Group #21445448 — subgroups

Subgroups — #21445448

Order 7808.

220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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	#16840139	C₂	1	1	yes	maximal, characteristic
2	#16840136	C₂	1	2	yes	maximal, complemented
3	#16840110	C₂	1	2	yes	maximal, complemented
4	#16839483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758201	—	2	4	no	—
7	C₂×D₄₈₈	—	2	2	no	—
8	#14519774	C₂²	1	1	yes	characteristic
9	#14519774	C₂²	1	1	yes	characteristic
10	#14519697	—	2	4	no	—
11	C₄×#92418	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
13	#106×C₆₁	—	2	2	no	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₆₁	—	2	2	no	—
16	C₂×D₂₄₄	—	2	2	no	—
17	C₂×D₂₄₄	—	2	1	no	—
18	C₂×D₂₄₄	—	2	1	no	—
19	C₂×D₂₄₄	—	2	2	no	—
20	C₂×C₈×C₆₁	D₄	1	2	yes	—
21	C₄⋊C₄×C₆₁	—	2	2	no	—
22	C₄⋊C₄×C₆₁	—	2	2	no	—
23	C₄²×C₆₁	C₂³	1	1	yes	characteristic
24	#11758201	—	4	8	no	—
25	C₂×#92418	D₄	1	4	yes	—
26	D₄₈₈	—	4	4	no	—
27	C₂²×D₆₁	—	4	1	no	—
28	C₂²×D₆₁	—	4	1	no	—
29	Q₈×C₆₁	—	4	4	no	—
30	C₂×C₄×C₆₁	—	4	2	no	—
31	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
33	D₂₄₄	—	4	2	no	—
34	D₂₄₄	—	4	2	no	—
35	D₂₄₄	—	4	4	no	—
36	D₂₄₄	—	4	4	no	—
37	C₈×C₆₁	SD₁₆	1	4	yes	complemented
38	#92418	—	2	4	no	—
39	C₂²×C₆₁	#127	1	1	yes	characteristic
40	C₂×D₆₁	—	8	1	no	—
41	C₂×D₆₁	—	8	1	no	—
42	C₂×D₆₁	—	8	2	no	—
43	C₂×D₆₁	—	8	2	no	—
44	C₄×C₆₁	—	8	2	no	—
45	C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
46	C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
47	#1715	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	#492	1	1	yes	characteristic
49	C₂×C₆₁	#496	1	2	yes	—
50	D₆₁	—	16	1	no	—
51	D₆₁	—	16	1	no	—
52	#498	D₆₁	1	1	yes	characteristic, complemented
53	#493	—	61	1	no	—
54	#492	—	61	2	no	—
55	#486	—	61	2	no	—
56	#322	—	61	1	no	—
57	C₆₁	#1715	1	1	yes	characteristic, complemented, Sylow
58	C₂×SD₁₆	—	122	4	no	—
59	C₂×D₈	—	122	2	no	—
60	C₄⋊Q₈	C₂×D₆₁	1	2	yes	—
61	#127	—	61	1	no	—
62	#127	—	61	1	no	—
63	#106	—	2	2	no	—
64	#102	—	122	4	no	—
65	C₄×C₈	—	61	2	no	—
66	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
67	C₂×Q₈	—	2	2	no	—
68	C₂×D₄	—	122	2	no	—
69	C₂×D₄	—	122	2	no	—
70	C₂×D₄	—	122	1	no	—
71	C₂×D₄	—	122	1	no	—
72	SD₁₆	—	244	8	no	—
73	D₈	—	244	4	no	—
74	C₂×C₈	—	61	4	no	—
75	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄²	C₂²×D₆₁	1	1	yes	characteristic
79	C₂³	—	244	1	no	—
80	C₂³	—	244	1	no	—
81	Q₈	—	4	4	no	—
82	D₄	—	244	2	no	—
83	D₄	—	244	2	no	—
84	D₄	—	244	4	no	—
85	D₄	—	244	4	no	—
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	D₄×D₆₁	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
89	C₈	—	122	4	no	—
90	C₈	#11758201	1	4	yes	complemented
91	C₂²	—	488	1	no	—
92	C₂²	—	488	1	no	—
93	C₂²	—	488	2	no	—
94	C₂²	—	488	2	no	—
95	C₂²	#14519773	1	1	yes	characteristic
96	C₄	—	8	2	no	—
97	C₄	C₂×#11758201	1	2	yes	—
98	C₄	#14519804	1	4	yes	—
99	C₂	—	976	1	no	—
100	C₂	—	976	1	no	—
101	C₂	#16840136	1	1	yes	characteristic
102	C₂	#16840148	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840139

C₂

yes

maximal, characteristic

#16840136

C₂

yes

maximal, complemented

#16840110

C₂

yes

maximal, complemented

#16839483

C₂

yes

maximal, characteristic, complemented

C₆₁×#498

C₂

yes

maximal, characteristic, complemented

C₂×#11758201

—

C₂×D₄₈₈

—

#14519774

C₂²

yes

characteristic

#14519774

C₂²

yes

characteristic

#14519697

—

C₄×#92418

C₂²

yes

—

C₄⋊Q₈×C₆₁

C₂²

yes

—

#106×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×C₈×C₆₁

D₄

yes

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

#11758201

—

C₂×#92418

D₄

yes

—

D₄₈₈

—

C₂²×D₆₁

—

C₂²×D₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

D₂₄₄

—

D₂₄₄

—

D₂₄₄

—

D₂₄₄

—

C₈×C₆₁

SD₁₆

yes

complemented

#92418

—

C₂²×C₆₁

#127

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×SD₁₆

yes

—

C₄×C₆₁

AGL(1,ℤ/8)

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

D₆₁

—

#498

D₆₁

yes

characteristic, complemented

—

—

—

—

C₆₁

#1715

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

122

—

C₂×D₈

—

122

—

C₄⋊Q₈

C₂×D₆₁

yes

—

—

—

—

—

122

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

122

—

C₂×D₄

—

122

—

C₂×D₄

—

122

—

C₂×D₄

—

122

—

SD₁₆

—

244

—

D₈

—

244

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₆₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

244

—

C₂³

—

244

—

Q₈

—

D₄

—

244

—

D₄

—

244

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

D₄×D₆₁

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

122

—

C₈

#11758201

yes

complemented

C₂²

—

488

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

#14519773

yes

characteristic

C₄

—

C₄

C₂×#11758201

yes

—

C₄

#14519804

yes

—

C₂

—

976

—

100

C₂

—

976

—

101

C₂

#16840136

yes

characteristic

102

C₂

#16840148

yes

—

	subgroup	G/H
center	C₂²	#14519773
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#498	C₂
socle	C₂²×C₆₁	#127
hypercenter	#498	D₆₁
hypocenter	C₆₁	#1715
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

#14519773

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#498

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. #16840136	C₂	semidirect
3. #16840110	C₂	semidirect
4. #16839483	C₂	semidirect
5. C₆₁×#498	C₂	semidirect
37. C₈×C₆₁	SD₁₆	semidirect
52. #498	D₆₁	semidirect
57. C₆₁	#1715	semidirect
90. C₈	#11758201	semidirect

H ≅ G/N

type

2. #16840136

C₂

semidirect

3. #16840110

C₂

semidirect

4. #16839483

C₂

semidirect

5. C₆₁×#498

C₂

semidirect

37. C₈×C₆₁

SD₁₆

semidirect

52. #498

D₆₁

semidirect

57. C₆₁

#1715

semidirect

90. C₈

#11758201

semidirect

Subgroups — #21445448

Conjugacy classes of subgroups

Complements