Group #21426204 — subgroups

Subgroups — #21426204

Order 7552.

150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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	C₂×Dic₄₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837643	C₂	1	2	yes	maximal
3	#16837230	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837207	C₂	1	2	yes	maximal, complemented
5	C₂×M₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₃₆	C₂²	1	2	yes	—
7	#14273706	—	2	2	no	—
8	Dic₄₇₂	—	2	2	no	—
9	#14273661	C₂²	1	2	yes	—
10	#14273652	—	2	2	no	—
11	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
12	M₃₂×C₅₉	—	2	2	no	—
13	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
16	C₂×Dic₁₁₈	—	2	2	no	—
17	C₂×C₈×C₅₉	—	2	1	no	—
18	C₂×C₈×C₅₉	—	2	1	no	—
19	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
21	C₂²⋊Dic₅₉	—	4	2	no	—
22	C₄⋊Dic₅₉	—	2	2	no	—
23	Dic₅₉⋊C₄	—	4	2	no	—
24	Dic₂₃₆	—	2	2	no	—
25	Dic₂₃₆	—	2	2	no	—
26	C₁₆×C₅₉	—	2	1	no	—
27	C₁₆×C₅₉	D₄	1	2	yes	—
28	C₂³×C₅₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₅₉	—	2	1	no	—
30	C₂×C₄×C₅₉	—	2	1	no	—
31	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₅₉	—	4	2	no	—
34	C₂×Dic₅₉	—	4	2	no	—
35	Dic₁₁₈	—	4	2	no	—
36	Dic₁₁₈	—	4	2	no	—
37	C₈×C₅₉	—	2	1	no	—
38	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₅₉	#41	1	1	yes	characteristic
40	C₂²×C₅₉	—	2	1	no	—
41	C₂²×C₅₉	—	2	2	no	—
42	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
43	C₄×C₅₉	—	2	1	no	—
44	C₄×C₅₉	#121	1	1	yes	characteristic
45	C₄×C₅₉	#135	1	1	yes	characteristic
46	Dic₅₉	—	8	2	no	—
47	Dic₅₉	—	8	2	no	—
48	#2219	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	—	4	1	no	—
50	C₂×C₅₉	#466	1	1	yes	characteristic
51	C₂×C₅₉	#510	1	2	yes	—
52	C₂×Q₃₂	—	59	1	no	—
53	C₂×M₃₂	D₅₉	1	1	yes	characteristic
54	#467	—	59	2	no	—
55	#367	—	59	1	no	—
56	#358	—	59	2	no	—
57	C₅₉	#2219	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	—	59	2	no	—
59	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
60	C₂²⋊Q₈	—	118	2	no	—
61	Q₃₂	—	118	2	no	—
62	M₃₂	—	2	2	no	—
63	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
64	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
65	#107	—	59	2	no	—
66	#103	—	118	2	no	—
67	C₂×Q₈	—	118	2	no	—
68	C₂²×C₄	D₂₃₆	1	1	yes	characteristic
69	Q₁₆	—	118	2	no	—
70	Q₁₆	—	118	2	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	D₂₃₆	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
75	C₄⋊C₄	—	118	2	no	—
76	C₄⋊C₄	—	236	2	no	—
77	C₂²⋊C₄	—	236	2	no	—
78	C₁₆	—	2	1	no	—
79	C₁₆	C₂²⋊D₅₉	1	2	yes	—
80	C₂³	D₄₇₂	1	1	yes	characteristic
81	Q₈	—	236	2	no	—
82	Q₈	—	236	2	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	236	2	no	—
86	C₂×C₄	—	236	2	no	—
87	C₂×C₄	D₄₇₂	1	1	yes	characteristic
88	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	#11745685	1	1	yes	characteristic
91	C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
92	C₂²	—	2	1	no	—
93	C₂²	—	2	2	no	—
94	C₂²	C₂×D₄₇₂	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	472	2	no	—
97	C₄	—	472	2	no	—
98	C₄	#14273701	1	1	yes	characteristic
99	C₄	#14273749	1	1	yes	characteristic
100	C₂	—	4	1	no	—
101	C₂	#16837638	1	1	yes	characteristic
102	C₂	#16837845	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₄₇₂

C₂

yes

maximal, characteristic, complemented

#16837643

C₂

yes

maximal

#16837230

C₂

yes

maximal, characteristic, complemented

#16837207

C₂

yes

maximal, complemented

C₂×M₃₂×C₅₉

C₂

yes

maximal, characteristic

C₂×Dic₂₃₆

C₂²

yes

—

#14273706

—

Dic₄₇₂

—

#14273661

C₂²

yes

—

#14273652

—

C₂²×C₈×C₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

—

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

Dic₂₃₆

—

Dic₂₃₆

—

C₁₆×C₅₉

—

C₁₆×C₅₉

D₄

yes

—

C₂³×C₅₉

D₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

D₈

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

#41

yes

characteristic

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

Dic₅₉

—

#2219

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#466

yes

characteristic

C₂×C₅₉

#510

yes

—

C₂×Q₃₂

—

C₂×M₃₂

D₅₉

yes

—

—

—

C₅₉

#2219

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂²×C₈

C₂×D₅₉

yes

characteristic

C₂²⋊Q₈

—

118

—

Q₃₂

—

118

—

M₃₂

—

C₂×C₁₆

C₂×D₅₉

yes

characteristic

C₂×C₁₆

C₂×D₅₉

yes

characteristic

#107

—

#103

—

118

—

C₂×Q₈

—

118

—

C₂²×C₄

D₂₃₆

yes

characteristic

Q₁₆

—

118

—

Q₁₆

—

118

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₂₃₆

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₁₆

—

C₁₆

C₂²⋊D₅₉

yes

—

C₂³

D₄₇₂

yes

characteristic

Q₈

—

236

—

Q₈

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

D₄₇₂

yes

characteristic

C₂×C₄

C₂×D₂₃₆

yes

characteristic

C₈

—

C₈

#11745685

yes

characteristic

C₈

C₂×C₂²⋊D₅₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

C₂×D₄₇₂

yes

characteristic

C₄

—

C₄

—

472

—

C₄

—

472

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#16837638

yes

characteristic

102

C₂

#16837845

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄₇₂
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₂×M₃₂×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	C₂×M₃₂	D₅₉
hypocenter	C₅₉	#2219
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

C₂×D₄₇₂

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₂×M₃₂×C₅₉

C₂

socle

C₂²×C₅₉

C₂×D₈

hypercenter

C₂×M₃₂

D₅₉

hypocenter

C₅₉

#2219

LCS

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
1. C₂×Dic₄₇₂	C₂	semidirect
3. #16837230	C₂	semidirect
4. #16837207	C₂	semidirect
57. C₅₉	#2219	semidirect

H ≅ G/N

type

1. C₂×Dic₄₇₂

C₂

semidirect

3. #16837230

C₂

semidirect

4. #16837207

C₂

semidirect

57. C₅₉

#2219

semidirect

Subgroups — #21426204

Conjugacy classes of subgroups

Complements