Group #23771782 — subgroups

Subgroups — #23771782

Order 10112.

408 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 165 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	#19098469	C₂	1	3	yes	maximal
2	#19098461	C₂	1	3	yes	maximal
3	#19098447	C₂	1	6	yes	maximal
4	#19098431	C₂	1	2	yes	maximal
5	C₄³×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
8	C₂×Dic₇₉⋊C₄	C₂²	1	6	yes	—
9	C₇₉⋊#95	C₂²	1	6	yes	—
10	C₇₉⋊#95	C₂²	1	6	yes	—
11	C₇₉⋊#95	C₂²	1	6	yes	—
12	C₂×C₄²×C₇₉	C₂²	1	3	yes	—
13	C₂×C₄²×C₇₉	C₂²	1	3	yes	—
14	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	2	6	no	—
16	C₂²×Dic₇₉	C₂³	1	2	yes	—
17	C₂²×Dic₇₉	C₂³	1	6	yes	—
18	C₄⋊Dic₇₉	—	2	6	no	—
19	Dic₇₉⋊C₄	—	2	12	no	—
20	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
21	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
22	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
23	C₄²×C₇₉	—	2	6	no	—
24	C₄²×C₇₉	—	2	6	no	—
25	C₄²×C₇₉	Q₈	1	4	yes	complemented
26	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
27	C₂×C₄×C₇₉	—	2	3	no	—
28	C₂×C₄×C₇₉	—	2	3	no	—
29	C₂×C₄×C₇₉	—	2	3	no	—
30	C₂×C₄×C₇₉	—	2	3	no	—
31	C₂×C₄×C₇₉	C₂×Q₈	1	6	yes	—
32	C₂×C₄×C₇₉	#41	1	6	yes	—
33	C₂×C₄×C₇₉	#41	1	6	yes	—
34	C₂×Dic₇₉	—	2	12	no	—
35	C₂×Dic₇₉	—	2	6	no	—
36	C₂×Dic₇₉	—	2	6	no	—
37	Dic₁₅₈	—	4	4	no	—
38	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
39	C₂²×C₇₉	C₂×#41	1	3	yes	—
40	C₂²×C₇₉	C₂×#41	1	3	yes	—
41	C₄×C₇₉	—	2	6	no	—
42	C₄×C₇₉	—	2	6	no	—
43	C₄×C₇₉	#126	1	4	yes	—
44	Dic₇₉	—	4	2	no	—
45	Dic₇₉	—	4	6	no	—
46	C₂×C₇₉	C₂×#126	1	1	yes	characteristic
47	C₂×C₇₉	#529	1	3	yes	—
48	C₂×C₇₉	#533	1	3	yes	—
49	#2863	—	79	1	no	maximal, Sylow
50	C₇₉	#2863	1	1	yes	characteristic, complemented, Sylow
51	#391	—	79	3	no	—
52	#389	—	79	3	no	—
53	#387	—	79	6	no	—
54	#383	—	79	2	no	—
55	C₄³	D₇₉	1	1	yes	characteristic
56	C₂²×Q₈	—	79	1	no	—
57	C₂×C₄⋊C₄	—	79	6	no	—
58	C₂×C₄⋊C₄	—	79	3	no	—
59	C₂×C₄²	C₂×D₇₉	1	3	yes	—
60	C₂×C₄²	C₂×D₇₉	1	3	yes	—
61	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
62	#95	—	79	6	no	—
63	#95	—	79	6	no	—
64	#95	—	79	6	no	—
65	C₂×Q₈	—	158	6	no	—
66	C₂²×C₄	—	79	2	no	—
67	C₂²×C₄	—	79	6	no	—
68	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
69	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
70	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
71	C₄⋊C₄	—	158	12	no	—
72	C₄⋊C₄	—	158	6	no	—
73	C₄²	—	2	6	no	—
74	C₄²	—	2	6	no	—
75	C₄²	Dic₁₅₈	1	4	yes	complemented
76	C₂³	C₂³×D₇₉	1	1	yes	characteristic
77	Q₈	—	316	4	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	158	6	no	—
83	C₂×C₄	—	158	12	no	—
84	C₂×C₄	—	158	6	no	—
85	C₂×C₄	C₂×Dic₁₅₈	1	6	yes	—
86	C₂×C₄	#11929624	1	6	yes	—
87	C₂×C₄	#11929624	1	6	yes	—
88	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
89	C₂²	C₂×#11929624	1	3	yes	—
90	C₂²	C₂×#11929624	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	2	6	no	—
93	C₄	—	316	2	no	—
94	C₄	—	316	6	no	—
95	C₄	#14579155	1	4	yes	—
96	C₂	C₂×#14579155	1	1	yes	characteristic
97	C₂	#19099097	1	3	yes	—
98	C₂	#19099120	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098469

C₂

yes

maximal

#19098461

C₂

yes

maximal

#19098447

C₂

yes

maximal

#19098431

C₂

yes

maximal

C₄³×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

Q₈

yes

complemented

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#126

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

C₂×#126

yes

characteristic

C₂×C₇₉

#529

yes

—

C₂×C₇₉

#533

yes

—

#2863

—

maximal, Sylow

C₇₉

#2863

yes

characteristic, complemented, Sylow

—

—

—

—

C₄³

D₇₉

yes

characteristic

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₉

yes

—

C₂×C₄²

C₂×D₇₉

yes

—

C₂×C₄²

C₂×D₇₉

yes

—

—

—

C₂×Q₈

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

C₄²

—

C₄²

Dic₁₅₈

yes

complemented

C₂³

C₂³×D₇₉

yes

characteristic

Q₈

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂×C₄

#11929624

yes

—

C₂×C₄

#11929624

yes

—

C₂²

C₂²×Dic₁₅₈

yes

characteristic

C₂²

C₂×#11929624

yes

—

C₂²

C₂×#11929624

yes

—

C₄

—

C₄

—

C₄

—

316

—

C₄

—

316

—

C₄

#14579155

yes

—

C₂

C₂×#14579155

yes

characteristic

C₂

#19099097

yes

—

C₂

#19099120

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	C₄³×C₇₉	C₂
hypercenter	C₄³	D₇₉
hypocenter	C₇₉	#2863
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

C₄³×C₇₉

C₂

hypercenter

C₄³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
25. C₄²×C₇₉	Q₈	semidirect
50. C₇₉	#2863	semidirect
75. C₄²	Dic₁₅₈	semidirect

H ≅ G/N

type

25. C₄²×C₇₉

Q₈

semidirect

50. C₇₉

#2863

semidirect

75. C₄²

Dic₁₅₈

semidirect

Subgroups — #23771782

Conjugacy classes of subgroups

Complements