Group #23765620 — subgroups

Subgroups — #23765620

Order 10112.

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	#19098821	C₂	1	1	yes	maximal, characteristic
2	#19098612	C₂	1	1	yes	maximal, characteristic
3	#19098386	C₂	1	2	yes	maximal, complemented
4	#19098380	C₂	1	2	yes	maximal, complemented
5	#349×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
7	C₂×#11929608	—	2	1	no	—
8	#14579140	—	2	1	no	—
9	#14579097	—	2	1	no	—
10	#14579097	C₂²	1	2	yes	—
11	#14579093	C₂²	1	1	yes	characteristic
12	#14579086	—	2	1	no	—
13	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	M₃₂×C₇₉	C₂²	1	2	yes	—
15	C₂×Dic₁₅₈	—	2	1	no	—
16	Dic₃₁₆	—	2	2	no	—
17	#11929608	—	2	2	no	—
18	#11929608	—	4	1	no	—
19	C₂×C₇₉⋊C₈	—	4	1	no	—
20	C₄⋊Dic₇₉	—	2	1	no	—
21	Dic₇₉⋊C₄	—	4	1	no	—
22	C₂²⋊Dic₇₉	—	4	1	no	—
23	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
24	M₁₆×C₇₉	—	2	2	no	—
25	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
27	C₁₆×C₇₉	—	2	2	no	—
28	C₂³×C₇₉	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₉	—	2	1	no	—
30	C₂×C₄×C₇₉	—	2	1	no	—
31	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₇₉	—	4	1	no	—
34	C₂×Dic₇₉	—	4	1	no	—
35	Dic₁₅₈	—	4	1	no	—
36	Dic₁₅₈	—	4	1	no	—
37	C₈×C₇₉	—	2	1	no	—
38	C₈×C₇₉	#41	1	2	yes	—
39	C₇₉⋊C₈	—	4	2	no	—
40	C₂²×C₇₉	—	2	1	no	—
41	C₂²×C₇₉	—	4	1	no	—
42	C₂²×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
43	C₄×C₇₉	—	2	1	no	—
44	C₄×C₇₉	#123	1	1	yes	characteristic
45	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
46	Dic₇₉	—	8	1	no	—
47	Dic₇₉	—	8	1	no	—
48	C₂×C₇₉	—	2	1	no	—
49	C₂×C₇₉	—	4	1	no	—
50	C₂×C₇₉	#481	1	1	yes	characteristic
51	#2239	—	79	1	no	maximal, Sylow
52	C₇₉	#2239	1	1	yes	characteristic, complemented, Sylow
53	#470	—	79	1	no	—
54	#430	—	79	1	no	—
55	#365	—	79	2	no	—
56	#362	—	79	2	no	—
57	#349	D₇₉	1	1	yes	characteristic
58	C₂×Q₁₆	—	79	1	no	—
59	C₂×M₁₆	—	158	1	no	—
60	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
61	C₂²⋊Q₈	—	158	1	no	—
62	M₃₂	C₂×D₇₉	1	2	yes	—
63	#108	—	79	2	no	—
64	#108	—	158	1	no	—
65	#106	—	79	1	no	—
66	#103	—	158	1	no	—
67	C₂×Q₈	—	158	1	no	—
68	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
69	Q₁₆	—	158	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	316	1	no	—
72	M₁₆	—	158	2	no	—
73	C₂×C₈	—	316	1	no	—
74	C₂×C₈	D₃₁₆	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
76	C₄⋊C₄	—	316	1	no	—
77	C₄⋊C₄	—	158	1	no	—
78	C₂²⋊C₄	—	316	1	no	—
79	C₁₆	—	2	2	no	—
80	C₂³	#11929613	1	1	yes	characteristic
81	Q₈	—	316	1	no	—
82	Q₈	—	316	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	316	1	no	—
86	C₂×C₄	—	316	1	no	—
87	C₂×C₄	#11929613	1	1	yes	characteristic
88	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	316	2	no	—
91	C₈	#11929623	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#11929613	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	632	1	no	—
97	C₄	—	632	1	no	—
98	C₄	#14579145	1	1	yes	characteristic
99	C₄	#14579189	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#19098882	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098821

C₂

yes

maximal, characteristic

#19098612

C₂

yes

maximal, characteristic

#19098386

C₂

yes

maximal, complemented

#19098380

C₂

yes

maximal, complemented

#349×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

—

—

—

C₂²

yes

—

#14579093

C₂²

yes

characteristic

#14579086

—

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

Dic₃₁₆

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

—

C₂³×C₇₉

SD₁₆

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

SD₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

#41

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×SD₁₆

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic

C₂×Q₁₆

—

C₂×M₁₆

—

158

—

C₂×M₁₆

C₂×D₇₉

yes

characteristic

C₂²⋊Q₈

—

158

—

M₃₂

C₂×D₇₉

yes

—

#108

—

#108

—

158

—

#106

—

#103

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

D₃₁₆

yes

characteristic

Q₁₆

—

158

—

M₁₆

—

M₁₆

—

316

—

M₁₆

—

158

—

C₂×C₈

—

316

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

C₁₆

—

C₂³

#11929613

yes

characteristic

Q₈

—

316

—

Q₈

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

#11929613

yes

characteristic

C₂×C₄

C₂×D₃₁₆

yes

characteristic

C₈

—

C₈

—

316

—

C₈

#11929623

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#11929613

yes

characteristic

C₄

—

C₄

—

632

—

C₄

—

632

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#19098882

yes

characteristic

	subgroup	G/H
center	C₂	#19098882
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#349×C₇₉	C₂
socle	C₂×C₇₉	#481
prime radical	C₂³×C₇₉	SD₁₆
hypercenter	#349	D₇₉
hypocenter	C₇₉	#2239
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₂

#19098882

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#349×C₇₉

C₂

socle

C₂×C₇₉

#481

prime radical

C₂³×C₇₉

SD₁₆

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
3. #19098386	C₂	semidirect
4. #19098380	C₂	semidirect
52. C₇₉	#2239	semidirect

H ≅ G/N

type

3. #19098386

C₂

semidirect

4. #19098380

C₂

semidirect

52. C₇₉

#2239

semidirect

Subgroups — #23765620

Conjugacy classes of subgroups

Complements