Group #21426316 — subgroups

Subgroups — #21426316

Order 7552.

124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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	#16837660	C₂	1	1	yes	maximal, characteristic
2	#16837451	C₂	1	1	yes	maximal, characteristic
3	#16837225	C₂	1	2	yes	maximal, complemented
4	#16837219	C₂	1	2	yes	maximal, complemented
5	C₅₉×#349	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₃₆	C₂²	1	1	yes	characteristic
7	C₂×#11745664	—	2	1	no	—
8	#14273706	—	2	1	no	—
9	#14273663	—	2	1	no	—
10	#14273663	C₂²	1	2	yes	—
11	#14273659	C₂²	1	1	yes	characteristic
12	#14273652	—	2	1	no	—
13	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	M₃₂×C₅₉	C₂²	1	2	yes	—
15	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
16	C₂×Dic₁₁₈	—	2	1	no	—
17	M₁₆×C₅₉	—	2	2	no	—
18	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
20	C₂²⋊Dic₅₉	—	4	1	no	—
21	C₄⋊Dic₅₉	—	2	1	no	—
22	Dic₅₉⋊C₄	—	4	1	no	—
23	#11745664	—	2	2	no	—
24	#11745664	—	4	1	no	—
25	C₂×C₅₉⋊C₈	—	4	1	no	—
26	Dic₂₃₆	—	2	2	no	—
27	C₁₆×C₅₉	—	2	2	no	—
28	C₂³×C₅₉	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₅₉	—	2	1	no	—
30	C₂×C₄×C₅₉	—	2	1	no	—
31	C₂×C₄×C₅₉	SD₁₆	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₅₉	—	4	1	no	—
34	C₂×Dic₅₉	—	4	1	no	—
35	Dic₁₁₈	—	4	1	no	—
36	Dic₁₁₈	—	4	1	no	—
37	C₈×C₅₉	—	2	1	no	—
38	C₈×C₅₉	#41	1	2	yes	—
39	C₅₉⋊C₈	—	4	2	no	—
40	C₂²×C₅₉	—	2	1	no	—
41	C₂²×C₅₉	—	4	1	no	—
42	C₂²×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
43	C₄×C₅₉	—	2	1	no	—
44	C₄×C₅₉	#123	1	1	yes	characteristic
45	C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
46	Dic₅₉	—	8	1	no	—
47	Dic₅₉	—	8	1	no	—
48	#2239	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	—	2	1	no	—
50	C₂×C₅₉	—	4	1	no	—
51	C₂×C₅₉	#481	1	1	yes	characteristic
52	#470	—	59	1	no	—
53	#430	—	59	1	no	—
54	#365	—	59	2	no	—
55	#362	—	59	2	no	—
56	#349	D₅₉	1	1	yes	characteristic
57	C₅₉	#2239	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	—	59	1	no	—
59	C₂×M₁₆	—	118	1	no	—
60	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
61	C₂²⋊Q₈	—	118	1	no	—
62	M₃₂	C₂×D₅₉	1	2	yes	—
63	#108	—	59	2	no	—
64	#108	—	118	1	no	—
65	#106	—	59	1	no	—
66	#103	—	118	1	no	—
67	C₂×Q₈	—	118	1	no	—
68	C₂²×C₄	D₂₃₆	1	1	yes	characteristic
69	Q₁₆	—	118	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	118	2	no	—
72	M₁₆	—	236	1	no	—
73	C₂×C₈	—	236	1	no	—
74	C₂×C₈	D₂₃₆	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
76	C₄⋊C₄	—	118	1	no	—
77	C₄⋊C₄	—	236	1	no	—
78	C₂²⋊C₄	—	236	1	no	—
79	C₁₆	—	2	2	no	—
80	C₂³	#11745660	1	1	yes	characteristic
81	Q₈	—	236	1	no	—
82	Q₈	—	236	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	236	1	no	—
86	C₂×C₄	—	236	1	no	—
87	C₂×C₄	#11745660	1	1	yes	characteristic
88	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	236	2	no	—
91	C₈	#11745687	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#11745660	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	472	1	no	—
97	C₄	—	472	1	no	—
98	C₄	#14273711	1	1	yes	characteristic
99	C₄	#14273755	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#16837721	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837660

C₂

yes

maximal, characteristic

#16837451

C₂

yes

maximal, characteristic

#16837225

C₂

yes

maximal, complemented

#16837219

C₂

yes

maximal, complemented

C₅₉×#349

C₂

yes

maximal, characteristic

C₂×Dic₂₃₆

C₂²

yes

—

—

—

C₂²

yes

—

#14273659

C₂²

yes

characteristic

#14273652

—

C₂×M₁₆×C₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

C₂²

yes

—

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

Dic₂₃₆

—

C₁₆×C₅₉

—

C₂³×C₅₉

SD₁₆

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

SD₁₆

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

#41

yes

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×SD₁₆

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

Dic₅₉

—

#2239

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

yes

—

—

—

—

D₅₉

yes

characteristic

C₅₉

#2239

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

118

—

C₂×M₁₆

C₂×D₅₉

yes

characteristic

C₂²⋊Q₈

—

118

—

M₃₂

C₂×D₅₉

yes

—

#108

—

#108

—

118

—

#106

—

#103

—

118

—

C₂×Q₈

—

118

—

C₂²×C₄

D₂₃₆

yes

characteristic

Q₁₆

—

118

—

M₁₆

—

M₁₆

—

118

—

M₁₆

—

236

—

C₂×C₈

—

236

—

C₂×C₈

D₂₃₆

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₁₆

—

C₂³

#11745660

yes

characteristic

Q₈

—

236

—

Q₈

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

#11745660

yes

characteristic

C₂×C₄

C₂×D₂₃₆

yes

characteristic

C₈

—

C₈

—

236

—

C₈

#11745687

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#11745660

yes

characteristic

C₄

—

C₄

—

472

—

C₄

—

472

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#16837721

yes

characteristic

	subgroup	G/H
center	C₂	#16837721
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#349	C₂
socle	C₂×C₅₉	#481
hypercenter	#349	D₅₉
hypocenter	C₅₉	#2239
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₂

#16837721

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#349

C₂

C₂×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
3. #16837225	C₂	semidirect
4. #16837219	C₂	semidirect
57. C₅₉	#2239	semidirect

H ≅ G/N

type

3. #16837225

C₂

semidirect

4. #16837219

C₂

semidirect

57. C₅₉

#2239

semidirect

Subgroups — #21426316

Conjugacy classes of subgroups

Complements