Group #21424915 — subgroups

Subgroups — #21424915

Order 7552.

308 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 105 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×#14273727	C₂	1	1	yes	maximal, characteristic
2	C₂×#14273650	C₂	1	4	yes	maximal
3	C₂×#14273638	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#382	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₁₈	C₂²	1	2	yes	—
6	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
7	#14273727	—	2	2	no	—
8	#14273727	C₄	1	4	yes	complemented
9	C₂×C₄⋊Dic₅₉	—	2	2	no	—
10	#14273650	—	2	8	no	—
11	#14273638	—	2	2	no	—
12	C₂×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
14	#95×C₅₉	—	2	2	no	—
15	C₂²×C₄×C₅₉	—	2	2	no	—
16	C₂²×C₄×C₅₉	D₄	1	2	yes	—
17	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₅₉	—	2	2	no	—
19	C₂×Dic₁₁₈	—	2	4	no	—
20	C₂×Dic₁₁₈	—	2	4	no	—
21	C₂×Dic₁₁₈	—	2	2	no	—
22	C₂×Dic₁₁₈	C₂×C₄	1	4	yes	—
23	C₄⋊C₄×C₅₉	—	2	4	no	—
24	C₄²×C₅₉	C₂×C₄	1	2	yes	—
25	C₄²×C₅₉	D₄	1	2	yes	—
26	C₄⋊Dic₅₉	—	2	8	no	—
27	C₂×C₅₉⋊C₈	—	2	2	no	—
28	C₂×C₅₉⋊C₈	—	2	2	no	—
29	C₂×C₅₉⋊C₈	D₄	1	4	yes	—
30	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₅₉	—	2	4	no	—
32	C₂×C₄×C₅₉	—	4	2	no	—
33	C₂×C₄×C₅₉	—	4	4	no	—
34	C₂×C₄×C₅₉	C₂²⋊C₄	1	4	yes	—
35	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
38	C₂×C₄×C₅₉	#41	1	2	yes	—
39	C₂×Dic₅₉	—	2	4	no	—
40	C₂×Dic₅₉	—	4	2	no	—
41	C₂×Dic₅₉	—	4	2	no	—
42	Dic₁₁₈	—	2	8	no	—
43	Dic₁₁₈	—	4	4	no	—
44	C₅₉⋊C₈	—	2	4	no	—
45	C₂²×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₅₉	#124	1	1	yes	characteristic
47	C₂²×C₅₉	#127	1	1	yes	characteristic
48	C₂²×C₅₉	#137	1	4	yes	—
49	C₄×C₅₉	—	2	4	no	—
50	C₄×C₅₉	—	8	2	no	—
51	C₄×C₅₉	C₄×D₄	1	2	yes	—
52	C₄×C₅₉	#121	1	2	yes	—
53	Dic₅₉	—	4	4	no	—
54	#1960	—	59	1	no	maximal, Sylow
55	C₂×C₅₉	#390	1	1	yes	characteristic
56	C₂×C₅₉	#419	1	2	yes	—
57	C₂×C₅₉	#491	1	2	yes	—
58	C₂×C₅₉	#497	1	2	yes	—
59	C₂×C₄⋊Q₈	—	59	1	no	—
60	C₂×#103	—	59	4	no	—
61	C₂×#97	—	59	1	no	—
62	#382	D₅₉	1	1	yes	characteristic
63	C₅₉	#1960	1	1	yes	characteristic, complemented, Sylow
64	C₂²×Q₈	—	59	2	no	—
65	C₂²×C₈	—	59	2	no	—
66	C₄⋊Q₈	—	59	4	no	—
67	C₄⋊Q₈	—	118	2	no	—
68	C₂×C₄⋊C₄	—	118	2	no	—
69	C₂×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
70	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
71	#103	—	118	8	no	—
72	#97	—	118	2	no	—
73	#95	—	2	2	no	—
74	C₂×Q₈	—	59	4	no	—
75	C₂×Q₈	—	118	2	no	—
76	C₂×Q₈	—	118	4	no	—
77	C₂×Q₈	—	118	4	no	—
78	C₂²×C₄	—	2	2	no	—
79	C₂²×C₄	—	118	2	no	—
80	C₂²×C₄	C₂²⋊D₅₉	1	2	yes	—
81	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
82	C₂×C₈	—	59	4	no	—
83	C₂×C₈	—	118	2	no	—
84	C₂×C₈	—	118	2	no	—
85	C₄⋊C₄	—	2	4	no	—
86	C₄⋊C₄	—	118	8	no	—
87	C₄²	C₄×D₅₉	1	2	yes	—
88	C₄²	D₂₃₆	1	2	yes	—
89	C₂³	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
90	Q₈	—	118	8	no	—
91	Q₈	—	236	4	no	—
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	—	4	2	no	—
94	C₂×C₄	—	4	4	no	—
95	C₂×C₄	—	118	4	no	—
96	C₂×C₄	—	236	2	no	—
97	C₂×C₄	—	236	2	no	—
98	C₂×C₄	(C₂×D₅₉)⋊C₄	1	4	yes	—
99	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
100	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
101	C₂×C₄	D₄×D₅₉	1	2	yes	—
102	C₂×C₄	#11745689	1	2	yes	—
103	C₈	—	118	4	no	—
104	C₂²	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
105	C₂²	#14273716	1	1	yes	characteristic
106	C₂²	#14273723	1	1	yes	characteristic
107	C₂²	#14273757	1	4	yes	—
108	C₄	—	2	4	no	—
109	C₄	—	8	2	no	—
110	C₄	—	236	4	no	—
111	C₄	#14273689	1	2	yes	—
112	C₄	#14273702	1	2	yes	—
113	C₂	#16837303	1	1	yes	characteristic
114	C₂	#16837410	1	2	yes	—
115	C₂	#16837772	1	2	yes	—
116	C₂	#16837797	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273727

C₂

yes

maximal, characteristic

C₂×#14273650

C₂

yes

maximal

C₂×#14273638

C₂

yes

maximal, characteristic

C₅₉×#382

C₂

yes

maximal, characteristic

C₂²×Dic₁₁₈

C₂²

yes

—

C₂²×C₅₉⋊C₈

C₂²

yes

—

#14273727

—

#14273727

C₄

yes

complemented

C₂×C₄⋊Dic₅₉

—

#14273650

—

#14273638

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

#95×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₂×C₄

yes

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂×C₄

yes

—

C₄²×C₅₉

D₄

yes

—

C₄⋊Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

D₄

yes

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₅₉⋊C₈

—

C₂²×C₅₉

C₂×C₂²⋊C₄

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₄×D₄

yes

—

C₄×C₅₉

#121

yes

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#491

yes

—

C₂×C₅₉

#497

yes

—

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×#97

—

#382

D₅₉

yes

characteristic

C₅₉

#1960

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

118

—

C₂×C₄⋊C₄

—

118

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#103

—

118

—

#97

—

118

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

118

—

C₂×Q₈

—

118

—

C₂×Q₈

—

118

—

C₂²×C₄

—

C₂²×C₄

—

118

—

C₂²×C₄

C₂²⋊D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₄⋊C₄

—

C₄⋊C₄

—

118

—

C₄²

C₄×D₅₉

yes

—

C₄²

D₂₃₆

yes

—

C₂³

C₂×C₂²⋊D₅₉

yes

characteristic

Q₈

—

118

—

Q₈

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

—

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

100

C₂×C₄

C₂×D₂₃₆

yes

characteristic

101

C₂×C₄

D₄×D₅₉

yes

—

102

C₂×C₄

#11745689

yes

—

103

C₈

—

118

—

104

C₂²

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

105

C₂²

#14273716

yes

characteristic

106

C₂²

#14273723

yes

characteristic

107

C₂²

#14273757

yes

—

108

C₄

—

109

C₄

—

110

C₄

—

236

—

111

C₄

#14273689

yes

—

112

C₄

#14273702

yes

—

113

C₂

#16837303

yes

characteristic

114

C₂

#16837410

yes

—

115

C₂

#16837772

yes

—

116

C₂

#16837797

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#382	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	#382	D₅₉
hypocenter	C₅₉	#1960
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₅₉×#382

C₂

socle

C₂³×C₅₉

C₂×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
8. #14273727	C₄	semidirect
63. C₅₉	#1960	semidirect

H ≅ G/N

type

8. #14273727

C₄

semidirect

63. C₅₉

#1960

semidirect

Subgroups — #21424915

Conjugacy classes of subgroups

Complements