Group #21426367 — subgroups

Subgroups — #21426367

Order 7552.

178 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 61 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	2	yes	maximal, complemented
2	C₂×#14273672	C₂	1	2	yes	maximal
3	#16837786	C₂	1	1	yes	maximal, characteristic
4	#16837782	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₃₆	—	2	1	no	—
7	C₂×Dic₂₃₆	C₂²	1	2	yes	—
8	C₂×Dic₂₃₆	C₂²	1	1	yes	characteristic
9	C₂×#11745660	—	2	1	no	—
10	C₂×D₄₇₂	C₂²	1	1	yes	characteristic
11	#14273727	—	2	1	no	—
12	#14273715	—	2	1	no	—
13	Dic₄₇₂	—	2	4	no	—
14	#14273672	—	2	4	no	—
15	C₂×C₁₆×C₅₉	C₂²	1	2	yes	—
16	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×D₂₃₆	—	2	1	no	—
18	C₂×Dic₁₁₈	—	2	1	no	—
19	C₂×Dic₁₁₈	—	2	2	no	—
20	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
22	C₄²×C₅₉	D₄	1	1	yes	characteristic
23	(C₂×D₅₉)⋊C₄	—	4	2	no	—
24	C₄⋊Dic₅₉	—	4	2	no	—
25	Dic₂₃₆	—	2	2	no	—
26	Dic₂₃₆	—	2	2	no	—
27	Dic₂₃₆	—	2	2	no	—
28	Dic₂₃₆	—	4	2	no	—
29	D₄₇₂	—	2	2	no	—
30	#11745660	—	4	2	no	—
31	C₁₆×C₅₉	D₄	1	4	yes	—
32	C₂²×D₅₉	—	4	1	no	—
33	C₂×C₄×C₅₉	D₈	1	2	yes	—
34	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₅₉	—	4	2	no	—
36	C₂×Dic₅₉	—	4	1	no	—
37	D₂₃₆	—	4	1	no	—
38	D₂₃₆	—	4	1	no	—
39	Dic₁₁₈	—	4	2	no	—
40	Dic₁₁₈	—	4	1	no	—
41	Dic₁₁₈	—	4	1	no	—
42	Dic₁₁₈	—	4	2	no	—
43	C₈×C₅₉	D₈	1	2	yes	—
44	C₈×C₅₉	C₂×D₄	1	2	yes	—
45	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
46	C₂×D₅₉	—	8	1	no	—
47	C₂×D₅₉	—	8	2	no	—
48	C₄×C₅₉	—	2	2	no	—
49	C₄×C₅₉	#127	1	1	yes	characteristic
50	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
51	Dic₅₉	—	8	1	no	—
52	Dic₅₉	—	8	2	no	—
53	#2251	—	59	1	no	maximal, Sylow
54	C₂×C₅₉	#493	1	1	yes	characteristic
55	C₂×C₅₉	#510	1	2	yes	—
56	D₅₉	—	16	1	no	—
57	C₂×Q₃₂	—	59	2	no	—
58	C₂×SD₃₂	—	59	2	no	—
59	#495	—	59	1	no	—
60	#494	—	59	1	no	—
61	#346	D₅₉	1	1	yes	characteristic, complemented
62	C₅₉	#2251	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	59	2	no	—
64	C₂×Q₁₆	—	59	1	no	—
65	C₂×Q₁₆	—	118	1	no	—
66	C₂×SD₁₆	—	118	1	no	—
67	C₂×D₈	—	59	1	no	—
68	C₄⋊Q₈	—	118	1	no	—
69	#124	—	118	1	no	—
70	Q₃₂	—	118	4	no	—
71	SD₃₂	—	118	4	no	—
72	C₂×C₁₆	C₂×D₅₉	1	2	yes	—
73	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
74	C₂×Q₈	—	118	1	no	—
75	C₂×Q₈	—	118	2	no	—
76	C₂×D₄	—	118	1	no	—
77	Q₁₆	—	118	2	no	—
78	Q₁₆	—	118	2	no	—
79	Q₁₆	—	118	2	no	—
80	Q₁₆	—	236	2	no	—
81	SD₁₆	—	236	2	no	—
82	D₈	—	118	2	no	—
83	C₂×C₈	D₂₃₆	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
85	C₄⋊C₄	—	236	2	no	—
86	C₂²⋊C₄	—	236	2	no	—
87	C₄²	D₂₃₆	1	1	yes	characteristic
88	C₁₆	D₂₃₆	1	4	yes	—
89	C₂³	—	236	1	no	—
90	Q₈	—	236	2	no	—
91	Q₈	—	236	1	no	—
92	Q₈	—	236	1	no	—
93	Q₈	—	236	2	no	—
94	D₄	—	236	1	no	—
95	D₄	—	236	1	no	—
96	C₂×C₄	—	236	1	no	—
97	C₂×C₄	—	236	2	no	—
98	C₂×C₄	D₄₇₂	1	2	yes	—
99	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
100	C₈	D₄₇₂	1	2	yes	—
101	C₈	C₂×D₂₃₆	1	2	yes	—
102	C₂²	—	472	1	no	—
103	C₂²	—	472	2	no	—
104	C₂²	C₂×D₄₇₂	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	472	1	no	—
107	C₄	—	472	2	no	—
108	C₄	#14273724	1	1	yes	characteristic
109	C₄	C₂×D₄₇₂	1	1	yes	characteristic
110	C₂	—	944	1	no	—
111	C₂	#16837779	1	1	yes	characteristic
112	C₂	#16837845	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₄₇₂

C₂

yes

maximal, complemented

C₂×#14273672

C₂

yes

maximal

#16837786

C₂

yes

maximal, characteristic

#16837782

C₂

yes

maximal, characteristic, complemented

C₅₉×#346

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

C₂²

yes

—

C₂×Dic₂₃₆

C₂²

yes

characteristic

C₂×#11745660

—

C₂×D₄₇₂

C₂²

yes

characteristic

#14273727

—

#14273715

—

Dic₄₇₂

—

#14273672

—

C₂×C₁₆×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×D₂₃₆

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

D₄

yes

characteristic

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

D₄₇₂

—

#11745660

—

C₁₆×C₅₉

D₄

yes

—

C₂²×D₅₉

—

C₂×C₄×C₅₉

D₈

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

D₂₃₆

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

D₈

yes

—

C₈×C₅₉

C₂×D₄

yes

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#127

yes

characteristic

C₄×C₅₉

C₂×D₈

yes

characteristic

Dic₅₉

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

D₅₉

—

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

—

#494

—

#346

D₅₉

yes

characteristic, complemented

C₅₉

#2251

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

118

—

C₂×SD₁₆

—

118

—

C₂×D₈

—

C₄⋊Q₈

—

118

—

#124

—

118

—

Q₃₂

—

118

—

SD₃₂

—

118

—

C₂×C₁₆

C₂×D₅₉

yes

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂×Q₈

—

118

—

C₂×Q₈

—

118

—

C₂×D₄

—

118

—

Q₁₆

—

118

—

Q₁₆

—

118

—

Q₁₆

—

118

—

Q₁₆

—

236

—

SD₁₆

—

236

—

D₈

—

118

—

C₂×C₈

D₂₃₆

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₄²

D₂₃₆

yes

characteristic

C₁₆

D₂₃₆

yes

—

C₂³

—

236

—

Q₈

—

236

—

Q₈

—

236

—

Q₈

—

236

—

Q₈

—

236

—

D₄

—

236

—

D₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

D₄₇₂

yes

—

C₂×C₄

C₂×D₂₃₆

yes

characteristic

100

C₈

D₄₇₂

yes

—

101

C₈

C₂×D₂₃₆

yes

—

102

C₂²

—

472

—

103

C₂²

—

472

—

104

C₂²

C₂×D₄₇₂

yes

characteristic

105

C₄

—

106

C₄

—

472

—

107

C₄

—

472

—

108

C₄

#14273724

yes

characteristic

109

C₄

C₂×D₄₇₂

yes

characteristic

110

C₂

—

944

—

111

C₂

#16837779

yes

characteristic

112

C₂

#16837845

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄₇₂
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#346	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#346	D₅₉
hypocenter	C₅₉	#2251
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

subgroup

G/H

center

C₂²

C₂×D₄₇₂

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#346

C₂

socle

C₂²×C₅₉

C₂×D₈

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

N	H ≅ G/N	type
1. C₂×Dic₄₇₂	C₂	semidirect
4. #16837782	C₂	semidirect
5. C₅₉×#346	C₂	semidirect
61. #346	D₅₉	semidirect
62. C₅₉	#2251	semidirect

H ≅ G/N

type

1. C₂×Dic₄₇₂

C₂

semidirect

4. #16837782

C₂

semidirect

5. C₅₉×#346

C₂

semidirect

61. #346

D₅₉

semidirect

62. C₅₉

#2251

semidirect

Subgroups — #21426367

Conjugacy classes of subgroups

Complements