Group #21445938 — subgroups

Subgroups — #21445938

Order 7808.

216 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 101 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×C₄⋊#92418	C₂	1	1	yes	maximal, characteristic
2	#16839608	C₂	1	1	yes	maximal, characteristic
3	#16839516	C₂	1	4	yes	maximal
4	C₂×C₄⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂×C₄×Dic₆₁	C₂²	1	2	yes	—
7	C₄⋊#92418	—	2	2	no	—
8	#14519684	C₄	1	2	yes	—
9	#14519684	C₄	1	2	yes	—
10	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₆₁	—	2	2	no	—
13	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₆₁	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	—	2	4	no	—
19	C₄²×C₆₁	D₄	1	2	yes	—
20	C₄²×C₆₁	Q₈	1	2	yes	—
21	C₄×Dic₆₁	—	2	2	no	—
22	C₄×Dic₆₁	—	2	2	no	—
23	C₂×#92418	—	2	2	no	—
24	C₂×#92418	—	2	4	no	—
25	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₆₁	—	2	2	no	—
27	C₂×C₄×C₆₁	—	2	2	no	—
28	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₆₁	#41	1	2	yes	—
33	C₂×C₄×C₆₁	#41	1	2	yes	—
34	C₂×Dic₆₁	—	2	4	no	—
35	C₂×Dic₆₁	—	2	4	no	—
36	C₂×Dic₆₁	—	2	4	no	—
37	C₈×C₆₁	—	4	2	no	—
38	#92418	—	4	2	no	—
39	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₆₁	#117	1	2	yes	—
41	C₂²×C₆₁	#131	1	2	yes	—
42	C₂²×C₆₁	#131	1	2	yes	—
43	C₄×C₆₁	—	2	2	no	—
44	C₄×C₆₁	—	2	2	no	—
45	C₄×C₆₁	#124	1	1	yes	characteristic
46	C₄×C₆₁	#124	1	1	yes	characteristic
47	C₄×C₆₁	#125	1	2	yes	—
48	Dic₆₁	—	4	4	no	—
49	#1832	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	#382	1	1	yes	characteristic
51	C₂×C₆₁	#424	1	1	yes	characteristic
52	C₂×C₆₁	#424	1	1	yes	characteristic
53	C₂×C₆₁	#433	1	4	yes	—
54	C₂×C₄⋊C₈	—	61	1	no	—
55	C₂×C₄⋊C₈	D₆₁	1	1	yes	characteristic
56	#376	—	61	1	no	—
57	#336	—	61	4	no	—
58	C₆₁	#1832	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	—	61	2	no	—
60	C₂²×C₈	C₂×D₆₁	1	2	yes	—
61	C₂×C₄²	—	61	2	no	—
62	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
63	C₄⋊C₈	—	2	2	no	—
64	C₄⋊C₈	—	122	2	no	—
65	#95	—	61	2	no	—
66	#95	—	61	2	no	—
67	C₂²×C₄	—	61	4	no	—
68	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
69	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
71	C₂×C₈	—	2	4	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	122	4	no	—
74	C₂×C₈	—	122	2	no	—
75	C₄²	—	122	2	no	—
76	C₄²	—	122	2	no	—
77	C₄²	Dic₁₂₂	1	2	yes	—
78	C₄²	C₂²⋊D₆₁	1	2	yes	—
79	C₂³	C₂×C₄×D₆₁	1	1	yes	characteristic
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	122	4	no	—
83	C₂×C₄	—	122	4	no	—
84	C₂×C₄	—	122	4	no	—
85	C₂×C₄	#11758196	1	2	yes	—
86	C₂×C₄	#11758196	1	2	yes	—
87	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
88	C₂×C₄	#11758224	1	2	yes	—
89	C₂×C₄	#11758226	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	244	2	no	—
93	C₂²	C₂×#11758196	1	1	yes	characteristic
94	C₂²	#14519735	1	2	yes	—
95	C₂²	#14519783	1	2	yes	—
96	C₂²	#14519785	1	2	yes	—
97	C₄	—	2	2	no	—
98	C₄	—	2	2	no	—
99	C₄	—	244	4	no	—
100	C₄	#14519764	1	1	yes	characteristic
101	C₄	#14519766	1	1	yes	characteristic
102	C₄	#14519768	1	2	yes	—
103	C₂	#16839627	1	1	yes	characteristic
104	C₂	#16839788	1	1	yes	characteristic
105	C₂	#16839790	1	1	yes	characteristic
106	C₂	#16839822	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#92418

C₂

yes

maximal, characteristic

#16839608

C₂

yes

maximal, characteristic

#16839516

C₂

yes

maximal

C₂×C₄⋊C₈×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

—

C₄⋊#92418

—

#14519684

C₄

yes

—

#14519684

C₄

yes

—

C₂²×C₈×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

D₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#117

yes

—

C₂²×C₆₁

#131

yes

—

C₂²×C₆₁

#131

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₆₁

yes

characteristic

#376

—

#336

—

C₆₁

#1832

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

122

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₄×D₆₁

yes

characteristic

C₂²×C₄

C₄×D₆₁

yes

characteristic

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

Dic₁₂₂

yes

—

C₄²

C₂²⋊D₆₁

yes

—

C₂³

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

#11758196

yes

—

C₂×C₄

#11758196

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

#11758224

yes

—

C₂×C₄

#11758226

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

244

—

C₂²

C₂×#11758196

yes

characteristic

C₂²

#14519735

yes

—

C₂²

#14519783

yes

—

C₂²

#14519785

yes

—

C₄

—

C₄

—

C₄

—

244

—

100

C₄

#14519764

yes

characteristic

101

C₄

#14519766

yes

characteristic

102

C₄

#14519768

yes

—

103

C₂

#16839627

yes

characteristic

104

C₂

#16839788

yes

characteristic

105

C₂

#16839790

yes

characteristic

106

C₂

#16839822

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₆₁
commutator, socle	C₂³×C₆₁	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₆₁	C₂
hypercenter	C₂×C₄⋊C₈	D₆₁
hypocenter	C₆₁	#1832
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₆₁

commutator, socle

C₂³×C₆₁

C₂²×C₄

Fitting

C₂×C₄⋊C₈×C₆₁

C₂

hypercenter

C₂×C₄⋊C₈

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₆₁

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
58. C₆₁	#1832	semidirect

H ≅ G/N

type

58. C₆₁

#1832

semidirect

Subgroups — #21445938

Conjugacy classes of subgroups

Complements