Group #31918438 — subgroups

Subgroups — #31918438

Order 18176.

194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 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	#22590619	C₂	1	1	yes	maximal, characteristic, complemented
2	#22586518	C₂	1	4	yes	maximal, complemented
3	#22586474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#2246	C₂	1	1	yes	maximal, characteristic
5	#17986401	—	2	1	no	—
6	C₂×C₇₁⋊C₃₂	C₂²	1	2	yes	—
7	#17985827	—	2	1	no	—
8	#17985825	C₂²	1	2	yes	—
9	C₂×D₁₆×C₇₁	—	2	1	no	—
10	C₂×D₁₆×C₇₁	C₂²	1	2	yes	—
11	#493×C₇₁	—	2	1	no	—
12	C₄×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
13	#14556120	—	4	1	no	—
14	#14556062	—	2	2	no	—
15	#14556060	—	4	1	no	—
16	C₇₁⋊C₃₂	—	2	2	no	—
17	C₂×D₈×C₇₁	—	2	2	no	—
18	C₂×D₈×C₇₁	—	4	1	no	—
19	#127×C₇₁	—	4	1	no	—
20	D₁₆×C₇₁	—	2	4	no	—
21	D₁₆×C₇₁	—	4	2	no	—
22	C₂×C₁₆×C₇₁	D₄	1	1	yes	characteristic
23	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
24	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
25	C₄⋊Dic₇₁	—	4	2	no	—
26	Dic₇₁⋊C₄	—	8	2	no	—
27	C₂×D₄×C₇₁	—	4	2	no	—
28	C₂×D₄×C₇₁	—	8	2	no	—
29	D₈×C₇₁	—	4	2	no	—
30	D₈×C₇₁	—	4	2	no	—
31	D₈×C₇₁	—	8	2	no	—
32	C₂×C₈×C₇₁	D₈	1	1	yes	characteristic
33	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
34	C₄²×C₇₁	D₈	1	1	yes	characteristic
35	C₁₆×C₇₁	SD₁₆	1	2	yes	—
36	C₁₆×C₇₁	#41	1	2	yes	—
37	C₂³×C₇₁	—	8	2	no	—
38	D₄×C₇₁	—	8	2	no	—
39	D₄×C₇₁	—	8	2	no	—
40	D₄×C₇₁	—	16	4	no	—
41	C₂×C₄×C₇₁	D₁₆	1	2	yes	—
42	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
43	C₂×Dic₇₁	—	8	2	no	—
44	C₈×C₇₁	SD₃₂	1	2	yes	—
45	C₈×C₇₁	#124	1	1	yes	characteristic
46	C₈×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
47	C₂²×C₇₁	—	16	2	no	—
48	C₂²×C₇₁	—	16	4	no	—
49	C₂²×C₇₁	C₂×D₁₆	1	1	yes	characteristic
50	C₄×C₇₁	—	2	2	no	—
51	C₄×C₇₁	#486	1	1	yes	characteristic
52	C₄×C₇₁	C₂×SD₃₂	1	1	yes	characteristic
53	Dic₇₁	—	16	2	no	—
54	#13723	—	71	1	no	maximal, Sylow
55	C₂×C₇₁	—	32	2	no	—
56	C₂×C₇₁	#2240	1	1	yes	characteristic
57	C₂×C₇₁	#2263	1	2	yes	—
58	#2253	—	71	1	no	—
59	#2246	D₇₁	1	1	yes	characteristic
60	#1415	—	71	4	no	—
61	#1397	—	71	1	no	—
62	C₇₁	#13723	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₁₆	—	2	1	no	—
64	C₂×D₁₆	C₂×D₇₁	1	2	yes	—
65	#499	—	142	1	no	—
66	#493	—	2	1	no	—
67	C₂×C₃₂	—	71	2	no	—
68	#367	—	142	1	no	—
69	#366	—	71	2	no	—
70	C₄×C₁₆	C₂×D₇₁	1	1	yes	characteristic
71	C₂×D₈	—	2	2	no	—
72	C₂×D₈	—	4	1	no	—
73	#127	—	4	1	no	—
74	#125	—	284	1	no	—
75	D₁₆	—	2	4	no	—
76	D₁₆	—	4	2	no	—
77	C₂×C₁₆	C₂²⋊D₇₁	1	1	yes	characteristic
78	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
79	#107	—	142	2	no	—
80	#106	—	284	1	no	—
81	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
82	C₃₂	—	142	2	no	—
83	C₂×D₄	—	4	2	no	—
84	C₂×D₄	—	8	2	no	—
85	D₈	—	4	2	no	—
86	D₈	—	4	2	no	—
87	D₈	—	8	2	no	—
88	C₂×C₈	#11765850	1	1	yes	characteristic
89	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
90	C₄⋊C₄	—	284	2	no	—
91	C₄⋊C₄	—	568	2	no	—
92	C₄²	#11765850	1	1	yes	characteristic
93	C₁₆	#11765853	1	2	yes	—
94	C₁₆	#11765864	1	2	yes	—
95	C₂³	—	8	2	no	—
96	D₄	—	8	2	no	—
97	D₄	—	8	2	no	—
98	D₄	—	16	4	no	—
99	C₂×C₄	—	568	2	no	—
100	C₂×C₄	#14556069	1	2	yes	—
101	C₂×C₄	C₂×#11765850	1	1	yes	characteristic
102	C₈	#14556072	1	2	yes	—
103	C₈	#14556115	1	1	yes	characteristic
104	C₈	C₂×#11765853	1	1	yes	characteristic
105	C₂²	—	16	2	no	—
106	C₂²	—	16	4	no	—
107	C₂²	C₂×#14556069	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	—	1136	2	no	—
110	C₄	#17986345	1	1	yes	characteristic
111	C₄	C₂×#14556072	1	1	yes	characteristic
112	C₂	—	32	2	no	—
113	C₂	#22590563	1	1	yes	characteristic
114	C₂	#22590653	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22590619

C₂

yes

maximal, characteristic, complemented

#22586518

C₂

yes

maximal, complemented

#22586474

C₂

yes

maximal, characteristic, complemented

C₇₁×#2246

C₂

yes

maximal, characteristic

#17986401

—

C₂×C₇₁⋊C₃₂

C₂²

yes

—

#17985827

—

#17985825

C₂²

yes

—

C₂×D₁₆×C₇₁

—

C₂×D₁₆×C₇₁

C₂²

yes

—

#493×C₇₁

—

C₄×C₁₆×C₇₁

C₂²

yes

—

—

—

C₇₁⋊C₃₂

—

C₂×D₈×C₇₁

—

C₂×D₈×C₇₁

—

#127×C₇₁

—

D₁₆×C₇₁

—

D₁₆×C₇₁

—

C₂×C₁₆×C₇₁

D₄

yes

characteristic

C₂×C₁₆×C₇₁

C₂³

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

D₈×C₇₁

—

D₈×C₇₁

—

D₈×C₇₁

—

C₂×C₈×C₇₁

D₈

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

D₈

yes

characteristic

C₁₆×C₇₁

SD₁₆

yes

—

C₁₆×C₇₁

#41

yes

—

C₂³×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

D₁₆

yes

—

C₂×C₄×C₇₁

C₂×D₈

yes

characteristic

C₂×Dic₇₁

—

C₈×C₇₁

SD₃₂

yes

—

C₈×C₇₁

#124

yes

characteristic

C₈×C₇₁

C₂×SD₁₆

yes

characteristic

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×D₁₆

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

#486

yes

characteristic

C₄×C₇₁

C₂×SD₃₂

yes

characteristic

Dic₇₁

—

#13723

—

maximal, Sylow

C₂×C₇₁

—

C₂×C₇₁

#2240

yes

characteristic

C₂×C₇₁

#2263

yes

—

#2253

—

#2246

D₇₁

yes

characteristic

#1415

—

#1397

—

C₇₁

#13723

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

C₂×D₁₆

C₂×D₇₁

yes

—

#499

—

142

—

#493

—

C₂×C₃₂

—

#367

—

142

—

#366

—

C₄×C₁₆

C₂×D₇₁

yes

characteristic

C₂×D₈

—

C₂×D₈

—

#127

—

#125

—

284

—

D₁₆

—

D₁₆

—

C₂×C₁₆

C₂²⋊D₇₁

yes

characteristic

C₂×C₁₆

C₂²×D₇₁

yes

characteristic

#107

—

142

—

#106

—

284

—

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

C₃₂

—

142

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

C₂×C₈

#11765850

yes

characteristic

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

C₄⋊C₄

—

284

—

C₄⋊C₄

—

568

—

C₄²

#11765850

yes

characteristic

C₁₆

#11765853

yes

—

C₁₆

#11765864

yes

—

C₂³

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

568

—

100

C₂×C₄

#14556069

yes

—

101

C₂×C₄

C₂×#11765850

yes

characteristic

102

C₈

#14556072

yes

—

103

C₈

#14556115

yes

characteristic

104

C₈

C₂×#11765853

yes

characteristic

105

C₂²

—

106

C₂²

—

107

C₂²

C₂×#14556069

yes

characteristic

108

C₄

—

109

C₄

—

1136

—

110

C₄

#17986345

yes

characteristic

111

C₄

C₂×#14556072

yes

characteristic

112

C₂

—

113

C₂

#22590563

yes

characteristic

114

C₂

#22590653

yes

—

	subgroup	G/H
center	C₂²	C₂×#14556069
commutator, cosocle	C₂×C₁₆×C₇₁	C₂³
Frattini	C₂×C₁₆	C₂²×D₇₁
Fitting, prime radical	C₇₁×#2246	C₂
socle	C₂²×C₇₁	C₂×D₁₆
hypercenter	#2246	D₇₁
hypocenter	C₇₁	#13723
LCS	G ▷ C₂×C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2246

subgroup

G/H

center

C₂²

C₂×#14556069

commutator, cosocle

C₂×C₁₆×C₇₁

C₂³

Frattini

C₂×C₁₆

C₂²×D₇₁

Fitting, prime radical

C₇₁×#2246

C₂

socle

C₂²×C₇₁

C₂×D₁₆

D₇₁

C₇₁

G ▷ C₂×C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2246

N	H ≅ G/N	type
1. #22590619	C₂	semidirect
2. #22586518	C₂	semidirect
3. #22586474	C₂	semidirect
62. C₇₁	#13723	semidirect

H ≅ G/N

type

1. #22590619

C₂

semidirect

2. #22586518

C₂

semidirect

3. #22586474

C₂

semidirect

62. C₇₁

#13723

semidirect

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

subgroup	index
#22590619	2
#22586518	2
#22586474	2
C₇₁×#2246	2
#13723	71

subgroup

index

C₇₁×#2246

Subgroups — #31918438

Conjugacy classes of subgroups

Complements

Maximal subgroups