Group #21460917 — subgroups

Subgroups — #21460917

Order 7808.

172 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 44 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×#14519838	C₂	1	2	yes	maximal
2	#16839667	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758217	—	2	2	no	—
4	#14519838	—	2	2	no	—
5	#14519838	C₄	1	4	yes	complemented
6	C₂²×Dic₁₂₂	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
8	#14519684	—	2	2	no	—
9	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	—	2	1	no	—
11	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₆₁	—	2	1	no	—
13	C₂²×Dic₆₁	D₄	1	2	yes	—
14	C₂×Dic₁₂₂	—	4	1	no	—
15	C₂×Dic₁₂₂	—	4	1	no	—
16	C₂×Dic₁₂₂	C₂×C₄	1	2	yes	—
17	C₂×Dic₁₂₂	D₄	1	1	yes	characteristic
18	C₂×Dic₁₂₂	Q₈	1	1	yes	characteristic
19	#11758217	—	2	4	no	—
20	#11758217	—	4	2	no	—
21	C₂×#92420	—	4	2	no	—
22	C₄⋊C₄×C₆₁	—	4	1	no	—
23	C₄×Dic₆₁	—	4	1	no	—
24	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	—	2	1	no	—
26	C₂×C₄×C₆₁	—	2	1	no	—
27	C₂×C₄×C₆₁	—	4	2	no	—
28	C₂×C₄×C₆₁	—	4	1	no	—
29	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×Dic₆₁	—	2	2	no	—
32	C₂×Dic₆₁	—	2	2	no	—
33	C₂×Dic₆₁	—	2	2	no	—
34	C₂×Dic₆₁	—	4	1	no	—
35	C₂×Dic₆₁	—	4	1	no	—
36	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
37	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
38	Dic₁₂₂	—	4	2	no	—
39	Dic₁₂₂	—	4	1	no	—
40	Dic₁₂₂	—	4	1	no	—
41	#92420	—	4	4	no	—
42	C₂²×C₆₁	—	2	1	no	—
43	C₂²×C₆₁	—	2	1	no	—
44	C₂²×C₆₁	#95	1	1	yes	characteristic
45	C₂²×C₆₁	#99	1	1	yes	characteristic
46	C₂²×C₆₁	#99	1	1	yes	characteristic
47	C₄×C₆₁	—	2	1	no	—
48	C₄×C₆₁	—	2	1	no	—
49	C₄×C₆₁	—	8	1	no	—
50	Dic₆₁	—	2	2	no	—
51	Dic₆₁	—	2	2	no	—
52	Dic₆₁	—	4	2	no	—
53	#1394	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	—	2	1	no	—
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	#342	1	1	yes	characteristic
57	C₂×C₆₁	#355	1	1	yes	characteristic
58	C₂×C₆₁	#356	1	1	yes	characteristic
59	C₂×#101	—	61	2	no	—
60	#391	—	61	1	no	—
61	C₆₁	#1394	1	1	yes	characteristic, complemented, Sylow
62	C₂²×Q₈	—	61	1	no	—
63	C₂×M₁₆	—	122	2	no	—
64	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
65	C₂×C₄²	—	61	1	no	—
66	#101	—	61	4	no	—
67	#101	—	122	2	no	—
68	#95	—	122	2	no	—
69	C₂×Q₈	—	61	2	no	—
70	C₂×Q₈	—	61	1	no	—
71	C₂×Q₈	—	61	1	no	—
72	C₂×Q₈	—	244	1	no	—
73	C₂×Q₈	—	244	1	no	—
74	C₂²×C₄	—	2	1	no	—
75	C₂²×C₄	—	61	2	no	—
76	C₂²×C₄	—	122	1	no	—
77	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
78	M₁₆	—	122	4	no	—
79	M₁₆	—	244	2	no	—
80	C₂×C₈	—	244	2	no	—
81	C₄⋊C₄	—	4	1	no	—
82	C₄²	—	244	1	no	—
83	C₂³	C₂²⋊#6923	1	1	yes	characteristic
84	Q₈	—	244	2	no	—
85	Q₈	—	244	1	no	—
86	Q₈	—	244	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	—	61	2	no	—
92	C₂×C₄	—	61	2	no	—
93	C₂×C₄	—	122	2	no	—
94	C₂×C₄	—	122	2	no	—
95	C₂×C₄	—	122	2	no	—
96	C₂×C₄	—	244	1	no	—
97	C₂×C₄	—	244	1	no	—
98	C₂×C₄	C₄×#6923	1	1	yes	characteristic
99	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
100	C₈	—	244	4	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	2	1	no	—
103	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
104	C₂²	#14519835	1	1	yes	characteristic
105	C₂²	#14519836	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	8	1	no	—
109	C₄	—	122	2	no	—
110	C₄	—	122	2	no	—
111	C₄	—	244	2	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	1	no	—
114	C₂	#16840640	1	1	yes	characteristic
115	C₂	#16840670	1	1	yes	characteristic
116	C₂	#16840672	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519838

C₂

yes

maximal

#16839667

C₂

yes

maximal, characteristic

C₂×#11758217

—

#14519838

—

#14519838

C₄

yes

complemented

C₂²×Dic₁₂₂

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

characteristic

#14519684

—

C₂×C₄⋊C₄×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

C₂×C₄

yes

—

C₂×Dic₁₂₂

D₄

yes

characteristic

C₂×Dic₁₂₂

Q₈

yes

—

—

—

C₄⋊C₄×C₆₁

—

C₄×Dic₆₁

—

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

Dic₁₂₂

—

Dic₁₂₂

—

Dic₁₂₂

—

#92420

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

#1394

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₆₁

#1394

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×M₁₆

—

122

—

C₂×C₄⋊C₄

#6923

yes

characteristic

C₂×C₄²

—

#101

—

#101

—

122

—

#95

—

122

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

244

—

C₂×Q₈

—

244

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

244

—

C₄⋊C₄

—

C₄²

—

244

—

C₂³

C₂²⋊#6923

yes

characteristic

Q₈

—

244

—

Q₈

—

244

—

Q₈

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

100

C₈

—

244

—

101

C₂²

—

102

C₂²

—

103

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

104

C₂²

#14519835

yes

characteristic

105

C₂²

#14519836

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

122

—

110

C₄

—

122

—

111

C₄

—

244

—

112

C₂

—

113

C₂

—

114

C₂

#16840640

yes

characteristic

115

C₂

#16840670

yes

characteristic

116

C₂

#16840672

yes

characteristic

	subgroup	G/H
center	C₂²	#14519835
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂²×C₆₁	#99
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#1394
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂²

#14519835

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×C₄⋊C₄×C₆₁

C₄

C₂²×C₆₁

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
5. #14519838	C₄	semidirect
61. C₆₁	#1394	semidirect

H ≅ G/N

type

5. #14519838

C₄

semidirect

61. C₆₁

#1394

semidirect

Subgroups — #21460917

Conjugacy classes of subgroups

Complements