D₁₇

yes

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²⋊C₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

#99

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

#3624

—

#3624

—

C₈×C₁₇

—

#3622

—

#1848

—

#1327

—

C₂²×C₁₇

#324

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

Dic₁₇

yes

Dic₁₇

yes

—

—

—

C₂×C₄×C₈

—

#349

—

C₂×C₁₇

—

C₂×C₁₇

#1325

yes

characteristic

D₁₇

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#3633

yes

characteristic

C₁₇

#7373

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

C₂×#3633

yes

characteristic

C₁₆

—

136

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#3633

yes

characteristic

C₈

—

C₈

—

100

C₈

—

101

C₈

—

136

—

102

C₂²

—

103

C₂²

—

104

C₂²

#11763895

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₂

—

111

C₂

—

112

C₂

#14545821

yes

characteristic

	subgroup	G/H
center	C₂	#14545821
commutator	C₄²×C₁₇	C₂×C₈
Frattini	C₄²	C₂×#3633
Fitting	C₄×C₈×C₁₇	C₈
socle	C₂×C₁₇	#1325
prime radical	C₂²×D₁₇	#101
cosocle	#11763813	C₂²
hypercenter	C₄×C₈	#3633
hypocenter	C₁₇	#7373
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂

#14545821

commutator

C₄²×C₁₇

C₂×C₈

Frattini

C₄²

C₂×#3633

Fitting

C₄×C₈×C₁₇

C₈

C₂×C₁₇

C₂²×D₁₇

C₂²

C₄×C₈

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
75. C₁₇	#7373	semidirect

H ≅ G/N

type

75. C₁₇

#7373

semidirect

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

subgroup	index
#14545824	2
#14544725	2
#7373	17

subgroup

index

#14545824

#14544725

#7373

Subgroups — #17981412

Conjugacy classes of subgroups

Complements

Maximal subgroups