Group #17948826 — subgroups

Subgroups — #17948826

Order 4352.

148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 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	#14545158	C₂	1	2	yes	maximal
2	#14530542	C₂	1	1	yes	maximal, characteristic
3	#11763731	—	2	2	no	—
4	#11763705	—	2	2	no	—
5	#11763702	C₄	1	4	yes	—
6	C₂×#10587483	C₄	1	1	yes	characteristic
7	#11762764	C₂²	1	1	yes	characteristic
8	#11762627	—	2	2	no	—
9	C₂²×C₁₆×C₁₇	C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
11	#10587612	Q₈	1	1	yes	characteristic
12	C₂×#63223	D₄	1	1	yes	characteristic
13	#10587538	—	2	4	no	—
14	C₂×C₁₆×C₁₇	—	2	1	no	—
15	C₂×C₁₆×C₁₇	—	4	1	no	—
16	#10587486	C₂×C₄	1	2	yes	—
17	C₈×Dic₁₇	D₄	1	2	yes	—
18	#10587483	—	4	1	no	—
19	C₂×#63214	—	2	1	no	—
20	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₇	—	2	1	no	—
22	C₂×C₈×C₁₇	—	2	1	no	—
23	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
24	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊Dic₁₇	—	2	1	no	—
26	C₄⋊Dic₁₇	—	2	1	no	—
27	C₄×Dic₁₇	C₄⋊C₄	1	2	yes	—
28	#63223	—	4	1	no	—
29	C₂×#3622	C₂²⋊C₄	1	2	yes	—
30	#63216	—	4	4	no	—
31	C₁₆×C₁₇	—	4	1	no	—
32	#63214	—	4	1	no	—
33	#7239	—	17	1	no	maximal, Sylow
34	C₂³×C₁₇	#108	1	1	yes	characteristic
35	C₂×C₄×C₁₇	—	2	1	no	—
36	C₂×C₄×C₁₇	—	2	1	no	—
37	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
38	C₂×C₄×C₁₇	#108	1	1	yes	characteristic
39	C₂×Dic₁₇	—	2	2	no	—
40	C₈×C₁₇	—	2	1	no	—
41	C₈×C₁₇	#100	1	1	yes	characteristic
42	C₈×C₁₇	#101	1	1	yes	characteristic
43	#3622	—	2	2	no	—
44	#2166	—	17	2	no	—
45	#2151	—	17	1	no	—
46	C₂²×C₁₇	—	2	1	no	—
47	C₂²×C₁₇	—	4	1	no	—
48	C₂²×C₁₇	#341	1	1	yes	characteristic
49	C₄×C₁₇	—	2	1	no	—
50	C₄×C₁₇	H(3,ℤ/4)	1	1	yes	characteristic
51	C₄×C₁₇	#343	1	1	yes	characteristic
52	Dic₁₇	—	4	2	no	—
53	C₂×M₃₂	—	17	1	no	—
54	C₂²×C₁₆	#595	1	1	yes	characteristic
55	#405	—	17	1	no	—
56	#364	—	34	2	no	—
57	C₄⋊C₁₆	—	34	2	no	—
58	#349	—	34	2	no	—
59	#347	—	17	4	no	—
60	C₂×C₁₇	—	2	1	no	—
61	C₂×C₁₇	—	4	1	no	—
62	C₂×C₁₇	#1290	1	1	yes	characteristic
63	C₂×M₁₆	—	17	1	no	—
64	C₂²×C₈	C₂×#595	1	1	yes	characteristic
65	#117	—	17	1	no	—
66	M₃₂	—	34	4	no	—
67	M₃₂	—	68	1	no	—
68	C₂×C₁₆	—	2	1	no	—
69	C₂×C₁₆	—	4	1	no	—
70	C₂×C₁₆	—	34	1	no	—
71	#97	—	17	2	no	—
72	C₄×C₈	—	17	2	no	—
73	C₁₇	#7239	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
75	M₁₆	—	68	1	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	—	17	2	no	—
79	C₂×C₈	C₄×#595	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
81	C₄⋊C₄	—	34	1	no	—
82	C₂²⋊C₄	—	34	1	no	—
83	C₄²	—	17	2	no	—
84	C₁₆	—	4	1	no	—
85	C₁₆	—	68	4	no	—
86	C₁₆	—	68	1	no	—
87	C₂³	#10587536	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	34	2	no	—
91	C₂×C₄	#10587535	1	1	yes	characteristic
92	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	34	2	no	—
95	C₈	#10587545	1	1	yes	characteristic
96	C₈	#10587553	1	1	yes	characteristic
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	#11763685	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	68	2	no	—
102	C₄	#11763677	1	1	yes	characteristic
103	C₄	#11763689	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	4	1	no	—
106	C₂	#14543649	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545158

C₂

yes

maximal

#14530542

C₂

yes

maximal, characteristic

#11763731

—

#11763705

—

#11763702

C₄

yes

—

C₂×#10587483

C₄

yes

characteristic

#11762764

C₂²

yes

characteristic

#11762627

—

C₂²×C₁₆×C₁₇

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

#10587612

Q₈

yes

characteristic

C₂×#63223

D₄

yes

characteristic

#10587538

—

C₂×C₁₆×C₁₇

—

C₂×C₁₆×C₁₇

—

#10587486

C₂×C₄

yes

—

C₈×Dic₁₇

D₄

yes

—

#10587483

—

C₂×#63214

—

C₂²×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄×Dic₁₇

C₄⋊C₄

yes

—

#63223

—

C₂×#3622

C₂²⋊C₄

yes

—

#63216

—

C₁₆×C₁₇

—

—

—

C₂³×C₁₇

yes

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×Dic₁₇

—

C₈×C₁₇

—

C₈×C₁₇

yes

C₈×C₁₇

yes

—

—

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

#341

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

C₂×M₃₂

—

C₂²×C₁₆

yes

—

—

C₄⋊C₁₆

—

#349

—

#347

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

#1290

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂×#595

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₁₇

#7239

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄⋊#595

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×#595

yes

characteristic

C₂×C₈

C₂²⋊#595

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

#10587536

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10587535

yes

characteristic

C₂×C₄

(C₂×#595)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

#11763685

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

#11763677

yes

characteristic

103

C₄

#11763689

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

#14543649

yes

characteristic

	subgroup	G/H
center	C₄	#11763677
commutator	C₂×C₈×C₁₇	C₄²
Frattini	C₂²×C₈	C₂×#595
Fitting	C₂²×C₁₆×C₁₇	C₄
socle	C₂×C₁₇	#1290
prime radical	C₂³×C₁₇	#108
cosocle	#11762764	C₂²
hypercenter	C₂²×C₁₆	#595
hypocenter	C₁₇	#7239
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₄

#11763677

commutator

C₂×C₈×C₁₇

C₄²

Frattini

C₂²×C₈

C₂×#595

Fitting

C₂²×C₁₆×C₁₇

C₄

C₂×C₁₇

C₂³×C₁₇

C₂²

C₂²×C₁₆

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
73. C₁₇	#7239	semidirect

H ≅ G/N

type

73. C₁₇

#7239

semidirect

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

subgroup	index
#14545158	2
#14530542	2
#7239	17

subgroup

index

#14545158

#14530542

#7239

Subgroups — #17948826

Conjugacy classes of subgroups

Complements

Maximal subgroups