Group #19134187 — subgroups

Subgroups — #19134187

Order 5504.

224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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	#14583304	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583276	C₂	1	1	yes	maximal, characteristic
3	#14583272	C₂	1	2	yes	maximal, complemented
4	#14583246	C₂	1	2	yes	maximal, complemented
5	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621873	—	2	4	no	—
7	C₂×D₃₄₄	—	2	2	no	—
8	#13063325	C₂²	1	2	yes	—
9	#13063322	C₂²	1	2	yes	—
10	#13063259	—	2	2	no	—
11	#13063247	—	2	4	no	—
12	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×D₁₇₂	—	2	2	no	—
16	C₂×D₁₇₂	—	2	2	no	—
17	C₂×D₁₇₂	—	2	2	no	—
18	C₂×Dic₈₆	—	2	2	no	—
19	C₂×C₈×C₄₃	D₄	1	2	yes	—
20	C₂×C₈×C₄₃	D₄	1	2	yes	—
21	C₂×C₈×C₄₃	D₄	1	2	yes	—
22	C₄²×C₄₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	—	2	2	no	—
25	D₃₄₄	—	4	4	no	—
26	#10621873	—	4	8	no	—
27	C₂²×D₄₃	—	4	2	no	—
28	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₄₃	—	4	2	no	—
32	D₁₇₂	—	4	4	no	—
33	D₁₇₂	—	4	4	no	—
34	D₁₇₂	—	4	4	no	—
35	Dic₈₆	—	4	4	no	—
36	C₈×C₄₃	—	2	2	no	—
37	C₈×C₄₃	D₈	1	4	yes	complemented
38	C₈×C₄₃	SD₁₆	1	4	yes	complemented
39	C₂²×C₄₃	#127	1	1	yes	characteristic
40	C₂×D₄₃	—	8	2	no	—
41	C₂×D₄₃	—	8	2	no	—
42	C₂×D₄₃	—	8	2	no	—
43	C₄×C₄₃	C₂×D₈	1	2	yes	—
44	C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
45	C₄×C₄₃	#135	1	2	yes	—
46	Dic₄₃	—	8	2	no	—
47	#1706	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	#492	1	1	yes	characteristic
49	C₂×C₄₃	#493	1	1	yes	characteristic
50	C₂×C₄₃	#495	1	1	yes	characteristic
51	D₄₃	—	16	2	no	—
52	#500	—	43	1	no	—
53	#493	—	43	1	no	—
54	#492	—	43	2	no	—
55	#486	—	43	2	no	—
56	C₈²	D₄₃	1	1	yes	characteristic, complemented
57	C₄₃	#1706	1	1	yes	characteristic, complemented, Sylow
58	C₂×SD₁₆	—	86	4	no	—
59	C₂×D₈	—	86	2	no	—
60	C₄⋊Q₈	—	43	2	no	—
61	#127	—	43	2	no	—
62	#107	—	86	2	no	—
63	#102	—	86	4	no	—
64	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
65	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
66	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
67	C₂×Q₈	—	86	2	no	—
68	C₂×D₄	—	86	2	no	—
69	C₂×D₄	—	86	2	no	—
70	C₂×D₄	—	86	2	no	—
71	SD₁₆	—	172	8	no	—
72	D₈	—	172	4	no	—
73	C₂×C₈	D₁₇₂	1	2	yes	—
74	C₂×C₈	D₁₇₂	1	2	yes	—
75	C₂×C₈	D₁₇₂	1	2	yes	—
76	C₄⋊C₄	—	86	2	no	—
77	C₄⋊C₄	—	86	2	no	—
78	C₄²	C₂²×D₄₃	1	1	yes	characteristic
79	C₂³	—	172	2	no	—
80	Q₈	—	172	4	no	—
81	D₄	—	172	4	no	—
82	D₄	—	172	4	no	—
83	D₄	—	172	4	no	—
84	C₂×C₄	—	172	2	no	—
85	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
86	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
87	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
88	C₈	—	2	2	no	—
89	C₈	#10621873	1	4	yes	complemented
90	C₈	D₃₄₄	1	4	yes	complemented
91	C₂²	—	344	2	no	—
92	C₂²	—	344	2	no	—
93	C₂²	—	344	2	no	—
94	C₂²	#13063322	1	1	yes	characteristic
95	C₄	—	344	2	no	—
96	C₄	C₂×D₃₄₄	1	2	yes	—
97	C₄	C₂×#10621873	1	2	yes	—
98	C₄	#13063347	1	2	yes	—
99	C₂	—	688	2	no	—
100	C₂	#14583272	1	1	yes	characteristic
101	C₂	#14583276	1	1	yes	characteristic
102	C₂	#14583283	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583304

C₂

yes

maximal, characteristic, complemented

#14583276

C₂

yes

maximal, characteristic

#14583272

C₂

yes

maximal, complemented

#14583246

C₂

yes

maximal, complemented

C₈²×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#10621873

—

C₂×D₃₄₄

—

#13063325

C₂²

yes

—

#13063322

C₂²

yes

—

#13063259

—

#13063247

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

D₃₄₄

—

#10621873

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

D₈

yes

complemented

C₈×C₄₃

SD₁₆

yes

complemented

C₂²×C₄₃

#127

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

C₂×D₈

yes

—

C₄×C₄₃

C₂×SD₁₆

yes

—

C₄×C₄₃

#135

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

—

C₈²

D₄₃

yes

characteristic, complemented

C₄₃

#1706

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

#107

—

#102

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

172

—

D₈

—

172

—

C₂×C₈

D₁₇₂

yes

—

C₂×C₈

D₁₇₂

yes

—

C₂×C₈

D₁₇₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

172

—

Q₈

—

172

—

D₄

—

172

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₈

—

C₈

#10621873

yes

complemented

C₈

D₃₄₄

yes

complemented

C₂²

—

344

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

#13063322

yes

characteristic

C₄

—

344

—

C₄

C₂×D₃₄₄

yes

—

C₄

C₂×#10621873

yes

—

C₄

#13063347

yes

—

C₂

—

688

—

100

C₂

#14583272

yes

characteristic

101

C₂

#14583276

yes

characteristic

102

C₂

#14583283

yes

characteristic

	subgroup	G/H
center	C₂²	#13063322
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₈²×C₄₃	C₂
socle	C₂²×C₄₃	#127
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	#1706
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

subgroup

G/H

center

C₂²

#13063322

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₈²×C₄₃

C₂

socle

C₂²×C₄₃

#127

hypercenter

C₈²

D₄₃

hypocenter

C₄₃

#1706

LCS

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈²

N	H ≅ G/N	type
1. #14583304	C₂	semidirect
3. #14583272	C₂	semidirect
4. #14583246	C₂	semidirect
5. C₈²×C₄₃	C₂	semidirect
37. C₈×C₄₃	D₈	semidirect
38. C₈×C₄₃	SD₁₆	semidirect
56. C₈²	D₄₃	semidirect
57. C₄₃	#1706	semidirect
89. C₈	#10621873	semidirect
90. C₈	D₃₄₄	semidirect

H ≅ G/N

type

1. #14583304

C₂

semidirect

3. #14583272

C₂

semidirect

4. #14583246

C₂

semidirect

5. C₈²×C₄₃

C₂

semidirect

37. C₈×C₄₃

D₈

semidirect

38. C₈×C₄₃

SD₁₆

semidirect

56. C₈²

D₄₃

semidirect

57. C₄₃

#1706

semidirect

89. C₈

#10621873

semidirect

90. C₈

D₃₄₄

semidirect

Subgroups — #19134187

Conjugacy classes of subgroups

Complements