Group #23771392 — subgroups

Subgroups — #23771392

Order 10112.

432 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 149 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	#19098483	C₂	1	3	yes	maximal
2	#19098482	C₂	1	2	yes	maximal
3	#19098468	C₂	1	3	yes	maximal
4	#19098467	C₂	1	6	yes	maximal
5	#395×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
7	C₂²×Dic₁₅₈	C₂²	1	3	yes	—
8	C₂×Dic₇₉⋊C₄	C₂²	1	6	yes	—
9	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
10	C₇₉⋊#95	C₂²	1	6	yes	—
11	C₇₉⋊#95	C₂²	1	6	yes	—
12	C₇₉⋊#95	C₂²	1	3	yes	—
13	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₇₉	C₂²	1	3	yes	—
15	#95×C₇₉	C₂²	1	3	yes	—
16	C₂×Dic₁₅₈	—	4	3	no	—
17	C₂×Dic₁₅₈	—	4	3	no	—
18	C₂×Dic₁₅₈	—	4	3	no	—
19	C₂×Dic₁₅₈	Q₈	1	12	yes	complemented
20	C₂²×Dic₇₉	C₂³	1	2	yes	—
21	C₂²×Dic₇₉	C₂³	1	6	yes	—
22	Dic₇₉⋊C₄	—	4	6	no	—
23	C₄×Dic₇₉	—	4	3	no	—
24	C₂×Q₈×C₇₉	—	4	3	no	—
25	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
27	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
28	C₄⋊C₄×C₇₉	—	4	3	no	—
29	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
30	Q₈×C₇₉	—	4	4	no	—
31	C₂×C₄×C₇₉	—	2	3	no	—
32	C₂×C₄×C₇₉	—	2	3	no	—
33	C₂×C₄×C₇₉	—	2	6	no	—
34	C₂×C₄×C₇₉	—	2	3	no	—
35	C₂×C₄×C₇₉	—	2	3	no	—
36	C₂×C₄×C₇₉	C₂×Q₈	1	6	yes	—
37	C₂×Dic₇₉	—	2	6	no	—
38	C₂×Dic₇₉	—	2	6	no	—
39	C₂×Dic₇₉	—	2	6	no	—
40	C₂×Dic₇₉	C₂×Q₈	1	12	yes	—
41	Dic₁₅₈	—	4	12	no	—
42	Dic₁₅₈	—	4	4	no	—
43	C₂²×C₇₉	C₂²×Q₈	1	3	yes	—
44	C₂²×C₇₉	H(5,𝔽₂)	1	3	yes	—
45	C₂²×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
46	C₄×C₇₉	—	2	6	no	—
47	C₄×C₇₉	—	4	3	no	—
48	C₄×C₇₉	—	4	1	no	—
49	Dic₇₉	—	2	12	no	—
50	Dic₇₉	—	4	2	no	—
51	C₂×C₇₉	#543	1	3	yes	—
52	C₂×C₇₉	Q₈²	1	3	yes	—
53	C₂×C₇₉	H(3,𝔽₄)	1	1	yes	characteristic
54	#2811	—	79	1	no	maximal, Sylow
55	C₇₉	#2811	1	1	yes	characteristic, complemented, Sylow
56	#395	—	79	2	no	—
57	#395	—	79	3	no	—
58	#395	D₇₉	1	1	yes	characteristic
59	#391	—	79	3	no	—
60	#391	—	79	6	no	—
61	C₂²×Q₈	—	79	1	no	—
62	C₂²×Q₈	—	79	3	no	—
63	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
64	C₂×C₄⋊C₄	—	79	6	no	—
65	C₂×C₄⋊C₄	C₂×D₇₉	1	3	yes	—
66	C₂×C₄²	—	79	3	no	—
67	#95	—	79	3	no	—
68	#95	—	79	6	no	—
69	#95	—	79	6	no	—
70	#95	C₂×D₇₉	1	3	yes	—
71	C₂×Q₈	—	4	3	no	—
72	C₂×Q₈	—	316	3	no	—
73	C₂×Q₈	—	316	3	no	—
74	C₂×Q₈	—	316	3	no	—
75	C₂×Q₈	—	79	12	no	—
76	C₂²×C₄	—	79	6	no	—
77	C₂²×C₄	—	79	2	no	—
78	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
80	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
81	C₄⋊C₄	—	4	3	no	—
82	C₄⋊C₄	—	316	6	no	—
83	C₄²	—	316	3	no	—
84	C₂³	C₂³×D₇₉	1	1	yes	characteristic
85	Q₈	—	4	4	no	—
86	Q₈	—	316	12	no	—
87	Q₈	—	316	4	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	6	no	—
93	C₂×C₄	—	79	12	no	—
94	C₂×C₄	—	158	6	no	—
95	C₂×C₄	—	158	6	no	—
96	C₂×C₄	—	158	6	no	—
97	C₂×C₄	Q₈×D₇₉	1	6	yes	—
98	C₂²	C₂×Q₈×D₇₉	1	3	yes	—
99	C₂²	#14579206	1	3	yes	—
100	C₂²	#14579207	1	1	yes	characteristic
101	C₄	—	2	6	no	—
102	C₄	—	4	3	no	—
103	C₄	—	4	1	no	—
104	C₄	—	316	2	no	—
105	C₄	—	158	12	no	—
106	C₂	#19099188	1	3	yes	—
107	C₂	#19099293	1	3	yes	—
108	C₂	#19099306	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098483

C₂

yes

maximal

#19098482

C₂

yes

maximal

#19098468

C₂

yes

maximal

#19098467

C₂

yes

maximal

#395×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

characteristic

C₂²×Dic₁₅₈

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

#95×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

Q₈

yes

complemented

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₂³×C₇₉

C₂⁴

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×Q₈

yes

—

Dic₁₅₈

—

Dic₁₅₈

—

C₂²×C₇₉

C₂²×Q₈

yes

—

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₂²×C₇₉

H(5,𝔽₂)

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#543

yes

—

C₂×C₇₉

Q₈²

yes

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#395

—

#395

—

#395

D₇₉

yes

characteristic

#391

—

#391

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

—

—

—

C₂×D₇₉

yes

—

C₂×Q₈

—

C₂×Q₈

—

316

—

C₂×Q₈

—

316

—

C₂×Q₈

—

316

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄²

—

316

—

C₂³

C₂³×D₇₉

yes

characteristic

Q₈

—

Q₈

—

316

—

Q₈

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

Q₈×D₇₉

yes

—

C₂²

C₂×Q₈×D₇₉

yes

—

C₂²

#14579206

yes

—

100

C₂²

#14579207

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

316

—

105

C₄

—

158

—

106

C₂

#19099188

yes

—

107

C₂

#19099293

yes

—

108

C₂

#19099306

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#395×C₇₉	C₂
hypercenter	#395	D₇₉
hypocenter	C₇₉	#2811
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #395

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#395×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #395

N	H ≅ G/N	type
19. C₂×Dic₁₅₈	Q₈	semidirect
55. C₇₉	#2811	semidirect

H ≅ G/N

type

19. C₂×Dic₁₅₈

Q₈

semidirect

55. C₇₉

#2811

semidirect

Subgroups — #23771392

Conjugacy classes of subgroups

Complements