Group #23765962 — subgroups

Subgroups — #23765962

Order 10112.

924 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 249 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	C₂×#14579158	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579123	C₂	1	6	yes	maximal, complemented
3	#19098464	C₂	1	6	yes	maximal, complemented
4	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#384×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₁₆	C₂²	1	6	yes	—
7	C₂²×C₄×D₇₉	C₂²	1	4	yes	—
8	#14579158	C₄	1	8	yes	complemented
9	#14579123	—	2	24	no	—
10	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	3	yes	—
13	C₂×C₄⋊C₄×C₇₉	C₂²	1	6	yes	—
14	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	C₂³×D₇₉	C₂³	1	4	yes	—
16	C₂×D₃₁₆	—	2	12	no	—
17	C₂×D₃₁₆	—	2	12	no	—
18	C₂×D₃₁₆	C₂×C₄	1	24	yes	complemented
19	C₂²×Dic₇₉	C₂³	1	3	yes	—
20	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×D₇₉	—	2	24	no	—
22	(C₂×D₇₉)⋊C₄	—	2	24	no	—
23	C₄×Dic₇₉	—	2	6	no	—
24	C₄×Dic₇₉	D₄	1	12	yes	complemented
25	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
27	C₄⋊C₄×C₇₉	—	2	12	no	—
28	C₄²×C₇₉	C₂×C₄	1	4	yes	complemented
29	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
30	C₂²×D₇₉	—	2	12	no	—
31	C₂²×D₇₉	—	2	12	no	—
32	C₂²×D₇₉	C₂²×C₄	1	8	yes	—
33	C₂×C₄×C₇₉	—	2	12	no	—
34	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
35	C₂×C₄×C₇₉	C₂×D₄	1	6	yes	—
36	C₂×C₄×C₇₉	#41	1	6	yes	—
37	C₂×Dic₇₉	—	2	6	no	—
38	C₂×Dic₇₉	C₂×D₄	1	6	yes	—
39	C₂×Dic₇₉	C₂×D₄	1	6	yes	—
40	D₃₁₆	—	2	48	no	—
41	C₄×D₇₉	—	4	16	no	—
42	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
43	C₂²×C₇₉	C₂²×D₄	1	3	yes	—
44	C₂²×C₇₉	C₂×#41	1	3	yes	—
45	C₂×D₇₉	—	2	24	no	—
46	C₂×D₇₉	—	4	4	no	—
47	C₂×D₇₉	—	4	12	no	—
48	C₄×C₇₉	—	4	4	no	—
49	C₄×C₇₉	C₄×D₄	1	12	yes	complemented
50	Dic₇₉	—	2	6	no	—
51	Dic₇₉	#127	1	4	yes	complemented
52	C₂×C₇₉	C₂×C₄×D₄	1	3	yes	—
53	C₂×C₇₉	C₂×#127	1	1	yes	characteristic
54	C₂×C₇₉	#532	1	3	yes	—
55	D₇₉	—	4	8	no	—
56	C₄×#127	—	79	1	no	maximal, Sylow
57	C₇₉	C₄×#127	1	1	yes	characteristic, complemented, Sylow
58	C₂×#127	—	79	1	no	—
59	C₂×C₄×D₄	—	79	6	no	—
60	#390	—	79	6	no	—
61	#384	D₇₉	1	1	yes	characteristic, complemented
62	C₄³	—	79	1	no	—
63	C₂²×D₄	—	79	6	no	—
64	C₂³×C₄	—	79	4	no	—
65	#127	—	79	8	no	—
66	C₄×D₄	—	158	24	no	—
67	C₂×C₄⋊C₄	C₂×D₇₉	1	6	yes	—
68	C₂×C₂²⋊C₄	—	79	12	no	—
69	C₂×C₄²	—	79	3	no	—
70	C₂×C₄²	—	79	3	no	—
71	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
72	C₂⁴	—	79	4	no	—
73	C₂×D₄	—	79	24	no	—
74	C₂×D₄	—	158	12	no	—
75	C₂×D₄	—	158	12	no	—
76	C₂²×C₄	—	79	1	no	—
77	C₂²×C₄	—	79	3	no	—
78	C₂²×C₄	—	158	24	no	—
79	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
80	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
81	C₄⋊C₄	—	2	12	no	—
82	C₂²⋊C₄	—	158	24	no	—
83	C₄²	—	79	12	no	—
84	C₄²	—	158	6	no	—
85	C₄²	C₄×D₇₉	1	4	yes	complemented
86	C₂³	—	79	8	no	—
87	C₂³	—	158	12	no	—
88	C₂³	—	158	12	no	—
89	C₂³	C₂³×D₇₉	1	1	yes	characteristic
90	D₄	—	158	48	no	—
91	C₂×C₄	—	2	12	no	—
92	C₂×C₄	—	316	16	no	—
93	C₂×C₄	—	79	6	no	—
94	C₂×C₄	—	79	6	no	—
95	C₂×C₄	—	158	6	no	—
96	C₂×C₄	C₂×C₄×D₇₉	1	6	yes	—
97	C₂×C₄	D₄×D₇₉	1	6	yes	—
98	C₂×C₄	#11929625	1	6	yes	—
99	C₂²	—	316	4	no	—
100	C₂²	—	316	12	no	—
101	C₂²	—	158	24	no	—
102	C₂²	C₂²×C₄×D₇₉	1	1	yes	characteristic
103	C₂²	C₂×D₄×D₇₉	1	3	yes	—
104	C₂²	C₂×#11929625	1	3	yes	—
105	C₄	—	4	4	no	—
106	C₄	—	79	4	no	—
107	C₄	—	158	6	no	—
108	C₄	#14579123	1	12	yes	complemented
109	C₂	—	316	8	no	—
110	C₂	C₂×#14579123	1	3	yes	—
111	C₂	#127×D₇₉	1	1	yes	characteristic
112	C₂	#19099114	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579158

C₂

yes

maximal, characteristic

C₂×#14579123

C₂

yes

maximal, complemented

#19098464

C₂

yes

maximal, complemented

C₄²×Dic₇₉

C₂

yes

maximal, characteristic, complemented

#384×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₁₆

C₂²

yes

—

C₂²×C₄×D₇₉

C₂²

yes

—

#14579158

C₄

yes

complemented

#14579123

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂³×D₇₉

C₂³

yes

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

C₂×C₄

yes

complemented

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂×C₄×D₇₉

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

complemented

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₂×D₄

yes

—

D₃₁₆

—

C₄×D₇₉

—

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

C₂²×D₄

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×D₄

yes

complemented

Dic₇₉

—

Dic₇₉

#127

yes

complemented

C₂×C₇₉

C₂×C₄×D₄

yes

—

C₂×C₇₉

C₂×#127

yes

characteristic

C₂×C₇₉

#532

yes

—

D₇₉

—

C₄×#127

—

maximal, Sylow

C₇₉

C₄×#127

yes

characteristic, complemented, Sylow

C₂×#127

—

C₂×C₄×D₄

—

#390

—

#384

D₇₉

yes

characteristic, complemented

C₄³

—

C₂²×D₄

—

C₂³×C₄

—

#127

—

C₄×D₄

—

158

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

158

—

C₄²

—

C₄²

—

158

—

C₄²

C₄×D₇₉

yes

complemented

C₂³

—

C₂³

—

158

—

C₂³

—

158

—

C₂³

C₂³×D₇₉

yes

characteristic

D₄

—

158

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

—

C₂×C₄

D₄×D₇₉

yes

—

C₂×C₄

#11929625

yes

—

C₂²

—

316

—

100

C₂²

—

316

—

101

C₂²

—

158

—

102

C₂²

C₂²×C₄×D₇₉

yes

characteristic

103

C₂²

C₂×D₄×D₇₉

yes

—

104

C₂²

C₂×#11929625

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

158

—

108

C₄

#14579123

yes

complemented

109

C₂

—

316

—

110

C₂

C₂×#14579123

yes

—

111

C₂

#127×D₇₉

yes

characteristic

112

C₂

#19099114

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₄
Fitting	#384×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂×#14579158	C₂
hypercenter	#384	D₇₉
hypocenter	C₇₉	C₄×#127
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator

C₂²×C₇₉

C₂³×C₄

Fitting

#384×C₇₉

C₂

socle, cosocle

C₂³×C₇₉

C₂⁴

C₂

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
2. C₂×#14579123	C₂	semidirect
3. #19098464	C₂	semidirect
4. C₄²×Dic₇₉	C₂	semidirect
5. #384×C₇₉	C₂	semidirect
8. #14579158	C₄	semidirect
18. C₂×D₃₁₆	C₂×C₄	semidirect
24. C₄×Dic₇₉	D₄	semidirect
28. C₄²×C₇₉	C₂×C₄	semidirect
49. C₄×C₇₉	C₄×D₄	semidirect
51. Dic₇₉	#127	semidirect
57. C₇₉	C₄×#127	semidirect
61. #384	D₇₉	semidirect
85. C₄²	C₄×D₇₉	semidirect
108. C₄	#14579123	semidirect

H ≅ G/N

type

2. C₂×#14579123

C₂

semidirect

3. #19098464

C₂

semidirect

4. C₄²×Dic₇₉

C₂

semidirect

5. #384×C₇₉

C₂

semidirect

8. #14579158

C₄

semidirect

18. C₂×D₃₁₆

C₂×C₄

semidirect

24. C₄×Dic₇₉

D₄

semidirect

28. C₄²×C₇₉

C₂×C₄

semidirect

49. C₄×C₇₉

C₄×D₄

semidirect

51. Dic₇₉

#127

semidirect

57. C₇₉

C₄×#127

semidirect

61. #384

D₇₉

semidirect

85. C₄²

C₄×D₇₉

semidirect

108. C₄

#14579123

semidirect

Subgroups — #23765962

Conjugacy classes of subgroups

Complements