Group #21443829 — subgroups

Subgroups — #21443829

Order 7808.

126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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	#16839998	C₂	1	1	yes	maximal, characteristic
2	#16839525	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₈₈	C₄	1	1	yes	characteristic, complemented
5	#14519751	—	2	1	no	—
6	C₂×C₄⋊Dic₆₁	—	2	1	no	—
7	#14519711	C₄	1	1	yes	characteristic, complemented
8	#14519699	—	2	1	no	—
9	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₆₁	—	2	1	no	—
11	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
12	C₂×C₂²⋊D₆₁	—	4	1	no	—
13	C₂²×Dic₆₁	—	4	1	no	—
14	C₂×D₂₄₄	—	2	1	no	—
15	C₂×C₈×C₆₁	—	4	1	no	—
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
18	#11758198	—	4	1	no	—
19	C₄⋊Dic₆₁	—	2	2	no	—
20	C₄⋊Dic₆₁	—	2	1	no	—
21	C₄⋊Dic₆₁	—	4	1	no	—
22	D₄₈₈	—	4	1	no	—
23	C₁₆×C₆₁	—	4	1	no	—
24	C₂³×C₆₁	D₈	1	1	yes	characteristic
25	C₂²×D₆₁	—	4	1	no	—
26	C₂×C₄×C₆₁	—	2	1	no	—
27	C₂×C₄×C₆₁	—	2	1	no	—
28	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
30	C₂²⋊D₆₁	—	8	1	no	—
31	C₂²⋊D₆₁	—	8	1	no	—
32	C₂×Dic₆₁	—	4	2	no	—
33	C₂×Dic₆₁	—	4	1	no	—
34	C₂×Dic₆₁	—	8	1	no	—
35	C₂×Dic₆₁	—	8	1	no	—
36	D₂₄₄	—	4	1	no	—
37	D₂₄₄	—	4	1	no	—
38	C₈×C₆₁	—	2	1	no	—
39	C₈×C₆₁	—	2	1	no	—
40	C₂²×C₆₁	—	2	1	no	—
41	C₂²×C₆₁	—	2	1	no	—
42	C₂²×C₆₁	#102	1	1	yes	characteristic
43	C₂²×C₆₁	D₁₆	1	1	yes	characteristic
44	C₂²×C₆₁	SD₃₂	1	1	yes	characteristic
45	C₂×D₆₁	—	8	1	no	—
46	C₂×D₆₁	—	8	1	no	—
47	C₂×D₆₁	—	8	1	no	—
48	C₄×C₆₁	—	2	1	no	—
49	C₄×C₆₁	#99	1	1	yes	characteristic
50	C₄×C₆₁	#104	1	1	yes	characteristic
51	Dic₆₁	—	8	2	no	—
52	Dic₆₁	—	8	1	no	—
53	#1347	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	—	2	1	no	—
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	#327	1	1	yes	characteristic
57	C₂×C₆₁	#357	1	1	yes	characteristic
58	C₂×C₆₁	#360	1	1	yes	characteristic
59	D₆₁	—	16	1	no	—
60	#466	—	61	1	no	—
61	C₂²⋊C₁₆	D₆₁	1	1	yes	characteristic, complemented
62	#340	—	61	1	no	—
63	C₆₁	#1347	1	1	yes	characteristic, complemented, Sylow
64	C₂×D₈	—	61	1	no	—
65	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
66	#121	—	122	1	no	—
67	C₂×C₄⋊C₄	—	122	1	no	—
68	C₂×C₁₆	—	2	1	no	—
69	#107	—	61	1	no	—
70	#102	—	122	1	no	—
71	C₂×D₄	—	122	1	no	—
72	C₂×D₄	—	244	1	no	—
73	C₂²×C₄	—	244	1	no	—
74	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
75	D₈	—	244	1	no	—
76	C₂×C₈	—	4	1	no	—
77	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
79	C₄⋊C₄	—	122	2	no	—
80	C₄⋊C₄	—	122	1	no	—
81	C₄⋊C₄	—	244	1	no	—
82	C₂²⋊C₄	—	244	1	no	—
83	C₁₆	—	4	1	no	—
84	C₂³	—	244	1	no	—
85	C₂³	D₄₈₈	1	1	yes	characteristic
86	D₄	—	488	1	no	—
87	D₄	—	488	1	no	—
88	D₄	—	244	1	no	—
89	D₄	—	244	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	488	1	no	—
93	C₂×C₄	—	488	1	no	—
94	C₂×C₄	—	244	2	no	—
95	C₂×C₄	—	244	1	no	—
96	C₂×C₄	#11758190	1	1	yes	characteristic
97	C₂×C₄	#11758198	1	1	yes	characteristic
98	C₈	—	2	1	no	—
99	C₈	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	488	1	no	—
103	C₂²	—	488	1	no	—
104	C₂²	—	488	1	no	—
105	C₂²	#14519699	1	1	yes	characteristic
106	C₂²	D₉₇₆	1	1	yes	characteristic
107	C₂²	#14519722	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	488	2	no	—
110	C₄	—	488	1	no	—
111	C₄	#14519691	1	1	yes	characteristic
112	C₄	#14519703	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	—	976	1	no	—
116	C₂	#16839497	1	1	yes	characteristic
117	C₂	#16839564	1	1	yes	characteristic
118	C₂	#16839573	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839998

C₂

yes

maximal, characteristic

#16839525

C₂

yes

maximal, characteristic, complemented

C₆₁×C₂²⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×D₄₈₈

C₄

yes

characteristic, complemented

#14519751

—

C₂×C₄⋊Dic₆₁

—

#14519711

C₄

yes

characteristic, complemented

#14519699

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

—

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂×C₂²⋊D₆₁

—

C₂²×Dic₆₁

—

C₂×D₂₄₄

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

#11758198

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

D₄₈₈

—

C₁₆×C₆₁

—

C₂³×C₆₁

D₈

yes

characteristic

C₂²×D₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

SD₁₆

yes

characteristic

C₂²⋊D₆₁

—

C₂²⋊D₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

C₈×C₆₁

—

C₈×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#102

yes

characteristic

C₂²×C₆₁

D₁₆

yes

characteristic

C₂²×C₆₁

SD₃₂

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

—

#1347

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#466

—

C₂²⋊C₁₆

D₆₁

yes

characteristic, complemented

#340

—

C₆₁

#1347

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

#121

—

122

—

C₂×C₄⋊C₄

—

122

—

C₂×C₁₆

—

#107

—

#102

—

122

—

C₂×D₄

—

122

—

C₂×D₄

—

244

—

C₂²×C₄

—

244

—

C₂²×C₄

D₂₄₄

yes

characteristic

D₈

—

244

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₁₆

—

C₂³

—

244

—

C₂³

D₄₈₈

yes

characteristic

D₄

—

488

—

D₄

—

488

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

488

—

C₂×C₄

—

488

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

488

—

103

C₂²

—

488

—

104

C₂²

—

488

—

105

C₂²

#14519699

yes

characteristic

106

C₂²

D₉₇₆

yes

characteristic

107

C₂²

#14519722

yes

characteristic

108

C₄

—

109

C₄

—

488

—

110

C₄

—

488

—

111

C₄

#14519691

yes

characteristic

112

C₄

#14519703

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

—

976

—

116

C₂

#16839497

yes

characteristic

117

C₂

#16839564

yes

characteristic

118

C₂

#16839573

yes

characteristic

	subgroup	G/H
center	C₂²	#14519699
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₂²×C₈	C₂×D₆₁
Fitting	C₆₁×C₂²⋊C₁₆	C₂
socle	C₂²×C₆₁	#102
hypercenter	C₂²⋊C₁₆	D₆₁
hypocenter	C₆₁	#1347
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂²

#14519699

commutator

C₂×C₈×C₆₁

C₂×C₄

Frattini

C₂²×C₈

C₂×D₆₁

Fitting

C₆₁×C₂²⋊C₁₆

C₂

socle

C₂²×C₆₁

#102

hypercenter

C₂²⋊C₁₆

D₆₁

hypocenter

C₆₁

#1347

LCS

G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
2. #16839525	C₂	semidirect
3. C₆₁×C₂²⋊C₁₆	C₂	semidirect
4. C₂×D₄₈₈	C₄	semidirect
7. #14519711	C₄	semidirect
61. C₂²⋊C₁₆	D₆₁	semidirect
63. C₆₁	#1347	semidirect

H ≅ G/N

type

2. #16839525

C₂

semidirect

3. C₆₁×C₂²⋊C₁₆

C₂

semidirect

4. C₂×D₄₈₈

C₄

semidirect

7. #14519711

C₄

semidirect

61. C₂²⋊C₁₆

D₆₁

semidirect

63. C₆₁

#1347

semidirect

Subgroups — #21443829

Conjugacy classes of subgroups

Complements