Group #14271727 — subgroups

Subgroups — #14271727

Order 1856.

334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 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×#41×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745309	C₂	1	2	yes	maximal, complemented
4	#11745302	C₂	1	2	yes	maximal, complemented
5	#11745299	C₂	1	4	yes	maximal, complemented
6	#11745292	C₂	1	4	yes	maximal, complemented
7	#11745288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₂₉	C₂²	1	2	yes	—
9	#41×C₂₉	—	2	4	no	—
10	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
11	C₂×D₄×C₂₉	C₂²	1	2	yes	—
12	C₂×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₂₉	C₂²	1	2	yes	complemented
15	C₂×C₂²⋊D₂₉	C₂²	1	8	yes	complemented
16	C₂×D₁₁₆	—	2	4	no	—
17	C₂×D₁₁₆	C₂²	1	2	yes	—
18	C₂×D₁₁₆	C₂²	1	2	yes	—
19	C₂²⋊Dic₂₉	C₂²	1	2	yes	—
20	#90781	C₂²	1	8	yes	complemented
21	C₄⋊Dic₂₉	C₂²	1	2	yes	complemented
22	C₄×Dic₂₉	C₂²	1	2	yes	complemented
23	C₂³×C₂₉	C₂³	1	2	yes	—
24	C₂³×C₂₉	C₂³	1	1	yes	characteristic
25	C₂²×D₂₉	—	2	4	no	—
26	C₂²×D₂₉	—	4	4	no	—
27	C₂²×D₂₉	C₂³	1	4	yes	—
28	Q₈×C₂₉	—	2	2	no	—
29	D₄×C₂₉	—	2	4	no	—
30	D₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	—	2	4	no	—
32	C₂×C₄×C₂₉	D₄	1	4	yes	complemented
33	C₂×C₄×C₂₉	C₂³	1	2	yes	—
34	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
36	C₂²⋊D₂₉	—	4	8	no	—
37	C₂×Dic₂₉	C₂³	1	4	yes	—
38	D₁₁₆	—	2	4	no	—
39	D₁₁₆	—	2	4	no	—
40	C₂²×C₂₉	—	2	2	no	—
41	C₂²×C₂₉	—	2	2	no	—
42	C₂²×C₂₉	—	2	4	no	—
43	C₂²×C₂₉	C₂×D₄	1	2	yes	—
44	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
45	C₂×D₂₉	—	2	4	no	—
46	C₂×D₂₉	—	2	8	no	—
47	C₂×D₂₉	—	4	8	no	—
48	C₄×C₂₉	—	2	2	no	—
49	C₄×C₂₉	C₂×D₄	1	2	yes	—
50	C₄×C₂₉	C₂×D₄	1	2	yes	—
51	Dic₂₉	—	2	4	no	—
52	#535	—	29	1	no	maximal, Sylow
53	C₂×C₂₉	—	2	2	no	—
54	C₂×C₂₉	—	4	2	no	—
55	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
56	C₂×C₂₉	H(5,𝔽₂)	1	2	yes	—
57	D₂₉	—	4	4	no	—
58	C₂×#41	D₂₉	1	1	yes	characteristic, complemented
59	C₂²×D₄	—	29	1	no	—
60	#127	—	29	2	no	—
61	#124	—	29	2	no	—
62	#121	—	29	4	no	—
63	#120	—	29	4	no	—
64	#117	—	29	1	no	—
65	C₂₉	#535	1	1	yes	characteristic, complemented, Sylow
66	C₂⁴	—	29	2	no	—
67	#41	—	2	4	no	—
68	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
69	C₂×D₄	—	29	8	no	—
70	C₂×D₄	—	29	2	no	—
71	C₂×D₄	—	29	2	no	—
72	C₂×D₄	—	58	4	no	—
73	C₂×D₄	C₂×D₂₉	1	2	yes	—
74	C₂×D₄	C₂×D₂₉	1	1	yes	characteristic, complemented
75	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
76	C₂²×C₄	C₂×D₂₉	1	2	yes	complemented
77	C₄⋊C₄	—	29	2	no	—
78	C₂²⋊C₄	—	29	2	no	—
79	C₂²⋊C₄	—	29	8	no	—
80	C₄²	—	29	2	no	—
81	C₂³	—	29	4	no	—
82	C₂³	—	58	4	no	—
83	C₂³	—	116	4	no	—
84	C₂³	C₂²×D₂₉	1	2	yes	—
85	C₂³	C₂²×D₂₉	1	1	yes	characteristic
86	Q₈	—	2	2	no	—
87	D₄	—	2	4	no	—
88	D₄	—	2	2	no	—
89	D₄	—	58	4	no	—
90	D₄	—	58	4	no	—
91	D₄	—	116	8	no	—
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	—	29	4	no	—
94	C₂×C₄	C₂²⋊D₂₉	1	4	yes	complemented
95	C₂×C₄	C₂²×D₂₉	1	2	yes	—
96	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
97	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
98	C₂²	—	2	2	no	—
99	C₂²	—	2	4	no	—
100	C₂²	—	2	2	no	—
101	C₂²	—	58	8	no	—
102	C₂²	—	58	4	no	—
103	C₂²	—	116	8	no	—
104	C₂²	C₂×C₂²⋊D₂₉	1	2	yes	—
105	C₂²	C₂³×D₂₉	1	1	yes	characteristic
106	C₄	—	2	2	no	—
107	C₄	—	58	4	no	—
108	C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
109	C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
110	C₂	—	2	2	no	—
111	C₂	—	4	2	no	—
112	C₂	—	116	4	no	—
113	C₂	#11745364	1	2	yes	—
114	C₂	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#41×C₂₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₁₆

C₂

yes

maximal, characteristic, complemented

#11745309

C₂

yes

maximal, complemented

#11745302

C₂

yes

maximal, complemented

#11745299

C₂

yes

maximal, complemented

#11745292

C₂

yes

maximal, complemented

#11745288

C₂

yes

maximal, characteristic, complemented

C₂³×D₂₉

C₂²

yes

—

#41×C₂₉

—

C₂×Q₈×C₂₉

C₂²

yes

characteristic, complemented

C₂×D₄×C₂₉

C₂²

yes

—

C₂×D₄×C₂₉

C₂²

yes

characteristic, complemented

C₂²×C₄×C₂₉

C₂²

yes

characteristic

C₂²×C₄×C₂₉

C₂²

yes

complemented

C₂×C₂²⋊D₂₉

C₂²

yes

complemented

C₂×D₁₁₆

—

C₂×D₁₁₆

C₂²

yes

—

C₂×D₁₁₆

C₂²

yes

—

C₂²⋊Dic₂₉

C₂²

yes

—

#90781

C₂²

yes

complemented

C₄⋊Dic₂₉

C₂²

yes

complemented

C₄×Dic₂₉

C₂²

yes

complemented

C₂³×C₂₉

C₂³

yes

—

C₂³×C₂₉

C₂³

yes

characteristic

C₂²×D₂₉

—

C₂²×D₂₉

—

C₂²×D₂₉

C₂³

yes

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

D₄

yes

complemented

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂²⋊D₂₉

—

C₂×Dic₂₉

C₂³

yes

—

D₁₁₆

—

D₁₁₆

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×D₄

yes

—

C₂²×C₂₉

C₂⁴

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×D₄

yes

—

C₄×C₂₉

C₂×D₄

yes

—

Dic₂₉

—

#535

—

maximal, Sylow

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂²×D₄

yes

characteristic

C₂×C₂₉

H(5,𝔽₂)

yes

—

D₂₉

—

C₂×#41

D₂₉

yes

characteristic, complemented

C₂²×D₄

—

—

—

—

—

—

C₂₉

#535

yes

characteristic, complemented, Sylow

C₂⁴

—

#41

—

C₂×Q₈

C₂×D₂₉

yes

characteristic, complemented

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×D₂₉

yes

—

C₂×D₄

C₂×D₂₉

yes

characteristic, complemented

C₂²×C₄

C₂×D₂₉

yes

characteristic

C₂²×C₄

C₂×D₂₉

yes

complemented

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

116

—

C₂³

C₂²×D₂₉

yes

—

C₂³

C₂²×D₂₉

yes

characteristic

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊D₂₉

yes

complemented

C₂×C₄

C₂²×D₂₉

yes

—

C₂×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₄

C₂²×D₂₉

yes

characteristic

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

116

—

104

C₂²

C₂×C₂²⋊D₂₉

yes

—

105

C₂²

C₂³×D₂₉

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

C₂×C₂²⋊D₂₉

yes

—

109

C₄

C₂×C₂²⋊D₂₉

yes

—

110

C₂

—

111

C₂

—

112

C₂

—

116

—

113

C₂

#11745364

yes

—

114

C₂

C₂²×C₂²⋊D₂₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂×#41×C₂₉	C₂
hypercenter	C₂×#41	D₂₉
hypocenter	C₂₉	#535
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×#41

subgroup

G/H

center, Frattini

C₂²

C₂³×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁴

Fitting

C₂×#41×C₂₉

C₂

hypercenter

C₂×#41

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ C₂×#41

N	H ≅ G/N	type
1. C₂×#41×C₂₉	C₂	semidirect
2. C₂²×D₁₁₆	C₂	semidirect
3. #11745309	C₂	semidirect
4. #11745302	C₂	semidirect
5. #11745299	C₂	semidirect
6. #11745292	C₂	semidirect
7. #11745288	C₂	semidirect
10. C₂×Q₈×C₂₉	C₂²	semidirect
12. C₂×D₄×C₂₉	C₂²	semidirect
14. C₂²×C₄×C₂₉	C₂²	semidirect
15. C₂×C₂²⋊D₂₉	C₂²	semidirect
20. #90781	C₂²	semidirect
21. C₄⋊Dic₂₉	C₂²	semidirect
22. C₄×Dic₂₉	C₂²	semidirect
32. C₂×C₄×C₂₉	D₄	semidirect
58. C₂×#41	D₂₉	semidirect
65. C₂₉	#535	semidirect
68. C₂×Q₈	C₂×D₂₉	semidirect
74. C₂×D₄	C₂×D₂₉	semidirect
76. C₂²×C₄	C₂×D₂₉	semidirect
94. C₂×C₄	C₂²⋊D₂₉	semidirect

H ≅ G/N

type

1. C₂×#41×C₂₉

C₂

semidirect

2. C₂²×D₁₁₆

C₂

semidirect

3. #11745309

C₂

semidirect

4. #11745302

C₂

semidirect

5. #11745299

C₂

semidirect

6. #11745292

C₂

semidirect

7. #11745288

C₂

semidirect

10. C₂×Q₈×C₂₉

C₂²

semidirect

12. C₂×D₄×C₂₉

C₂²

semidirect

14. C₂²×C₄×C₂₉

C₂²

semidirect

15. C₂×C₂²⋊D₂₉

C₂²

semidirect

20. #90781

C₂²

semidirect

21. C₄⋊Dic₂₉

C₂²

semidirect

22. C₄×Dic₂₉

C₂²

semidirect

32. C₂×C₄×C₂₉

D₄

semidirect

58. C₂×#41

D₂₉

semidirect

65. C₂₉

#535

semidirect

68. C₂×Q₈

C₂×D₂₉

semidirect

74. C₂×D₄

C₂×D₂₉

semidirect

76. C₂²×C₄

C₂×D₂₉

semidirect

94. C₂×C₄

C₂²⋊D₂₉

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#41×C₂₉	2
C₂²×D₁₁₆	2
#11745309	2
#11745302	2
#11745299	2
#11745292	2
#11745288	2
#535	29

subgroup

index

C₂×#41×C₂₉

C₂²×D₁₁₆

Subgroups — #14271727

Conjugacy classes of subgroups

Complements

Maximal subgroups