Group #44507074 — subgroups

Subgroups — #44507074

Order 30848.

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	#29508094	C₂	1	1	yes	maximal, characteristic
2	#29508091	C₂	1	2	yes	maximal, complemented
3	#29508065	C₂	1	2	yes	maximal, complemented
4	#29507438	C₂	1	1	yes	maximal, characteristic, complemented
5	#498×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16838757	—	2	4	no	—
7	C₂×D₁₉₂₈	—	2	2	no	—
8	#21440639	C₂²	1	1	yes	characteristic
9	#21440639	C₂²	1	1	yes	characteristic
10	#21440562	—	2	4	no	—
11	C₄×#14515349	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₂₄₁	C₂²	1	2	yes	—
13	#106×C₂₄₁	—	2	2	no	—
14	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
15	C₂×D₉₆₄	—	2	2	no	—
16	C₂×D₉₆₄	—	2	1	no	—
17	C₂×D₉₆₄	—	2	1	no	—
18	C₂×D₉₆₄	—	2	2	no	—
19	#16838757	—	4	8	no	—
20	D₁₉₂₈	—	4	4	no	—
21	C₂×#14515349	D₄	1	4	yes	—
22	C₂×Q₈×C₂₄₁	—	2	2	no	—
23	C₂×C₈×C₂₄₁	D₄	1	2	yes	—
24	C₄⋊C₄×C₂₄₁	—	2	2	no	—
25	C₄⋊C₄×C₂₄₁	—	2	2	no	—
26	C₄²×C₂₄₁	C₂³	1	1	yes	characteristic
27	C₂²×D₂₄₁	—	4	1	no	—
28	C₂²×D₂₄₁	—	4	1	no	—
29	D₉₆₄	—	4	2	no	—
30	D₉₆₄	—	4	2	no	—
31	D₉₆₄	—	4	4	no	—
32	D₉₆₄	—	4	4	no	—
33	#14515349	—	2	4	no	—
34	Q₈×C₂₄₁	—	4	4	no	—
35	C₂×C₄×C₂₄₁	—	4	2	no	—
36	C₂×C₄×C₂₄₁	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
38	C₈×C₂₄₁	SD₁₆	1	4	yes	complemented
39	C₂²×C₂₄₁	#127	1	1	yes	characteristic
40	C₂×D₂₄₁	—	8	1	no	—
41	C₂×D₂₄₁	—	8	1	no	—
42	C₂×D₂₄₁	—	8	2	no	—
43	C₂×D₂₄₁	—	8	2	no	—
44	C₄×C₂₄₁	—	8	2	no	—
45	C₄×C₂₄₁	C₂×SD₁₆	1	2	yes	—
46	C₄×C₂₄₁	AGL(1,ℤ/8)	1	4	yes	—
47	C₂×C₂₄₁	#492	1	1	yes	characteristic
48	C₂×C₂₄₁	#496	1	2	yes	—
49	D₂₄₁	—	16	1	no	—
50	D₂₄₁	—	16	1	no	—
51	C₂₄₁	#1715	1	1	yes	characteristic, complemented, Sylow
52	#1715	—	241	1	no	maximal, Sylow
53	#498	D₂₄₁	1	1	yes	characteristic, complemented
54	#493	—	241	1	no	—
55	#492	—	241	2	no	—
56	#486	—	241	2	no	—
57	#322	—	241	1	no	—
58	C₂×SD₁₆	—	482	4	no	—
59	C₂×D₈	—	482	2	no	—
60	C₄⋊Q₈	C₂×D₂₄₁	1	2	yes	—
61	#127	—	241	1	no	—
62	#127	—	241	1	no	—
63	#106	—	2	2	no	—
64	#102	—	482	4	no	—
65	C₄×C₈	—	241	2	no	—
66	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
67	C₂×Q₈	—	2	2	no	—
68	C₂×D₄	—	482	2	no	—
69	C₂×D₄	—	482	2	no	—
70	C₂×D₄	—	482	1	no	—
71	C₂×D₄	—	482	1	no	—
72	SD₁₆	—	964	8	no	—
73	D₈	—	964	4	no	—
74	C₂×C₈	—	241	4	no	—
75	C₂×C₈	C₂²⋊D₂₄₁	1	2	yes	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄²	C₂²×D₂₄₁	1	1	yes	characteristic
79	C₂³	—	964	1	no	—
80	C₂³	—	964	1	no	—
81	Q₈	—	4	4	no	—
82	D₄	—	964	2	no	—
83	D₄	—	964	2	no	—
84	D₄	—	964	4	no	—
85	D₄	—	964	4	no	—
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	D₄×D₂₄₁	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₂₄₁	1	1	yes	characteristic
89	C₈	—	482	4	no	—
90	C₈	#16838757	1	4	yes	complemented
91	C₂²	—	1928	2	no	—
92	C₂²	—	1928	2	no	—
93	C₂²	—	1928	1	no	—
94	C₂²	—	1928	1	no	—
95	C₂²	#21440638	1	1	yes	characteristic
96	C₄	—	8	2	no	—
97	C₄	C₂×#16838757	1	2	yes	—
98	C₄	#21440669	1	4	yes	—
99	C₂	—	3856	1	no	—
100	C₂	—	3856	1	no	—
101	C₂	#29508091	1	1	yes	characteristic
102	C₂	#29508103	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#29508094

C₂

yes

maximal, characteristic

#29508091

C₂

yes

maximal, complemented

#29508065

C₂

yes

maximal, complemented

#29507438

C₂

yes

maximal, characteristic, complemented

#498×C₂₄₁

C₂

yes

maximal, characteristic, complemented

C₂×#16838757

—

C₂×D₁₉₂₈

—

#21440639

C₂²

yes

characteristic

#21440639

C₂²

yes

characteristic

#21440562

—

C₄×#14515349

C₂²

yes

—

C₄⋊Q₈×C₂₄₁

C₂²

yes

—

#106×C₂₄₁

—

C₄×C₈×C₂₄₁

C₂²

yes

characteristic

C₂×D₉₆₄

—

C₂×D₉₆₄

—

C₂×D₉₆₄

—

C₂×D₉₆₄

—

#16838757

—

D₁₉₂₈

—

C₂×#14515349

D₄

yes

—

C₂×Q₈×C₂₄₁

—

C₂×C₈×C₂₄₁

D₄

yes

—

C₄⋊C₄×C₂₄₁

—

C₄⋊C₄×C₂₄₁

—

C₄²×C₂₄₁

C₂³

yes

characteristic

C₂²×D₂₄₁

—

C₂²×D₂₄₁

—

D₉₆₄

—

D₉₆₄

—

D₉₆₄

—

D₉₆₄

—

#14515349

—

Q₈×C₂₄₁

—

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

characteristic

C₈×C₂₄₁

SD₁₆

yes

complemented

C₂²×C₂₄₁

#127

yes

characteristic

C₂×D₂₄₁

—

C₂×D₂₄₁

—

C₂×D₂₄₁

—

C₂×D₂₄₁

—

C₄×C₂₄₁

—

C₄×C₂₄₁

C₂×SD₁₆

yes

—

C₄×C₂₄₁

AGL(1,ℤ/8)

yes

—

C₂×C₂₄₁

#492

yes

characteristic

C₂×C₂₄₁

#496

yes

—

D₂₄₁

—

D₂₄₁

—

C₂₄₁

#1715

yes

characteristic, complemented, Sylow

#1715

—

241

maximal, Sylow

#498

D₂₄₁

yes

characteristic, complemented

#493

—

241

—

#492

—

241

—

#486

—

241

—

#322

—

241

—

C₂×SD₁₆

—

482

—

C₂×D₈

—

482

—

C₄⋊Q₈

C₂×D₂₄₁

yes

—

#127

—

241

—

#127

—

241

—

#106

—

#102

—

482

—

C₄×C₈

—

241

—

C₄×C₈

C₂×D₂₄₁

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

482

—

C₂×D₄

—

482

—

C₂×D₄

—

482

—

C₂×D₄

—

482

—

SD₁₆

—

964

—

D₈

—

964

—

C₂×C₈

—

241

—

C₂×C₈

C₂²⋊D₂₄₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₂₄₁

yes

characteristic

C₂³

—

964

—

C₂³

—

964

—

Q₈

—

D₄

—

964

—

D₄

—

964

—

D₄

—

964

—

D₄

—

964

—

C₂×C₄

—

C₂×C₄

D₄×D₂₄₁

yes

—

C₂×C₄

C₂×C₂²⋊D₂₄₁

yes

characteristic

C₈

—

482

—

C₈

#16838757

yes

complemented

C₂²

—

1928

—

C₂²

—

1928

—

C₂²

—

1928

—

C₂²

—

1928

—

C₂²

#21440638

yes

characteristic

C₄

—

C₄

C₂×#16838757

yes

—

C₄

#21440669

yes

—

C₂

—

3856

—

100

C₂

—

3856

—

101

C₂

#29508091

yes

characteristic

102

C₂

#29508103

yes

—

	subgroup	G/H
center	C₂²	#21440638
commutator, cosocle	C₄²×C₂₄₁	C₂³
Frattini	C₄²	C₂²×D₂₄₁
Fitting	#498×C₂₄₁	C₂
socle	C₂²×C₂₄₁	#127
prime radical	#29508094	C₂
hypercenter	#498	D₂₄₁
hypocenter	C₂₄₁	#1715
LCS	G ▷ C₄²×C₂₄₁ ▷ C₂²×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

#21440638

commutator, cosocle

C₄²×C₂₄₁

C₂³

Frattini

C₄²

C₂²×D₂₄₁

Fitting

#498×C₂₄₁

C₂

C₂²×C₂₄₁

C₂

D₂₄₁

C₂₄₁

G ▷ C₄²×C₂₄₁ ▷ C₂²×C₂₄₁ ▷ C₂₄₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. #29508091	C₂	semidirect
3. #29508065	C₂	semidirect
4. #29507438	C₂	semidirect
5. #498×C₂₄₁	C₂	semidirect
38. C₈×C₂₄₁	SD₁₆	semidirect
51. C₂₄₁	#1715	semidirect
53. #498	D₂₄₁	semidirect
90. C₈	#16838757	semidirect

H ≅ G/N

type

2. #29508091

C₂

semidirect

3. #29508065

C₂

semidirect

4. #29507438

C₂

semidirect

5. #498×C₂₄₁

C₂

semidirect

38. C₈×C₂₄₁

SD₁₆

semidirect

51. C₂₄₁

#1715

semidirect

53. #498

D₂₄₁

semidirect

90. C₈

#16838757

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#29508094	2
#29508091	2
#29508065	2
#29507438	2
#498×C₂₄₁	2
#1715	241

subgroup

index

#498×C₂₄₁

241

Subgroups — #44507074

Conjugacy classes of subgroups

Complements

Maximal subgroups