Group #25011332 — subgroups

Subgroups — #25011332

Order 11008.

262 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 103 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	#19136868	C₂	1	4	yes	maximal
2	#19134213	C₂	1	1	yes	maximal, characteristic
3	C₈×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1713	C₂	1	1	yes	maximal, characteristic
5	#14583304	—	2	1	no	—
6	#14583304	C₂²	1	2	yes	—
7	#14583279	—	2	1	no	—
8	#14582724	—	2	8	no	—
9	C₄×C₄₃⋊C₁₆	C₂²	1	2	yes	—
10	C₄₃×#500	—	2	1	no	—
11	C₄₃×#500	C₂²	1	2	yes	—
12	C₄₃×#494	—	2	1	no	—
13	C₈²×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₇₂	—	4	2	no	—
15	#13063325	—	2	2	no	—
16	C₂×C₄₃⋊C₁₆	D₄	1	4	yes	—
17	#13063259	—	2	4	no	—
18	#13063259	—	4	2	no	—
19	C₂×Q₁₆×C₄₃	—	4	2	no	—
20	C₄⋊Q₈×C₄₃	—	2	2	no	—
21	#107×C₄₃	—	2	4	no	—
22	#107×C₄₃	—	4	2	no	—
23	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
25	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₂×Q₈×C₄₃	—	4	2	no	—
27	C₂×Dic₈₆	—	4	2	no	—
28	Q₁₆×C₄₃	—	8	4	no	—
29	C₂×C₈×C₄₃	D₈	1	2	yes	—
30	C₂×C₈×C₄₃	D₈	1	2	yes	—
31	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
32	C₄⋊C₄×C₄₃	—	4	2	no	—
33	C₄⋊C₄×C₄₃	—	4	2	no	—
34	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₄⋊Dic₄₃	—	4	2	no	—
36	C₄⋊Dic₄₃	—	4	2	no	—
37	Dic₁₇₂	—	8	4	no	—
38	C₄₃⋊C₁₆	Q₁₆	1	8	yes	complemented
39	Q₈×C₄₃	—	8	4	no	—
40	C₂×C₄×C₄₃	—	8	2	no	—
41	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
43	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
44	C₂×Dic₄₃	—	8	2	no	—
45	Dic₈₆	—	8	4	no	—
46	C₈×C₄₃	D₁₆	1	4	yes	—
47	C₈×C₄₃	Q₃₂	1	4	yes	—
48	C₈×C₄₃	C₂×Q₁₆	1	4	yes	—
49	#12521	—	43	1	no	maximal, Sylow
50	C₂²×C₄₃	#493	1	1	yes	characteristic
51	C₄×C₄₃	—	16	2	no	—
52	C₄×C₄₃	#494	1	2	yes	—
53	C₄×C₄₃	C₂×D₁₆	1	2	yes	—
54	C₄×C₄₃	C₂×Q₃₂	1	2	yes	—
55	Dic₄₃	—	16	2	no	—
56	#2252	—	43	4	no	—
57	#1713	—	43	1	no	—
58	#1713	D₄₃	1	1	yes	characteristic
59	C₈×C₁₆	—	43	1	no	—
60	C₂×C₄₃	#1713	1	1	yes	characteristic
61	C₂×C₄₃	#2246	1	1	yes	characteristic
62	C₂×C₄₃	#2247	1	1	yes	characteristic
63	#500	—	2	1	no	—
64	#500	—	43	2	no	—
65	#500	—	86	1	no	—
66	#500	C₂×D₄₃	1	2	yes	—
67	#494	—	2	1	no	—
68	#494	—	86	1	no	—
69	#366	—	86	8	no	—
70	C₄×C₁₆	—	43	2	no	—
71	C₈²	C₂×D₄₃	1	1	yes	characteristic
72	C₄₃	#12521	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₁₆	—	4	2	no	—
74	C₂×Q₁₆	—	172	2	no	—
75	C₄⋊Q₈	—	2	2	no	—
76	C₄⋊Q₈	—	86	2	no	—
77	C₂×C₁₆	—	43	4	no	—
78	#107	—	2	4	no	—
79	#107	—	4	2	no	—
80	#107	—	86	4	no	—
81	#107	—	172	2	no	—
82	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
83	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
84	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
85	C₂×Q₈	—	4	2	no	—
86	C₂×Q₈	—	172	2	no	—
87	Q₁₆	—	8	4	no	—
88	Q₁₆	—	344	4	no	—
89	C₂×C₈	#10621882	1	2	yes	—
90	C₂×C₈	#10621882	1	2	yes	—
91	C₂×C₈	D₄×D₄₃	1	2	yes	—
92	C₄⋊C₄	—	4	2	no	—
93	C₄⋊C₄	—	4	2	no	—
94	C₄⋊C₄	—	172	2	no	—
95	C₄⋊C₄	—	172	2	no	—
96	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
97	C₁₆	—	43	8	no	—
98	Q₈	—	8	4	no	—
99	Q₈	—	344	4	no	—
100	C₂×C₄	—	8	2	no	—
101	C₂×C₄	—	344	2	no	—
102	C₂×C₄	#13063321	1	1	yes	characteristic
103	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
104	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
105	C₈	#13063266	1	4	yes	—
106	C₈	#13063271	1	4	yes	—
107	C₈	Q₁₆×D₄₃	1	4	yes	—
108	C₂²	#14583275	1	1	yes	characteristic
109	C₄	—	16	2	no	—
110	C₄	—	688	2	no	—
111	C₄	#14583277	1	2	yes	—
112	C₄	C₂×#13063266	1	2	yes	—
113	C₄	C₂×#13063271	1	2	yes	—
114	C₂	#19134211	1	1	yes	characteristic
115	C₂	#19136844	1	1	yes	characteristic
116	C₂	#19136847	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136868

C₂

yes

maximal

#19134213

C₂

yes

maximal, characteristic

C₈×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic

C₄₃×#1713

C₂

yes

maximal, characteristic

#14583304

—

#14583304

C₂²

yes

—

#14583279

—

#14582724

—

C₄×C₄₃⋊C₁₆

C₂²

yes

—

C₄₃×#500

—

C₄₃×#500

C₂²

yes

—

C₄₃×#494

—

C₈²×C₄₃

C₂²

yes

characteristic

C₂×Dic₁₇₂

—

#13063325

—

C₂×C₄₃⋊C₁₆

D₄

yes

—

#13063259

—

#13063259

—

C₂×Q₁₆×C₄₃

—

C₄⋊Q₈×C₄₃

—

#107×C₄₃

—

#107×C₄₃

—

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

D₈

yes

—

C₂×C₈×C₄₃

D₈

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

C₄₃⋊C₁₆

Q₁₆

yes

complemented

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

D₁₆

yes

—

C₈×C₄₃

Q₃₂

yes

—

C₈×C₄₃

C₂×Q₁₆

yes

—

—

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

#494

yes

—

C₄×C₄₃

C₂×D₁₆

yes

—

C₄×C₄₃

C₂×Q₃₂

yes

—

Dic₄₃

—

#2252

—

#1713

—

#1713

D₄₃

yes

characteristic

C₈×C₁₆

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

C₂×D₄₃

yes

—

#494

—

#494

—

#366

—

C₄×C₁₆

—

C₈²

C₂×D₄₃

yes

characteristic

C₄₃

#12521

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

172

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₁₆

—

—

—

—

—

172

—

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

C₄×C₈

C₂²×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

172

—

Q₁₆

—

Q₁₆

—

344

—

C₂×C₈

#10621882

yes

—

C₂×C₈

#10621882

yes

—

C₂×C₈

D₄×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

344

—

100

C₂×C₄

—

101

C₂×C₄

—

344

—

102

C₂×C₄

#13063321

yes

characteristic

103

C₂×C₄

C₂×#10621882

yes

characteristic

104

C₂×C₄

C₂×#10621882

yes

characteristic

105

C₈

#13063266

yes

—

106

C₈

#13063271

yes

—

107

C₈

Q₁₆×D₄₃

yes

—

108

C₂²

#14583275

yes

characteristic

109

C₄

—

110

C₄

—

688

—

111

C₄

#14583277

yes

—

112

C₄

C₂×#13063266

yes

—

113

C₄

C₂×#13063271

yes

—

114

C₂

#19134211

yes

characteristic

115

C₂

#19136844

yes

characteristic

116

C₂

#19136847

yes

characteristic

	subgroup	G/H
center	C₂²	#14583275
commutator, cosocle	C₄×C₈×C₄₃	C₂³
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×#1713	C₂
socle, prime radical	C₂²×C₄₃	#493
hypercenter	#1713	D₄₃
hypocenter	C₄₃	#12521
LCS	G ▷ C₄×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

subgroup

G/H

center

C₂²

#14583275

commutator, cosocle

C₄×C₈×C₄₃

C₂³

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₄₃×#1713

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

N	H ≅ G/N	type
38. C₄₃⋊C₁₆	Q₁₆	semidirect
72. C₄₃	#12521	semidirect

H ≅ G/N

type

38. C₄₃⋊C₁₆

Q₁₆

semidirect

72. C₄₃

#12521

semidirect

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

subgroup	index
#19136868	2
#19134213	2
C₈×C₄₃⋊C₁₆	2
C₄₃×#1713	2
#12521	43

subgroup

index

#19136868

#19134213

C₈×C₄₃⋊C₁₆

C₄₃×#1713

#12521

Subgroups — #25011332

Conjugacy classes of subgroups

Complements

Maximal subgroups